Systematic Nanoscale Analysis of Endocytosis Links Efficient Vesicle Formation to Patterned Actin Nucleation.

Clathrin-mediated endocytosis is an essential cellular function in all eukaryotes that is driven by a self-assembled macromolecular machine of over 50 different proteins in tens to hundreds of copies. How these proteins are organized to produce endocytic vesicles with high precision and efficiency is not understood. Here, we developed high-throughput superresolution microscopy to reconstruct the nanoscale structural organization of 23 endocytic proteins from over 100,000 endocytic sites in yeast. We found that proteins assemble by radially ordered recruitment according to function. WASP family proteins form a circular nanoscale template on the membrane to spatially control actin nucleation during vesicle formation. Mathematical modeling of actin polymerization showed that this WASP nano-template optimizes force generation for membrane invagination and substantially increases the efficiency of endocytosis. Such nanoscale pre-patterning of actin nucleation may represent a general design principle for directional force generation in membrane remodeling processes such as during cell migration and division.

Collective Hall current in chiral active fluids: Coupling of phase and mass transport through traveling bands.

Active fluids composed of constituents that are constantly driven away from thermal equilibrium can support spontaneous currents and can be engineered to have unconventional transport properties. Here, we report the emergence of (meta)stable traveling bands in computer simulations of aligning circle swimmers. These bands are different from polar flocks and, through coupling phase with mass transport, induce a bulk particle current with a component perpendicular to the propagation direction, thus giving rise to a collective Hall (or Magnus) effect. Traveling bands require sufficiently small orbits and undergo a discontinuous transition into a synchronized state with transient polar clusters for large orbital radii. Within a minimal hydrodynamic theory, we show that the bands can be understood as nondispersive soliton solutions fully accounting for the numerically observed properties.

Plastocyanin and Cytochrome f Complex Structures Obtained by NMR, Molecular Dynamics, and AlphaFold 3 Methods Compared to Cryo-EM Data.

Plastocyanin is a small mobile protein that facilitates electron transfer through the formation of short-lived protein-protein complexes with cytochrome bf and photosystem 1. Due to the transient nature of plastocyanin-cytochrome f complex, the lack of a long-lived tight complex makes it impossible to determine its structure by X-ray diffraction analysis. Up to today, a number of slightly different structures of such complexes have been obtained by experimental and computer methods. Now, artificial intelligence gives us the possibility to predict the structures of intermolecular complexes. In this study, we compare encounter and final complexes obtained by Brownian and molecular dynamics methods, as well as the structures predicted by AlphaFold 3, with NMR and cryo-EM data. Surprisingly, the best match for the plastocyanin electron density obtained by cryo-EM was demonstrated by an AlphaFold 3 structure. The orientation of plastocyanin in this structure almost completely coincides with its orientation obtained by molecular dynamics calculation, and, at the same time, it is different from the orientation of plastocyanin predicted on the basis of NMR data. This is even more unexpected given that only NMR structures for the plastocyanin-cytochrome f complex are available in the PDB database, which was used to train AlphaFold 3.

Interaction of Methylene Blue with Severe Acute Respiratory Syndrome Coronavirus 2 Envelope Revealed by Molecular Modeling.

Methylene blue has multiple antiviral properties against Severe Acute Respiratory Syndrome-related Coronavirus 2 (SARS-CoV-2). The ability of methylene blue to inhibit different stages of the virus life cycle, both in light-independent and photodynamic processes, is used in clinical practice. At the same time, the molecular aspects of the interactions of methylene blue with molecular components of coronaviruses are not fully understood. Here, we use Brownian dynamics to identify methylene blue binding sites on the SARS-CoV-2 envelope. The local lipid and protein composition of the coronavirus envelope plays a crucial role in the binding of this cationic dye. Viral structures targeted by methylene blue include the S and E proteins and negatively charged lipids. We compare the obtained results with known experimental data on the antiviral effects of methylene blue to elucidate the molecular basis of its activity against coronaviruses.

Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology.

Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that structural-maintenance-of-chromosomes (SMC) proteins-such as cohesins and condensins-can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.

Electrostatic Map of the SARS-CoV-2 Virion Specifies Binding Sites of the Antiviral Cationic Photosensitizer.

