Ion diffusion captures composition-dependent anomalies in water-DMSO binary mixtures.

Aqueous dimethyl sulfoxide (Aq-DMSO) binary mixture exhibits many fascinating composition-dependent anomalies that are explained by using the peculiarities of the water-DMSO hydrogen bond. Ions can couple strongly to these composition-dependent anomalies to produce exotic dynamics of their own. We carry out theoretical studies using computer simulations to understand the structural and dynamical aspects of rigid monovalent cations (Li+, Na+, K+, Rb+, and Cs+) in aqueous DMSO solutions, with chloride as the counterion. We uncover a number of composition-dependent ion diffusion anomalies, which can be traced back to the interplay between the size-dependent charge density of the ion and the resulting difference in interactions of the ion with water and DMSO molecules. Size and composition dependence of the diffusion coefficients of the five ions exhibit fascinating variations that can be explained partially.

Rate theory of gas-liquid nucleation: Quest for the elusive quantitative accuracy.

The task of a first principles theoretical calculation of the rate of gas-liquid nucleation has remained largely incomplete despite the existence of reliable results from unbiased simulation studies at large supersaturation. Although the classical nucleation theory formulated by Becker-Doring-Zeldovich about a century ago provides an elegant, widely used picture of nucleation in a first-order phase transition, the theory finds difficulties in predicting the rate accurately, especially in the case of gas-to-liquid nucleation. Here, we use a multiple-order parameter description to construct the nucleation free energy surface needed to calculate the nucleation rate. A multidimensional non-Markovian (MDNM) rate theory formulation that generalizes Langer's well-known nucleation theory by using the Grote-Hynes MDNM treatment is used to obtain the rate of barrier crossing. We find good agreement of the theory with the rate obtained by direct unbiased molecular dynamics simulations-the latter is feasible at large supersaturation, S. The theory gives an experimentally strong dependence of the rate of nucleation on supersaturation, S. Interestingly, we find a strong influence of the frequency-dependent friction coefficient at the barrier top. This arises from multiple recrossings of the barrier surface. We find that a Markovian theory, such as Langer's formulation, fails to capture the rate quantitatively. In addition, the multidimensional transition state theory expression performs poorly, revealing the underlying role of the friction coefficient.

Exploration of Stokes hydrodynamic law at molecular length scales.

The celebrated generalized Stokes law predicts that the velocity of a particle pulled through a liquid by an external force, Fex, is directly proportional to the force and inversely proportional to the friction ζ acted by the medium on the particle. We investigate the range of validity of the generalized Stokes law at molecular length scales by employing computer simulations to calculate friction by pulling a tagged particle with a constant force. We thus calculate friction for two model interaction potentials, Lennard-Jones and soft sphere, for several particle sizes, ranging from radius (a) smaller than the solvent particles to three times larger. We next obtain friction from diffusion (D) by using Einstein's relation between diffusion and friction ζ in an unperturbed liquid. We find a quantitative agreement between the two at a small-to-intermediate pulling force regime for all the sizes studied. The law does break down at a large pulling force beyond a threshold value. Importantly, the range of validity of Stokes' scheme to obtain friction increases substantially if we turn off the attractive part of the interaction potential. Additionally, we calculate the viscosity (η) of the unperturbed liquid and find a good agreement with the Stokes-Einstein relation ζ = Cηa for the viscosity dependence with a value of C close to 5 π, which is intermediate between the slip and stick boundary condition.

Memory effects in the efficiency control of energy transfer under incoherent light excitation in noisy environments.

Fluctuations in energy gap and coupling constants between chromophores can play an important role in absorption and energy transfer across a collection of two-level systems. In photosynthesis, light-induced quantum coherence can affect the efficiency of energy transfer to the designated "trap" state. Theoretically, the interplay between fluctuations and coherence has been studied often, employing either a Markovian or a perturbative approximation. In this study, we depart from these approaches to incorporate memory effects by using Kubo's quantum stochastic Liouville equation. We introduce the effects of decay of the created excitation (to the ground state) on the desired propagation and trapping that provides a direction of flow of the excitation. In the presence of light-induced pumping, we establish a relation between the efficiency, the mean survival time, and the correlation decay time of the bath-induced fluctuations. A decrease in the steady-state coherence during the transition from the non-Markovian regime to the Markovian limit results in a decrease in efficiency. As in the well-known Haken-Strobl model, the ratio of the square of fluctuation strength to the rate plays a critical role in determining the mechanism of energy transfer and in shaping the characteristics of the efficiency profile. We recover a connection between the transfer flux and the imaginary part of coherences in both equilibrium and excited bath states, in both correlated and uncorrelated bath models. We uncover a non-monotonic dependence of efficiency on site energy heterogeneity for both correlated and uncorrelated bath models.

Nonlinear composition dependence of hydrogen bond lifetime in water-DMSO binary mixtures: The role of hydrophobic interaction.

