The Journal of Chemical Physics

Molecular dynamics simulations of nucleic acids are performed using a solvent-buffer distance of 10 [A] between the solute surface and the simulation box boundary. Although this cell size has been extensively explored in protein simulations, its implications for nucleic acid dynamics are not well understood. Nucleic acids are elongated, highly charged, and flexible structures with hydration and dynamical properties distinct from those of proteins and therefore, they may require different solvent-layer considerations in simulations. In this study, we investigated the effect of simulation cell size on nucleic acid dynamics by simulating a 30-base-pair double-helical nucleic acid structure and its two single-stranded forms using solvent-buffer distances of 3, 5, 10, 15, and 20 [A]. Smaller cells may impose restricted hydration, molecular crowding, and periodic image interactions. However, larger cells provide solvent space for conformational relaxation. A total of 45 s of molecular dynamics simulations were performed (3 structures x 5 cell sizes x 3 replicates x 1 s). Our results show that while the commonly used 10 [A] buffer may be sufficient to maintain the stability of the double-stranded nucleic acid, larger cells are required to capture the conformational dynamics of single-stranded structures. In both, increasing the cell size to 15 or 20 [A] enables broader conformational sampling. The first hydration shell exhibits reduced crowding in the 20 [A] cell, consistent with more relaxed conformations. At larger cell sizes, single-stranded nucleic acids adopt compact, self-associated conformations for stability. Together, this study presents physical insight into how simulation cell size and solvent environment influence nucleic acid dynamics.

Dynamic models are central to the computational life sciences but typically contain unknown parameters that must be inferred from experimental data. High-throughput measurements have made this task increasingly challenging, yielding high-dimensional search spaces and non-convex objectives with many local optima. This makes the choice of optimisation method critical. However, existing empirical studies either consider only a limited number of benchmark problems or only a narrow spectrum of local, global and hybrid optimisation methods. Here, we present a comprehensive benchmark of a broad range of optimisation methods on a curated collection of parameter estimation problems, comprising 990 method-problem-pairs executed on two independent supercomputing infrastructures. Our evaluation quantifies success rates, solution quality and computational cost, revealing characteristic strengths and limitations of each approach. We find that optimisation methods separated into clear performance tiers. Building on these results, we implemented a new hybrid strategy that combines enhanced scatter search with the best-performing local solver, which showed robust performance and improved on the other scatter-search variants we tested. Our results provide practical guidance for selecting optimisation methods and thereby support more accurate and reliable model calibration.

Approximate Bayesian computation sequential Monte Carlo (ABC-SMC) propagates its particles with a perturbation kernel, and with the standard Normal kernel it degrades sharply as the parameter dimension grows, a failure usually attributed to dimension itself. We show instead that it is governed by the quality of the summary statistics, with dimension entering only through a separate and milder mechanism, and that the two must act together for the Normal kernel to break. The first ingredient is covariance overinflation: the kernel covariance, estimated from the particle cloud, overshoots the true posterior covariance by a factor set by information loss in the summary statistics. We derive this overscaling factor in closed form for a Gaussian model with sufficient statistics and show that it stays modest at any dimension, shrinking toward its baseline value as the tolerance tightens; the extreme values seen in practice (of order 103) are a signature of insufficient summaries, not of dimension. The second ingredient is perturbation overconcentration: the normalised Normal step size concentrates around one as the dimension grows, so every proposal overshoots by the same factor. Either ingredient alone is harmless; only their combination breaks the Normal kernel. A Cauchy kernel (multivariate t with one degree of freedom) removes the concentration, keeping a positive acceptance rate under arbitrary overscaling at a bounded worst-case cost of 1.87x in expected squared jump distance. In a Metropolis-Hastings framework we derive closed-form acceptance rates for both kernels that illustrate the advantage of the Cauchy kernel in this limit. A series of full ABC-SMC computational experiments on five problems at d = 12, including a hierarchical gene-expression model, show the Cauchy reducing the sliced Wasserstein distance to the reference posterior by factors of up to 50 with the same simulation budget. Since the summary statistics are commonly insufficient for the models that require ABC, overinflation is structural and the Cauchy perturbation kernel is the right default for problems in higher dimensions.

