The goal of this research is to develop and implement a methodology for the design of peptides with predefined structure. This thesis research established an evolutionary de novo peptide design system based on the genetic algorithms (GAs) and chemical synthesis method, and furthermore, investigated the impact of GAs on the design of peptide with predefined structure. While the irrational design provides a flexible formulation for the design of peptides with predefined structure, the GAs implement the optimization search of the combinatorial space thereof. However, the design of peptide with predefined structure is a challenging problem to the GA-based method. How to effectively convert the design goal into GA representation is the first question. How to efficiently obtain the target peptides is the second. In order to solve these problems, an experimental system was established on helical conformations due to their simple structure, diverse oligomers, and easy determination and interpretation using circular dichroism (CD) spectrum.

In Chapter 1, the motivation, goal, and significance of this research was proposed. They are to develop and implement a methodology for the design of peptides with predefined structure. This thesis research thus investigated the impact of GAs on the design of peptide with predefined structure, and established an evolutionary de novo peptide design system based on the GAs and chemical synthesis method.

The most important and basic concepts related to protein folding and design, the evolutionary algorithms, especially the GAs, and , furthermore, evolutionary design were then introduced. After brief review of work done by previous researchers, the irrational design problem was formalized as a combination of the evolutionary algorithm with experimental measurement, in addition to discussing the evaluation of protein properties and basic operations of the GAs for irrational protein design. In this thesis research, the challenging problems were how to effectively convert the design goal into GA representation and how to efficiently obtain the target peptides.

An experimental system based on helical model structure was created to solve these problems because the helical conformations possess the characteristics, such as, simple structure, diverse oligomers, easy determination and interpretation using CD spectrum, etc. The solutions to the challenging problems were thus induced on the helical peptide design system: conversion of the design goal into a feasible sequence space for GA search; establishment of a new GA enabling to efficiently search the sequence space; construction of a more efficient and robust peptide design system comprising the above two constituents. Following that, it provided a discussion of the objective, scope, and contributions for this research effort. This chapter ended by outlining the contents of the remaining chapters.

In Chapter 2, a method converting irrational design problem satisfying design goal into GA representation was proposed. Different from all other GA applications, the objective in this research was a structure, not a parameter. Some description of the structure has to be used as the fitness function, but none can tell one structure from all other structures. It means that using a description of peptides GAs can evolve the fitness evaluation of the peptides in full search space, but cannot identify the detailed structures of the peptides in the search process. Pre-selection of the areas in the full search space provides a way to solve this problem. The search space was first divided into feasible areas, where the structures of peptides satisfy the design goal, and infeasible areas, where the structures of the peptides possibly violate the design goal. The peptides with predefined structure can thus be searched by GA in the constrained sequence space or the feasible areas in full sequence space. A method based on model structure of peptides was proposed to create constrained sequence space satisfying both the design goal and GA requirements.

The monomeric helix was selected as the model structure of the design problem. After a literature review of de novo design of monomeric helical peptides, a corresponding search space comprising only three amino acids Glu, Lys, and Ala was established by the developed method. The helicity determined by CD spectrum was used as the fitness evaluation of peptides. Furthermore, a simple GA was selected to the evolutionary search of the helix. Consequently, a practical peptide design system was established by combining the GA representation of monomeric helical peptides with a simple GA search method.

Sixteen helical peptides with the helicity better than the model peptide were obtained through a four-generation evolution with this system. This method was successfully evaluated by the attempt to the monomeric helical peptide design using the simple GA. The results indicated that the GA showed its efficacy and efficiency in searching for the target peptides, and furthermore, that the helicity combining with the feasible sequence space for monomeric helix provided an effective evaluation of the status of peptide pools in the search process. The statistical analysis revealed that the primary determinants of the monomeric helix were the electrostatic attractions between the oppositely charged residues Glu and Lys spaced three or four residues. Although this monomeric helical peptide design was used as a case study, the design principles might be applied to other kinds of problems as well. Indeed, the chapter could be seen as a guide for GA usage in peptide design.

In Chapter 3, a method of improving the efficiency of peptide design was proposed. The major limitation of the evolutionary method developed in this thesis research was the experimental effort required to the determination of the structure of the peptides. Whereas an ill setting often results in either a low efficiency in design or poor quality solutions at the end of the GA run, the GAs set at suitable parameter setting can fulfill their work with less number of generations and smaller size of populations. Thus, the minimization of the experimental effort in peptide design could be reached by exploring for a specific GA for the peptide design.

