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. 2010 Jan;38(2):e10.
doi: 10.1093/nar/gkp906. Epub 2009 Nov 4.

Optimizing nucleotide sequence ensembles for combinatorial protein libraries using a genetic algorithm

Roger A Craig  1 , Jin Lu, Jinquan Luo, Lei Shi, Li Liao
Affiliations

Optimizing nucleotide sequence ensembles for combinatorial protein libraries using a genetic algorithm

Roger A Craig et al. Nucleic Acids Res. 2010 Jan.

Abstract

Protein libraries are essential to the field of protein engineering. Increasingly, probabilistic protein design is being used to synthesize combinatorial protein libraries, which allow the protein engineer to explore a vast space of amino acid sequences, while at the same time placing restrictions on the amino acid distributions. To this end, if site-specific amino acid probabilities are input as the target, then the codon nucleotide distributions that match this target distribution can be used to generate a partially randomized gene library. However, it turns out to be a highly nontrivial computational task to find the codon nucleotide distributions that exactly matches a given target distribution of amino acids. We first showed that for any given target distribution an exact solution may not exist at all. Formulated as a constrained optimization problem, we then developed a genetic algorithm-based approach to find codon nucleotide distributions that match as closely as possible to the target amino acid distribution. As compared with the previous gradient descent method on various objective functions, the new method consistently gave more optimized distributions as measured by the relative entropy between the calculated and the target distributions. To simulate the actual lab solutions, new objective functions were designed to allow for two separate sets of codons in seeking a better match to the target amino acid distribution.

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Figures

Figure 1.
Figure 1.
Schematic illustration of point mutation and cross-over for generating new distributions. The top panel shows a point mutation from ‘0’ to ‘1’ at the third position of the string ‘0101 1011 0011 0001’, which encodes the amounts of nucleotides (A = 5, C = 11, G = 3 and T = 1), translating to a distribution (A = 25%, C = 55%, G = 15% and T = 5%) after normalization. A cross-over is shown for the bottom two strings in the left column, with a pivot point at the middle of each string, leading to two new strings in the right column, each is composed of two substrings, respectively, from the two original strings splitting at the pivot point, as indicated by their corresponding colors.
Figure 2.
Figure 2.
R-values for calculated distributions achieved by various objective functions with one, two test tube and the method of Wang and Saven (5).
Figure 3.
Figure 3.
Site 28 of SH3 domain with one and two codon distributions using the RE + LS objective function.
Figure 4.
Figure 4.
Single codon nucleotide probability distribution for site 28 of SH3 domain using the RE + LS objective function.
Figure 5.
Figure 5.
Nucleotide probability distributions for two weighted codons for site 28 of SH3 domain generated using the RE + LS objective function. The first and second codon nucleotide distributions are weighted 0.29 and 0.71, respectively.
Figure 6.
Figure 6.
Site 54 of SH3 domain with one and two codon distributions using the RE + LS objective function.
Figure 7.
Figure 7.
Single codon nucleotide probability distribution for site 54 of SH3 domain using the RE + LS objective function.
Figure 8.
Figure 8.
Nucleotide probability distributions for two weighted codons for site 54 of SH3 domain generated using the RE + LS objective function. The first and second codon nucleotide distributions are weighted 0.25 and 0.75, respectively.
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