External and internal constraints on eukaryotic chemotaxis

Decoding complex transport patterns in flow-induced autologous chemotaxis of multicellular systems

Cell migration via autologous chemotaxis in the presence of interstitial fluid flow is important in cancer metastasis and embryonic development. Despite significant recent progress, our understanding of flow-induced autologous chemotaxis of multicellular systems remains poor. The literature presents inconsistent findings regarding the effectiveness of collective autologous chemotaxis of densely packed cells under interstitial fluid flow. Here, we present a high-fidelity computational model to analyze the migration of multicellular systems performing autologous chemotaxis in the presence of interstitial fluid flow. Our simulations show that the details of the complex transport dynamics of the chemoattractant and fluid flow patterns that occur in the extracellular space, previously overlooked, are essential to understand this cell migration mechanism. We find that, although flow-induced autologous chemotaxis is a robust migration mechanism for individual cells, the cell-cell interactions that occur in multicellular systems render autologous chemotaxis an inefficient mechanism of collective cell migration. Our results offer new perspectives on the potential role of autologous chemotaxis in the tumor microenvironment, where fluid flow is an important modulator of transport.

Suppressing collective cell motion with bidirectional guidance cues

In natural environments, cells move in the presence of multiple physical and chemical guidance cues. Using a model system for such guided cell migration, Dictyostelium discoideum (Dicty), we investigate how chemical and physical signals compete in guiding the motion of cell groups. In Dicty cells, chemical signals can lead to collective streaming behavior, in which cells follow one another head-to-tail and aggregate into clusters of ∼10^{5} cells. We use experiments and numerical simulations to show that streaming and aggregation can be suppressed by the addition of a physical guidance cue of comparable strength to the chemical signals, parallel nanoridges. The bidirectional character of physical guidance by ridges is a determining factor in the suppression of streaming and aggregation. Thus, combining multiple types of guidance cues is a powerful approach to trigger or explain a broad range of collective cell behaviors.

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.

Dynamic cluster field modeling of collective chemotaxis

Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in several biological processes, such as cancer metastasis, wound healing, and embryogenesis. Understanding collective chemotaxis has challenged experimental, theoretical and computational scientists because cells can sense very small chemoattractant gradients that are tightly controlled by cell-cell interactions and the regulation of the chemoattractant distribution by the cells. Computational models of collective cell migration that offer a high-fidelity resolution of the cell motion and chemoattractant dynamics in the extracellular space have been limited to a small number of cells. Here, we present Dynamic cluster field modeling (DCF), a novel computational method that enables simulations of collective chemotaxis of cellular systems with O ( 1000 ) cells and high-resolution transport dynamics of the chemoattractant in the time-evolving extracellular space. We illustrate the efficiency and predictive capabilities of our approach by comparing our numerical simulations with experiments in multiple scenarios that involve chemoattractant secretion and uptake by the migrating cells, cell migration in confined spaces, regulation of the attractant distribution by cell motion, and interactions of the chemoattractant with an enzyme. The proposed algorithm opens new opportunities to address outstanding problems that involve collective cell migration in the central nervous system, immune response and cancer metastasis.

Eukaryotic Chemotaxis under Periodic Stimulation Shows Temporal Gradient Dependence

When cells of the social amoeba Dictyostelium discoideum are starved of nutrients they start to synthesize and secrete the chemical messenger and chemoattractant cyclic adenosine monophosphate (cAMP). This signal is relayed by other cells, resulting in the establishment of periodic waves. The cells aggregate through chemotaxis toward the center of these waves. We investigated the chemotactic response of individual cells to repeated exposure to waves of cAMP generated by a microfluidic device. For fast-moving waves (short period), the chemotactic ability of the cells was found to increase upon exposure to more waves, suggesting the development of a memory over several cycles. This effect was not significant for slow-moving waves (large period). We show that the experimental results are consistent with a local excitation global inhibition-based model, extended by including a component that rises and decays slowly and that is activated by the temporal gradient of cAMP concentration. The observed enhancement in chemotaxis is relevant to populations in the wild: once sustained, periodic waves of the chemoattractant are established, it is beneficial to cells to improve their chemotactic ability in order to reach the aggregation center sooner.

Trade-offs in concentration sensing in dynamic environments

When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in an environment that changes over time, past measurements may not reflect current conditions-creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell's environment control this trade-off? What properties of the environment make it variable enough that this trade-off is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g., folic acid). In this case, the environment changes because the bacteria swim-leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies ranging from not time averaging at all to averaging over an arbitrarily long time or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment.

