Minimal coarse-grained models for molecular self-organisation in biology

Exploring protein-mediated compaction of DNA by coarse-grained simulations and unsupervised learning

Protein-DNA interactions and protein-mediated DNA compaction play key roles in a range of biological processes. The length scales typically involved in DNA bending, bridging, looping, and compaction (≥1 kbp) are challenging to address experimentally or by all-atom molecular dynamics simulations, making coarse-grained simulations a natural approach. Here, we present a simple and generic coarse-grained model for DNA-protein and protein-protein interactions and investigate the role of the latter in the protein-induced compaction of DNA. Our approach models the DNA as a discrete worm-like chain. The proteins are treated in the grand canonical ensemble, and the protein-DNA binding strength is taken from experimental measurements. Protein-DNA interactions are modeled as an isotropic binding potential with an imposed binding valency without specific assumptions about the binding geometry. To systematically and quantitatively classify DNA-protein complexes, we present an unsupervised machine learning pipeline that receives a large set of structural order parameters as input, reduces the dimensionality via principal-component analysis, and groups the results using a Gaussian mixture model. We apply our method to recent data on the compaction of viral genome-length DNA by HIV integrase and find that protein-protein interactions are critical to the formation of looped intermediate structures seen experimentally. Our methodology is broadly applicable to DNA-binding proteins and protein-induced DNA compaction and provides a systematic and semi-quantitative approach for analyzing their mesoscale complexes.

Recent advances in computational prediction of molecular properties in food chemistry

The combination of food chemistry and computational simulation has brought many impacts to food research, moving from experimental chemistry to computer chemistry. This paper will systematically review in detail the important role played by computational simulations in the development of the molecular structure of food, mainly from the atomic, molecular, and multicomponent dimension. It will also discuss how different computational chemistry models can be constructed and analyzed to obtain reliable conclusions. From the calculation principle to case analysis, this paper focuses on the selection and application of quantum mechanics, molecular mechanics and coarse-grained molecular dynamics in food chemistry research. Finally, experiments and computations of food chemistry are compared and summarized to obtain the best balance between them. The above review and outlook will provide an important reference for the intersection of food chemistry and computational chemistry, and is expected to provide innovative thinking for structural research in food chemistry.

Self-organization of mortal filaments and its role in bacterial division ring formation

Filaments in the cell commonly treadmill. Driven by energy consumption, they grow on one end while shrinking on the other, causing filaments to appear motile even though individual proteins remain static. This process is characteristic of cytoskeletal filaments and leads to collective filament self-organization. Here we show that treadmilling drives filament nematic ordering by dissolving misaligned filaments. Taking the bacterial FtsZ protein involved in cell division as an example, we show that this mechanism aligns FtsZ filaments in vitro and drives the organization of the division ring in living Bacillus subtilis cells. We find that ordering via local dissolution also allows the system to quickly respond to chemical and geometrical biases in the cell, enabling us to quantitatively explain the ring formation dynamics in vivo. Beyond FtsZ and other cytoskeletal filaments, our study identifies a mechanism for self-organization via constant birth and death of energy-consuming filaments.

Which Coverages of Arc-Shaped Proteins Are Required for Membrane Tubulation?

Arc-shaped BIN/Amphiphysin/Rvs (BAR) domain proteins generate curvature by binding to membranes and induce membrane tubulation at sufficiently large protein coverages. For the amphiphysin N-BAR domain, Le Roux et al., Nat. Commun. 2021, 12, 6550, measured a threshold coverage of 0.44 ± 0.097 for nanotubules emerging from the supported lipid bilayer. In this article, we systematically investigate membrane tubulation induced by arc-shaped protein-like particles with coarse-grained modeling and simulations and determine the threshold coverages at different particle-particle interaction strengths and membrane spontaneous curvatures. In our simulations, the binding of arc-shaped particles induces a membrane shape transition from spherical vesicles to tubules at a particle threshold coverage of about 0.5, which is rather robust to variations of the direct attractive particle interactions or spontaneous membrane curvature in the coarse-grained model. Our study suggests that threshold coverages of around or slightly below 0.5 are a general requirement for membrane tubulation by arc-shaped BAR domain proteins.

