Entropy Tug-of-War Determines Solvent Effects in the Liquid-Liquid Phase Separation of a Globular Protein.

Liquid-liquid phase separation (LLPS) plays a key role in the compartmentalization of cells via the formation of biomolecular condensates. Here, we combined atomistic molecular dynamics (MD) simulations and terahertz (THz) spectroscopy to determine the solvent entropy contribution to the formation of condensates of the human eye lens protein γD-Crystallin. The MD simulations reveal an entropy tug-of-war between water molecules that are released from the protein droplets and those that are retained within the condensates, two categories of water molecules that were also assigned spectroscopically. A recently developed THz-calorimetry method enables quantitative comparison of the experimental and computational entropy changes of the released water molecules. The strong correlation mutually validates the two approaches and opens the way to a detailed atomic-level understanding of the different driving forces underlying the LLPS.

Melting and Bubble Formation in a Double-Stranded DNA: Microscopic Aspects of Early Base-Pair Opening Events and the Role of Water.

Despite its rigid structure, DNA is a remarkably flexible molecule. Flexibility is essential for biological functions (such as transcription and gene repair), which require large-amplitude structural changes such as bubble formation. The bubbles thus formed are required to have a certain stability of their own and survive long on the time scale of molecular motions. A molecular understanding of fluctuations leading to quasi-stable structures is not available. Through extensive atomistic molecular dynamics simulations, we identify a sequence of microscopic events that culminate in local bubble formation, which is initiated by base-pair (BP) opening, resulting from the cleavage of native BP hydrogen bonds (HBs). This is followed by the formation of mismatched BPs with non-native contacts. These metastable structures can either revert to their original forms or undergo a flipping transition to form a local bubble that can span across 3-4 BPs. A substantial distortion of the DNA backbone and a disruption of BP stacking are observed because of the structural changes induced by these local perturbations. We also explored how water helps in the entire process. A small number of water molecules undergo rearrangement to stabilize the intermediate states by forming HBs with DNA bases. Water thus acts as a lubricant that counteracts the enthalpic penalty suffered from the loss of native BP contacts. Although the process of bubble formation is reversible, the sequence of steps involved poses an entropic barrier, preventing it from easily retracing the path to the native state.

Thermodynamic forces from protein and water govern condensate formation of an intrinsically disordered protein domain.

Liquid-liquid phase separation (LLPS) can drive a multitude of cellular processes by compartmentalizing biological cells via the formation of dense liquid biomolecular condensates, which can function as membraneless organelles. Despite its importance, the molecular-level understanding of the underlying thermodynamics of this process remains incomplete. In this study, we use atomistic molecular dynamics simulations of the low complexity domain (LCD) of human fused in sarcoma (FUS) protein to investigate the contributions of water and protein molecules to the free energy changes that govern LLPS. Both protein and water components are found to have comparably sizeable thermodynamic contributions to the formation of FUS condensates. Moreover, we quantify the counteracting effects of water molecules that are released into the bulk upon condensate formation and the waters retained within the protein droplets. Among the various factors considered, solvation entropy and protein interaction enthalpy are identified as the most important contributions, while solvation enthalpy and protein entropy changes are smaller. These results provide detailed molecular insights on the intricate thermodynamic interplay between protein- and solvation-related forces underlying the formation of biomolecular condensates.

Bimodal 1/f Noise and Anticorrelation between DNA-Water and DNA-Ion Energy Fluctuations.

The coupling between the conformational fluctuations of DNA and its surrounding environment, consisting of water and ions in solution, remains poorly understood and relatively less investigated as compared to proteins. Here, with the help of molecular dynamics simulations and statistical mechanical analyses, we explore the dynamical coupling among DNA, water, and counterions through correlations among respective energy fluctuations in both double- (ds-) and single-stranded (ss-) DNA solutions. Fluctuations in the collective DNA-water and DNA-ion interaction energies are found to be strongly anticorrelated across all the systems. The fluctuations of DNA self-energy, however, are weakly coupled to DNA-water and DNA-ion interactions in ds-DNA. An enhancement of the DNA-water coupling is observed in ss-DNA, where the system is less rigid. All the interaction energies exhibit 1/f noise in their energy power spectra with surprisingly prominent bimodality in the DNA-water and DNA-ion fluctuations. The nature of the energy spectra appears to be indifferent to the relative rigidity of the DNA. We discuss the role of the observed correlations in ion-water motions on a DNA duplex in the experimentally observed anomalous slow dielectric relaxation and solvation dynamics and in furthering our understanding of the DNA energy landscape.

