Quantifying information transmission in eukaryotic gradient sensing and chemotactic response

Gradient sensing limit of an elongated cell with orientational control

Eukaryotic cells perform chemotaxis by determining the direction of chemical gradients based on stochastic sensing of concentrations at the cell surface. To examine the efficiency of this process, previous studies have investigated the limit of estimation accuracy for gradients. However, most studies have treated a circular cell shape, and the few considering elongated shapes assume the elongated direction as fixed. This leaves the question of how adaptive regulation of cell shape affects the estimation limit. Dynamics of cell shape during gradient sensing is biologically ubiquitous and can influence the estimation by altering the way the concentration is measured, and cells may strategically regulate their shape to improve estimation accuracy. To address this gap, we investigate the estimation limits in dynamic situations where elongated cells change their orientation adaptively depending on the sensed signal. We approach this problem by analyzing the stationary solution of the Bayesian nonlinear filtering equation. By applying diffusion approximation to the ligand-receptor binding process and the Laplace method for the posterior expectation under a high signal-to-noise ratio regime, we obtain an analytical expression for the estimation limit. This expression indicates that estimation accuracy can be improved by aligning the elongated direction perpendicular to the estimated direction, which is also confirmed by numerical simulations. Our analysis provides a basis for clarifying the interplay between estimation and control in gradient sensing and sheds light on how cells optimize their shape to enhance chemotactic efficiency.

Gradient sensing via cell communication

Experimental evidence lends support to the conjecture that cell-to-cell communication plays a role in the gradient sensing of chemical species by certain chains of cells. Models have been formulated to explore this idea. For cells with no identifiable sensing structure, Mugler et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E689 (2016)10.1073/pnas.1509597112] have defined a particular local excitation, global inhibition (LEGI) model that pits nearest-neighbor communication against local reactions in a noisy environment to suggest how this sensing capability might arise in a physical system. In this study, we generalize the nearest-neighbor communication mechanism in the aforementioned LEGI model in order to explore the extent to which the gradient sensing characteristics depend on the parametrization of the communication itself, as well as on the cell size, the radius of influence of neighboring cells, and the influence of the background noise. Using our generalization and a collection of particular candidate communication models, we find that the precision of gradient sensing is indeed sensitive to the particular communication model, and we derive physical and analytic explanations for these results. The framework established and the associated results should prove useful in understanding the appropriateness of particular cell-to-cell communication models in gradient sensing studies.

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.

Decoding the chemotactic signal

From an individual bacterium to the cells that compose the human immune system, cellular chemotaxis plays a fundamental role in allowing cells to navigate, interpret, and respond to their environments. While many features of cellular chemotaxis are shared among systems as diverse as bacteria and human immune cells, the machinery that guides the migration of these model organisms varies widely. In this article, we review current literature on the diversity of chemoattractant ligands, the cell surface receptors that detect and process chemotactic gradients, and the link between signal recognition and the regulation of cellular machinery that allow for efficient directed cellular movement. These facets of cellular chemotaxis are compared among E. coli, Dictyostelium discoideum, and mammalian neutrophils to derive organizational principles by which diverse cell systems sense and respond to chemotactic gradients to initiate cellular migration.

Extracellular Processing of Molecular Gradients by Eukaryotic Cells Can Improve Gradient Detection Accuracy

Eukaryotic cells sense molecular gradients by measuring spatial concentration variation through the difference in the number of occupied receptors to which molecules can bind. They also secrete enzymes that degrade these molecules, and it is presently not well understood how this affects the local gradient perceived by cells. Numerical and analytical results show that these enzymes can substantially increase the signal-to-noise ratio of the receptor difference and allow cells to respond to a much broader range of molecular concentrations and gradients than they would without these enzymes.

Cell-cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and little is known about how multicellular signal processing modulates single-cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored whether cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow epidermal growth factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.

