Thermodynamics and Kinetics of Aggregation of Flexible Peripheral Membrane Proteins

Making the cut: Multiscale simulation of membrane remodeling

Biological membranes are dynamic heterogeneous materials, and their shape and organization are tightly coupled to the properties of the proteins in and around them. However, the length scales of lipid and protein dynamics are far below the size of membrane-bound organelles, much less an entire cell. Therefore, multiscale modeling approaches are often necessary to build a comprehensive picture of the interplay of these factors, and have provided critical insights into our understanding of membrane dynamics. Here, we review computational methods for studying membrane remodeling, as well as passive and active examples of protein-driven membrane remodeling. As the field advances towards the modeling of key aspects of organelles and whole cells - an increasingly accessible regime of study - we summarize here recent successes and offer comments on future trends.

Dynamic framework for large-scale modeling of membranes and peripheral proteins

In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.

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.

Spatially resolved protein map of intact human cytomegalovirus virions

Herpesviruses assemble large enveloped particles that are difficult to characterize structurally due to their size, fragility and complex multilayered proteome with partially amorphous nature. Here we used crosslinking mass spectrometry and quantitative proteomics to derive a spatially resolved interactome map of intact human cytomegalovirus virions. This enabled the de novo allocation of 32 viral proteins into four spatially resolved virion layers, each organized by a dominant viral scaffold protein. The viral protein UL32 engages with all layers in an N-to-C-terminal radial orientation, bridging nucleocapsid to viral envelope. We observed the layer-specific incorporation of 82 host proteins, of which 39 are selectively recruited. We uncovered how UL32, by recruitment of PP-1 phosphatase, antagonizes binding to 14-3-3 proteins. This mechanism assures effective viral biogenesis, suggesting a perturbing role of UL32-14-3-3 interaction. Finally, we integrated these data into a coarse-grained model to provide global insights into the native configuration of virus and host protein interactions inside herpesvirions.

Mesoscale simulations: An indispensable approach to understand biomembranes

Computer simulation techniques form a versatile tool, a computational microscope, for exploring biological processes. This tool has been particularly effective in exploring different features of biological membranes. In recent years, thanks to elegant multiscale simulation schemes, some fundamental limitations of investigations by distinct simulation techniques have been resolved. As a result, we are now capable of exploring processes spanning multiple scales beyond the capacity of any single technique. In this perspective, we argue that mesoscale simulations require more attention and must be further developed to fill evident gaps in a quest toward simulating and modeling living cell membranes.

Stochastic Approximation to MBAR and TRAM: Batchwise Free Energy Estimation

The dynamics of molecules are governed by rare event transitions between long-lived (metastable) states. To explore these transitions efficiently, many enhanced sampling protocols have been introduced that involve using simulations with biases or changed temperatures. Two established statistically optimal estimators for obtaining unbiased equilibrium properties from such simulations are the multistate Bennett acceptance ratio (MBAR) and the transition-based reweighting analysis method (TRAM). Both MBAR and TRAM are solved iteratively and can suffer from long convergence times. Here, we introduce stochastic approximators (SA) for both estimators, resulting in SAMBAR and SATRAM, which are shown to converge faster than their deterministic counterparts, without significant accuracy loss. Both methods are demonstrated on different molecular systems.

Modeling membrane reshaping driven by dynamic protein assemblies

Remodeling of membranes in living systems is almost universally coupled to self-assembly of soluble proteins. Proteins assemble into semi-rigid shells that reshape attached membranes, and into filaments that protrude membranes. These assemblies are temporary, building from reversible protein and membrane interactions that must nucleate in the proper location. The interactions are strongly influenced by the nonequilibrium environment of the cell, such as gradients of components or active modifications by kinases. From a modeling perspective, understanding mechanisms and control thus requires 1. time-dependent approaches that ideally incorporate 2. macromolecular structure, 3. out-of-equilibrium processes, and 4. deformable membranes over microns and seconds. Realistically, tradeoffs must be made with these last three features. However, we see recent developments from the highly coarsened molecule-based scale, the continuum reaction-diffusion scale, and hybrid approaches as stimulating efforts in diverse applications. We discuss here methodological advances and progress towards simulating these processes as they occur physiologically.

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.

Close, but not too close: a mesoscopic description of (a)symmetry and membrane shaping mechanisms

Biomembranes are fundamental to our understanding of the cell, the basic building block of all life. An intriguing aspect of membranes is their ability to assume a variety of shapes, which is crucial for cell function. Here, we review various membrane shaping mechanisms with special focus on the current understanding of how local curvature and local rigidity induced by membrane proteins leads to emerging forces and consequently large-scale membrane deformations. We also argue that describing the interaction of rigid proteins with membranes purely in terms of local membrane curvature is incomplete and that changes in the membrane rigidity moduli must also be considered.

High-fidelity molecular dynamics trajectory reconstruction with bi-directional neural networks

Molecular dynamics (MD) simulations are a cornerstone in science, enabling the investigation of a system’s thermodynamics all the way to analyzing intricate molecular interactions. In general, creating extended molecular trajectories can be a computationally expensive process, for example, when running ab-initio simulations. Hence, repeating such calculations to either obtain more accurate thermodynamics or to get a higher resolution in the dynamics generated by a fine-grained quantum interaction can be time- and computational resource-consuming. In this work, we explore different machine learning methodologies to increase the resolution of MD trajectories on-demand within a post-processing step. As a proof of concept, we analyse the performance of bi-directional neural networks (NNs) such as neural ODEs, Hamiltonian networks, recurrent NNs and long short-term memories, as well as the uni-directional variants as a reference, for MD simulations (here: the MD17 dataset). We have found that Bi-LSTMs are the best performing models; by utilizing the local time-symmetry of thermostated trajectories they can even learn long-range correlations and display high robustness to noisy dynamics across molecular complexity. Our models can reach accuracies of up to 10−4 Å in trajectory interpolation, which leads to the faithful reconstruction of several unseen high-frequency molecular vibration cycles. This renders the comparison between the learned and reference trajectories indistinguishable. The results reported in this work can serve (1) as a baseline for larger systems, as well as (2) for the construction of better MD integrators.

Investigating the entropic nature of membrane-mediated interactions driving the aggregation of peripheral proteins

Peripheral membrane-associated proteins are known to accumulate on the surface of biomembranes as a result of membrane-mediated interactions. For a pair of rotationally-symmetric curvature-inducing proteins, membrane mechanics at the low-temperature limit predicts pure repulsion. On the other hand, temperature-dependent entropic forces arise between pairs of stiff-binding proteins suppressing membrane fluctuations. These Casimir-like interactions have thus been suggested as candidates for attractive forces leading to aggregation. With dense assemblies of peripheral proteins on the membrane, both these abstractions encounter short-range and multi-body complications. Here, we make use of a particle-based membrane model augmented with flexible peripheral proteins to quantify purely membrane-mediated interactions and investigate their underlying nature. We introduce a continuous reaction coordinate corresponding to the progression of protein aggregation. We obtain free energy and entropy landscapes for different surface concentrations along this reaction coordinate. In parallel, we investigate time-dependent estimates of membrane entropy corresponding to membrane undulations and coarse-grained director field and how they change dynamically with protein aggregation. Congruent outcomes of the two approaches point to the conclusion that for low surface concentrations, interactions with an entropic nature may drive the aggregation. But at high concentrations, enthalpic contributions due to concerted membrane deformation by protein clusters are dominant.