Spatially Resolved Hydration Thermodynamics in Biomolecular Systems.

Water is essential for the structure, dynamics, energetics, and thus the function of biomolecules. It is a formidable challenge to elicit, in microscopic detail, the role of the solvation-related driving forces of biomolecular processes, such as the enthalpy and entropy contributions to the underlying free-energy landscape. In this Perspective, we discuss recent developments and applications of computational methods that provide a spatially resolved map of hydration thermodynamics in biomolecular systems and thus yield atomic-level insights to guide the interpretation of experimental observations. An emphasis is on the challenge of quantifying the hydration entropy, which requires characterization of both the motions of the biomolecules and of the water molecules in their surrounding.

Tug-of-War between Internal and External Frictions and Viscosity Dependence of Rate in Biological Reactions.

The role of water in biological processes is studied in three reactions, namely, the Fe-CO bond rupture in myoglobin, GB1 unfolding, and insulin dimer dissociation. We compute both internal and external components of friction on relevant reaction coordinates. In all of the three cases, the cross-correlation between forces from protein and water is found to be large and negative that serves to reduce the total friction significantly, increase the calculated reaction rate, and weaken solvent viscosity dependence. The computed force spectrum reveals bimodal 1/f noise, suggesting the use of a non-Markovian rate theory.

Stochastic formulation of multiwave pandemic: decomposition of growth into inherent susceptibility and external infectivity distributions.

Many known and unknown factors play significant roles in the persistence of an infectious disease, but two that are often ignored in theoretical modelling are the distributions of (i) inherent susceptibility ( σ inh ) and (ii) external infectivity ( ι ext ), in a population. While the former is determined by the immunity of an individual towards a disease, the latter depends on the exposure of a susceptible person to the infection. We model the spatio-temporal propagation of a pandemic as a chemical reaction kinetics on a network using a modified SAIR (Susceptible-Asymptomatic-Infected-Removed) model to include these two distributions. The resulting integro-differential equations are solved using Kinetic Monte Carlo Cellular Automata (KMC-CA) simulations. Coupling between σ inh and ι ext are combined into a new parameter Ω, defined as Ω = σ inh × Î¹ ext ; infection occurs only if the value of Ω is greater than a Pandemic Infection Parameter (PIP), Ω 0 . Not only does this parameter provide a microscopic viewpoint of the reproduction number R0 advocated by the conventional SIR model, but it also takes into consideration the viral load experienced by a susceptible person. We find that the neglect of this coupling could compromise quantitative predictions and lead to incorrect estimates of the infections required to achieve the herd immunity threshold. The figure represents the network model for spread of infectious diseases considered in this work. It also shows the resultant multiwave infection graph by inclusion of inherent susceptibility and external infectivity distributions and migration of infected individuals.

Structural Stability of Insulin Oligomers and Protein Association-Dissociation Processes: Free Energy Landscape and Universal Role of Water.

Association and dissociation of proteins are important biochemical events. In this Feature Article, we analyze the available studies of these processes for insulin oligomers in aqueous solution. We focus on the solvation of the insulin monomer in water, stability and dissociation of its dimer, and structural integrity of the hexamer. The intricate role of water in solvation of the dimer- and hexamer-forming surfaces, in long-range interactions between the monomers and the stability of the oligomers, is discussed. Ten water molecules inside the central cavity stabilize the structure of the insulin hexamer. We discuss how different order parameters can be used to understand the dissociation of the insulin dimer. The calculation of the rate using a recently computed multidimensional free energy provides considerable insight into the interplay between protein and water dynamics.

Rate of Insulin Dimer Dissociation: Interplay between Memory Effects and Higher Dimensionality.

We calculate the rate of dissociation of an insulin dimer into two monomers in water. The rate of this complex reaction is determined by multiple factors that are elucidated. By employing advanced sampling techniques, we first obtain the reaction free energy surface for the dimer dissociation as a function of two order parameters, namely, the distance between the center-of-mass of two monomers (R) and the number of cross-contacts (Q) among the backbone Cα atoms of two monomers. We then construct an orthogonal 2D reaction energy surface by introducing the reaction coordinate X to denote the minimum energy pathway and a conjugate coordinate Y that spans the orthogonal direction. The free energy landscape is rugged with multiple maxima and minima. We calculate the rate by employing not only the non-Markovian multidimensional rate theory but also several other theoretical approaches. The necessary reaction frequencies and the frictions are calculated from the time correlation function formalism. Our best estimate of the rate is 0.4 µs-1. Our study reveals interesting opposite influences of dimensionality and memory in determining the rate constant of the reaction. We gain interesting insights into the dimer dissociation process by looking directly at the trajectories obtained from molecular dynamics simulation.

