US2023151022A1PendingUtilityA1

Prins reaction and compounds useful in the synthesis of halichondrin macrolides and analogs thereof

Assignee: EISAI R&D MAN CO LTDPriority: Jan 3, 2018Filed: Dec 28, 2022Published: May 18, 2023
Est. expiryJan 3, 2038(~11.4 yrs left)· nominal 20-yr term from priority
A61K 31/35C07D 307/28C07D 493/22C07D 493/04C07D 307/20C07D 407/14C07D 407/06A61P 35/00C07F 9/6561A61K 31/335
72
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Claims

Abstract

The invention provides methods utilizing Prins reaction in the preparation of compounds that may be useful as intermediates in the synthesis of halichondrin macrolides and analogs thereof. The invention also provides compounds that may be useful as intermediates in the synthesis of a halichondrin macrolides and methods for preparing the same.

Claims

exact text as granted — not AI-modified
What is claimed is: 
     
         1 . A method of preparing a compound of formula (A), the method comprising producing the compound of formula (A) from a compound of formula (B), a compound of formula (C), and R 5 OH:
 wherein R 5  is optionally substituted acyl;   wherein the compound of formula (A) is:   
       
         
           
           
               
               
           
         
         
           wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
         
       
       
         
           
           
               
               
           
         
         
           
             wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond; 
  (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
  (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
  (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
  (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
           
         
       
       
         
           
           
               
               
           
         
         
           
             
                wherein each P′ is independently H or a hydroxyl protecting group; 
             
             E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
             G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
             each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
             n, when present, is 0, 1, or 2; 
             k is 0 or 1; 
             R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group; 
             R 4  is optionally substituted alkyl, optionally substituted alkenyl, optionally substituted alkynyl, 
           
         
       
       
         
           
           
               
               
           
         
         
           
             wherein
 each P 7  is independently H or a hydroxyl protecting group; and 
 R 8  is —CH 2 CH 2 —COOR C , —CH═CH—COOR C , —CH 2 CH 2 —SO 2 R D , or —CH═CH—SO 2 R D ; 
 
             R 6  is H, optionally substituted alkyl, or optionally substituted arylalkyl; 
             each Y is independently —COOR C  or —SO 2 R D ; 
             each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
             each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
           
         
         wherein the compound of formula (B) is: 
       
       
         
           
           
               
               
           
         
         and 
         wherein the compound of formula (C) is:
   R 4 -R 7 ,  (C)
 
 wherein R 7  is —CHO or 
 
       
       
         
           
           
               
               
           
         
         
            wherein each R 7A  is independently an optionally substituted alkyl. 
         
       
     
     
         2 . The method of  claim 1 , wherein the producing the compound of formula (A) comprises reacting the compound of formula (B), the compound of formula (C), R 5 OH, and a Lewis acid. 
     
     
         3 . The method of  claim 2 , wherein the Lewis acid is an oxophilic Lewis acid. 
     
     
         4 . The method of  claim 3 , wherein the oxophilic Lewis acid is boron trifluoride or a solvate thereof. 
     
     
         5 . The method of any one of  claims 1  to  3 , further comprising producing the compound of formula (B) comprising reacting a compound of formula (D), a compound of formula (E), and a second Lewis acid, wherein the compound of formula (D) is: 
       
         
           
           
               
               
           
         
         and 
         where the compound of formula (E) is: 
       
       
         
           
           
               
               
           
         
         
           where R S  is silyl. 
         
       
     
     
         6 . The method of  claim 5 , wherein the second Lewis acid is an oxophilic second Lewis acid. 
     
     
         7 . The method of  claim 6 , wherein the oxophilic second Lewis acid is boron trifluoride or a solvate thereof. 
     
     
         8 . The method of any one of  claims 5  to  7 , wherein the Lewis acid and the second Lewis acid are same. 
     
     
         9 . The method of any one of  claims 5  to  8 , wherein the preparing the compound of formula (B) and the preparing the compound of formula (A) are performed as a single-pot transformation. 
     
     
         10 . The method of any one of  claims 5  to  9 , further comprising epimerizing the product of reacting the compound of formula (D), the compound of formula (E), and the second Lewis acid. 
     
     
         11 . The method of any one of  claims 5  to  10 , wherein the preparing the compound of formula (B) and the preparing the compound of formula (A) are performed as a single-pot transformation. 
     
     
         12 . A method of preparing a compound of formula (B), the method comprising producing the compound of formula (B) from a compound of formula (D) and a compound of formula (E);
 wherein the compound of formula (B) is:   
       
         
           
           
               
               
           
         
         wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
           R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group; 
           R 6  is H, optionally substituted alkyl, or optionally substituted aryl; and 
           Y is independently —COOR C  or —SO 2 R D ; 
           R C , when present, is optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
           R D , when present, is optionally substituted aryl or optionally substituted non-enolizable alkyl; 
         
         wherein the compound of formula (D) is: 
       
       
         
           
           
               
               
           
         
         and 
         wherein the compound of formula (E) is: 
       
       
         
           
           
               
               
           
         
         
           wherein R S  is silyl. 
         
       
     
     
         13 . The method of  claim 12 , wherein the producing the compound of formula (B) comprises reacting the compound of formula (D), the compound of formula (E), and a Lewis acid. 
     
     
         14 . The method of  claim 13 , wherein the Lewis acid is an oxophilic Lewis acid. 
     
     
         15 . The method of  claim 14 , wherein the oxophilic Lewis acid is boron trifluoride or a solvate thereof. 
     
     
         17 . The method of any one of  claims 13  to  15 , further comprising epimerizing the product of reacting the compound of formula (D), the compound of formula (E), and the Lewis acid. 
     
     
         18 . A method of preparing 
       
         
           
           
               
               
           
         
         a halichondrin macrolide or analog thereof, 
       
       wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           each of A 1 , A 2 , and A 3  is independently H or OP″, wherein each P″ is independently H or a hydroxyl protecting group; 
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; and 
           X 1  is —CH 2 — or —O—; 
           the method comprising: 
           (A) producing a compound of formula (IA) from a compound of formula (IIC), a compound of formula (III), and R 5 OH, wherein the compound of formula (IA) is: 
         
       
       
         
           
           
               
               
           
         
         
           
             wherein 
             R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), where P 6  is H or a hydroxyl protecting group, and each Y is independently —COOR C  or —SO 2 R D ; 
             R 4  is 
           
         
       
       
         
           
           
               
               
           
         
         
           
             
               wherein 
                each P 7  is independently H or a hydroxyl protecting group; 
                R 8  is —CH 2 CH 2 —COOR C , —CH═CH—COOR C , —CH 2 CH 2 —SO 2 R D , or —CH═CH—SO 2 R D ; 
                each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
                each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; and 
             
           
           R S  is optionally substituted acyl; 
         
         wherein the compound of formula (IIC) is: 
       
       
         
           
           
               
               
           
         
         and 
         wherein the compound of formula (III) is:
   R 4 -R 7 ,  (III)
 
 
         wherein R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; and 
         (B) producing the halichondrin macrolide or analog thereof from the compound of formula (IA). 
       
     
     
         19 . A method of preparing: 
       
         
           
           
               
               
           
         
         a halichondrin macrolide or analog thereof, 
       
       wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
         
         each of A 1 , A 2 , and A 3  is independently H or OP″, wherein each P″ is independently H or a hydroxyl protecting group; 
         E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
         G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
         each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
         n, when present, is 0, 1, or 2; 
         k is 0 or 1; and 
         X 1  is —CH 2 — or —O—; 
         the method comprising: 
         (A) producing a compound of formula (IVB) from a compound of formula (IIA), a compound of formula (IIB), a compound of formula (IIIA), a compound of formula (IVA), and R 5 OH, 
         wherein the compound of formula (IIA) is: 
       
       
         
           
           
               
               
           
         
         wherein
 R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and each Y is independently-COOR C  or —SO 2 R D ; 
 each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
 each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
 R E  is —CHO or —CH (1+m) (OR F ) (2−m) , 
 wherein
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0, and 
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene; 
 
 
         wherein the compound of formula (IIB) is: 
       
       
         
           
           
               
               
           
         
         wherein R S  is silyl; 
         wherein the compound of formula (IIIA) is:
   R 4A -R 7 ,  (IIIA)
 
 
         wherein
 R 4A  is 
 
       
       
         
           
           
               
               
           
         
         
           wherein R C  is optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl, and each P 7  is independently H or a hydroxyl protecting group; 
           R 7  is —CHO or 
         
       
       
         
           
           
               
               
           
         
         
           wherein each R 7A  is independently an optionally substituted alkyl; 
         
         wherein the compound of formula (IVA) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         each P 9  is independently a hydroxyl protecting group; 
         R 9  is —CHO or —COOH;
 (a1) R 10  is H or a hydroxyl protecting group, R 11  is alkyl ether, and R 12  is H; 
 (a2) R 10  is H or a hydroxyl protecting group, and R 11  and R 12  combine to form a double bond; 
 or 
 (a3) R 10  and R 11  combine to form a bond, and R 12  is H; 
 (b1) A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
 or 
 (b2) A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; and 
 
 (c1) R 1  is H, and P 8  is H or a hydroxyl protecting group; 
 or 
 (c2) R 1  and P 8  combine to form a double bond; 
 
         and 
         each P″, when present, is independently H or a hydroxyl protecting group; 
         wherein the compound of formula (IVB) is: 
       
       
         
           
           
               
               
           
         
         wherein
 X 1  is —O—, —C(Y) 2 —, —CH(Y)—, or —CH 2 —; 
 X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; and 
 R G  is 
 
       
       
         
           
           
               
               
           
         
         
           wherein 
           R 5  is an optionally substituted acyl; and 
           X 2  is H or —CH 2 -X 2A -CH 2 —CH═CH 2 , wherein X 2A  is —O—, —C(R H ) 2 —, or —NR I —, wherein each 
         
         R H  is independently H or —COOR J , R J  is an N-protecting group, and R 1  is C 1-6  alkyl; and 
         (B) producing a compound of formula (IVC) from the compound of formula (IVB), wherein the compound of formula (IVC) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 1  is 
       
       
         
           
           
               
               
           
         
         
           wherein L 2  and L 3  combine to form a bond; 
         
         (C) producing a compound of formula (IVD) from the compound of formula (IVC), wherein the compound of formula (IVD) is: 
       
       
         
           
           
               
               
           
         
         wherein each of A 1  and A 2  is independently H or —OP″; 
         and 
         (D) producing the halichondrin macrolide or analog thereof from the compound of formula (IVD). 
       
