Environmental sensing, information transfer, and cellular decision-making

Information Processing in Biochemical Networks

Living systems are characterized by controlled flows of matter, energy, and information. While the biophysics community has productively engaged with the first two, addressing information flows has been more challenging, with some scattered success in evolutionary theory and a more coherent track record in neuroscience. Nevertheless, interdisciplinary work of the past two decades at the interface of biophysics, quantitative biology, and engineering has led to an emerging mathematical language for describing information flows at the molecular scale. This is where the central processes of life unfold: from detection and transduction of environmental signals to the readout or copying of genetic information and the triggering of adaptive cellular responses. Such processes are coordinated by complex biochemical reaction networks that operate at room temperature, are out of equilibrium, and use low copy numbers of diverse molecular species with limited interaction specificity. Here we review how flows of information through biochemical networks can be formalized using information-theoretic quantities, quantified from data, and computed within various modeling frameworks. Optimization of information flows is presented as a candidate design principle that navigates the relevant time, energy, crosstalk, and metabolic constraints to predict reliable cellular signaling and gene regulation architectures built of individually noisy components.

Individual yeast cells signal at different levels but each with good precision

Different isogenic cells exhibit different responses to the same extracellular signals. Several authors assumed that this variation arose from stochastic signalling noise with the implication that single eukaryotic cells could not detect their surroundings accurately, but work by us and others has shown that the variation is dominated instead by persistent cell-to-cell differences. Here, we analysed previously published data to quantify the sources of variation in pheromone-induced gene expression in Saccharomyces cerevisiae. We found that 91% of response variation was due to stable cell-to-cell differences, 8% from experimental measurement error, and 1% from signalling noise and expression noise. Low noise enabled precise signalling; individual cells could transmit over 3 bits of information through the pheromone response system and so respond differently to eight different pheromone concentrations. Additionally, if individual cells could reference their responses against constitutively expressed proteins, then cells could determine absolute pheromone concentrations with 2 bits of accuracy. These results help explain how individual yeast cells can accurately sense and respond to different extracellular pheromone concentrations.

Release of extracellular DNA by Pseudomonas sp. as a major determinant for biofilm switching and an early indicator for cell population control

In Pseudomonas sp., the switch from planktonic to sessile state is driven by extracellular DNA release. We observed a subpopulation of cells associated with eDNA in the planktonic phase, as indicated by propidium iodide staining. Surprisingly, the size of this subpopulation was directly correlated with the overall biofilm-forming capacity of the population. This challenges the prevailing understanding of phenotypic switching and confirms that biofilm formation in Pseudomonas is a collective process governed by eDNA release. Automated flow cytometry tracked the process, and PI-positive cells were identified as an early indicator of biofilm formation. Automated glucose pulsing successfully reduced biofilm formation by interfering with PI-positive cell proliferation. This study provides insights into the collective determinants of biofilm switching in Pseudomonas putida and introduces a potential strategy for controlling biofilm formation.

Inter-organ correlations in inflammation regulation: a novel biological paradigm in a murine model

Interactions between immune system constituents are mediated through direct contact or the transfer of mediators. The study aimed to assess the correlation between system components and out-of-body signals in a model of liver inflammation. In the first experiment, mice injected with Concanavalin A (ConA) were housed in a cage with a tube on top containing healthy livers or livers harvested from mice injected with ConA. In the second experiment, mice were housed in a cage with a tube that contained splenocytes harvested from naïve donors or from naïve donors treated in vitro with dexamethasone. Mice were tested for serum aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels. External whole livers and spleens influenced the immune-mediated inflammatory response of mice. When ConA-injected mice were housed in cages with tubes containing livers harvested from naïve mice, ALT serum levels were significantly reduced. ALT serum levels were significantly elevated when mice were kept in cages with a tube containing livers harvested from ConA-injected mice. In the second part of the experiment, mice injected with ConA and housed in cages with a tube on top that contained splenocytes harvested from naïve donors had increased ALT levels. Similarly, mice with tubes containing splenocytes from dexamethasone-treated naïve donors also showed elevated ALT levels. The data suggest that correlations between immune system constituents can be established using out-of-body whole livers or spleens without contact or transfer of mediators.

Engineering Sequestration-Based Biomolecular Classifiers with Shared Resources

Constructing molecular classifiers that enable cells to recognize linear and nonlinear input patterns would expand the biocomputational capabilities of engineered cells, thereby unlocking their potential in diagnostics and therapeutic applications. While several biomolecular classifier schemes have been designed, the effects of biological constraints such as resource limitation and competitive binding on the function of those classifiers have been left unexplored. Here, we first demonstrate the design of a sigma factor-based perceptron as a molecular classifier working based on the principles of molecular sequestration between the sigma factor and its antisigma molecule. We then investigate how the output of the biomolecular perceptron, i.e., its response pattern or decision boundary, is affected by the competitive binding of sigma factors to a pool of shared and limited resources of core RNA polymerase. Finally, we reveal the influence of sharing limited resources on multilayer perceptron neural networks and outline design principles that enable the construction of nonlinear classifiers using sigma-based biomolecular neural networks in the presence of competitive resource-sharing effects.