Lipid droplets (LDs) are cellular organelles responsible for lipid storage and metabolism. The mechanism of biogenesis of LDs involves phase separation of neutral lipids from the surrounding phospholipids, which generates oil lenses embedded in lipid bilayers, also known as nascent LDs. As nascent LDs grow, at some point they bud out of the bilayer, forming nearly spherical droplets. Nascent LDs have different propensity to bud, and it has been proposed that their shape provides information on such propensity; however, LD shape is difficult to determine experimentally. Here we studied the shape of lipid droplets using MD simulations at the coarse-grained level, and compared it to the predictions by an established theory. Our general system setup features an oil lens embedded into a flat, periodic bilayer. We found that the shape of simulated nascent LDs resembles a spherical cap (i.e., it has constant curvature over most of the surface), in excellent agreement with the theory, already for very small droplet sizes. The aspect ratio (height/radius) of nascent LDs increases with increasing LD volume, increasing membrane softness, and increasing surface tension between oil and water, also in agreement with theoretical predictions; however, it remains lower than 1 (i.e., the ratio for a sphere) for LDs of up to 40 nm in diameter. Fitting the simulated LD shapes with a theoretical shape equation suggests that a non-zero surface tension is present in both the monolayer and in the bilayer region. The existence of a relatively high surface tension in the bilayer region is confirmed by local stress calculations, and indicates that the periodic system setup does not reproduce the properties of nascent LDs in the endoplasmic reticulum, where the bilayer tension is two orders of magnitude lower. However, the simulations provide a microscopic view into the properties of droplet embedded vesicles.

Protein folding is the process by which a polypeptide chain organizes into its three-dimensional structure through a balance of stabilizing and destabilizing interactions encoded by the sequence. A central question in protein biophysics is how thermodynamic factors guide a polypeptide toward its native folded state despite the rugged energy landscape and the competing influence of nonnative interactions. In many biomolecular processes, cooperativity provides a mechanism by which multiple weak interactions act collectively to generate a robust response. In the context of protein folding, such cooperative effects may arise when the formation of one native contact enhances the stability or likelihood of nearby native contacts, thereby promoting collective organization toward the folded state. At the same time, folding is opposed by the much larger number of non-native interactions, whose heterogeneity can introduce frustration and destabilize folding even when the average native bias favors the folded phase. The interplay of these competing effects in determining foldability remains unclear in statistical-mechanical models. Here, we address this problem using a one-dimensional spin-glass model of protein folding with explicit shared-residue cooperative interactions encoded through wedge-based motifs. We show that modest cooperative bias can stabilize folding even where the noncooperative system remains unfolded, whereas non-native energetic fluctuation suppresses folding and shifts the transition to higher cooperative strengths. We further find that partial cooperative coverage is sufficient to lower the folding threshold. Therefore, the model provides a mean-field framework for incorporating cooperative interaction strength into the native one-dimensional model of protein folding and for describing how local cooperativity reshapes the folding transition.

"Mirror life", self-replicating organisms composed of non-natural-chirality biomacromolecules, presents a future threat with potentially global consequences. Consequently, there is strong agreement among experts that it should not be created. However, there is some disagreement over how effective existing medical countermeasures might prove against mirror bacteria in the event that they were created. Here, we leverage computational chemistry methods including docking and molecular dynamics to determine the likely binding efficacy of existing antibiotics against natural and mirror bacterial protein targets. We find that most existing antibiotics fail to bind to mirror bacterial protein targets, unlike their natural-chirality targets. This suggests altered binding of current medical countermeasures, which may impact the antimicrobial activity against mirror bacteria were the latter were created.

