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1.
Proc Natl Acad Sci U S A ; 121(8): e2310238121, 2024 Feb 20.
Article in English | MEDLINE | ID: mdl-38359294

ABSTRACT

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding "memory" within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of "encoding" that gives insight into the constraints on control-both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.


Subject(s)
Actins , Nanostructures , Actins/metabolism , Nanostructures/chemistry
2.
Proc Natl Acad Sci U S A ; 121(25): e2322962121, 2024 Jun 18.
Article in English | MEDLINE | ID: mdl-38870054

ABSTRACT

Metallic alloys often form phases-known as solid solutions-in which chemical elements are spread out on the same crystal lattice in an almost random manner. The tendency of certain chemical motifs to be more common than others is known as chemical short-range order (SRO), and it has received substantial consideration in alloys with multiple chemical elements present in large concentrations due to their extreme configurational complexity (e.g., high-entropy alloys). SRO renders solid solutions "slightly less random than completely random," which is a physically intuitive picture, but not easily quantifiable due to the sheer number of possible chemical motifs and their subtle spatial distribution on the lattice. Here, we present a multiscale method to predict and quantify the SRO state of an alloy with atomic resolution, incorporating machine learning techniques to bridge the gap between electronic-structure calculations and the characteristic length scale of SRO. The result is an approach capable of predicting SRO length scale in agreement with experimental measurements while comprehensively correlating SRO with fundamental quantities such as local lattice distortions. This work advances the quantitative understanding of solid-solution phases, paving the way for the rigorous incorporation of SRO length scales into predictive mechanical and thermodynamic models.

3.
Proc Natl Acad Sci U S A ; 121(39): e2408459121, 2024 Sep 24.
Article in English | MEDLINE | ID: mdl-39298480

ABSTRACT

We report a neutron spin echo (NSE) study of the nanoscale dynamics of the cell-cell adhesion cadherin-catenin complex bound to vinculin. Our measurements and theoretical physics analyses of the NSE data reveal that the dynamics of full-length α-catenin, ß-catenin, and vinculin residing in the cadherin-catenin-vinculin complex become activated, involving nanoscale motions in this complex. The cadherin-catenin complex is the central component of the cell-cell adherens junction (AJ) and is fundamental to embryogenesis, tissue wound healing, neuronal plasticity, cancer metastasis, and cardiovascular health and disease. A highly dynamic cadherin-catenin-vinculin complex provides the molecular dynamics basis for the flexibility and elasticity that are necessary for the AJs to function as force transducers. Our theoretical physics analysis provides a way to elucidate these driving nanoscale motions within the complex without requiring large-scale numerical simulations, providing insights not accessible by other techniques. We propose a three-way "motorman" entropic spring model for the dynamic cadherin-catenin-vinculin complex, which allows the complex to function as a flexible and elastic force transducer.


Subject(s)
Cadherins , Vinculin , Vinculin/metabolism , Vinculin/chemistry , Cadherins/metabolism , Cadherins/chemistry , alpha Catenin/metabolism , alpha Catenin/chemistry , Humans , beta Catenin/metabolism , beta Catenin/chemistry , Protein Binding , Adherens Junctions/metabolism , Neutrons , Molecular Dynamics Simulation , Spectrum Analysis/methods , Animals , Catenins/metabolism , Cell Adhesion/physiology
4.
Proc Natl Acad Sci U S A ; 121(19): e2219385121, 2024 May 07.
Article in English | MEDLINE | ID: mdl-38701120

ABSTRACT

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid [Formula: see text], quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse-graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a nonvanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other nondissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible nonreciprocal phase transition.

5.
Proc Natl Acad Sci U S A ; 121(8): e2309504121, 2024 Feb 20.
Article in English | MEDLINE | ID: mdl-38346190

ABSTRACT

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical learning theory fail to account for observed phenomena like the double descent or the impact of relational semantics on generalization error. Motivated by experimental observations of "transductive" double descent in key networks and datasets, we use analytical tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model. Our results illuminate the nuances of learning on homophilic versus heterophilic data and predict double descent whose existence in GNNs has been questioned by recent work. We show how risk is shaped by the interplay between the graph noise, feature noise, and the number of training labels. Our findings apply beyond stylized models, capturing qualitative trends in real-world GNNs and datasets. As a case in point, we use our analytic insights to improve performance of state-of-the-art graph convolution networks on heterophilic datasets.

