An adaptive extended Kalman filtering approach to nonlinear dynamic gene regulatory networks via short gene expression time series

Abstract

Gene regulation is one of the most amazing processes in which living cells are involved. Different genes may cooperate to produce a particular reaction if more than one genes are suppressed by a gene. The gene triggers a certain genetic disease, for instance, through inactivating the gene that is responsible for cancer, the disease produced by this gene may be controlled. Gene control and interaction might be defined by a gene regulatory network. DNA microarray technology has provided an efficient method for evaluating expression levels of thousands of genes in a single experiment. It enables to trace the levels of the expression of thousands of genes at once. Evaluating gene expression levels may be beneficial for medical diagnosis, treatment and drug design in different circumstances. With an intent to understand the effective biological data and to identify the connections between the individual genes, most of the current research efforts are focused on clustering. Recently, remodelling of the gene regulatory networks over the data on the time series has become an increasing field of interest. As a matter of fact, choosing a good model for the gene regulatory networks is required for a significant data analysis. Several gene expression experiments produce data on short time series only on a few points in time due to the high costs of the evaluation. Time series generally represent the dynamic responses to, some medicines or other treatment methods. As a consequence, modelling the time series of the gene expressions which is needed to pick the functional information over the data on time series has become an increasingly interesting field of study. Since gene regulatory networks form a naturally stochastic structure, the observed data on the time series may be modelled by using non-linear stochastic state space models and the parameters included in the model may be estimated with the Extended Kalman Filter (EKF) method. There have been many studies regarding this topic made in the literature. However, the fact that the model is nonlinear may cause some problems on the estimations of Kalman Filter (KF) method. For this reason, the researches on the adaptive methods in the EKF are going on with the aim of supporting the estimations. In this research, application of the developed model on the gene regulatory networks has been examined. With the aim of corroborating estimation method, it has been decided that the adaptive extended Kalman Filter (AEKF) was proper for being used and malaria gene expression has been applied for the set of data on the time series. A results have been compared with the results of the former research [1], and it has been understood that the estimation results obtained through the developed model were more preferable.