Multiplexing biochemical signals

Cells function as a ternary logic gate to decide migration direction under integrated chemical and fluidic cues

Cells sense various environmental cues and subsequently process intracellular signals to decide their migration direction in many physiological and pathological processes. Although several signaling molecules and networks have been identified in these directed migrations, it still remains ambiguous to predict the migration direction under multiple and integrated cues, specifically chemical and fluidic cues. Here, we investigated the cellular signal processing machinery by reverse-engineering directed cell migration under integrated chemical and fluidic cues. We imposed controlled chemical and fluidic cues to cells using a microfluidic platform and analyzed the extracellular coupling of the cues with respect to the cellular detection limit. Then, the cell's migratory behavior was reverse-engineered to build a cellular signal processing system as a logic gate, which is based on a "selection" gate. This framework is further discussed with a minimal intracellular signaling network of a shared pathway model. The proposed framework of the ternary logic gate suggests a systematic view to understand how cells decode multiple cues and make decisions about the migration direction.

Optimal ligand discrimination by asymmetric dimerization and turnover of interferon receptors

In multicellular organisms, antiviral defense mechanisms evoke a reliable collective immune response despite the noisy nature of biochemical communication between tissue cells. A molecular hub of this response, the interferon I receptor (IFNAR), discriminates between ligand types by their affinity regardless of concentration. To understand how ligand type can be decoded robustly by a single receptor, we frame ligand discrimination as an information-theoretic problem and systematically compare the major classes of receptor architectures: allosteric, homodimerizing, and heterodimerizing. We demonstrate that asymmetric heterodimers achieve the best discrimination power over the entire physiological range of local ligand concentrations. This design enables sensing of ligand presence and type, and it buffers against moderate concentration fluctuations. In addition, receptor turnover, which drives the receptor system out of thermodynamic equilibrium, allows alignment of activation points for ligands of different affinities and thereby makes ligand discrimination practically independent of concentration. IFNAR exhibits this optimal architecture, and our findings thus suggest that this specialized receptor can robustly decode digital messages carried by its different ligands.

The many bits of positional information

Half a century after Lewis Wolpert's seminal conceptual advance on how cellular fates distribute in space, we provide a brief historical perspective on how the concept of positional information emerged and influenced the field of developmental biology and beyond. We focus on a modern interpretation of this concept in terms of information theory, largely centered on its application to cell specification in the early Drosophila embryo. We argue that a true physical variable (position) is encoded in local concentrations of patterning molecules, that this mapping is stochastic, and that the processes by which positions and corresponding cell fates are determined based on these concentrations need to take such stochasticity into account. With this approach, we shift the focus from biological mechanisms, molecules, genes and pathways to quantitative systems-level questions: where does positional information reside, how it is transformed and accessed during development, and what fundamental limits it is subject to?

Disease evolution in reaction networks: Implications for a diagnostic problem

We study the time evolution of symptoms (signs) with some defects in the dynamics of a reaction network as a (microscopic) model for the progress of disease phenotypes. To this end, we take a large population of reaction networks and follow the stochastic dynamics of the system to see how the development of defects affects the macroscopic states of the signs probability distribution. We start from some plausible definitions for the healthy and disease states along with a dynamical model for the emergence of diseases by a reverse simulated annealing algorithm. The healthy state is defined as a state of maximum objective function, which here is the sum of mutual information between a subset of signal variables and the subset of assigned response variables. A disease phenotype is defined with two parameters controlling the rate of mutations in reactions and the rate of accepting mutations that reduce the objective function. The model can provide the time dependence of the sign probabilities given a disease phenotype. This allows us to obtain the accuracy of diagnosis as a function of time by using a probabilistic model of signs and diseases. The trade-off between the diagnosis accuracy (increasing in time) and the objective function (decreasing in time) can be used to suggest an optimal time for medical intervention. Our model would be useful in particular for a dynamical (history-based) diagnostic problem, to estimate the likelihood of a disease hypothesis given the temporal evolution of the signs.

Here, we use concepts from statistical physics and reaction network dynamics to introduce a measure to quantify the tradeoff between the accuracy of diagnosis and an early diagnosis. This measure is used to suggest an optimal time for medical intervention depending on the number of observed signs (medical tests). We present a stochastic model using a reverse simulated annealing algorithm for numerical simulation of disease evolution. The model can provide the time dependence of the sign probabilities given a disease phenotype. This in turn allows us to anticipate the accuracy of diagnosis as a function of time by using a probabilistic model of signs and diseases.