Coarse-grained modeling of DNA-RNA hybrids

We introduce oxNA, a new model for the simulation of DNA-RNA hybrids that is based on two previously developed coarse-grained models-oxDNA and oxRNA. The model naturally reproduces the physical properties of hybrid duplexes, including their structure, persistence length, and force-extension characteristics. By parameterizing the DNA-RNA hydrogen bonding interaction, we fit the model's thermodynamic properties to experimental data using both average-sequence and sequence-dependent parameters. To demonstrate the model's applicability, we provide three examples of its use-calculating the free energy profiles of hybrid strand displacement reactions, studying the resolution of a short R-loop, and simulating RNA-scaffolded wireframe origami.

Elucidating the role of water in collagen self-assembly by isotopically modulating collagen hydration

Water is known to play an important role in collagen self-assembly, but it is still largely unclear how water-collagen interactions influence the assembly process and determine the fibril network properties. Here, we use the H[Formula: see text]O/D[Formula: see text]O isotope effect on the hydrogen-bond strength in water to investigate the role of hydration in collagen self-assembly. We dissolve collagen in H[Formula: see text]O and D[Formula: see text]O and compare the growth kinetics and the structure of the collagen assemblies formed in these water isotopomers. Surprisingly, collagen assembly occurs ten times faster in D[Formula: see text]O than in H[Formula: see text]O, and collagen in D[Formula: see text]O self-assembles into much thinner fibrils, that form a more inhomogeneous and softer network, with a fourfold reduction in elastic modulus when compared to H[Formula: see text]O. Combining spectroscopic measurements with atomistic simulations, we show that collagen in D[Formula: see text]O is less hydrated than in H[Formula: see text]O. This partial dehydration lowers the enthalpic penalty for water removal and reorganization at the collagen-water interface, increasing the self-assembly rate and the number of nucleation centers, leading to thinner fibrils and a softer network. Coarse-grained simulations show that the acceleration in the initial nucleation rate can be reproduced by the enhancement of electrostatic interactions. These results show that water acts as a mediator between collagen monomers, by modulating their interactions so as to optimize the assembly process and, thus, the final network properties. We believe that isotopically modulating the hydration of proteins can be a valuable method to investigate the role of water in protein structural dynamics and protein self-assembly.

Dynamic DNA Assembly by Programmable Hybridization Chain Reaction Mimicking Tubulin

Dynamic biological structures involve the continual turnover of molecules within supramolecular assemblies such as tubulin. Inspired by dynamic biology self-organizing systems, we build an artificial dynamic structure based on DNA nanotechnology through a nonequilibrium chemical system. Herein, a metastable domain (MD), essentially a stem-loop structure, was introduced into DNA hairpins within hybridization chain reaction (HCR), thereby imparting dynamic activity to the DNA polymers. Hairpins with MD thermodynamically assemble to a high-energy polymer in the presence of trigger strands. The polymer can relax back to the stable unassembled state once the invader is added and finally relax to the activated hairpin by an anti-invader. Reversible assembly/disassembly of the HCR is achieved through invader/anti-invader cycles. We accomplished kinetic modulation, reversible conformational switching, cascading regulation, and enzyme activity control through the MD-HCR. We believe that the design of the MD-HCR could inspire the development of autonomous biological functions within artificial systems.

