Mesoscale simulation of biomembranes with FreeDTS.

We present FreeDTS software for performing computational research on biomembranes at the mesoscale. In this software, a membrane is represented by a dynamically triangulated surface equipped with vertex-based inclusions to integrate the effects of integral and peripheral membrane proteins. Several algorithms are included in the software to simulate complex membranes at different conditions such as framed membranes with constant tension, vesicles and high-genus membranes with various fixed volumes or constant pressure differences and applying external forces to membrane regions. Furthermore, the software allows the user to turn off the shape evolution of the membrane and focus solely on the organization of proteins. As a result, we can take realistic membrane shapes obtained from, for example, cryo-electron tomography and backmap them into a finer simulation model. In addition to many biomembrane applications, this software brings us a step closer to simulating realistic biomembranes with molecular resolution. Here we provide several interesting showcases of the power of the software but leave a wide range of potential applications for interested users.

Bottom-up approach to explore alpha-amylase assisted membrane remodelling.

Soluble alpha-amylases play an important role in the catabolism of polysaccharides. In this work, we show that the malt α -amylase can interact with the lipid membrane and further alter its mechanical properties. Vesicle fluctuation spectroscopy is used for quantitative measurement of the membrane bending rigidity of phosphatidylcholines lipid vesicles from the shape fluctuation based on the whole contour of Giant Unilamellar Vesicles (GUVs). The bending rigidity of the 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine lipid vesicles in water increases significantly with the presence of 0.14 micromolar alpha-amylase (AA) in the exterior solution. It appears that the enzyme present in the external solution interacts with the outer layer of the bilayer membrane, leading to an asymmetry of the solution on either side of the bilayer membrane and altering its elasticity. At AA concentration of 1.5 micromolars and above, changes in the morphology of the GUV membrane are observed. The interaction between AA in the external solution and the external leaflet causes the bilayer membrane to curve spontaneously, leading to the formation of outbuds, giving a positive spontaneous curvature of C0 ≤ 0.05 µm-1 at ≈ 1 mg / ml of the AA concentration. We validate and characterize its concentration-dependent role in stabilizing the membrane curvature. Our findings indicate that the involvement of the enzyme, depending on the concentration, can have a considerable effect on the mechanical characteristics of the membrane.

Macromolecular Crowding Is Surprisingly Unable to Deform the Structure of a Model Biomolecular Condensate.

The crowded interior of a living cell makes performing experiments on simpler in vitro systems attractive. Although these reveal interesting phenomena, their biological relevance can be questionable. A topical example is the phase separation of intrinsically disordered proteins into biomolecular condensates, which is proposed to underlie the membrane-less compartmentalization of many cellular functions. How a cell reliably controls biochemical reactions in compartments open to the compositionally-varying cytoplasm is an important question for understanding cellular homeostasis. Computer simulations are often used to study the phase behavior of model biomolecular condensates, but the number of relevant parameters increases as the number of protein components increases. It is unfeasible to exhaustively simulate such models for all parameter combinations, although interesting phenomena are almost certainly hidden in their high-dimensional parameter space. Here, we have studied the phase behavior of a model biomolecular condensate in the presence of a polymeric crowding agent. We used a novel compute framework to execute dozens of simultaneous simulations spanning the protein/crowder concentration space. We then combined the results into a graphical representation for human interpretation, which provided an efficient way to search the model's high-dimensional parameter space. We found that steric repulsion from the crowder drives a near-critical system across the phase boundary, but the molecular arrangement within the resulting biomolecular condensate is rather insensitive to the crowder concentration and molecular weight. We propose that a cell may use the local cytoplasmic concentration to assist the formation of biomolecular condensates, while relying on the dense phase to reliably provide a stable, structured, fluid milieu for cellular biochemistry despite being open to its changing environment.

Model biomolecular condensates have heterogeneous structure quantitatively dependent on the interaction profile of their constituent macromolecules.

Biomolecular condensates play numerous roles in cells by selectively concentrating client proteins while excluding others. These functions are likely to be sensitive to the spatial organization of the scaffold proteins forming the condensate. We use coarse-grained molecular simulations to show that model intrinsically-disordered proteins phase separate into a heterogeneous, structured fluid characterized by a well-defined length scale. The proteins are modelled as semi-flexible polymers with punctate, multifunctional binding sites in good solvent conditions. Their dense phase is highly solvated with a spatial structure that is more sensitive to the separation of the binding sites than their affinity. We introduce graph theoretic measures to quantify their heterogeneity, and find that it increases with increasing binding site number, and exhibits multi-timescale dynamics. The model proteins also swell on passing from the dilute solution to the dense phase. The simulations predict that the structure of the dense phase is modulated by the location and affinity of binding sites distant from the termini of the proteins, while sites near the termini more strongly affect its phase behaviour. The relations uncovered between the arrangement of weak interaction sites on disordered proteins and the material properties of their dense phase can be experimentally tested to give insight into the biophysical properties, pathological effects, and rational design of biomolecular condensates.

Computational Approaches to Explore Bacterial Toxin Entry into the Host Cell.

