T. Ochiai

A Constructive Approach to Gene Expression Dynamics

Recently, experiments on mRNA abundance (gene expression) have revealed that gene expression shows a stationary organization described by a scale-free distribution. Here we propose a constructive approach to gene expression dynamics which restores the scale-free exponent and describes the intermediate state dynamics. This approach requires only one assumption: Markov property.

A mathematical model for generating bipartite graphs and its application to protein networks

Complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology. Most of these systems can be organized into networks composed of nodes and interacting edges. Here, we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes. We then use this model to investigate protein-domain networks. A protein can be composed of up to hundreds of domains. Each domain represents a conserved sequence segment with specific functional tasks. We analyze the distribution of domains in Homo sapiens and Arabidopsis thaliana organisms and the statistical analysis shows that while (a) the number of domain types shared by k proteins exhibits a power-law distribution, (b) the number of proteins composed of k types of domains decays as an exponential distribution. The proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of (a) power-law and (b) exponential distributions. Our theoretical and computational results show that this model requires (1) growth process and (2) copy mechanism.

A stochastic approach to multi-gene expression dynamics

Abstract In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of the cell functions. In this process, the correlation among genes is crucial to determine the specific functions of genes. Here, we propose a novel multi-dimensional stochastic approach to deal with the gene correlation phenomena. Interestingly, our stochastic framework suggests that the study of the gene correlation requires only one theoretical assumption— Markov property —and the experimental transition probability, which characterizes the gene correlation system. Finally, a gene expression experiment is proposed for future applications of the model.

Transcription and noise in negative feedback loops

Recently, several studies have investigated the transcription process associated to specific genetic regulatory networks. In this work, we present a stochastic approach for analyzing the dynamics and effect of negative feedback loops (FBL) on the transcriptional noise. First, our analysis allows us to identify a bimodal activity depending on the strength of self-repression coupling D. In the strong coupling region D>>1, our findings indicate that the variance of the transcriptional noise is reduced 28% more than described earlier. Secondly, the contribution of the noise effect to the abundance of regulating protein becomes manifest when the coefficient of variation is computed. In the strong coupling region, this coefficient was found to be independent of all parameters and in fair agreement with the experimentally observed values. Finally, our analysis reveals that the regulating protein is significantly induced by the intrinsic and external noise in the strong coupling region. In short, it indicates that the existence of inherent noise in FBL makes it possible to produce a basal amount of proteins even though the repression level D is very strong.