Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

All-Atom Simulations Reveal the Effect of Membrane Composition on the Signaling of the NKG2A/CD94/HLA-E Immune Receptor Complex

Understanding how membrane composition influences the dynamics and function of transmembrane proteins is crucial for the comprehensive elucidation of cellular signaling mechanisms and the development of targeted therapeutics. In this study, we employed all-atom molecular dynamics simulations to investigate the impact of different membrane compositions on the conformational dynamics of the NKG2A/CD94/HLA-E immune receptor complex, a key negative regulator of natural killer cell cytotoxic activity. Our results reveal significant variations in the behavior of the immune complex structure across five different membrane compositions, which include POPC, POPA, DPPC, and DLPC phospholipids, and a mixed POPC/cholesterol system. These variations are particularly evident in the intracellular domain of NKG2A, manifested as changes in mobility, tyrosine exposure, and interdomain communication. Additionally, we found that a large concentration of negative charge at the surface of the POPA-based membrane greatly increased the number of contacts with lipid molecules and significantly decreased the exposure of intracellular NKG2A ITIM regions to water molecules, thus likely halting the signal transduction process. Furthermore, the DPPC model with a membrane possessing a high transition temperature in a gel-like state became curved, affecting the exposure of one ITIM region. The decreased membrane thickness in the DPLC model caused a significant transmembrane domain tilt, altering the linker protrusion angle and potentially disrupting the hydrogen bonding network in the extracellular domain. Overall, our findings highlight the importance of considering membrane composition in the analysis of transmembrane protein dynamics and in the exploration of novel strategies for the external modulation of their signaling pathways.

Nanomaterials and methods for cancer therapy: 2D materials, biomolecules, and molecular dynamics simulations

This review explores the potential of biomolecule-based nanomaterials, i.e., protein, peptide, nucleic acid, and polysaccharide-based nanomaterials, in cancer nanomedicine. It highlights the wide range of design possibilities for creating multifunctional nanomedicines using these biomolecule-based nanomaterials. This review also analyzes the primary obstacles in cancer nanomedicine that can be resolved through the usage of nanomaterials based on biomolecules. It also examines the unique in vivo characteristics, programmability, and biological functionalities of these biomolecule-based nanomaterials. This summary outlines the most recent advancements in the development of two-dimensional semiconductor-based nanomaterials for cancer theranostic purposes. It focuses on the latest developments in molecular simulations and modelling to provide a clear understanding of important uses, techniques, and concepts of nanomaterials in drug delivery and synthesis processes. Finally, the review addresses the challenges in molecular simulations, and generating, analyzing, and developing biomolecule-based and two-dimensional semiconductor-based nanomaterials, and highlights the barriers that must be overcome to facilitate their application in clinical settings.

SMARTINI3 parametrization of multi-scale membrane models via unsupervised learning methods

In this study, we utilize genetic algorithms to develop a realistic implicit solvent ultra-coarse-grained (ultra-CG) membrane model comprising only three interaction sites. The key philosophy of the ultra-CG membrane model SMARTINI3 is its compatibility with realistic membrane proteins, for example, modeled within the Martini coarse-grained (CG) model, as well as with the widely used GROMACS software for molecular simulations. Our objective is to parameterize this ultra-CG model to accurately reproduce the experimentally observed structural and thermodynamic properties of Phosphatidylcholine (PC) membranes in real units, including properties such as area per lipid, area compressibility, bending modulus, line tension, phase transition temperature, density profile, and radial distribution function. In our example, we specifically focus on the properties of a POPC membrane, although the developed membrane model could be perceived as a generic model of lipid membranes. To optimize the performance of the model (the fitness), we conduct a series of evolutionary runs with diverse random initial population sizes (ranging from 96 to 384). We demonstrate that the ultra-CG membrane model we developed exhibits authentic lipid membrane behaviors, including self-assembly into bilayers, vesicle formation, membrane fusion, and gel phase formation. Moreover, we demonstrate compatibility with the Martini coarse-grained model by successfully reproducing the behavior of a transmembrane domain embedded within a lipid bilayer. This facilitates the simulation of realistic membrane proteins within an ultra-CG bilayer membrane, enhancing the accuracy and applicability of our model in biophysical studies.