Fitness cost associated with cell phenotypic switching drives population diversification dynamics and controllability

Isogenic cell populations can cope with stress conditions by switching to alternative phenotypes. Even if it can lead to increased fitness in a natural context, this feature is typically unwanted for a range of applications (e.g., bioproduction, synthetic biology, and biomedicine) where it tends to make cellular response unpredictable. However, little is known about the diversification profiles that can be adopted by a cell population. Here, we characterize the diversification dynamics for various systems (bacteria and yeast) and for different phenotypes (utilization of alternative carbon sources, general stress response and more complex development patterns). Our results suggest that the diversification dynamics and the fitness cost associated with cell switching are coupled. To quantify the contribution of the switching cost on population dynamics, we design a stochastic model that let us reproduce the dynamics observed experimentally and identify three diversification regimes, i.e., constrained (at low switching cost), dispersed (at medium and high switching cost), and bursty (for very high switching cost). Furthermore, we use a cell-machine interface called Segregostat to demonstrate that different levels of control can be applied to these diversification regimes, enabling applications involving more precise cellular responses.

Advances in automated and reactive flow cytometry for synthetic biotechnology

Automated flow cytometry (FC) has been initially considered for bioprocess monitoring and optimization. More recently, new physical and software interfaces have been made available, facilitating the access to this technology for labs and industries. It also comes with new capabilities, such as being able to act on the cultivation conditions based on population data. This approach, known as reactive FC, extended the range of applications of automated FC to bioprocess control and the stabilization of cocultures, but also to the broad field of synthetic and systems biology for the characterization of gene circuits. However, several issues must be addressed before automated and reactive FC can be considered standard and modular technologies.

Computational capabilities of a multicellular reservoir computing system

The capacity of cells to process information is currently used to design cell-based tools for ecological, industrial, and biomedical applications such as detecting dangerous chemicals or for bioremediation. In most applications, individual cells are used as the information processing unit. However, single cell engineering is limited by the necessary molecular complexity and the accompanying metabolic burden of synthetic circuits. To overcome these limitations, synthetic biologists have begun engineering multicellular systems that combine cells with designed subfunctions. To further advance information processing in synthetic multicellular systems, we introduce the application of reservoir computing. Reservoir computers (RCs) approximate a temporal signal processing task via a fixed-rule dynamic network (the reservoir) with a regression-based readout. Importantly, RCs eliminate the need of network rewiring, as different tasks can be approximated with the same reservoir. Previous work has already demonstrated the capacity of single cells, as well as populations of neurons, to act as reservoirs. In this work, we extend reservoir computing in multicellular populations with the widespread mechanism of diffusion-based cell-to-cell signaling. As a proof-of-concept, we simulated a reservoir made of a 3D community of cells communicating via diffusible molecules and used it to approximate a range of binary signal processing tasks, focusing on two benchmark functions-computing median and parity functions from binary input signals. We demonstrate that a diffusion-based multicellular reservoir is a feasible synthetic framework for performing complex temporal computing tasks that provides a computational advantage over single cell reservoirs. We also identified a number of biological properties that can affect the computational performance of these processing systems.

Cell Decision Making through the Lens of Bayesian Learning

Cell decision making refers to the process by which cells gather information from their local microenvironment and regulate their internal states to create appropriate responses. Microenvironmental cell sensing plays a key role in this process. Our hypothesis is that cell decision-making regulation is dictated by Bayesian learning. In this article, we explore the implications of this hypothesis for internal state temporal evolution. By using a timescale separation between internal and external variables on the mesoscopic scale, we derive a hierarchical Fokker-Planck equation for cell-microenvironment dynamics. By combining this with the Bayesian learning hypothesis, we find that changes in microenvironmental entropy dominate the cell state probability distribution. Finally, we use these ideas to understand how cell sensing impacts cell decision making. Notably, our formalism allows us to understand cell state dynamics even without exact biochemical information about cell sensing processes by considering a few key parameters.

Targeted Quantification of Protein Phosphorylation and Its Contributions towards Mathematical Modeling of Signaling Pathways

Post-translational modifications (PTMs) are key regulatory mechanisms that can control protein function. Of these, phosphorylation is the most common and widely studied. Because of its importance in regulating cell signaling, precise and accurate measurements of protein phosphorylation across wide dynamic ranges are crucial to understanding how signaling pathways function. Although immunological assays are commonly used to detect phosphoproteins, their lack of sensitivity, specificity, and selectivity often make them unreliable for quantitative measurements of complex biological samples. Recent advances in Mass Spectrometry (MS)-based targeted proteomics have made it a more useful approach than immunoassays for studying the dynamics of protein phosphorylation. Selected reaction monitoring (SRM)-also known as multiple reaction monitoring (MRM)-and parallel reaction monitoring (PRM) can quantify relative and absolute abundances of protein phosphorylation in multiplexed fashions targeting specific pathways. In addition, the refinement of these tools by enrichment and fractionation strategies has improved measurement of phosphorylation of low-abundance proteins. The quantitative data generated are particularly useful for building and parameterizing mathematical models of complex phospho-signaling pathways. Potentially, these models can provide a framework for linking analytical measurements of clinical samples to better diagnosis and treatment of disease.

Fluctuation relations for irreversible emergence of information

Information theory and Thermodynamics have developed closer in the last years, with a growing application palette in which the formal equivalence between the Shannon and Gibbs entropies is exploited. The main barrier to connect both disciplines is the fact that information does not imply a dynamics, whereas thermodynamic systems unfold with time, often away from equilibrium. Here, we analyze chain-like systems comprising linear sequences of physical objects carrying symbolic meaning. We show that, after defining a reading direction, both reversible and irreversible informations emerge naturally from the principle of microscopic reversibility in the evolution of the chains driven by a protocol. We find fluctuation equalities that relate entropy, the relevant concept in communication, and energy, the thermodynamically significant quantity, examined along sequences whose content evolves under writing and revision protocols. Our results are applicable to nanoscale chains, where information transfer is subject to thermal noise, and extendable to virtually any communication system.

