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From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.
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When described by a low-dimensional reaction coordinate, the folding rates of most proteins are determined by a subtle interplay between free-energy barriers, which separate folded and unfolded states, and friction. While it is commonplace to extract free-energy profiles from molecular trajectories, a direct evaluation of friction is far more elusive and typically relies on fits of measured reaction rates to memoryless reaction-rate theories. Here, using memory-kernel extraction methods founded on a generalized Langevin equation (GLE) formalism, we directly calculate the time-dependent friction acting on the fraction of native contacts reaction coordinate Q, evaluated for eight fast-folding proteins, taken from a published set of large-scale molecular dynamics protein simulations. Our results reveal that, across the diverse range of proteins represented in this dataset, friction is more influential than free-energy barriers in determining protein folding rates. We also show that proteins fold in a regime where the finite decay time of friction significantly reduces the folding times, in some instances by as much as a factor of 10, compared to predictions based on memoryless friction.
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Simulação de Dinâmica Molecular , Dobramento de Proteína , Fricção , Proteínas/metabolismoRESUMO
Deviations between macrorheological and particle-based microrheological measurements are often considered to be a nuisance and neglected. We study aqueous poly(ethylene oxide) (PEO) hydrogels for varying PEO concentrations and chain lengths that contain microscopic tracer particles and show that these deviations reveal the nanoscopic viscoelastic properties of the particle-hydrogel interface. Based on the transient Stokes equation, we first demonstrate that the deviations are not due to finite particle radius, compressibility, or surface-slip effects. Small-angle neutron scattering rules out hydrogel heterogeneities. Instead, we show that a generalized Stokes-Einstein relation, accounting for an interfacial shell around tracers with viscoelastic properties that deviate from bulk, consistently explains our macrorheological and microrheological measurements. The extracted shell diameter is comparable to the PEO end-to-end distance, indicating the importance of dangling chain ends. Our methodology reveals the nanoscopic interfacial rheology of hydrogels and is applicable to different kinds of viscoelastic fluids and particles.
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We present a method to differentiate organisms solely by their motion based on the generalized Langevin equation (GLE) and use it to distinguish two different swimming modes of strongly confined unicellular microalgae Chlamydomonas reinhardtii. The GLE is a general model for active or passive motion of organisms and particles that can be derived from a time-dependent general many-body Hamiltonian and in particular includes non-Markovian effects (i.e., the trajectory memory of its past). We extract all GLE parameters from individual cell trajectories and perform an unbiased cluster analysis to group them into different classes. For the specific cell population employed in the experiments, the GLE-based assignment into the two different swimming modes works perfectly, as checked by control experiments. The classification and sorting of single cells and organisms is important in different areas; our method, which is based on motion trajectories, offers wide-ranging applications in biology and medicine.
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Chlamydomonas reinhardtii , Chlamydomonas reinhardtii/citologia , Chlamydomonas reinhardtii/fisiologia , Movimento , Modelos Biológicos , Análise de Célula Única , Análise por Conglomerados , Movimento (Física)RESUMO
Polar surfaces in water typically repel each other at close separations, even if they are charge-neutral. This so-called hydration repulsion balances the van der Waals attraction and gives rise to a stable nanometric water layer between the polar surfaces. The resulting hydration water layer is crucial for the properties of concentrated suspensions of lipid membranes and hydrophilic particles in biology and technology, but its origin is unclear. It has been suggested that surface-induced molecular water structuring is responsible for the hydration repulsion, but a quantitative proof of this water-structuring hypothesis is missing. To gain an understanding of the mechanism causing hydration repulsion, we perform molecular simulations of different planar polar surfaces in water. Our simulated hydration forces between phospholipid bilayers agree perfectly with experiments, validating the simulation model and methods. For the comparison with theory, it is important to split the simulated total surface interaction force into a direct contribution from surface-surface molecular interactions and an indirect water-mediated contribution. We find the indirect hydration force and the structural water-ordering profiles from the simulations to be in perfect agreement with the predictions from theoretical models that account for the surface-induced water ordering, which strongly supports the water-structuring hypothesis for the hydration force. However, the comparison between the simulations for polar surfaces with different headgroup architectures reveals significantly different decay lengths of the indirect water-mediated hydration-force, which for laterally homogeneous water structuring would imply different bulk-water properties. We conclude that laterally inhomogeneous water ordering, induced by laterally inhomogeneous surface structures, shapes the hydration repulsion between polar surfaces in a decisive manner. Thus, the indirect water-mediated part of the hydration repulsion is caused by surface-induced water structuring but is surface-specific and thus nonuniversal.