Physical limits on galvanotaxis

Eukaryotic cells can polarize and migrate in response to electric fields via "galvanotaxis," which aids wound healing. Experimental evidence suggests cells sense electric fields via molecules on the cell's surface redistributing via electrophoresis and electroosmosis, though the sensing species has not yet been conclusively identified. We develop a model that links sensor redistribution and galvanotaxis using maximum likelihood estimation. Our model predicts a single universal curve for how galvanotactic directionality depends on field strength. We can collapse measurements of galvanotaxis in keratocytes, neural crest cells, and granulocytes to this curve, suggesting that stochasticity due to the finite number of sensors may limit galvanotactic accuracy. We find cells can achieve experimentally observed directionalities with either a few (∼100) highly polarized sensors or many (∼10^{4}) sensors with an ∼6-10% change in concentration across the cell. We also identify additional signatures of galvanotaxis via sensor redistribution, including the presence of a tradeoff between accuracy and variance in cells being controlled by rapidly switching fields. Our approach shows how the physics of noise at the molecular scale can limit cell-scale galvanotaxis, providing important constraints on sensor properties and allowing for new tests to determine the specific molecules underlying galvanotaxis.

MACC1-induced migration in tumors: Current state and perspective

Malignant tumors are still a global, heavy health burden. Many tumor types cannot be treated curatively, underlining the need for new treatment targets. In recent years, metastasis associated in colon cancer 1 (MACC1) was identified as a promising biomarker and drug target, as it is promoting tumor migration, initiation, proliferation, and others in a multitude of solid cancers. Here, we will summarize the current knowledge about MACC1-induced tumor cell migration with a special focus on the cytoskeletal and adhesive systems. In addition, a brief overview of several in vitro models used for the analysis of cell migration is given. In this context, we will point to issues with the currently most prevalent models used to study MACC1-dependent migration. Lastly, open questions about MACC1-dependent effects on tumor cell migration will be addressed.

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.

Collective gradient sensing with limited positional information

Eukaryotic cells sense chemical gradients to decide where and when to move. Clusters of cells can sense gradients more accurately than individual cells by integrating measurements of the concentration made across the cluster. Is this gradient-sensing accuracy impeded when cells have limited knowledge of their position within the cluster, i.e., limited positional information? We apply maximum likelihood estimation to study gradient-sensing accuracy of a cluster of cells with finite positional information. If cells must estimate their location within the cluster, this lowers the accuracy of collective gradient sensing. We compare our results with a tug-of-war model where cells respond to the gradient by polarizing away from their neighbors without relying on their positional information. As the cell positional uncertainty increases, there is a trade-off where the tug-of-war model responds more accurately to the chemical gradient. However, for sufficiently large cell clusters or sufficiently shallow chemical gradients, the tug-of-war model will always be suboptimal to one that integrates information from all cells, even if positional uncertainty is high.

Limitations on concentration measurements and gradient discerning times in cellular systems

This work reports on two results. At first we revisit the Berg and Purcell calculation that provides a lower bound to the error in concentration measurement by cells by considering the realistic case when the cell starts measuring the moment it comes in contact with the chemoattractants, instead of measuring after equilibrating with the chemotactic concentration as done in the classic Berg and Purcell paper. We find that the error in concentration measurement is still the same as evaluated by Berg and Purcell. We next derive a lower bound on measurement time below which it is not possible for the cell to discern extracellular chemotactic gradients through spatial sensing mechanisms. This bound is independent of diffusion rate and concentration of the chemoattracts and is instead set by detachment rate of ligands from the cell receptors. The result could help explain experimental observations.

Close to Optimal Cell Sensing Ensures the Robustness of Tissue Differentiation Process: The Avian Photoreceptor Mosaic Case

The way that progenitor cell fate decisions and the associated environmental sensing are regulated to ensure the robustness of the spatial and temporal order in which cells are generated towards a fully differentiating tissue still remains elusive. Here, we investigate how cells regulate their sensing intensity and radius to guarantee the required thermodynamic robustness of a differentiated tissue. In particular, we are interested in finding the conditions where dedifferentiation at cell level is possible (microscopic reversibility), but tissue maintains its spatial order and differentiation integrity (macroscopic irreversibility). In order to tackle this, we exploit the recently postulated Least microEnvironmental Uncertainty Principle (LEUP) to develop a theory of stochastic thermodynamics for cell differentiation. To assess the predictive and explanatory power of our theory, we challenge it against the avian photoreceptor mosaic data. By calibrating a single parameter, the LEUP can predict the cone color spatial distribution in the avian retina and, at the same time, suggest that such a spatial pattern is associated with quasi-optimal cell sensing. By means of the stochastic thermodynamics formalism, we find out that thermodynamic robustness of differentiated tissues depends on cell metabolism and cell sensing properties. In turn, we calculate the limits of the cell sensing radius that ensure the robustness of differentiated tissue spatial order. Finally, we further constrain our model predictions to the avian photoreceptor mosaic.