Efficient information coding and degeneracy in the nervous system

Efficient information coding (EIC) is a universal biological framework rooted in the fundamental principle that system responses should match their natural stimulus statistics for maximizing environmental information. Quantitatively assessed through information theory, such adaptation to the environment occurs at all biological levels and timescales. The context dependence of environmental stimuli and the need for stable adaptations make EIC a daunting task. We argue that biological complexity is the principal architect that subserves deft execution of stable EIC. Complexity in a system is characterized by several functionally segregated subsystems that show a high degree of functional integration when they interact with each other. Complex biological systems manifest heterogeneities and degeneracy, wherein structurally different subsystems could interact to yield the same functional outcome. We argue that complex systems offer several choices that effectively implement EIC and homeostasis for each of the different contexts encountered by the system.

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.

Pathway-resolved decomposition demonstrates correlation and noise dependencies of redundant information processing in recurrent feed-forward topologies

In a biochemical assay that converts fan-in networks into feed-forward loops (FFLs), we show that the inter-regulator redundant information about the output gene product can be decomposed into finer components, mediated by the constituent pathways. Variance-based information within the linear noise regime facilitates quantifying these submodular redundancies. Contrary to the conventional wisdom on information decomposition, we report that information redundancy depends nontrivially on inter-regulator correlation. For the type-1 coherent (C1) and incoherent (I1) FFLs, the direct regulatory path-mediated redundancy is certainly correlation independent. However, components induced by the indirect regulatory path and interpathway interference are correlation dependent in (non)linear fashion. The trade-off between information redundancy and similarly decomposable extrinsic noise from input to output node has been demonstrated for the pathways and full motifs. Our analyses suggest that the interpathway cross redundancy positively and negatively influences the superposition of elementary redundancies in the C1- and I1-FFLs, respectively. Their corresponding total extrinsic noise is produced by the weighted sum and difference of the pathway-specific components. We find that the I1-FFL is able to manufacture more varied redundancy and extrinsic noise responses compared to the C1-FFL. Underlying the differing characteristics of the composite metrics across FFL variants, there exist uniformly behaving pathway-dependent elements. The decomposition framework has been meticulously explored in biologically rational parametric realizations through analytical estimates and stochastic simulations.

Escherichia coli chemotaxis is information limited

Organisms acquire and use information from their environment to guide their behaviour. However, it is unclear whether this information quantitatively limits their behavioural performance. Here, we relate information to the ability of Escherichia coli to navigate up chemical gradients, the behaviour known as chemotaxis. First, we derive a theoretical limit on the speed with which cells climb gradients, given the rate at which they acquire information. Next, we measure cells' gradient-climbing speeds and the rate of information acquisition by their chemotaxis signaling pathway. We find that E. coli make behavioural decisions with much less than the one bit required to determine whether they are swimming up-gradient. Some of this information is irrelevant to gradient climbing, and some is lost in communication to behaviour. Despite these limitations, E. coli climb gradients at speeds within a factor of two of the theoretical bound. Thus, information can limit the performance of an organism, and sensory-motor pathways may have evolved to efficiently use information acquired from the environment.

Design and development of engineered receptors for cell and tissue engineering

Advances in synthetic biology have provided genetic tools to reprogram cells to obtain desired cellular functions that include tools to enable the customization of cells to sense an extracellular signal and respond with a desired output. These include a variety of engineered receptors capable of transmembrane signaling that transmit information from outside of the cell to inside when specific ligands bind to them. Recent advances in synthetic receptor engineering have enabled the reprogramming of cell and tissue behavior, controlling cell fate decisions, and providing new vehicles for therapeutic delivery.

Cellular Signaling beyond the Wiener-Kolmogorov Limit

Accurate propagation of signals through stochastic biochemical networks involves significant expenditure of cellular resources. The same is true for regulatory mechanisms that suppress fluctuations in biomolecular populations. Wiener-Kolmogorov (WK) optimal noise filter theory, originally developed for engineering problems, has recently emerged as a valuable tool to estimate the maximum performance achievable in such biological systems for a given metabolic cost. However, WK theory has one assumption that potentially limits its applicability: it relies on a linear, continuum description of the reaction dynamics. Despite this, up to now no explicit test of the theory in nonlinear signaling systems with discrete molecular populations has ever seen performance beyond the WK bound. Here we report the first direct evidence of the bound being broken. To accomplish this, we develop a theoretical framework for multilevel signaling cascades, including the possibility of feedback interactions between input and output. In the absence of feedback, we introduce an analytical approach that allows us to calculate exact moments of the stationary distribution for a nonlinear system. With feedback, we rely on numerical solutions of the system's master equation. The results show WK violations in two common network motifs: a two-level signaling cascade and a negative feedback loop. However, the magnitude of the violation is biologically negligible, particularly in the parameter regime where signaling is most effective. The results demonstrate that while WK theory does not provide strict bounds, its predictions for performance limits are excellent approximations, even for nonlinear systems.