Lateral diffusion of ions near membrane surface

Biological membranes isolate living cells from their environment, while allowing selective molecular transport between the inner and outer realms. For example, Na+ and K+ permeability through ionic channels contributes to neural conduction. Whether the ionic currents arise directly from cations in the bulk, or from the interface, is currently unclear. There are only scant results concerning lateral diffusion of ions on aquated membrane surfaces (and strong belief that this occurs through binding to a diffusing lipid). We performed classical molecular dynamics (MD) simulations of monovalent ions, Na+, K+, and Cl-, near the surface of the zwitterionic palmitoyl-oleoyl-phosphatidylcholine (POPC) membrane. Realistic force-fields for lipids (Amber's Lipid17 and Lipid21) and water (TIP4P-Ew) are tested for the mass and charge densities and the electrostatic potential across the membrane. These calculations reveal that the chloride can bind to the choline moiety through an intervening water molecule by forming a CH⋯OH hydrogen bond, while cations bind to both the phosphatic and carbonyl oxygens of phosphatidylcholine moieties. Upon transitioning from the bulk to the interface, a cation sheds some of its hydration water, which are replaced by headgroup atoms. Notably, an interfacial cation can bind 1-4 headgroup atoms, which is a key to understanding its surface hopping mechanism. We find that cation binding to three headgroup atoms immobilizes it, while binding to four energizes it. Consequently, the lateral cation diffusion rate is only 15-25 times slower than in the bulk, and 4-5 times faster than lipid self-diffusion. K+ diffusion is notably more anomalous than Na+, switching from sub- to super-diffusion after about 2 ns.

Multiscale modelling of transport in polymer-based reverse-osmosis/nanofiltration membranes: present and future

Nanofiltration (NF) and reverse osmosis (RO) processes are physical separation technologies used to remove contaminants from liquid streams by employing dense polymer-based membranes with nanometric voids that confine fluids at the nanoscale. At this level, physical properties such as solvent and solute permeabilities are intricately linked to molecular interactions. Initially, numerous studies focused on developing macroscopic transport models to gain insights into separation properties at the nanometer scale. However, continuum-based models have limitations in nanoconfined situations that can be overcome by force field molecular simulations. Continuum-based models heavily rely on bulk properties, often neglecting critical factors like liquid structuring, pore geometry, and molecular/chemical specifics. Molecular/mesoscale simulations, while encompassing these details, often face limitations in time and spatial scales. Therefore, achieving a comprehensive understanding of transport requires a synergistic integration of both approaches through a multiscale approach that effectively combines and merges both scales. This review aims to provide a comprehensive overview of the state-of-the-art in multiscale modeling of transport through NF/RO membranes, spanning from the nanoscale to continuum media.

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.

Recent developments in molecular modeling tools and applications related to pharmaceutical and biomedical research

In modern pharmaceutical and biomedical research, molecular modeling represents a useful tool to explore processes and their mechanistic bases at the molecular level. Integrating experimental and virtual analysis is a fruitful approach to study ligand-receptor interaction in chemical, biochemical and biological environments. In these fields, molecular docking and molecular dynamics are considered privileged techniques for modeling (bio)macromolecules and related complexes. This review aims to present the current landscape of molecular modeling in pharmaceutical and biomedical research by examining selected representative applications published in the last years and highlighting current topics and trends of this field. Thus, a systematic compilation of all published literature has not been attempted herein. After a brief overview of the main theoretical and computational tools used to investigate mechanisms at molecular level, recent applications of molecular modeling in drug discovery, ligand binding and for studying protein conformation and function will be discussed. Furthermore, specific sections will be devoted to the application of molecular modeling for unravelling enantioselective mechanisms underlying the enantioseparation of chiral compounds of pharmaceutical and biomedical interest as well as for studying new forms of noncovalent interactivity identified in biochemical and biological environments. The general aim of this review is to provide the reader with a modern overview of the topic, highlighting advancements and outlooks as well as drawbacks and pitfalls still affecting the applicability of theoretical and computational methods in the field of pharmaceutical and biomedical research.

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.

Data-driven dynamical coarse-graining for condensed matter systems

Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in a solution, where the molecule(s) and the solvent dynamics need to be integrated, rendering the simulations computationally costly and often unfeasible for physically/biologically relevant time scales. Standard coarse graining approaches can reproduce equilibrium distributions and structural features but do not properly include the dynamics. In this work, we develop a general data-driven coarse-graining methodology inspired by the Mori-Zwanzig formalism, which shows that macroscopic systems with a large number of degrees of freedom can be described by a few relevant variables and additional noise and memory terms. Our coarse-graining method consists of numerical integrators for the distinguished components, where the noise and interaction terms with other system components are substituted by a random variable sampled from a data-driven model. The model is parameterized using data from multiple short-time full-system simulations, and then, it is used to run long-time simulations. Applying our methodology to three systems-a distinguished particle under a harmonic and a bistable potential and a dimer with two metastable configurations-the resulting coarse-grained models are capable of reproducing not only the equilibrium distributions but also the dynamic behavior due to temporal correlations and memory effects. Remarkably, our method even reproduces the transition dynamics between metastable states, which is challenging to capture correctly. Our approach is not constrained to specific dynamics and can be extended to systems beyond Langevin dynamics, and, in principle, even to non-equilibrium dynamics.