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Nanoscale fluid transport is typically pictured in terms of atomic-scale dynamics, as is natural in the real-space framework of molecular simulations. An alternative Fourier-space picture, that involves the collective charge fluctuation modes of both the liquid and the confining wall, has recently been successful at predicting new nanofluidic phenomena such as quantum friction and near-field heat transfer, that rely on the coupling of those fluctuations. Here, we study the charge fluctuation modes of a two-dimensional (planar) nanofluidic channel. Introducing confined response functions that generalize the notion of surface response function, we show that the channel walls exhibit coupled plasmon modes as soon as the confinement is comparable to the plasmon wavelength. Conversely, the water fluctuations remain remarkably bulk-like, with significant confinement effects arising only when the wall spacing is reduced to 7 Å. We apply the confined response formalism to predict the dependence of the solid-water quantum friction and thermal boundary conductance on channel width for model channel wall materials. Our results provide a general framework for Coulomb interactions of fluctuating matter under nanoscale confinement.
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Surface phenomena in aqueous environments such as long-range hydrophobic attraction, macromolecular adhesion, and even biofouling are predominantly influenced by a fundamental parameter-the water contact angle. The minimal contact angle required for these and related phenomena to occur has been repeatedly reported to be around 65° and is commonly referred to as the "Berg limit." However, the universality of this specific threshold across diverse contexts has remained puzzling. In this perspective article, we aim to rationalize the reoccurrence of this enigmatic contact angle. We show that the relevant scenarios can be effectively conceptualized as three-phase problems involving the surface of interest, water, and a generic oil-like material that is representative of the nonpolar constituents within interacting entities. Our analysis reveals that attraction and adhesion emerge when substrates display an underwater oleophilic character, corresponding to a "hydrophobicity under oil", which occurs for contact angles above approximately 65°. This streamlined view provides valuable insights into macromolecular interactions and holds implications for technological applications.
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There has been much success recently in theoretically simulating parts of complex biological systems on the molecular level, with the goal of first-principles modeling of whole cells. However, there is the question of whether such simulations can be performed because of the enormous complexity of cells. We establish approximate equations to estimate computation times required to simulate highly simplified models of cells by either molecular dynamics calculations or by solving molecular kinetic equations. Our equations place limits on the complexity of cells that can be theoretically understood with these two methods and provide a first step in developing what can be considered biological uncertainty relations for molecular models of cells. While a molecular kinetics description of the genetically simplest bacterial cell may indeed soon be possible, neither theoretical description for a multicellular system, such as the human brain, will be possible for many decades and may never be possible even with quantum computing.
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Metodologias Computacionais , Cinética , Simulação de Dinâmica Molecular/normas , Teoria Quântica , Humanos , Modelos BiológicosRESUMO
We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide [Formula: see text] for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote-Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.
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Cadeias de Markov , Simulação de Dinâmica Molecular , Dobramento de Proteína , Proteínas/química , Modelos Químicos , Conformação Proteica , TermodinâmicaRESUMO
As virus outbreaks continue to pose a challenge, a nonspecific viral inhibitor can provide significant benefits, especially against respiratory viruses. Polyglycerol sulfates recently emerge as promising agents that mediate interactions between cells and viruses through electrostatics, leading to virus inhibition. Similarly, hydrophobic C60 fullerene can prevent virus infection via interactions with hydrophobic cavities of surface proteins. Here, two strategies are combined to inhibit infection of SARS-CoV-2 variants in vitro. Effective inhibitory concentrations in the millimolar range highlight the significance of bare fullerene's hydrophobic moiety and electrostatic interactions of polysulfates with surface proteins of SARS-CoV-2. Furthermore, microscale thermophoresis measurements support that fullerene linear polyglycerol sulfates interact with the SARS-CoV-2 virus via its spike protein, and highlight importance of electrostatic interactions within it. All-atom molecular dynamics simulations reveal that the fullerene binding site is situated close to the receptor binding domain, within 4 nm of polyglycerol sulfate binding sites, feasibly allowing both portions of the material to interact simultaneously.
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COVID-19 , Fulerenos , Humanos , SARS-CoV-2 , Fulerenos/farmacologia , Ligação ProteicaRESUMO
Based on a Hamiltonian that incorporates the elastic coupling between a tracer particle and the embedding active viscoelastic biomatter, we derive a generalized non-Markovian Langevin model for the nonequilibrium mechanical tracer response. Our analytical expressions for the frequency-dependent tracer response function and the tracer positional autocorrelation function agree quantitatively with experimental data for red blood cells and actomyosin networks with and without adenosine triphosphate over the entire frequency range and in particular reproduce the low-frequency violation of the fluctuation-dissipation theorem. The viscoelastic power laws, the elastic constants and effective friction coefficients extracted from the experimental data allow straightforward physical interpretation.