Mapping the dynamic transfer functions of eukaryotic gene regulation

Biological information can be encoded within the dynamics of signaling components, which has been implicated in a broad range of physiological processes including stress response, oncogenesis, and stem cell differentiation. To study the complexity of information transfer across the eukaryotic promoter, we screened 119 dynamic conditions-modulating the pulse frequency, amplitude, and pulse width of light-regulating the binding of an epigenome editor to a fluorescent reporter. This system revealed tunable gene expression and filtering behaviors and provided a quantification of the limit to the amount of information that can be reliably transferred across a single promoter as ∼1.7 bits. Using a library of over 100 orthogonal chromatin regulators, we further determined that chromatin state could be used to tune mutual information and expression levels, as well as completely alter the input-output transfer function of the promoter. This system unlocks the information-rich content of eukaryotic gene regulation.

Evaluation of Lee et al.: Clarity and interpretation of mutual information in promoter transfer functions

One snapshot of the peer review process for "Mapping the dynamic transfer functions of eukaryotic gene regulation" (Lee et al., 2021) appears below.

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.

STIM1, STIM2, and PDI Participate in Cellular Fate Decisions in Low Energy Availability Induced by 3-NP in Male Rats

Impairment in the energetic function of mitochondria is seen in many neurologic disorders like neurodegeneration. It disrupts ATP production, gives rise to oxidative stress, and ultimately challenges the viability of neurons. In this situation, neural cells use complex crosstalk between various subcellular elements to make live-or-die decisions about their fate. This study aimed to describe a part of the molecular changes and the outcome of the cellular decision during an energy crisis in neural cells in a time-dependent manner in the striatum. Adult male rats were treated with single or multiple 3-nitropropionic acid (3-NP) doses, a mitochondrial toxin, for 1 to 5 days. We found that protein disulfide isomerase (PDI) activity was decreased on the third day and remained lower than the control group up to the fifth day. However, on the day 1 and day 2 of 3-NP treatment, the stromal interaction molecule (STIM) 1 and STIM2 significantly decreased. On the third day, STIM1 and STIM2 were increased and reached the level of controls and remained the same up to the fifth day. In this condition, cell death was significantly higher than the controls from the third day up to the fifth day. We also showed that even a single dose of 3-NP reduced the brain volume. These data suggest that the STIM1, STIM2, and PDI activity changes may be involved in the outcome of cellular fate decisions. It also suggests that cells may reduce STIM1 and STIM2 as a defense mechanism against low energy availability.

Microswimmers learning chemotaxis with genetic algorithms

Various microorganisms and some mammalian cells are able to swim in viscous fluids by performing nonreciprocal body deformations, such as rotating attached flagella or by distorting their entire body. In order to perform chemotaxis (i.e., to move toward and to stay at high concentrations of nutrients), they adapt their swimming gaits in a nontrivial manner. Here, we propose a computational model, which features autonomous shape adaptation of microswimmers moving in one dimension toward high field concentrations. As an internal decision-making machinery, we use artificial neural networks, which control the motion of the microswimmer. We present two methods to measure chemical gradients, spatial and temporal sensing, as known for swimming mammalian cells and bacteria, respectively. Using the genetic algorithm NeuroEvolution of Augmenting Topologies, surprisingly simple neural networks evolve. These networks control the shape deformations of the microswimmers and allow them to navigate in static and complex time-dependent chemical environments. By introducing noisy signal transmission in the neural network, the well-known biased run-and-tumble motion emerges. Our work demonstrates that the evolution of a simple and interpretable internal decision-making machinery coupled to the environment allows navigation in diverse chemical landscapes. These findings are of relevance for intracellular biochemical sensing mechanisms of single cells or for the simple nervous system of small multicellular organisms such as Caenorhabditis elegans.

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?

Signaling pathways have an inherent need for noise to acquire information

BACKGROUND

All living systems acquire information about their environment. At the cellular level, they do so through signaling pathways. Such pathways rely on reversible binding interactions between molecules that detect and transmit the presence of an extracellular cue or signal to the cell's interior. These interactions are inherently stochastic and thus noisy. On the one hand, noise can cause a signaling pathway to produce the same response for different stimuli, which reduces the amount of information a pathway acquires. On the other hand, in processes such as stochastic resonance, noise can improve the detection of weak stimuli and thus the acquisition of information. It is not clear whether the kinetic parameters that determine a pathway's operation cause noise to reduce or increase the acquisition of information.

RESULTS

We analyze how the kinetic properties of the reversible binding interactions used by signaling pathways affect the relationship between noise, the response to a signal, and information acquisition. Our results show that, under a wide range of biologically sensible parameter values, a noisy dynamic of reversible binding interactions is necessary to produce distinct responses to different stimuli. As a consequence, noise is indispensable for the acquisition of information in signaling pathways.

CONCLUSIONS

Our observations go beyond previous work by showing that noise plays a positive role in signaling pathways, demonstrating that noise is essential when such pathways acquire information.

Rosa26 docking sites for investigating genetic circuit silencing in stem cells

Approaches in mammalian synthetic biology have transformed how cells can be programmed to have reliable and predictable behavior, however, the majority of mammalian synthetic biology has been accomplished using immortalized cell lines that are easy to grow and easy to transfect. Genetic circuits that integrate into the genome of these immortalized cell lines remain functional for many generations, often for the lifetime of the cells, yet when genetic circuits are integrated into the genome of stem cells gene silencing is observed within a few generations. To investigate the reactivation of silenced genetic circuits in stem cells, the Rosa26 locus of mouse pluripotent stem cells was modified to contain docking sites for site-specific integration of genetic circuits. We show that the silencing of genetic circuits can be reversed with the addition of sodium butyrate, a histone deacetylase inhibitor. These findings demonstrate an approach to reactivate the function of genetic circuits in pluripotent stem cells to ensure robust function over many generations. Altogether, this work introduces an approach to overcome the silencing of genetic circuits in pluripotent stem cells that may enable the use of genetic circuits in pluripotent stem cells for long-term function.

