Monte Carlo simulations of plasma membrane corral-induced EGFR clustering

Implications of different membrane compartmentalization models in particle-based in silico studies

Studying membrane dynamics is important to understand the cellular response to environmental stimuli. A decisive spatial characteristic of the plasma membrane is its compartmental structure created by the actin-based membrane-skeleton (fences) and anchored transmembrane proteins (pickets). Particle-based reaction-diffusion simulation of the membrane offers a suitable temporal and spatial resolution to analyse its spatially heterogeneous and stochastic dynamics. Fences have been modelled via hop probabilities, potentials or explicit picket fences. Our study analyses the different approaches' constraints and their impact on simulation results and performance. Each of the methods comes with its own constraints; the picket fences require small timesteps, potential fences might induce a bias in diffusion in crowded systems, and probabilistic fences, in addition to carefully scaling the probability with the timesteps, induce higher computational costs for each propagation step.

Single-molecule labeling for studying trafficking of renal transporters

The ability to detect and track single molecules presents the advantage of visualizing the complex behavior of transmembrane proteins with a time and space resolution that would otherwise be lost with traditional labeling and biochemical techniques. Development of new imaging probes has provided a robust method to study their trafficking and surface dynamics. This mini-review focuses on the current technology available for single-molecule labeling of transmembrane proteins, their advantages, and limitations. We also discuss the application of these techniques to the study of renal transporter trafficking in light of recent research.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

Plasma Membrane Organization of Epidermal Growth Factor Receptor in Resting and Ligand-Bound States

The spatial arrangement of the epidermal growth factor receptor (EGFR) on the cellular plasma membrane is one of the prime factors that control its downstream signaling pathways and related functions. However, the molecular organization, which spans the scale from nanometers to micrometer-size clusters, has not been resolved in detail, mainly due to a lack of techniques with the required spatiotemporal resolution. Therefore, we used imaging total internal reflection-fluorescence correlation spectroscopy to investigate EGFR dynamics on live CHO-K1 plasma membranes in resting and ligand-bound states. In combination with the fluorescence correlation spectroscopy diffusion law, this provides information on the subresolution organization of EGFR on cell membranes. We found that overall EGFR organization is sensitive to both cholesterol and the actin cytoskeleton. EGFR in the resting state is partly trapped in cholesterol-containing domains, whereas another fraction exhibits cholesterol independent trapping on the membrane. Disruption of the cytoskeleton leads to a broader range of EGFR diffusion coefficients and a reduction of hop diffusion. In the ligand-bound state we found a dose-dependent behavior. At 10 ng/mL EGF the EGFR is endocytosed and recycled to the membrane, whereas diffusion and organization do not change significantly. At 100 ng/mL EGF the EGFR forms clusters, which are subsequently internalized, whereas outside the clusters diffusivity increases and the organization of the receptor remains unchanged. After disruption of cholesterol-containing domains or actin cytoskeleton, EGF induces microscopic EGFR clusters on the membrane and endocytosis is inhibited.

Effect of Spatial Inhomogeneities on the Membrane Surface on Receptor Dimerization and Signal Initiation

Important signal transduction pathways originate on the plasma membrane, where microdomains may transiently entrap diffusing receptors. This results in a non-random distribution of receptors even in the resting state, which can be visualized as “clusters” by high resolution imaging methods. Here, we explore how spatial in-homogeneities in the plasma membrane might influence the dimerization and phosphorylation status of ErbB2 and ErbB3, two receptor tyrosine kinases that preferentially heterodimerize and are often co-expressed in cancer. This theoretical study is based upon spatial stochastic simulations of the two-dimensional membrane landscape, where variables include differential distributions and overlap of transient confinement zones (“domains”) for the two receptor species. The in silico model is parameterized and validated using data from single particle tracking experiments. We report key differences in signaling output based on the degree of overlap between domains and the relative retention of receptors in such domains, expressed as escape probability. Results predict that a high overlap of domains, which favors transient co-confinement of both receptor species, will enhance the rate of hetero-interactions. Where domains do not overlap, simulations confirm expectations that homo-interactions are favored. Since ErbB3 is uniquely dependent on ErbB2 interactions for activation of its catalytic activity, variations in domain overlap or escape probability markedly alter the predicted patterns and time course of ErbB3 and ErbB2 phosphorylation. Taken together, these results implicate membrane domain organization as an important modulator of signal initiation, motivating the design of novel experimental approaches to measure these important parameters across a wider range of receptor systems.

Confined diffusion of transmembrane proteins and lipids induced by the same actin meshwork lining the plasma membrane

Ultraspeed single-molecule tracking with <25-μs resolution and electron tomography show that transmembrane proteins and phospholipids in the plasma membrane hop among submicrometer compartments of the same size, probably delimited by the anchored-transmembrane-protein pickets lining the actin-based membrane-skeleton fence, once every 1–58 ms.

The mechanisms by which the diffusion rate in the plasma membrane (PM) is regulated remain unresolved, despite their importance in spatially regulating the reaction rates in the PM. Proposed models include entrapment in nanoscale noncontiguous domains found in PtK2 cells, slow diffusion due to crowding, and actin-induced compartmentalization. Here, by applying single-particle tracking at high time resolutions, mainly to the PtK2-cell PM, we found confined diffusion plus hop movements (termed “hop diffusion”) for both a nonraft phospholipid and a transmembrane protein, transferrin receptor, and equal compartment sizes for these two molecules in all five of the cell lines used here (actual sizes were cell dependent), even after treatment with actin-modulating drugs. The cross-section size and the cytoplasmic domain size both affected the hop frequency. Electron tomography identified the actin-based membrane skeleton (MSK) located within 8.8 nm from the PM cytoplasmic surface of PtK2 cells and demonstrated that the MSK mesh size was the same as the compartment size for PM molecular diffusion. The extracellular matrix and extracellular domains of membrane proteins were not involved in hop diffusion. These results support a model of anchored TM-protein pickets lining actin-based MSK as a major mechanism for regulating diffusion.