     
     
         20 . The method of  claim 19 , wherein step (A) comprises:
 (E) producing a compound of formula (IA) from the compound of formula (IIA), the compound of formula (IIIA), and R 5 OH, wherein the compound of formula (IA) is:   
       
         
           
           
               
               
           
         
         and 
         (F) producing the compound of formula (IVB) from the compound of formula (IF) and the compound of formula (IVA). 
       
     
     
         21 . The method of  claim 20 , wherein step (E) comprises reacting the compound of formula (IIA), the compound of formula (IIIA), R 5 OH, and a Lewis acid. 
     
     
         22 . The method of  claim 21 , wherein the Lewis acid is an oxophilic Lewis acid. 
     
     
         23 . The method of  claim 22 , wherein the oxophilic Lewis acid is boron trifluoride or a solvate thereof. 
     
     
         24 . The method of any one of  claims 20  to  23 , wherein step (F) comprises reacting R 4A  that is 
       
         
           
           
               
               
           
         
         with a glycol cleaving agent, and a Horner-Wadsworth-Emmons reaction with (R C O) 2 P(O)—CH 2 —COOR C  to produce R 4A  that is 
       
       
         
           
           
               
               
           
         
       
     
     
         25 . The method of any one of  claims 20  to  24 , wherein step (F) comprises reacting R 4A  that is 
       
         
           
           
               
               
           
         
         with a 1,2-reducing agent and further reacting with an allyl halide or allyl pseudohalide. 
       
     
     
         26 . The method of any one of  claims 19  to  25 , wherein R 9  is —CHO, X 1  is —C(Y) 2 —, —CH(Y)—, or —CH 2 —, and step (A) comprises reacting R 9  with R 1  that is —CH(Y) 2  or —CH 2 (Y) treated with a Brønsted base. 
     
     
         27 . The method of any one of  claims 19  to  25 , wherein X 1  is —O—, and step (A) comprises esterifying R 1  that is —OP 6 , where P 6  is H, with R 9  that is —COOH. 
     
     
         28 . The method of any one of  claims 19  to  27 , wherein step (B) comprises reacting the compound of formula (IVB) with an olefin metathesis catalyst 
     
     
         29 . The method of any one of  claims 19  to  28 , wherein P 9  is H, R 16  is H, and step (C) comprises:
 oxidizing the compound of formula (IVC) to produce a compound of formula (IVCa): 
 
       
         
           
           
               
               
           
         
         and reacting the compound of formula (IVCa) with a 1,4-reducing agent to produce the compound of formula (IVD). 
       
     
     
         30 . The method of any one of  claims 19  to  29 , wherein the compound of formula (IVB) is, or is converted to, a compound of formula (IVBa) prior to producing the compound of formula (IVC), wherein the compound of formula (IVBa) is: 
       
         
           
           
               
               
           
         
       
     
     
         31 . The method of any one of  claims 19  to  30 , wherein the producing the halichondrin macrolide or analog thereof comprises reacting the compound of formula (IVD) with a hydroxyl protecting group removing agent. 
     
     
         32 . A method of preparing: 
       
         
           
           
               
               
           
         
         a halichondrin macrolide or analog thereof, 
       
       wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P is independently H or a hydroxyl protecting group; 
           
         
         each of A 1 , A 2 , and A 3  is independently H or OP″, wherein each P″ is independently H or a hydroxyl protecting group; 
         E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
         G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
         each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
         n, when present, is 0, 1, or 2; 
         k is 0 or 1; and 
         X 1  is —CH 2 — or —O—; 
         the method comprising: 
         (A) producing a compound of formula (VB) from a compound of formula (IIA), a compound of formula (IIB), a compound of formula (IIIB), a compound of formula (VA), and R 5 OH, 
         wherein R 5  is optionally substituted acyl; 
         wherein the compound of formula (IIA) is: 
       
       
         
           
           
               
               
           
         
         wherein
 R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and each Y is independently —COOR C  or —SO 2 R D ; 
 each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
 R D , when present, is optionally substituted aryl or optionally substituted non-enolizable alkyl; 
 R E  is —CHO or —CH (1+m) (OR F ) (2−m) , 
 wherein
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0, and 
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene; 
 
 
         wherein the compound of formula (IIB) is: 
       
       
         
           
           
               
               
           
         
         wherein R S  is silyl; 
         wherein the compound of formula (IIIB) is:
   R 4B -R 7 ,  (IIIB)
 
 
         wherein
 R 4B  is but-3-en-1-yl, 
 
       
       
         
           
           
               
               
           
         
         
           wherein each P 7  is independently H or a hydroxyl protecting group; and 
           R 7  is —CHO or 
         
       
       
         
           
           
               
               
           
         
         
           wherein each R 7A  is independently an optionally substituted alkyl; 
         
         wherein the compound of formula (VA) is: 
       
       
         
           
           
               
               
           
         
         wherein
 a designates (R)-stereogenic center, and Z is a sulfonate, chloride, bromide, or iodide; or a designates (S)-stereogenic center, and Z is OR 16 , wherein R 16  is a hydroxyl protecting group;
 (a1) R 10  is a hydroxyl protecting group, R 1  is alkyl ether, and R 12  is H; 
 (a2) R 10  is a hydroxyl protecting group, and R 1  and R 12  combine to form a double bond; 
 or 
 (a3) R 10  and R 11  combine to form a bond, and R 12  is H; 
 (b1) A 1  and R 14  combine to form oxo, R 13  is a hydroxyl protecting group, and R 15  is H; 
 or 
 (b2) A 1  is H or —OP″, and:
 (i) R 13  is a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
 
 Y 1  is iodide, bromide, or trifluoromethanesulfonate; 
 R 9  is —CHO or —COOH; 
 each P 9  is independently a hydroxyl protecting group, and X 3  is oxo; or both P 9  groups and X 3 , together with the atoms to which each is attached, combine to form a ketal; and 
 each P′ is independently a hydroxyl protecting group; and 
 
         wherein the compound of formula (VB) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, wherein each Y is independently —COOR C  or —SO 2 R D ; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
         each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; and 
         R K  is 
       
       
         
           
           
               
               
           
         
         (B) producing a compound of formula (VC) from the compound of formula (VB), wherein the compound of formula (VC) is: 
       
       
         
           
           
               
               
           
         
         wherein
 L 1  is 
 
       
       
         
           
           
               
               
           
         
         
           wherein L 2  and L 3  combine to form a bond; 
           b designates (S)-stereogenic center, if a designates (R)-stereogenic center; 
           and 
           b designates (R)-stereogenic center, if a designates (S)-stereogenic center; and 
         
         (C) producing the halichondrin macrolide or analog thereof from the compound of formula (VC). 
       
     
     
         33 . The method of  claim 32 , wherein step (A) comprises:
 (D) producing a compound of formula (ID) from the compound of formula (IIA), the compound of formula (IIB), the compound of formula (IIIB), and R 5 OH, wherein the compound of formula (ID) is:   
       
         
           
           
               
               
           
         
         and 
         (E) producing the compound of formula (VB) from the compound of formula (ID) and the compound of formula (VA). 
       
     
     
         34 . The method of  claim 33 , wherein the producing the compound of formula (ID) comprises reacting the compound of formula (IIC), the compound of formula (IIIB), R 5 OH, and a Lewis acid. 
     
     
         35 . The method of  claim 34 , wherein the Lewis acid is boron trifluoride or a solvate thereof. 
     
     
         36 . The method of any one of  claims 33  to  35 , wherein step (D) comprises a Sakurai reaction between the compound of formula (IIA) and the compound of formula (IIB) to produce a compound of formula (IIC), and a Prins reaction between the compound of formula (IIC), the compound of formula (IIIB), and R 5 OH, wherein the compound of formula (IIC) is: 
       
         
           
           
               
               
           
         
       
     
     
         37 . The method of any one of  claims 32  to  36 , wherein X 1  is —CH 2 —, —CH(Y)—, or —C(Y) 2 —, and step (A) comprises reacting R 9 , wherein R 9  is —CHO, with R 1  that is —CH(Y) 2  or —CH 2 (Y) treated with a Brønsted base, to produce —CO—X 1 —. 
     