6.
Proc Natl Acad Sci U S A ; 120(50): e2308226120, 2023 Dec 12.
Article in English | MEDLINE | ID: mdl-38048467

ABSTRACT

The statistics of a passive tracer immersed in a suspension of active particles (swimmers) is derived from first principles by considering a perturbative expansion of the tracer interaction with the microscopic swimmer field. To first order in the swimmer density, the tracer statistics is shown to be exactly represented by a spatial Poisson process combined with independent tracer-swimmer scattering events, rigorously reducing the multiparticle dynamics to two-body interactions. The Poisson representation is valid in any dimension, for arbitrary interaction forces and for a large class of swimmer dynamics. The framework not only allows for the systematic calculation of the tracer statistics in various dynamical regimes but highlights in particular surprising universal features that are independent of the swimmer dynamics such as a time-independent velocity distribution.

7.
Proc Natl Acad Sci U S A ; 120(16): e2218007120, 2023 04 18.
Article in English | MEDLINE | ID: mdl-37053187

ABSTRACT

We perform targeted attack, a systematic computational unlinking of the network, to analyze its effects on global communication across the brain network through its giant cluster. Across diffusion magnetic resonance images from individuals in the UK Biobank, Adolescent Brain Cognitive Development Study and Developing Human Connectome Project, we find that targeted attack procedures on increasing white matter tract lengths and densities are remarkably invariant to aging and disease. Time-reversing the attack computation suggests a mechanism for how brains develop, for which we derive an analytical equation using percolation theory. Based on a close match between theory and experiment, our results demonstrate that tracts are limited to emanate from regions already in the giant cluster and tracts that appear earliest in neurodevelopment are those that become the longest and densest.


Subject(s)
Connectome , White Matter , Adolescent , Humans , Brain/diagnostic imaging , White Matter/diagnostic imaging , White Matter/pathology , Magnetic Resonance Imaging , Cognition , Connectome/methods , Diffusion Magnetic Resonance Imaging
8.
Proc Natl Acad Sci U S A ; 120(11): e2122352120, 2023 03 14.
Article in English | MEDLINE | ID: mdl-36897966

ABSTRACT

A crucial challenge in medicine is choosing which drug (or combination) will be the most advantageous for a particular patient. Usually, drug response rates differ substantially, and the reasons for this response unpredictability remain ambiguous. Consequently, it is central to classify features that contribute to the observed drug response variability. Pancreatic cancer is one of the deadliest cancers with limited therapeutic achievements due to the massive presence of stroma that generates an environment that enables tumor growth, metastasis, and drug resistance. To understand the cancer-stroma cross talk within the tumor microenvironment and to develop personalized adjuvant therapies, there is a necessity for effective approaches that offer measurable data to monitor the effect of drugs at the single-cell level. Here, we develop a computational approach, based on cell imaging, that quantifies the cellular cross talk between pancreatic tumor cells (L3.6pl or AsPC1) and pancreatic stellate cells (PSCs), coordinating their kinetics in presence of the chemotherapeutic agent gemcitabine. We report significant heterogeneity in the organization of cellular interactions in response to the drug. For L3.6pl cells, gemcitabine sensibly decreases stroma-stroma interactions but increases stroma-cancer interactions, overall enhancing motility and crowding. In the AsPC1 case, gemcitabine promotes the interactions among tumor cells, but it does not affect stroma-cancer interplay, possibly suggesting a milder effect of the drug on cell dynamics.


