Cooperative Clustering Digitizes Biochemical Signaling and Enhances its Fidelity

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.

Lifetime of actin-dependent protein nanoclusters

Protein nanoclusters (PNCs) are dynamic collections of a few proteins that spatially organize in nanometer-length clusters. PNCs are one of the principal forms of spatial organization of membrane proteins, and they have been shown or hypothesized to be important in various cellular processes, including cell signaling. PNCs show remarkable diversity in size, shape, and lifetime. In particular, the lifetime of PNCs can vary over a wide range of timescales. The diversity in size and shape can be explained by the interaction of the clustering proteins with the actin cytoskeleton or the lipid membrane, but very little is known about the processes that determine the lifetime of the nanoclusters. In this paper, using mathematical modeling of the cluster dynamics, we model the biophysical processes that determine the lifetime of actin-dependent PNCs. In particular, we investigated the role of actin aster fragmentation, which had been suggested to be a key determinant of the PNC lifetime, and we found that it is important only for a small class of PNCs. A simple extension of our model allowed us to investigate the kinetics of protein-ligand interaction near PNCs. We found an anomalous increase in the lifetime of ligands near PNCs, which agrees remarkably well with experimental data on RAS-RAF kinetics. In particular, analysis of the RAS-RAF data through our model provides falsifiable predictions and novel hypotheses that will not only shed light on the role of RAS-RAF kinetics in various cancers, but also will be useful in studying membrane protein clustering in general.

Correction of multiple-blinking artifacts in photoactivated localization microscopy

Photoactivated localization microscopy (PALM) produces an array of localization coordinates by means of photoactivatable fluorescent proteins. However, observations are subject to fluorophore multiple blinking and each protein is included in the dataset an unknown number of times at different positions, due to localization error. This causes artificial clustering to be observed in the data. We present a 'model-based correction' (MBC) workflow using calibration-free estimation of blinking dynamics and model-based clustering to produce a corrected set of localization coordinates representing the true underlying fluorophore locations with enhanced localization precision, outperforming the state of the art. The corrected data can be reliably tested for spatial randomness or analyzed by other clustering approaches, and descriptors such as the absolute number of fluorophores per cluster are now quantifiable, which we validate with simulated data and experimental data with known ground truth. Using MBC, we confirm that the adapter protein, the linker for activation of T cells, is clustered at the T cell immunological synapse.

Precision of Protein Thermometry

Temperature sensing is a ubiquitous cell behavior, but the fundamental limits to the precision of temperature sensing are poorly understood. Unlike in chemical concentration sensing, the precision of temperature sensing is not limited by extrinsic fluctuations in the temperature field itself. Instead, we find that precision is limited by the intrinsic copy number, turnover, and binding kinetics of temperature-sensitive proteins. Developing a model based on the canonical TlpA protein, we find that a cell can estimate temperature to within 2%. We compare this prediction with in vivo data on temperature sensing in bacteria.

The Role of Protein and Lipid Clustering in Lymphocyte Activation

Lymphocytes must strike a delicate balance between activating in response to signals from potentially pathogenic organisms and avoiding activation from stimuli emanating from the body's own cells. For cells, such as T or B cells, maximizing the efficiency and fidelity, whilst minimizing the crosstalk, of complex signaling pathways is crucial. One way of achieving this control is by carefully orchestrating the spatiotemporal organization of signaling molecules, thereby regulating the rates of protein-protein interactions. This is particularly true at the plasma membrane where proximal signaling events take place and the phenomenon of protein microclustering has been extensively observed and characterized. This review will focus on what is known about the heterogeneous distribution of proteins and lipids at the cell surface, illustrating how such distributions can influence signaling in health and disease. We particularly focus on nanoscale molecular organization, which has recently become accessible for study through advances in microscope technology and analysis methodology.

Multi-color Molecular Visualization of Signaling Proteins Reveals How C-Terminal Src Kinase Nanoclusters Regulate T Cell Receptor Activation

Elucidating the mechanisms that controlled T cell activation requires visualization of the spatial organization of multiple proteins on the submicron scale. Here, we use stoichiometrically accurate, multiplexed, single-molecule super-resolution microscopy (DNA-PAINT) to image the nanoscale spatial architecture of the primary inhibitor of the T cell signaling pathway, Csk, and two binding partners implicated in its membrane association, PAG and TRAF3. Combined with a newly developed co-clustering analysis framework, we find that Csk forms nanoscale clusters proximal to the plasma membrane that are lost post-stimulation and are re-recruited at later time points. Unexpectedly, these clusters do not co-localize with PAG at the membrane but instead provide a ready pool of monomers to downregulate signaling. By generating CRISPR-Cas9 knockout T cells, our data also identify that a major risk factor for autoimmune diseases, the protein tyrosine phosphatase non-receptor type 22 (PTPN22) locus, is essential for Csk nanocluster re-recruitment and for maintenance of the synaptic PAG population.

