Novel statistical ensemble analysis for simulating extrinsic noise-driven response in NF-{\kappa}B signaling network

TLDR: In this paper, the extrinsic noise is regarded as fluctuations in the values of kinetic parameters and such fluctuations are modeled by randomly sampling the kinetic rate constants from a uniform distribution.

Abstract: Cellular responses in the single cells are known to be highly heterogeneous and individualistic due to the strong influence by extrinsic and intrinsic noise. Here, we are concerned about how to model the extrinsic noise-induced heterogeneous response in the single cells under the constraints of experimentally obtained population-averaged response, but without much detailed kinetic information. We propose a novel statistical ensemble scheme where extrinsic noise is regarded as fluctuations in the values of kinetic parameters and such fluctuations are modeled by randomly sampling the kinetic rate constants from a uniform distribution. We consider a large number of signaling system replicates, each of which has the same network topology, but a uniquely different set of kinetic rate constants. A protein dynamic response from each replicate should represent the dynamics in a single cell and the statistical ensemble average should be regarded as a population-level response averaged over a population of the cells. We devise an optimization algorithm to find the correct uniform distribution of the network parameters, which produces the correct statistical distribution of the response whose ensemble average and distribution agree well with the population-level experimental data and the experimentally observed heterogeneity. We apply this statistical ensemble analysis to a NF-{\kappa}B signaling system and (1) predict the distributions of the heterogeneous NF-{\kappa}B (either oscillatory or non-oscillatory) dynamic patterns and of the dynamic features (e.g., period), (2) predict that both the distribution and the statistical ensemble average of the NF-{\kappa}B dynamic response depends sensitively on the dosage of stimulant, and lastly (3) demonstrate the sigmoidally shaped dose-response from the statistical ensemble average and the individual replicates.