Subject(s)
Carcinoma, Pancreatic Ductal , Pancreatic Neoplasms , Humans , Carcinoma, Pancreatic Ductal/pathology , Pancreatic Neoplasms/pathology , Gemcitabine , Cell Communication , Cell Line, Tumor , Tumor Microenvironment
9.
Proc Natl Acad Sci U S A ; 120(33): e2210500120, 2023 Aug 15.
Article in English | MEDLINE | ID: mdl-37549273

ABSTRACT

Simulations can help unravel the complicated ways in which molecular structure determines function. Here, we use molecular simulations to show how slight alterations of a molecular motor's structure can cause the motor's typical dynamical behavior to reverse directions. Inspired by autonomous synthetic catenane motors, we study the molecular dynamics of a minimal motor model, consisting of a shuttling ring that moves along a track containing interspersed binding sites and catalytic sites. The binding sites attract the shuttling ring while the catalytic sites speed up a reaction between molecular species, which can be thought of as fuel and waste. When that fuel and waste are held in nonequilibrium steady-state concentrations, the free energy from the reaction drives directed motion of the shuttling ring along the track. Using this model and nonequilibrium molecular dynamics, we show that the shuttling ring's direction can be reversed by simply adjusting the spacing between binding and catalytic sites on the track. We present a steric mechanism behind the current reversal, supported by kinetic measurements from the simulations. These results demonstrate how molecular simulation can guide future development of artificial molecular motors.

10.
Proc Natl Acad Sci U S A ; 120(31): e2305573120, 2023 Aug.
Article in English | MEDLINE | ID: mdl-37487093

ABSTRACT

Flexible metal-organic frameworks (MOFs) exhibit an adsorption-induced structural transition known as "gate opening" or "breathing," resulting in an S-shaped adsorption isotherm. This unique feature of flexible MOFs offers significant advantages, such as a large working capacity, high selectivity, and intrinsic thermal management capability, positioning them as crucial candidates for revolutionizing adsorption separation processes. Therefore, the interest in the industrial applications of flexible MOFs is increasing, and the adsorption engineering for flexible MOFs is becoming important. However, despite the establishment of the theoretical background for adsorption-induced structural transitions, no theoretical equation is available to describe S-shaped adsorption isotherms of flexible MOFs. Researchers rely on various empirical equations for process simulations that can lead to unreliable outcomes or may overlook insights into improving material performance owing to parameters without physical meaning. In this study, we derive a theoretical equation based on statistical mechanics that could be a standard for the structural transition type adsorption isotherms, as the Langmuir equation represents type I isotherms. The versatility of the derived equation is shown through four examples of flexible MOFs that exhibit gate opening and breathing. The consistency of the formula with existing theories, including the osmotic free energy analysis and intrinsic thermal management capabilities, is also discussed. The developed theoretical equation may lead to more reliable and insightful outcomes in adsorption separation processes, further advancing the direction of industrial applications of flexible MOFs.

11.
Proc Natl Acad Sci U S A ; 120(50): e2312484120, 2023 Dec 12.
Article in English | MEDLINE | ID: mdl-38060556

ABSTRACT

We present a hybrid scheme based on classical density functional theory and machine learning for determining the equilibrium structure and thermodynamics of inhomogeneous fluids. The exact functional map from the density profile to the one-body direct correlation function is represented locally by a deep neural network. We substantiate the general framework for the hard sphere fluid and use grand canonical Monte Carlo simulation data of systems in randomized external environments during training and as reference. Functional calculus is implemented on the basis of the neural network to access higher-order correlation functions via automatic differentiation and the free energy via functional line integration. Thermal Noether sum rules are validated explicitly. We demonstrate the use of the neural functional in the self-consistent calculation of density profiles. The results outperform those from state-of-the-art fundamental measure density functional theory. The low cost of solving an associated Euler-Lagrange equation allows to bridge the gap from the system size of the original training data to macroscopic predictions upon maintaining near-simulation microscopic precision. These results establish the machine learning of functionals as an effective tool in the multiscale description of soft matter.

