Polymer time crystal: Mechanical activation of reversible bonds by low-amplitude high frequency excitations.

Reversible supramolecular bonds play an important role in materials science and in biological systems. The equilibrium between open and closed bonds and the association rate can be controlled thermally, chemically, by mechanical pulling, by ultrasound, or by catalysts. In practice, these intrinsic equilibrium methods either suffer from a limited range of tunability or may damage the material. Here, we present a nonequilibrium strategy that exploits the dissipative properties of the system to control and change the dynamic properties of sacrificial and reversible networks. We show theoretically and numerically how high-frequency mechanical oscillations of very low amplitude can open or close bonds. This mechanism indicates how reversible bonds could alleviate mechanical fatigue of materials especially at low temperatures where they are fragile. In another area, it suggests that the system can be actively modified by the application of ultrasound to induce gel-fluid transitions and to activate or deactivate adhesion properties.

Unwrapping NPT Simulations to Calculate Diffusion Coefficients.

In molecular dynamics simulations in the NPT ensemble at constant pressure, the size and shape of the periodic simulation box fluctuate with time. For particle images far from the origin, the rescaling of the box by the barostat results in unbounded position displacements. Special care is thus required when a particle trajectory is unwrapped from a projection into the central box under periodic boundary conditions to a trajectory in full three-dimensional space, e.g., for the calculation of translational diffusion coefficients. Here, we review and compare different schemes in use for trajectory unwrapping. We also specify the corresponding rewrapping schemes to put an unwrapped trajectory back into the central box. On this basis, we then identify a scheme for the calculation of diffusion coefficients from NPT simulations, which is a primary application of trajectory unwrapping. In this scheme, the wrapped and unwrapped trajectory are mutually consistent and their statistical properties are preserved. We conclude with advice on best practice for the consistent unwrapping of constant-pressure simulation trajectories and the calculation of accurate translational diffusion coefficients.

Visualizing the disordered nuclear transport machinery in situ.

The approximately 120 MDa mammalian nuclear pore complex (NPC) acts as a gatekeeper for the transport between the nucleus and cytosol1. The central channel of the NPC is filled with hundreds of intrinsically disordered proteins (IDPs) called FG-nucleoporins (FG-NUPs)2,3. Although the structure of the NPC scaffold has been resolved in remarkable detail, the actual transport machinery built up by FG-NUPs-about 50 MDa-is depicted as an approximately 60-nm hole in even highly resolved tomograms and/or structures computed with artificial intelligence4-11. Here we directly probed conformations of the vital FG-NUP98 inside NPCs in live cells and in permeabilized cells with an intact transport machinery by using a synthetic biology-enabled site-specific small-molecule labelling approach paired with highly time-resolved fluorescence microscopy. Single permeabilized cell measurements of the distance distribution of FG-NUP98 segments combined with coarse-grained molecular simulations of the NPC allowed us to map the uncharted molecular environment inside the nanosized transport channel. We determined that the channel provides-in the terminology of the Flory polymer theory12-a 'good solvent' environment. This enables the FG domain to adopt expanded conformations and thus control transport between the nucleus and cytoplasm. With more than 30% of the proteome being formed from IDPs, our study opens a window into resolving disorder-function relationships of IDPs in situ, which are important in various processes, such as cellular signalling, phase separation, ageing and viral entry.

Circuit Topology Analysis of Polymer Folding Reactions.

Circuit topology is emerging as a versatile measure to classify the internal structures of folded linear polymers such as proteins and nucleic acids. The topology framework can be applied to a wide range of problems, most notably molecular folding reactions that are central to biology and molecular engineering. In this Outlook, we discuss the state-of-the art of the technology and elaborate on the opportunities and challenges that lie ahead.

Open-boundary Hamiltonian adaptive resolution. From grand canonical to non-equilibrium molecular dynamics simulations.

