Appropriate modeling and simulation frameworks for studying extrinsic noise in spatial settings will be increasingly important as cell biologists dissect the relative contributions of intrinsic and extrinsic fluctuations to total stochasticity on ever finer scales. Here we extend the URDME
software framework with a solver that incorporates extrinsic noise into a spatial, mesoscopic setting.
The extrinsic noise acts multiplicatively on the chemical rate parameters. The example we have chosen to demonstrate our method is a model of experimentally observed, spatiotemporally Min protein oscillations in a single E. Coli cell developed by Huang and co-workers. We first work on a parameter analysis of this model to find the parameters which are most sensitive to perturbations. It is shown that even small extrinsic fluctuations in rate constants can lead to a large increase in uncertainty in the spatiotemporally averaged gradient of MinD compared to the case when the source of noise is purely intrinsic.
When extrinsic fluctuations are modelled as a coloured noise process the sensitivity of a system may depend critically on the typical lifetime of the noise. We observe this phenomena in our numerical experiments and use it to illustrate the importance of taking the timescale of interacting processes into account when analyzing a model’s robustness to noise. Further, we use a modified method from perturbation theory to analyze the influence of this additional timescale.