12.
Brief Bioinform ; 25(1)2023 11 22.
Article in English | MEDLINE | ID: mdl-38095857

ABSTRACT

Molecular dynamics (MD) is the primary computational method by which modern structural biology explores macromolecule structure and function. Boltzmann generators have been proposed as an alternative to MD, by replacing the integration of molecular systems over time with the training of generative neural networks. This neural network approach to MD enables convergence to thermodynamic equilibrium faster than traditional MD; however, critical gaps in the theory and computational feasibility of Boltzmann generators significantly reduce their usability. Here, we develop a mathematical foundation to overcome these barriers; we demonstrate that the Boltzmann generator approach is sufficiently rapid to replace traditional MD for complex macromolecules, such as proteins in specific applications, and we provide a comprehensive toolkit for the exploration of molecular energy landscapes with neural networks.


Subject(s)
Molecular Dynamics Simulation , Proteins , Proteins/chemistry , Neural Networks, Computer , Thermodynamics
13.
Annu Rev Phys Chem ; 75(1): 21-45, 2024 Jun.
Article in English | MEDLINE | ID: mdl-38941523

ABSTRACT

Low-resolution coarse-grained (CG) models provide remarkable computational and conceptual advantages for simulating soft materials. In principle, bottom-up CG models can reproduce all structural and thermodynamic properties of atomically detailed models that can be observed at the resolution of the CG model. This review discusses recent progress in developing theory and computational methods for achieving this promise. We first briefly review variational approaches for parameterizing interaction potentials and their relationship to machine learning methods. We then discuss recent approaches for simultaneously improving both the transferability and thermodynamic properties of bottom-up models by rigorously addressing the density and temperature dependence of these potentials. We also briefly discuss exciting progress in modeling high-resolution observables with low-resolution CG models. More generally, we highlight the essential role of the bottom-up framework not only for fundamentally understanding the limitations of prior CG models but also for developing robust computational methods that resolve these limitations in practice.

14.
Proc Natl Acad Sci U S A ; 119(32): e2122907119, 2022 Aug 09.
Article in English | MEDLINE | ID: mdl-35917354

ABSTRACT

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases-a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase-that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.

15.
Proc Natl Acad Sci U S A ; 119(24): e2121405119, 2022 Jun 14.
Article in English | MEDLINE | ID: mdl-35675427

ABSTRACT

Nonequilibrium interfacial thermodynamics has important implications for crucial biological, physical, and industrial-scale transport processes. Here, we discuss a theory of local equilibrium for multiphase multicomponent interfaces that builds upon the "sharp" interface concept first introduced by Gibbs, allowing for a description of nonequilibrium interfacial processes such as those arising in evaporation, condensation, adsorption, etc. By requiring that the thermodynamics be insensitive to the precise location of the dividing surface, one can identify conditions for local equilibrium and develop methods for measuring the values of intensive variables at the interface. We then use extensive, high-precision nonequilibrium molecular dynamics (NEMD) simulations to verify the theory and establish the validity of the local equilibrium hypothesis. In particular, we demonstrate that equilibrium equations of state are also valid out of equilibrium, and can be used to determine interfacial temperature and chemical potential(s) that are consistent with nonequilibrium generalizations of the Clapeyron and Gibbs adsorption equations. We also show, for example, that, far from equilibrium, temperature or chemical potential differences need not be uniform across an interface and may instead exhibit pronounced discontinuities. However, even in these circumstances, we demonstrate that the local equilibrium hypothesis and its implications remain valid. These results provide a thermodynamic foundation and computational tools for studying or revisiting a wide variety of interfacial transport phenomena.

16.
Proc Natl Acad Sci U S A ; 119(4)2022 01 25.
Article in English | MEDLINE | ID: mdl-35042813

ABSTRACT

Entropy alone can self-assemble hard nanoparticles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Molecular simulation is a powerful tool used extensively to study the self-assembly of ordered phases from disordered fluid phases of atoms, molecules, or nanoparticles. However, it is not yet possible to predict colloidal crystal structures a priori from particle shape as we can for atomic crystals from electronic valency. Here, we present such a first-principles theory. By calculating and minimizing excluded volume within the framework of statistical mechanics, we describe the directional entropic forces that collectively emerge between hard shapes, in familiar terms used to describe chemical bonds. We validate our theory by demonstrating that it predicts thermodynamically preferred structures for four families of hard polyhedra that match, in every instance, previous simulation results. The success of this first-principles approach to entropic colloidal crystal structure prediction furthers fundamental understanding of both entropically driven crystallization and conceptual pictures of bonding in matter.