Cell dispersal by localized degradation of a chemoattractant

Chemotaxis, the guided motion of cells by chemical gradients, plays a crucial role in many biological processes. In the social amoeba Dictyostelium discoideum, chemotaxis is critical for the formation of cell aggregates during starvation. The cells in these aggregates generate a pulse of the chemoattractant, cyclic adenosine 3',5'-monophosphate (cAMP), every 6 min to 10 min, resulting in surrounding cells moving toward the aggregate. In addition to periodic pulses of cAMP, the cells also secrete phosphodiesterase (PDE), which degrades cAMP and prevents the accumulation of the chemoattractant. Here we show that small aggregates of Dictyostelium can disperse, with cells moving away from instead of toward the aggregate. This surprising behavior often exhibited oscillatory cycles of motion toward and away from the aggregate. Furthermore, the onset of outward cell motion was associated with a doubling of the cAMP signaling period. Computational modeling suggests that this dispersal arises from a competition between secreted cAMP and PDE, creating a cAMP gradient that is directed away from the aggregate, resulting in outward cell motion. The model was able to predict the effect of PDE inhibition as well as global addition of exogenous PDE, and these predictions were subsequently verified in experiments. These results suggest that localized degradation of a chemoattractant is a mechanism for morphogenesis.

Self-organized cell migration across scales - from single cell movement to tissue formation

Self-organization is a key feature of many biological and developmental processes, including cell migration. Although cell migration has traditionally been viewed as a biological response to extrinsic signals, advances within the past two decades have highlighted the importance of intrinsic self-organizing properties to direct cell migration on multiple scales. In this Review, we will explore self-organizing mechanisms that lay the foundation for both single and collective cell migration. Based on in vitro and in vivo examples, we will discuss theoretical concepts that underlie the persistent migration of single cells in the absence of directional guidance cues, and the formation of an autonomous cell collective that drives coordinated migration. Finally, we highlight the general implications of self-organizing principles guiding cell migration for biological and medical research.

Cellular memory in eukaryotic chemotaxis depends on the background chemoattractant concentration

Cells of the social amoeba Dictyostelium discoideum migrate to a source of periodic traveling waves of chemoattractant as part of a self-organized aggregation process. An important part of this process is cellular memory, which enables cells to respond to the front of the wave and ignore the downward gradient in the back of the wave. During this aggregation, the background concentration of the chemoattractant gradually rises. In our microfluidic experiments, we exogenously applied periodic waves of chemoattractant with various background levels. We find that increasing background does not make detection of the wave more difficult, as would be naively expected. Instead, we see that the chemotactic efficiency significantly increases for intermediate values of the background concentration but decreases to almost zero for large values in a switch-like manner. These results are consistent with a computational model that contains a bistable memory module, along with a nonadaptive component. Within this model, an intermediate background level helps preserve directed migration by keeping the memory activated, but when the background level is higher, the directional stimulus from the wave is no longer sufficient to activate the bistable memory, suppressing directed migration. These results suggest that raising levels of chemoattractant background may facilitate the self-organized aggregation in Dictyostelium colonies.

Novel micropatterning technique reveals dependence of cell-substrate adhesion and migration of social amoebas on parental strain, development, and fluorescent markers

Cell-substrate adhesion of the social amoeba Dictyostelium discoideum, a model organism often used for the study of chemotaxis, is non-specific and does not involve focal adhesion complexes. Therefore, micropatterned substrates where adherent Dictyostelium cells are constrained to designated microscopic regions are difficult to make. Here we present a micropatterning technique for Dictyostelium cells that relies on coating the substrate with an ∼1μm thick layer of polyethylene glycol (PEG) gel. We show that, when plated on a substrate with narrow parallel stripes of PEG-gel and glass, Dictyostelium cells nearly exclusive adhere to and migrate along the glass stripes, thus providing a model system to study one-dimensional migration of amoeboid cells. Surprisingly, we find substantial differences in the adhesion to PEG-gel and glass stripes between vegetative and developed cells and between two different axenic laboratory strains of Dictyostelium, AX2 and AX4. Even more surprisingly, we find that the distribution of Dictyostelium cells between PEG-gel and glass stripes is significantly affected by the expression of several fluorescent protein markers of the cytoskeleton. We carry out atomic force microscopy based single cell force spectroscopy measurements that confirm that the force of adhesion to PEG-gel substrate can be significantly different between vegetative and developed cells, AX2 and AX4 cells, and cells with and without fluorescent markers. Thus, the choice of parental background, the degree of development, and the expression of fluorescent protein markers can all have a profound effect on cell-substrate adhesion and should be considered when comparing migration of cells and when designing micropatterned substrates.

SCHEEPDOG: Programming Electric Cues to Dynamically Herd Large-Scale Cell Migration

Directed cell migration is critical across biological processes spanning healing to cancer invasion, yet no existing tools allow real-time interactive guidance over such migration. We present a new bioreactor that harnesses electrotaxis-directed cell migration along electric field gradients-by integrating four independent electrodes under computer control to dynamically program electric field patterns, and hence steer cell migration. Using this platform, we programmed and characterized multiple precise, two-dimensional collective migration maneuvers in renal epithelia and primary skin keratinocyte ensembles. First, we demonstrated on-demand, 90-degree collective turning. Next, we developed a universal electrical stimulation scheme capable of programming arbitrary 2D migration maneuvers such as precise angular turns and migration in a complete circle. Our stimulation scheme proves that cells effectively time-average electric field cues, helping to elucidate the transduction timescales in electrotaxis. Together, this work represents an enabling platform for controlling cell migration with broad utility across many cell types.