     
         38 . The method of any one of  claims 32  to  36 , wherein X 1  is —O—, and step (A) comprises esterifying R 9  that is —COOH with R 1  that is —OP 6 , where P 6  is H, to produce —CO—X 1 —. 
     
     
         39 . The method of any one of  claims 32  to  38 , wherein step (B) comprises reacting the compound of formula (VB) with a Cr(II) salt and a Ni(II) salt. 
     
     
         40 . The method of any one of  claims 32  to  39 , wherein step (C) comprises a step of nucleophilic ring-closing of the compound of formula (VC). 
     
     
         41 . The method of any one of  claims 32  to  40 , wherein both P 9  groups and X 3 , together with the atoms to which each is attached, combine to form a ketal. 
     
     
         42 . The method of any one of  claims 32  to  41 , wherein R 10  and R 11  combine to form a bond, and R 12  is H. 
     
     
         43 . The method of any one of  claims 32  to  42 , wherein R 4B  is but-3-en-1-yl, and step (A) comprises OP 7  reacting the but-3-en-1-yl group with a dihydroxylating agent to produce R 4B  that is 
       
         
           
           
               
               
           
         
         and cleaving the 
       
       
         
           
           
               
               
           
         
         through a reaction with a glycol cleaving agent. 
       
     
     
         44 . The method of any one of  claims 32  to  42 , wherein R 4B  is 
       
         
           
           
               
               
           
         
         and step (A) comprises reacting the 
       
       
         
           
           
               
               
           
         
         with an oxidizing agent capable of converting an alcohol into a carbonyl group. 
       
     
     
         45 . The method of any one of  claims 32  to  42 , wherein R 4B  is 
       
         
           
           
               
               
           
         
         and step (A) comprises cleaving the 
       
       
         
           
           
               
               
           
         
         through a reaction with a glycol cleaving agent. 
       
     
     
         46 . A method of preparing: 
       
         
           
           
               
               
           
         
         a halichondrin macrolide or analog thereof, 
       
       wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
         
         each of A 1 , A 2 , and A 3  is independently H or OP″, wherein each P″ is independently H or a hydroxyl protecting group; 
         E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
         G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
         each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
         n, when present, is 0, 1, or 2; 
         k is 0 or 1; and 
         X 1  is —CH 2 — or —O—; 
         the method comprising: 
         (A) producing a compound of formula (IF) from a compound of formula (IIA), a compound of formula (IIB), a compound of formula (IIIC), and R 5 OH, 
         wherein R 5  is optionally substituted acyl; 
         wherein the compound of formula (IF) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and each Y is independently-COOR C  or —SO 2 R D ; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
         each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
         R 4C  is 
       
       
         
           
           
               
               
           
         
          wherein R C  is optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl, and each P 7  is independently H or a hydroxyl protecting group; and 
         R 5  is optionally substituted acyl; 
         wherein the compound of formula (IIA) is: 
       
       
         
           
           
               
               
           
         
         wherein
 R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and each Y is independently —COOR C  or —SO 2 R D ; 
 each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
 R D , when present, is optionally substituted aryl or optionally substituted non-enolizable alkyl; 
 R E  is —CHO or —CH (1+m) (OR F ) (2−m) , 
 wherein
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0, and 
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene; 
 
 
         wherein the compound of formula (IIB) is: 
       
       
         
           
           
               
               
           
         
         wherein R S  is silyl; 
         and 
         wherein the compound of formula (IIIC) is:
   R 4C -R 7 ,  (IIIC)
 
 
         wherein R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; 
         (B) producing a compound of formula (IG) from the compound of formula (IF), wherein the compound of formula (IG) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         R E 1 is 
       
       
         
           
           
               
               
           
         
         and 
         (C) producing the halichondrin macrolide or analog thereof from the compound of formula (IG) and one or more intermediates. 
       
     
     
         47 . The method of  claim 46 , wherein step (B) comprises reacting R 4C  that is 
       
         
           
           
               
               
           
         
         with a glycol cleaving agent to produce an aldehyde, reacting the aldehyde with (R C O) 2 P(O)—CH 2 —COOR C  to produce R 4C  that is 
       
       
         
           
           
               
               
           
         
       
     
     
         48 . The method of  claim 46  or  47 , wherein step (B) comprises reducing R 4C  that is 
       
         
           
           
               
               
           
         
         with a 1,4-reducing agent to produce R 4C  that is 
       
       
         
           
           
               
               
           
         
       
     
     
         49 . The method of  claim 46 , wherein step (B) comprises reducing R 4C  that is 
       
         
           
           
               
               
           
         
         with an allylic reducing agent to produce R 4C  that is 
       
       
         
           
           
               
               
           
         
       
     
     
         50 . The method of  claim 46 ,  48 , or  49 , wherein step (B) comprises reducing R 4C  that is 
       
         
           
           
               
               
           
         
         with a 1,2-reducing agent to produce a carbonyl group in R E 1. 
       
     
     
         51 . The method of  claim 49 , wherein the reducing R 4C  that is 
       
         
           
           
               
               
           
         
         comprises an esterification reaction producing R 4C  that is 
       
       
         
           
           
               
               
           
         
       
     
     
         52 . The method of  claim 46 , wherein step (B) comprises reacting R 4C  that is 
       
         
           
           
               
               
           
         
         with an oxidizing agent capable of converting an alcohol to a carbonyl group in R E 1. 
       
     
     
         53 . The method of any one of  claims 46  to  52 , wherein the one or more intermediates is a compound of formula (VIA): 
       
         
           
           
               
               
           
         
         wherein 
         R 10A  is —CH 2 —CH═CH 2 , —(CH 2 ) 2 —CH═CH 2 , or —(CH 2 ) 3 —OP 10 ; 
         each R 10 , R 13 , P 5  and P 10  is independently a hydroxyl protecting group; 
         A 1  is H or —OP″; and 
         Y 1  is chloro, bromo, iodo, trifluoromethanesulfonate, or trialkylsilane; 
         and step (C) comprises: 
         (D) producing a compound of formula (VIB) from the compound of formula (IG) and the compound of formula (VIA), wherein the compound of formula (VIB) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 4  is 
       
       
         
           
           
               
               
           
         
         R 1  is —OP 6  or —CH(Y), wherein P 6  is H or a hydroxyl protecting group, and Y is —COOR C  or —CHO;
 A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
 or 
 A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
 
         and 
         each P 9  is independently a hydroxyl protecting group, and X 3  is oxo or X 3 , together with the carbon atom to which it is attached, is —(CH(OP 11 ))—, wherein P 11  is H or a hydroxyl protecting group; or both P 9  groups and X 3 , together with the atoms to which each is attached, combine to form a ketal. 
       
     
     
         54 . The method of  claim 53 , wherein step (D) comprises reacting the compound of formula (VIA) and the compound of formula (IG) with a Cr(II) salt and a Ni(II) salt. 
     
     
         55 . The method of  claim 53  or  54 , wherein R 10A  is —CH 2 —CH═CH 2 , and step (C) comprises:
 (E) producing a compound of formula (VIC) from the compound of formula (VIB) and R 17 —CH 2 CH═CH 2 , wherein R 17  is —COOH or a metallic or metalloid moiety, and the compound of formula (VIC) is: 
 
       
         
           
           
               
               
           
         
         wherein 
         L 5  is 
       
       
         
           
           
               
               
           
         
         X 1  is —CH 2 — or —O—; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, wherein P 12  is H or a hydroxyl protecting group; 
         (F) producing a compound of formula (VID) from the compound of formula (VIC), wherein the compound of formula (VID) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 1 , is 
       
       
         
           
           
               
               
           
         
          wherein L 2  and L 3  combine to form a bond; and 
         (G) producing the halichondrin macrolide or analog thereof from the compound of formula (VID). 
       
     
     
         56 . The method of  claim 55 , wherein R 1  is —CH 2 (Y), X 1  is —CH 2 —, X 4  is oxo or —(CH(OP 12 ))—, and step (E) comprises reacting the compound of formula (VIB) with R 17 —CH 2 CH═CH 2 , wherein R 17  is a metallic or metalloid moiety. 
     
     
         57 . The method of  claim 55 , wherein R 1  is —OP 6 , P 6  is H, X 1  is —O—, X 4  is oxo, and step (E) comprises esterifying the compound of formula (VIB) with R 17 —CH 2 CH═CH 2 , wherein R 17  is —COOH. 
     
     
         58 . The method of any one of  claims 55  to  57 , wherein the producing step (F) comprises reacting the compound of formula (VIC) with an olefin metathesis catalyst. 
     
     
         59 . The method of any one of  claims 55  to  58 , wherein step (G) comprises reacting the compound of formula (VID) with a hydroxyl protecting group removing agent. 
     
     
         60 . The method of  claim 53  or  54 , wherein R 10A  is —CH 2 —CH 2 —CH═CH 2 , R 1  is —OP 6  or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and Y is —COOR C , and step (C) comprises:
 (H) producing a compound of formula (VIE) from the compound of formula (VIB) and R 17 —CH═CH 2 , wherein R 17  is —COOH or a metallic or metalloid moiety, wherein the compound of formula (VIE) is: 
 
       
         
           
           
               
               
           
         
         wherein 
         L 6  is 
       
       
         
           
           
               
               
           
         
         X 1  is —CH 2 — or —O—; and 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, wherein P 12  is H or a hydroxyl protecting group; 
         (I) producing a compound of formula (VIF) from the compound of formula (VIE), wherein the compound of formula (VIF) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 1  is 
       
       
         
           
           
               
               
           
         
          wherein L 2  and L 3  combine to form a bond; and 
         (J) producing the halichondrin macrolide or analog thereof from the compound of formula (VIF). 
       