17.
Proc Natl Acad Sci U S A ; 119(6)2022 02 08.
Article in English | MEDLINE | ID: mdl-35131847

ABSTRACT

Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free energy differences are sensitively affected by the description of electronic structure, the statistical mechanics of the nuclei and the cell, and thermal expansion. The importance of these effects has been individually established, but rigorous free energy calculations for general molecular compounds, which simultaneously account for all effects, have hitherto not been computationally viable. Here we present an efficient "end to end" framework that seamlessly combines state-of-the art electronic structure calculations, machine-learning potentials, and advanced free energy methods to calculate ab initio Gibbs free energies for general organic molecular materials. The facile generation of machine-learning potentials for a diverse set of polymorphic compounds-benzene, glycine, and succinic acid-and predictions of thermodynamic stabilities in qualitative and quantitative agreement with experiments highlight that predictive thermodynamic studies of industrially relevant molecular materials are no longer a daunting task.

18.
Proc Natl Acad Sci U S A ; 119(3)2022 01 18.
Article in English | MEDLINE | ID: mdl-35022230

ABSTRACT

Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and magnesium with 0.1 kcal/mol precision using optical tweezers. Notably, force-distance curves (FDCs) exhibit strong irreversible effects with hysteresis and several intermediates, precluding the extraction of the NNBP energies with currently available methods. The combination of a suitable RNA synthesis with a tailored pulling protocol allowed us to obtain the fully reversible FDCs necessary to derive the NNBP energies. We demonstrate the equivalence of sodium and magnesium free-energy salt corrections at the level of individual NNBP. To characterize the irreversibility of the unzipping-rezipping process, we introduce a barrier energy landscape of the stem-loop structures forming along the complementary strands, which compete against the formation of the native hairpin. This landscape correlates with the hysteresis observed along the FDCs. RNA sequence analysis shows that base stacking and base pairing stabilize the stem-loops that kinetically trap the long-lived intermediates observed in the FDC. Stem-loops formation appears as a general mechanism to explain a wide range of behaviors observed in RNA folding.


Subject(s)
Nucleic Acid Conformation , RNA Folding , Biomechanical Phenomena , Magnesium/chemistry , RNA/chemistry , Sodium/chemistry , Thermodynamics
19.
Proteins ; 2024 Sep 11.
Article in English | MEDLINE | ID: mdl-39258438

ABSTRACT

Predicting the precise locations of metal binding sites within metalloproteins is a crucial challenge in biophysics. A fast, accurate, and interpretable computational prediction method can complement the experimental studies. In the current work, we have developed a method to predict the location of Ca2+ ions in calcium-binding proteins using a physics-based method with an all-atom description of the proteins, which is substantially faster than the molecular dynamics simulation-based methods with accuracy as good as data-driven approaches. Our methodology uses the three-dimensional reference interaction site model (3D-RISM), a statistical mechanical theory, to calculate Ca2+ ion density around protein structures, and the locations of the Ca2+ ions are obtained from the density. We have taken previously used datasets to assess the efficacy of our method as compared to previous works. Our accuracy is 88%, comparable with the FEATURE program, one of the well-known data-driven methods. Moreover, our method is physical, and the reasons for failures can be ascertained in most cases. We have thoroughly examined the failed cases using different structural and crystallographic measures, such as B-factor, R-factor, electron density map, and geometry at the binding site. It has been found that x-ray structures have issues in many of the failed cases, such as geometric irregularities and dubious assignment of ion positions. Our algorithm, along with the checks for structural accuracy, is a major step in predicting calcium ion positions in metalloproteins.

20.
Annu Rev Phys Chem ; 74: 1-27, 2023 04 24.
Article in English | MEDLINE | ID: mdl-36719975

ABSTRACT

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective we celebrate his work at these frontiers.


Subject(s)
Physics , Male , Humans , Retrospective Studies , Chemistry, Physical
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