Biophysical mechanism for ras-nanocluster formation and signaling in plasma membrane

Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: phase behavior and structural properties

Competing short-range attractive (SA) and long range repulsive (LR) particle interactions can be used to describe three-dimensional charge-stabilized colloid or protein dispersions at low added salt concentrations, as well as membrane proteins with interaction contributions mediated by lipid molecules. Using Langevin dynamics (LD) simulations, we determine the generalized phase diagram, cluster shapes and size distributions of a generic quasi-two-dimensional (Q2D) dispersion of spherical SALR particles confined to in-plane motion inside a bulk fluid. The SA and LR interaction parts are modelled by a generalized Lennard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the detected equilibrium and non-equilibrium Q2D phases are distinctly different from those observed in three-dimensional (3D) SALR systems, by exhibiting different levels of hexagonal ordering. We discuss a thermodynamic perturbation theory prediction for the metastable binodal line of a reference system of particles with SA interactions only, which in the explored Q2D-SALR phase diagram region separates cluster from non-clustered phases. The transition from the high-temperature (small SA) dispersed fluid (DF) phase to the lower-temperature equilibrium cluster (EC) fluid phase is characterised by a low-wavenumber peak height of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller value (≈1.4) than in 3D SALR systems. With decreasing temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster segments formed in a cluster-percolated (CP) gel-like phase. This transition can be quantified by a hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the CP phase are insensitive to changes in the attraction strength.

Positive feedback in Ras activation by full-length SOS arises from autoinhibition release mechanism

Signaling through the Ras-MAPK pathway can exhibit switch-like activation, which has been attributed to the underlying positive feedback and bimodality in the activation of RasGDP to RasGTP by SOS. SOS contains both catalytic and allosteric Ras binding sites, and a common assumption is that allosteric activation selectively by RasGTP provides the mechanism of positive feedback. However, recent single-molecule studies have revealed that SOS catalytic rates are independent of the nucleotide state of Ras in the allosteric binding site, raising doubt about this as a positive feedback mechanism. Here, we perform detailed kinetic analyses of receptor-mediated recruitment of full-length SOS to the membrane while simultaneously monitoring its catalytic activation of Ras. These results, along with kinetic modeling, expose the autoinhibition release step in SOS, rather than either recruitment or allosteric activation, as the underlying mechanism giving rise to positive feedback in Ras activation.

Cooperativity and oscillations: Regulatory mechanisms of K-Ras nanoclusters

K-Ras nanoclusters (NCs) concentrate all required molecules belonging to the extracellular signal-regulated kinase (ERK) mitogen-activated protein kinase (MAPK) pathway in a small area where signaling events take place, increasing efficiency and specificity of signaling. Such nanostructures are characterized by controlled sizes and lifetimes distributions, but there is a poor understanding of the mechanisms involved in their dynamics of growth/decay. Here, a minimum computational model is presented to analyze the behavior of K-Ras NCs as cooperative dynamic structures that self-regulate their growth and decay according to their size. Indeed, the proposed model reveals that the growth and the local production of a K-Ras nanocluster depend positively on its actual size, whilst its lifetime is inversely proportional to the root of its size. The cooperative binding between the structural constituents of the NC (K-Ras proteins) induces oscillations in the size distributions of K-Ras NCs allowing them to range within controlled values, regulating the growth/decay dynamics of these NCs. Thereby, the size of a K-Ras NC is proposed as a key factor to regulate cell signaling, opening a range of possibilities to develop strategies for use in chronic diseases and cancer.

Altered CXCR4 dynamics at the cell membrane impairs directed cell migration in WHIM syndrome patients

SignificanceNew imaging-based approaches are incorporating new concepts to our knowledge of biological processes. The analysis of receptor dynamics involved in cell movement using single-particle tracking demonstrates that cells require chemokine-mediated receptor clustering to sense appropriately chemoattractant gradients. Here, we report that this process does not occur in T cells expressing CXCR4^R334X, a mutant form of CXCR4 linked to WHIM syndrome (warts, hypogammaglobulinemia, infections, myelokathexis). The underlaying molecular mechanism involves inappropriate actin cytoskeleton remodeling due to the inadequate β-arrestin1 activation by CXCR4^R334X, which alters its lateral mobility and spatial organization. These defects, associated to CXCR4^R334X expression, contribute to the retention of hematopoietic precursors in bone marrow niches and explain the severe immunological symptoms associated with WHIM syndrome.

