Markov Property and Scale-free Organization of Gene Expression

Evolutional gene expression organization has recently been studied by measuring the mRNA abundance (gene expression) for tens of thousands of genes in parallel (GeneChips arrays) [3]. These experiments on mRNA abundance have revealed that gene expression exhibits a scale-free organization, which is highly conserved in all the major five kingdoms of life, from Bacteria to Human [3]. Therefore, the gene expression distribution p(k) (probability that a gene has an amount of expression k) decays as a power-law k−γ [1]. In order to uncover the origin of this scale-free organization, we consider a stochastic process with Markov property (i.e., the future is governed by the present and does not depend on the past). This assumption is very natural for biology since all biological systems obey the physical laws, which also manifest this property. Surprisingly, scale-free organization spontaneously emerges from Markov property in the following construction (Fig. 1). (See [2] for more details.)