Emergence of selectivity and specificity in a coarse-grained model of the nuclear pore complex with sequence-agnostic FG-Nups

The role of hydrophobicity of phenylalanine-glycine nucleoporins (FG-Nups) in determining the transport of receptor-bound cargo across the nuclear pore complex (NPC) is investigated using Langevin dynamics simulations. A coarse-grained, minimal model of the NPC, comprising a cylindrical pore and hydrophobic-hydrophilic random copolymers for FG-Nups was employed. Karyopherin-bound receptor-cargo complexes (Kaps) were modeled as rigid, coarse-grained spheres without (inert) and with (patchy) FG-binding hydrophobic domains. With a sequence-agnostic description of FG-Nups and the absence of any anisotropies associated with either NPC or cargo, the model described tracer transport only as a function of FG-Nup hydrophobicity, f. The simulations showed the emergence of two important features of cargo transport, namely, NPC selectivity and specificity. NPC selectivity to patchy tracers emerged due to hydrophobic Kap-FG interactions and despite the sequence-agnostic description of FG-Nups. Furthermore, NPC selectivity was observed only in a specific range of FG-hydrophobic fraction, 0.05 ≤ f ≤ 0.20, resulting in specificity of NPC transport with respect to f. Significantly, this range corresponded to the number fraction of FG-repeats observed in both S. cerevisiae and H. sapiens NPCs. This established the central role of the FG-hydrophobic fraction in determining NPC transport, and provided a biophysical basis for conservation of the FG-Nup hydrophobic fraction across evolutionarily distant NPCs. Specificity in NPC transport emerged from the formation of a hydrogel-like network inside the pore with a characteristic mesh size dependent on f. This network rejected cargo for f > 0.2 based on size exclusion, which resulted in enhanced translocation probability for 0.05 ≤ f ≤ 0.20. Extended brush configurations outside the pore resulted in entropic repulsion and exclusion of inert cargo in this range. Thus, our minimal NPC model exhibited a hybrid cargo translocation mechanism, with aspects of both virtual gate and selective-phase models, in this range of FG-hydrophobic fraction.

Computational modeling of membrane trafficking processes: From large molecular assemblies to chemical specificity

In the last decade, molecular dynamics (MD) simulations have become an essential tool to investigate the molecular properties of membrane trafficking processes, often in conjunction with experimental approaches. The combination of MD simulations with recent developments in structural biology, such as cryo-electron microscopy and artificial intelligence-based structure determination, opens new, exciting possibilities for future investigations. However, the full potential of MD simulations to provide a molecular view of the complex and dynamic processes involving membrane trafficking can only be realized if certain limitations are addressed, and especially those concerning the quality of coarse-grain models, which, despite recent successes in describing large-scale systems, still suffer from far-from-ideal chemical accuracy. In this review, we will highlight recent success stories of MD simulations in the investigation of membrane trafficking processes, their implications for future research, and the challenges that lie ahead in this specific research domain.

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface

The Spindle Assembly Abnormal Protein 6 (SAS-6) forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is strongly facilitated on a surface, shifting the reaction equilibrium by four orders of magnitude compared to the bulk. Moreover, a fraction of non-canonical symmetries (i.e., different from nine) was observed. In order to understand which aspects of the system are relevant to ensure efficient self-assembly and selection of the nine-fold symmetry, we have performed Brownian dynamics computer simulation with patchy particles and then compared our results with the experimental ones. Adsorption onto the surface was simulated by a grand canonical Monte Carlo procedure and random sequential adsorption kinetics. Furthermore, self-assembly was described by Langevin equations with hydrodynamic mobility matrices. We find that as long as the interaction energies are weak, the assembly kinetics can be described well by coagulation-fragmentation equations in the reaction-limited approximation. By contrast, larger interaction energies lead to kinetic trapping and diffusion-limited assembly. We find that the selection of nine-fold symmetry requires a small value for the angular interaction range. These predictions are confirmed by the experimentally observed reaction constant and angle fluctuations. Overall, our simulations suggest that the SAS-6 system works at the crossover between a relatively weak binding energy that avoids kinetic trapping and a small angular range that favors the nine-fold symmetry.