     
     
         61 . The method of  claim 60 , wherein step (I) comprises reacting the compound of formula (VIE) with an olefin metathesis catalyst. 
     
     
         62 . The method of  claim 60  or  61 , wherein step (J) comprises reacting the compound of formula (VIF) with a hydroxyl protecting group removing agent. 
     
     
         63 . The method of  claim 53  or  54 , wherein R 10A  is —(CH 2 ) 3 —OP 10 , and step (C) comprises:
 (K) producing a compound of formula (VIG) from the compound of formula (VIB) and (R C O) 2 P(O)—CH 2 —R P , wherein each R C  is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl, and R P  is H or —COOH, and wherein the compound of formula (VIG) is: 
 
       
         
           
           
               
               
           
         
         wherein 
         L 7  is 
       
       
         
           
           
               
               
           
         
         and 
         X 1  is —CH 2 — or —O—; 
         (L) producing a compound of formula (VIF) from the compound of formula (VIG), wherein the compound of formula (VIF) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 1  is 
       
       
         
           
           
               
               
           
         
          wherein L 2  and L 3  combine to form a bond; and 
         X 4  is oxo; 
         and 
         (M) producing the halichondrin macrolide or analog thereof from the compound of formula (VIF). 
       
     
     
         64 . The method of  claim 63 , wherein the producing step (K) comprises:
 reacting the compound of formula (VIB) with (R C O) 2 P(O)—CH 2 —R P  under Claisen reaction conditions, wherein R P  is H and R 1  is —CH 2 (Y), or   esterifying the compound of formula (VIB) with (R C O) 2 P(O)—CH 2 -R P , wherein R P  is —COOH and R 1  is —OP 6 , wherein P 6  is H.   
     
     
         65 . The method of  claim 63  or  64 , wherein step (M) comprises reacting the compound of formula (VIF) with a hydroxyl protecting group removing agent. 
     
     
         66 . The method of any one of  claims 46  to  52 , wherein step (C) comprises:
 (N) producing a compound of formula (VIIB) from the compound of formula (IG) and a compound of formula (VIIA): 
 
       
         
           
           
               
               
           
         
         wherein 
         (i) R 10  is a hydroxyl protecting group, R 1  is alkyl ether, and R 12  is H; 
         (ii) R 10  is a hydroxyl protecting group, and R 1  and R 12  combine to form a double bond; 
         or 
         (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
         R 9  is —CH 2 —OP″ or —COOP; 
         R 13  and each P 9  is independently a hydroxyl protecting group; 
         A 1  is H or —OP″; 
         each P″ is independently H or a hydroxyl protecting group; and 
         Y 1  is chloro, bromo, iodo, trifluoromethanesulfonate, or trialkylsilane; 
         wherein the compound of formula (VIIB) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 4  is 
       
       
         
           
           
               
               
           
         
         R 1  is —OP 6 , —CH 2 (Y), or —CH(Y) 2 , wherein P 6  is H or a hydroxyl protecting group, and Y is —COOR C  or —CHO;
 A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
 or 
 A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
 
         R 9  is —CHO or —COOP; 
         and 
         each P 9  is independently a hydroxyl protecting group, and X 3  is oxo or X 3 , together with the carbon atom to which it is attached, is —(CH(OP 11 ))—, wherein P 1  is H or a hydroxyl protecting group; or both P 9  groups and X 3 , together with the atoms to which each is attached, combine to form a ketal; 
         (O) producing a compound of formula (VIIC) from the compound of formula (VIIB), wherein the compound of formula (VIIC) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 1  is 
       
       
         
           
           
               
               
           
         
         
           wherein L 2  and L 3  combine to form a bond; 
         
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, wherein each Y is independently —COOR C  or —SO 2 R D ; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
         each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; and 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; 
         and 
         (P) producing the halichondrin macrolide or analog thereof from the compound of formula (VIIC). 
       
     
     
         67 . The method of  claim 66 , wherein step (N) comprises reacting the compound of formula (VIIA) and the compound of formula (IH) with a Cr(II) salt and a Ni(II) salt. 
     
     
         68 . The method of  claim 66  or  67 , wherein step (O) comprises an esterification reaction between R 1  that is —OP 6 , wherein P 6  is H, and R 9  that is —COOH. 
     
     
         69 . The method of  claim 66  or  67 , wherein step (O) comprises a reaction between R 1  that is —CH(Y) 2  or —CH 2 (Y), and R 9  that is —CHO. 
     
     
         70 . The method of any one of  claims 66  to  69 , wherein step (P) comprises reacting the compound of formula (VIIC) with a hydroxyl protecting group removing agent. 
     
     
         71 . A method of preparing: 
       
         
           
           
               
               
           
         
         a halichondrin macrolide or analog thereof, 
       
       wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
         
         each of A 1 , A 2 , and A 3  is independently H or OP″, wherein each P″ is independently H or a hydroxyl protecting group; 
         E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
         G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
         each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
         n, when present, is 0, 1, or 2; 
         k is 0 or 1; and 
         X 1  is —CH 2 — or —O—; 
         the method comprising: 
         (A) producing a compound of formula (VIID) from a compound of formula (IIA), a compound of formula (IIB), a compound of formula (IIIC), a compound of formula (VIIA), and R 5 OH, 
         wherein R 5  is optionally substituted acyl; 
         wherein the compound of formula (IIA) is: 
       
       
         
           
           
               
               
           
         
         wherein
 R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and each Y is independently-COOR C  or —SO 2 R D ; 
 each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
 each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
 R E  is —CHO or —CH (1+m) (OR F ) (2−m) , 
 wherein
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0, and 
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene; 
 
 
         wherein the compound of formula (IIB) is: 
       
       
         
           
           
               
               
           
         
         wherein R S  is silyl; 
         wherein the compound of formula (IIIC) is:
   R 4C -R 7 ,  (IIIC)
 
 
         wherein 
         R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; 
         R 4C  is 
       
       
         
           
           
               
               
           
         
         
           wherein each P 7 , when present, is independently H or a hydroxyl protecting group; 
         
         wherein the compound of formula (VIIA) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         (i) R 10  is a hydroxyl protecting group, R 11  is alkyl ether, and R 12  is H; 
         (ii) R 10  is a hydroxyl protecting group, and R 11  and R 12  combine to form a double bond; 
         or 
         (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
         R 9  is —CHO or —COOH; 
         R 13  and each P 9  is independently a hydroxyl protecting group; 
         A 1  is H or —OP″, wherein P″ is H or a hydroxyl protecting group; and 
         Y 1  is chloro, bromo, iodo, trifluoromethanesulfonate, or trialkylsilane; 
         wherein the compound of formula (VIID) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, wherein each Y is independently —COOR C  or —SO 2 R D ; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; 
         R L  is 
       
       
         
           
           
               
               
           
         
         
           wherein 
           R 18  is —CHO or —CH 2 OP 7 ; 
           R 5  is optionally substituted acyl; 
         
         (B) producing a compound of formula (VIIE) from the compound of formula (VIID), wherein the compound of formula (VIIE) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 1  is 
       
       
         
           
           
               
               
           
         
         
           wherein L 2  and L 3  combine to form a bond; 
         
         each P 9  is independently a hydroxyl protecting group, and X 3  is oxo or X 3 , together with the carbon atom to which it is attached, is —(CH(OP 11 ))—, wherein P 1  is H or a hydroxyl protecting group; 
         and 
         (C) producing the halichondrin macrolide or analog thereof from the compound of formula (VIIC). 
       
     
     
         72 . The method of  claim 71 , wherein step (A) comprises:
 (D) producing a compound of formula (IIC) from the compound of formula (IIA) and the compound of formula (IIB), wherein the compound of formula (IIC) is:   
       
         
           
           
               
               
           
         
         (E) producing a compound of formula (IF) from the compound of formula (IIC), the compound of formula (IIIC), and R 5 OH, wherein the compound of formula (IF) is: 
       
       
         
           
           
               
               
           
         
         and 
         (F) producing the compound of formula (VIIB) from the compound of formula (VIIA) and the compound of formula (IF). 
       
     
     
         73 . The method of  claim 72 , wherein the producing the compound of formula (IF) comprises reacting the compound of formula (IIC), the compound of formula (IIIC), R 5 OH, and a Lewis acid. 
     
     
         74 . The method of  claim 73 , wherein the Lewis acid is an oxophilic Lewis acid. 
     
     
         75 . The method of  claim 74 , wherein the oxophilic Lewis acid is boron trifluoride or a solvate thereof. 
     
     
         76 . The method of any one of  claims 71  to  75 , wherein step (F) comprises:
 (G) producing a compound of formula (IH) from the compound of formula (IF), wherein the compound of formula (IH) is: 
 
       
         
           
           
               
               
           
         
         and 
         (H) producing the compound of formula (VIID) from the compound of formula (IH) and the compound of formula (VIIA). 
       
     
     
         77 . The method of  claim 76 , wherein the producing step (G) comprises reacting the compound of formula (IF) with an allylic reducing agent. 
     
     
         78 . The method of any one of  claims 71  to  77 , wherein step (A) comprises reducing R 4C  that is 
       
         
           
           
               
               
           
         
         with a 1,2-reducing agent. 
       