Information theory in systems biology. Part II: protein-protein interaction and signaling networks

By the development of information theory in 1948 by Claude Shannon to address the problems in the field of data storage and data communication over (noisy) communication channel, it has been successfully applied in many other research areas such as bioinformatics and systems biology. In this manuscript, we attempt to review some of the existing literatures in systems biology, which are using the information theory measures in their calculations. As we have reviewed most of the existing information-theoretic methods in gene regulatory and metabolic networks in the first part of the review, so in the second part of our study, the application of information theory in other types of biological networks including protein-protein interaction and signaling networks will be surveyed.

The biophysical model for accuracy of cellular sensing spatial gradients of multiple chemoattractants

Spatial gradients of surrounding chemoattractants are the key factors in determining the directionality of eukaryotic cell movement. Thus, it is important for cells to accurately measure the spatial gradients of surrounding chemoattractants. Here, we study the precision of sensing the spatial gradients of multiple chemoattractants using cooperative receptor clusters. Cooperative receptors on cells are modeled as an Ising chain of Monod-Wyman-Changeux clusters subject to multiple chemical-gradient fields to study the physical limits of multiple chemoattractants spatial gradients sensing. We found that eukaryotic cells cannot sense each chemoattractant gradient individually. Instead, cells can only sense a weighted sum of surrounding chemical gradients. Moreover, the precision of sensing one chemical gradient is signicantly affected by coexisting chemoattractant concentrations. These findings can provide a further insight into the role of chemoattractants in immune response and help develop novel treatments for inflammatory diseases.

High fidelity information processing in folic acid chemotaxis of Dictyostelium amoebae

Living cells depend upon the detection of chemical signals for their existence. Eukaryotic cells can sense a concentration difference as low as a few per cent across their bodies. This process was previously suggested to be limited by the receptor-ligand binding fluctuations. Here, we first determine the chemotaxis response of Dictyostelium cells to static folic acid gradients and show that they can significantly exceed this sensitivity, responding to gradients as shallow as 0.2% across the cell body. Second, using a previously developed information theory framework, we compare the total information gained about the gradient (based on the cell response) to its upper limit: the information gained at the receptor-ligand binding step. We find that the model originally applied to cAMP sensing fails as demonstrated by the violation of the data processing inequality, i.e. the total information exceeds the information at the receptor-ligand binding step. We propose an extended model with multiple known receptor types and with cells allowed to perform several independent measurements of receptor occupancy. This does not violate the data processing inequality and implies the receptor-ligand binding noise dominates both for low- and high-chemoattractant concentrations. We also speculate that the interplay between exploration and exploitation is used as a strategy for accurate sensing of otherwise unmeasurable levels of a chemoattractant.

Systems biology: the role of engineering in the reverse engineering of biological signaling

One of the principle tasks of systems biology has been the reverse engineering of signaling networks. Because of the striking similarities to engineering systems, a number of analysis and design tools from engineering disciplines have been used in this process. This review looks at several examples including the analysis of homeostasis using control theory, the attenuation of noise using signal processing, statistical inference and the use of information theory to understand both binary decision systems and the response of eukaryotic chemotactic cells.

Physical limits on cellular directional mechanosensing

Many eukaryotic cells are able to perform directional mechanosensing by directly measuring minute spatial differences in the mechanical stress on their membranes. Here, we explore the limits of a single mechanosensitive channel activation using a two-state double-well model for the gating mechanism. We then focus on the physical limits of directional mechanosensing by a single cell having multiple mechanosensors and subjected to a shear flow inducing a nonuniform membrane tension. Our results demonstrate that the accuracy in sensing the mechanostimulus direction not only increases with cell size and exposure to a signal, but also grows for cells with a near-critical membrane prestress. Finally, the existence of a nonlinear threshold effect, fundamentally limiting the cell's ability to effectively perform directional mechanosensing at a low signal-to-noise ratio, is uncovered.

Enhanced cellular sensitivity from partitioning the integrin receptors into multiple clusters

Integrins are essential receptors for the development and functioning of multicellular organisms because they mediate cell adhesion and migration, and regulate cell proliferation and apoptosis. In response to cues in the extracellular matrix, they are observed to organize into many clusters. The number and size of such clusters are observed to vary according to the concentration of and affinity for the extracellular ligand. The realization of a cluster point pattern is governed by a doubly stochastic process, controlling the number of clusters and the number of points per cluster. We construct entropy measures for the separation of two doubly stochastic processes and demonstrate how the self-organization of integrins in multiple clusters contributes to the accuracy in sensing the extracellular environment.