Estimating information in time-varying signals

Across diverse biological systems-ranging from neural networks to intracellular signaling and genetic regulatory networks-the information about changes in the environment is frequently encoded in the full temporal dynamics of the network nodes. A pressing data-analysis challenge has thus been to efficiently estimate the amount of information that these dynamics convey from experimental data. Here we develop and evaluate decoding-based estimation methods to lower bound the mutual information about a finite set of inputs, encoded in single-cell high-dimensional time series data. For biological reaction networks governed by the chemical Master equation, we derive model-based information approximations and analytical upper bounds, against which we benchmark our proposed model-free decoding estimators. In contrast to the frequently-used k-nearest-neighbor estimator, decoding-based estimators robustly extract a large fraction of the available information from high-dimensional trajectories with a realistic number of data samples. We apply these estimators to previously published data on Erk and Ca2+ signaling in mammalian cells and to yeast stress-response, and find that substantial amount of information about environmental state can be encoded by non-trivial response statistics even in stationary signals. We argue that these single-cell, decoding-based information estimates, rather than the commonly-used tests for significant differences between selected population response statistics, provide a proper and unbiased measure for the performance of biological signaling networks.

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.

Multidimensional biochemical information processing of dynamical patterns

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 multidimensional information from dynamical concentration patterns of signaling molecules. We herein study how biochemical systems can process multidimensional 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 find that, when the noise intensity is lower, decoders with different linear response functions, i.e., distinct decoders, can extract much information. However, when the noise intensity is higher, distinct decoders do not provide the maximum amount of information. This indicates that, when transmitting information by dynamical patterns, embedding information in multiple patterns is not optimal when the noise intensity is very large. Furthermore, we explore the biochemical implementations of these decoders using control theory and demonstrate that these decoders can be implemented biochemically through the modification of cascade-type networks, which are prevalent in actual signaling pathways.

Biochemical Machines for the Interconversion of Mutual Information and Work

We propose a physically realizable information-driven device consisting of an enzyme in a chemical bath, interacting with pairs of molecules prepared in correlated states. These correlations persist without direct interaction and thus store free energy equal to the mutual information. The enzyme can harness this free energy, and that stored in the individual molecular states, to do chemical work. Alternatively, the enzyme can use the chemical driving to create mutual information. A modified system can function without external intervention, approaching biological systems more closely.

Communication shapes sensory response in multicellular networks

Collective sensing by interacting cells is observed in a variety of biological systems, and yet, a quantitative understanding of how sensory information is collectively encoded is lacking. Here, we investigate the ATP-induced calcium dynamics of monolayers of fibroblast cells that communicate via gap junctions. Combining experiments and stochastic modeling, we find that increasing the ATP stimulus increases the propensity for calcium oscillations, despite large cell-to-cell variability. The model further predicts that the oscillation propensity increases with not only the stimulus, but also the cell density due to increased communication. Experiments confirm this prediction, showing that cell density modulates the collective sensory response. We further implicate cell-cell communication by coculturing the fibroblasts with cancer cells, which we show act as "defects" in the communication network, thereby reducing the oscillation propensity. These results suggest that multicellular networks sit at a point in parameter space where cell-cell communication has a significant effect on the sensory response, allowing cells to simultaneously respond to a sensory input and the presence of neighbors.

Laguerre Filter Analysis with Partial Least Square Regression Reveals a Priming Effect of ERK and CREB on c-FOS Induction

Signaling networks are made up of limited numbers of molecules and yet can code information that controls different cellular states through temporal patterns and a combination of signaling molecules. In this study, we used a data-driven modeling approach, the Laguerre filter with partial least square regression, to describe how temporal and combinatorial patterns of signaling molecules are decoded by their downstream targets. The Laguerre filter is a time series model used to represent a nonlinear system based on Volterra series expansion. Furthermore, with this approach, each component of the Volterra series expansion is expanded by Laguerre basis functions. We combined two approaches, application of a Laguerre filter and partial least squares (PLS) regression, and applied the combined approach to analysis of a signal transduction network. We applied the Laguerre filter with PLS regression to identify input and output (IO) relationships between MAP kinases and the products of immediate early genes (IEGs). We found that Laguerre filter with PLS regression performs better than Laguerre filter with ordinary regression for the reproduction of a time series of IEGs. Analysis of the nonlinear characteristics extracted using the Laguerre filter revealed a priming effect of ERK and CREB on c-FOS induction. Specifically, we found that the effects of a first pulse of ERK enhance the subsequent effects on c-FOS induction of treatment with a second pulse of ERK, a finding consistent with prior molecular biological knowledge. The variable importance of projections and output loadings in PLS regression predicted the upstream dependency of each IEG. Thus, a Laguerre filter with partial least square regression approach appears to be a powerful method to find the processing mechanism of temporal patterns and combination of signaling molecules by their downstream gene expression.

