Application of a free-energy-landscape approach to study tension-dependent bilayer tubulation mediated by curvature-inducing proteins

Asymmetric crowders and membrane morphology at the nexus of intracellular trafficking and oncology

A definitive understanding of the interplay between protein binding/migration and membrane curvature evolution is emerging but needs further study. The mechanisms defining such phenomena are critical to intracellular transport and trafficking of proteins. Among trafficking modalities, exosomes have drawn attention in cancer research as these nano-sized naturally occurring vehicles are implicated in intercellular communication in the tumor microenvironment, suppressing anti-tumor immunity and preparing the metastatic niche for progression. A significant question in the field is how the release and composition of tumor exosomes are regulated. In this perspective article, we explore how physical factors such as geometry and tissue mechanics regulate cell cortical tension to influence exosome production by co-opting the biophysics as well as the signaling dynamics of intracellular trafficking pathways and how these exosomes contribute to the suppression of anti-tumor immunity and promote metastasis. We describe a multiscale modeling approach whose impact goes beyond the fundamental investigation of specific cellular processes toward actual clinical translation. Exosomal mechanisms are critical to developing and approving liquid biopsy technologies, poised to transform future non-invasive, longitudinal profiling of evolving tumors and resistance to cancer therapies to bring us one step closer to the promise of personalized medicine.

Free energy calculations for membrane morphological transformations and insights to physical biology and oncology

In this chapter, we aim to bridge basic molecular and cellular principles surrounding membrane curvature generation with rewiring of cellular signals in cancer through multiscale models. We describe a general framework that integrates signaling with other cellular functions like trafficking, cell-cell and cell-matrix adhesion, and motility. The guiding question in our approach is: how does a physical change in cell membrane configuration caused by external stimuli (including those by the extracellular microenvironment) alter trafficking, signaling and subsequent cell fate? We answer this question by constructing a modeling framework based on stochastic spatial continuum models of cell membrane deformations. We apply this framework to explore the link between trafficking, signaling in the tumor microenvironment, and cell fate. At each stage, we aim to connect the results of our predictions with cellular experiments.

Crowding-induced membrane remodeling: Interplay of membrane tension, polymer density, architecture

The plasma membrane hosts a wide range of biomolecules, mainly proteins and carbohydrates, that mediate cellular interactions with its environment. The crowding of such biomolecules regulates cellular morphologies and cellular trafficking. Recent discoveries have shown that the structure and density of cell surface polymers and hence the signaling machinery change with the state of the cell, especially in cancer progression. The alterations in membrane-attached glycocalyx and glycosylation of proteins and lipids are common features of cancer cells. The overexpression of glycocalyx polymers, such as mucin and hyaluronan, strongly correlates with cancer metastasis. Here, we present a mesoscale biophysics-based model that accounts for the shape regulation of membranes by crowding of membrane-attached biopolymer-glycocalyx and actin networks. Our computational model is based on the dynamically triangulated Monte Carlo model for membranes and coarse-grained representations of polymer chains. The model allows us to investigate the crowding-induced shape transformations in cell membranes in a tension- and graft polymer density-dependent manner. Our results show that the number of membrane protrusions and their shape depend on membrane tension, with higher membrane tension inducing more tubular protrusions than the vesicular shapes formed at low tension at high surface coverage of polymers. The shape transformations occur above the threshold density predicted by the polymer brush theory, but this threshold also depends on the membrane tension. Increasing the size of the polymer, either by changing the length or by adding side chains, is shown to increase the crowding-induced curvature. The effect of crowding is more prominent for flexible polymers than for semiflexible rigid polymers. We also present an extension of the model that incorporates properties of the actin-like filament networks and demonstrate how tubular structures can be generated by biopolymer crowding on the cytosolic side of cell membranes.

Data driven and biophysical insights into the regulation of trafficking vesicles by extracellular matrix stiffness

Biomechanical signals from remodeled extracellular matrix (ECM) promote tumor progression. Here, we show that cell-matrix and cell-cell communication may be inherently linked and tuned through mechanisms of mechanosensitive biogenesis of trafficking vesicles. Pan-cancer analysis of cancer cells' mechanical properties (focusing primarily on cell stiffness) on substrates of varied stiffness and composition elucidated a heterogeneous cellular response to mechanical stimuli. Through machine learning, we identified a fingerprint of cytoskeleton-related proteins that accurately characterize cell stiffness in different ECM conditions. Expression of their respective genes correlates with patient prognosis across different tumor types. The levels of selected cytoskeleton proteins indicated that cortical tension mirrors the increase (or decrease) in cell stiffness with a change in ECM stiffness. A mechanistic biophysical model shows that the tendency for curvature generation by curvature-inducing proteins has an ultrasensitive dependence on cortical tension. This study thus highlights the effect of ECM stiffness, mediated by cortical tension, in modulating vesicle biogenesis.

