CAN MARKOV CHAIN MODELS MIMIC BIOLOGICAL REGULATION?

Abstract

A fundamental question in biology is whether the network of interactions that regulate gene expression can be modeled by existing mathematical techniques. Studies of the ability to predict a gene's state based on the states of other genes suggest that it may be possible to abstract sufficient information to build models of the system that retain steady-state behavioral characteristics of the real system. This study tests this possibility by: (i) constructing a finite state homogeneous Markov chain model using a small set of interesting genes; (ii) estimating the model parameters based on the observed experimental data; (iii) exploring the dynamics of this small genetic regulatory network by analyzing its steady-state (long-run) behavior and comparing the resulting model behavior to the observed behavior of the original system. The data used in this study are from a survey of melanoma where predictive relationships (coefficient of determination, CoD) between 587 genes from 31 samples were examined. Ten genes with strong interactive connectivity were chosen to formulate a finite state Markov chain on the basis of their role as drivers in the acquisition of an invasive phenotype in melanoma cells. Simulations with different perturbation probabilities and different iteration times were run. Following convergence of the chain to steady-state behavior, millions of samples of the results of further transitions were collected to estimate the steady-state distribution of network. In these samples, only a limited number of states possessed significant probability of occurrence. This behavior is nicely congruent with biological behavior, as cells appear to occupy only a negligible portion of the state space available to them. The model produced both some of the exact state vectors observed in the data, and also a number of state vectors that were near neighbors of the state vectors from the original data. By combining these similar states, a good representation of the observed states in the original data could be achieved. From this study, we find that, in this limited context, Markov chain simulation emulates well the dynamic behavior of a small regulatory network.