Nonequilibrium biochemical structures in two space dimensions with local activation and regulation

Integrin receptor (IR) clustering is an example of pattern self-organization in biological systems. This paper describes a model for receptor activation whose content is guided by two major principles in cellular signal transduction: (i) Proteins cycle between different conformational states; (ii) the dynamics of their conformational dynamics is environment dependent. Based on a simple activation pathway where these two hypotheses are formulated in a self-consistent way, this paper focuses mainly on stochastic simulations valid in the limit of a small number of molecules. It is shown that coherent clustering can lead to digital signaling and receptor competition in biochemical systems where the model gives a recruitment mechanism for the reinforcement of the mechanical linkage with the extracellular matrix. Together with previous works, this paper provides a workable model for cell integrin adhesive structures when feedback mediated by membrane diffusing signals is dominant. Consequences are discussed in the framework of published data concerning the local production of a key phospholipid for cell signaling (PIP_{2}).

An agent-based model of molecular aggregation at the cell membrane

Molecular clustering at the plasma membrane has long been identified as a key process and is associated with regulating signalling pathways across cell types. Recent advances in microscopy, in particular the rise of super-resolution, have allowed the experimental observation of nanoscale molecular clusters in the plasma membrane. However, modelling approaches capable of recapitulating these observations are in their infancy, partly because of the extremely complex array of biophysical factors which influence molecular distributions and dynamics in the plasma membrane. We propose here a highly abstracted approach: an agent-based model dedicated to the study of molecular aggregation at the plasma membrane. We show that when molecules are modelled as though they can act (diffuse) in a manner which is influenced by their molecular neighbourhood, many of the distributions observed in cells can be recapitulated, even though such sensing and response is not possible for real membrane molecules. As such, agent-based offers a unique platform which may lead to a new understanding of how molecular clustering in extremely complex molecular environments can be abstracted, simulated and interpreted using simple rules.

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.

Receptor crosstalk improves concentration sensing of multiple ligands

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

The Interplay of Structural and Cellular Biophysics Controls Clustering of Multivalent Molecules

Dynamic molecular clusters are assembled through weak multivalent interactions and are platforms for cellular functions, especially receptor-mediated signaling. Clustering is also a prerequisite for liquid-liquid phase separation. It is not well understood, however, how molecular structure and cellular organization control clustering. Using coarse-grained kinetic Langevin dynamics, we performed computational experiments on a prototypical ternary system modeled after membrane-bound nephrin, the adaptor Nck1, and the actin nucleation promoting factor NWASP. Steady-state cluster size distributions favored stoichiometries that optimized binding (stoichiometry matching) but still were quite broad. At high concentrations, the system can be driven beyond the saturation boundary such that cluster size is limited only by the number of available molecules. This behavior would be predictive of phase separation. Domains close to binding sites sterically inhibited clustering much less than terminal domains because the latter effectively restrict access to the cluster interior. Increased flexibility of interacting molecules diminished clustering by shielding binding sites within compact conformations. Membrane association of nephrin increased the cluster size distribution in a density-dependent manner. These properties provide insights into how molecular ensembles function to localize and amplify cell signaling.

Gradients of Rac1 Nanoclusters Support Spatial Patterns of Rac1 Signaling

Rac1 is a small RhoGTPase switch that orchestrates actin branching in space and time and protrusion/retraction cycles of the lamellipodia at the cell front during mesenchymal migration. Biosensor imaging has revealed a graded concentration of active GTP-loaded Rac1 in protruding regions of the cell. Here, using single-molecule imaging and super-resolution microscopy, we show an additional supramolecular organization of Rac1. We find that Rac1 partitions and is immobilized into nanoclusters of 50-100 molecules each. These nanoclusters assemble because of the interaction of the polybasic tail of Rac1 with the phosphoinositide lipids PIP2 and PIP3. The additional interactions with GEFs and possibly GAPs, downstream effectors, and other partners are responsible for an enrichment of Rac1 nanoclusters in protruding regions of the cell. Our results show that subcellular patterns of Rac1 activity are supported by gradients of signaling nanodomains of heterogeneous molecular composition, which presumably act as discrete signaling platforms.