Quantification of Curvature Sensing Behavior of Curvature-Inducing Proteins on Model Wavy Substrates

Curvature-inducing proteins are involved in a variety of membrane remodeling processes in the cell. Several in vitro experiments have quantified the curvature sensing behavior of these proteins in model lipid systems. One such system consists of a membrane bilayer laid atop a wavy substrate (Hsieh in Langmuir 28:12838-12843, 2012). In these experiments, the bilayer conforms to the wavy substrate, and curvature-inducing proteins show preferential segregation on the wavy membrane. Using a mesoscale computational membrane model based on the Helfrich Hamiltonian, here we present a study which analyzes the curvature sensing characteristics of this membrane-protein system, and elucidates key physical principles governing protein segregation on the wavy substrate and other in vitro systems. In this article we compute the local protein densities from the free energy landscape associated with membrane remodeling by curvature-inducing proteins. In specific, we use the Widom insertion technique to compute the free energy landscape for an inhomogeneous system with spatially varying density and the results obtained with this minimal model show excellent agreement with experimental studies that demonstrate the association between membrane curvature and local protein density. The free energy-based framework employed in this study can be used for different membrane morphologies and varied protein characteristics to gain mechanistic insights into protein sorting on membranes.

Probing lipid membrane bending mechanics using gold nanorod tracking

Lipid bilayer membranes undergo rapid bending undulations with wavelengths from tens of nanometers to tens of microns due to thermal fluctuations. Here, we probe such undulations and the membranes' mechanics by measuring the time-varying orientation of single gold nanorods (GNRs) adhered to the membrane, using high-speed dark field microscopy. In a lipid vesicle, such measurements allow the determination of the membrane's viscosity, bending rigidity, and tension as well as the friction coefficient for sliding of the monolayers over one another. The in-plane rotation of the GNR is hindered by undulations in a tension dependent manner, consistent with simulations. The motion of single GNRs adhered to the plasma membrane of living cultured cells similarly reveals the membrane's complex physics and coupling to the cell's actomyosin cortex.

Biophysical Considerations in the Rational Design and Cellular Targeting of Flexible Polymeric Nanoparticles

How nanoparticle (NP) mechanical properties impact multivalent ligand-receptor-mediated binding to cell surfaces, the avidity, propensity for internalization, and effects due to crowding remains unknown or unquantified. Through computational analyses, the effects of NP composition from soft, deformable NPs to rigid spheres, effect of tethers, the crowding of NPs at the membrane surface, and the cell membrane properties such as cytoskeletal interactions are addressed. Analyses of binding mechanisms of three distinct NPs that differ in type and rigidity (core-corona flexible NP, rigid NP, and rigid-tethered NP) but are otherwise similar in size and ligand surface density are reported; moreover, for the case of flexible NP, NP stiffness is tuned by varying the internal crosslinking density. Biophysical modeling of NP binding to membranes together with thermodynamic analysis powered by free energy calculations is employed, and it is shown that efficient cellular targeting and uptake of NP functionalized with targeting ligand molecules can be shaped by factors including NP flexibility and crowding, receptor-ligand binding avidity, state of the membrane cytoskeleton, and curvature inducing proteins. Rational design principles that confer tension, membrane excess area, and cytoskeletal sensing properties to the NP which can be exploited for cell-specific targeting of NP are uncovered.

Emergent membrane morphologies in relaxed and tense membranes in presence of reversible adhesive pinning interactions

The morphologies of cell membranes, and specifically the local curvature distributions are determined either by its intrinsic components such as lipids and membrane-associated proteins or by the adhesion forces due to membrane interactions with the cytoskeleton, extracellular matrix (ECM) and other cells in the tissue, as well as physical variables such as membrane and frame tensions. We present a computational analysis for a model of pinned membranes based on the dynamically triangulated Monte Carlo (MC) model for membranes. We show that membrane adhesion to ECM or a substrate promotes curvature generation on cell membranes, and this process depends on the excess area, or equivalently membrane tension, and the density of adhesion sites. This biophysics based model predicts adhesion induced biogenesis of microvesicles in cell membranes. For a moderate density of adhesion sites and high excess membrane area, an increase in membrane tension can result in the formation of microvesicles and tubules on the membrane. We also demonstrate the significance of intrinsically curved proteins in promoting vesiculation on pinned membranes. The results presented here are relevant to the understanding of microvesicle biogenesis and curved membrane topographies due to physical factors such as substrate stiffness and ECM interactions.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

