The Effects of Spatial Heterogeneity and in vivo Crowding on the Lac Genetic Circuit

Abstract

Standard deterministic and stochastic models used to explore the dynamics of cellular biochemical networks typically ignore spatial degrees of freedom (by assuming the cell is well-stirred). Spatial heterogeneity has been neglected due to the lack of both data regarding cellular localization and computational methodologies to simulate such models. Advances in in vivo imaging techniques, including cryo-electron tomography and single-molecule fluorescence microscopy, have begun to reveal the organization and dynamics of biomolecules inside the cell. Likewise, graphics processing units (GPUs) now provide the computational power to perform three-dimensional simulations of cell-scale models.Here, the effects of incorporating spatial information and molecular crowding into a stochastic model of the lactose utilization genetic circuit are reported. We use our recently developed lattice-based Monte Carlo simulation technique [1] to sample the reaction-diffusion master equation describing the lac circuit in an Escherichia coli cell. Parameters are obtained from published in vivo single molecule studies. By comparing to the well-stirred model, it is shown that spatial degrees of freedom introduce a source of noise into the circuit. Such spatial noise is a component of the extrinsic noise of a genetic system and we put bounds on its contribution. In certain fluctuating environments, spatial noise is found to influence the switching properties of the circuit leading to population distributions that cannot be predicted using well-stirred models. Finally, the model suggests new single molecule experiments to probe the lac circuit and provides estimates of the spatial and temporal resolution required. The integration of lattice microbe models with systems biology descriptions of cellular networks is also discussed.[1] Roberts, Stone, Sepulveda, Hwu, and Luthey-Schulten, “Long time-scale simulations of in vivo diffusion using GPU hardware”, In The Eighth IEEE International Workshop on High-Performance Computational Biology (2009).