     
     
         79 . The method of any one of  claims 71  to  77 , wherein step (A) comprises reducing R 4C  that is 
       
         
           
           
               
               
           
         
         with a 1,4-reducing agent to produce a reduction product, and reducing the reduction product with a 1,2-reducing agent. 
       
     
     
         80 . The method of any one of  claims 71  to  77 , wherein step (A) comprises reducing R 4C  that is 
       
         
           
           
               
               
           
         
         with an allylic reducing agent to produce an acid product, and reducing the acid product with a 1,2-reducing agent capable of converting the carboxylic acid to an aldehyde. 
       
     
     
         81 . The method of any one of  claims 71  to  77 , wherein step (A) comprises cleaving R 4C  that is 
       
         
           
           
               
               
           
         
         with a glycol cleaving agent to produce an aldehyde, reacting the aldehyde (R C O) 2 P(O)—CH 2 —COOR C  to produce an enoate, reacting the enoate with a 1,4-reducing agent to produce R 4C  that is 
       
       
         
           
           
               
               
           
         
         and reacting R 4C  that is 
       
       
         
           
           
               
               
           
         
         with a 1,2-reducing agent capable of converting the carboxylic acid to an aldehyde. 
       
     
     
         82 . The method of any one of  claims 71  to  81 , wherein step (A) comprises an esterification reaction between R 1  that is —OP 6 , where P 6  is H, and R 9  that is —COOH. 
     
     
         83 . The method of any one of  claims 71  to  81 , wherein step (A) comprises a reaction between R 1  that is —CH(Y) 2  or —CH 2 (Y), and R 9  that is —CHO. 
     
     
         84 . The method of any one of  claims 71  to  78 , wherein step (B) comprises reacting the compound of formulas (VIID) with a Cr(II) salt and a Ni(II) salt. 
     
     
         85 . The method of any one of  claims 71  to  84 , wherein step (C) comprises reacting the compound of formula (VIIE) with a hydroxyl protecting group removing agent. 
     
     
         86 . A method of preparing: 
       
         
           
           
               
               
           
         
         a halichondrin macrolide or analog thereof, 
       
       wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
         
         each of A 1 , A 2 , and A 3  is independently H or OP″, wherein each P″ is independently H or a hydroxyl protecting group; 
         E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
         G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
         each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
         n, when present, is 0, 1, or 2; 
         k is 0 or 1; and 
         X 1  is —CH 2 — or —O—; 
         the method comprising: 
         (A) producing a compound of formula (VIIIB) from a compound of formula (VIIIA), a compound of formula (IIA), a compound of formula (IIB), and a compound of formula (IIIC), and R 5 OH, 
         wherein R 5  is optionally substituted acyl; 
         wherein the compound of formula (IIA) is: 
       
       
         
           
           
               
               
           
         
         wherein
 R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and each Y is independently-COOR C  or —SO 2 R D ; 
 each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
 each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
 R E  is —CHO or —CH (1+m) (OR F ) (2−m) , 
 wherein
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0 
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene; 
 
 
         wherein the compound of formula (IIB) is: 
       
       
         
           
           
               
               
           
         
         wherein R S  is silyl; 
         wherein the compound of formula (IIIC) is:
   R 4C -R 7 ,  (IIIC)
 
 
         wherein 
         R 4C  is 
       
       
         
           
           
               
               
           
         
         
           wherein 
           each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
           each P 7 , when present, is independently H or a hydroxyl protecting group; 
         
         R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; 
         and 
         wherein the compound of formula (VIIIA) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         (i) R 10  is a hydroxyl protecting group, R 1  is alkyl ether, and R 12  is H; 
         (ii) R 10  is a hydroxyl protecting group, and R 4  and R 5  combine to form a double bond; 
         or 
         (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
         R 9  is —CHO or —COOH; 
         and 
         each P 9  and R 13  is independently a hydroxyl protecting group; 
         wherein the compound of formula (VIIIB) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, wherein each Y is independently —COOR C  or —SO 2 R D ; 
         R M  is 
       
       
         
           
           
               
               
           
         
         
           wherein 
           R 5  is optionally substituted acyl; and 
           X 3  is oxo or X 3 , together with the carbon atom to which it is attached, is —(CH(OP 11 ))—, 
         
         wherein P 1  is H or a hydroxyl protecting group; and 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; 
         (B) producing a compound of formula (VIIIC) from the compound of formula (VIIIB), wherein the compound of formula (VIIIC) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         L 1  is 
       
       
         
           
           
               
               
           
         
         
           wherein L 2  and L 3  combine to form a bond; 
         
         A 1  is H or —OP″, wherein P″ is H or a hydroxyl protecting group; and 
         (C) producing the halichondrin macrolide or analog thereof from the compound of formula (VIIIC). 
       
     
     
         87 . The method of  claim 86 , wherein step (A) comprises:
 (D) producing a compound of formula (IIC) from the compound of formula (IIA) and the compound of formula (IIB), wherein the compound of formula (IIC) is:   
       
         
           
           
               
               
           
         
         (E) producing a compound of formula (IF) from the compound of formula (IIC), the compound of formula (IIIC), and R 5 OH, wherein the compound of formula (IF) is: 
       
       
         
           
           
               
               
           
         
         (F) producing a compound of formula (IJ) from the compound of formula (IF), wherein the compound of formula (IJ) is: 
       
       
         
           
           
               
               
           
         
         and 
         (G) producing the compound of formula (VIIIB) from the compound of formula (VIIIA) and the compound of formula (IJ). 
       
     
     
         88 . The method of  claim 87 , wherein step (D) comprises reacting the compound of formula (IIB), the compound of formula (IIA), and a Lewis acid. 
     
     
         89 . The method of  claim 87  or  88 , wherein step (E) comprises reacting the compound of formula (IIC), the compound of formula (IIIC), R 5 OH and a Lewis acid. 
     
     
         90 . The method of  claim 88  or  89 , wherein the Lewis acid in step (D) and the Lewis acid in step (E) are different. 
     
     
         91 . The method of any one of  claims 88  to  90 , wherein the Lewis acid is an oxophilic Lewis acid. 
     
     
         92 . The method of  claim 91 , wherein the oxophilic Lewis acid is boron trifluoride or a solvate thereof. 
     
     
         93 . The method of any one of  claims 87  to  92 , wherein step (F) comprises converting 
       
         
           
           
               
               
           
         
         using an allylic reducing agent. 
       
     
     
         94 . The method of claim any one of  claims 86  to  92 , wherein step (A) comprises reacting R 4C  that is 
       
         
           
           
               
               
           
         
         with a 1,2-reducing agent to produce a product, and reacting the product with a vinyl nucleophile. 
       
     
     
         95 . The method of any one of  claims 86  to  92 , wherein step (A) comprises reacting R 4C  that is 
       
         
           
           
               
               
           
         
         with a 1,4-reducing agent to produce a product, reducing the product with a 1,2-reducing agent to produce a reduced product, and reacting the reduced product with a vinyl nucleophile. 
       
     
     
         96 . The method of any one of  claims 86  to  92 , wherein step (A) comprises reacting R 4C  that is 
       
         
           
           
               
               
           
         
         with an allylic reducing agent to produce an acid, reducing the acid with a 1,2-reducing agent to produce a reduced product, and reacting the reduced product with a vinyl nucleophile. 
       
     
     
         97 . The method of any one of  claims 86  to  92 , wherein step (A) comprises cleaving R 4C  that is 
       
         
           
           
               
               
           
         
         with a glycol cleaving agent to produce an aldehyde, reacting the aldehyde with (R C O) 2 P(O)—CH 2 —COOR C  to produce an enoate, reacting the enoate with a 1,4-reducing agent to produce a product, reducing the product with a 1,2-reducing agent to product a reduced product, and reacting the reduced product with a vinyl nucleophile. 
       
     
     
         98 . The method of any one of  claims 86  to  97 , wherein step (A) comprises an esterification reaction between R 1  that is —OP 6 , where P 6  is H, and R 9  that is —COOH. 
     
     
         99 . The method of any one of  claims 86  to  97 , wherein step (A) comprises a reaction between R 1  that is —CH(Y) 2  or —CH 2 (Y), and R 9 , wherein R 9  is —CHO. 
     
     
         100 . The method of any one of  claims 86  to  99 , wherein step (B) comprises reacting the compound of formula (VIIIB) with an olefin metathesis catalyst. 
     
     
         101 . The method of any one of  claims 86  to  100 , wherein step (C) comprises reacting the compound of formula (VIIIC) with a hydroxyl protecting group removing agent. 
     