How input fluctuations reshape the dynamics of a biological switching system

An important task in quantitative biology is to understand the role of stochasticity in biochemical regulation. Here, as an extension of our recent work [Phys. Rev. Lett. 107, 148101 (2011)], we study how input fluctuations affect the stochastic dynamics of a simple biological switch. In our model, the on transition rate of the switch is directly regulated by a noisy input signal, which is described as a non-negative mean-reverting diffusion process. This continuous process can be a good approximation of the discrete birth-death process and is much more analytically tractable. Within this setup, we apply the Feynman-Kac theorem to investigate the statistical features of the output switching dynamics. Consistent with our previous findings, the input noise is found to effectively suppress the input-dependent transitions. We show analytically that this effect becomes significant when the input signal fluctuates greatly in amplitude and reverts slowly to its mean.

A framework for designing and analyzing binary decision-making strategies in cellular systems

Cells make many binary (all-or-nothing) decisions based on noisy signals gathered from their environment and processed through noisy decision-making pathways. Reducing the effect of noise to improve the fidelity of decision-making comes at the expense of increased complexity, creating a tradeoff between performance and metabolic cost. We present a framework based on rate distortion theory, a branch of information theory, to quantify this tradeoff and design binary decision-making strategies that balance low cost and accuracy in optimal ways. With this framework, we show that several observed behaviors of binary decision-making systems, including random strategies, hysteresis, and irreversibility, are optimal in an information-theoretic sense for various situations. This framework can also be used to quantify the goals around which a decision-making system is optimized and to evaluate the optimality of cellular decision-making systems by a fundamental information-theoretic criterion. As proof of concept, we use the framework to quantify the goals of the externally triggered apoptosis pathway.

Pursuit of food versus pursuit of information in a Markovian perception-action loop model of foraging

Efficient coding, redundancy reduction, and other information theoretic optimization principles have successfully explained the organization of many biological phenomena, from the physiology of sensory receptive fields to the variability of certain DNA sequence ensembles. Here we examine the hypothesis that behavioral strategies that are optimal for survival must necessarily involve efficient information processing, and ask whether there can be circumstances in which deliberately sacrificing some information can lead to higher utility? To this end, we present an analytically tractable model for a particular instance of a perception-action loop: a creature searching for a randomly moving food source confined to a 1D ring world. The model incorporates the statistical structure of the creature's world, the effects of the creature's actions on that structure, and the creature's strategic decision process. The underlying model takes the form of a Markov process on an infinite dimensional state space. To analyze it we construct an exact coarse graining that reduces the model to a Markov process on a finite number of "information states". This mathematical technique allows us to make quantitative comparisons between the performance of an information-theoretically optimal strategy with other candidate search strategies on a food gathering task. We find that 1. Information optimal search does not necessarily optimize utility (expected food gain). 2. The rank ordering of search strategies by information performance does not predict their ordering by expected food obtained. 3. The relative advantage of different strategies depends on the statistical structure of the environment, in particular the variability of motion of the source. We conclude that there is no simple relationship between information and utility. Even in the absence of information processing costs or bandwidth constraints, behavioral optimality does not imply information efficiency, nor is there a simple tradeoff between the two objectives of gaining information about a food source versus obtaining the food itself. For a wide range of values of the food source's movement parameter, the strategy of collecting the most information possible about the unknown source location carries an ineliminable structural cost, leading to a situation in which a foraging creature could actually choose to be less well-informed while simultaneously being, on average, better fed.

Cellular ability to sense spatial gradients in the presence of multiple competitive ligands

Many eukaryotic and prokaryotic cells can exhibit remarkable sensing ability under small gradients of chemical compounds. In this study, we approach this phenomenon by considering the contribution of multiple ligands to the chemical kinetics within the Michaelis-Menten model. This work was inspired by the recent theoretical findings of Hu et al. [Phys. Rev. Lett. 105, 048104 (2010)]. Our treatment with practical binding energies and chemical potentials provides results that are consistent with experimental observations.