γ-Secretase Partitioning into Lipid Bilayers Remodels Membrane Microdomains after Direct Insertion

γ-Secretase is a multisubunit complex that catalyzes intramembranous cleavage of transmembrane proteins. The lipid environment forms membrane microdomains that serve as spatio-temporal platforms for proteins to function properly. Despite substantial advances in the regulation of γ-secretase, the effect of the local membrane lipid microenvironment on the regulation of γ-secretase is poorly understood. Here, we characterized and quantified the partitioning of γ-secretase and its substrates, the amyloid precursor protein (APP) and Notch, into lipid bilayers using solid-supported model membranes. Notch substrate is preferentially localized in the liquid-disordered (L_d) lipid domains, whereas APP and γ-secretase partition as single or higher complex in both phases but highly favor the ordered phase, especially after recruiting lipids from the ordered phase, indicating that the activity and specificity of γ-secretase against these two substrates are modulated by membrane lateral organization. Moreover, time-elapse measurements reveal that γ-secretase can recruit specific membrane components from the cholesterol-rich L_o phase and thus creates a favorable lipid environment for substrate recognition and therefore activity. This work offers insight into how γ-secretase and lipid modulate each other and control its activity and specificity.

Shared behavioral mechanisms underlie C. elegans aggregation and swarming

In complex biological systems, simple individual-level behavioral rules can give rise to emergent group-level behavior. While collective behavior has been well studied in cells and larger organisms, the mesoscopic scale is less understood, as it is unclear which sensory inputs and physical processes matter a priori. Here, we investigate collective feeding in the roundworm C. elegans at this intermediate scale, using quantitative phenotyping and agent-based modeling to identify behavioral rules underlying both aggregation and swarming-a dynamic phenotype only observed at longer timescales. Using fluorescence multi-worm tracking, we quantify aggregation in terms of individual dynamics and population-level statistics. Then we use agent-based simulations and approximate Bayesian inference to identify three key behavioral rules for aggregation: cluster-edge reversals, a density-dependent switch between crawling speeds, and taxis towards neighboring worms. Our simulations suggest that swarming is simply driven by local food depletion but otherwise employs the same behavioral mechanisms as the initial aggregation.

A molecular assembly phase transition and kinetic proofreading modulate Ras activation by SOS

The guanine nucleotide exchange factor (GEF) Son of Sevenless (SOS) is a key Ras activator that is autoinhibited in the cytosol and activates upon membrane recruitment. Autoinhibition release involves structural rearrangements of the protein at the membrane and thus introduces a delay between initial recruitment and activation. In this study, we designed a single-molecule assay to resolve the time between initial receptor-mediated membrane recruitment and the initiation of GEF activity of individual SOS molecules on microarrays of Ras-functionalized supported membranes. The rise-and-fall shape of the measured SOS activation time distribution and the long mean time scale to activation (~50 seconds) establish a basis for kinetic proofreading in the receptor-mediated activation of Ras. We further demonstrate that this kinetic proofreading is modulated by the LAT (linker for activation of T cells)-Grb2-SOS phosphotyrosine-driven phase transition at the membrane.

eGFRD in all dimensions

Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present "eGFRD2," a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions.

Separating Actin-Dependent Chemokine Receptor Nanoclustering from Dimerization Indicates a Role for Clustering in CXCR4 Signaling and Function

A current challenge in cell motility studies is to understand the molecular and physical mechanisms that govern chemokine receptor nanoscale organization at the cell membrane, and their influence on cell response. Using single-particle tracking and super-resolution microscopy, we found that the chemokine receptor CXCR4 forms basal nanoclusters in resting T cells, whose extent, dynamics, and signaling strength are modulated by the orchestrated action of the actin cytoskeleton, the co-receptor CD4, and its ligand CXCL12. We identified three CXCR4 structural residues that are crucial for nanoclustering and generated an oligomerization-defective mutant that dimerized but did not form nanoclusters in response to CXCL12, which severely impaired signaling. Overall, our data provide new insights to the field of chemokine biology by showing that receptor dimerization in the absence of nanoclustering is unable to fully support CXCL12-mediated responses, including signaling and cell function in vivo.