A negative-feedback loop maintains optimal chemokine concentrations for directional cell migration

Chemoattractant gradients frequently guide migrating cells. To achieve the most directional signal, such gradients should be maintained with concentrations around the dissociation constant (Kd)1-6 of the chemoreceptor. Whether this actually occurs in animals is unknown. Here we investigate whether a moving tissue, the zebrafish posterior lateral line primordium, buffers its attractant in this concentration range to achieve robust migration. We find that the Cxcl12 (also known as Sdf1) attractant gradient ranges from 0 to 12 nM, values similar to the 3.4 nM Kd of its receptor Cxcr4. When we increase the Kd of Cxcl12 for Cxcr4, primordium migration is less directional. Furthermore, a negative-feedback loop between Cxcl12 and its clearance receptor Ackr3 (also known as Cxcr7) regulates the Cxcl12 concentrations. Breaking this negative feedback by blocking the phosphorylation of the cytoplasmic tail of Ackr3 also results in less directional primordium migration. Thus, directed migration of the primordium is dependent on a close match between the Cxcl12 concentration and the Kd of Cxcl12 for Cxcr4, which is maintained by buffering of the chemokine levels. Quantitative modelling confirms the plausibility of this mechanism. We anticipate that buffering of attractant concentration is a general mechanism for ensuring robust cell migration.

Dynamic Buffering of Extracellular Chemokine by a Dedicated Scavenger Pathway Enables Robust Adaptation during Directed Tissue Migration

How tissues migrate robustly through changing guidance landscapes is poorly understood. Here, quantitative imaging is combined with inducible perturbation experiments to investigate the mechanisms that ensure robust tissue migration in vivo. We show that tissues exposed to acute "chemokine floods" halt transiently before they perfectly adapt, i.e., return to the baseline migration behavior in the continued presence of elevated chemokine levels. A chemokine-triggered phosphorylation of the atypical chemokine receptor Cxcr7b reroutes it from constitutive ubiquitination-regulated degradation to plasma membrane recycling, thus coupling scavenging capacity to extracellular chemokine levels. Finally, tissues expressing phosphorylation-deficient Cxcr7b migrate normally in the presence of physiological chemokine levels but show delayed recovery when challenged with elevated chemokine concentrations. This work establishes that adaptation to chemokine fluctuations can be "outsourced" from canonical GPCR signaling to an autonomously acting scavenger receptor that both senses and dynamically buffers chemokine levels to increase the robustness of tissue migration.

Elements of qualitative cognition: An information topology perspective

Elementary quantitative and qualitative aspects of consciousness are investigated conjointly from the biology, neuroscience, physic and mathematic point of view, by the mean of a theory written with Bennequin that derives and extends information theory within algebraic topology. Information structures, that accounts for statistical dependencies within n-body interacting systems are interpreted a la Leibniz as a monadic-panpsychic framework where consciousness is information and physical, and arise from collective interactions. The electrodynamic intrinsic nature of consciousness, sustained by an analogical code, is illustrated by standard neuroscience and psychophysic results. It accounts for the diversity of the learning mechanisms, including adaptive and homeostatic processes on multiple scales, and details their expression within information theory. The axiomatization and logic of cognition are rooted in measure theory expressed within a topos intrinsic probabilistic constructive logic. Information topology provides a synthesis of the main models of consciousness (Neural Assemblies, Integrated Information, Global Neuronal Workspace, Free Energy Principle) within a formal Gestalt theory, an expression of information structures and patterns in correspondence with Galois cohomology and discrete symmetries. The methods provide new formalization of deep neural network with homologicaly imposed architecture applied to challenges in AI-machine learning.

Leader cells in collective chemotaxis: Optimality and trade-offs

Clusters of cells can work together in order to follow a signal gradient, chemotaxing even when single cells do not. Cells in different regions of collectively migrating neural crest streams show different gene expression profiles, suggesting that cells may specialize to leader and follower roles. We use a minimal mathematical model to understand when this specialization is advantageous. In our model, leader cells sense the gradient with an accuracy that depends on the kinetics of ligand-receptor binding, while follower cells follow the cluster's direction with a finite error. Intuitively, specialization into leaders and followers should be optimal when a few cells have more information than the rest of the cluster, such as in the presence of a sharp transition in chemoattractant concentration. We do find this-but also find that high levels of specialization can be optimal in the opposite limit of very shallow gradients. We also predict that the best location for leaders may not be at the front of the cluster. In following leaders, clusters may have to choose between speed and flexibility. Clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters.