Unfolding of Dynamical Events in the Early Stage of Insulin Dimer Dissociation.

The dissociation of an insulin dimer is an important biochemical event that could also serve as a prototype of dissociations in similar biomolecular assemblies. We use a recently developed multidimensional free energy landscape for insulin dimer dissociation to unearth the microscopic and mechanistic aspects of the initial stages of the process that could hold the key to understanding the stability and the rate. The following sequence of events occurs in the initial stages: (i) The backbone hydrogen bonds break partially at the antiparallel ß-sheet junction, (ii) the two α-helices (chain B) move away from each other while several residues (chain A) move closer, and (iii) a flow of adjacent water molecules occurs into the junction region. Interestingly, the intermonomeric center-to-center distance does not increase, but the number of native contacts exhibits a sharp decrease. Subsequent steps involve further disengagement of hydrophobic groups. This process is slow because of an entropic bottleneck created by the existence of the large configuration space available in the native state (NS), which is inhabited by low-frequency conformational fluctuations. We carry out a density-of-states analyses in the dimer NS to unearth distinctive features not present in the monomers. These low-frequency modes are also responsible for a large entropic stabilization of the NS. Hydrophobic disengagement in the early stage leads to the formation of a twisted intermediate state which itself is a metastable minimum (IS-1). The subsequent progress leads to another dimeric complex (IS-2), which is on the dissociative pathway and characterized by a further decrease in the native contacts. The dissociation process provides insights into the workings of a biomolecular assembly.

Mathematical modeling and cellular automata simulation of infectious disease dynamics: Applications to the understanding of herd immunity.

The complexity associated with an epidemic defies any quantitatively reliable predictive theoretical scheme. Here, we pursue a generalized mathematical model and cellular automata simulations to study the dynamics of infectious diseases and apply it in the context of the COVID-19 spread. Our model is inspired by the theory of coupled chemical reactions to treat multiple parallel reaction pathways. We essentially ask the question: how hard could the time evolution toward the desired herd immunity (HI) be on the lives of people? We demonstrate that the answer to this question requires the study of two implicit functions, which are determined by several rate constants, which are time-dependent themselves. Implementation of different strategies to counter the spread of the disease requires a certain degree of a quantitative understanding of the time-dependence of the outcome. Here, we compartmentalize the susceptible population into two categories, (i) vulnerables and (ii) resilients (including asymptomatic carriers), and study the dynamical evolution of the disease progression. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population and the complex dependence on the rate of attainment of herd immunity. We attempt to study and quantify possible adverse effects of the progression rate of the epidemic on the recovery rates of vulnerables, in the course of attaining HI. We find the important result that slower attainment of the HI is relatively less fatal. However, slower progress toward HI could be complicated by many intervening factors.

Destabilization of Insulin Hexamer in Water-Ethanol Binary Mixture.

We report combined experimental and simulation studies which reveal that the structural integrity of insulin hexamer, the storehouse of the important hormone in our body, is compromised by the interactions with ethanol. X-ray crystal structures suggest that ethanol replaces water molecules inside the insulin hexamer cavity. At the maximum physiologically tolerable concentration of ethanol (∼0.6% v/v), molecular dynamics simulations show that ethanol molecules get exchanged between the bulk and the cavity with a free energy cost of ∼5 kcal mol-1. However, biological time scales are orders of magnitude longer than that achievable by molecular dynamics simulations. Hence, to accelerate the process we investigate insulin hexamer in ∼30% v/v ethanol concentration. We find that the entrance and exit of ethanol from the hexamer cavity lead to the modification of atomic contacts in the protein. This causes large-scale fluctuations that force the protein out of its native state free energy minimum. Structural perturbations are also observed at lower ethanol concentration. The computational findings are consistent with dynamic light scattering experiments that suggest an abrupt reduction in the population of insulin hexamers at a critical ethanol concentration. The structural changes triggered by interaction of ethanol with the insulin hexamer are likely to represent a general dynamic event of amphiphilic cosolvent induced changes in macromolecular assemblies with the consequent effects on cellular homeostasis.