A Rationale for Mesoscopic Domain Formation in Biomembranes

Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also be observed in vitro on model systems such as supported membranes or lipid vesicles. Lipid mixtures separating in liquid-ordered and liquid-disordered phases below a demixing temperature play a pivotal role in this context. Protein-protein and protein-lipid interactions also contribute to membrane shaping by promoting small domains or clusters. Such phase separations displaying characteristic length-scales falling in-between the nanoscopic, molecular scale on the one hand and the macroscopic scale on the other hand, are named mesophases in soft condensed matter physics. In this review, we propose a classification of the diverse mechanisms leading to mesophase separation in biomembranes. We distinguish between mechanisms relying upon equilibrium thermodynamics and those involving out-of-equilibrium mechanisms, notably active membrane recycling. In equilibrium, we especially focus on the many mechanisms that dwell on an up-down symmetry breaking between the upper and lower bilayer leaflets. Symmetry breaking is an ubiquitous mechanism in condensed matter physics at the heart of several important phenomena. In the present case, it can be either spontaneous (domain buckling) or explicit, i.e., due to an external cause (global or local vesicle bending properties). Whenever possible, theoretical predictions and simulation results are confronted to experiments on model systems or living cells, which enables us to identify the most realistic mechanisms from a biological perspective.

A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient, short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we developed a multiscale model verified by quantitative microscopy to describe behaviors ranging widely from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell—cell communication and hence aggregation, we analyzed cell—cell correlations, showing evidence of self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. By comparing wild-type and mutant cells with impaired aggregation, we found the longest cell—cell communication distance in wild-type cells, suggesting that criticality provides an adaptive advantage and optimally sized aggregates for the dispersal of spores.

A multiscale model and imaging data show that cells of the slime mold Dictyostelium discoideum maximize their cell—cell communication range during aggregation by a critical-like state known from phase transitions in physical systems.

Cells are often coupled to each other in cell collectives, such as aggregates during early development, tissues in the developed organism, and tumors in disease. How do cells communicate over macroscopic distances much larger than the typical cell—cell distance to decide how they should behave? Here, we developed a multiscale model of social amoeba, spanning behavior from individuals to thousands of cells. We show that local cell—cell coupling via secreted chemicals may be tuned to a critical value, resulting in emergent long-range communication and heightened sensitivity. Hence, these aggregates are remarkably similar to bacterial biofilms and neuronal networks, all communicating in a pulselike fashion. Similar organizing principles may also aid our understanding of the remarkable robustness in cancer development.

Cooperative Clustering Digitizes Biochemical Signaling and Enhances its Fidelity

Many membrane-bound molecules in cells form small clusters. It has been hypothesized that these clusters convert an analog extracellular signal into a digital intracellular signal and that this conversion increases signaling fidelity. However, the mechanism by which clusters digitize a signal and the subsequent effects on fidelity remain poorly understood. Here we demonstrate using a stochastic model of cooperative cluster formation that sufficient cooperation leads to digital signaling. We show that despite reducing the number of output states, which decreases fidelity, digitization also reduces noise in the system, which increases fidelity. The tradeoff between these effects leads to an optimal cluster size that agrees with experimental measurements.

Nanodomains in Biomembranes with Recycling

Cell membranes are out of thermodynamic equilibrium notably because of membrane recycling, i.e., active exchange of material with the cytosol. We propose an analytically tractable model of biomembrane predicting the effects of recycling on the size of protein nanodomains also called protein clusters. The model includes a short-range attraction between proteins and a weaker long-range repulsion which ensures the existence of so-called cluster phases in equilibrium, where monomeric proteins coexist with finite-size domains. Our main finding is that, when taking recycling into account, the typical cluster size at steady state increases logarithmically with the recycling rate at fixed protein concentration. Using physically realistic model parameters, the predicted 2-fold increase due to recycling in living cells is most likely experimentally measurable with the help of super-resolution microscopy.

On characterizing protein spatial clusters with correlation approaches

Spatial aggregation of proteins might have functional importance, e.g., in signaling, and nano-imaging can be used to study them. Such studies require accurate characterization of clusters based on noisy data. A set of spatial correlation approaches free of underlying cluster processes and input parameters have been widely used for this purpose. They include the radius of maximal aggregation r_a obtained from Ripley’s L(r) − r function as an estimator of cluster size, and the estimation of various cluster parameters based on an exponential model of the Pair Correlation Function(PCF). While convenient, the accuracy of these methods is not clear: e.g., does it depend on how the molecules are distributed within the clusters, or on cluster parameters? We analyze these methods for a variety of cluster models. We find that r_a relates to true cluster size by a factor that is nonlinearly dependent on parameters and that can be arbitrarily large. For the PCF method, for the models analyzed, we obtain linear relationships between the estimators and true parameters, and the estimators were found to be within ±100% of true parameters, depending on the model. Our results, based on an extendable general framework, point to the need for caution in applying these methods.

