From topology to dynamics in biochemical networks

摘要: Abstract formulations of the regulation gene expression as random Boolean switching networks have been studied extensively over past three decades. These models developed to make statistical predictions types dynamics observed in biological based on network topology and interaction bias, p. For values mean connectivity chosen correspond real networks, these predict disordered dynamics. However, chaotic seems be absent from functioning a normal cell. While use fixed number inputs for each element network, recent experimental evidence suggests that several distributions connectivity. We therefore study randomly constructed with inputs, K, element. distributions: delta function, Poisson, power law (scale free). analytically show critical value bias parameter, p, above which steady state behavior is observed, independent distribution limit elements N→∞. also numerically. Using different measures (types attractors, fraction are active, length period), we finite, scale-free more ordered than either Poisson or function below point. Thus biochemical characterized by wide per element, may provide source order living cells.