Many bacteria secrete toxic protein complexes that modify and disrupt essential processes in the infected cell that can lead to cell death. To conduct their action, these toxins often need to cross the cell membrane and reach a specific substrate inside the cell. The investigation of these protein complexes is essential not only for understanding their biological functions but also for the rational design of targeted drug delivery vehicles that must navigate across the cell membrane to deliver their therapeutic payload. Despite the immense advances in experimental techniques, the investigations of the toxin entry mechanism have remained challenging. Computer simulations are robust complementary tools that allow for the exploration of biological processes in exceptional detail. In this review, we first highlight the strength of computational methods, with a special focus on all-atom molecular dynamics, coarse-grained, and mesoscopic models, for exploring different stages of the toxin protein entry mechanism. We then summarize recent developments that are significantly advancing our understanding, notably of the glycolipid-lectin (GL-Lect) endocytosis of bacterial Shiga and cholera toxins. The methods discussed here are also applicable to the design of membrane-penetrating nanoparticles and the study of the phenomenon of protein phase separation at the surface of the membrane. Finally, we discuss other likely routes for future development.

Creasing of flexible membranes at vanishing tension.

The properties of freestanding tensionless interfaces and membranes at low bending rigidity κ are dominated by strong fluctuations and self-avoidance and are thus outside the range of standard perturbative analysis. We analyze this regime by a simple discretized, self-avoiding membrane model on a frame subject to periodic boundary conditions by use of Monte Carlo simulation and dynamically triangulated surface techniques. We find that at low bending rigidities, the membrane properties fall into three regimes: Below the collapse transition κ_{BP} it is subject to branched polymer instability where the framed surface is not defined, in a range below a threshold rigidity κ_{c} the conformational correlation function are characterized by power-law behavior with a continuously varying exponent α, 2<α≤4 and above κ_{c}, α=4 characteristic for linearized bending excitations. Response functions specific heat and area compressibility display pronounced peaks close to κ_{c}. The results may be important for the description of soft interface systems, such as microemulsions and membranes with in-plane cooperative phenomena.

Fluctuations and conformational stability of a membrane patch with curvature inducing inclusions.

Membranes with curvature inducing inclusions display a range of cooperative phenomena, which can be linked to biomembrane function, e.g. membrane tubulation, vesiculation, softening and spontaneous tension. We investigate how these phenomena are related for a fluctuating, framed membrane through analysis of a descretized membrane model by Monte Carlo simulation techniques. The membrane model is based on a dynamically triangulated surface equipped with non-interacting, up-down symmetry breaking inclusions where only terms coupled linearly to mean-curvature are maintained. We show that the lateral configurational entropy plays a key role for the mechanical properties of the semi-flexible membrane, e.g. a pronounced softening at intermediate inclusion coverages of the membrane and generation of membrane tension. Tensionless framed membranes will remain quasi-flat up to some threshold coverage, where a shape instability occurs with formation of pearling or tubular membranes, which below full coverage is associated with segregation of inclusions between the curved and flat membrane geometries. For inclusions with preference for highly curved membranes the instability appears at dilute inclusion coverages and is accompanied by strong configurational fluctuations.

A Multi-Scale Approach to Membrane Remodeling Processes.

We present a multi-scale simulation procedure to describe membrane-related biological processes that span over a wide range of length scales. At macroscopic length-scale, a membrane is described as a flexible thin film modeled by a dynamic triangulated surface with its spatial conformations governed by an elastic energy containing only a few model parameters. An implicit protein model allows us to include complex effects of membrane-protein interactions in the macroscopic description. The gist of this multi-scale approach is a scheme to calibrate the implicit protein model using finer scale simulation techniques e.g., all atom and coarse grain molecular dynamics. We previously used this approach and properly described the formation of membrane tubular invaginations upon binding of B-subunit of Shiga toxin. Here, we provide a perspective of our multi-scale approach, summarizing its main features and sketching possible routes for future development.

Clustering on Membranes: Fluctuations and More.

Clustering of extracellular ligands and proteins on the plasma membrane is required to perform specific cellular functions, such as signaling and endocytosis. Attractive forces that originate in perturbations of the membrane's physical properties contribute to this clustering, in addition to direct protein-protein interactions. However, these membrane-mediated forces have not all been equally considered, despite their importance. In this review, we describe how line tension, lipid depletion, and membrane curvature contribute to membrane-mediated clustering. Additional attractive forces that arise from protein-induced perturbation of a membrane's fluctuations are also described. This review aims to provide a survey of the current understanding of membrane-mediated clustering and how this supports precise biological functions.

The tension of framed membranes from computer simulations.

We have analyzed the behavior of a randomly triangulated, self-avoiding surface model of a flexible, fluid membrane subject to a circular boundary by Wang-Landau Monte Carlo computer simulation techniques. The dependence of the canonical free energy and frame tension on the frame area is obtained for flexible membranes. It is shown that for low bending rigidities the framed membrane is only stable above a threshold tension, suggesting a discontinuous transition from the collapsed (branched polymer) state to a finite tension extended state. In a tension range above this threshold tension the membranes display power-law characteristics for the equation of state, while higher tension levels includes both an extended linear (elastic) as well as a highly non-linear stretching regime. For semi-flexible membranes a transition from extended to buckled conformations takes place at negative frame tensions. Our analysis indicates that at zero frame tension the crumpling transition of fluid membranes show characteristics of both critical behavior and a discontinuous transition at low bending rigidities.