Inferring a nonlinear biochemical network model from a heterogeneous single-cell time course data

Mathematical modeling and analysis of biochemical reaction networks are key routines in computational systems biology and biophysics; however, it remains difficult to choose the most valid model. Here, we propose a computational framework for data-driven and systematic inference of a nonlinear biochemical network model. The framework is based on the expectation-maximization algorithm combined with particle smoother and sparse regularization techniques. In this method, a “redundant” model consisting of an excessive number of nodes and regulatory paths is iteratively updated by eliminating unnecessary paths, resulting in an inference of the most likely model. Using artificial single-cell time-course data showing heterogeneous oscillatory behaviors, we demonstrated that this algorithm successfully inferred the true network without any prior knowledge of network topology or parameter values. Furthermore, we showed that both the regulatory paths among nodes and the optimal number of nodes in the network could be systematically determined. The method presented in this study provides a general framework for inferring a nonlinear biochemical network model from heterogeneous single-cell time-course data.

Common mechanisms of catalysis in small and heterotrimeric GTPases and their respective GAPs

GTPases are central switches in cells. Their dysfunctions are involved in severe diseases. The small GTPase Ras regulates cell growth, differentiation and apoptosis by transmitting external signals to the nucleus. In one group of oncogenic mutations, the 'switch-off' reaction is inhibited, leading to persistent activation of the signaling pathway. The switch reaction is regulated by GTPase-activating proteins (GAPs), which catalyze GTP hydrolysis in Ras, and by guanine nucleotide exchange factors, which catalyze the exchange of GDP for GTP. Heterotrimeric G-proteins are activated by G-protein coupled receptors and are inactivated by GTP hydrolysis in the Gα subunit. Their GAPs are called regulators of G-protein signaling. In the same way that Ras serves as a prototype for small GTPases, Gαi1 is the most well-studied Gα subunit. By utilizing X-ray structural models, time-resolved infrared-difference spectroscopy, and biomolecular simulations, we elucidated the detailed molecular reaction mechanism of the GTP hydrolysis in Ras and Gαi1. In both proteins, the charge distribution of GTP is driven towards the transition state, and an arginine is precisely positioned to facilitate nucleophilic attack of water. In addition to these mechanistic details of GTP hydrolysis, Ras dimerization as an emerging factor in signal transduction is discussed in this review.

Single-Molecule Imaging of Nav1.6 on the Surface of Hippocampal Neurons Reveals Somatic Nanoclusters

Voltage-gated sodium (Nav) channels are responsible for the depolarizing phase of the action potential in most nerve cells, and Nav channel localization to the axon initial segment is vital to action potential initiation. Nav channels in the soma play a role in the transfer of axonal output information to the rest of the neuron and in synaptic plasticity, although little is known about Nav channel localization and dynamics within this neuronal compartment. This study uses single-particle tracking and photoactivation localization microscopy to analyze cell-surface Nav1.6 within the soma of cultured hippocampal neurons. Mean-square displacement analysis of individual trajectories indicated that half of the somatic Nav1.6 channels localized to stable nanoclusters ∼230 nm in diameter. Strikingly, these domains were stabilized at specific sites on the cell membrane for >30 min, notably via an ankyrin-independent mechanism, indicating that the means by which Nav1.6 nanoclusters are maintained in the soma is biologically different from axonal localization. Nonclustered Nav1.6 channels showed anomalous diffusion, as determined by mean-square-displacement analysis. High-density single-particle tracking of Nav channels labeled with photoactivatable fluorophores in combination with Bayesian inference analysis was employed to characterize the surface nanoclusters. A subpopulation of mobile Nav1.6 was observed to be transiently trapped in the nanoclusters. Somatic Nav1.6 nanoclusters represent a new, to our knowledge, type of Nav channel localization, and are hypothesized to be sites of localized channel regulation.