     
         102 . A method of preparing: 
       
         
           
           
               
               
           
         
         a halichondrin macrolide or analog thereof, 
       
       wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
         
         each of A 1 , A 2 , and A 3  is independently H or OP″, wherein each P″ is independently H or a hydroxyl protecting group; 
         E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
         G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
         each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
         n, when present, is 0, 1, or 2; 
         k is 0 or 1; and 
         X 1  is —CH 2 — or —O—; 
         the method comprising: 
         (A) producing a compound of formula (IXB) from a compound of formula (IXA), a compound of formula (IIB), a compound of formula (IIA), a compound of formula (IIIE), and R 5 OH, 
         wherein R 5  is optionally substituted acyl; 
         wherein the compound of formula (IXA) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         R 9  is —CHO or —COOP″; 
         (a1) R 10  is a hydroxyl protecting group, R 1  is alkyl ether, and R 12  is H; 
         (a2) R 10  is a hydroxyl protecting group, and R 1  and R 12  combine to form a double bond; 
         or 
         (a3) R 10  and R 11  combine to form a bond, and R 12  is H;
 A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
 or 
 A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
 
         R O  is —CHO, —CH 2 OP″, —CH═CH 2 , —CH(OP″)CH 2 OP″, —C(O)—CH 2 P(O)(OR C ) 2 , or halogen; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
         each P″ is independently H or a hydroxyl protecting group; and 
         each P 9  is independently a hydroxyl protecting group; 
         wherein the compound of formula (IIA) is: 
       
       
         
           
           
               
               
           
         
         wherein
 R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group, and each Y is independently-COOR C  or —SO 2 R D ; 
 each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
 R E  is —CHO or —CH (1+m) (OR F ) (2−m) , 
 wherein 
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0, and
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene; 
 
 
         wherein the compound of formula (IIIE) is:
   R 4E -R 7 ,  (IIIE)
 
 
         wherein 
         R 4E  is 
       
       
         
           
           
               
               
           
         
         wherein
 each P 7  is independently H or a hydroxyl protecting group; and 
 R 8  is —CH 2 CH 2 —COOR C , —CH═CH—COOR C , —CH 2 CH 2 —SO 2 R D , or —CH═CH—SO 2 R D ; and 
 
         R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; 
         wherein the compound of formula (IIB) is: 
       
       
         
           
           
               
               
           
         
         wherein R S  is silyl; 
         and 
         wherein the compound of formula (IXB) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—; 
         L 1  is 
       
       
         
           
           
               
               
           
         
          wherein L 2  and L 3  combine to form a bond; 
         R 5  is optionally substituted acyl;
 A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
 or 
 A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15 , together with the atoms to which each is attached, combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
 each P 9  is independently H or a hydroxyl protecting group, and X 3  is oxo, or X 3 , together with the atom to which it is attached, combines to form —(CH(OP 11 ))—, wherein P 1  is H or a hydroxyl protecting group; 
 or 
 both P 9  and X 3 , together with the atoms to which each is attached, combine to form a ketal; 
 
         and 
         R 19A  is H, —OP″, or Y, and R 19B  is H; or R 19A  and R 19B , together with the atoms to which each is attached, combine to form a double bond; and 
         (B) producing the halichondrin macrolide or analog thereof from the compound of formula (IXB). 
       
     
     
         103 . The method of  claim 102 , wherein step (A) comprises reacting R E  that is —CHO with the compound of formula (IIB) and a first Lewis acid to produce a group of the structure 
       
         
           
           
               
               
           
         
       
     
     
         104 . The method of  claim 103 , wherein step (A) comprises reacting the group of the structure 
       
         
           
           
               
               
           
         
         with R 7 , R 5 OH, and a second Lewis acid to produce a group of the structure 
       
       
         
           
           
               
               
           
         
       
     
     
         105 . The method of  claim 104 , wherein the first Lewis acid and/or second Lewis acid is an oxophilic Lewis acid. 
     
     
         106 . The method of  claim 104  or  105 , wherein the first Lewis acid is same as the second Lewis acid. 
     
     
         107 . The method of any one of  claims 102  to  106 , wherein step (A) comprises converting R 4E  that is 
       
         
           
           
               
               
           
         
         to a group of the structure 
       
       
         
           
           
               
               
           
         
         and reacting this group with R O  that is —C(O)—CH 2 P(O)(OR C ) 2  under Horner-Wadsworth-Emmons reaction conditions. 
       
     
     
         108 . The method of any one of  claims 102  to  106 , wherein step (A) comprises reacting R 4E  that is 
       
         
           
           
               
               
           
         
         with R O  that is —CHO under Claisen reaction conditions, wherein R 8  is —CH 2 CH 2 —COOR C  or —CH 2 CH 2 —SO 2 R D . 
       
     
     
         109 . The method of any one of  claims 102  to  106 , wherein step (A) comprises converting R 4E  that is 
       
         
           
           
               
               
           
         
         to a group of the structure 
       
       
         
           
           
               
               
           
         
         and reacting this group with R O  that is a halogen under Nozaki-Hiyama-Kishi reaction conditions, wherein R 8 , when present, is —CH 2 CH 2 —COOR C  or —CH═CH—COOR C , and R 14  and R 15  combine to form a double bond. 
       
     
     
         110 . The method of any one of  claims 102  to  109 , wherein step (A) comprises reacting R 1  that is —OP 6  and R 9  under esterification reaction conditions to produce a group of the structure —X 1 —C(O)—, wherein P 6  is H, R 9  is —COOH, and X 1  is —O—. 
     
     
         111 . The method of any one of  claims 102  to  110 , wherein step (A) comprises reacting R 1  that is —CH(Y) 2  or —CH 2 (Y) with R 9  under Claisen reaction conditions to produce a group of the structure —X 1 —C(O)—, wherein R 9  is —CHO, and X 1  is —C(Y) 2 — or —CH(Y)—, respectively. 
     
     
         112 . The method of any one of  claims 102  to  111 , wherein step (B) comprises reacting the compound of formula (IXB) with a hydroxyl protecting group removing agent. 
     
     
         113 . The method of any one of  claims 1  to  112 , wherein D′ is OP 1 , wherein P 1  is alkyl. 
     
     
         114 . The method of any one of  claims 1  to  113 , wherein D is H. 
     
     
         115 . The method of any one of  claims 1  to  114 , wherein A is of the following structure: 
       
         
           
           
               
               
           
         
       
     
     
         116 . The method of any one of  claims 1  to  115 , wherein k is 0. 
     
     
         117 . The method of any one of  claims 1  to  116 , wherein R 3  is —(CH 2 ) n NP 3 P 4  or —(CH 2 ) n OP 5 , wherein n is 0. 
     
     
         118 . The method of any one of  claims 1  to  112 , wherein D′ is H. 
     
     
         119 . The method of any one of  claims 1  to  112  and  118 , wherein A and D combine to form the following structure: 
       
         
           
           
               
               
           
         
         wherein, the bond to oxygen atom originates at the carbon atom, to which D is attached in formula (IA), and 
         wherein R 3  is —(CH 2 ) n NP 3 P 4  or —(CH 2 ) n OP 5 , wherein n is 2. 
       
     
     
         120 . The method of any one of  claims 1  to  112 ,  118 , and  119 , wherein k is 1, and E is optionally substituted alkyl. 
     
     
         121 . The method of any one of  claims 1  to  120 , wherein G is O. 
     
     
         122 . A method of preparing: 
       
         
           
           
               
               
           
         
         wherein R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          and
 each R 7A  is independently alkyl or a hydroxyl protecting group; or 
 both R 7A  combine to form an optionally substituted alkylene; 
 
       
       the method comprising:
 (A) producing a compound of formula (Z2) from a compound of formula (Z1) and 
 
       
         
           
           
               
               
           
         
          wherein each R O  is independently optionally substituted alkyl, wherein the compound of formula (Z1) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         each R 20A  is independently a hydroxyl protecting group, or both R 20A , together with the atoms to which each is attached, combine to form an acetal, ketal, cyclic carbonate, dicarbonyl-dioxo, or silylene-dioxo; 
         each R 20B  is independently a hydroxyl protecting group, or both R 20B , together with the atoms to which each is attached, combine to form an acetal, ketal, cyclic carbonate, dicarbonyl-dioxo, or silylene-dioxo; 
         P 12A  is H; 
         P 12B  is H or a hydroxyl protecting group; 
         and the compound of formula (Z2) is: 
       
       
         
           
           
               
               
           
         
         (B) producing a compound of formula (Z3) from the compound of formula (Z2) and 
       
       
         
           
           
               
               
           
         
          wherein each R 21  is independently optionally substituted alkyl, wherein the compound of formula (Z3) is: 
       
       
         
           
           
               
               
           
         
         (C) producing a compound of formula (Z4) from the compound of formula (Z3), wherein the compound of formula (Z4) is: 
       
       
         
           
           
               
               
           
         
         wherein X 5  is a halogen; 
         (D) producing a compound of formula (Z5) from the compound of formula (Z4), wherein the compound of formula (Z5) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         R 20A  is H or a hydroxyl protecting group; and 
         each R 20B  is independently H or a hydroxyl protecting group, or both R 20B , together with the atoms to which each is attached, combine to form an acetal, ketal, cyclic carbonate, dicarbonyl-dioxo, or silylene-dioxo; 
         (E) producing a compound of formula (Z6) from the compound of formula (Z5) and R 7A OH 
       
       
         
           
           
               
               
           
         
         (F) producing a compound of formula (Z7) from the compound of formula (Z6) and 
       
       
         
           
           
               
               
           
         
          wherein each R 22  is independently optionally substituted alkyl, and the compound of formula (Z7) is: 
       
       
         
           
           
               
               
           
         
         and 
         (G) producing the compound of formula (Z) from the compound of formula (Z7). 
       
     
     
         123 . The method of  claim 122 , wherein step (E) comprises reacting the compound of formula (Z5) with R 7A OH and a Brønsted acid. 
     
