Effect of feedback on the fidelity of information transmission of time-varying signals

Emergence of temporal noise hierarchy in co-regulated genes of multi-output feed-forward loop

Natural variations in gene expression, called noise, are fundamental to biological systems. The expression noise can be beneficial or detrimental to cellular functions. While the impact of noise on individual genes is well-established, our understanding of how noise behaves when multiple genes are co-expressed by shared regulatory elements within transcription networks remains elusive. This lack of understanding extends to how the architecture and regulatory features of these networks influence noise. To address this gap, we study the multi-output feed-forward loop motif. The motif is prevalent in bacteria and yeast and influences co-expression of multiple genes by shared transcription factors (TFs). Focusing on a two-output variant of the motif, the present study explores the interplay between its architecture, co-expression (symmetric and asymmetric) patterns of the two genes, and the associated noise dynamics. We employ a stochastic modeling approach to investigate how the binding affinities of the TFs influence symmetric and asymmetric expression patterns and the resulting noise dynamics in the co-expressed genes. This knowledge could guide the development of strategies for manipulating gene expression patterns through targeted modulation of TF binding affinities.

Characterizing the nonmonotonic behavior of mutual information along biochemical reaction cascades

Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal populations even in identical environments. Experimentally observed joint probability distributions can then be used to quantify the covariability and mutual information between molecular abundances along signaling cascades. However, because stationary state abundances along stochastic biochemical reaction cascades are not conditionally independent, their mutual information is not constrained by the data-processing inequality. Here, we report the conditions under which the mutual information between stationary state abundances increases along a cascade of biochemical reactions. This nonmonotonic behavior can be intuitively understood in terms of noise propagation and time-averaging stochastic fluctuations that are short-lived compared to an extrinsic signal. Our results reemphasize that mutual information measurements of stationary state distributions of cellular components may be of limited utility for characterizing cellular signaling processes because they do not measure information transfer.

Trade-offs between cost and information in cellular prediction

Living cells can leverage correlations in environmental fluctuations to predict the future environment and mount a response ahead of time. To this end, cells need to encode the past signal into the output of the intracellular network from which the future input is predicted. Yet, storing information is costly while not all features of the past signal are equally informative on the future input signal. Here, we show for two classes of input signals that cellular networks can reach the fundamental bound on the predictive information as set by the information extracted from the past signal: Push-pull networks can reach this information bound for Markovian signals, while networks that take a temporal derivative can reach the bound for predicting the future derivative of non-Markovian signals. However, the bits of past information that are most informative about the future signal are also prohibitively costly. As a result, the optimal system that maximizes the predictive information for a given resource cost is, in general, not at the information bound. Applying our theory to the chemotaxis network of Escherichia coli reveals that its adaptive kernel is optimal for predicting future concentration changes over a broad range of background concentrations, and that the system has been tailored to predicting these changes in shallow gradients.

Quantifying information of intracellular signaling: progress with machine learning

Cells convey information about their extracellular environment to their core functional machineries. Studying the capacity of intracellular signaling pathways to transmit information addresses fundamental questions about living systems. Here, we review how information-theoretic approaches have been used to quantify information transmission by signaling pathways that are functionally pleiotropic and subject to molecular stochasticity. We describe how recent advances in machine learning have been leveraged to address the challenges of complex temporal trajectory datasets and how these have contributed to our understanding of how cells employ temporal coding to appropriately adapt to environmental perturbations.

Information transmission in a two-step cascade: interplay of activation and repression

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 of activation and repression on mutual information, net synergy, and signal-to-noise ratio. Using the Gaussian framework and 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 through stochastic simulations.