3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse

Single-molecule localisation microscopy (SMLM) allows the localisation of fluorophores with a precision of 10-30 nm, revealing the cell's nanoscale architecture at the molecular level. Recently, SMLM has been extended to 3D, providing a unique insight into cellular machinery. Although cluster analysis techniques have been developed for 2D SMLM data sets, few have been applied to 3D. This lack of quantification tools can be explained by the relative novelty of imaging techniques such as interferometric photo-activated localisation microscopy (iPALM). Also, existing methods that could be extended to 3D SMLM are usually subject to user defined analysis parameters, which remains a major drawback. Here, we present a new open source cluster analysis method for 3D SMLM data, free of user definable parameters, relying on a model-based Bayesian approach which takes full account of the individual localisation precisions in all three dimensions. The accuracy and reliability of the method is validated using simulated data sets. This tool is then deployed on novel experimental data as a proof of concept, illustrating the recruitment of LAT to the T-cell immunological synapse in data acquired by iPALM providing ~10 nm isotropic resolution.

A Bayesian cluster analysis method for single-molecule localization microscopy data

Cell function is regulated by the spatiotemporal organization of the signaling machinery, and a key facet of this is molecular clustering. Here, we present a protocol for the analysis of clustering in data generated by 2D single-molecule localization microscopy (SMLM)-for example, photoactivated localization microscopy (PALM) or stochastic optical reconstruction microscopy (STORM). Three features of such data can cause standard cluster analysis approaches to be ineffective: (i) the data take the form of a list of points rather than a pixel array; (ii) there is a non-negligible unclustered background density of points that must be accounted for; and (iii) each localization has an associated uncertainty in regard to its position. These issues are overcome using a Bayesian, model-based approach. Many possible cluster configurations are proposed and scored against a generative model, which assumes Gaussian clusters overlaid on a completely spatially random (CSR) background, before every point is scrambled by its localization precision. We present the process of generating simulated and experimental data that are suitable to our algorithm, the analysis itself, and the extraction and interpretation of key cluster descriptors such as the number of clusters, cluster radii and the number of localizations per cluster. Variations in these descriptors can be interpreted as arising from changes in the organization of the cellular nanoarchitecture. The protocol requires no specific programming ability, and the processing time for one data set, typically containing 30 regions of interest, is ∼18 h; user input takes ∼1 h.

C2-domain mediated nano-cluster formation increases calcium signaling efficiency

Conventional protein kinase Cs (cPKCs) are key signaling proteins for transducing intracellular Ca²⁺ signals into downstream phosphorylation events. However, the lifetime of individual membrane-bound activated cPKCs is an order of magnitude shorter than the average time needed for target-protein phosphorylation. Here, we employed intermolecular Förster resonance energy transfer (FRET) in living cells combined with computational analysis to study the spatial organization of cPKCs bound to the plasma membrane. We discovered Ca²⁺-dependent cPKC nano-clusters that significantly extend cPKC’s plasma-membrane residence time. These protein patterns resulted from self-assembly mediated by Ca²⁺-binding C2-domains, which are widely used for membrane-targeting of Ca²⁺-sensing proteins. We also established clustering of other unrelated C2-domain containing proteins, suggesting that nano-cluster formation is a key step for efficient cellular Ca²⁺-signaling.

Superresolution imaging of the cytoplasmic phosphatase PTPN22 links integrin-mediated T cell adhesion with autoimmunity

Integrins are heterodimeric transmembrane proteins that play a fundamental role in the migration of leukocytes to sites of infection or injury. We found that protein tyrosine phosphatase nonreceptor type 22 (PTPN22) inhibits signaling by the integrin lymphocyte function-associated antigen-1 (LFA-1) in effector T cells. PTPN22 colocalized with its substrates at the leading edge of cells migrating on surfaces coated with the LFA-1 ligand intercellular adhesion molecule-1 (ICAM-1). Knockout or knockdown of PTPN22 or expression of the autoimmune disease-associated PTPN22-R620W variant resulted in the enhanced phosphorylation of signaling molecules downstream of integrins. Superresolution imaging revealed that PTPN22-R620 (wild-type PTPN22) was present as large clusters in unstimulated T cells and that these disaggregated upon stimulation of LFA-1, enabling increased association of PTPN22 with its binding partners at the leading edge. The failure of PTPN22-R620W molecules to be retained at the leading edge led to increased LFA-1 clustering and integrin-mediated cell adhesion. Our data define a previously uncharacterized mechanism for fine-tuning integrin signaling in T cells, as well as a paradigm of autoimmunity in humans in which disease susceptibility is underpinned by inherited phosphatase mutations that perturb integrin function.