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume, and chemical potential. In practice, following the Hamiltonian adaptive resolution strategy, the system is partitioned into a domain of interest and a reservoir of non-interacting, ideal gas particles. An external potential, applied only in the interfacial region, balances the excess chemical potential of the system. To ensure that the size of the reservoir is infinite, we introduce a particle insertion/deletion algorithm to control the density in the ideal gas region. We show that it is possible to study non-equilibrium phenomena with this open-boundary molecular dynamics method. To this aim, we consider a prototypical confined liquid under the influence of an external constant density gradient. The resulting pressure-driven flow across the atomistic system exhibits a velocity profile consistent with the corresponding solution of the Navier-Stokes equation. This method conserves, on average, linear momentum and closely resembles experimental conditions. Moreover, it can be used to study various direct and indirect out-of-equilibrium conditions in complex molecular systems.

Tackling the Limitations of Copolymeric Small Interfering RNA Delivery Agents by a Combined Experimental-Computational Approach.

Despite the first successful applications of nonviral delivery vectors for small interfering RNA in the treatment of illnesses, such as the respiratory syncytial virus infection, the preparation of a clinically suitable, safe, and efficient delivery system still remains a challenge. In this study, we tackle the drawbacks of the existing systems by a combined experimental-computational in-depth investigation of the influence of the polymer architecture over the binding and transfection efficiency. For that purpose, a library of diblock copolymers with a molar mass of 30 kDa and a narrow dispersity (D < 1.12) was synthesized. We studied in detail the impact of an altered block size and/or composition of cationic diblock copolymers on the viability of each respective structure as a delivery agent for polynucleotides. The experimental investigation was further complemented by a computational study employing molecular simulations as well as an analytical description of systemic properties. This is the first report in which molecular dynamics simulations of RNA/cationic polymer complexes have been performed. Specifically, we developed and employed a coarse-grained model of the system at the molecular level to study the interactions between polymer chains and small interfering RNA. We were further able to confirm a threshold lengthbinding block/lengthnonbinding block ratio, which is required for efficient complexation of siRNA, and it was possible to find a correlation between the length of the cationic block and the size of the resulting polyplex. Hence, the combined insights from the experiments and the theoretical investigation resulted in a wealth of information about the properties of cationic diblock copolymers employed as RNA delivery agents, in particular regarding the molecular and mechanistic details of the interaction between the two components of a polyplex.

Steering a solute between coexisting solvation states: Revisiting nonequilibrium work relations and the calculation of free energy differences.

By analogy with single-molecule pulling experiments, we present a computational framework to obtain free energy differences between complex solvation states. To illustrate our approach, we focus on the calculation of solvation free energies (SFEs). However, the method can be readily extended to cases involving more complex solutes and solvation conditions as well as to the calculation of binding free energies. The main idea is to drag the solute across the simulation box where atomistic and ideal gas representations of the solvent coexist at constant temperature and chemical potential. At finite pulling speeds, the resulting work allows one to extract SFEs via nonequilibrium relations, whereas at infinitely slow pulling speeds, this process becomes equivalent to the thermodynamic integration method. Results for small molecules well agree with literature data and pave the way to systematic studies of arbitrarily large and complex molecules.

Mapping a single-molecule folding process onto a topological space.

Physics of protein folding has been dominated by conceptual frameworks including the nucleation-propagation mechanism and the diffusion-collision model, and none address the topological properties of a chain during a folding process. Single-molecule interrogation of folded biomolecules has enabled real-time monitoring of folding processes at an unprecedented resolution. Despite these advances, the topology landscape has not been fully mapped for any chain. Using a novel circuit topology approach, we map the topology landscape of a model polymeric chain. Inspired by single-molecule mechanical interrogation studies, we restrained the ends of a chain and followed fold nucleation dynamics. We find that, before the nucleation, transient local entropic loops dominate. Although the nucleation length of globules is dependent on the cohesive interaction, the ultimate topological states of the collapsed polymer are largely independent of the interaction but depend on the speed of the folding process. After the nucleation, transient topological rearrangements are observed that converge to a steady-state, where the fold grows in a self-similar manner.