Role of integrated noise in pathway-specific signal propagation in feed-forward loops

Cells impose optimal noise control mechanism in diverse situations to cope with distinct environmental cues. Sometimes, it is desirable for the cell to utilize fluctuations for noise-driven processes. In other cases, noise can be harmful to the cell to show optimal fitness. It is, therefore, important to unravel the noise propagation mechanism inside the cell. Such noise controlling mechanism is accomplished by using gene transcription regulatory networks. One such gene regulatory network is feed-forward loop, having three regulatory nodes S, X and Y. Here, we consider the most abundant type 1 of coherent and incoherent feed-forward loops with both OR and AND logic functions, forming four different architectures. In OR logic function, the functions representing S and X act additively for the regulation of Y, while in AND logic function, the same functions (S and X) act multiplicatively for the regulation of Y. Measurement of susceptibility of the signal at output Y is done using elasticity of each regulation in FFLs. Using susceptibility, we demonstrate the nature of pathway integration by which one-step and two-step pathways get overlapped. The integration type is competitive for motifs having OR gate, while it is noncompetitive for the same with AND gate. The pathway integration property explains the output noise behavior of the motifs properly but cannot infer about the mechanism by which the upstream noise propagates to output. To account this, the total output noise is decomposed, which results in integrated noise as an additional noise source along with pathway-specific noise components. The integrated noise is found to appear as a consequence of integration between the pathways and has different functional characteristics explaining noise amplification and noise attenuation property of coherent and incoherent feed-forward loops, respectively. The noise decomposition also quantifies the contribution of different noise sources toward total noise. Finally, the noise propagation is being tuned as a function of input signal noise and its time scale of fluctuations, which shows considerable intrinsic noise strength and relatively slow relaxation time scale causes a higher degree of noise propagation in FFLs.

Dissipation in Non-Steady State Regulatory Circuits

In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by specific examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that, even in the fast switching limit, function out of equilibrium.

Multivariate information processing characterizes fitness of a cascaded gene-transcription machinery

We report that a genetic two-step activation cascade processes diverse flavors of information, e.g., synergy, redundancy, and unique information. Our computations measuring reduction in Shannon entropies and reduction in variances produce differently behaving absolute magnitudes of these informational flavors. We find that similarity can be brought in if these terms are evaluated in fractions with respect to corresponding total information. Each of the input signal and final gene-product is found to generate common or redundant information fractions (mostly) to predict each other, whereas they also complement one another to harness synergistic information fraction, predicting the intermediate biochemical species. For an optimally growing signal to maintain fixed steady-state abundance of activated downstream gene-products, the interaction information fractions for this cascade module shift from net-redundancy to information-independence.

Optimal entrainment of circadian clocks in the presence of noise

Circadian clocks are biochemical oscillators that allow organisms to estimate the time of the day. These oscillators are inherently noisy due to the discrete nature of the reactants and the stochastic character of their interactions. To keep these oscillators in sync with the daily day-night rhythm in the presence of noise, circadian clocks must be coupled to the dark-light cycle. In this paper, we study the entrainment of phase oscillators as a function of the intrinsic noise in the system. Using stochastic simulations, we compute the optimal coupling strength, intrinsic frequency, and shape of the phase-response curve, that maximize the mutual information between the phase of the clock and time. We show that the optimal coupling strength and intrinsic frequency increase with the noise, but that the shape of the phase-response curve varies nonmonotonically with the noise: in the low-noise regime, it features a dead zone that increases in width as the noise increases, while in the high-noise regime, the width decreases with the noise. These results arise from a tradeoff between maximizing stability-noise suppression-and maximizing linearity of the input-output, i.e., time-phase, relation. We also show that three analytic approximations-the linear-noise approximation, the phase-averaging method, and linear-response theory-accurately describe different regimes of the coupling strength and the noise.

Interplay of synergy and redundancy in diamond motif

The formalism of partial information decomposition provides a number of independent components which altogether constitute the total information provided by the source variable(s) about the target variable(s). These non-overlapping terms are recognized as unique information, synergistic information, and redundant information. The metric of net synergy conceived as the difference between synergistic and redundant information is capable of detecting effective synergy, effective redundancy, and information independence among stochastic variables. The net synergy can be quantified using appropriate combinations of different Shannon mutual information terms. The utilization of the net synergy in network motifs with the nodes representing different biochemical species, involved in information sharing, uncovers rich store for exciting results. In the current study, we use this formalism to obtain a comprehensive understanding of the relative information processing mechanism in a diamond motif and two of its sub-motifs, namely, bifurcation and integration motif embedded within the diamond motif. The emerging patterns of effective synergy and effective redundancy and their contribution toward ensuring high fidelity information transmission are duly compared in the sub-motifs. Investigation on the metric of net synergy in independent bifurcation and integration motifs are also executed. In all of these computations, the crucial roles played by various systemic time scales, activation coefficients, and signal integration mechanisms at the output of the network topologies are especially emphasized. Following this plan of action, we become confident that the origin of effective synergy and effective redundancy can be architecturally justified by decomposing a diamond motif into bifurcation and integration motif. According to our conjecture, the presence of a common source of fluctuations creates effective redundancy. Our calculations reveal that effective redundancy empowers signal fidelity. Moreover, to achieve this, input signaling species avoids strong interaction with downstream intermediates. This strategy is capable of making the diamond motif noise-tolerant. Apart from the topological features, our study also puts forward the active contribution of additive and multiplicative signal integration mechanisms to nurture effective redundancy and effective synergy.

