Liquid-Liquid Phase Separation of the Intrinsically Disordered Domain of the Fused in Sarcoma Protein Results in Substantial Slowing of Hydration Dynamics.

Formation of liquid condensates plays a critical role in biology via localization of different components or via altered hydrodynamic transport, yet the hydrogen-bonding environment within condensates, pivotal for solvation, has remained elusive. We explore the hydrogen-bond dynamics within condensates formed by the low-complexity domain of the fused in sarcoma protein. Probing the hydrogen-bond dynamics sensed by condensate proteins using two-dimensional infrared spectroscopy of the protein amide I vibrations, we find that frequency-frequency correlations of the amide I vibration decay on a picosecond time scale. Interestingly, these dynamics are markedly slower for proteins in the condensate than in a homogeneous protein solution, indicative of different hydration dynamics. All-atom molecular dynamics simulations confirm that lifetimes of hydrogen-bonds between water and the protein are longer in the condensates than in the protein in solution. Altered hydrogen-bonding dynamics may contribute to unique solvation and reaction dynamics in such condensates.

Broad chemical transferability in structure-based coarse-graining.

Compared to top-down coarse-grained (CG) models, bottom-up approaches are capable of offering higher structural fidelity. This fidelity results from the tight link to a higher resolution reference, making the CG model chemically specific. Unfortunately, chemical specificity can be at odds with compound-screening strategies, which call for transferable parameterizations. Here, we present an approach to reconcile bottom-up, structure-preserving CG models with chemical transferability. We consider the bottom-up CG parameterization of 3441 C7O2 small-molecule isomers. Our approach combines atomic representations, unsupervised learning, and a large-scale extended-ensemble force-matching parameterization. We first identify a subset of 19 representative molecules, which maximally encode the local environment of all gas-phase conformers. Reference interactions between the 19 representative molecules were obtained from both homogeneous bulk liquids and various binary mixtures. An extended-ensemble parameterization over all 703 state points leads to a CG model that is both structure-based and chemically transferable. Remarkably, the resulting force field is on average more structurally accurate than single-state-point equivalents. Averaging over the extended ensemble acts as a mean-force regularizer, smoothing out both force and structural correlations that are overly specific to a single-state point. Our approach aims at transferability through a set of CG bead types that can be used to easily construct new molecules while retaining the benefits of a structure-based parameterization.

Finite-size scaling and thermodynamics of model supercooled liquids: long-range concentration fluctuations and the role of attractive interactions.

We compute partial structure factors, Kirkwood-Buff integrals (KBIs) and chemical potentials of model supercooled liquids with and without attractive interactions. We aim at investigating whether relatively small differences in the tail of the radial distribution functions result in contrasting thermodynamic properties. Our results suggest that the attractive potential favours the nucleation of long-range structures. Indeed, upon decreasing temperature, Bathia-Thornton structure factors display anomalous behaviour in the k→0 limit. KBIs extrapolated to the thermodynamic limit confirm this picture, and excess coordination numbers identify the anomaly with long-range concentration fluctuations. By contrast, the purely repulsive system remains perfectly miscible for the same temperature interval and only reveals qualitatively similar concentration fluctuations in the crystalline state. Furthermore, differences in both isothermal compressibilities and chemical potentials show that thermodynamics is not entirely governed by the short-range repulsive part of the interaction potential, emphasising the nonperturbative role of attractive interactions. Finally, at higher density, where both systems display nearly identical dynamical properties and repulsive interactions become dominant, the anomaly disappears, and both systems also exhibit similar thermodynamic properties.

Dynamical properties across different coarse-grained models for ionic liquids.

Room-temperature ionic liquids (RTILs) stand out among molecular liquids for their rich physicochemical characteristics, including structural and dynamic heterogeneity. The significance of electrostatic interactions in RTILs results in long characteristic length- and timescales, and has motivated the development of a number of coarse-grained (CG) simulation models. In this study, we aim to better understand the connection between certain CG parameterization strategies and the dynamical properties and transferability of the resulting models. We systematically compare five CG models: a model largely parameterized from experimental thermodynamic observables; a refinement of this model to increase its structural accuracy; and three models that reproduce a given set of structural distribution functions by construction, with varying intramolecular parameterizations and reference temperatures. All five CG models display limited structural transferability over temperature, and also result in various effective dynamical speedup factors, relative to a reference atomistic model. On the other hand, the structure-based CG models tend to result in more consistent cation-anion relative diffusion than the thermodynamic-based models, for a single thermodynamic state point. By linking short- and long-timescale dynamical behaviors, we demonstrate that the varying dynamical properties of the different CG models can be largely collapsed onto a single curve, which provides evidence for a route to constructing dynamically-consistent CG models of RTILs.