     
         124 . The method of  claim 122  or  123 , wherein step (F) comprises reacting the compound of formula (Z6) with a glycol cleaving agent to produce an aldehyde product, and reacting the aldehyde product with 
       
         
           
           
               
               
           
         
         under Horner-Wadsworth-Emmons reaction conditions. 
       
     
     
         125 . The method of any one of  claims 122  to  124 , wherein step (G) comprises reacting the compound of formula (Z6) with a 1,4-reducing agent. 
     
     
         126 . A method of preparing: 
       
         
           
           
               
               
           
         
         wherein 
         R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          and
 each R 7A  is independently alkyl or a hydroxyl protecting group; or 
 both R 7A  combine to form an optionally substituted alkylene; 
 
         R 8  is —CH 2 CH 2 —COOR C , —CH═CH—COOR C , —CH 2 CH 2 —SO 2 R D , or —CH═CH—SO 2 R D ; 
         R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
         R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
         the method comprising: 
         (A) producing a compound of formula (Z2) from a compound of formula (Z1) and 
       
       
         
           
           
               
               
           
         
          wherein each R O  is independently optionally substituted alkyl, wherein the compound of formula (Z1) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         each R 20A  is independently a hydroxyl protecting group, or both R 20A , together with the atoms to which each is attached, combine to form an acetal, ketal, cyclic carbonate, dicarbonyl-dioxo, or silylene-dioxo; 
         each R 20B  is independently a hydroxyl protecting group, or both R 20B , together with the atoms to which each is attached, combine to form an acetal, ketal, cyclic carbonate, dicarbonyl-dioxo, or silylene-dioxo; 
         P 12A  is H; 
         P 12B  is H or a hydroxyl protecting group; 
         and the compound of formula (Z2) is: 
       
       
         
           
           
               
               
           
         
         (B) producing a compound of formula (Z3) from the compound of formula (Z2) and 
       
       
         
           
           
               
               
           
         
          wherein each R 21  is independently optionally substituted alkyl, wherein the compound of formula (Z3) is: 
       
       
         
           
           
               
               
           
         
         (C) producing a compound of formula (Z4) from the compound of formula (Z3), wherein the compound of formula (Z4) is: 
       
       
         
           
           
               
               
           
         
         wherein X 5  is a halogen; 
         (D) producing a compound of formula (Z5) from the compound of formula (Z4), wherein the compound of formula (Z5) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         R 20A  is H or a hydroxyl protecting group; and 
         each R 20B  is independently H or a hydroxyl protecting group, or both R 20B , together with the atoms to which each is attached, combine to form an acetal, ketal, cyclic carbonate, dicarbonyl-dioxo, or silylene-dioxo; 
         (E) producing a compound of formula (Z5A) from the compound of formula (Z5) and R 7A OH, wherein the compound of formula (Z5A) is: 
       
       
         
           
           
               
               
           
         
         wherein 
         R 20A  is H or a hydroxyl protecting group; and 
         each R 20B  is independently H or a hydroxyl protecting group, or both R 20B , together with the atoms to which each is attached, combine to form an acetal, ketal, cyclic carbonate, dicarbonyl-dioxo, or silylene-dioxo; 
         (F) producing a compound of formula (Z5B) from the compound of formula (Z5A), wherein the compound of formula (Z5B) is: 
       
       
         
           
           
               
               
           
         
         wherein R 23  is H or —OR 20A ; 
         and 
         (G) producing the compound of formula (Z8) from the compound of formula (Z5B) and 
       
       
         
           
           
               
               
           
         
          in which each R 22  is independently optionally substituted alkyl. 
       
     
     
         127 . The method of  claim 126 , wherein step (E) comprises reacting the compound of formula (Z5) with R 7A OH and a Brønsted acid. 
     
     
         128 . The method of  claim 126  or  127 , wherein step (F) comprises reacting the compound of formula (Z5A), in which both R 20B  are H, with a glycol cleaving agent. 
     
     
         129 . The method of any one of  claims 126  to  128 , wherein step (E) or step (F) further comprises reacting —OR 20A , wherein R 20A  is optionally substituted acyl with an allylic reducing agent. 
     
     
         130 . The method of any one of  claims 126  to  129 , wherein step (G) comprises reacting the compound of formula (Z5B) with 
       
         
           
           
               
               
           
         
         under Horner-Wadsworth-Emmons reaction conditions to produce the compound of formula (Z8), in which R 8  is —CH═CH—COOR C  or —CH═CH—SO 2 R D , respectively. 
       
     
     
         131 . The method of  claim 130 , wherein step (G) further comprises reacting the compound of formula (Z8), in which R 8  is —CH═CH—COOR C  or —CH═CH—SO 2 R D , with a 1,4-reducing agent to produce the compound of formula (Z8), in which R 8  is —CH 2 CH 2 —COOR C  or —CH 2 CH 2 —SO 2 R D , respectively. 
     
     
         132 . The method of any one of  claims 122  to  131 , wherein the producing the compound of formula (Z2) comprises reacting the compound of formula (Z1) with 
       
         
           
           
               
               
           
         
         under Horner-Wadsworth-Emmons reaction conditions. 
       
     
     
         133 . The method of any one of  claims 122  to  132 , wherein step (B) comprises reacting the compound of formula (Z2) with a 1,2-reducing agent to produce a reduction product, and reacting the reduction product with 
       
         
           
           
               
               
           
         
         under Horner-Wadsworth-Emmons reaction conditions. 
       
     
     
         134 . The method of any one of  claims 122  to  133 , wherein step (C) comprises substituting free hydroxyl group in the compound of formula (Z3) with a halogen. 
     
     
         135 . The method of any one of  claims 122  to  134 , wherein step (D) comprises subjecting the compound of formula (Z4) to reductive metal conditions. 
     
     
         136 . A compound of formula (II): 
       
         
           
           
               
               
           
         
         wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         R 1  is —OP 6 , —CH(Y) 2 , or —CH 2 (Y), wherein P 6  is H or a hydroxyl protecting group; 
         R B  is H, optionally substituted alkyl, or optionally substituted aryl; and 
         Y is independently —COOR C  or —SO 2 R D ; 
         R C , when present, is optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
         R D , when present, is optionally substituted aryl or optionally substituted non-enolizable alkyl. 
       
     
     
         137 . A compound of formula (VIIAa): 
       
         
           
           
               
               
           
         
         where
 R 7  is —CH 2 OP A , —CHO, or 
 
       
       
         
           
           
               
               
           
         
         
            where each R 7A  is independently an optionally substituted alkyl; 
           R 9  is —CH 2 —OP″, —CHO, or —COOP″; 
           (i) R 10  is a hydroxyl protecting group, R 11  is alkyl ether, and R 12  is H; 
           (ii) R 10  is a hydroxyl protecting group, and R 11  and R 12  combine to form a double bond; 
           or 
           (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
           A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
           or 
           A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
           each P″ is independently H or a hydroxyl protecting group; and 
           each P 9  is independently a hydroxyl protecting group, and X 3  is oxo or X 3 , together with the carbon atom to which it is attached, is —(CH(OP 11 ))—, where P 11  is H or a hydroxyl protecting group; or both P 9  groups and X 3 , together with the atoms to which each is attached, combine to form a ketal. 
         
       
     
     
         138 . A compound of formula (VIAa): 
       
         
           
           
               
               
           
         
         where 
         R 7  is —CHO or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; 
         R 10A  is —CH 2 —CH═CH 2 , —(CH 2 ) 2 —CH═CH 2 , or —(CH 2 ) 3 —OP 10 ; 
         each of R 10  and P 10  is independently a hydroxyl protecting group; 
         A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
         or 
         A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
         and 
         each P 9  is independently a hydroxyl protecting group, and X 3  is oxo or X 3 , together with the carbon atom to which it is attached, is —(CH(OP 11 ))—, wherein P 1  is H or a hydroxyl protecting group; or both P 9  groups and X 3 , together with the atoms to which each is attached, combine to form ketal. 
       
     
     
         139 . A compound of formula (IID) or (IIF): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         X 1  is —CH 2 — or —O—; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; and 
         R E  is —CHO or —CH (1+m) (OR F ) (2−m) , wherein
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0, and 
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene. 
 
       
     
     
         140 . A compound of formula (IIE) or (IIG): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         X 1  is —CH 2 — or —O—; and 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group. 
       
     
     
         141 . A compound of formula (IIH): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         each R C  is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
         X 1  is —CH 2 — or —O—; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; and 
         R E  is —CHO or —CH (1+m) (OR F ) (2−m) , wherein
 m is 1, and R F  is a hydroxyl protecting group, 
 or 
 m is 0, and 
 (i) each R F  is independently an alkyl or hydroxyl protecting group, or 
 (ii) both R F  combine to form an alkylene. 
 
       
     
     
         142 . A compound of formula (IIi): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         each R C  is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
         X 1  is —CH 2 — or —O—. 
       
     
     
         143 . A compound of formula (VIIID): 
       
         
           
           
               
               
           
         
         wherein
 each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
         
         E is H, optionally substituted alkyl, or optionally substituted alkoxy;
 G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
 each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
 n, when present, is 0, 1, or 2; 
 k is 0 or 1; 
 
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, wherein each Y is independently —COOR C  or —SO 2 R D ; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, wherein P 12  is H or a hydroxyl protecting group; 
         each P 9  and R 13  is independently a hydroxyl protecting group;
 (i) R 10  is a hydroxyl protecting group, R 1  is alkyl ether, and R 12  is H; 
 (ii) R 10  is a hydroxyl protecting group, and R 4  and R 5  combine to form a double bond; or 
 (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
 
         R M1  is 
       
       
         
           
           
               
               
           
         
         wherein 
         R 5  is optionally substituted acyl; 
         P 13  is H or a hydroxyl protecting group; and 
         R 4C  is 
       
       
         
           
           
               
               
           
         
         wherein R C  is optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and P 7 , when present, is independently H or a hydroxyl protecting group. 
       