At the micron scale, where cell organelles display an amazing complexity in their shape and organization, the physical properties of a biological membrane can be better-understood using continuum models subject to thermal (stochastic) undulations. Yet, the chief orchestrators of these complex and intriguing shapes are a specialized class of membrane associating often peripheral proteins called curvature remodeling proteins (CRPs) that operate at the molecular level through specific protein-lipid interactions. We review multiscale methodologies to model these systems at the molecular as well as at the mesoscopic and cellular scales, and also present a free energy perspective of membrane remodeling through the organization and assembly of CRPs. We discuss the morphological space of nearly planar to highly curved membranes, methods to include thermal fluctuations, and review studies that model such proteins as curvature fields to describe the emergent curved morphologies. We also discuss several mesoscale models applied to a variety of cellular processes, where the phenomenological parameters (such as curvature field strength) are often mapped to models of real systems based on molecular simulations. Much insight can be gained from the calculation of free energies of membranes states with protein fields, which enable accurate mapping of the state and parameter values at which the membrane undergoes morphological transformations such as vesiculation or tubulation. By tuning the strength, anisotropy, and spatial organization of the curvature-field, one can generate a rich array of membrane morphologies that are highly relevant to shapes of several cellular organelles. We review applications of these models to budding of vesicles commonly seen in cellular signaling and trafficking processes such as clathrin mediated endocytosis, sorting by the ESCRT protein complexes, and cellular exocytosis regulated by the exocyst complex. We discuss future prospects where such models can be combined with other models for cytoskeletal assembly, and discuss their role in understanding the effects of cell membrane tension and the mechanics of the extracellular microenvironment on cellular processes.

Formation and Stability of Lipid Membrane Nanotubes

Lipid membrane nanotubes are abundant in living cells, even though tubules are energetically less stable than sheet-like structures. According to membrane elastic theory, the tubular endoplasmic reticulum (ER), with its high area-to-volume ratio, appears to be particularly unstable. We explore how tubular membrane structures can nevertheless be induced and why they persist. In Monte Carlo simulations of a fluid-elastic membrane model subject to thermal fluctuations and without constraints on symmetry, we find that a steady increase in the area-to-volume ratio readily induces tubular structures. In simulations mimicking the ER wrapped around the cell nucleus, tubules emerge naturally as the membrane area increases. Once formed, a high energy barrier separates tubules from the thermodynamically favored sheet-like membrane structures. Remarkably, this barrier persists even at large area-to-volume ratios, protecting tubules against shape transformations despite enormous driving forces toward sheet-like structures. Molecular dynamics simulations of a molecular membrane model confirm the metastability of tubular structures. Volume reduction by osmotic regulation and membrane area growth by lipid production and by fusion of small vesicles emerge as powerful factors in the induction and stabilization of tubular membrane structures.

Curvature-undulation coupling as a basis for curvature sensing and generation in bilayer membranes

We present coarse-grained molecular dynamics simulations of the epsin N-terminal homology domain interacting with a lipid bilayer and demonstrate a rigorous theoretical formalism and analysis method for computing the induced curvature field in varying concentrations of the protein in the dilute limit. Our theory is based on the description of the height-height undulation spectrum in the presence of a curvature field. We formulated an objective function to compare the acquired undulation spectrum from the simulations to that of the theory. We recover the curvature field parameters by minimizing the objective function even in the limit where the protein-induced membrane curvature is of the same order as the amplitude due to thermal undulations. The coupling between curvature and undulations leads to significant predictions: (i) Under dilute conditions, the proteins can sense a site of spontaneous curvature at distances much larger than their size; (ii) as the density of proteins increases the coupling focuses and stabilizes the curvature field to the site of the proteins; and (iii) the mapping of the protein localization and the induction of a stable curvature is a cooperative process that can be described through a Hill function.

Epsin N-terminal Homology Domain (ENTH) Activity as a Function of Membrane Tension

The epsin N-terminal homology domain (ENTH) is a major player in clathrin-mediated endocytosis. To investigate the influence of initial membrane tension on ENTH binding and activity, we established a bilayer system based on adhered giant unilamellar vesicles (GUVs) to be able to control and adjust the membrane tension σ covering a broad regime. The shape of each individual adhered GUV as well as its adhesion area was monitored by spinning disc confocal laser microscopy. Control of σ in a range of 0.08-1.02 mN/m was achieved by altering the Mg(2+) concentration in solution, which changes the surface adhesion energy per unit area of the GUVs. Specific binding of ENTH to phosphatidylinositol 4,5-bisphosphate leads to a substantial increase in adhesion area of the sessile GUV. At low tension (<0.1 mN/m) binding of ENTH can induce tubular structures, whereas at higher membrane tension the ENTH interaction deflates the sessile GUV and thereby increases the adhesion area. The increase in adhesion area is mainly attributed to a decrease in the area compressibility modulus KA We propose that the insertion of the ENTH helix-0 into the membrane is largely responsible for the observed decrease in KA, which is supported by the observation that the mutant ENTH L6E shows a reduced increase in adhesion area. These results demonstrate that even in the absence of tubule formation, the area compressibility modulus and, as such, the bending rigidity of the membrane is considerably reduced upon ENTH binding. This renders membrane bending and tubule formation energetically less costly.