Stability, Speed, and Constraints for Structural Coarse-Graining in VOTCA

Structural coarse-graining involves the inverse problem of deriving pair potentials that reproduce target radial distribution functions. Despite its clear mathematical formulation, there are open questions about the existing methods concerning speed, stability, and physical representability of the resulting potentials. In this work, we make progress on several aspects of iterative methods used to solve the inverse problem. Based on integral equation theory, we derive fast Gauss-Newton schemes applicable to very general systems, including molecules with bonds and mixtures. Our methods are similar to inverse Monte Carlo in terms of convergence speed and have a similar cost per iteration as iterative Boltzmann inversion. We investigate stability problems in our schemes and in the inverse Monte Carlo method and propose modifications to fix them. Furthermore, we establish how the pair potential can be constrained at each iteration to reproduce the pressure, Kirkwood-Buff integral, or the enthalpy of vaporization. We demonstrate the potential of our approach in deriving coarse-grained force fields for nine different solvents and their mixtures. All methods described are implemented in the free and open VOTCA software framework for systematic coarse-graining.

The dawn of interoperating spatial models in cell biology

Spatial simulations are becoming an increasingly ubiquitous component in the cycle of discovery, experimentation, and communication across the sciences. In cell biology, many researchers share a vision of developing multiscale models that recapitulate observable behaviors spanning from atoms to cells to tissues. For this dream to become a reality, however, simulation technologies must provide a means for integration and interoperability as they advance. Already, the field has developed numerous methods that span scales of length, time, and complexity to create an extensive body of effective simulation approaches, and although these approaches rarely interoperate, they collectively cover a large spectrum of knowledge that future models may handle in a more unified manner. Here, we discuss the importance of making the data, workflows, and outputs of spatial simulations shareable and interoperable; and how democratization could encourage diverse biologists to participate more easily in developing models to advance our understanding of biological systems.

The stoichiometric interaction model for mesoscopic MD simulations of liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) has received considerable attention in recent years for explaining the formation of cellular biomolecular condensates. The fluidity and the complexity of their components make molecular simulation approaches indispensable for gaining structural insights. Domain-resolution mesoscopic model simulations have been explored for cases in which condensates are formed by multivalent proteins with tandem domains. One problem with this approach is that interdomain pairwise interactions cannot regulate the valency of the binding domains. To overcome this problem, we propose a new potential, the stoichiometric interaction (SI) potential. First, we verified that the SI potential maintained the valency of the interacting domains for the test systems. We then examined a well-studied LLPS model system containing tandem repeats of SH3 domains and proline-rich motifs. We found that the SI potential alone cannot reproduce the phase diagram of LLPS quantitatively. We had to combine the SI and a pairwise interaction; the former and the latter represent the specific and nonspecific interactions, respectively. Biomolecular condensates with the mixed SI and pairwise interaction exhibited fluidity, whereas those with the pairwise interaction alone showed no detectable diffusion. We also compared the phase diagrams of the systems containing different numbers of tandem domains with those obtained from the experiments and found quantitative agreement in all but one case.

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.

Building an extensible cell wall

This article recounts, from my perspective of four decades in this field, evolving paradigms of primary cell wall structure and the mechanism of surface enlargement of growing cell walls. Updates of the structures, physical interactions, and roles of cellulose, xyloglucan, and pectins are presented. This leads to an example of how a conceptual depiction of wall structure can be translated into an explicit quantitative model based on molecular dynamics methods. Comparison of the model's mechanical behavior with experimental results provides insights into the molecular basis of complex mechanical behaviors of primary cell wall and uncovers the dominant role of cellulose-cellulose interactions in forming a strong yet extensible network.