Electrostatics is an important part of virus life. Understanding the detailed distribution of charges over the surface of a virus is important to predict its interactions with host cells, antibodies, drugs, and different materials. Using a coarse-grained model of the entire viral envelope developed by D. Korkin and S.-J. Marrink's scientific groups, we created an electrostatic map of the external surface of SARS-CoV-2 and found a highly heterogeneous distribution of the electrostatic potential field of the viral envelope. Numerous negative patches originate mainly from negatively charged lipid domains in the viral membrane and negatively charged areas on the "stalks" of the spike (S) proteins. Membrane (M) and envelope (E) proteins with the total positive charge tend to colocalize with the negatively charged lipids. In the E protein pentamer exposed to the outer surface, negatively charged glutamate residues and surrounding lipids form a negative electrostatic potential ring around the channel entrance. We simulated the interaction of the antiviral octacationic photosensitizer octakis(cholinyl)zinc phthalocyanine with the surface structures of the entire model virion using the Brownian dynamics computational method implemented in ProKSim software (version r661). All mentioned negatively charged envelope components attracted the photosensitizer molecules and are thus potential targets for reactive oxygen generated in photosensitized reactions.

Simulation of different three-dimensional polymer models of interphase chromosomes compared to experiments-an evaluation and review framework of the 3D genome organization.

Despite all the efforts the three-dimensional higher-order architecture and dynamics in the cell nucleus are still debated. The regulation of genes, their transcription, replication, as well as differentiation in Eukarya is, however, closely connected to this architecture and dynamics. Here, an evaluation and review framework is setup to investigate the folding of a 30 nm chromatin fibre into chromosome territories by comparing computer simulations of two different chromatin topologies to experiments: The Multi-Loop-Subcompartment (MLS) model, in which small loops form rosettes connected by chromatin linkers, and the Random-Walk/Giant-Loop (RW/GL) model, in which large loops are attached to a flexible non-protein backbone, were simulated for various loop, rosette, and linker sizes. The 30 nm chromatin fibre was modelled as a polymer chain with stretching, bending, and excluded volume interactions. A spherical boundary potential simulated the confinement by other chromosomes and the nuclear envelope. Monte Carlo and Brownian Dynamics methods were applied to generate chain configurations at thermodynamic equilibrium. Both the MLS and the RW/GL models form chromosome territories, with different morphologies: The MLS rosettes form distinct subchromosomal domains, compatible in size as those from light microscopic observations. In contrast, the big RW/GL loops lead to a more homogeneous chromatin distribution. Only the MLS model agrees with the low overlap of chromosomes, their arms, and subchromosomal domains found experimentally. A review of experimental spatial distance measurements between genomic markers labelled by FISH as a function of their genomic separation from different publications and comparison to simulated spatial distances also favours an MLS-like model with loops and linkers of 63 to 126 kbp. The chromatin folding topology also reduces the apparent persistence length of the chromatin fibre to a value significantly lower than the free solution persistence length, explaining the low persistence lengths found various experiments. The predicted large spaces between the chromatin fibres allow typically sized biological molecules to reach nearly every location in the nucleus by moderately obstructed diffusion and disagrees with the much simplified assumption that defined channels between territories for molecular transport as in the Interchromosomal Domain (ICD) hypothesis exist. All this is also in agreement with recent selective high-resolution chromosome interaction capture (T2C) experiments, the scaling behaviour of the DNA sequence, the dynamics of the chromatin fibre, the nuclear diffusion of molecules, as well as other experiments. In summary, this polymer simulation framework compared to experimental data clearly favours only a quasi-chromatin fibre forming a stable multi-loop aggregate/rosette like genome organization and dynamics whose local topology is tightly connected to the global morphology and dynamics of the cell nucleus.

Chromatosome Structure and Dynamics from Molecular Simulations.

Chromatosomes are fundamental units of chromatin structure that are formed when a linker histone protein binds to a nucleosome. The positioning of the linker histone on the nucleosome influences the packing of chromatin. Recent simulations and experiments have shown that chromatosomes adopt an ensemble of structures that differ in the geometry of the linker histone-nucleosome interaction. In this article we review the application of Brownian, Monte Carlo, and molecular dynamics simulations to predict the structure of linker histone-nucleosome complexes, to study the binding mechanisms involved, and to predict how this binding affects chromatin fiber structure. These simulations have revealed the sensitivityof the chromatosome structure to variations in DNA and linker histone sequence, as well as to posttranslational modifications, thereby explaining the structural variability observed in experiments. We propose that a concerted application of experimental and computational approaches will reveal the determinants of chromatosome structural variability and how it impacts chromatin packing.