Perspectives on Ligand/Protein Binding Kinetics Simulations: Force Fields, Machine Learning, Sampling, and User-Friendliness

Computational techniques applied to drug discovery have gained considerable popularity for their ability to filter potentially active drugs from inactive ones, reducing the time scale and costs of preclinical investigations. The main focus of these studies has historically been the search for compounds endowed with high affinity for a specific molecular target to ensure the formation of stable and long-lasting complexes. Recent evidence has also correlated the in vivo drug efficacy with its binding kinetics, thus opening new fascinating scenarios for ligand/protein binding kinetic simulations in drug discovery. The present article examines the state of the art in the field, providing a brief summary of the most popular and advanced ligand/protein binding kinetics techniques and evaluating their current limitations and the potential solutions to reach more accurate kinetic models. Particular emphasis is put on the need for a paradigm change in the present methodologies toward ligand and protein parametrization, the force field problem, characterization of the transition states, the sampling issue, and algorithms' performance, user-friendliness, and data openness.

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.

Phase behaviour of coarse-grained fluids

Soft condensed matter structures often challenge us with complex many-body phenomena governed by collective modes spanning wide spatial and temporal domains. In order to successfully tackle such problems, mesoscopic coarse-grained (CG) statistical models are being developed, providing a dramatic reduction in computational complexity. CG models provide an intermediate step in the complex statistical framework of linking the thermodynamics of condensed phases with the properties of their constituent atoms and molecules. These allow us to offload part of the problem to the CG model itself and reformulate the remainder in terms of reduced CG phase space. However, such exchange of pawns to chess pieces, or 'Hamiltonian renormalization', is a radical step and the thermodynamics of the primary atomic and CG models could be quite distinct. Here, we present a comprehensive study of the phase diagram including binodal and interfacial properties of a dissipative particle dynamics (DPD) model, extended to include finite-range attraction to support the liquid-gas equilibrium. Despite the similarities with the atomic model potentials, its phase envelope is markedly different featuring several anomalies such as an unusually broad liquid range, change in concavity of the liquid coexistence branch with variation of the model parameters, volume contraction on fusion, temperature of maximum density in the liquid phase and negative thermal expansion in the solid phase. These results provide new insight into the connection between simple potential models and complex emergent condensed matter phenomena.

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.

Engineered Biomimetic Membranes for Organ-on-a-Chip

Organ-on-a-chip (OOC) systems are engineered nanobiosystems to mimic the physiochemical environment of a specific organ in the body. Among various components of OOC systems, biomimetic membranes have been regarded as one of the most important key components to develop controllable biomimetic bioanalysis systems. Here, we review the preparation and characterization of biomimetic membranes in comparison with the features of the extracellular matrix. After that, we review and discuss the latest applications of engineered biomimetic membranes to fabricate various organs on a chip, such as liver, kidney, intestine, lung, skin, heart, vasculature and blood vessels, brain, and multiorgans with perspectives for further biomedical applications.

Temporally Coherent Backmapping of Molecular Trajectories From Coarse-Grained to Atomistic Resolution

Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done efficiently using coarse-grained simulations, from which meaningful physicochemical information can be inferred if the corresponding all-atom configurations are reconstructed. However, this procedure of backmapping to reintroduce the lost atomistic detail into coarse-grain structures has proven a challenging task due to the many feasible atomistic configurations that can be associated with one coarse-grain structure. Existing backmapping methods are strictly frame-based, relying on either heuristics to replace coarse-grain particles with atomic fragments and subsequent relaxation or parametrized models to propose atomic coordinates separately and independently for each coarse-grain structure. These approaches neglect information from previous trajectory frames that is critical to ensuring temporal coherence of the backmapped trajectory, while also offering information potentially helpful to producing higher-fidelity atomic reconstructions. In this work, we present a deep learning-enabled data-driven approach for temporally coherent backmapping that explicitly incorporates information from preceding trajectory structures. Our method trains a conditional variational autoencoder to nondeterministically reconstruct atomistic detail conditioned on both the target coarse-grain configuration and the previously reconstructed atomistic configuration. We demonstrate our backmapping approach on two exemplar biomolecular systems: alanine dipeptide and the miniprotein chignolin. We show that our backmapped trajectories accurately recover the structural, thermodynamic, and kinetic properties of the atomistic trajectory data.