     
     
         144 . A compound of formula (IVAb): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, wherein each Y is independently —COOR C  or —SO 2 R D ; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
         each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; 
         each P 9  is independently a hydroxyl protecting group; 
         (a1) R 10  is H or a hydroxyl protecting group, R 1  is alkyl ether, and R 12  is H; 
         (a2) R 10  is H or a hydroxyl protecting group, and R 1  and R 12  combine to form a double bond; 
         or 
         (a3) R 10  and R 11  combine to form a bond, and R 12  is H; 
         (b1) A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
         or 
         (b2) A 1  is H or —OP″, and:
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; and 
 
         (c1) R 16  is H, and P 8  is H or a hydroxyl protecting group; 
         or 
         (c2) R 16  and P 8  combine to form a double bond; 
       
       and 
       each P″, when present, is independently H or a hydroxyl protecting group. 
     
     
         145 . A compound of formula (VAb): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         a designates (R)-stereogenic center, and Z is a sulfonate, chloride, bromide, or iodide; or a designates (S)-stereogenic center, and Z is OR 16 , where R 16  is a hydroxyl protecting group; 
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, where each Y is independently —COOR C  or —SO 2 R D ; 
         each P 9  is independently a hydroxyl protecting group, and X 3  is oxo; or both P 9  groups and X 3 , together with the atoms to which each is attached, combine to form ketal; 
         Y 1  is iodide, bromide, or trifluoromethanesulfonate; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; and 
         each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
         (a1) R 10  is a hydroxyl protecting group, R 11  is alkyl ether, and R 12  is H; 
         (a2) R 10  is a hydroxyl protecting group, and R 11  and R 12  combine to form a double bond; 
         or 
         (a3) R 10  and R 11  combine to form a bond, and R 12  is H; 
         (b1) A 1  and R 14  combine to form oxo, R 13  is a hydroxyl protecting group, and R 15  is H; 
         or 
         (b2) A 1  is H or —OP″, and:
 (i) R 13  is a hydroxyl protecting group, and R 14  and R 15  combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; 
 
         and 
         each P″ is independently a hydroxyl protecting group. 
       
     
     
         146 . A compound of formula (IXD): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
           each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl; 
           n, when present, is 0, 1, or 2; 
           k is 0 or 1; 
         
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, each Y is independently —COOR C  or —SO 2 R D ; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
         each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; 
         R 7  is —CHO, —CH 2 OP A  or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; 
         (i) R 10  is a hydroxyl protecting group, R 11  is alkyl ether, and R 12  is H; 
         (ii) R 10  is a hydroxyl protecting group, and R 11  and R 12  combine to form a double bond; or 
         (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
         A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
         or 
         A 1  is H or —OP″, and
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15 , together with the atoms to which each is attached, combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; each P 9  is independently H or a hydroxyl protecting group, 
 
         each P 9  is independently a hydroxyl protecting group, and X 3  is oxo, or X 3 , together with the atom to which it is attached, combines to form —(CH(OP 11 ))—, where P 11  is H or a hydroxyl protecting group; or both P 9  and X 3 , together with the atoms to which each is attached, combine to form a ketal; and 
         R 19A  is H, —OP″, or Y, and R 19B  is H; or R 19A  and R 19B , together with the atoms to which each is attached, combine to form a double bond. 
       
     
     
         147 . A compound of formula (IXF): 
       
         
           
           
               
               
           
         
         wherein 
         each of D and D′ is independently H, optionally substituted alkyl, or OP 1 , provided that only one of D and D′ is OP 1 , wherein P 1  is H, alkyl, a hydroxyl protecting group, and A is a C 1-6  saturated or C 2-6  unsaturated hydrocarbon skeleton, the skeleton being unsubstituted or having from 1 to 10 substituents independently selected from the group consisting of cyano, halo, azido, oxo, and Q 1 , or A is a group of formula (1): 
       
       
         
           
           
               
               
           
         
         wherein
 L is —(CH(OP 2 ))—, —(C(OH)(OP 2 ))—, or —C(O)—; 
 R 2  is H and P 1  is absent, H, alkyl, or a hydroxyl protecting group, or R 2  and P 1  combine to form a bond;
 (i) R 3  is H, and P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group; 
 (ii) R 3  is —(CH 2 ) n NP 3 P 4 , wherein P 3  is H or an N-protecting group, and (a) P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 4  is H or an N-protecting group, (b) P 2  and P 4  combine to form an alkylidene, or (c) each of P 2  and P 4  is H; 
 (iii) R 3  is —(CH 2 ) n OP 5 , wherein P 2  is absent, H, optionally substituted alkyl, or a hydroxyl protecting group, and P 5  is H, optionally substituted alkyl, or a hydroxyl protecting group; or P 2  and P 5 , together with the atoms to which each is attached, combine to form a ketal, a cyclic carbonate, a dicarbonyl-dioxo, or silylene-dioxo; or 
 (iv) R 3  and P 2  combine to form an optionally substituted ethylene or a structure selected from the group consisting of: 
 
 
       
       
         
           
           
               
               
           
         
         
           
              wherein each P′ is independently H or a hydroxyl protecting group; 
           
           E is H, optionally substituted alkyl, or optionally substituted alkoxy; 
           G is O, S, CH 2 , or NR N , wherein R N  is H, an N-protecting group, or optionally substituted alkyl; 
         
         each Q 1  is independently OR A , SR A , SO 2 R A , OSO 2 R A , NR B R A , NR B (CO)R A , NR B (CO)(CO)R A , NR B (CO)NR B R A , NR B (CO)OR A , (CO)OR A , O(CO)R A , (CO)NR B R A , or O(CO)NR B R A , wherein each of R A  and R B  is independently H, alkyl, haloalkyl, hydroxyalkyl, aminoalkyl, aryl, haloaryl, hydroxyaryl, alkoxyaryl, arylalkyl, alkylaryl, haloarylalkyl, alkylhaloaryl, (alkoxyaryl)alkyl, heterocyclic radical, or heterocyclic radical-alkyl;
 n, when present, is 0, 1, or 2; 
 k is 0 or 1; 
 
         X 1  is —CH 2 —, —CH(Y)—, —C(Y) 2 —, or —O—, wherein each Y is independently —COOR C  or —SO 2 R D ; 
         X 4  is oxo, or X 4 , together with the atom to which it is attached, is —(CH(OP 12 ))—, where P 12  is H or a hydroxyl protecting group; 
         each R C , when present, is independently optionally substituted alkyl, optionally substituted aryl, or optionally substituted arylalkyl; 
         each R D , when present, is independently optionally substituted aryl or optionally substituted non-enolizable alkyl; 
         R O  is —CHO, —CH 2 OP″, —CH═CH 2 , —CH(OP″)CH 2 OP″, —C(O)—CH 2 P(O)(OR C ) 2 , or halogen; 
         (i) R 10  is a hydroxyl protecting group, R 11  is alkyl ether, and R 12  is H; 
         (ii) R 10  is a hydroxyl protecting group, and R 11  and R 12  combine to form a double bond; or 
         (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
         A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
         or 
         A 1  is H or —OP″, and
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15 , together with the atoms to which each is attached, combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; each P 9  is independently H or a hydroxyl protecting group; 
 
         and 
         each of P″, P 9 , and P 13  is independently H or a hydroxyl protecting group. 
       
     
     
         148 . A compound of formula (IXG): 
       
         
           
           
               
               
           
         
         wherein 
         R 7  is —CHO, —CH 2 OP A , or 
       
       
         
           
           
               
               
           
         
          wherein each R 7A  is independently an optionally substituted alkyl; 
         (i) R 10  is a hydroxyl protecting group, R 11  is alkyl ether, and R 12  is H; 
         (ii) R 10  is a hydroxyl protecting group, and R 1  and R 12  combine to form a double bond; or 
         (iii) R 10  and R 11  combine to form a bond, and R 12  is H; 
         A 1  and R 14  combine to form oxo, R 13  is H or a hydroxyl protecting group, and R 15  is H; 
         or 
         A 1  is H or —OP″, and
 (i) R 13  is H or a hydroxyl protecting group, and R 14  and R 15 , together with the atoms to which each is attached, combine to form a double bond; 
 or 
 (ii) R 13  and R 14  combine to form a bond, and R 15  is H or —OP″; each P 9  is independently H or a hydroxyl protecting group, 
 
         each P 9  is independently a hydroxyl protecting group, and X 3  is oxo, or X 3 , together with the atom to which it is attached, combines to form —(CH(OP 11 ))—, where P 1  is H or a hydroxyl protecting group; or both P 9  and X 3 , together with the atoms to which each is attached, combine to form a ketal; and 
         R 19A  is H, —OP″, or Y, and R 19B  is H; or R 19A  and R 19B , together with the atoms to which each is attached, combine to form a double bond. 
       
     
     
         149 . A compound of formula (Z), (Z1), (Z2), (Z3), (Z4), (Z5), (Z5A), (Z5B), or (Z6).

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