Systematic model reduction captures the dynamics of extrinsic noise in biochemical subnetworks

Memory effects in biochemical networks as the natural counterpart of extrinsic noise

We show that in the generic situation where a biological network, e.g. a protein interaction network, is in fact a subnetwork embedded in a larger "bulk" network, the presence of the bulk causes not just extrinsic noise but also memory effects. This means that the dynamics of the subnetwork will depend not only on its present state, but also its past. We use projection techniques to get explicit expressions for the memory functions that encode such memory effects, for generic protein interaction networks involving binary and unary reactions such as complex formation and phosphorylation, respec…

一个数学框架用于研究图形表示中生物过程的组织原则

A mathematical framework to study organising principles in graphical representations of biochemical processes

本文提出一种基于范畴论的数学框架，用于研究生物化学过程图形表示中的组织原则，通过结构化余弦理论构建双范畴，实现生物化学反应网络的可组合性和抽象能力。

Michaelis-Menten dynamics in protein subnetworks

To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past, and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe e.g. enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks…

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks…

Colored extrinsic fluctuations and stochastic gene expression

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are 'colored'). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuati…

Moment-based analysis of biochemical networks in a heterogeneous population of communicating cells

Cells can utilize chemical communication to exchange information and coordinate their behavior in the presence of noise. Communication can reduce noise to shape a collective response, or amplify noise to generate distinct phenotypic subpopulations. Here we discuss a moment-based approach to study how cell-cell communication affects noise in biochemical networks that arises from both intrinsic and extrinsic sources. We derive a system of approximate differential equations that captures lower-order moments of a population of cells, which communicate by secreting and sensing a diffusing molecule.…