Systematic measurements of interleaflet friction in supported bilayers

When lipid membranes curve or are subjected to strong shear forces, the two apposed leaflets of the bilayer slide past each other. The drag that one leaflet creates on the other is quantified by the coefficient of interleaflet friction, b. Existing measurements of this coefficient range over several orders of magnitude, so we used a recently developed microfluidic technique to measure it systematically in supported lipid membranes. Fluid shear stress was used to force the top leaflet of a supported membrane to slide over the stationary lower leaflet. Here, we show that this technique yields a reproducible measurement of the friction coefficient and is sensitive enough to detect differences in friction between membranes made from saturated and unsaturated lipids. Adding cholesterol to saturated and unsaturated membranes increased interleaflet friction significantly. We also discovered that fluid shear stress can reversibly induce gel phase in supported lipid bilayers that are close to the gel-transition temperature.

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.

Systematic bottom-up molecular coarse-graining via force and torque matching using anisotropic particles

We derive a systematic and general method for parametrizing coarse-grained molecular models consisting of anisotropic particles from fine-grained (e.g. all-atom) models for condensed-phase molecular dynamics simulations. The method, which we call anisotropic force-matching coarse-graining (AFM-CG), is based on rigorous statistical mechanical principles, enforcing consistency between the coarse-grained and fine-grained phase-space distributions to derive equations for the coarse-grained forces, torques, masses, and moments of inertia in terms of properties of a condensed-phase fine-grained system. We verify the accuracy and efficiency of the method by coarse-graining liquid-state systems of two different anisotropic organic molecules, benzene and perylene, and show that the parametrized coarse-grained models more accurately describe properties of these systems than previous anisotropic coarse-grained models parametrized using other methods that do not account for finite-temperature and many-body effects on the condensed-phase coarse-grained interactions. The AFM-CG method will be useful for developing accurate and efficient dynamical simulation models of condensed-phase systems of molecules consisting of large, rigid, anisotropic fragments, such as liquid crystals, organic semiconductors, and nucleic acids.

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.

Physical mechanisms of ESCRT-III-driven cell division

Living systems propagate by undergoing rounds of cell growth and division. Cell division is at heart a physical process that requires mechanical forces, usually exerted by assemblies of cytoskeletal polymers. Here we developed a physical model for the ESCRT-III-mediated division of archaeal cells, which despite their structural simplicity share machinery and evolutionary origins with eukaryotes. By comparing the dynamics of simulations with data collected from live cell imaging experiments, we propose that this branch of life uses a previously unidentified division mechanism. Active changes in the curvature of elastic cytoskeletal filaments can lead to filament perversions and supercoiling, to drive ring constriction and deform the overlying membrane. Abscission is then completed following filament disassembly. The model was also used to explore how different adenosine triphosphate (ATP)-driven processes that govern the way the structure of the filament is changed likely impact the robustness and symmetry of the resulting division. Comparisons between midcell constriction dynamics in simulations and experiments reveal a good agreement with the process when changes in curvature are implemented at random positions along the filament, supporting this as a possible mechanism of ESCRT-III-dependent division in this system. Beyond archaea, this study pinpoints a general mechanism of cytokinesis based on dynamic coupling between a coiling filament and the membrane.

Thermodynamics and Kinetics of Aggregation of Flexible Peripheral Membrane Proteins

Biomembrane remodeling is essential for cellular trafficking, with membrane-binding peripheral proteins playing a key role in it. Significant membrane remodeling as in endo- and exocytosis is often due to aggregates of many proteins with direct or membrane-mediated interactions. Understanding this process via computer simulations is extremely challenging: protein-membrane systems involve time and length scales that make atomistic simulations impractical, while most coarse-grained models fall short in resolving dynamics and physical effects of protein and membrane flexibility. Here, we develop a coarse-grained model of the bilayer membrane bestrewed with rotationally symmetric flexible proteins, parametrized to reflect local curvatures and lateral dynamics of proteins. We investigate the kinetics, equilibrium distributions, and the free energy landscape governing the formation and breakup of protein clusters on the surface of the membrane. We demonstrate how the flexibility of the proteins as well as their surface concentration play deciding roles in highly selective macroscopic aggregation behavior.

Three-dimensional morphodynamic simulations of macropinocytic cups

Macropinocytosis refers to the non-specific uptake of extracellular fluid, which plays ubiquitous roles in cell growth, immune surveillance, and virus entry. Despite its widespread occurrence, it remains unclear how its initial cup-shaped plasma membrane extensions form without any external solid support, as opposed to the process of particle uptake during phagocytosis. Here, by developing a computational framework that describes the coupling between the bistable reaction-diffusion processes of active signaling patches and membrane deformation, we demonstrated that the protrusive force localized to the edge of the patches can give rise to a self-enclosing cup structure, without further assumptions of local bending or contraction. Efficient uptake requires a balance among the patch size, magnitude of protrusive force, and cortical tension. Furthermore, our model exhibits cyclic cup formation, coexistence of multiple cups, and cup-splitting, indicating that these complex morphologies self-organize via a common mutually-dependent process of reaction-diffusion and membrane deformation.