Thermodynamic and kinetic characterization of transmembrane helix association

The transient dimerization of transmembrane proteins is an important event in several cellular processes and here we use coarse-grain and meso-scale modeling methods to quantify their underlying dynamics.

Analytical solution of steady-state equations for chemical reaction networks with bilinear rate laws

True steady states are a rare occurrence in living organisms, yet their knowledge is essential for quasi-steady-state approximations, multistability analysis, and other important tools in the investigation of chemical reaction networks (CRN) used to describe molecular processes on the cellular level. Here, we present an approach that can provide closed form steady-state solutions to complex systems, resulting from CRN with binary reactions and mass-action rate laws. We map the nonlinear algebraic problem of finding steady states onto a linear problem in a higher-dimensional space. We show that the linearized version of the steady-state equations obeys the linear conservation laws of the original CRN. We identify two classes of problems for which complete, minimally parameterized solutions may be obtained using only the machinery of linear systems and a judicious choice of the variables used as free parameters. We exemplify our method, providing explicit formulae, on CRN describing signal initiation of two important types of RTK receptor-ligand systems, VEGF and EGF-ErbB1.

Studying the role of lipid rafts on protein receptor bindings with cellular automata

It is widely accepted that lipid rafts promote receptor clustering and thereby facilitate signaling transduction. The role of lipid rafts in inducing and promoting receptor accumulation within the cell membrane has been explored by several computational and experimental studies. However, it remains unclear whether lipid rafts influence the recruitment and binding of proteins from the cytosol as well. To provide an answer to this question a spatial membrane model has been developed based on cellular automata. Our results indicate that lipid rafts indeed influence protein receptor bindings. In particular processes with slow dissociation and binding kinetics are promoted by lipid rafts, whereas fast binding processes are slightly hampered. However, the impact depends on a variety of parameters, such as the size and mobility of the lipid rafts, the induced slow down of receptors within rafts, and also the dissociation and binding kinetics of the cytosolic proteins. Thus, for any individual signaling pathway the influence of lipid rafts on protein binding might be different. To facilitate analyzing this influence given a specific pathway, our approach has been generalized into LiRaM, a modeling and simulation tool for lipid rafts models.

Mathematical simulation of membrane protein clustering for efficient signal transduction

Initiation and propagation of cell signaling depend on productive interactions among signaling proteins at the plasma membrane. These diffusion-limited interactions can be influenced by features of the membrane that introduce barriers, such as cytoskeletal corrals, or microdomains that transiently confine both transmembrane receptors and membrane-tethered peripheral proteins. Membrane topographical features can lead to clustering of receptors and other membrane components, even under very dynamic conditions. This review considers the experimental and mathematical evidence that protein clustering impacts cell signaling in complex ways. Simulation approaches used to consider these stochastic processes are discussed.

Regulation from within: the cytoskeleton in transmembrane signaling

There is mounting evidence that the plasma membrane is highly dynamic and organized in a complex manner. The cortical cytoskeleton is proving to be a particularly important regulator of plasmalemmal organization, modulating the mobility of proteins and lipids in the membrane, facilitating their segregation, and influencing their clustering. This organization plays a critical role in receptor-mediated signaling, especially in the case of immunoreceptors, which require lateral clustering for their activation. Based on recent developments, we discuss the structures and mechanisms whereby the cortical cytoskeleton regulates membrane dynamics and organization, and how the nonuniform distribution of immunoreceptors and their self-association may affect activation and signaling.

Spatial regulation of receptor tyrosine kinases in development and cancer

During development and tissue homeostasis, patterns of cellular organization, proliferation and movement are highly choreographed. Receptor tyrosine kinases (RTKs) have a crucial role in establishing these patterns. Individual cells and tissues exhibit tight spatial control of the RTKs that they express, enabling tissue morphogenesis and function, while preventing unwarranted cell division and migration that can contribute to tumorigenesis. Indeed, RTKs are deregulated in most human cancers and are a major focus of targeted therapeutics. A growing appreciation of the essential role of spatial RTK regulation during development prompts the realization that spatial deregulation of RTKs is likely to contribute broadly to cancer development and may affect the sensitivity and resistance of cancer to pharmacological RTK inhibitors.

Confining domains lead to reaction bursts: reaction kinetics in the plasma membrane

Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity.

Reaction kinetics in the plasma membrane

A great puzzle in science is establishing a bottom up understanding of life by revealing how a collection of molecules gives rise to a living cell that can survive, communicate, and reproduce. In the confines of physics, chemistry, or material science laboratories where it possible to study complex interactions between molecules in a well-defined environment, our understanding of collective behavior is substantially developed. However, the environment in which molecules of a biological cell perform their functions is far from ideal or controllable. The environment inside cellular regions such as the plasma membrane is heterogeneous and dynamic, and functional molecules such as proteins are both dynamic and promiscuous, as they interact with countless other molecules. This makes it extremely challenging to grasp the inner mechanism of the cells, both experimentally and theoretically. On the bright side, this presents scientists with a colorful playground that waits to be explored: the mesoscopic world inside the cell. This review covers some of the recent experimental and theoretical developments in the study of molecular interactions in the plasma membrane, viewed as a heterogeneous medium where the number of reactants can be small, sometimes countable, and its implications for biological function.