Motion-Based Detection of Lanthanides(III) Using Self-Propelled Droplets

The directional and controllable transportation of self-propelled chemical objects in response to chemical signals in environmental media holds considerable promise for diverse applications. We investigated the chemotaxis of oil droplets loaded with surfactants to detect spatial gradients of lanthanide(III) ions, among which Dy³⁺ and Tm³⁺ were the most effective chemoattractants for steering droplets toward the targets. Patterns within a chemotactic index of the lanthanide series exhibited a convex tetrad effect and a breakpoint at Gd³⁺. The Jørgensen-Kawabe equation, which is based on the refined spin-pairing energy theory, quantitatively demonstrated the tetrad effect. The self-propelled droplets served as a motion-based detection mechanism for lanthanides(III).

Chemotaxis Model for Breast Cancer Cells Based on Signal/Noise Ratio

Chemotaxis, a biased migration of cells under a chemical gradient, plays a significant role in diverse biological phenomena including cancer metastasis. Stromal cells release signaling proteins to induce chemotaxis, which leads to organ-specific metastasis. Epidermal growth factor (EGF) is an example of the chemical attractants, and its gradient stimulates metastasis of breast cancer cells. Hence, the interactions between EGF and breast cancer cells have long been a subject of interest for oncologists and clinicians. However, most current approaches do not systematically separate the effects of gradient and absolute concentration of EGF on chemotaxis of breast cancer cells. In this work, we develop a theoretical model based on signal/noise ratio to represent stochastic properties and report our microfluidic experiments to verify the analytical predictions from the model. The results demonstrate that even under the same EGF concentration gradients (0-50 or 0-150 ng/mL), breast cancer cells reveal a more evident chemotaxis pattern when the absolute EGF concentrations are low. Moreover, we found that reducing the number of EGF receptors (EGFRs) with addition of EGFR antibody (1 ng/mL) can promote chemotaxis at an EGF gradient of 0-1 ng/mL as shown by chemotaxis index (0.121 ± 0.037, reduced EGFRs vs. 0.003 ± 0.041, control). This counterintuitive finding suggests that EGFR-targeted therapy may stimulate metastasis of breast cancer because the partial suppression of the receptors makes the number of receptors close to the optimal one for chemotaxis. This analysis should be considered in anticancer drug design.

Collective gradient sensing and chemotaxis: modeling and recent developments

Cells measure a vast variety of signals, from their environment's stiffness to chemical concentrations and gradients; physical principles strongly limit how accurately they can do this. However, when many cells work together, they can cooperate to exceed the accuracy of any single cell. In this topical review, I will discuss the experimental evidence showing that cells collectively sense gradients of many signal types, and the models and physical principles involved. I also propose new routes by which experiments and theory can expand our understanding of these problems.

A computational model for how cells choose temporal or spatial sensing during chemotaxis

Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable.

Unicellular organisms and other single cells often have to migrate towards food sources or away from predators by sensing chemicals present in the environment. There are two ways for a cell to sense these external chemicals: temporal sensing, where the cell senses the external chemical at two different time points after it has moved through a certain distance, or spatial sensing, where the cell senses the external chemical at two different locations on its cellular surface (e.g., the front and rear of the cell) simultaneously. It has been thought that small unicellular organisms employ temporal sensing as their small size prohibits sensing at two different locations on the cellular surface. Using computational modeling, we find that the choice between temporal and spatial sensing is determined by the ratio of cell velocity to the product of cell diameter and rate of signaling, as well as the diffusivities of the signaling proteins. Predictions from our model agree with experimental observations over a wide range of cells, where a fast-moving, small cell performs better comparing the chemoattractant at different times in its trajectory; whereas, a slow-moving, big cell performs better by comparing the chemoattractant concentration at its two ends.

Adaptation of Living Systems

Adaptation refers to the biological phenomenon where living systems change their internal states in response to changes in their environments in order to maintain certain key functions critical for their survival and fitness. Adaptation is one of the most ubiquitous and arguably one of the most fundamental properties of living systems. It occurs throughout all biological scales, from adaptation of populations of species over evolutionary time to adaptation of a single cell to different environmental stresses during its life span. In this article, we review some of the recent progress made in understanding molecular mechanisms of cellular level adaptation. We take the minimalist (or the physicist) approach and study the simplest systems that exhibit generic adaptive behaviors. We focus on understanding the basic biochemical interaction networks in living matter that are responsible for adaptation dynamics. By combining theoretical modeling with quantitative experimentation, we demonstrate universal features in adaptation as well as important differences in different cellular systems, including chemotaxis in bacterium cells (Escherichia coli) and eukaryotic cells (Dictyostelium). Future work in extending the modeling framework to study adaptation in more complex systems such as sensory neurons are discussed.

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-to-cell variation sets a tissue-rheology-dependent bound on collective gradient sensing

When a single cell senses a chemical gradient and chemotaxes, stochastic receptor-ligand binding can be a fundamental limit to the cell's accuracy. For clusters of cells responding to gradients, however, there is a critical difference: Even genetically identical cells have differing responses to chemical signals. With theory and simulation, we show collective chemotaxis is limited by cell-to-cell variation in signaling. We find that when different cells cooperate, the resulting bias can be much larger than the effects of ligand-receptor binding. Specifically, when a strongly responding cell is at one end of a cell cluster, cluster motion is biased toward that cell. These errors are mitigated if clusters average measurements over times long enough for cells to rearrange. In consequence, fluid clusters are better able to sense gradients: We derive a link between cluster accuracy, cell-to-cell variation, and the cluster rheology. Because of this connection, increasing the noisiness of individual cell motion can actually increase the collective accuracy of a cluster by improving fluidity.