Coarse-grained conformational surface hopping: Methodology and transferability.

Coarse-grained (CG) conformational surface hopping (SH) adapts the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately describe classical molecular dynamics at a reduced level. The SH scheme couples distinct conformational basins (states), each described by its own force field (surface), resulting in a significant improvement of the approximation to the many-body potential of mean force [T. Bereau and J. F. Rudzinski, Phys. Rev. Lett. 121, 256002 (2018)]. The present study first describes CG SH in more detail, through both a toy model and a three-bead model of hexane. We further extend the methodology to non-bonded interactions and report its impact on liquid properties. Finally, we investigate the transferability of the surfaces to distinct systems and thermodynamic state points, through a simple tuning of the state probabilities. In particular, applications to variations in temperature and chemical composition show good agreement with reference atomistic calculations, introducing a promising "weak-transferability regime," where CG force fields can be shared across thermodynamic and chemical neighborhoods.

Investigating the Conformational Ensembles of Intrinsically Disordered Proteins with a Simple Physics-Based Model.

Intrinsically disordered proteins (IDPs) play an important role in an array of biological processes but present a number of fundamental challenges for computational modeling. Recently, simple polymer models have regained popularity for interpreting the experimental characterization of IDPs. Homopolymer theory provides a strong foundation for understanding generic features of phenomena ranging from single-chain conformational dynamics to the properties of entangled polymer melts, but is difficult to extend to the copolymer context. This challenge is magnified for proteins due to the variety of competing interactions and large deviations in side-chain properties. In this work, we apply a simple physics-based coarse-grained model for describing largely disordered conformational ensembles of peptides, based on the premise that sampling sterically forbidden conformations can compromise the faithful description of both static and dynamical properties. The Hamiltonian of the employed model can be easily adjusted to investigate the impact of distinct interactions and sequence specificity on the randomness of the resulting conformational ensemble. In particular, starting with a bead-spring-like model and then adding more detailed interactions one by one, we construct a hierarchical set of models and perform a detailed comparison of their properties. Our analysis clarifies the role of generic attractions, electrostatics, and side-chain sterics, while providing a foundation for developing efficient models for IDPs that retain an accurate description of the hierarchy of conformational dynamics, which is nontrivially influenced by interactions with surrounding proteins and solvent molecules.

Automated detection of many-particle solvation states for accurate characterizations of diffusion kinetics.

Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations that accurately characterize the relevant dynamics. Well-established, low-dimensional order parameters for constructing this representation have led to widespread application of Markov state models to study conformational dynamics in biomolecular systems. On the contrary, applications to characterize single-molecule diffusion processes have been scarce and typically employ system-specific, higher-dimensional order parameters to characterize the local solvation state of the molecule. In this work, we propose an automated method for generating a coarse configuration-space representation, using generic features of the solvation structure-the coordination numbers about each particle. To overcome the inherent noisy behavior of these low-dimensional observables, we treat the features as indicators of an underlying, latent Markov process. The resulting hidden Markov models filter the trajectories of each feature into the most likely latent solvation state at each time step. The filtered trajectories are then used to construct a configuration-space discretization, which accurately describes the diffusion kinetics. The method is validated on a standard model for glassy liquids, where particle jumps between local cages determine the diffusion properties of the system. Not only do the resulting models provide quantitatively accurate characterizations of the diffusion constant, but they also reveal a mechanistic description of diffusive jumps, quantifying the heterogeneity of local diffusion.

Direct route to reproducing pair distribution functions with coarse-grained models via transformed atomistic cross correlations.

Coarse-grained (CG) models are often parameterized to reproduce one-dimensional structural correlation functions of an atomically detailed model along the degrees of freedom governing each interaction potential. While cross correlations between these degrees of freedom inform the optimal set of interaction parameters, the correlations generated from the higher-resolution simulations are often too complex to act as an accurate proxy for the CG correlations. Instead, the most popular methods determine the interaction parameters iteratively while assuming that individual interactions are uncorrelated. While these iterative methods have been validated for a wide range of systems, they also have disadvantages when parameterizing models for multicomponent systems or when refining previously established models to better reproduce particular structural features. In this work, we propose two distinct approaches for the direct (i.e., noniterative) parameterization of a CG model by adjusting the high-resolution cross correlations of an atomistic model in order to more accurately reflect correlations that will be generated by the resulting CG model. The derived models more accurately describe the low-order structural features of the underlying AA model while necessarily generating inherently distinct cross correlations compared with the atomically detailed reference model. We demonstrate the proposed methods for a one-site-per-molecule representation of liquid water, where pairwise interactions are incapable of reproducing the true tetrahedral solvation structure. We then investigate the precise role that distinct cross-correlation features play in determining the correct pair correlation functions, evaluating the importance of the placement of correlation features as well as the balance between features appearing in different solvation shells.