Optimal information transfer in enzymatic networks: A field theoretic formulation

Signaling in enzymatic networks is typically triggered by environmental fluctuations, resulting in a series of stochastic chemical reactions, leading to corruption of the signal by noise. For example, information flow is initiated by binding of extracellular ligands to receptors, which is transmitted through a cascade involving kinase-phosphatase stochastic chemical reactions. For a class of such networks, we develop a general field-theoretic approach to calculate the error in signal transmission as a function of an appropriate control variable. Application of the theory to a simple push-pull network, a module in the kinase-phosphatase cascade, recovers the exact results for error in signal transmission previously obtained using umbral calculus [Hinczewski and Thirumalai, Phys. Rev. X 4, 041017 (2014)2160-330810.1103/PhysRevX.4.041017]. We illustrate the generality of the theory by studying the minimal errors in noise reduction in a reaction cascade with two connected push-pull modules. Such a cascade behaves as an effective three-species network with a pseudointermediate. In this case, optimal information transfer, resulting in the smallest square of the error between the input and output, occurs with a time delay, which is given by the inverse of the decay rate of the pseudointermediate. Surprisingly, in these examples the minimum error computed using simulations that take nonlinearities and discrete nature of molecules into account coincides with the predictions of a linear theory. In contrast, there are substantial deviations between simulations and predictions of the linear theory in error in signal propagation in an enzymatic push-pull network for a certain range of parameters. Inclusion of second-order perturbative corrections shows that differences between simulations and theoretical predictions are minimized. Our study establishes that a field theoretic formulation of stochastic biological signaling offers a systematic way to understand error propagation in networks of arbitrary complexity.

Fluctuation sensitivity of a transcriptional signaling cascade

The internal biochemical state of a cell is regulated by a vast transcriptional network that kinetically correlates the concentrations of numerous proteins. Fluctuations in protein concentration that encode crucial information about this changing state must compete with fluctuations caused by the noisy cellular environment in order to successfully transmit information across the network. Oftentimes, one protein must regulate another through a sequence of intermediaries, and conventional wisdom, derived from the data processing inequality of information theory, leads us to expect that longer sequences should lose more information to noise. Using the metric of mutual information to characterize the fluctuation sensitivity of transcriptional signaling cascades, we find, counter to this expectation, that longer chains of regulatory interactions can instead lead to enhanced informational efficiency. We derive an analytic expression for the mutual information from a generalized chemical kinetics model that we reduce to simple, mass-action kinetics by linearizing for small fluctuations about the basal biological steady state, and we find that at long times this expression depends only on a simple ratio of protein production to destruction rates and the length of the cascade. We place bounds on the values of these parameters by requiring that the mutual information be at least one bit-otherwise, any received signal would be indistinguishable from noise-and we find not only that nature has devised a way to circumvent the data processing inequality, but that it must be circumvented to attain this one-bit threshold. We demonstrate how this result places informational and biochemical efficiency at odds with one another by correlating high transcription factor binding affinities with low informational output, and we conclude with an analysis of the validity of our assumptions and propose how they might be tested experimentally.

Redundancy in information transmission in a two-step cascade

We present a stochastic framework to study signal transmission in a generic two-step cascade S→X→Y. Starting from a set of Langevin equations obeying Gaussian noise processes we calculate the variance and covariance while considering both linear and nonlinear production terms for different biochemical species of the cascade. These quantities are then used to calculate the net synergy within the purview of partial information decomposition. We show that redundancy in information transmission is essentially an important consequence of Markovian property of the two-step cascade motif. We also show that redundancy increases fidelity of the signaling pathway.