The molecular mechanics-generalized Born surface area method (MMGBSA) is one of the most commonly used end state approaches used for the calculation of the binding free energy towards computational drug design and screening studies. It is customary to break up the free energy into van der Waals, electrostatic, polar solvation (GB), and nonpolar solvation (SA) terms and then either correlate these terms with experiment or assign physical meaning to each term. Here, we demonstrate that this assumption of independent fitting coefficients for decomposed energy terms could be invalid. Through analytic derivation and large-scale molecular dynamics simulations, we show that (i) the protein and ligand Coulomb interaction energy and the GB solvation correction are almost perfectly collinear (R2[≥]0.99) reflecting their designed role as vacuum electrostatics plus solvent screening, and (ii) the van der Waals interaction and SA term likewise exhibit strong correlation, as both depend primarily on buried surface area. Interaction entropy and C2 entropy corrections are also found to be strongly dependent on underlying electrostatic fluctuations, further reinforcing redundancy. These findings hold both at the level of instantaneous trajectory fluctuations and when averaged across a diverse set of 139 protein-protein complexes and persist in both single-trajectory and three trajectory MMGBSA protocols. Our results caution against using decomposed MMGBSA terms as independent predictors in regression models and suggest instead combining correlated terms into effective polar, nonpolar, and entropic contributions. Our study provides a systematic diagnosis of collinearity in MMGBSA and highlights pathways toward more interpretable and statistically robust predictive modeling.

Small-angle X-ray or neutron scattering (SAXS/SANS) analysis of large unilamellar vesicles (LUVs) is often limited by high-dimensional bilayer models and the lack of dedicated, statistically rigorous workflows. Here, we introduce SAS_MoCa, an open-source Python package that integrates a compositional scattering density profile (SDP) description of lipid bilayers with a separated form factor (SFF) treatment of vesicle size and polydispersity, and couples these highly parameterized models to an adaptive thermodynamic simulated annealing algorithm formulated within a constrained Bayesian framework. SAS_MoCa enables users to incorporate quantitative prior information from, e.g., previous SAXS/SANS studies, dynamic light scattering, NMR, or molecular simulations, and returns full posterior parameter distributions, uncertainties (reported as medians and median absolute deviations) and correlations even from single SAXS curves. Validation on POPC, POPE and DMPC SAXS-only data demonstrates that the method yields reproducible structural parameters with uncertainties comparable to joint SAXS/contrast-variation SANS analyses. The modular architecture of SAS_MoCa facilitates extension to additional lipid systems and future joint SAXS/SANS or SANS-only applications.

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

Biological membranes contain a diverse set of membrane proteins surrounded by many different lipids, and the lateral organization and function of these molecules are closely intertwined. Here, we use coarse-grained molecular dynamics (MD) simulations to explore how hydrophobic mismatch between the length of transmembrane (TM) proteins and the thickness of the surrounding lipid membrane impacts the spatial distribution of the lipids. We constructed idealized cylindrically symmetric proteins, inspired by the Mattress Model developed in the 1980s, and simulated these model proteins in different lipid compositions. We found that unsaturated lipids were attracted to short TM proteins that thinned the membrane, while fully saturated lipids were attracted to long TM proteins that induced membrane extension. A simple mechanical description of the membrane deformation energy coupled to a lipid mixing model accurately predicted the enrichment/depletion, which was up to 33% in some cases. Our simulations also highlight that lipid sorting behavior is sensitive to protein tilt and protein surface roughness. By teasing out the fundamental physical principles in these simple models, our results provide a foundational understanding of how proteins and lipids form complex and transient assemblies, which we believe will be important for interpreting lipid-protein interactions for a host of membrane proteins that regulate cellular membranes and cell function.