Inchworm movement of two rings switching onto a thread by biased Brownian diffusion represent a three-body problem.

The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.

Stretching of Bombyx mori Silk Protein in Flow.

The flow-induced self-assembly of entangled Bombyx mori silk proteins is hypothesised to be aided by the 'registration' of aligned protein chains using intermolecularly interacting 'sticky' patches. This suggests that upon chain alignment, a hierarchical network forms that collectively stretches and induces nucleation in a precisely controlled way. Through the lens of polymer physics, we argue that if all chains would stretch to a similar extent, a clear correlation length of the stickers in the direction of the flow emerges, which may indeed favour such a registration effect. Through simulations in both extensional flow and shear, we show that there is, on the other hand, a very broad distribution of protein-chain stretch, which suggests the registration of proteins is not directly coupled to the applied strain, but may be a slow statistical process. This qualitative prediction seems to be consistent with the large strains (i.e., at long time scales) required to induce gelation in our rheological measurements under constant shear. We discuss our perspective of how the flow-induced self-assembly of silk may be addressed by new experiments and model development.

A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space.

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, hybrid Monte Carlo on Hilbert spaces (Beskos, et al. Stoch. Proc. Applic. 2011), that provides finite-dimensional approximations of measures π, which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method that is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space Π having the target π as a marginal, together with a Hamiltonian flow that preserves Π. In the previous work, the authors explored a method where the phase space π was augmented with Brownian bridges. With this new choice, π is augmented by Ornstein-Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the acceptance rate in the MCMC method. This contrasts with the covariance of OU bridges, which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally, the Metropolis-Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier.

Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere.

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

Kinetics of Drug Binding and Residence Time.

The kinetics of drug binding and unbinding is assuming an increasingly crucial role in the long, costly process of bringing a new medicine to patients. For example, the time a drug spends in contact with its biological target is known as residence time (the inverse of the kinetic constant of the drug-target unbinding, 1/koff). Recent reports suggest that residence time could predict drug efficacy in vivo, perhaps even more effectively than conventional thermodynamic parameters (free energy, enthalpy, entropy). There are many experimental and computational methods for predicting drug-target residence time at an early stage of drug discovery programs. Here, we review and discuss the methodological approaches to estimating drug binding kinetics and residence time. We first introduce the theoretical background of drug binding kinetics from a physicochemical standpoint. We then analyze the recent literature in the field, starting from the experimental methodologies and applications thereof and moving to theoretical and computational approaches to the kinetics of drug binding and unbinding. We acknowledge the central role of molecular dynamics and related methods, which comprise a great number of the computational methods and applications reviewed here. However, we also consider kinetic Monte Carlo. We conclude with the outlook that drug (un)binding kinetics may soon become a go/no go step in the discovery and development of new medicines.

Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions.

Incorporating atomistic and molecular information into models of cellular behaviour is challenging because of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels. Multiscale or multi-resolution methodologies address this difficulty by using molecular dynamics (MD) and coarse-grained models in different parts of the cell. Their applicability depends on the accuracy and properties of the coarse-grained model which approximates the detailed MD description. A family of stochastic coarse-grained (SCG) models, written as relatively low-dimensional systems of nonlinear stochastic differential equations, is presented. The nonlinear SCG model incorporates the non-Gaussian force distribution which is observed in MD simulations and which cannot be described by linear models. It is shown that the nonlinearities can be chosen in such a way that they do not complicate parametrization of the SCG description by detailed MD simulations. The solution of the SCG model is found in terms of gamma functions.

Living Supramolecular Polymerization of Rod-Coil Block Copolymers: Kinetics, Origin of Uniformity, and Its Implication.

We conduct Brownian dynamics simulations to explore the kinetics of living supramolecular polymerization using seeded growth of rod-coil block copolymers as a model system. We model the kinetics of supramolecular polymerization by developing kinetic theory for classical living covalent polymerization with length-dependent rate coefficients. The rate coefficient in the proposed kinetics theory decreases with increasing cylindrical micelle length, which is attributed to micelle rigidity and unique diffusion behavior. Like living covalent polymerization, living supramolecular polymerization can produce low-dispersity assemblies with rigidity via different mechanisms. The results nicely explain the available experimental observations.