Mechanism of Solvent Control of Protein Dynamics.

We find that the coupled interactions between protein and water polarization fluctuations play a dominant role in driving the configuration space random walk of solvated proteins. We perform atomistic molecular dynamics simulations on five proteins. Owing to a very low dielectric constant of protein, its dipolar groups experience forces from water along with local forces due to protein atoms. Energy fluctuations reveal a pronounced anticorrelation between protein and water contributions. The protein energy spectrum shows bimodal 1/f noise, which can be attributed to the influence of water on the dynamics of protein.

DNA Solvation Dynamics.

Experiments have revealed that DNA solvation dynamics is characterized by multiple time scales ranging from a few picoseconds to a few hundred nanoseconds and in some cases even up to several microseconds. The last part of decay is not only slow but can also be described by a power law (PL). The microscopic origin of this PL is yet to be clearly established. Here we present a theoretical study employing multiple approaches from time dependent statistical mechanics and computer simulations. The present study shows that water dynamics may not account for the slow PL decay because the longest time scales describing water dynamics could be at most of the order of 100 ps. We find that the DNA solvation dynamics is complex, due to multiple different contributions to solvation energy. Our investigations also show that the primary candidates for this exotic nature of solvation dynamics are the response of the counterions and ions of the buffer solution. We first employ the well-known Oosawa model of polyelectrolyte solution that includes effects of counterion fluctuations to construct a frequency dependent dielectric function. We use it in the continuum model of Bagchi, Fleming, and Oxtoby (BOF). We find that it fails to explain the slow PL decay of DNA solvation dynamics. We then extend the Oosawa model by employing the continuous time random walk technique developed by Scher, Montroll and Lax. We find that this approach could explain the long time PL decay, in terms of the collective response of the counterions. To check the nature of random walk of counterions along the phosphate backbone, we carry out atomistic molecular dynamics (MD) simulations with a long (38 base pair) DNA. We indeed find frequent occurrence of random walk of tagged counterions along the phosphate backbone. We next propose a generalized random walk model for counterion hopping on phosphate backbone (observed in our MD simulations) and carry out kinetic Monte Carlo simulations to show that the nonexponential contribution to solvation dynamics can indeed come from dynamics of such ions. We also employ a mode coupling theory (MCT) analysis to understand the slow relaxation that can originate from ions in solution due to the use of the buffer. Explicit evaluation suggests that buffer ion contribution could explain a logarithmic time dependence in the nanosecond time scale but not a power law. To further understand the nonexponentiality of solvation dynamics at relatively shorter times (less than 100 ps) we carry out atomistic MD simulations with explicit water molecules. Log-normal distributions of relaxation times of water dynamics inside the grooves may be responsible for the initial multiexponential decay of solvation dynamics. We find that the observed faster solvation of groove bound probe than that of the intercalated probe could arise from the self-motion of the probe.

Unique Features of Metformin: A Combined Experimental, Theoretical, and Simulation Study of Its Structure, Dynamics, and Interaction Energetics with DNA Grooves.

There are certain small molecules that exhibit extraordinarily diverse biological activities. Metformin is one of them. It is widely used as an antidiabetic drug for type-two diabetes. Recent lines of evidence of its role in antitumor activities and increasing the survival rates of cancer patients (namely, colorectal, breast, pancreas, and prostate cancer) are emerging. However, theoretical studies of the structure and dynamics of metformin have not yet been fully explored. In this work, we investigate the characteristic structural and dynamical features of three monoprotonated forms of metformin hydrochloride with the help of experiments, quantum chemical calculations, and atomistic molecular dynamics simulations. We validate our force field by comparing simulation results to those of the experimental findings. Energetics of proton transfer between two planar monoprotonated forms reveals a low energy barrier, which leads us to speculate a possible coexistence of them. Nevertheless, among the protonation states, we find that the nonplanar tautomeric form is the most stable. Our calculated values of the self-diffusion coefficient agree quantitatively with NMR results. Metformin forms strong hydrogen bonds with surrounding water molecules, and its solvation dynamics shows unique features. Because of an extended positive charge distribution, metformin possesses features of being a permanent cationic partner toward several targets. We study its interaction and binding ability with DNA using UV spectroscopy, circular dichroism, fluorimetry, and metadynamics simulation. We find a nonintercalative mode of interaction. Metformin feasibly forms a minor/major groove-bound state within a few tens of nanoseconds, preferably with AT-rich domains. A significant decrease in the free energy of binding is observed when it binds to a minor groove of DNA.