Collagen fibril assembly: New approaches to unanswered questions

Collagen fibrils are essential for metazoan life. They are the largest, most abundant, and most versatile protein polymers in animals, where they occur in the extracellular matrix to form the structural basis of tissues and organs. Collagen fibrils were first observed at the turn of the 20th century. During the last 40 years, the genes that encode the family of collagens have been identified, the structure of the collagen triple helix has been solved, the many enzymes involved in the post-translational modifications of collagens have been identified, mutations in the genes encoding collagen and collagen-associated proteins have been linked to heritable disorders, and changes in collagen levels have been associated with a wide range of diseases, including cancer. Yet despite extensive research, a full understanding of how cells assemble collagen fibrils remains elusive. Here, we review current models of collagen fibril self-assembly, and how cells might exert control over the self-assembly process to define the number, length and organisation of fibrils in tissues.

The future of biomolecular simulation in the pharmaceutical industry: what we can learn from aerodynamics modelling and weather prediction. Part 1. understanding the physical and computational complexity of in silico drug design

The predictive power of simulation has become embedded in the infrastructure of modern economies. Computer-aided design is ubiquitous throughout industry. In aeronautical engineering, built infrastructure and materials manufacturing, simulations are routinely used to compute the performance of potential designs before construction. The ability to predict the behaviour of products is a driver of innovation by reducing the cost barrier to new designs, but also because radically novel ideas can be piloted with relatively little risk. Accurate weather forecasting is essential to guide domestic and military flight paths, and therefore the underpinning simulations are critical enough to have implications for national security. However, in the pharmaceutical and biotechnological industries, the application of computer simulations remains limited by the capabilities of the technology with respect to the complexity of molecular biology and human physiology. Over the last 30 years, molecular-modelling tools have gradually gained a degree of acceptance in the pharmaceutical industry. Drug discovery has begun to benefit from physics-based simulations. While such simulations have great potential for improved molecular design, much scepticism remains about their value. The motivations for such reservations in industry and areas where simulations show promise for efficiency gains in preclinical research are discussed. In this, the first of two complementary papers, the scientific and technical progress that needs to be made to improve the predictive power of biomolecular simulations, and how this might be achieved, is firstly discussed (Part 1). In Part 2, the status of computer simulations in pharma is contrasted with aerodynamics modelling and weather forecasting, and comments are made on the cultural changes needed for equivalent computational technologies to become integrated into life-science industries.

Where Biology and Traditional Polymers Meet: The Potential of Associating Sequence-Defined Polymers for Materials Science

Polymers with precisely defined monomeric sequences present an exquisite tool for controlling material properties by harnessing both the robustness of synthetic polymers and the ability to tailor the inter- and intramolecular interactions so crucial to many biological materials. While polymer scientists traditionally synthesized and studied the physics of long molecules best described by their statistical nature, many biological polymers derive their highly tailored functions from precisely controlled sequences. Therefore, significant effort has been applied toward developing new methods of synthesizing, characterizing, and understanding the physics of non-natural sequence-defined polymers. This perspective considers the synergistic advantages that can be achieved via tailoring both precise sequence control and attributes of traditional polymers in a single system. Here, we focus on the potential of sequence-defined polymers in highly associating systems, with a focus on the unique properties, such as enhanced proton conductivity, that can be attained by incorporating sequence. In particular, we examine these materials as key model systems for studying previously unresolvable questions in polymer physics including the role of chain shape near interfaces and how to tailor compatibilization between dissimilar polymer blocks. Finally, we discuss the critical challenges-in particular, truly scalable synthetic approaches, characterization and modeling tools, and robust control and understanding of assembly pathways-that must be overcome for sequence-defined polymers to attain their potential and achieve ubiquity.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