A Multi-Scale Study of Water Dynamics under Confinement, Exploiting Numerical Simulations in Relation to NMR Relaxometry, PGSE and NMR Micro-Imaging Experiments: An Application to the Clay/Water Interface.

Water mobility within the porous network of dense clay sediments was investigated over a broad dynamical range by using 2H nuclear magnetic resonance spectroscopy. Multi-quanta 2H NMR spectroscopy and relaxation measurements were first performed to identify the contributions of the various relaxation mechanisms monitoring the time evolution of the nuclear magnetisation of the confined heavy water. Secondly, multi-quanta spin-locking NMR relaxation measurements were then performed over a broad frequency domain, probing the mobility of the confined water molecules on a time-scale varying between microseconds and milliseconds. Thirdly, 1H NMR pulsed-gradient spin-echo attenuation experiments were performed to quantify water mobility on a time-scale limited by the NMR transverse relaxation time of the confined NMR probe, typically a few milliseconds. Fourthly, the long living quantum state of the magnetisation of quadrupolar nuclei was exploited to probe a two-time correlation function at a time-scale reaching one second. Finally, magnetic resonance imaging measurements allow probing the same dynamical process on time-scales varying between seconds and several hours. In that context, multi-scale modelling is required to interpret these NMR measurements and extract information on the influences of the structural properties of the porous network on the apparent mobility of the diffusing water molecules. That dual experimental and numerical approach appears generalizable to a large variety of porous networks, including zeolites, micelles and synthetic or biological membranes.

DiTe2: Calculating the diffusion tensor for flexible molecules.

We report on an extended hydrodynamic modeling of the friction tensorial properties of flexible molecules including all types of natural, Z-Matrix like, internal coordinates. We implement the new methodology by extending and updating the software DiTe [Barone et al. J. Comput. Chem. 30, 2 (2009)]. DiTe (DIffusion TEnsor) implements a hydrodynamic modeling of the generalized translational, rotational, and configurational friction and diffusion tensors of flexible molecules in which flexibility is described in terms of dihedral angles. The new tool, DiTe2, has been renewed to include also stretching and bending types of internal mobility. Furthermore, DiTe2 is able to calculate the friction and diffusion tensors along collective (or reaction) coordinates defined as linear combinations of the internal natural ones. A number of tests are reported to show the new features of DiTe2. As leitmotiv for the tests, the calmodulin protein is taken into consideration, described both at all-atom and coarse-grained levels. © 2018 Wiley Periodicals, Inc.

Computational Methods Used to Explore Transport Events in Biological Systems.

Transport of various molecules facilitated with membrane proteins is necessary for maintaining homeostasis in living cells. In humans, dysfunction of these proteins leads to many diseases. Thus, understanding how the membrane proteins function may help using them as therapeutic targets. To successfully investigate the mechanistic aspects of transport, the choice of appropriate methods is crucial. We review the computational methods that have proven most effective in investigating transport events, specifically, deterministic time-dependent classical molecular dynamics and its enhanced sampling variants, as well as methods based on Brownian dynamics. We describe technical aspects of these methods and examples of their novel variants or combinations that have been recently and successfully applied in the transport studies. We also discuss the difficulties related to these methods and provide possible solutions to avoid them.

Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches.

Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers.

A 3D Multiscale Model to Explore the Role of EGFR Overexpression in Tumourigenesis.

The epidermal growth factor receptor (EGFR) signalling cascade is one of the main pathways that regulate the survival and division of mammalian cells. It is also one of the most altered transduction pathways in cancer. Acquired mutations in the EGFR/ERK pathway can cause the overexpression of EGFR on the surface of the cell, while others downregulate the inactivation of switched on intracellular proteins such as Ras and Raf. This upregulates the activity of ERK and promotes cell division. We develop a 3D multiscale model to explore the role of EGFR overexpression on tumour initiation. In this model, cells are described as individual objects that move, interact, divide, proliferate, and die by apoptosis. We use Brownian Dynamics to describe the extracellular and intracellular regulations of cells as well as the spatial and stochastic effects influencing them. The fate of each cell depends on the number of active transcription factors in the nucleus. We use numerical simulations to investigate the individual and combined effects of mutations on the intracellular regulation of individual cells. Next, we show that the distance between active receptors increase the level of EGFR/ERK signalling. We demonstrate the usefulness of the model by quantifying the impact of mutational alterations in the EGFR/ERK pathway on the growth rate of in silico tumours.