What Gives an Insulin Hexamer Its Unique Shape and Stability? Role of Ten Confined Water Molecules.

Self-assembly of proteins often gives rise to interesting quasi-stable structures that serve important biological purposes. Insulin hexamer is such an assembly. While monomer is the biologically active form of insulin, hexamer serves as the storehouse of the hormone. The hexamer also prevents the formation of higher order aggregates. While several studies explored the role of bivalent metal ions like Zn2+, Ca2+, etc., in the stabilization of the hexameric form, the role of water molecules has been ignored. We combine molecular dynamics simulations, quantum calculations, and X-ray analyses to discover that a team of approximately 10 water molecules confined inside a barrel-shaped nanocavity at the center of insulin hexamer is one of the major causes that account for the unusual stability of the biomolecular assembly. These cavity water molecules exhibit interesting dynamical features like intermittent escape and reentrance. We find that these water molecules are dynamically slower than the bulk and weave an intricate hydrogen bond network among themselves and with neighboring protein residues to generate a robust backbone at the center of the hexamer that holds the association strongly from inside and maintains the barrel shape.

Origin of diverse time scales in the protein hydration layer solvation dynamics: A simulation study.

In order to inquire the microscopic origin of observed multiple time scales in solvation dynamics, we carry out several computer experiments. We perform atomistic molecular dynamics simulations on three protein-water systems, namely, lysozyme, myoglobin, and sweet protein monellin. In these experiments, we mutate the charges of the neighbouring amino acid side chains of certain natural probes (tryptophan) and also freeze the side chain motions. In order to distinguish between different contributions, we decompose the total solvation energy response in terms of various components present in the system. This allows us to capture the interplay among different self- and cross-energy correlation terms. Freezing the protein motions removes the slowest component that results from side chain fluctuations, but a part of slowness remains. This leads to the conclusion that the slow component approximately in the 20-80 ps range arises from slow water molecules present in the hydration layer. While the more than 100 ps component has multiple origins, namely, adjacent charges in amino acid side chains, hydrogen bonded water molecules and a dynamically coupled motion between side chain and water. In addition, the charges enforce a structural ordering of nearby water molecules and helps to form a local long-lived hydrogen bonded network. Further separation of the spatial and temporal responses in solvation dynamics reveals different roles of hydration and bulk water. We find that the hydration layer water molecules are largely responsible for the slow component, whereas the initial ultrafast decay arises predominantly (approximately 80%) due to the bulk. This agrees with earlier theoretical observations. We also attempt to rationalise our results with the help of a molecular hydrodynamic theory that was developed using classical time dependent density functional theory in a semi-quantitative manner.

Distinguishing dynamical features of water inside protein hydration layer: Distribution reveals what is hidden behind the average.

Since the pioneering works of Pethig, Grant, and Wüthrich on a protein hydration layer, many studies have been devoted to find out if there are any "general and universal" characteristic features that can distinguish water molecules inside the protein hydration layer from bulk. Given that the surface itself varies from protein to protein, and that each surface facing the water is heterogeneous, search for universal features has been elusive. Here, we perform an atomistic molecular dynamics simulation in order to propose and demonstrate that such defining characteristics can emerge if we look not at average properties but the distribution of relaxation times. We present results of calculations of distributions of residence times and rotational relaxation times for four different protein-water systems and compare them with the same quantities in the bulk. The distributions in the hydration layer are unusually broad and log-normal in nature due to the simultaneous presence of peptide backbones that form weak hydrogen bonds, hydrophobic amino acid side chains that form no hydrogen bond, and charged polar groups that form a strong hydrogen bond with the surrounding water molecules. The broad distribution is responsible for the non-exponential dielectric response and also agrees with large specific heat of the hydration water. Our calculations reveal that while the average time constant is just about 2-3 times larger than that of bulk water, it provides a poor representation of the real behaviour. In particular, the average leads to the erroneous conclusion that water in the hydration layer is bulk-like. However, the observed and calculated lower value of static dielectric constant of hydration layer remained difficult to reconcile with the broad distribution observed in dynamical properties. We offer a plausible explanation of these unique properties.