Information transmission from NFkB signaling dynamics to gene expression

The dynamic signal encoding paradigm suggests that information flows from the extracellular environment into specific signaling patterns (encoding) that are then read by downstream effectors to control cellular behavior. Previous work empirically quantified the information content of dynamic signaling patterns. However, whether this information can be faithfully transmitted to the gene expression level is unclear. Here we used NFkB signaling as a model to understand the accuracy of information transmission from signaling dynamics into gene expression. Using a detailed mathematical model, we simulated realistic NFkB signaling patterns with different degrees of variability. The NFkB patterns were used as an input to a simple gene expression model. Analysis of information transmission between ligand and NFkB and ligand and gene expression allows us to determine information loss in transmission between receptors to dynamic signaling patterns and between signaling dynamics to gene expression. Information loss could occur due to biochemical noise or due to a lack of specificity. We found that noise-free gene expression has very little information loss suggesting that gene expression can preserve specificity in NFkB patterns. As expected, the addition of noise to the gene expression model results in information loss. Interestingly, this effect can be mitigated by a specific choice of parameters that can substantially reduce information loss due to biochemical noise during gene expression. Overall our results show that the cellular capacity for information transmission from dynamic signaling patterns to gene expression can be high enough to preserve ligand specificity and thereby the accuracy of cellular response to environmental cues.

First-principles prediction of the information processing capacity of a simple genetic circuit

Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to survive in changing environments. Recent work has explored the use of information theory as a framework to understand the accuracy with which cells can ascertain the state of their surroundings. Yet the predictive power of these approaches is limited and has not been rigorously tested using precision measurements. To that end, we generate a minimal model for a simple genetic circuit in which all parameter values for the model come from independently published data sets. We then predict the information processing capacity of the genetic circuit for a suite of biophysical parameters such as protein copy number and protein-DNA affinity. We compare these parameter-free predictions with an experimental determination of protein expression distributions and the resulting information processing capacity of E. coli cells. We find that our minimal model captures the scaling of the cell-to-cell variability in the data and the inferred information processing capacity of our simple genetic circuit up to a systematic deviation.

A mechanism for hunchback promoters to readout morphogenetic positional information in less than a minute

Cell fate decisions in the fly embryo are rapid: hunchback genes decide in minutes whether nuclei follow the anterior/posterior developmental blueprint by reading out positional information in the Bicoid morphogen. This developmental system is a prototype of regulatory decision processes that combine speed and accuracy. Traditional arguments based on fixed-time sampling of Bicoid concentration indicate that an accurate readout is impossible within the experimental times. This raises the general issue of how speed-accuracy tradeoffs are achieved. Here, we compare fixed-time to on-the-fly decisions, based on comparing the likelihoods of anterior/posterior locations. We found that these more efficient schemes complete reliable cell fate decisions within the short embryological timescales. We discuss the influence of promoter architectures on decision times and error rates, present concrete examples that rapidly readout the morphogen, and predictions for new experiments. Lastly, we suggest a simple mechanism for RNA production and degradation that approximates the log-likelihood function.

Receptor Organization Determines the Limits of Single-Cell Source Location Detection

Many types of cells require the ability to pinpoint the location of an external stimulus from the arrival of diffusing signaling molecules at cell-surface receptors. How does the organization (number and spatial configuration) of these receptors shape the limit of a cell's ability to infer the source location? In the idealized scenario of a spherical cell, we apply asymptotic analysis to compute splitting probabilities between individual receptors and formulate an information-theoretic framework to quantify the role of receptor organization. Clustered configurations of receptors provide an advantage in detecting sources aligned with the clusters, suggesting a possible multiscale mechanism for single-cell source inference.

Short Residence Times of DNA-Bound Transcription Factors Can Reduce Gene Expression Noise and Increase the Transmission of Information in a Gene Regulation System

Gene expression noise is not just ubiquitous but also variable, and we still do not understand some of the most elementary factors that affect it. Among them is the residence time of a transcription factor (TF) on DNA, the mean time that a DNA-bound TF remains bound. Here, we use a stochastic model of transcriptional regulation to study how residence time affects the gene expression noise that arises when a TF induces gene expression. We find that the effect of residence time on gene expression noise depends on the TF’s concentration and its affinity to DNA, which determine the level of induction of the gene. At high levels of induction, residence time has no effect on gene expression noise. However, as the level of induction decreases, short residence times reduce gene expression noise. The reason is that fast on-off TF binding dynamics prevent long periods where proteins are predominantly synthesized or degraded, which can cause excessive fluctuations in gene expression. As a consequence, short residence times can help a gene regulation system acquire information about the cellular environment it operates in. Our predictions are consistent with the observation that experimentally measured residence times are usually modest and lie between seconds to minutes.

Intracellular Energy Variability Modulates Cellular Decision-Making Capacity

Cells generate phenotypic diversity both during development and in response to stressful and changing environments, aiding survival. Functionally vital cell fate decisions from a range of phenotypic choices are made by regulatory networks, the dynamics of which rely on gene expression and hence depend on the cellular energy budget (and particularly ATP levels). However, despite pronounced cell-to-cell ATP differences observed across biological systems, the influence of energy availability on regulatory network dynamics is often overlooked as a cellular decision-making modulator, limiting our knowledge of how energy budgets affect cell behaviour. Here, we consider a mathematical model of a highly generalisable, ATP-dependent, decision-making regulatory network, and show that cell-to-cell ATP variability changes the sets of decisions a cell can make. Our model shows that increasing intracellular energy levels can increase the number of supported stable phenotypes, corresponding to increased decision-making capacity. Model cells with sub-threshold intracellular energy are limited to a singular phenotype, forcing the adoption of a specific cell fate. We suggest that energetic differences between cells may be an important consideration to help explain observed variability in cellular decision-making across biological systems.