The lifetime of a hydrogen bond between water and dimethyl sulfoxide (DMSO) is found to be considerably longer than that between two water molecules in neat water. This is counter-intuitive because the charge on the oxygen in DMSO is considerably less than that in water. Additionally, the strength of the water-dimethyl sulfoxide (w-D) hydrogen bond is found to be strongly composition dependent; the lifetime of the hydrogen bond is ten times larger at 30% than at very low concentrations. Using computer simulations, we perform microscopic structural and dynamic analysis to find that these anomalies arise at least partly from an "action-at-a-distance" effect where the attraction between the hydrophobic methyl groups results in the self-aggregation of DMSO molecules that "cages" both the rotational and linear motions of the molecules involved. This is reflected in the observed strong correlation of the lifetime with the local coordination number of the associated methyl groups. The elongated w-D h-bond lifetime causes a slowdown of collective dynamics and affects the lifetime of the w-w h-bond. This nonlinear feedback mechanism explains the strong composition dependence of viscosity and is anticipated to play a dominant role in many self-assemblies. Furthermore, the w-D hydrogen bond breaking mechanism changes from low to high DMSO concentration, a phenomenon not anticipated a priori. We introduce a new order parameter-based free energy surface of the bond breaking pathway. A two-dimensional transition state rate theory calculation is performed for the lifetime of the w-D h-bond that is found to be semi-quantitatively accurate.

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum.

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel-Fulcher-Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

Dynamical control by water at a molecular level in protein dimer association and dissociation.

Water, often termed as the "lubricant of life," is expected to play an active role in navigating protein dissociation-association reactions. In order to unearth the molecular details, we first compute the free-energy surface (FES) of insulin dimer dissociation employing metadynamics simulation, and then carry out analyses of insulin dimerization and dissociation using atomistic molecular-dynamics simulation in explicit water. We select two sets of initial configurations from 1) the dissociated state and 2) the transition state, and follow time evolution using several long trajectories (∼1-2 µs). During the process we not only monitor configuration of protein monomers, but also the properties of water. Although the equilibrium structural properties of water between the two monomers approach bulklike characteristics at a separation distance of ∼5 nm, the dynamics differ considerably. The complex association process is observed to be accompanied by several structural and dynamical changes of the system, such as large-scale correlated water density fluctuations, coupled conformational fluctuation of protein monomers, a dewettinglike transition with the change of intermonomeric distance RMM from ∼4 to ∼2 nm, orientation of monomers and hydrophobic hydration in the monomers. A quasistable, solvent-shared, protein monomer pair (SSPMP) forms at around 2 nm during association process which is a local free-energy minimum having ∼50-60% of native contacts. Simulations starting with arrangements sampled from the transition state (TS) of the dimer dissociation reveal that the final outcome depends on relative orientation of the backbone in the "hotspot" region.

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.

Correlation lengths in nanoconfined water and transport properties.

We report the existence of disparate static and dynamic correlation lengths that could describe the influence of confinement on nanoconfined water (NCW). Various aspects of viscous properties, such as anisotropy and viscoelasticity, of NCW are studied by varying the separation distance "d" between two confining hydrophobic plates. The transverse component of the mean square stress exhibits slow spatial decay (measured from the surface) beyond ∼1.8 nm, which was not reported before. The static correlation length obtained from fitting the exponential decay of the transverse mean-square stress with d is 0.75 nm, while the decay time of the stress-stress time correlation function gives a dynamic correlation length of only 0.35 nm. The shortness of the dynamic correlation length seems to arise from the low sensitivity of orientational relaxation to confinement. In the frequency-dependent viscosity, we observe a new peak at about 50 cm-1 that is not present in the bulk. This new peak is prominent even at 3 nm separations. The peak is absent in the bulk, although it is close to the intermolecular -O-O-O- bending mode well known in liquid water. We further explore the relationship between diffusion and viscosity in NCW by varying d.

Non-Markovian rate theory on a multidimensional reaction surface: Complex interplay between enhanced configuration space and memory.

A theory of barrier crossing rate on a multidimensional reaction energy surface is presented. The theory is a generalization of the earlier theoretical schemes to higher dimensions, with the inclusion of non-Markovian friction along both the reactive and the nonreactive coordinates. The theory additionally includes the bilinear coupling between the reactive and the nonreactive modes at the Hamiltonian level. Under suitable conditions, we recover the rate expressions of Langer and Hynes and establish a connection with the rate treatment of Pollak. Within the phenomenology of generalized Langevin equation description, our formulation provides an improvement over the existing ones because we explicitly include both the non-Markovian effects along the reaction coordinate and the bilinear coupling at the Hamiltonian level. At intermediate-to-large friction, an increase in dimensionality by itself tends to reduce the rate, while the inclusion of the memory effects increases the rate. The theory predicts an increase in rate when off-diagonal friction terms are included. We present a model calculation to study isomerization of a stilbene-like molecule using the prescription of Hochstrasser and co-workers on a two-dimensional reaction energy surface, employing Zwanzig-Bixon hydrodynamic theory of frequency-dependent friction. The calculated rate shows a departure from the predictions of Langer's theory and also from the two-dimensional transition state theory.

