Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · q-bio/0612041

Optimal signal processing in small stochastic biochemical networks

Etay Ziv·Ilya Nemenman·Chris H. Wiggins
View original source ↗Read source document ↗Export metadata ↓

Abstract

We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we may do this without specifying the function performed by the network. Specifically, we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations. We perform this analysis for all biochemical circuits, including various feedback loops, that can be built out of 3 chemical species, each under the control of one regulator. We find that a generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity. These high-information solutions are robust to tenfold changes in most of the networks' biochemical parameters; moreover they are easier to achieve in networks containing cycles with an odd number of negative regulators (overall negative feedback) due to their decreased molecular noise (a result which we derive analytically). Finally, we demonstrate that a single circuit can support multiple high-information solutions. These findings suggest a potential resolution of the "cross-talk" dilemma as well as the previously unexplained observation that transcription factors which undergo proteolysis are more likely to be auto-repressive.

Explore related subjects

q-bio.MNq-bio.QM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Etay Ziv, Ilya Nemenman, Chris H. Wiggins. 2006-12-21. Optimal signal processing in small stochastic biochemical networks. https://doi.org/10.1371/journal.pone.0001077

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Accelerating reaction network identification via frequency-domain analysis

The identification of intracellular reaction networks from single-cell data lies at the heart of many biological studies, as it can unravel key mechanisms in living organisms and provide insights for their rational engineering. However, the stochastic and nonlinear nature of these reacting systems poses significant challenges for this identification problem, making the state-of-the-art methods (e.g., particle-filtering-based approaches) computationally demanding. This paper reports a noteworthy numerical observation that for certain systems, the Fourier transform can render the likelihood of the measurement data approximately Gaussian, therefore resulting in a substantially accelerated Bayesian inference algorithm. A gene transcription example is presented to illustrate this finding and demonstrate the efficiency of {the proposed Fourier-based method}.

q-bio.MN↗
arXiv2026

Can a self-sustaining chemical network emerge due to just a few catalysts?

Understanding how self-sustaining chemical reaction networks can emerge from simple molecules is an important question in chemical approaches to the origin of life. Reflexively autocatalytic and food-generated (RAF) sets provide a mathematical framework for investigating this question. This line of research goes back to the early work of Kauffman on autocatalytic reaction networks and was subsequently developed through the probabilistic framework of Mossel and Steel. Further contributions by Hordijk, Steel, and collaborators extended the theory to more heterogeneous forms of catalysis, including reaction-dependent probabilities or power-law distributions of catalytic activity. We introduce a stochastic model that combines heterogeneous molecular catalytic activity with reaction-dependent molecule-reaction compatibility. By assigning random catalytic weights to molecules and incorporating compatibility through an explicit formulation of catalysis probabilities, our model provides a concrete and flexible setting that captures both sources of heterogeneity while remaining mathematically tractable. We establish novel and general criteria for RAF formation and nonformation. We further demonstrate that classical phase-transition criteria need not remain valid in the presence of reaction-dependent catalysis. For heavy-tailed catalytic weights, we identify and rigorously quantify an additional phase transition. In models with finite-mean catalytic weights, RAF formation and nonformation are governed by a catalytic intensity parameter. For infinite-mean weights, however, we show that RAFs may emerge with probability tending to one even when the catalytic intensity parameter tends to zero.

q-bio.MN↗
arXiv2026

Modeling Gene Expression Noise: From Transcriptional Dynamics to Cell Growth and Division

Gene expression is inherently noisy, leading to substantial cell-to-cell variation in mRNA and protein levels. The telegraph model and the simpler bursty model provide good fits to single-cell count distributions and have been used extensively to understand transcriptional kinetics and estimate the kinetic parameters. However, these models all describe a static cell. Here, we review models of stochastic gene expression in growing and dividing cells which aim to understand how a cell's own life history, from its birth, through copying its genome, to its division, leaves a distinct fluctuation signature on molecule numbers. We discuss the biochemical and biophysical processes captured by these models, their analytical tractability, the concept of cyclo-stationary behavior, when this is well approximated by the steady-state of static models and how the distributions of molecular numbers measured under these conditions sensitively depend on the experimental setup. This is followed by a discussion of how these models are fitted to single-cell measurements, how biological variability can be separated from measurement noise, and which computational advances make this feasible for thousands of genes. We finish by highlighting the open problems in the field.

q-bio.MN↗