Cells communicate with their environment by integrating signals, often chemical in nature, triggered by specific molecules bind to specific membrane-bound receptors, resulting in a downstream signaling cascade. Arguably, G-protein-coupled receptors (GPCRs) constitute the most pharmacologically important family of such receptors, binding small molecules, peptides, lipids, and hormones with high specificity. However, despite a highly conserved fold and sequence similarity, GPCRs are still mostly studied on a case-by-case basis. Here, we infer a general, evolutionarily conserved mechanism of class A GPCR activation. By leveraging coevolution and machine learning methods applied to all class A GPCRs structures, we derive a mathematical description (a so-called collective variable - CV) of the receptor's activation state which is independent of its sequence. Then, we bias molecular dynamics simulations along this CV to obtain transitions between activation states of a diverse set of class A GPCR family members. To demonstrate that our model generalizes beyond GPCRs in our training set, we obtain conformational transitions of an orphan receptor, GPR183. Finally, we show that we can model ligand effect on the receptors by converging Free Energy Surfaces of activation of the {beta}2-adrenergic receptor within this common mechanism framework. These results, to our knowledge, prove for the first time the existence of a mechanism uniting all class A GPCRs. Our approach thus facilitates direct comparisons between receptors and opens up the possibility of structural and dynamical studies of many orphan and understudied GPCRs. It also serves as a blueprint for inferring family-wide protein mechanisms.

Mechanistic ordinary differential equation models are widely used in systems biology to represent biochemical networks, population dynamics, cell-state transitions, and other biological processes; however, their predictive value depends critically on accurate parameter estimation from noisy and often sparse experimental data. In this tutorial, we present the Weak-form Estimation of Nonlinear Dynamics (WENDy) method as a forward-solver-free approach that reformulates parameter estimation as a covariance-corrected weak-form regression problem by integrating the model equations against compactly supported test functions. We present the background on the methodology through the lens of the familiar logistic equation, and we demonstrate applications of the method on real experimental data through two systems biology examples: a glycolytic oscillator with relatively dense time-course data and a sparse epithelial-mesenchymal cellstate transition model with multiple experimental replicates. Ultimately, using WENDy, we estimate interpretable biological parameters with uncertainty for systems with noisy and sometimes sparse available experimental data.

Small molecule modifiers whence bound, allosterically, will alter the binding of a macromolecule to one- or more-cognate substrates/partners via conformational and non-conformational changes. Although allostery is inferred directly from empirical data, the mathematical basis of these models, constraints deployed and choice of parameter(s) are not clear. Here, we present and characterize a discrete-to-continuous mathematical model for ensemble distributions of a ligand-interacting macromolecular species across milieux-dependent conformational states and examine its role in the genesis and progression of cooperative binding. The premise, of our model, is a set of occupancy matrices (sparse, binary, strictly delocalized) which can be partitioned by a probability-based hyperparameter into mutually exclusive proper subsets of occupancy matrices with identical multinomial probabilities. Since each subset is canonical with a constituent occupancy matrix, it is characterized by a unique multinomial probability. The inner product of combinatorial pairs of all mutually exclusive subsets of occupancy matrices, with an expression for the summed transitional probabilities (finite differences between unique multinomial probabilities), is the differentiable matrix of strictly positive real-valued numbers for the system of ensemble distributions. Whilst the harmonic mean is presented as a generic solution for a system of ensemble distributions, the row-wise definite integral for each column is the finite union of open intervals (contiguous, strictly monotone) which in tandem with a set of interval-specific and bounded transitional probabilities constitutes a piecewise smooth curve (path-connected-, closed- and compact-set). Our discrete-to-continuous model is phenomenological and able to recapitulate the basic tenets of cooperative binding whilst offering insights into the genesis and progression of the same.

Mathematical models of enzyme cycles form the basis of quantifying key features of metabolism and membrane transport. These models are often integrated into more comprehensive models such as whole-cell models to understand emergent behaviours between interacting components. However, it is currently computationally infeasible to simulate the full dynamical behaviour of every enzyme at a network scale. Model reduction is frequently used to improve computational efficiency, but in general, these approaches do not preserve physical and thermodynamic consistency. Here, we outline a general method for simplifying enzyme kinetics models while retaining mass, charge and energy balance. We base our approach on the bond graph, which is a general methodology for modelling biological systems from fundamental physical laws. This approach ensures that key physical constraints are enforced in every model, regardless of their complexity. Our thermodynamic model reduction framework is readily extended to electrogenic transporters through the coupling of chemical and electrical processes. Through the application of our approach to both hypothetical enzyme cycles and real data from the Na+/K+ ATPase, we show that it can rapidly screen for plausible network structures in circumstances where enzyme catalytic mechanisms may not be fully characterised, facilitating biological discovery and drug development.