Structural-kinetic-thermodynamic relationships identified from physics-based molecular simulation models.

Coarse-grained molecular simulation models have provided immense, often general, insight into the complex behavior of condensed-phase systems but suffer from a lost connection to the true dynamical properties of the underlying system. In general, the physics that is built into a model shapes the free-energy landscape, restricting the attainable static and kinetic properties. In this work, we perform a detailed investigation into the property interrelationships resulting from these restrictions, for a representative system of the helix-coil transition. Inspired by high-throughput studies, we systematically vary force-field parameters and monitor their structural, kinetic, and thermodynamic properties. The focus of our investigation is a simple coarse-grained model, which accurately represents the underlying structural ensemble, i.e., effectively avoids sterically-forbidden configurations. As a result of this built-in physics, we observe a rather large restriction in the topology of the networks characterizing the simulation kinetics. When screening across force-field parameters, we find that structurally accurate models also best reproduce the kinetics, suggesting structural-kinetic relationships for these models. Additionally, an investigation into thermodynamic properties reveals a link between the cooperativity of the transition and the network topology at a single reference temperature.

Accurate Structure-Based Coarse Graining Leads to Consistent Barrier-Crossing Dynamics.

Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed. Here, we extend the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately sample the conformational ensemble of a classical system in equilibrium. In analogy to describing different electronic configurations, a surface-hopping scheme couples distinct conformational basins beyond the additivity of the Hamiltonian. The incorporation of more surfaces leads systematically toward improved cross-correlations. The resulting models naturally achieve consistent long-time dynamics for systems governed by barrier-crossing events.

BOCS: Bottom-up Open-source Coarse-graining Software.

We present the BOCS toolkit as a suite of open source software tools for parametrizing bottom-up coarse-grained (CG) models to accurately reproduce structural and thermodynamic properties of high-resolution models. The BOCS toolkit complements available software packages by providing robust implementations of both the multiscale coarse-graining (MS-CG) force-matching method and also the generalized-Yvon-Born-Green (g-YBG) method. The g-YBG method allows one to analyze and to calculate MS-CG potentials in terms of structural correlations. Additionally, the BOCS toolkit implements an extended ensemble framework for optimizing the transferability of bottom-up potentials, as well as a self-consistent pressure-matching method for accurately modeling the pressure equation of state for homogeneous systems. We illustrate these capabilities by parametrizing transferable potentials for CG models that accurately model the structure, pressure, and compressibility of liquid alkane systems and by quantifying the role of many-body correlations in determining the calculated pair potential for a one-site CG model of liquid methanol.

Extended Ensemble Approach to Transferable Potentials for Low-Resolution Coarse-Grained Models of Ionomers.

We develop an extended ensemble method for constructing transferable, low-resolution coarse-grained (CG) models of polyethylene-oxide (PEO)-based ionomer chains with varying composition at multiple temperatures. In particular, we consider ionomer chains consisting of 4 isophthalate groups, which may be neutral or sulfonated, that are linked by 13 PEO repeat units. The CG models represent each isophthalate group with a single CG site and also explicitly represent the diffusing sodium counterions but do not explicitly represent the PEO backbone. We define the extended ensemble as a collection of equilibrium ensembles that are obtained from united atom (UA) simulations at 2 different temperatures for 7 chemically distinct ionomers with varying degrees of sulfonation. We employ a global force-matching method to determine the set of interaction potentials that, when appropriately combined, provide an optimal approximation to the many-body potential of mean force for each system in the extended ensemble. This optimized xn force field employs long-ranged Coulomb potentials with system-specific dielectric constants that systematically decrease with increasing sulfonation and temperature. An empirical exponential model reasonably describes the sensitivity of the dielectric to sulfonation, but we find it more challenging to model the temperature-dependence of the dielectrics. Nevertheless, given appropriate dielectric constants, the transferable xn force field reasonably describes the ion pairing that is observed in the UA simulations as a function of sulfonation and temperature. Remarkably, despite eliminating any explicit description of the PEO backbone, the CG model predicts string-like ion aggregates that appear qualitatively consistent with the ionomer peak observed in X-ray scattering experiments and, moreover, with the temperature dependence of this peak.