Spatially Resolved Thermodynamic Integration: An Efficient Method To Compute Chemical Potentials of Dense Fluids.

Many popular methods for the calculation of chemical potentials rely on the insertion of test particles into the target system. In the case of liquids and liquid mixtures, this procedure increases in difficulty upon increasing density or concentration, and the use of sophisticated enhanced sampling techniques becomes inevitable. In this work, we propose an alternative strategy, spatially resolved thermodynamic integration, or SPARTIAN for short. Here, molecules are described with atomistic resolution in a simulation subregion and as ideal gas particles in a larger reservoir. All molecules are free to diffuse between subdomains adapting their resolution on the fly. To enforce a uniform density profile across the simulation box, a single-molecule external potential is computed, applied, and identified with the difference in chemical potential between the two resolutions. Since the reservoir is represented as an ideal gas bath, this difference exactly amounts to the excess chemical potential of the target system. The present approach surpasses the high density/concentration limitation of particle insertion methods because the ideal gas molecules entering the target system region spontaneously adapt to the local environment. The ideal gas representation contributes negligibly to the computational cost of the simulation, thus allowing one to make use of large reservoirs at minimal expenses. The method has been validated by computing excess chemical potentials for pure Lennard-Jones liquids and mixtures, SPC and SPC/E liquid water, and aqueous solutions of sodium chloride. The reported results well reproduce literature data for these systems.

Concurrent coupling of realistic and ideal models of liquids and solids in Hamiltonian adaptive resolution simulations.

To understand the properties of a complex system it is often illuminating to perform a comparison with a simpler, even idealised one. A prototypical application of this approach is the calculation of free energies and chemical potentials in liquids, which can be decomposed in the sum of ideal and excess contributions. In the same spirit, in computer simulations it is possible to extract useful information on a given system making use of setups where two models, an accurate one and a simpler one, are concurrently employed and directly coupled. Here, we tackle the issue of coupling atomistic or, more in general, interacting models of a system with the corresponding idealised representations: for a liquid, this is the ideal gas, i.e. a collection of non-interacting particles; for a solid, we employ the ideal Einstein crystal, a construct in which particles are decoupled from one another and restrained by a harmonic, exactly integrable potential. We describe in detail the practical and technical aspects of these simulations, and suggest that the concurrent usage and coupling of realistic and ideal models represents a promising strategy to investigate liquids and solids in silico.

Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method.

The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood-Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard-Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions.

Topology of polymer chains under nanoscale confinement.

Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of lp under a spherical confinement of radius Rc. At low values of lp/Rc, the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high lp/Rc, the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of lp/Rc, at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.

Development of a Virtual Cell Model to Predict Cell Response to Substrate Topography.

Cells can sense and respond to changes in the topographical, chemical, and mechanical information in their environment. Engineered substrates are increasingly being developed that exploit these physical attributes to direct cell responses (most notably mesenchymal stem cells) and therefore control cell behavior toward desired applications. However, there are very few methods available for robust and accurate modeling that can predict cell behavior prior to experimental evaluations, and this typically means that many cell test iterations are needed to identify best material features. Here, we developed a unifying computational framework to create a multicomponent cell model, called the "virtual cell model" that has the capability to predict changes in whole cell and cell nucleus characteristics (in terms of shape, direction, and even chromatin conformation) on a range of cell substrates. Modeling data were correlated with cell culture experimental outcomes in order to confirm the applicability of the virtual cell model and demonstrating the ability to reflect the qualitative behavior of mesenchymal stem cells. This may provide a reliable, efficient, and fast high-throughput approach for the development of optimized substrates for a broad range of cellular applications including stem cell differentiation.

Topology of internally constrained polymer chains.

