The phenome analysis for the leaf morphogenesis shows greater advances than that for other species. Although the phenome analysis is useful for an elucidation of relationship between genotype and phenotype, it is difficult to identify a complicated biochemical reaction system between genotype and phenotype. In this study, we proposed a novel mathematical model for the time-variant morphogenesis of leaf primordiums to infer the complicated system, and discussed an availability of the proposed model on the elucidation of the morphogenesis. The mathematical model was designed by integrating a reaction-diffusion equation with a cellular automaton theory. The proposed model could realize several well-known complicated pattern formations involving reconnection phenomena of the leaf venation such as Arabidopsis thaliana's and gingko's leaf. Thus, the proposed model is available for the elucidation of the leaf morphogenesis.

MOTIVATION: Classifying genes into clusters depending on their expression profiles is one of the most important analysis techniques for microarray data. Because temporal gene expression profiles are indicative of the dynamic functional properties of genes, the application of clustering analysis to time-course data allows the more precise division of genes into functional classes. Conventional clustering methods treat the sampling data at each time point as data obtained under different experimental conditions without considering the continuity of time-course data between time periods t and t+1. Here, we propose a method designated mathematical model-based clustering (MMBC). RESULTS: The proposed method, designated MMBC, was applied to artificial data and time-course data obtained using Saccharomyces cerevisiae. Our method is able to divide data into clusters more accurately and coherently than conventional clustering methods. Furthermore, MMBC is more tolerant to noise than conventional clustering methods. AVAILABILITY: Software is available upon request. CONTACT: [email protected].

We improve network-structure-search evolutionary algorithm (NSS-EA) that is a search method for inference of genetic networks by S-system. Search methods for inference of genetic networks by S-system should meet the following requirements: 1) efficient search of a set of satisfactory structures; 2) search of structures satisfying biological knowledge; and 3) search of the true structure, NSS-EA is an excellent method from the viewpoints of Requirement 1 and 2. However, it has a problem from the viewpoint of Requirement 3. In order to solve this problem, first, we improve the parameter search process by using the time course data of disrupted strains as well as that of a wild type when evaluating genetic networks. Second, we propose four new structure-search operators taking account of mutual interactions among substances. We show the effectiveness of the proposed improvements for NSS-EA from the viewpoint of Requirement 3 by comparing the performance of the original NSS-EA and the improved NSS-EA on a five-substance benchmark problem.

In this paper, we propose a framework for enabling for researchers of genetic algorithms (GAs) to easily develop GAs running on the grid, named "grid-oriented genetic algorithms (GOGAs)", and actually "gridify" a GA for estimating genetic networks, which is being developed by our group, in order to examine usability of the proposed GOGA framework. We also evaluate the scalability of the "gridified" GA by applying it to a five-gene genetic network estimation problem on a grid testbed constructed in our laboratory.

This paper presents the network-structure search evolutionary algorithm (NSS-EA) for inference of genetic networks by S-systems. NSS-EA efficiently finds multiple different network structures which explain gene-expression time-course data observed in biological experiments. In inference of genetic networks by S-system, we are required to find as many network structures that explain experimentally-observed data as possible. This is because, in general, it is difficult to obtain sufficient time-course data by which we can determine a network structure uniquely. A network structure is determined by whether each system parameter of its S-system is positive, negative or zero. Tominaga et al. and Ueda et al. have proposed methods that repeatedly run real-coded genetic algorithms (GAs) for searching the system parameters of S-system with different random number series in each GA run to obtain multiple different network structures. These methods have two serious problems that the same network structures can be repeatedly found in multiple GA runs and that a biological knowledge that the number of substances interacting with one substance is relatively small is not taken into account. This is because how many and what kind of structures are found by real-coded GAs depend on the random number series used by the Gas. In this paper, we try to solve the above problems by explicitly separating the process of searching network structure, i.e. searching the signs of system parameters of S-system, and that of searching the values of the system parameters. Through some numerical experiments, we show that the proposed method, NSS-EA, can efficiently find more different kinds of network structures than the conventional methods.