Space efficient polymer sets

Abstract

The disclosure features a collection that comprises a plurality of polymers, typically nucleic acid molecules in a compact form. The molecules include all possible sequences or at least a certain percentage of all possible sequences, of a particular length.

1 . A collection of nucleic acid polymers, the collection comprising a plurality of polymers in which each polymer has a unique sequence, wherein 
 (i) the polymers of the plurality collectively provide at least 80% of all possible sites of length k, k being greater than 6, the sites being composed of a set comprised of four canonical nucleotides;    (ii) each nucleic acid polymer of the plurality has a length greater than 1.2 k nucleotides, and    (iii) the number of unique polymers in the plurality is less than 0.5 times 80% of the number of all possible sites of length k.    
     
     
         2 . The collection of  claim 1  wherein the polymers of the plurality collectively provide at least 98% of all possible sites of length k, and the number of unique polymers in the plurality is less than 0.5 times 98% of the number of all possible sites of length k.  
     
     
         3 . The collection of  claim 2  wherein the polymers of the plurality collectively provide all possible sites of length k, and the number of unique polymers in the plurality is less than 0.5 times the number of all possible sites of length k.  
     
     
         4 . The collection of  claim 1  wherein k is between 7 and 10.  
     
     
         5 . The collection of  claim 1  wherein each of the represented sites of length k is represented at least twice, each time in a different context.  
     
     
         6 . The collection of  claim 1  wherein each polymer of the plurality is physically associated with a substrate.  
     
     
         7 . The collection of  claim 6  wherein the substrate is a bead, and each polymer is physically associated with a different bead.  
     
     
         8 . The collection of  claim 6  wherein the substrate is a planar array, and each polymer is physically associated with a different address of the same array.  
     
     
         9 . The collection of  claim 1  wherein each polymer of the plurality is in solution.  
     
     
         10 . The collection of  claim 9  wherein the collection is divided into a plurality of pools, each pool comprising a subset of polymers of the plurality.  
     
     
         11 . The collection of  claim 1  wherein each polymer is doublestranded.  
     
     
         12 . The collection of  claim 1  wherein each polymer is DNA.  
     
     
         13 . The collection of  claim 1  wherein the compaction ratio is less than 0.2.  
     
     
         14 . The collection of  claim 1  wherein the set of canonical nucleotides consists of adenine, thymidine, guanine and cytosine.  
     
     
         15 . The collection of  claim 1  wherein the set of canonical nucleotides consists of adenine, uracil, guanine and cytosine.  
     
     
         16 . The collection of  claim 1  wherein at least two of the sites are composed of a set of nucleotides that comprises one non-naturally occurring nucleotide in addition to the four canonical nucleotides.  
     
     
         17 . A nucleic acid array comprising a plurality of addresses, each address of the plurality comprising a nucleic acid molecule wherein 
 (i) the array comprises nucleic acid molecules, the molecules collectively providing at least 80% of all possible sites of length k, k being greater than 6,    (ii) each nucleic acid molecule is associated with an address of the plurality and has a length greater than 1.5 k nucleotides, and    (iii) the array has fewer addresses than 0.5 times 80% the number of all possible sites of length k.    
     
     
         18 . The array of  claim 17  wherein the array comprises a planar substrate.  
     
     
         19 . The array of  claim 17  wherein the nucleic acid molecules are double-stranded DNAs.  
     
     
         20 . A method of evaluating interaction specificity of a test compound, the method comprising: 
 contacting the test compound to a plurality of nucleic acid molecules,    wherein    (i) the polymers of the plurality collectively provide at least 80% of all possible sites of length k, k being greater than 6, the sites being composed of a set of four canonical nucleotides;    (ii) each nucleic acid polymer of the plurality has a length greater than 1.2 k nucleotides, and    (iii) the number of unique polymers in the plurality is less than 0.5 times 80% of the number of all possible sites of length k; and    evaluating interactions between the test compound and one or a subset of nucleic acid molecules of the plurality.    
     
     
         21 . The method of  claim 20  wherein the nucleic acid molecules are in immobilized on an array and the test compound is in solution prior to the contacting, and the step of evaluating comprises detecting the test compound on the array.  
     
     
         22 . The method of  claim 20  wherein the nucleic acid molecules are in immobilized on an array and the test compound is in solution prior to the contacting, and the step of evaluating comprises detecting an alteration in one or more of the nucleic acid molecules on the array.  
     
     
         23 . The method of  claim 22  wherein the test compound comprises a nucleic acid-modifying enzyme.  
     
     
         24 . The method of  claim 20  wherein the nucleic acid molecules are in solution and the test compound is immobilized on a substrate, and the step of evaluating comprises washing the substrate and identifying nucleic acid molecules that are separated by the washing.  
     
     
         25 . The method of  claim 24  further comprising amplifying nucleic acid molecules that are bound to the substrate.  
     
     
         26 . The method of  claim 20  wherein the test compound comprises a protein or nucleic acid.  
     
     
         27 . The method of  claim 20  wherein the test compound has enzymatic activity.  
     
     
         28 . The method of  claim 19  wherein the test compound is a methylase, a nuclease, or a polymerase.  
     
     
         29 . The method of  claim 20  wherein the test compound has a molecular weight less than 2000 Daltons.  
     
     
         30 . The method of  claim 20  further comprising formulating the test compound as a pharmaceutical composition.  
     
     
         31 . The method of  claim 30  further comprising administering the test compound to a subject.  
     
     
         32 . A method of design a collection of nucleic acids, the method comprising: 
 enumerating, in a string, all permutations of four identifiers in words of a preselected length k, wherein each permutation occurs a limited number of times in the string;    segmenting the string into segments of less than length of 100; and    synthesizing oligonucleotides according to the sequence of the identifiers in each of the segments.    
     
     
         33 . The method of  claim 32  wherein the step of enumerating comprises using linear shift register.  
     
     
         34 . The method of  claim 32  wherein each word of the preselected length occurs exactly once in the string.  
     
     
         35 . The method of  claim 32  wherein k is between 6 and 12.  
     
     
         36 . The method of  claim 32  wherein the string is segmented into segments of less than a length of 50.  
     
     
         37 . The method of  claim 32  wherein the segments include overlapping ends.  
     
     
         38 . The method of  claim 32  further comprising disposing each of the oligonucleotides on a planar substrate.