Extending the dynamic range of transcription factor action by translational regulation

A crucial step in the regulation of gene expression is binding of transcription factor (TF) proteins to regulatory sites along the DNA. But transcription factors act at nanomolar concentrations, and noise due to random arrival of these molecules at their binding sites can severely limit the precision of regulation. Recent work on the optimization of information flow through regulatory networks indicates that the lower end of the dynamic range of concentrations is simply inaccessible, overwhelmed by the impact of this noise. Motivated by the behavior of homeodomain proteins, such as the maternal morphogen Bicoid in the fruit fly embryo, we suggest a scheme in which transcription factors also act as indirect translational regulators, binding to the mRNA of other regulatory proteins. Intuitively, each mRNA molecule acts as an independent sensor of the input concentration, and averaging over these multiple sensors reduces the noise. We analyze information flow through this scheme and identify conditions under which it outperforms direct transcriptional regulation. Our results suggest that the dual role of homeodomain proteins is not just a historical accident, but a solution to a crucial physics problem in the regulation of gene expression.

Optimal Prediction by Cellular Signaling Networks

Living cells can enhance their fitness by anticipating environmental change. We study how accurately linear signaling networks in cells can predict future signals. We find that maximal predictive power results from a combination of input-noise suppression, linear extrapolation, and selective readout of correlated past signal values. Single-layer networks generate exponential response kernels, which suffice to predict Markovian signals optimally. Multilayer networks allow oscillatory kernels that can optimally predict non-Markovian signals. At low noise, these kernels exploit the signal derivative for extrapolation, while at high noise, they capitalize on signal values in the past that are strongly correlated with the future signal. We show how the common motifs of negative feedback and incoherent feed-forward can implement these optimal response functions. Simulations reveal that E. coli can reliably predict concentration changes for chemotaxis, and that the integration time of its response kernel arises from a trade-off between rapid response and noise suppression.

Information transfer through a signaling module with feedback: A perturbative approach

Signal transduction in biological cells is effected by signaling pathways that typically include multiple feedback loops. Here we analyze information transfer through a prototypical signaling module with biochemical feedback. The module switches stochastically between an inactive and active state; the input to the module governs the activation rate while the output (i.e., the product concentration) perturbs the inactivation rate. Using a novel perturbative approach, we compute the rate with which information about the input is gained from observation of the output. We obtain an explicit analytical result valid to first order in feedback strength and to second order in the strength of input. The total information gained during an extended time interval is found to depend on the feedback strength only through the total number of activation/inactivation events.

Optimizing information flow in small genetic networks. IV. Spatial coupling

We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the input) by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively different regulatory strategy emerges where individual cells respond to the input in a nearly steplike fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.

Role of relaxation time scale in noisy signal transduction

Intra-cellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and derive the expressions for Fano factor and mutual information in close analytical form. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions.

Systems biology. Accurate information transmission through dynamic biochemical signaling networks

Stochasticity inherent to biochemical reactions (intrinsic noise) and variability in cellular states (extrinsic noise) degrade information transmitted through signaling networks. We analyzed the ability of temporal signal modulation--that is, dynamics--to reduce noise-induced information loss. In the extracellular signal-regulated kinase (ERK), calcium (Ca(2+)), and nuclear factor kappa-B (NF-κB) pathways, response dynamics resulted in significantly greater information transmission capacities compared to nondynamic responses. Theoretical analysis demonstrated that signaling dynamics has a key role in overcoming extrinsic noise. Experimental measurements of information transmission in the ERK network under varying signal-to-noise levels confirmed our predictions and showed that signaling dynamics mitigate, and can potentially eliminate, extrinsic noise-induced information loss. By curbing the information-degrading effects of cell-to-cell variability, dynamic responses substantially increase the accuracy of biochemical signaling networks.