Where Biology Meets Physics--A Converging View on Membrane Microdomain Dynamics

For several decades, the phenomenon of membrane component segregation into microdomains has been a well-known and highly debated subject, and varying concepts including the raft hypothesis, the fence-and-picket model, hydrophobic-mismatch, and specific protein-protein interactions have been offered as explanations. Here, we review the level of insight into the molecular architecture of membrane domains one is capable of obtaining through biological experimentation. Using SNARE proteins as a paradigm, comprehensive data suggest that several dozens of molecules crowd together into almost circular spots smaller than 100 nm. Such clusters are highly dynamical as they constantly capture and lose molecules. The organization has a strong influence on the functional availability of proteins and likely provides a molecular scaffold for more complex protein networks. Despite this high level of insight, fundamental open questions remain, applying not only to SNARE protein domains but more generally to all types of membrane domains. In this context, we explain the view of physical models and how they are beneficial in advancing our concept of micropatterning. While biological models generally remain qualitative and descriptive, physics aims towards making them quantitative and providing reproducible numbers, in order to discriminate between different mechanisms which have been proposed to account for experimental observations. Despite the fundamental differences in biological and physical approaches as far as cell membrane microdomains are concerned, we are able to show that convergence on common points of views is in reach.

The nanoscale organization of signaling domains at the plasma membrane

In this chapter, we present an overview of the role of the nanoscale organization of signaling domains in regulating key cellular processes. In particular, we illustrate the importance of protein and lipid nanodomains as triggers and mediators of cell signaling. As particular examples, we summarize the state of the art of understanding the role of nanodomains in the mounting of an immune response, cellular adhesion, intercellular communication, and cell proliferation. Thus, this chapter underlines the essential role the nanoscale organization of key signaling proteins and lipid domains. We will also see how nanodomains play an important role in the lifecycle of many pathogens relevant to human disease and therefore illustrate how these structures may become future therapeutic targets.

Modeling curvature-dependent subcellular localization of the small sporulation protein SpoVM in Bacillus subtilis

Recent in vivo experiments suggest that in the bacterium, Bacillus subtilis, the cue for the localization of the small sporulation protein, SpoVM, an essential factor in spore coat formation, is curvature of the bacterial plasma membrane. In vitro measurements of SpoVM adsorption to vesicles of varying sizes also find high sensitivity of adsorption to vesicle radius. This curvature-dependent adsorption is puzzling given the orders of magnitude difference in length scale between an individual protein and the radius of curvature of the cell or vesicle, suggesting protein clustering on the membrane. Here we develop a minimal model to study the relationship between curvature-dependent membrane adsorption and clustering of SpoVM. Based on our analysis, we hypothesize that the radius dependence of SpoVM adsorption observed in vitro is governed primarily by membrane tension, while for in-vivo localization of SpoVM, we propose a highly sensitive mechanism for curvature sensing based on the formation of macroscopic protein clusters on the membrane.

The efficacy of Raf kinase recruitment to the GTPase H-ras depends on H-ras membrane conformer-specific nanoclustering

Solution structures and biochemical data have provided a wealth of mechanistic insight into Ras GTPases. However, information on how much the membrane organization of these lipid-modified proteins impacts on their signaling is still scarce. Ras proteins are organized into membrane nanoclusters, which are necessary for Ras-MAPK signaling. Using quantitative conventional and super-resolution fluorescence methods, as well as mathematical modeling, we investigated nanoclustering of H-ras helix α4 and hypervariable region mutants that have different bona fide conformations on the membrane. By following the emergence of conformer-specific nanoclusters in the plasma membrane of mammalian cells, we found that conformers impart distinct nanoclustering responses depending on the cytoplasmic levels of the nanocluster scaffold galectin-1. Computational modeling revealed that complexes containing H-ras conformers and galectin-1 affect both the number and lifetime of nanoclusters and thus determine the specific Raf effector recruitment. Our results show that mutations in Ras can affect its nanoclustering response and thus allosterically effector recruitment and downstream signaling. We postulate that cancer- and developmental disease-linked mutations that are associated with the Ras membrane conformation may exhibit so far unrecognized Ras nanoclustering and therefore signaling alterations.

