Signal detection, modularity and the correlation between extrinsic and intrinsic noise in biochemical networks

Understanding cell function requires an accurate description of how noise is transmitted through biochemical networks. We present an analytical result for the power spectrum of the output signal of a biochemical network that takes into account the correlations between the noise in the input signal (the extrinsic noise) and the noise in the reactions that constitute the network (the intrinsic noise). These correlations arise from the fact that the reactions by which biochemical signals are detected necessarily affect the signaling molecules and the detection components of the network simultaneously. We show that anti-correlation between the extrinsic and intrinsic noise enhances the robustness of zero-order ultrasensitive networks to biochemical noise. We discuss the consequences of the correlation between extrinsic and intrinsic noise for a modular description of noise transmission through large biochemical networks in the context of the mitogen-activated protein kinase cascade.