A numerical structure characterization based on physico-chemical properties of amino acids was established to evaluate the structure of de novo sequences. The performance of GAs could thus be evaluated by measuring their evolutionary speed in the numerical fitness landscape of this peptide design problem. With this benchmark, the task of setting GA parameters, such as, crossover rates, mutation rates, step numbers of multi-step variation, and population sizes, could be handled by the simulations. New operations: multi-step crossover-mutation or multi-step variation (msv) and elitist strategy called SeedLibrary, were created by modifying the genetic operations in simple GA to perform a more efficient and more robust exploration of target peptides than that of simple GA, even with a small population size. The GAs containing these new operations was called msvGAs in this research.

As results of simulations, a suitable multi-step variation operation and corresponding parameter setting were identified. Closer inspection of the developed algorithms and their performance revealed that more robust and more powerful search was realized with the proposed msvGA and the suitable parameter setting. Therefore, an improved GA, the msvGA set at the identified configuration and parameter setting, was achieved. This GA characterized less sensitive to parameter setting and more efficient in the search of target peptides than the simple GA, thus providing a way to search the sequence space with both the minimized size of population and minimized number of generations. In addition, different from almost all previous studies, where GAs were set by the simulations on function optimization, here, the msvGAs was evaluated by the simulations on the virtual protein design problem. The suitable parameter setting identified in this study provided a suitable parameter setting to an analogous protein design problem, the real peptide design system, according to the principle of "parameter setting by analogy".

In Chapter 4, the observation of the feasible sequence space in monomeric helical peptide design in Chapter 2 and the examination of the improved GA designed by an analogy problem in Chapter 3 were further extended to the experiment of parallel homodimeric coiled-coil peptide design. This extension allows simultaneous evolution of complexity structures of peptides even with a small population size.

The feasible sequence space for this design was established by using the general information about the structure, which had been studied by previous researchers. As the results of synthesis experiment, twenty homodimeric coiled-coil peptides having the helicity more than that of the referent peptide GCN4p, the model structure of this study, were obtained through a five-generation evolution. Therefore, these results verified the effect of the improved GA in this real design of peptides with parallel homodimeric helical topology. Results also indicated that the improved GA did indeed make the design system more efficient and robust than that using a simple GA, and demonstrated that the target peptides were efficiently achieved even with only a half of the population size used by a simple GA in the monomeric helical peptide design.

The size-exclusion chromatography HPLC experimental results furthermore showed that the established homodimeric helical peptide search space effectively excluded the infeasible sequences, which could not be determined by only a description of helix, the CD signal. Thus, a combination of the fitness evaluation of peptide structure, which was used in GA evolution, with the constrained search space, which provides the search range for the GA, can perform an effective evaluation of peptide structure for the GA.

Furthermore, with the statistical analysis of the sequence patterns in the evolutionary process the dynamics of the GAs were explained. The GAs converge the determinants of structure at very different speeds; thus, the significant determents are converged in a few generations and the target peptides could be obtained in these generations. These statistics of the homodimeric helical peptides showed that the important intra-helical and inter-helical interactions were converged in only five generations. Among them, the most important interactions were those between the oppositely charged amino acids Glu or Gln and Lys or Arg. The statistical results furthermore emphasized the importance of the orientation of the interactions and spacing between the interacting residues.

In Chapter 5, the thesis was concluded with the summary of the research effort, including a discussion of the benefits provided by the proposed methods. The effort converting design goal into constrained sequence space overcome the potential infeasibility of the sequences in full combinatorial sequence space, thus providing a platform for structure design using GAs. Furthermore, the efficiency of the peptide design was improved by a GA containing multi-step crossover-mutation operation, new elitist strategy, and suitable parameter setting. The evolutionary de novo design system comprising these identified constituents could be used to design the peptide having specific structure more effectively and more efficiently. The chapter finally listed the suggestions for future work in the same direction.