Importance of crowding in signaling, genetic, and metabolic networks

It is now well established that the cell is a highly crowded environment. Yet, the effects of crowding on the dynamics of signaling pathways, gene regulation networks, and metabolic networks are still largely unknown. Crowding can alter both molecular diffusion and the equilibria of biomolecular reactions. In this chapter, we first discuss how diffusion can affect biochemical networks. Diffusion of transcription factors can increase noise in gene expression, while diffusion of proteins between intracellular compartments or between cells can reduce concentration fluctuations. In push-pull networks diffusion can impede information transmission, while in multisite protein modification networks diffusion can qualitatively change the macroscopic response of the system, such as the loss or emergence of bistability. Moreover, diffusion can directly change the metabolic flux. We describe how crowding affects diffusion, and thus how all these phenomena are influenced by crowding. Yet, a potentially more important effect of crowding on biochemical networks is mediated via the shift in the equilibria of bimolecular reactions, and we provide computational evidence that supports this idea. Finally, we discuss how the effects of crowding can be incorporated in models of biochemical networks.

Rotational and translational dynamics of ras proteins upon binding to model membrane systems

Plasma-membrane-associated Ras proteins typically control signal transduction processes. As nanoclustering and membrane viscosity sensing provide plausible signaling mechanisms, determination of the rotational and translational dynamics of membrane-bound Ras isoforms can help to link their dynamic mobility to their function. Herein, by using time-resolved fluorescence anisotropy and correlation spectroscopic measurements, we obtain the rotational-correlation time and the translational diffusion coefficient of lipidated boron-dipyrromethene-labeled Ras, both in bulk Ras and upon membrane binding. The results show that the second lipidation motif of N-Ras triggers dimer formation in bulk solution, whereas K-Ras4B is monomeric. Upon membrane binding, an essentially free rotation of the G-domain is observed, along with a high lateral mobility; the latter is essentially limited by the viscosity of the membrane and by lipid-mediated electrostatic interactions. This high diffusional mobility warrants rapid recognition-binding sequences in the membrane-bound state, thereby facilitating efficient interactions between the Ras proteins and scaffolding or effector proteins. The lipid-like rapid lateral diffusion observed here complies with in vivo data.

Spatial partitioning improves the reliability of biochemical signaling

Spatial heterogeneity is a hallmark of living systems, even at the molecular scale in individual cells. A key example is the partitioning of membrane-bound proteins via lipid domain formation or cytoskeleton-induced corralling. However, the impact of this spatial heterogeneity on biochemical signaling processes is poorly understood. Here, we demonstrate that partitioning improves the reliability of biochemical signaling. We exactly solve a stochastic model describing a ubiquitous motif in membrane signaling. The solution reveals that partitioning improves signaling reliability via two effects: it moderates the nonlinearity of the switching response, and it reduces noise in the response by suppressing correlations between molecules. An optimal partition size arises from a trade-off between minimizing the number of proteins per partition to improve signaling reliability and ensuring sufficient proteins per partition to maintain signal propagation. The predicted optimal partition size agrees quantitatively with experimentally observed systems. These results persist in spatial simulations with explicit diffusion barriers. Our findings suggest that molecular partitioning is not merely a consequence of the complexity of cellular substructures, but also plays an important functional role in cell signaling.

Membrane clustering and the role of rebinding in biochemical signaling

In many cellular signaling pathways, key components form clusters at the cell membrane. Although much work has focused on the mechanisms behind such cluster formation, the implications for downstream signaling remain poorly understood. Here, motivated by recent experiments, we use particle-based simulation to study a covalent modification network in which the activating component is either clustered or randomly distributed on the membrane. We find that whereas clustering reduces the response of a single-modification network, it can enhance the response of a double-modification network. The reduction is a bulk effect: a cluster presents a smaller effective target to a substrate molecule in the bulk. The enhancement, on the other hand, is a local effect: a cluster promotes the rapid rebinding and second activation of singly activated substrate molecules. As such, the enhancement relies on frequent collisions on a short timescale, leading to an optimal ratio of diffusion to association that agrees with typical measured rates. We complement simulation with analytic results at both the mean-field and first-passage distribution levels. Our results emphasize the importance of spatially resolved models, showing that significant effects of spatial correlations persist even in spatially averaged quantities such as response curves.

A bistable model of cell polarity

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

A density-dependent switch drives stochastic clustering and polarization of signaling molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered "off" state is desired? And, what limits the spread of clusters when an "on" state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the "neutral drift polarity model." Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization.

