Scaling-Law and Fluctuation in Gene Expression

In our post-genomic era, by using DNA microarrays and GeneChips technologies, the amount of mRNA contained in cells from different tissues and organisms can be collected at different time points. Moreover, the abundance of mRNA of a gene (i.e., gene expression) fluctuates in time, and it reveals correlations among many genes. Although there are currently many efforts to understand the gene regulation and transcriptional control, we have only a limited knowledge of these processes due to the huge quantity of genes involved and their intrinsic complexity. In order to obtain a better description on the collective behaviour of thousands of genes, we search for dynamical organizing principles in gene expression fluctuations, which are common for all living organisms. In this work, the dynamics of fluctuations in gene expression time series is investigated. By using collected data of gene expression from yeast and human organisms, we found that the fluctuations of gene expression level and the average value of gene expression over time are strongly correlated and obey a scaling law with exponent one. As this feature is found in yeast and human organisms, it suggests that probably this coupling is a common dynamical organizing property of all living systems. To understand these observations, we propose a stochastic model which can explain these collective fluctuations, and predict the scaling exponent. Intriguingly, the same scaling-law was found in [3] for natural and transport systems as rivers, WWW and highways. In contrast, more technological systems as Internet routers and Microchips, revealed a scaling law with exponent 1/2. A complete version of our work can be found in [4].