Kalman-like Self-Tuned Sensitivity in Biophysical Sensing

Living organisms need to be sensitive to a changing environment while also ignoring uninformative environmental fluctuations. Here, we argue that living cells can navigate these conflicting demands by dynamically tuning their environmental sensitivity. We analyze the circadian clock in Synechococcus elongatus, showing that clock-metabolism coupling can detect mismatch between clock predictions and the day-night light cycle, temporarily raise the clock's sensitivity to light changes, and thus re-entraining faster. We find analogous behavior in recent experiments on switching between slow and fast osmotic-stress-response pathways in yeast. In both cases, cells can raise their sensitivity to new external information in epochs of frequent challenging stress, much like a Kalman filter with adaptive gain in signal processing. Our work suggests a new class of experiments that probe the history dependence of environmental sensitivity in biophysical sensing mechanisms.

Emergent microscale gradients give rise to metabolic cross-feeding and antibiotic tolerance in clonal bacterial populations

Bacteria often live in spatially structured groups such as biofilms. In these groups, cells can collectively generate gradients through the uptake and release of compounds. In turn, individual cells adapt their activities to the environment shaped by the whole group. Here, we studied how these processes can generate phenotypic variation in clonal populations and how this variation contributes to the resilience of the population to antibiotics. We grew two-dimensional populations of Escherichia coli in microfluidic chambers where limiting amounts of glucose were supplied from one side. We found that the collective metabolic activity of cells created microscale gradients where nutrient concentration varied over a few cell lengths. As a result, growth rates and gene expression levels varied strongly between neighbouring cells. Furthermore, we found evidence for a metabolic cross-feeding interaction between glucose-fermenting and acetate-respiring subpopulations. Finally, we found that subpopulations of cells were able to survive an antibiotic pulse that was lethal in well-mixed conditions, likely due to the presence of a slow-growing subpopulation. Our work shows that emergent metabolic gradients can have important consequences for the functionality of bacterial populations as they create opportunities for metabolic interactions and increase the populations' tolerance to environmental stressors. This article is part of a discussion meeting issue 'Single cell ecology'.

Maximal information transmission is compatible with ultrasensitive biological pathways

Cells are often considered input-output devices that maximize the transmission of information by converting extracellular stimuli (input) via signaling pathways (communication channel) to cell behavior (output). However, in biological systems outputs might feed back into inputs due to cell motility, and the biological channel can change by mutations during evolution. Here, we show that the conventional channel capacity obtained by optimizing the input distribution for a fixed channel may not reflect the global optimum. In a new approach we analytically identify both input distributions and input-output curves that optimally transmit information, given constraints from noise and the dynamic range of the channel. We find a universal optimal input distribution only depending on the input noise, and we generalize our formalism to multiple outputs (or inputs). Applying our formalism to Escherichia coli chemotaxis, we find that its pathway is compatible with optimal information transmission despite the ultrasensitive rotary motors.

Fitness Gain of Individually Sensed Information by Cells

Mutual information and its causal variant, directed information, have been widely used to quantitatively characterize the performance of biological sensing and information transduction. However, once coupled with selection in response to decision-making, the sensing signal could have more or less evolutionary value than its mutual or directed information. In this work, we show that an individually sensed signal always has a better fitness value, on average, than its mutual or directed information. The fitness gain, which satisfies fluctuation relations (FRs), is attributed to the selection of organisms in a population that obtain a better sensing signal by chance. A new quantity, similar to the coarse-grained entropy production in information thermodynamics, is introduced to quantify the total fitness gain from individual sensing, which also satisfies FRs. Using this quantity, the optimizing fitness gain of individual sensing is shown to be related to fidelity allocations for individual environmental histories. Our results are supplemented by numerical verifications of FRs, and a discussion on how this problem is linked to information encoding and decoding.

On Information Extraction and Decoding Mechanisms Improved by Noisy Amplification in Signaling Pathways

The cells need to process information about extracellular stimuli. They encode, transmit and decode the information to elicit an appropriate response. Studies aimed at understanding how such information is decoded in the signaling pathways to generate a specific cellular response have become essential. Eukaryotic cells decode information through two different mechanisms: the feed-forward loop and the promoter affinity. Here, we investigate how these two mechanisms improve information transmission. A detailed comparison is made between the stochastic model of the MAPK/ERK pathway and a stochastic minimal decoding model. The maximal amount of transmittable information was computed. The results suggest that the decoding mechanism of the MAPK/ERK pathway improve the channel capacity because it behaves as a noisy amplifier. We show a positive dependence between the noisy amplification and the amount of information extracted. Additionally, we show that the extrinsic noise can be tuned to improve information transmission. This investigation has revealed that the feed-forward loop and the promoter affinity motifs extract information thanks to processes of amplification and noise addition. Moreover, the channel capacity is enhanced when both decoding mechanisms are coupled. Altogether, these findings suggest novel characteristics in how decoding mechanisms improve information transmission.

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.