Roles of the cytoskeleton in regulating EphA2 signals

The lateral organizations of receptors in the cell membrane display a tremendous amount of complexity. In some cases, receptor functions can be attributed to specific spatial arrangements in the plasma membrane. We recently found that one member of the largest subfamily of receptor tyrosine kinases (RTKs), EphA2, is organized over micrometer length scales by the cell's own cytoskeleton, and that this can regulate receptor signaling functions. Spatial organization of the receptor was found to be highly associated with invasive character, and mechanical disruption of receptor organization altered key down-stream events in the EphA2 signaling pathway. In this Addendum article, we put forth possible models for why EphA2 and other receptors may employ mechanical and spatial inputs mediated by the cytoskeleton. We speculate that this class of input may be common, and contributes to the intricacies of cellular signaling.

Clusters of proteins in biomembranes: insights into the roles of interaction potential shapes and of protein diversity

It has recently been proposed that proteins embedded in lipidic biomembranes can spontaneously self-organize into stable small clusters, or membrane nanodomains, due to the competition between short-range attractive and longer-range repulsive forces between proteins, specific to these systems. In this paper, we carry on our investigation, by Monte Carlo simulations, of different aspects of cluster phases of proteins in biomembranes. First, we compare different long-range potentials (including notably three-body terms) to demonstrate that the existence of cluster phases should be quite generic. Furthermore, a real membrane contains hundreds of different protein species that are far from being randomly distributed in these nanodomains. We take this protein diversity into account by modulating protein-protein interaction potentials both at short and longer range. We confirm theoretical predictions in terms of biological cluster specialization by deciphering how clusters recruit only a few protein species. In this respect, we highlight that cluster phases can turn out to be an advantage at the biological level, for example by enhancing the cell response to external stimuli.

Optimal receptor-cluster size determined by intrinsic and extrinsic noise

Biological cells sense external chemical stimuli in their environment using cell-surface receptors. To increase the sensitivity of sensing, receptors often cluster. This process occurs most noticeably in bacterial chemotaxis, a paradigm for sensing and signaling in general. While amplification of weak stimuli is useful in the absence of noise, its usefulness is less clear in the presence of extrinsic input noise and intrinsic signaling noise. Here, exemplified in a bacterial chemotaxis system, we combine the allosteric Monod-Wyman-Changeux model for signal amplification by receptor complexes with calculations of noise to study their interconnectedness. Importantly, we calculate the signal-to-noise ratio, describing the balance of beneficial and detrimental effects of clustering for the cell. Interestingly, we find that there is no advantage for the cell to build receptor complexes for noisy input stimuli in the absence of intrinsic signaling noise. However, with intrinsic noise, an optimal complex size arises in line with estimates of the size of chemoreceptor complexes in bacteria and protein aggregates in lipid rafts of eukaryotic cells.

Chemotactic response and adaptation dynamics in Escherichia coli

Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia coli is integral for detecting chemicals over a wide range of background concentrations, ultimately allowing cells to swim towards sources of attractant and away from repellents. Its biochemical mechanism based on methylation and demethylation of chemoreceptors has long been known. Despite the importance of adaptation for cell memory and behavior, the dynamics of adaptation are difficult to reconcile with current models of precise adaptation. Here, we follow time courses of signaling in response to concentration step changes of attractant using in vivo fluorescence resonance energy transfer measurements. Specifically, we use a condensed representation of adaptation time courses for efficient evaluation of different adaptation models. To quantitatively explain the data, we finally develop a dynamic model for signaling and adaptation based on the attractant flow in the experiment, signaling by cooperative receptor complexes, and multiple layers of feedback regulation for adaptation. We experimentally confirm the predicted effects of changing the enzyme-expression level and bypassing the negative feedback for demethylation. Our data analysis suggests significant imprecision in adaptation for large additions. Furthermore, our model predicts highly regulated, ultrafast adaptation in response to removal of attractant, which may be useful for fast reorientation of the cell and noise reduction in adaptation.

Signalling complexes and clusters: functional advantages and methodological hurdles

Signalling molecules integrate, codify and transport information in cells. Organisation of these molecules in complexes and clusters improves the efficiency, fidelity and robustness of cellular signalling. Here, we summarise current views on how signalling molecules assemble into macromolecular complexes and clusters and how they use their physical properties to transduce environmental information into a variety of cellular processes. In addition, we discuss recent innovations in live-cell imaging at the sub-micrometer scale and the challenges of object (particle) tracking, both of which help us to observe signalling complexes and clusters and to examine their dynamic character.