Integral membrane proteins remodel the surrounding lipid bilayer, but quantifying the resulting deformations and linking them to protein density in the membrane has remained challenging. Here, we introduce an integrative methodology that combines all-atom molecular dynamics (MD) simulations with multiscale small-angle X-ray scattering (SAXS) analysis to connect membrane strain to the protein/lipid ratio in proteoliposomes. Using outer membrane phospholipase A (OmpLA) reconstituted into lipid bilayers with both increased and decreased hydrophobic thickness, we systematically probe the effects of positive and negative hydrophobic mismatch.MD simulations demonstrate that OmpLA causes anisotropic, oscillatory thickness deformations extending up to eight times the radius of the first lipid shell surrounding the protein, yet the net change in average membrane thickness remains below 1%. Through our multiscale SAXS analysis, we quantitatively extract structural parameters, ranging from proteoliposome size to internal membrane architecture, using constrained Bayesian inference, with priors derived from MD findings. Specifically, we determine the protein/lipid molar ratio and average membrane strain, revealing excellent agreement between experiment and simulation. In thinner bilayers, substantial protein loss limits the analysis, highlighting the role of bilayer stability in sample preparation. Moreover, the predominance of OmpLA monomers in the thicker membranes is consistent with weak, membrane-mediated repulsive interactions between protein inclusions. Collectively, this integrative approach establishes a framework for quantifying protein-lipid interactions across molecular and mesoscale dimensions.

Chemical exchange saturation transfer (CEST) has become an indispensable NMR method to characterize slow exchange affecting biomacromolecules, especially for cases involving exchange between a major state and a minor state, the latter of which is often invisible in the spectrum. The CEST method is based on successive irradiation of selective regions of the NMR spectrum using a weak radiofrequency field, B1, while observing the effect on the visible major state when the B1 field saturates the invisible minor state. The need for selective saturation of narrow spectral regions has to date required acquisition of many tens of two-dimensional CEST spectra to sample the entire spectrum with sufficient resolution. Here we present the ACCEST method which measures an entire CEST profile from a single two-dimensional accordion-CEST spectrum plus a reference spectrum. ACCEST is based on the concept of accordion spectroscopy, where in the present implementation the carrier frequency of the weak saturating B1 field is stepped in synchrony with the dwell-time incrementation in the indirect dimension of the two-dimensional spectrum. We benchmarked ACCEST against conventional CEST, resulting in excellent agreement for both backbone 15N and methyl 13C CEST profiles. ACCEST offers substantial time savings that scale linearly with the number of spectra required in the corresponding conventional CEST experiment. Thus, ACCEST can dramatically speed up lengthy serial experiments, such as ligand titrations or temperature-dependent studies, and enable studies of non-equilibrium systems or samples with limited lifetimes.

Plexin-B1 is a transmembrane receptor that integrates signals from Rho-family and Ras-family (Rap1b) GTPases to regulate cellular processes. While ligand simulated activation of the receptor is largely understood, the role of membrane composition and GTPase allosteric effects on plexin structure, internal protein dynamics, and function is still to be elucidated. Here, we performed multi-replica, 1 s all-atom simulations of Plexin-B1-GTPase complexes on PIP2- and PIP3-containing membranes to investigate the effects of these two signaling lipids, as well as on the GTPases. We found that both Rap1b and Rnd1 stably associate with the membrane, with PIP2 promoting broader lipid engagement and stronger Rap1b-Plexin-B1 interactions, whereas PIP3 enhances Rnd1-Plexin contacts and induces a membrane proximal orientation of Plexins juxtamembrane helix and makes contacts with a previously discovered activation switch loop. Contact map and network analyses revealed lipid-dependent shifts in allosteric communication, with PIP2 favoring Rap1b-centric hotspots and PIP3 favoring Rnd1-centric pathways. These predictions allow us to suggest a model for plexin intracellular region activation where both the identity of phosphoinositides and GTPase context synergistically stabilize Plexin-B1 membrane engagement, alter structural dynamics, and allosteric networks. Thus, we propose that the membrane is an active modulator of plexin receptor signaling.