Discrete Modeling of Amoeboid Locomotion and Chemotaxis in Dictyostelium discoideum by Tracking Pseudopodium Growth Direction

Dictyostelium discoideum amoeba is a well-established model organism for studying the crawling locomotion of eukaryotic cells. These amoebae extend pseudopodium - a temporary actin-based protrusion of their body membrane to probe the medium and crawl through it. Experiments show highly-ordered patterns in the growth direction of these pseudopodia, which results in persistence cell motility. Here, we propose a discrete model for studying and investigating the cell locomotion based on the experimental evidences. According to our model, Dictyostelium selects its pseudopodium growth direction based on a second-order Markov chain process, in the absence of external cues. Consequently, compared to a random walk process, our model indicates stronger growth in the mean-square displacement of cells, which is consistent with empirical findings. In the presence of external chemical stimulants, cells tend to align with the gradient of chemoattractant molecules. To quantify this tendency, we define a coupling coefficient between the pseudopodium extension direction and the gradient of an external stimulant, which depends on the local stimulant concentration and its gradient. Additionally, we generalize the model to weak-coupling regime by utilizing perturbation methods.

Fluctuation relations between hierarchical kinetically equivalent networks with Arrhenius-type transitions and their roles in systems and structural biology

The legality of using simple kinetic schemes to determine the stochastic properties of a complex system depends on whether the fluctuations generated from hierarchical equivalent schemes are consistent with one another. To analyze this consistency, we perform lumping processes on the stochastic differential equations and the generalized fluctuation-dissipation theorem and apply them to networks with the frequently encountered Arrhenius-type transition rates. The explicit Langevin force derived from those networks enables us to calculate the state fluctuations caused by the intrinsic and extrinsic noises on the free energy surface and deduce their relations between kinetically equivalent networks. In addition to its applicability to wide classes of network related systems, such as those in structural and systems biology, the result sheds light on the fluctuation relations for general physical variables in Keizer's canonical theory.

Local sampling paints a global picture: Local concentration measurements sense direction in complex chemical gradients

Detecting and interpreting extracellular spatial signals is essential for cellular orientation within complex environments, such as during directed cell migration or growth in multicellular development. Although the molecular understanding of how cells read spatial signals like chemical gradients is still lacking, recent work has revealed that stochastic processes at different temporal and spatial scales are at the core of this gradient sensing process in a wide range of eukaryotes. Fast biochemical reactions like those underlying GTPase activity dynamics form a functional module together with slower cell morphological changes driven by membrane remodelling. This biochemical-morphological module explores the environment by stochastic local concentration sampling to determine the source of the gradient signal, enabling efficient signal detection and interpretation before polarised growth or migration towards the gradient source is initiated. Here we review recent data describing local sampling and propose a model of local fast and slow feedback counteracted by gradient-dependent substrate limitation to be at the core of gradient sensing by local sampling.

A dual-docking microfluidic cell migration assay (D2-Chip) for testing neutrophil chemotaxis and the memory effect

Chemotaxis is a classic mechanism for guiding cell migration and an important topic in both fundamental cell biology and health sciences. Neutrophils are a widely used model to study eukaryotic cell migration and neutrophil chemotaxis itself can lead to protective or harmful immune actions to the body. While much has been learnt from past research about how neutrophils effectively navigate through a chemoattractant gradient, many interesting questions remain unclear. For example, while it is tempting to model neutrophil chemotaxis using the well-established biased random walk theory, the experimental proof was challenged by the cell's highly persistent migrating nature. A special experimental design is required to test the key predictions from the random walk model. Another question that has interested the cell migration community for decades concerns the existence of chemotactic memory and its underlying mechanism. Although chemotactic memory has been suggested in various studies, a clear quantitative experimental demonstration will improve our understanding of the migratory memory effect. Motivated by these questions, we developed a microfluidic cell migration assay (so-called dual-docking chip or D2-Chip) that can test both the biased random walk model and the memory effect for neutrophil chemotaxis on a single chip enabled by multi-region gradient generation and dual-region cell alignment. Our results provide experimental support for the biased random walk model and chemotactic memory for neutrophil chemotaxis. Quantitative data analyses provide new insights into neutrophil chemotaxis and memory by making connections to entropic disorder, cell morphology and oscillating migratory response.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of "collective guidance" computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster's size-clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.