Linear chains with intra-chain contacts can adopt different topologies and allow transitions between them, but it remains unclear how this process can be controlled. This question is important to systems ranging from proteins to chromosomes, which can adopt different conformations that are key to their function and toxicity. Here, we investigate how the topological dynamics of a simple linear chain is affected by interactions with a binding partner, using Monte Carlo and Molecular Dynamics simulations. We show that two point contacts with a binding partner are sufficient to accelerate or decelerate the formation of particular topologies within linear chains. Computed ''folding-time landscapes" that detail the folding time within the topology space show that such contacts deform these landscapes and hence alter the occupation probability of topological states. The results provide a mechanism by which chain topologies can be controlled externally, which opens up the possibility of regulating topological dynamics and the formation of more complex topologies. The findings may have important implications for understanding the mechanism of chaperone action as well as genome architecture and evolution.

Cooperation within von Willebrand factors enhances adsorption mechanism.

von Willebrand factor (VWF) is a naturally collapsed protein that participates in primary haemostasis and coagulation events. The clotting process is triggered by the adsorption and conformational changes of the plasma VWFs localized to the collagen fibres found near the site of injury. We develop coarse-grained models to simulate the adsorption dynamics of VWF flowing near the adhesive collagen fibres at different shear rates and investigate the effect of factors such as interaction and cooperativity of VWFs on the success of adsorption events. The adsorption probability of a flowing VWF confined to the receptor field is enhanced when it encounters an adhered VWF in proximity to the collagen receptors. This enhancement is observed within a wide range of shear rates and is mostly controlled by the attractive van der Waals interactions rather than the hydrodynamic interactions among VWF monomers. The cooperativity between the VWFs acts as an effective mechanism for enhancing VWF adsorption to the collagen fibres. Additionally, this implies that the adsorption of such molecules is nonlinearly dependent on the density of flowing VWFs. These findings are important for studies of primary haemostasis as well as general adsorption dynamics processes in polymer physics.

Cell-imprinted substrates act as an artificial niche for skin regeneration.

Bioinspired materials can mimic the stem cell environment and modulate stem cell differentiation and proliferation. In this study, biomimetic micro/nanoenvironments were fabricated by cell-imprinted substrates based on mature human keratinocyte morphological templates. The data obtained from atomic force microscopy and field emission scanning electron microscopy revealed that the keratinocyte-cell-imprinted poly(dimethylsiloxane) casting procedure could imitate the surface morphology of the plasma membrane, ranging from the nanoscale to the macroscale, which may provide the required topographical cell fingerprints to induce differentiation. Gene expression levels of the genes analyzed (involucrin, collagen type I, and keratin 10) together with protein expression data showed that human adipose-derived stem cells (ADSCs) seeded on these cell-imprinted substrates were driven to adopt the specific shape and characteristics of keratinocytes. The observed morphology of the ADSCs grown on the keratinocyte casts was noticeably different from that of stem cells cultivated on the stem-cell-imprinted substrates. Since the shape and geometry of the nucleus could potentially alter the gene expression, we used molecular dynamics to probe the effect of the confining geometry on the chain arrangement of simulated chromatin fibers in the nuclei. The results obtained suggested that induction of mature cell shapes onto stem cells can influence nucleus deformation of the stem cells followed by regulation of target genes. This might pave the way for a reliable, efficient, and cheap approach of controlling stem cell differentiation toward skin cells for wound healing applications.

Confinement dynamics of a semiflexible chain inside nano-spheres.

We study the conformations of a semiflexible chain, confined in nano-scaled spherical cavities, under two distinct processes of confinement. Radial contraction and packaging are employed as two confining procedures. The former method is performed by gradually decreasing the diameter of a spherical shell which envelopes a confined chain. The latter procedure is carried out by injecting the chain inside a spherical shell through a hole on the shell surface. The chain is modeled with a rigid body molecular dynamics simulation and its parameters are adjusted to DNA base-pair elasticity. Directional order parameter is employed to analyze and compare the confined chain and the conformations of the chain for two different sizes of the spheres are studied in both procedures. It is shown that for the confined chains in the sphere sizes of our study, they appear in spiral or tennis-ball structures, and the tennis-ball structure is more likely to be observed in more compact confinements. Our results also show that the dynamical procedure of confinement and the rate of the confinement are influential parameters of the structure of the chain inside spherical cavities.