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.

Non-monotonic dynamics and crosstalk in signaling pathways and their implications for pharmacology

Currently, drug discovery approaches commonly assume a monotonic dose-response relationship. However, the assumption of monotonicity is increasingly being challenged. Here we show that for two simple interacting linear signaling pathways that carry two different signals with different physiological responses, a non-monotonic input-output relation can arise with simple network topologies including coherent and incoherent feed-forward loops. We show that non-monotonicity of the response functions has severe implications for pharmacological treatment. Fundamental constraints are imposed on the effectiveness and toxicity of any drug independent of its chemical nature and selectivity due to the specific network structure.

Limits on information transduction through amplitude and frequency regulation of transcription factor activity

Signaling pathways often transmit multiple signals through a single shared transcription factor (TF) and encode signal information by differentially regulating TF dynamics. However, signal information will be lost unless it can be reliably decoded by downstream genes. To understand the limits on dynamic information transduction, we apply information theory to quantify how much gene expression information the yeast TF Msn2 can transduce to target genes in the amplitude or frequency of its activation dynamics. We find that although the amount of information transmitted by Msn2 to single target genes is limited, information transduction can be increased by modulating promoter cis-elements or by integrating information from multiple genes. By correcting for extrinsic noise, we estimate an upper bound on information transduction. Overall, we find that information transduction through amplitude and frequency regulation of Msn2 is limited to error-free transduction of signal identity, but not signal intensity information.

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.

Environmental sensing, information transfer, and cellular decision-making

The recognition that gene expression can be substantially stochastic poses the question of how cells respond to dynamic environments using biochemistry that itself fluctuates. The study of cellular decision-making aims to solve this puzzle by focusing on quantitative understanding of the variation seen across isogenic populations in response to extracellular change. This behaviour is complex, and a theoretical framework within which to embed experimental results is needed. Here we review current approaches, with an emphasis on information theory, sequential data processing, and optimality arguments. We conclude by highlighting some limitations of these techniques and the importance of connecting both theory and experiment to measures of fitness.

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.

Secreting and sensing the same molecule allows cells to achieve versatile social behaviors

Cells that secrete and sense the same signaling molecule are ubiquitous. To uncover the functional capabilities of the core "secrete-and-sense" circuit motif shared by these cells, we engineered yeast to secrete and sense the mating pheromone. Perturbing each circuit element revealed parameters that control the degree to which the cell communicated with itself versus with its neighbors. This tunable interplay of self-communication and neighbor communication enables cells to span a diverse repertoire of cellular behaviors. These include a cell being asocial by responding only to itself and social through quorum sensing, and an isogenic population of cells splitting into social and asocial subpopulations. A mathematical model explained these behaviors. The versatility of the secrete-and-sense circuit motif may explain its recurrence across species.

Negative feedback self-regulation contributes to robust and high-fidelity transmembrane signal transduction

We present a minimal motif model for transmembrane cell signalling. The model assumes signalling events taking place in spatially distributed nanoclusters regulated by a birth/death dynamics. The combination of these spatio-temporal aspects can be modulated to provide a robust and high-fidelity response behaviour without invoking sophisticated modelling of the signalling process as a sequence of cascade reactions and fine-tuned parameters. Our results show that the fact that the distributed signalling events take place in nanoclusters with a finite lifetime regulated by local production is sufficient to obtain a robust and high-fidelity response.

Systems biology. How information theory handles cell signaling and uncertainty

Information theory allows analyses of cell signaling capabilities without necessarily requiring detailed knowledge of the signaling networks.

Effects of multiple enzyme-substrate interactions in basic units of cellular signal processing

Covalent modification cycles are a ubiquitous feature of cellular signalling networks. In these systems, the interaction of an active enzyme with the unmodified form of its substrate is essential for signalling to occur. However, this interaction is not necessarily the only enzyme-substrate interaction possible. In this paper, we analyse the behaviour of a basic model of signalling in which additional, non-essential enzyme-substrate interactions are possible. These interactions include those between the inactive form of an enzyme and its substrate, and between the active form of an enzyme and its product. We find that these additional interactions can result in increased sensitivity and biphasic responses, respectively. The dynamics of the responses are also significantly altered by the presence of additional interactions. Finally, we evaluate the consequences of these interactions in two variations of our basic model, involving double modification of substrate and scaffold-mediated signalling, respectively. We conclude that the molecular details of protein-protein interactions are important in determining the signalling properties of enzymatic signalling pathways.