A Worldwide Competition to Compare the Speed and Chemotactic Accuracy of Neutrophil-Like Cells

Chemotaxis is the ability to migrate towards the source of chemical gradients. It underlies the ability of neutrophils and other immune cells to hone in on their targets and defend against invading pathogens. Given the importance of neutrophil migration to health and disease, it is crucial to understand the basic mechanisms controlling chemotaxis so that strategies can be developed to modulate cell migration in clinical settings. Because of the complexity of human genetics, Dictyostelium and HL60 cells have long served as models system for studying chemotaxis. Since many of our current insights into chemotaxis have been gained from these two model systems, we decided to compare them side by side in a set of winner-take-all races, the Dicty World Races. These worldwide competitions challenge researchers to genetically engineer and pharmacologically enhance the model systems to compete in microfluidic racecourses. These races bring together technological innovations in genetic engineering and precision measurement of cell motility. Fourteen teams participated in the inaugural Dicty World Race 2014 and contributed cell lines, which they tuned for enhanced speed and chemotactic accuracy. The race enabled large-scale analyses of chemotaxis in complex environments and revealed an intriguing balance of speed and accuracy of the model cell lines. The successes of the first race validated the concept of using fun-spirited competition to gain insights into the complex mechanisms controlling chemotaxis, while the challenges of the first race will guide further technological development and planning of future events.

Emergent Collective Chemotaxis without Single-Cell Gradient Sensing

Many eukaryotic cells chemotax, sensing and following chemical gradients. However, experiments show that even under conditions when single cells cannot chemotax, small clusters may still follow a gradient. This behavior is observed in neural crest cells, in lymphocytes, and during border cell migration in Drosophila, but its origin remains puzzling. Here, we propose a new mechanism underlying this "collective guidance," and study a model based on this mechanism both analytically and computationally. Our approach posits that contact inhibition of locomotion, where cells polarize away from cell-cell contact, is regulated by the chemoattractant. Individual cells must measure the mean attractant value, but need not measure its gradient, to give rise to directional motility for a cell cluster. We present analytic formulas for how the cluster velocity and chemotactic index depend on the number and organization of cells in the cluster. The presence of strong orientation effects provides a simple test for our theory of collective guidance.

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.

How to bake a brain: yeast as a model neuron

More than 30 years ago Dan Koshland published an inspirational essay presenting the bacterium as a model neuron (Koshland, Trends Neurosci 6:133-137, 1983). In the article he argued that there are several similarities between neurons and bacterial cells in "how signals are processed within a cell or how this processing machinery can be modified to produce plasticity". He then explored the bacterial chemosensory system to emphasize its attributes that are analogous to information processing in neurons. In this review, we wish to expand Koshland's original idea by adding the yeast cell to the list of useful models of a neuron. The fact that yeasts and neurons are specialized versions of the eukaryotic cell sharing all principal components sets the stage for a grand evolutionary tinkering where these components are employed in qualitatively different tasks, but following analogous molecular logic. By way of example, we argue that evolutionarily conserved key components involved in polarization processes (from budding or mating in Saccharomyces cervisiae to neurite outgrowth or spinogenesis in neurons) are shared between yeast and neurons. This orthologous conservation of modules makes S. cervisiae an excellent model organism to investigate neurobiological questions. We substantiate this claim by providing examples of yeast models used for studying neurological diseases.

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.

Microfluidics: reframing biological enquiry

The underlying physical properties of microfluidic tools have led to new biological insights through the development of microsystems that can manipulate, mimic and measure biology at a resolution that has not been possible with macroscale tools. Microsystems readily handle sub-microlitre volumes, precisely route predictable laminar fluid flows and match both perturbations and measurements to the length scales and timescales of biological systems. The advent of fabrication techniques that do not require highly specialized engineering facilities is fuelling the broad dissemination of microfluidic systems and their adaptation to specific biological questions. We describe how our understanding of molecular and cell biology is being and will continue to be advanced by precision microfluidic approaches and posit that microfluidic tools - in conjunction with advanced imaging, bioinformatics and molecular biology approaches - will transform biology into a precision science.

Cell-cell signalling in sexual chemotaxis: a basis for gametic differentiation, mating types and sexes

While sex requires two parents, there is no obvious need for them to be differentiated into distinct mating types or sexes. Yet this is the predominate state of nature. Here, we argue that mating types could play a decisive role because they prevent the apparent inevitability of self-stimulation during sexual signalling. We rigorously assess this hypothesis by developing a model for signaller-detector dynamics based on chemical diffusion, chemotaxis and cell movement. Our model examines the conditions under which chemotaxis improves partner finding. Varying parameter values within ranges typical of protists and their environments, we show that simultaneous secretion and detection of a single chemoattractant can cause a multifold movement impediment and severely hinder mate finding. Mutually exclusive roles result in faster pair formation, even when cells conferring the same roles cannot pair up. This arrangement also allows the separate mating types to optimize their signalling or detecting roles, which is effectively impossible for cells that are both secretors and detectors. Our findings suggest that asymmetric roles in sexual chemotaxis (and possibly other forms of sexual signalling) are crucial, even without morphological differences, and may underlie the evolution of gametic differentiation among both mating types and sexes.

