Cells must continuously sense and respond to time-varying environmental stimuli. These signals are transmitted and processed by biochemical signalling networks. However, the biochemical reactions making up these networks are intrinsically noisy, which limits the reliability of intracellular signalling. Here we use information theory to characterise the reliability of transmission of time-varying signals through elementary biochemical reactions in the presence of noise. We calculate the mutual information for both instantaneous measurements and trajectories of biochemical systems for a Gaussian model. Our results indicate that the same network can have radically different characteristics for the transmission of instantaneous signals and trajectories. For trajectories, the ability of a network to respond to changes in the input signal is determined by the timing of reaction events, and is independent of the correlation time of the output of the network. We also study how reliably signals on different time-scales can be transmitted by considering the frequency-dependent coherence and gain-to-noise ratio. We find that a detector that does not consume the ligand molecule upon detection can more reliably transmit slowly varying signals, while an absorbing detector can more reliably transmit rapidly varying signals. Furthermore, we find that while one reaction may more reliably transmit information than another when considered in isolation, when placed within a signalling cascade the relative performance of the two reactions can be reversed. This means that optimising signal transmission at a single level of a signalling cascade can reduce signalling performance for the cascade as a whole.
Biochemical networks can respond to temporal characteristics of time-varying signals. To understand how reliably biochemical networks can transmit information we must consider how an input signal as a function of time--the input trajectory--can be mapped onto an output trajectory. Here we estimate the mutual information between in- and output trajectories using a Gaussian model. We study how reliably the chemotaxis network of E. coli can transmit information on the ligand concentration to the flagellar motor, and find the input power spectrum that maximizes the information transmission rate.
Living cells encode and transmit information in the temporal dynamics of biochemical components. Gaining a detailed understanding of the input-output relationship in biological systems therefore requires quantitative measures that capture the interdependence between complete time trajectories of biochemical components. Mutual information provides such a measure but its calculation in the context of stochastic reaction networks is associated with mathematical challenges. Here we show how to estimate the mutual information between complete paths of two molecular species that interact with each o…
We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuous-time Markov chain formalism, frequently used to describe intracellular processes involving lowly abundant molecular species. Previously, we have shown how the path mutual information can be calculated for such systems when two molecular components interact directly with one another with no intermediate molecular components being present. In this work, we generalize this approach to bioc…
State- versus Reaction-Based Information Processing in Biochemical Networks
Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；AMOLF（阿莫夫基金会）；Scuola Internazionale Superiore di Studi Avanzati（高等高级研究国际学院）
Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two stable steady states of the switch to generate transition trajectories in a ratchet-like manner. We demonstrate its use by …
Cells receive signaling molecules by receptors and relay information via sensory networks so that they can respond properly depending on the type of signal. Recent studies have shown that cells can extract multi-dimensional information from dynamical concentration patterns of signaling molecules. We herein study how biochemical systems can process multi-dimensional information embedded in dynamical patterns. We model the decoding networks by linear response functions, and optimize the functions with the calculus of variations to maximize the mutual information between patterns and output. We f…
Retroactivity arises when the coupling of a molecular network $\mathcal{U}$ to a downstream network $\mathcal{D}$ results in signal propagation back from $\mathcal{D}$ to $\mathcal{U}$. The phenomenon represents a breakdown in modularity of biochemical circuits and hampers the rational design of complex functional networks. Considering simple models of signal-transduction architectures, we demonstrate the strong dependence of retroactivity on the properties of the upstream system, and explore the cost and efficacy of fuel-consuming insulating motifs that can mitigate retroactive effects. We fi…
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 chemica…
We develop an approach aimed at optimizing the parameters of a network of biochemical logic gates for reduction of the "analog" noise buildup. Experiments for three coupled enzymatic AND gates are reported, illustrating our procedure. Specifically, starch - one of the controlled network inputs - is converted to maltose by beta-amylase. With the use of phosphate (another controlled input), maltose phosphorylase then produces glucose. Finally, nicotinamide adenine dinucleotide (NAD+) - the third controlled input - is reduced under the action of glucose dehydrogenase to yield the optically detect…
Living cells are continually exposed to environmental signals that vary in time. These signals are detected and processed by biochemical networks, which are often highly stochastic. To understand how cells cope with a fluctuating environment, we therefore have to understand how reliably biochemical networks can transmit time-varying signals. To this end, we must understand both the noise characteristics and the amplification properties of networks. In this manuscript, we use information theory to study how reliably signalling cascades employing autoregulation and feedback can transmit time-var…
Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are assumed. Yet, it is increasingly becoming clear that even microscopic spatial inhomogeneities oftentimes can induce significant differences on the macroscopic level. Since experimental observation of single-molecule behavior is extremely challenging, theoretical modeling of biochemical reactions on the single-particle level is an important tool for understanding…
We present an information-theoretic formalism to study signal transduction in four architectural variants of a model two-step cascade with increasing input population. Our results categorize these four types into two classes depending upon the effect played out by activation and repression on mutual information, net synergy, and signal-to-noise ratio. Within the Gaussian framework and using the linear noise approximation, we derive the analytic expressions for these metrics to establish their underlying relationships in terms of the biochemical parameters. We also verify our approximations thr…
Feedback in sensory biochemical networks can give rise to bifurcations in cells' behavioral response. These bifurcations share many properties with thermodynamic critical points. Evidence suggests that biological systems may operate near these critical points, but the functional benefit of doing so remains poorly understood. Here we investigate a simple biochemical model with nonlinear feedback and multicellular communication to determine if criticality provides a functional benefit in terms of the ability to gain information about a stochastic chemical signal. We find that when signal fluctua…
Information transmission in biological signaling circuits has often been described using the metaphor of a noise filter. Cellular systems need accurate, real-time data about their environmental conditions, but the biochemical reaction networks that propagate, amplify, and process signals work with noisy representations of that data. Biology must implement strategies that not only filter the noise, but also predict the current state of the environment based on information delayed due to the finite speed of chemical signaling. The idea of a biochemical noise filter is actually more than just a m…
Biochemical computing attempts to process information with biomolecules and biological objects. In this work we review our results on analysis and optimization of single biochemical logic gates based on enzymatic reactions, and a network of three gates, for reduction of the "analog" noise buildup. For a single gate, optimization is achieved by analyzing the enzymatic reactions within a framework of kinetic equations. We demonstrate that using co-substrates with much smaller affinities than the primary substrate, a negligible increase in the noise output from the logic gate is obtained as compa…
Quantitatively predictive models of biomolecular circuits are important tools for the design of synthetic biology and molecular communication circuits. The information content of typical time-lapse single-cell data for the inference of kinetic parameters is not only limited by measurement uncertainty and intrinsic stochasticity, but also by the employed perturbations. Novel microfluidic devices enable the synthesis of temporal chemical concentration profiles. The informativeness of a perturbation can be quantified based on mutual information. We propose an approximate method to perform optimal…
