Yeast Network and Report of New Stochastic-Credibility Cell Cycle Models

A cell division cycle is a set of events that take place in a cell, characterized by a period of cell growing and cell duplication, these processes taking place in five phases. Many genes and proteins regulate cell division. There are presented mechanisms that stop and restart cell divisions for budding yeast, by considering stochastic noise (extrinsic noise). Fuzzy phenomenon was introduced by Li and Liu and it is based on credibility measure. A Wiener-Liu process (hybrid process) is a mixture of randomness and fuzziness. We consider the study of a generic cell cycle model for budding yeast, representing a complex network of interactions between genes and proteins. In this sense, the present work has two parts: first we give a short review the state-of-art in yeast gene interaction networks studies, and next we report our own results. We study this model by considering stochastic approach (by writing stochastic system of differential equations), fuzzy approach (the fuzzy system of differential equations associated to the deterministic system) and hybrid system of differential equations, as a combination of randomness and fuzziness.