Hydrodynamic coupling for particle-based solvent-free membrane models

The great challenge with biological membrane systems is the wide range of scales involved, from nanometers and picoseconds for individual lipids to the micrometers and beyond millisecond for cellular signaling processes. While solvent-free coarse-grained membrane models are convenient for large-scale simulations and promising to provide insight into slow processes involving membranes, these models usually have unrealistic kinetics. One major obstacle is the lack of an equally convenient way of introducing hydrodynamic coupling without significantly increasing the computational cost of the model. To address this, we introduce a framework based on anisotropic Langevin dynamics, for which major in-plane and out-of-plane hydrodynamic effects are modeled via friction and diffusion tensors from analytical or semi-analytical solutions to Stokes hydrodynamic equations. Using this framework, in conjunction with our recently developed membrane model, we obtain accurate dispersion relations for planar membrane patches, both free-standing and in the vicinity of a wall. We briefly discuss how non-equilibrium dynamics is affected by hydrodynamic interactions. We also measure the surface viscosity of the model membrane and discuss the affecting dissipative mechanisms.

Simulating realistic membrane shapes

Biological membranes exhibit diversity in their shapes and complexity in chemical compositions that are linked to many cellular functions. These two central features of biomembranes have been the subject of numerous simulation studies, using a diverse range of computational techniques. Currently, the field is able to capture this complexity at increasing levels of realism and connect the microscopic view on protein-lipid interactions to cellular morphologies at the level of entire organelles. Here we highlight recent advances in this topic, identify current bottlenecks, and sketch possible ways ahead.

An Appraisal of Computer Simulation Approaches in Elucidating Biomolecular Recognition Pathways

Computer simulation approaches in biomolecular recognition processes have come a long way. In this Perspective, we highlight a series of recent success stories in which computer simulations have played a remarkable role in elucidating the atomic resolution mechanism of kinetic processes of protein-ligand binding in a quantitative fashion. In particular, we show that a robust combination of unbiased simulation, harnessed by a high-fidelity computing environment, and Markov state modeling approaches has been instrumental in revealing novel protein-ligand recognition pathways in multiple systems. We also elucidate the role of recent developments in enhanced sampling approaches in providing the much-needed impetus in accelerating simulation of the ligand recognition process. We identify multiple key issues, including force fields and the sampling bottleneck, which are currently preventing the field from achieving quantitative reconstruction of experimental measurements. Finally, we suggest a possible way forward via adoption of multiscale approaches and coarse-grained simulations as next steps toward efficient elucidation of ligand binding kinetics.

Computational and Experimental Approaches to Investigate Lipid Nanoparticles as Drug and Gene Delivery Systems

Lipid nanoparticles (LNPs) have been widely applied in drug and gene delivery. More than twenty years ago, DoxilTM was the first LNPs-based drug approved by the US Food and Drug Administration (FDA). Since then, with decades of research and development, more and more LNP-based therapeutics have been used to treat diverse diseases, which often offer the benefits of reduced toxicity and/or enhanced efficacy compared to the active ingredients alone. Here, we provide a review of recent advances in the development of efficient and robust LNPs for drug/gene delivery. We emphasize the importance of rationally combining experimental and computational approaches, especially those providing multiscale structural and functional information of LNPs, to the design of novel and powerful LNP-based delivery systems.

Quantitative Synaptic Biology: A Perspective on Techniques, Numbers and Expectations

Synapses play a central role for the processing of information in the brain and have been analyzed in countless biochemical, electrophysiological, imaging, and computational studies. The functionality and plasticity of synapses are nevertheless still difficult to predict, and conflicting hypotheses have been proposed for many synaptic processes. In this review, we argue that the cause of these problems is a lack of understanding of the spatiotemporal dynamics of key synaptic components. Fortunately, a number of emerging imaging approaches, going beyond super-resolution, should be able to provide required protein positions in space at different points in time. Mathematical models can then integrate the resulting information to allow the prediction of the spatiotemporal dynamics. We argue that these models, to deal with the complexity of synaptic processes, need to be designed in a sufficiently abstract way. Taken together, we suggest that a well-designed combination of imaging and modelling approaches will result in a far more complete understanding of synaptic function than currently possible.