Noise and information transmission in promoters with multiple internal States

Based on the measurements of noise in gene expression performed during the past decade, it has become customary to think of gene regulation in terms of a two-state model, where the promoter of a gene can stochastically switch between an ON and an OFF state. As experiments are becoming increasingly precise and the deviations from the two-state model start to be observable, we ask about the experimental signatures of complex multistate promoters, as well as the functional consequences of this additional complexity. In detail, we i), extend the calculations for noise in gene expression to promoters described by state transition diagrams with multiple states, ii), systematically compute the experimentally accessible noise characteristics for these complex promoters, and iii), use information theory to evaluate the channel capacities of complex promoter architectures and compare them with the baseline provided by the two-state model. We find that adding internal states to the promoter generically decreases channel capacity, except in certain cases, three of which (cooperativity, dual-role regulation, promoter cycling) we analyze in detail.

Multiplexing oscillatory biochemical signals

In recent years it has been increasingly recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that the protein signaling network of living cells has a bow-tie structure and that components are often shared between different signaling pathways. Here we show by mathematical modeling that living cells can multiplex a constant and an oscillatory signal: they can transmit these two signals simultaneously through a common signaling pathway, and yet respond to them specifically and reliably. We find that information transmission is reduced not only by noise arising from the intrinsic stochasticity of biochemical reactions, but also by crosstalk between the different channels. Yet, under biologically relevant conditions more than 2 bits of information can be transmitted per channel, even when the two signals are transmitted simultaneously. These observations suggest that oscillatory signals are ideal for multiplexing signals.

Transcription factor binding kinetics constrain noise suppression via negative feedback

Negative autoregulation, where a transcription factor regulates its own expression by preventing transcription, is commonly used to suppress fluctuations in gene expression. Recent single molecule in vivo imaging has shown that it takes significant time for a transcription factor molecule to bind its chromosomal binding site. Given the slow association kinetics, transcription factor mediated feedback cannot at the same time be fast and strong. Here we show that with a limited association rate follows an optimal transcription factor binding strength where noise is maximally suppressed. At the optimal binding strength the binding site is free a fixed fraction of the time independent of the transcription factor concentration. One consequence is that high-copy number transcription factors should bind weakly to their operators, which is observed for transcription factors in Escherichia coli. The results demonstrate that a binding site's strength may be uncorrelated to its functional importance.

Positional information, in bits

Cells in a developing embryo have no direct way of "measuring" their physical position. Through a variety of processes, however, the expression levels of multiple genes come to be correlated with position, and these expression levels thus form a code for "positional information." We show how to measure this information, in bits, using the gap genes in the Drosophila embryo as an example. Individual genes carry nearly two bits of information, twice as much as would be expected if the expression patterns consisted only of on/off domains separated by sharp boundaries. Taken together, four gap genes carry enough information to define a cell's location with an error bar of ~1 along the anterior/posterior axis of the embryo. This precision is nearly enough for each cell to have a unique identity, which is the maximum information the system can use, and is nearly constant along the length of the embryo. We argue that this constancy is a signature of optimality in the transmission of information from primary morphogen inputs to the output of the gap gene network.

Time-dependent information transmission in a model regulatory circuit

Many biological regulatory systems respond with a physiological delay when processing signals. A simple model of regulation which respects these features shows how the ability of a delayed output to transmit information is limited: at short times by the time scale of the dynamic input, at long times by that of the dynamic output. We find that topologies of maximally informative networks correspond to commonly occurring biological circuits linked to stress response and that circuits functioning out of steady state may exploit absorbing states to transmit information optimally.

The fidelity of dynamic signaling by noisy biomolecular networks

Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.

Cells do not live in constant conditions, but in environments that change over time. To adapt to their surroundings, cells must therefore sense fluctuating concentrations and ‘interpret’ the state of their environment to see whether, for example, a change in the pattern of gene expression is needed. This task is achieved via the noisy computations of biomolecular networks. But what levels of signaling fidelity can be achieved and how are dynamic signals encoded in the network's outputs? Here we present a general technique for analyzing such questions. We identify two sources of signaling error: dynamic error, which occurs when the network responds to features of the input other than the signal of interest; and mechanistic error, which arises because of the inevitable stochasticity of biochemical reactions. We show analytically that increased biochemical noise can sometimes improve fidelity and that, for genetic autoregulation, feedback can be deleterious. Our approach also allows us to predict the dynamic signal for which a given signaling network has highest fidelity and to design networks to maximize fidelity for a given signal. We thus propose a new way to analyze the flow of information in signaling networks, particularly for the dynamic environments expected in nature.