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We investigate the effect of pectin on the structure and ion transport properties of the room-temperature ionic liquid electrolyte 1-n-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) using molecular dynamics simulations. We find that pectin induces intriguing structural changes in the electrolyte that disrupt large ionic aggregates and promote the formation of smaller ionic clusters, which is a promising finding for ionic conductivity. Due to pectin in [BMIM][PF6] electrolytes, the diffusion coefficient of cations and anions is observed to decrease by a factor of four for a loading of 25 wt. % of pectin in [BMIM][PF6] electrolyte. A strong correlation between the ionic diffusivities (D) and ion-pair relaxation timescales (τc) is observed such that D â¼ τc-0.75 for cations and D â¼ τc-0.82 for anions. The relaxation timescale exponents indicate that the ion transport mechanisms in pectin-[BMIM][PF6] electrolytes are slightly distinct from those found in neat [BMIM][PF6] electrolytes (Dâ¼τc-1). Since pectin marginally affects ionic diffusivities at the gain of smaller ionic aggregates and viscosity, our results suggest that pectin-ionic liquid electrolytes offer improved properties for battery applications, including ionic conductivity, mechanical stability, and biodegradability.
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Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients, and time- or frequency-dependent response functions. We investigate the influence of periodic boundary conditions on the velocity autocorrelation function and the frequency-dependent friction of a particle in a fluid, and show that the long-time behavior (starting at the picosecond timescale) is significantly affected. We develop an analytical correction allowing us to subtract the periodic boundary condition effects. By this, we unmask the power-law long-time tails of the memory kernel and the velocity autocorrelation function in liquid water and a Lennard-Jones fluid from simulations with rather small box sizes.
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To make the physics of person-to-person virus transmission from emitted droplets of oral fluid while speaking easily understood, we present simple and transparent algebraic equations that capture the essential physics of the problem. Calculations with these equations provide a straightforward way of determining whether emitted droplets remain airborne or rapidly fall to the ground, after accounting for the decrease in droplet size from water evaporation. At a relative humidity of 50%, for example, droplets with initial radii larger than about 50 µm rapidly fall to the ground, while smaller, potentially virus-containing droplets shrink in size from water evaporation and remain airborne for many minutes. Estimates of airborne virion emission rates while speaking strongly support the proposal that mouth coverings can help contain the COVID-19 pandemic.
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Betacoronavirus/fisiologia , Infecções por Coronavirus/transmissão , Pneumonia Viral/transmissão , Fala , Aerossóis , COVID-19 , Infecções por Coronavirus/prevenção & controle , Infecções por Coronavirus/virologia , Humanos , Máscaras , Modelos Teóricos , Pandemias/prevenção & controle , Tamanho da Partícula , Pneumonia Viral/prevenção & controle , Pneumonia Viral/virologia , SARS-CoV-2 , Saliva/virologia , Fatores de TempoRESUMO
Biological and technological processes that involve liquids under negative pressure are vulnerable to the formation of cavities. Maximal negative pressures found in plants are around -100 bar, even though cavitation in pure bulk water only occurs at much more negative pressures on the relevant timescales. Here, we investigate the influence of small solutes and lipid bilayers, both constituents of all biological liquids, on the formation of cavities under negative pressures. By combining molecular dynamics simulations with kinetic modeling, we quantify cavitation rates on biologically relevant length scales and timescales. We find that lipid bilayers, in contrast to small solutes, increase the rate of cavitation, which remains unproblematically low at the pressures found in most plants. Only when the negative pressures approach -100 bar does cavitation occur on biologically relevant timescales. Our results suggest that bilayer-based cavitation is what generally limits the magnitude of negative pressures in liquids that contain lipid bilayers.
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Bicamadas Lipídicas/química , Simulação de Dinâmica Molecular , Pressão , CinéticaRESUMO
Evidence is strengthening to suggest that the novel SARS-CoV-2 mutant Omicron, with its more than 60 mutations, will spread and dominate worldwide. Although the mutations in the spike protein are known, the molecular basis for why the additional mutations in the spike protein that have not previously occurred account for Omicron's higher infection potential, is not understood. We propose, based on chemical rational and molecular dynamics simulations, that the elevated occurrence of positively charged amino acids in certain domains of the spike protein (Delta: +4; Omicron: +5 vs. wild type) increases binding to cellular polyanionic receptors, such as heparan sulfate due to multivalent charge-charge interactions. This observation is a starting point for targeted drug development.