Genetic control of morphogenesis in Dictyostelium

Cells grow, move, expand, shrink and die in the process of generating the characteristic shapes of organisms. Although the structures generated during development of the social amoeba Dictyostelium discoideum look nothing like the structures seen in metazoan embryogenesis, some of the morphogenetic processes used in their making are surprisingly similar. Recent advances in understanding the molecular basis for directed cell migration, cell type specific sorting, differential adhesion, secretion of matrix components, pattern formation, regulation and terminal differentiation are reviewed. Genes involved in Dictyostelium aggregation, slug formation, and culmination of fruiting bodies are discussed.

Properties of cooperatively induced phases in sensing models

A large number of eukaryotic cells are able to directly detect external chemical gradients with great accuracy and the ultimate limit to their sensitivity has been a topic of debate for many years. Previous work has been done to understand many aspects of this process but little attention has been paid to the possibility of emergent sensing states. Here we examine how cooperation between sensors existing in a two-dimensional network, as they do on the cell's surface, can both enhance and fundamentally alter the response of the cell to a spatially varying signal. We show that weakly interacting sensors linearly amplify the cell's response to an external gradient while a network of strongly interacting sensors form a collective nonlinear response with two separate domains of active and inactive sensors forming what have called a "1/2-state." In our analysis we examine the cell's ability to sense the direction of a signal and pay special attention to the substantially different behavior realized in the strongly interacting regime.

Microfluidic analysis of extracellular matrix-bFGF crosstalk on primary human myoblast chemoproliferation, chemokinesis, and chemotaxis

Exposing myoblasts to basic fibroblast growth factor (bFGF), which is released after muscle injury, results in receptor phosphorylation, faster migration, and increased proliferation. These effects occur on time scales that extend across three orders of magnitude (10(0)-10(3) minutes). Finite element modeling of Transwell assays, which are traditionally used to assess chemotaxis, revealed that the bFGF gradient formed across the membrane pore is short-lived and diminishes 45% within the first minute. Thus, to evaluate bFGF-induced migration over 10(2) minutes, we employed a microfluidic assay capable of producing a stable, linear concentration gradient to perform single-cell analyses of chemokinesis and chemotaxis. We hypothesized that the composition of the underlying extracellular matrix (ECM) may affect the behavioral response of myoblasts to soluble bFGF, as previous work with other cell types has suggested crosstalk between integrin and fibroblast growth factor (FGF) receptors. Consistent with this notion, we found that bFGF significantly reduced the doubling time of myoblasts cultured on laminin but not fibronectin or collagen. Laminin also promoted significantly faster migration speeds (13.4 μm h(-1)) than either fibronectin (10.6 μm h(-1)) or collagen (7.6 μm h(-1)) without bFGF stimulation. Chemokinesis driven by bFGF further increased migration speed in a strictly additive manner, resulting in an average increase of 2.3 μm h(-1) across all ECMs tested. We observed relatively mild chemoattraction (∼67% of myoblast population) in response to bFGF gradients of 3.2 ng mL(-1) mm(-1) regardless of ECM identity. Thus, while ECM-bFGF crosstalk did impact chemoproliferation, it did not have a significant effect on chemokinesis or chemotaxis. These data suggest that the main physiological effect of bFGF on myoblast migration is chemokinesis and that changes in the surrounding ECM, resulting from aging and/or disease may impact muscle regeneration by altering myoblast migration and proliferation.

Modelling the heart as a communication system

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in two-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.

How receptor diffusion influences gradient sensing

Chemotaxis, or directed motion in chemical gradients, is critical for various biological processes. Many eukaryotic cells perform spatial sensing, i.e. they detect gradients by comparing spatial differences in binding occupancy of chemosensory receptors across their membrane. In many theoretical models of spatial sensing, it is assumed, for the sake of simplicity, that the receptors concerned do not move. However, in reality, receptors undergo diverse modes of diffusion, and can traverse considerable distances in the time it takes such cells to turn in an external gradient. This sets a physical limit on the accuracy of spatial sensing, which we explore using a model in which receptors diffuse freely over the membrane. We find that the Fisher information carried in binding and unbinding events decreases monotonically with the diffusion constant of the receptors.

Evolutionarily conserved coupling of adaptive and excitable networks mediates eukaryotic chemotaxis

Numerous models explain how cells sense and migrate towards shallow chemoattractant gradients. Studies show that an excitable signal transduction network acts as a pacemaker that controls the cytoskeleton to drive motility. Here we show that this network is required to link stimuli to actin polymerization and chemotactic motility and we distinguish the various models of chemotaxis. First, signalling activity is suppressed towards the low side in a gradient or following removal of uniform chemoattractant. Second, signalling activities display a rapid shut off and a slower adaptation during which responsiveness to subsequent test stimuli decline. Simulations of various models indicate that these properties require coupled adaptive and excitable networks. Adaptation involves a G-protein-independent inhibitor, as stimulation of cells lacking G-protein function suppresses basal activities. The salient features of the coupled networks were observed for different chemoattractants in Dictyostelium and in human neutrophils, suggesting an evolutionarily conserved mechanism for eukaryotic chemotaxis.