Communication: Consistent interpretation of molecular simulation kinetics using Markov state models biased with external information.

Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and reference (e.g., from experiments or higher-level simulations) observables. To bound the microscopic information generated by computer simulations within reference measurements, we propose a method that reweights the microscopic transitions of the system to improve consistency with a set of coarse kinetic observables. The method employs the well-developed Markov state modeling framework to efficiently link microscopic dynamics with long-time scale constraints, thereby consistently addressing a wide range of time scales. To emphasize the robustness of the method, we consider two distinct coarse-grained models with significant kinetic inconsistencies. When applied to the simulated conformational dynamics of small peptides, the reweighting procedure systematically improves the time scale separation of the slowest processes. Additionally, constraining the forward and backward rates between metastable states leads to slight improvement of their relative stabilities and, thus, refined equilibrium properties of the resulting model. Finally, we find that difficulties in simultaneously describing both the simulated data and the provided constraints can help identify specific limitations of the underlying simulation approach.

Bottom-Up Coarse-Graining of Peptide Ensembles and Helix-Coil Transitions.

This work investigates the capability of bottom-up methods for parametrizing minimal coarse-grained (CG) models of disordered and helical peptides. We consider four high-resolution peptide ensembles that demonstrate varying degrees of complexity. For each high-resolution ensemble, we parametrize a CG model via the multiscale coarse-graining (MS-CG) method, which employs a generalized Yvon-Born-Green (g-YBG) relation to determine potentials directly (i.e., without iteration) from the high-resolution ensemble. The MS-CG method accurately describes high-resolution models that fluctuate about a single conformation. However, given the minimal resolution and simple molecular mechanics potential, the MS-CG method provides a less accurate description for a high-resolution peptide model that samples a disordered ensemble with multiple distinct conformations. We employ an iterative g-YBG method to develop a CG model that more accurately describes the relevant distribution functions and free energy surfaces for this disordered ensemble. Nevertheless, this more accurate model does not reproduce the cooperative helix-coil transition that is sampled by the high resolution model. By comparing the different models, we demonstrate that the errors in the MS-CG model primarily stem from the lack of cooperative interactions afforded by the minimal representation and molecular mechanics potential. This work demonstrates the potential of the MS-CG method for accurately modeling complex biomolecular structures, but also highlights the importance of more complex potentials for modeling cooperative transitions with a minimal CG representation.

Scaling behavior and local structure of ion aggregates in single-ion conductors.

Single-ion conductors are attractive electrolyte materials because of their inherent safety and ease of processing. Most ions in a sodium-neutralized PEO sulfonated-isophthalate ionomer electrolyte exist as one dimensional chains, restricted in dimensionality by the steric hindrance of the attached polymer. Because the ions are slow to reconfigure, atomistic MD simulations of this material are unable to adequately sample equilibrium ion structures. We apply a novel coarse-graining scheme using a generalized-YBG procedure in which the polymer backbone is completely removed and implicitly represented by the effective potentials of the remaining ions. The ion-only coarse-grained simulation allows for substantial sampling of equilibrium aggregate configurations. We extend the wormlike micelle theory to model ion chain equilibrium. Our aggregates are random walks which become more positively charged with increasing size. Defects occur on the string-like structure in the form of "dust" and "knots," which form due to cation coordination with open sites along the string. The presence of these defects suggest that cation hopping along open third-coordination sites could be an important mechanism of charge transport using ion aggregates.

Investigation of coarse-grained mappings via an iterative generalized Yvon-Born-Green method.

