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. Since the number of obtained equations grows combinatorially with number of considered cells, we employ a previously proposed model reduction technique, which exploits symmetries in the underlying moment dynamics. Importantly, the number of equations obtained in this way is independent of the number of considered cells such that the method scales to arbitrary population sizes. Based on this approach, we study how cell-cell communication affects population variability in several biochemical networks. Moreover, we analyze the accuracy and computational efficiency of the moment-based approximation by comparing it with moments obtained from stochastic simulations.Comment: 6 pages, 5 Figure

A Characterization of Scale Invariant Responses in Enzymatic Networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of enzymatic networks. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions

Optimal signal processing in small stochastic biochemical networks

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.Comment: 41 pages 7 figures, 5 table

Information processing and signal integration in bacterial quorum sensing

Bacteria communicate using secreted chemical signaling molecules called autoinducers in a process known as quorum sensing. The quorum-sensing network of the marine bacterium {\it Vibrio harveyi} employs three autoinducers, each known to encode distinct ecological information. Yet how cells integrate and interpret the information contained within the three autoinducer signals remains a mystery. Here, we develop a new framework for analyzing signal integration based on Information Theory and use it to analyze quorum sensing in {\it V. harveyi}. We quantify how much the cells can learn about individual autoinducers and explain the experimentally observed input-output relation of the {\it V. harveyi} quorum-sensing circuit. Our results suggest that the need to limit interference between input signals places strong constraints on the architecture of bacterial signal-integration networks, and that bacteria likely have evolved active strategies for minimizing this interference. Here we analyze two such strategies: manipulation of autoinducer production and feedback on receptor number ratios.Comment: Supporting information is in appendi