本論文は、ペプチドの構造に関する分子進化をコンピュータにより効率よくかつ加速的に行わせるためのアルゴリズムとその実証に関するものであり、5章より構成されている。

第1章は緒論であり、本研究の行われた背景について述べ、本研究の目的と意義を明らかにしている。

第2章では、遺伝的アルゴリズムによりペプチドが一量体のα-ヘリックス構造をとるように進化させることを試みている。遺伝的アルゴリズムとは選択、交叉、変異といった進化の主要な特徴を模倣したアルゴリズムで、主に数値計算や画像処理などの分野に応用されているが、これを生体分子の人工進化に利用することで、限られた時間内で良好な解、すなわち目的の構造を持ったペプチドを得ることが可能になると述べている。特に本研究では、ペプチドの全配列空間を探索するのではなく、より目的の配列が存在する可能性の高い空間を選択的に探索することによって、従来の遺伝的アルゴリズムをより向上させることを試みている。遺伝的アルゴリズムによって得られた各ペプチドのα-ヘリックス含量の評価は円偏光二色性(CD)スペクトルによって行っている。本研究ではまず一世代内のすべてのペプチドについて222 nmにおける分子楕円率を測定してそれらの値を適応度とし、最初に生成した集団からより高い分子楕円率を備えたペプチドを選択・保存している。次にこれらのペプチド間またはペプチド内で交叉および変異をコンピュータに演算させることにより、次世代集団のペプチド配列を決定している。そしてこの世代の各ペプチドを実際に合成しCDスペクトルを測定している。これらの操作を繰り返すことによって、より高いα-ヘリックス含量を持つペプチドの探索を行っている。設計したペプチドの長さは16残基で、電荷を持つリシンとグルタミン酸、そして無極性のアラニンの3種類のアミノ酸で構成されている。ペプチド集団は一世代あたり32とし、交叉確率は1.0、変異確率は0.09に設定している。この結果、分子楕円率の最大値と平均値はともに進化の世代を経るにつれて上昇したことを明らかにしている。

第3章では、遺伝的アルゴリズムでより効率的にペプチドを進化させるアルゴリズムを検討している。まず交叉方法については、任意に選んだ2ペプチド間で3点交叉させる手法を選択している。また、この3点交叉と変異の操作を8回繰り返すことによって、より広い配列空間を探索できるようにしている。さらに、ある程度機能が認められたペプチドが次の進化のプロセスで全く失われることがないように、前の世代で機能が上位にランクされたペプチドをシードライブラリーとして保存し、次世代の創製に活用できるようなプログラムを構築している。ペプチドの構成ブロックは20または8種類のアミノ酸とし、ペプチドの長さが5,10または20残基の配列空間を用いている。このようにして設計した遺伝的アルゴリズムを利用して、ペプチドを進化させるシミュレーションを行っている。その結果,一世代あたりのペプチド数が少なくても従来の遺伝的アルゴリズムに比べてより高い効率で進化させることができたと述べている。また、設定する交叉確率や変異確率は探索すべき配列空間の大きさと密接な関係があることを明らかにしている。さらにその中から最適な交叉確率や変異確率、一世代あたりの最適ペプチド数を決定している。

第4章では、第3章で示された改良型遺伝的アルゴリズムを用いて、二量化したα-ヘリックスペプチドの進化を試みている。1残基目のバリンまたはアスパラギン、および4残基目のロイシンを保存し、それ以外の5つの位置に8種類の親水性アミノ酸が選ばれるよう設計している。改良されたアルゴリズムでは、ペプチド集団は一世代あたり16と設定し、交叉確率を0.9、変異確率を0.05に設定している。これらのペプチドのα-ヘリックス含量をCDスペクトルにより評価し、さらに222 nmにおける分子楕円率を測定している。この結果、得られたペプチドは従来知られているペプチドよりもはるかに高いα-ヘリックス含量を有していることを明らかにしている。また各世代の分子楕円率の最大値と平均値の解析から、本改良型遺伝的アルゴリズムは一量体α-ヘリックスペプチドの設計で使われた遺伝的アルゴリズムより速くペプチドを進化させることができると述べている。さらに、これにより得られた、高いα-ヘリックス含量を示すペプチドはすべて二量体であることをサイズ排除クロマトグラフィーにより確認している。

第5章は結論であり、本研究を要約して得られた研究成果をまとめている。

以上のように、本論文は、遺伝的アルゴリズムをペプチドの進化に応用するため、目的の配列が存在する可能性の高い空間を選択的に探索することによって、効率よくペプチド構造を進化させることに成功している。また、より効率を向上させるために、コンピュータ上での進化をシミュレーションし、より普遍性の高い進化のためのパラメータを決定している。さらにこのパラメータを実際のペプチドの進化に応用することによって、従来知られているペプチドよりもさらに目的の構造を有するペプチドを多く獲得することに成功している。

よって本論文は博士(工学)の学位請求論文として合格と認められる。