Physical modeling of multivalent interactions in the nuclear pore complex

In the nuclear pore complex, intrinsically disordered proteins (FG Nups), along with their interactions with more globular proteins called nuclear transport receptors (NTRs), are vital to the selectivity of transport into and out of the cell nucleus. Although such interactions can be modeled at different levels of coarse graining, in vitro experimental data have been quantitatively described by minimal models that describe FG Nups as cohesive homogeneous polymers and NTRs as uniformly cohesive spheres, in which the heterogeneous effects have been smeared out. By definition, these minimal models do not account for the explicit heterogeneities in FG Nup sequences, essentially a string of cohesive and noncohesive polymer units, and at the NTR surface. Here, we develop computational and analytical models that do take into account such heterogeneity in a minimal fashion and compare them with experimental data on single-molecule interactions between FG Nups and NTRs. Overall, we find that the heterogeneous nature of FG Nups and NTRs does play a role in determining equilibrium binding properties but is of much greater significance when it comes to unbinding and binding kinetics. Using our models, we predict how binding equilibria and kinetics depend on the distribution of cohesive blocks in the FG Nup sequences and of the binding pockets at the NTR surface, with multivalency playing a key role. Finally, we observe that single-molecule binding kinetics has a rather minor influence on the diffusion of NTRs in polymer melts consisting of FG-Nup-like sequences.

Thermodynamics and kinetics of phase separation of protein-RNA mixtures by a minimal model

Intracellular liquid-liquid phase separation enables the formation of biomolecular condensates, such as ribonucleoprotein granules, which play a crucial role in the spatiotemporal organization of biomolecules (e.g., proteins and RNAs). Here, we introduce a patchy-particle polymer model to investigate liquid-liquid phase separation of protein-RNA mixtures. We demonstrate that at low to moderate concentrations, RNA enhances the stability of RNA-binding protein condensates because it increases the molecular connectivity of the condensed-liquid phase. Importantly, we find that RNA can also accelerate the nucleation stage of phase separation. Additionally, we assess how the capacity of RNA to increase the stability of condensates is modulated by the relative protein-protein/protein-RNA binding strengths. We find that phase separation and multiphase organization of multicomponent condensates is favored when the RNA binds with higher affinity to the lower-valency proteins in the mixture than to the cognate higher-valency proteins. Collectively, our results shed light on the roles of RNA in ribonucleoprotein granule formation and the internal structuring of stress granules.

Moltemplate: A Tool for Coarse-Grained Modeling of Complex Biological Matter and Soft Condensed Matter Physics

Coarse-grained models have long been considered indispensable tools in the investigation of biomolecular dynamics and assembly. However, the process of simulating such models is arduous because unconventional force fields and particle attributes are often needed, and some systems are not in thermal equilibrium. Although modern molecular dynamics programs are highly adaptable, software designed for preparing all-atom simulations typically makes restrictive assumptions about the nature of the particles and the forces acting on them. Consequently, the use of coarse-grained models has remained challenging. Moltemplate is a file format for storing coarse-grained molecular models and the forces that act on them, as well as a program that converts moltemplate files into input files for LAMMPS, a popular molecular dynamics engine. Moltemplate has broad scope and an emphasis on generality. It accommodates new kinds of forces as they are developed for LAMMPS, making moltemplate a popular tool with thousands of users in computational chemistry, materials science, and structural biology. To demonstrate its wide functionality, we provide examples of using moltemplate to prepare simulations of fluids using many-body forces, coarse-grained organic semiconductors, and the motor-driven supercoiling and condensation of an entire bacterial chromosome.

Membrane morphologies induced by mixtures of arc-shaped particles with opposite curvature

Biological membranes are shaped by various proteins that either generate inward or outward membrane curvature. In this article, we investigate the membrane morphologies induced by mixtures of arc-shaped particles with coarse-grained modeling and simulations. The particles bind to the membranes either with their inward, concave side or their outward, convex side and, thus, generate membrane curvature of opposite sign. We find that small fractions of convex-binding particles can stabilize three-way junctions of membrane tubules, as suggested for the protein lunapark in the endoplasmic reticulum of cells. For comparable fractions of concave-binding and convex-binding particles, we observe lines of particles of the same type, and diverse membrane morphologies with grooves and bulges induced by these particle lines. The alignment and segregation of the particles is driven by indirect, membrane-mediated interactions.