Biomolecular condensates are dynamic assemblies whose functions depend on continuous exchange of molecular components with the surrounding environment. While scaffold molecules drive phase separation and condensate architecture, many functional components are clients that are recruited through interactions with the scaffold-rich environment. Despite their prevalence, how client-scaffold interactions shape client exchange dynamics remains poorly understood. Here, we develop a reaction-diffusion model for client exchange in scaffold-driven condensates, in which clients switch between a scaffold-bound state and an unbound state. Bound clients exchange through scaffold-mediated transport, whereas unbound clients diffuse through the pore space of the condensate. Using the fluorescence recovery of fully photobleached condensates as a measure of client exchange, we compare transport through these two pathways with bound-unbound conversion and identify three limiting regimes. In the slow-conversion regime, bound and unbound clients recover through distinct scaffold- and pore-mediated pathways. In the intermediate-conversion regime, recovery of bound clients becomes limited by client unbinding. In the fast-conversion regime, local equilibrium between bound and unbound clients produces an effective single-state recovery. We further propose a unifying description that connects these regimes and quantitatively captures the apparent recovery timescales extracted from numerical simulations across condensate sizes. Our results provide a framework for interpreting component-specific exchange dynamics, and highlight client size, client-scaffold binding, and condensate porosity as key regulators of client turnover in multicomponent condensates.

A priori assessment of target proteins' druggability remains an unsolved problem in the field of drug development. The empirical approaches widely used to solve this problem demonstrate low efficiency. In this work, we investigated the factor of hydration of a representative set of 65 evolutionarily and structurally unrelated human enzymes in a water environment. This factor depends only on the structure of the proteins, and not on the physical and chemical properties of any potential ligands. The results show that, unlike the widely used approaches based on calculations of the accessible surface area (ASA), the content of low-entropy water molecules (LEW) in the active sites of human enzymes is systematically higher than that in other areas of their surface, including inactive cavities. Optimal criteria and a step-by-step procedure for identifying protein ligand binding sites are proposed. The proposed approach, based on the calculation of the LEW content in the first hydration layer of potentially interesting target proteins, makes it possible to evaluate their medicinal suitability even before the development of any ligands. The article also presents the results of a comparative analysis of experimental Raman spectroscopy data and the results of molecular dynamics simulations of water hydrogen bonds using three widely used water models (TIP3P, OPC3, and TIP5P) and standard algorithms for calculating hydrogen bond networks.

There is a vast literature on the voltage gating of ion channels, with a fairly large fraction concerned with potassium channels, especially of the KV1 family, including Shaker. Experimental evidence derived from protein structure has been interpreted to give gating mechanisms that largely disregard water. We propose that the K+ ion, in order to pass through the gating region and enter the cavity pore, must be largely dehydrated. Competitive interactions of each single hydration shell water at the gate, with counterions, protein, or other water molecules, can remove one water at a time. There are several such interactions for the ion hydration shell; for the ion to pass through the gating region, there must be enough such interactions to leave the ion with at most two hydrating water molecules, in which case the gate is open. Protein conformational changes are secondary, small, and mostly unimportant. The hypothesis has a second part: protons, previously shown to be candidate carriers of the gating current (Kariev and Green, JPC B, 2019, Membranes, 2022, 2024) are capable of reaching the gate; adding four protons to the gate prevents dehydration, leaving the ion with at least three hydrating water molecules, enough to block passage. Quantum calculations presented here support the dehydration part of the hypothesis; they also mostly support the second part, concerning the protons, but further work will be required to fully confirm this. The hypothesis explains the experimental finding that the P475D mutant is essentially constitutively open, while the P475S mutant, with a wider gate opening, is closed at all relevant potentials; the computations presented here show the mechanism for this in detail, further confirming the first part of the hypothesis, and largely but not completely confirming the second part, concerning protons, while showing where further work is needed. This mechanism can also qualitatively account for flicker noise and fluctuations, and their consequences.