Metabolic activity affects the response of single cells to a nutrient switch in structured populations

Microbes live in ever-changing environments where they need to adapt their metabolism to different nutrient conditions. Many studies have characterized the response of genetically identical cells to nutrient switches in homogeneous cultures; however, in nature, microbes often live in spatially structured groups such as biofilms where cells can create metabolic gradients by consuming and releasing nutrients. Consequently, cells experience different local microenvironments and vary in their phenotype. How does this phenotypic variation affect the ability of cells to cope with nutrient switches? Here, we address this question by growing dense populations of Escherichia coli in microfluidic chambers and studying a switch from glucose to acetate at the single-cell level. Before the switch, cells vary in their metabolic activity: some grow on glucose, while others cross-feed on acetate. After the switch, only few cells can resume growth after a period of lag. The probability to resume growth depends on a cells' phenotype prior to the switch: it is highest for cells cross-feeding on acetate, while it depends in a non-monotonic way on the growth rate for cells growing on glucose. Our results suggest that the strong phenotypic variation in spatially structured populations might enhance their ability to cope with fluctuating environments.

Exploring the information transmission properties of noise-induced dynamics: application to glioma differentiation

Background

Cells operate in an uncertain environment, where critical cell decisions must be enacted in the presence of biochemical noise. Information theory can measure the extent to which such noise perturbs normal cellular function, in which cells must perceive environmental cues and relay signals accurately to make timely and informed decisions. Using multivariate response data can greatly improve estimates of the latent information content underlying important cell fates, like differentiation.

Results

We undertake an information theoretic analysis of two stochastic models concerning glioma differentiation therapy, an alternative cancer treatment modality whose underlying intracellular mechanisms remain poorly understood. Discernible changes in response dynamics, as captured by summary measures, were observed at low noise levels. Mitigating certain feedback mechanisms present in the signaling network improved information transmission overall, as did targeted subsampling and clustering of response dynamics.

Conclusion

Computing the channel capacity of noisy signaling pathways present great probative value in uncovering the prevalent trends in noise-induced dynamics. Areas of high dynamical variation can provide concise snapshots of informative system behavior that may otherwise be overlooked. Through this approach, we can examine the delicate interplay between noise and information, from signal to response, through the observed behavior of relevant system components.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2970-7) contains supplementary material, which is available to authorized users.

Counting growth factors in single cells with infrared quantum dots to measure discrete stimulation distributions

The distribution of single-cell properties across a population of cells can be measured using diverse tools, but no technology directly quantifies the biochemical stimulation events regulating these properties. Here we report digital counting of growth factors in single cells using fluorescent quantum dots and calibrated three-dimensional deconvolution microscopy (QDC-3DM) to reveal physiologically relevant cell stimulation distributions. We calibrate the fluorescence intensities of individual compact quantum dots labeled with epidermal growth factor (EGF) and demonstrate the necessity of near-infrared emission to overcome intrinsic cellular autofluoresence at the single-molecule level. When applied to human triple-negative breast cancer cells, we observe proportionality between stimulation and both receptor internalization and inhibitor response, reflecting stimulation heterogeneity contributions to intrinsic variability. We anticipate that QDC-3DM can be applied to analyze any peptidic ligand to reveal single-cell correlations between external stimulation and phenotypic variability, cell fate, and drug response.

Measuring growth factors in single cells at physiologically relevant stimulation doses is challenging. Here the authors use fluorescent quantum dots and calibrated three-dimensional deconvolution microscopy to digitally count growth factors in single cells and reveal stimulation distributions in cancer cells.

Receptor crosstalk improves concentration sensing of multiple ligands

Cells need to reliably sense external ligand concentrations to achieve various biological functions such as chemotaxis or signaling. The molecular recognition of ligands by surface receptors is degenerate in many systems, leading to crosstalk between ligand-receptor pairs. Crosstalk is often thought of as a deviation from optimal specific recognition, as the binding of noncognate ligands can interfere with the detection of the receptor's cognate ligand, possibly leading to a false triggering of a downstream signaling pathway. Here we quantify the optimal precision of sensing the concentrations of multiple ligands by a collection of promiscuous receptors. We demonstrate that crosstalk can improve precision in concentration sensing and discrimination tasks. To achieve superior precision, the additional information about ligand concentrations contained in short binding events of the noncognate ligand should be exploited. We present a proofreading scheme to realize an approximate estimation of multiple ligand concentrations that reaches a precision close to the derived optimal bounds. Our results help rationalize the observed ubiquity of receptor crosstalk in molecular sensing.

Negative feedback increases information transmission, enabling bacteria to discriminate sublethal antibiotic concentrations

In the cell, noise constrains information transmission through signaling pathways and regulatory networks. There is growing evidence that the channel capacity of cellular pathways is limited to a few bits, questioning whether cells quantify external stimuli or rely on threshold detection and binary on/off decisions. Here, using fluorescence microscopy and information theory, we analyzed the ability of the transcriptional regulator TetR to sense and quantify the antibiotic tetracycline. The results showed that noise filtering by negative feedback increased information transmission up to 2 bits, generating a graded response able to discriminate different antibiotic concentrations. This response matched the antibiotic subinhibitory selection window, suggesting that information transmission through TetR is optimized to quantify sublethal antibiotic levels. Noise filtering by negative feedback may thus boost the discriminative power of cellular sensors, enabling signal quantification.