Fundamental limits on sensing chemical concentrations with linear biochemical networks

Living cells often need to extract information from biochemical signals that are noisy. We study how accurately cells can measure chemical concentrations with signaling networks that are linear. For stationary signals of long duration, they can reach, but not beat, the Berg-Purcell limit, which relies on uniformly averaging in time the fluctuations in the input signal. For short times or nonstationary signals, however, they can beat the Berg-Purcell limit, by nonuniformly time averaging the input. We derive the optimal weighting function for time averaging and use it to provide the fundamental limit of measuring chemical concentrations with linear signaling networks.

Feed-forward loops and diamond motifs lead to tunable transmission of information in the frequency domain

Using a Gaussian model, we study the transmission of time-varying biochemical signals through feed-forward motifs and diamond motifs. To this end, we compute the frequency dependence of the gain, the noise, as well as their ratio, the gain-to-noise ratio, which measures how reliably a network transmits signals at different frequencies. We find that both coherent and incoherent feed-forward motifs can either act as low-pass or high-pass filters for information: The frequency dependence of the gain-to-noise ratio increases or decreases with increasing frequency, respectively. Our analysis of diamond motifs reveals that cooperative activation of the output component can increase the gain-to-noise ratio. This means that from the perspective of information transmission, it can be beneficial to split the input signal in two and recombine the two propagated signals at the output. Cooperative activation can be implemented via the formation of homo- or heteromultimers that then bind and activate the output component or via the binding of individual molecules of the intermediate species to the output component.

Optimizing information flow in small genetic networks. III. A self-interacting gene

Living cells must control the reading out or "expression" of information encoded in their genomes, and this regulation often is mediated by transcription factors--proteins that bind to DNA and either enhance or repress the expression of nearby genes. But the expression of transcription factor proteins is itself regulated, and many transcription factors regulate their own expression in addition to responding to other input signals. Here we analyze the simplest of such self-regulatory circuits, asking how parameters can be chosen to optimize information transmission from inputs to outputs in the steady state. Some nonzero level of self-regulation is almost always optimal, with self-activation dominant when transcription factor concentrations are low and self-repression dominant when concentrations are high. In steady state the optimal self-activation is never strong enough to induce bistability, although there is a limit in which the optimal parameters are very close to the critical point.

Theoretical aspects of cellular decision-making and information-processing

Microscopic biological processes have extraordinary complexity and variety at the sub-cellular, intra-cellular, and multi-cellular levels. In dealing with such complex phenomena, conceptual and theoretical frameworks are crucial, which enable us to understand seemingly different intra- and inter-cellular phenomena from unified viewpoints. Decision-making is one such concept that has attracted much attention recently. Since a number of cellular behavior can be regarded as processes to make specific actions in response to external stimuli, decision-making can cover and has been used to explain a broad range of different cellular phenomena [Balázsi et al. (Cell 144(6):910, 2011), Zeng et al. (Cell 141(4):682, 2010)]. Decision-making is also closely related to cellular information-processing because appropriate decisions cannot be made without exploiting the information that the external stimuli contain. Efficiency of information transduction and processing by intra-cellular networks determines the amount of information obtained, which in turn limits the efficiency of subsequent decision-making. Furthermore, information-processing itself can serve as another concept that is crucial for understanding of other biological processes than decision-making. In this work, we review recent theoretical developments on cellular decision-making and information-processing by focusing on the relation between these two concepts.

Spatial distribution and dose-response relationship for different operation modes in a reaction-diffusion model of the MAPK cascade

The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.

Information transmission in genetic regulatory networks: a review

Genetic regulatory networks enable cells to respond to changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform, and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of genetic regulatory networks. Transmitting information between a network's inputs and outputs has been proposed as one such possible measure of function, relevant in certain biological contexts. Here we summarize recent developments in the application of information theory to gene regulatory networks. We first review basic concepts in information theory necessary for understanding recent work. We then discuss the functional complexity of gene regulation, which arises from the molecular nature of the regulatory interactions. We end by reviewing some experiments that support the view that genetic networks responsible for early development of multicellular organisms might be maximizing transmitted 'positional information'.