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COVID-19 , SARS-CoV-2 , Glicoproteína da Espícula de Coronavírus , COVID-19/virologia , Humanos , Mutação , SARS-CoV-2/genética , Glicoproteína da Espícula de Coronavírus/química , Glicoproteína da Espícula de Coronavírus/genéticaRESUMO
The basement membrane (BM) is a special type of extracellular matrix and presents the major barrier cancer cells have to overcome multiple times to form metastases. Here we show that BM stiffness is a major determinant of metastases formation in several tissues and identify netrin-4 (Net4) as a key regulator of BM stiffness. Mechanistically, our biophysical and functional analyses in combination with mathematical simulations show that Net4 softens the mechanical properties of native BMs by opening laminin node complexes, decreasing cancer cell potential to transmigrate this barrier despite creating bigger pores. Our results therefore reveal that BM stiffness is dominant over pore size, and that the mechanical properties of 'normal' BMs determine metastases formation and patient survival independent of cancer-mediated alterations. Thus, identifying individual Net4 protein levels within native BMs in major metastatic organs may have the potential to define patient survival even before tumour formation. The ratio of Net4 to laminin molecules determines BM stiffness, such that the more Net4, the softer the BM, thereby decreasing cancer cell invasion activity.
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Membrana Basal/metabolismo , Fenômenos Mecânicos , Metástase Neoplásica , Fenômenos Biomecânicos , Linhagem Celular Tumoral , Humanos , Netrinas/metabolismoRESUMO
Recent experiments have reported lower critical solution temperature (LCST) phase behavior of aqueous solutions of proteins induced by multivalent ions, where the solution phase separates upon heating. This phenomenon is linked to complex hydration effects that result in a net entropy gain upon phase separation. To decipher the underlying molecular mechanism, we use all-atom molecular dynamics simulations along with the two-phase thermodynamic method for entropy calculation. Based on simulations of a single BSA protein in various salt solutions (NaCl, CaCl2, MgCl2, and YCl3) at temperatures (T) ranging 283-323 K, we find that the cation-protein binding affinity increases with T, reflecting its thermodynamic driving force to be entropic in origin. We show that in the cation binding process, many tightly bound water molecules from the solvation shells of a cation and the protein are released to the bulk, resulting in entropy gain. To rationalize the LCST behavior, we calculate the ζ-potential that shows charge inversion of the protein for solutions containing multivalent ions. The ζ-potential increases with T. Performing simulations of two BSA proteins, we demonstrate that the protein-protein binding is mediated by multiple cation bridges and involves similar dehydration effects that cause a large entropy gain which more than compensates for rotational and translational entropy losses of the proteins. Thus, the LCST behavior is entropy-driven, but the associated solvation effects are markedly different from hydrophobic hydration. Our findings have direct implications for tuning the phase behavior of biological and soft-matter systems, e.g., protein condensation and crystallization.
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Proteínas , Água , Cátions , Entropia , Soluções , TermodinâmicaRESUMO
The rational design of perfluorinated amphiphiles to control the supramolecular aggregation in an aqueous medium is still a key challenge for the engineering of supramolecular architectures. Here, the synthesis and physical properties of six novel non-ionic amphiphiles are presented. The effect of mixed alkylated and perfluorinated segments in a single amphiphile is also studied and compared with only alkylated and perfluorinated units. To explore their morphological behavior in an aqueous medium, dynamic light scattering (DLS) and cryogenic transmission electron microscopy/electron microscopy (cryo-TEM/EM) measurements are used. The assembly mechanisms with theoretical investigations are further confirmed, using the Martini model to perform large-scale coarse-grained molecular dynamics simulations. These novel synthesized amphiphiles offer a greater and more systematic understanding of how perfluorinated systems assemble in an aqueous medium and suggest new directions for rational designing of new amphiphilic systems and interpreting their assembly process.
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Simulação de Dinâmica Molecular , Microscopia Eletrônica de TransmissãoRESUMO
Although conceptually simple, the air-water interface displays rich behavior and is subject to intense experimental and theoretical investigations. Different definitions of the electrostatic surface potential as well as different calculation methods, each relevant for distinct experimental scenarios, lead to widely varying potential magnitudes and sometimes even different signs. Based on quantum-chemical density-functional-theory molecular dynamics (DFT-MD) simulations, different surface potentials are evaluated and compared to force-field (FF) MD simulations. As well explained in the literature, the laterally averaged electrostatic surface potential, accessible to electron holography, is dominated by the trace of the water molecular quadrupole moment, and using DFT-MD amounts to +4.35 V inside the water phase, very different from results obtained with FF water models which yield negative values of the order of -0.4 to -0.6 V. Thus, when predicting potentials within water molecules, as relevant for photoelectron spectroscopy and non-linear interface-specific spectroscopy, DFT simulations should be used. The electrochemical surface potential, relevant for ion transfer reactions and ion surface adsorption, is much smaller, less than 200 mV in magnitude, and depends specifically on the ion radius. Charge transfer between interfacial water molecules leads to a sizable surface potential as well. However, when probing electrokinetics by explicitly applying a lateral electric field in DFT-MD simulations, the electrokinetic ζ-potential turns out to be negligible, in agreement with predictions using continuous hydrodynamic models. Thus, interfacial polarization charges from intermolecular charge transfer do not lead to significant electrokinetic mobility at the pristine vapor-liquid water interface, even assuming these transfer charges are mobile in an external electric field.