Decision-making of the benthic diatom Seminavis robusta searching for inorganic nutrients and pheromones

Microorganisms encounter a diversity of chemical stimuli that trigger individual responses and influence population dynamics. However, microbial behavior under the influence of different incentives and microbial decision-making is poorly understood. Benthic marine diatoms that react to sexual attractants as well as to nutrient gradients face such multiple constraints. Here, we document and model behavioral complexity and context-sensitive responses of these motile unicellular algae to sex pheromones and the nutrient silicate. Throughout the life cycle of the model diatom Seminavis robusta nutrient-starved cells localize sources of silicate by combined chemokinetic and chemotactic motility. However, with an increasing need for sex to restore the initial cell size, a change in behavior favoring the attraction-pheromone-guided search for a mating partner takes place. When sex becomes inevitable to prevent cell death, safeguard mechanisms are abandoned, and cells prioritize the search for mating partners. Such selection processes help to explain biofilm organization and to understand species interactions in complex communities.

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.

Sensitivity of asymmetric rate-dependent critical systems to initial conditions: Insights into cellular decision making

The work reported here aims to address the effects of time-dependent parameters and stochasticity on decision making in biological systems. We achieve this by extending previous studies that resorted to simple bifurcation normal forms, although in the present case we focus primarily on the issue of the system's sensitivity to initial conditions in the presence of two different noise distributions, Gaussian and Lévy. In addition, we also assess the impact of two-way sweeping at different rates through the critical region of a canonical Pitchfork bifurcation with a constant external asymmetry. The parallel with decision making in biocircuits is performed on this simple system since it is equivalent in its available states and dynamics to more complex genetic circuits published previously. Overall we verify that rate-dependent effects, previously reported as being important features of bifurcating systems, are specific to particular initial conditions. Processing of each starting state, which for the normal form underlying this study is akin to a classification task, is affected by the balance between sweeping speed through critical regions and the type of fluctuations added. For the heavy-tailed noise, two-way dynamic bifurcations are more efficient in processing the external signals, here understood to be jointly represented by the critical parameter profile and the external asymmetry amplitude, when compared to the system relying on escape dynamics. This is particular to the case when the system starts at an attractor not favored by the asymmetry and, in conjunction, when the sweeping amplitude is large.

Bottom-up approaches in synthetic biology and biomaterials for tissue engineering applications

Synthetic biologists use engineering principles to design and construct genetic circuits for programming cells with novel functions. A bottom-up approach is commonly used to design and construct genetic circuits by piecing together functional modules that are capable of reprogramming cells with novel behavior. While genetic circuits control cell operations through the tight regulation of gene expression, a diverse array of environmental factors within the extracellular space also has a significant impact on cell behavior. This extracellular space offers an addition route for synthetic biologists to apply their engineering principles to program cell-responsive modules within the extracellular space using biomaterials. In this review, we discuss how taking a bottom-up approach to build genetic circuits using DNA modules can be applied to biomaterials for controlling cell behavior from the extracellular milieu. We suggest that, by collectively controlling intrinsic and extrinsic signals in synthetic biology and biomaterials, tissue engineering outcomes can be improved.

Gonadotropin-releasing hormone signaling: An information theoretic approach

Gonadotropin-releasing hormone (GnRH) is a peptide hormone that mediates central control of reproduction, acting via G-protein coupled receptors that are primarily G_q coupled and mediate GnRH effects on the synthesis and secretion of luteinizing hormone and follicle-stimulating hormone. A great deal is known about the GnRH receptor signaling network but GnRH is secreted in short pulses and much less is known about how gonadotropes decode this pulsatile signal. Similarly, single cell measures reveal considerable cell-cell heterogeneity in responses to GnRH but the impact of this variability on signaling is largely unknown. Ordinary differential equation-based mathematical models have been used to explore the decoding of pulse dynamics and information theory-derived statistical measures are increasingly used to address the influence of cell-cell variability on the amount of information transferred by signaling pathways. Here, we describe both approaches for GnRH signaling, with emphasis on novel insights gained from the information theoretic approach and on the fundamental question of why GnRH is secreted in pulses.

Biophysical clocks face a trade-off between internal and external noise resistance

Many organisms use free running circadian clocks to anticipate the day night cycle. However, others organisms use simple stimulus-response strategies ('hourglass clocks') and it is not clear when such strategies are sufficient or even preferable to free running clocks. Here, we find that free running clocks, such as those found in the cyanobacterium Synechococcus elongatus and humans, can efficiently project out light intensity fluctuations due to weather patterns ('external noise') by exploiting their limit cycle attractor. However, such limit cycles are necessarily vulnerable to 'internal noise'. Hence, at sufficiently high internal noise, point attractor-based 'hourglass' clocks, such as those found in a smaller cyanobacterium with low protein copy number, Prochlorococcus marinus, can outperform free running clocks. By interpolating between these two regimes in a diverse range of oscillators drawn from across biology, we demonstrate biochemical clock architectures that are best suited to different relative strengths of external and internal noise.

Genetic tool development and systemic regulation in biosynthetic technology

With the increased development in research, innovation, and policy interest in recent years, biosynthetic technology has developed rapidly, which combines engineering, electronics, computer science, mathematics, and other disciplines based on classical genetic engineering and metabolic engineering. It gives a wider perspective and a deeper level to perceive the nature of life via cell mechanism, regulatory networks, or biological evolution. Currently, synthetic biology has made great breakthrough in energy, chemical industry, and medicine industries, particularly in the programmable genetic control at multiple levels of regulation to perform designed goals. In this review, the most advanced and comprehensive developments achieved in biosynthetic technology were represented, including genetic engineering as well as synthetic genomics. In addition, the superiority together with the limitations of the current genome-editing tools were summarized.