Low resolution coarse-grained (CG) models enable highly efficient simulations of complex systems. The interactions in CG models are often iteratively refined over multiple simulations until they reproduce the one-dimensional (1-D) distribution functions, e.g., radial distribution functions (rdfs), of an all-atom (AA) model. In contrast, the multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to determine CG potentials directly (i.e., without iteration) from the correlations observed for the AA model. However, MS-CG models do not necessarily reproduce the 1-D distribution functions of the AA model. Consequently, recent studies have incorporated the g-YBG equation into iterative methods for more accurately reproducing AA rdfs. In this work, we consider a theoretical framework for an iterative g-YBG method. We numerically demonstrate that the method robustly determines accurate models for both hexane and also a more complex molecule, 3-hexylthiophene. By examining the MS-CG and iterative g-YBG models for several distinct CG representations of both molecules, we investigate the approximations of the MS-CG method and their sensitivity to the CG mapping. More generally, we explicitly demonstrate that CG models often reproduce 1-D distribution functions of AA models at the expense of distorting the cross-correlations between the corresponding degrees of freedom. In particular, CG models that accurately reproduce intramolecular 1-D distribution functions may still provide a poor description of the molecular conformations sampled by the AA model. We demonstrate a simple and predictive analysis for determining CG mappings that promote an accurate description of these molecular conformations.

Influence of target concentration and background binding on in vitro selection of affinity reagents.

Nucleic acid-based aptamers possess many useful features that make them a promising alternative to antibodies and other affinity reagents, including well-established chemical synthesis, reversible folding, thermal stability and low cost. However, the selection process typically used to generate aptamers (SELEX) often requires significant resources and can fail to yield aptamers with sufficient affinity and specificity. A number of seminal theoretical models and numerical simulations have been reported in the literature offering insights into experimental factors that govern the effectiveness of the selection process. Though useful, these previous models have not considered the full spectrum of experimental factors or the potential impact of tuning these parameters at each round over the course of a multi-round selection process. We have developed an improved mathematical model to address this important question, and report that both target concentration and the degree of non-specific background binding are critical determinants of SELEX efficiency. Although smaller target concentrations should theoretically offer superior selection outcome, we show that the level of background binding dramatically affect the target concentration that will yield maximum enrichment at each round of selection. Thus, our model enables experimentalists to determine appropriate target concentrations as a means for protocol optimization. Finally, we perform a comparative analysis of two different selection methods over multiple rounds of selection, and show that methods with inherently lower background binding offer dramatic advantages in selection efficiency.

The role of many-body correlations in determining potentials for coarse-grained models of equilibrium structure.

Coarse-grained (CG) models often employ pair potentials that are parametrized to reproduce radial distribution functions (rdf's) determined for an atomistic model. This implies that the CG model must reproduce the corresponding atomistic mean forces. These mean forces include not only a direct contribution from the corresponding interaction but also correlated contributions from the surrounding environment. The many-body correlations that influence this second contribution present significant challenges for accurately reproducing atomistic distribution functions. This work presents a detailed investigation of these many-body correlations and their significance for determining CG potentials while using liquid heptane as a model system. We employ a transparent geometric framework for directly determining CG potentials that has been previously developed within the context of the multiscale coarse-graining and generalized Yvon-Born-Green methods. In this framework, a metric tensor quantifies the relevant many-body correlations and precisely decomposes atomistic mean forces into contributions from specific interactions, which then determine the CG force field. Numerical investigations reveal that this metric tensor reflects both the CG representation and also subtle correlations between molecular geometry and intermolecular packing, but can be largely interpreted in terms of generic considerations. Our calculations demonstrate that contributions from correlated interactions can significantly impact the pair mean force and, thus, also the CG force field. Finally, an eigenvector analysis investigates the importance of these interactions for reproducing atomistic distribution functions.

Coarse-graining entropy, forces, and structures.

Coarse-grained (CG) models enable highly efficient simulations of complex processes that cannot be effectively studied with more detailed models. CG models are often parameterized using either force- or structure-motivated approaches. The present work investigates parallels between these seemingly divergent approaches by examining the relative entropy and multiscale coarse-graining (MS-CG) methods. We demonstrate that both approaches can be expressed in terms of an information function that discriminates between the ensembles generated by atomistic and CG models. While it is well known that the relative entropy approach minimizes the average of this information function, the present work demonstrates that the MS-CG method minimizes the average of its gradient squared. We generalize previous results by establishing conditions for the uniqueness of structure-based potentials and identify similarities with corresponding conditions for the uniqueness of MS-CG potentials. We analyze the mapping entropy and extend the MS-CG and generalized-Yvon-Born-Green formalisms for more complex potentials. Finally, we present numerical calculations that highlight similarities and differences between structure- and force-based approaches. We demonstrate that both methods obtain identical results, not only for a complete basis set, but also for an incomplete harmonic basis set in Cartesian coordinates. However, the two methods differ when the incomplete basis set includes higher order polynomials of Cartesian coordinates or is expressed as functions of curvilinear coordinates.