Mechanosensitive self-assembly of myosin II minifilaments

Self-assembly and force generation are two central processes in biological systems that usually are considered in separation. However, the signals that activate nonmuscle myosin II molecular motors simultaneously lead to self-assembly into myosin II minifilaments as well as progression of the motor heads through the cross-bridge cycle. Here we investigate theoretically the possible effects of coupling these two processes. Our assembly model, which builds on a consensus architecture of the minifilament, predicts a critical aggregation concentration at which the assembly kinetics slows down dramatically. The combined model predicts that increasing actin filament concentration and force both lead to a decrease in the critical aggregation concentration. We suggest that due to these effects, myosin II minifilaments in a filamentous context might be in a critical state that reacts faster to varying conditions than in solution. We finally compare our model to experiments by simulating fluorescence recovery after photobleaching.

Modeling Fibrillogenesis of Collagen-Mimetic Molecules

One of the most robust examples of self-assembly in living organisms is the formation of collagen architectures. Collagen type I molecules are a crucial component of the extracellular matrix, where they self-assemble into fibrils of well-defined axial striped patterns. This striped fibrillar pattern is preserved across the animal kingdom and is important for the determination of cell phenotype, cell adhesion, and tissue regulation and signaling. The understanding of the physical processes that determine such a robust morphology of self-assembled collagen fibrils is currently almost completely missing. Here, we develop a minimal coarse-grained computational model to identify the physical principles of the assembly of collagen-mimetic molecules. We find that screened electrostatic interactions can drive the formation of collagen-like filaments of well-defined striped morphologies. The fibril axial pattern is determined solely by the distribution of charges on the molecule and is robust to the changes in protein concentration, monomer rigidity, and environmental conditions. We show that the striped fibrillar pattern cannot be easily predicted from the interactions between two monomers but is an emergent result of multibody interactions. Our results can help address collagen remodeling in diseases and aging and guide the design of collagen scaffolds for biotechnological applications.

Challenges in protein docking

Current developments in protein docking aim at improvement of applicability, accuracy and utility of modeling macromolecular complexes. The challenges include the need for greater emphasis on protein docking to molecules of different types, proper accounting for conformational flexibility upon binding, new promising methodologies based on residue co-evolution and deep learning, affinity prediction, and further development of fully automated docking servers. Importantly, new developments increasingly focus on realistic modeling of protein interactions in vivo, including crowded environment inside a cell, which involves multiple transient encounters, and propagating the system in time. This opinion paper offers the author's perspective on these challenges in structural modeling of protein interactions and the future of protein docking.

Liquid network connectivity regulates the stability and composition of biomolecular condensates with many components

One of the key mechanisms used by cells to control the spatiotemporal organization of their many components is the formation and dissolution of biomolecular condensates through liquid-liquid phase separation (LLPS). Using a minimal coarse-grained model that allows us to simulate thousands of interacting multivalent proteins, we investigate the physical parameters dictating the stability and composition of multicomponent biomolecular condensates. We demonstrate that the molecular connectivity of the condensed-liquid network-i.e., the number of weak attractive protein-protein interactions per unit of volume-determines the stability (e.g., in temperature, pH, salt concentration) of multicomponent condensates, where stability is positively correlated with connectivity. While the connectivity of scaffolds (biomolecules essential for LLPS) dominates the phase landscape, introduction of clients (species recruited via scaffold-client interactions) fine-tunes it by transforming the scaffold-scaffold bond network. Whereas low-valency clients that compete for scaffold-scaffold binding sites decrease connectivity and stability, those that bind to alternate scaffold sites not required for LLPS or that have higher-than-scaffold valencies form additional scaffold-client-scaffold bridges increasing stability. Proteins that establish more connections (via increased valencies, promiscuous binding, and topologies that enable multivalent interactions) support the stability of and are enriched within multicomponent condensates. Importantly, proteins that increase the connectivity of multicomponent condensates have higher critical points as pure systems or, if pure LLPS is unfeasible, as binary scaffold-client mixtures. Hence, critical points of accessible systems (i.e., with just a few components) might serve as a unified thermodynamic parameter to predict the composition of multicomponent condensates.

