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To analyze the evolutionary dynamics of a mutant population in an evolutionary experiment, it is necessary to sequence a vast number of mutants by high-throughput (next-generation) sequencing technologies, which enable rapid and parallel analysis of multikilobase sequences. However, the observed sequences include many errors of base call. Therefore, if next-generation sequencing is applied to analysis of a heterogeneous population of various mutant sequences, it is necessary to discriminate between true bases as point mutations and errors of base call in the observed sequences, and to subject the sequences to error-correction processes. To address this issue, we have developed a novel method of error correction based on the Potts model and a maximum a posteriori probability (MAP) estimate of its parameters corresponding to the "true sequences". Our method of error correction utilizes (1) the "quality scores" which are assigned to individual bases in the observed sequences and (2) the neighborhood relationship among the observed sequences mapped in sequence space. The computer experiments of error correction of artificially generated sequences supported the effectiveness of our method, showing that 50-90% of errors were removed. Interestingly, this method is analogous to a probabilistic model based method of image restoration developed in the field of information engineering., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

In this paper, we consider two complementary cost functions for the landscape exploring processes to obtain the global optimum sequence through in vitro evolution protocol: one is the entropic cost C(etp), which is based on the deviation from the uniformity of a mutant distribution in sequence space, and the other is the energetic cost C(eng), which is based on the total number of sequences to be generated and evaluated. Based on a prior knowledge about the structure of a given fitness landscapes, the conductor of the experiment can think up the efficient search algorithm (ESA), which requires the minimum number of points (=sequences) to be searched up to the global optimum. For five typical fitness landscapes, we considered their respective (putative) ESA, C(etp)(*) and C(eng)(*) based on the ESA. As a result, we found a trade-off relationship between C(etp)(*) and C(eng)(*) for every case, that is, C(eng)(*)+C(etp)(*) is approximately equal to the logarithm of the volume of the sequence space. C(etp)(*) and C(eng)(*) are interpreted in terms of the information-theoretic concepts., (Copyright 2010 Elsevier Ireland Ltd. All rights reserved.)

In vitro molecular evolution creates a lot of peptide aptamers that bind to each target protein. In many cases, their binding sites on a protein surface are not known. Then, predicting the binding sites through computation within a reasonable time is desirable. With this aim, we have developed a novel system of fast and robust blind docking of a peptide to a fixed protein structure at low computational costs. Our algorithm is based on the following scheme. Representing each of the amino acid residues by a single point corresponding to its side-chain center, the structure of a target protein and that of a ligand peptide are coarse-grained. The peptide, which is described as a flexible bead model, is movable along the grid-points which are set surrounding the protein. An arbitrary state of the protein-peptide complex is subjected to Delaunay tessellation. Then, the fitness of a peptide-coordination to the protein is measured by a four-body statistical pseudo-potential. Through 1000 trials of a simple hill-climbing optimization, the best 15 peptide-coordinations with the 1st-15th highest fitness values are selected as candidates for the putative coordination. Retrieving the available 28 protein-peptide complexes from the Protein Databank, we carried out the blind docking test for each system. The best 15 peptide-coordinations fell into several clusters by the cluster analysis based on their spatial distribution. We found that, in most cases, the largest cluster or second largest cluster correspond to nearly correct binding sites, and that the mean (+/- standard deviation) of GTGD over all the 28 cases is 4.8 A(+/-3.8 A), where GTGD represents the distance from the putative binding site to the correct binding site., (Copyright 2009 Elsevier Ltd. All rights reserved.)

In our previous report [Aita, T., Morinaga, S., Hosimi, Y., 2004. Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor I. Bull. Math. Biol. 66, 1371-1403], an analogy between thermodynamics and adaptive walks on a Mt. Fuji-type fitness landscape in an artificial selection system was presented. Introducing the 'free fitness' as the sum of a fitness term and an entropy term and 'evolutionary force' as the gradient of free fitness on a fitness coordinate, we demonstrated that the adaptive walk (=evolution) is driven by the evolutionary force in the direction in which free fitness increases. In this report, we examine the effect of various modifications of the original model on the properties of the adaptive walk. The modifications were as follows: first, mutation distance d was distributed obeying binomial distribution; second, the selection process obeyed the natural selection protocol; third, ruggedness was introduced to the landscape according to the NK model; fourth, a noise was included in the fitness measurement. The effect of each modification was described in the same theoretical framework as the original model by introducing 'effective' quantities such as the effective mutation distance or the effective screening size.