Bond Type and Discretization of Nonmuscle Myosin II Are Critical for Simulated Contractile Dynamics

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, cross-link, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is nonmuscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and cross-link actin filaments (F-actin). The multivalence of NMMII ensembles and their multiple roles have confounded the resolution of crucial questions, including how the number of NMMII subunits affects dynamics and what affects the relative contribution of ensembles' cross-linking versus motoring activities. Because biophysical measurements of ensembles are sparse, modeling of actomyosin networks has aided in discovering the complex behaviors of NMMII ensembles. Myosin ensembles have been modeled via several strategies with variable discretization or coarse graining and unbinding dynamics, and although general assumptions that simplify motor ensembles result in global contractile behaviors, it remains unclear which strategies most accurately depict cellular activity. Here, we used an agent-based platform, Cytosim, to implement several models of NMMII ensembles. Comparing the effects of bond type, we found that ensembles of catch-slip and catch motors were the best force generators and binders of filaments. Slip motor ensembles were capable of generating force but unbound frequently, resulting in slower contractile rates of contractile networks. Coarse graining of these ensemble types from two sets of 16 motors on opposite ends of a stiff rod to two binders, each representing 16 motors, reduced force generation, contractility, and the total connectivity of filament networks for all ensemble types. A parallel cluster model, previously used to describe ensemble dynamics via statistical mechanics, allowed better contractility with coarse graining, though connectivity was still markedly reduced for this ensemble type with coarse graining. Together, our results reveal substantial tradeoffs associated with the process of coarse graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.

Integrating transposable elements in the 3D genome

Chromosome organisation is increasingly recognised as an essential component of genome regulation, cell fate and cell health. Within the realm of transposable elements (TEs) however, the spatial information of how genomes are folded is still only rarely integrated in experimental studies or accounted for in modelling. Whilst polymer physics is recognised as an important tool to understand the mechanisms of genome folding, in this commentary we discuss its potential applicability to aspects of TE biology. Based on recent works on the relationship between genome organisation and TE integration, we argue that existing polymer models may be extended to create a predictive framework for the study of TE integration patterns. We suggest that these models may offer orthogonal and generic insights into the integration profiles (or "topography") of TEs across organisms. In addition, we provide simple polymer physics arguments and preliminary molecular dynamics simulations of TEs inserting into heterogeneously flexible polymers. By considering this simple model, we show how polymer folding and local flexibility may generically affect TE integration patterns. The preliminary discussion reported in this commentary is aimed to lay the foundations for a large-scale analysis of TE integration dynamics and topography as a function of the three-dimensional host genome.

Visualizing in Vivo Dynamics of Designer Nanoscaffolds

Enzymes of natural biochemical pathways are routinely subcellularly organized in space and time in order to improve pathway efficacy and control. Designer scaffolding platforms are under development to confer similar benefits upon engineered pathways. Herein, we evaluate bacterial microcompartment shell (pfam0936-domain) proteins as modules for constructing well-defined nanometer scale scaffolds in vivo. We use a suite of visualization techniques to evaluate scaffold assembly and dynamics. We demonstrate recruitment of target cargo molecules onto assembled scaffolds by appending reciprocally interacting adaptor domains. These interactions can be refined by fine-tuning the scaffold expression level. Real-time observation of this system reveals a nucleation-limited step where multiple scaffolds initially form within a cell. Over time, nucleated scaffolds reorganize into a single intracellular assembly, likely due to interscaffold competition for protein subunits. Our results suggest design considerations for using self-assembling proteins as building blocks to construct nanoscaffolds, while also providing a platform to visualize scaffold-cargo dynamics in vivo.