Ethanol exchange between two graphene surfaces in nanoconfined aqueous solution: Rate and mechanism.

We observe, by computer simulations, a remarkable long-distance, rare, but repetitive, exchange of ethanol molecules between two parallel graphene surfaces in nanoconfined, aqueous, ethanol solutions. We compute the rate of exchange as a function of the separation (d) between the two surfaces. We discover that the initiating (or, the launching) step in this exchange is the attainment of an instantaneous orientation of the carbon-oxygen bond vector relative to the graphene surface. This observation led us to construct a two-dimensional free energy surface for this exchange, with respect to two order parameters, namely, (i) the perpendicular distance of ethanol molecule from the graphene surfaces, z, and (ii) the orientation of the O-C bond vector, θ, of the tagged ethanol molecule. For d = 3 nm, the rate of exchange is found to be 0.44 ns-1 for the force field used. We also vary the force field and determine the sensitivity of the rate. From the free energy landscape, one could determine the minimum energy pathway. We use both, the transition state theory and Kramers' theory, to calculate the rate. The calculated rate agrees well with the simulated value as mentioned above. We find that the rate of exchange phenomenon is sensitive to the interaction strength of graphene and the hydrophobic group of ethanol. The free energy landscape exchange shows dependence on the distance separation of the two hydrophobic surfaces and reveals interesting features.

Excitation Energy Transfer Efficiency in Fluctuating Environments: Role of Quantum Coherence in the Presence of Memory Effects.

Several recent studies have interrogated the role of quantum coherence in affecting the transfer efficiency of an optical excitation to the designated "trap" state where the energy can be used for subsequent reactions, as in photosynthesis. However, these studies invoke a Markovian approximation for the time correlation function describing the environment-induced stochastic fluctuations. Here, we employ Kubo's quantum stochastic Liouville equation (QSLE) to include memory effects. We extend the existing QSLE scheme to introduce decay of a newly created excitation due to radiative and nonradiative channels and also by desired trapping toward the targeted chromophore. We show that the theoretical formalism based on the QSLE correctly reproduces the rate equation description in the Markovian limit, with the rate constants determined by an appropriate quantum limiting procedure. We find that under certain conditions, the efficiency of excitation transfer to the trap gains from the combined presence of quantum coherence and temporally correlated stochastic fluctuations. We work out different limiting situations in order to discover and quantify the optimum conditions for the energy transfer to the trapped state. We find that maximum energy transfer efficiency is achieved in the intermediate limit between coherent and incoherent transport.

Anomalous dielectric response of nanoconfined water.

In order to develop a microscopic level understanding of the anomalous dielectric properties of nanoconfined water (NCW), we study and compare three different systems, namely, (i) NCW between parallel graphene sheets (NCW-GSs), (ii) NCW inside graphene covered nanosphere (NCW-Sph), and (iii) a collection of one- and two-dimensional constrained Ising spins with fixed orientations at the termini. We evaluate the dielectric constant and study the scaling of ε with size by using linear response theory and computer simulations. We find that the perpendicular component remains anomalously low at smaller inter-plate separations (d) over a relatively wide range of d. For NCW-Sph, we could evaluate the dielectric constant exactly and again find a low value and a slow convergence to the bulk. To obtain a measure of surface influence into the bulk, we introduce and calculate correlation lengths to find values of ∼9 nm for NCW-GS and ∼5 nm for NCW-Sph, which are surprisingly large, especially for water. We discover that the dipole moment autocorrelations exhibit an unexpected ultrafast decay. We observe the presence of a ubiquitous frequency of ∼1000 cm-1, associated only with the perpendicular component for NCW-GS. This (caging) frequency seems to play a pivotal role in controlling both static and dynamic dielectric responses in the perpendicular direction. It disappears with an increase in d in a manner that corroborates with the estimated correlation length. A similar observation is obtained for NCW-Sph. Interestingly, one- and two-dimensional Ising model systems that follow Glauber spin-flip dynamics reproduce the general characteristics.

An exact solution in the theory of fluorescence resonance energy transfer with vibrational relaxation.

The elegant expression of Förster that predicts the well-known 1/R6 distance (R) dependence of the rate of energy transfer, although widely used, was derived using several approximations. Notable among them is the neglect of the vibrational relaxation in the reactant (donor) and product (acceptor) manifolds. Vibrational relaxation can play an important role when the energy transfer rate is faster than the vibrational relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibrational states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we develop a Green's function-based generalized formalism and obtain an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibrational relaxation. We find that the application of the well-known Förster's expression might lead to overestimation of R.

Water Layer at Hydrophobic Surface: Electrically Dead but Dynamically Alive?

The origin of the anomalous low value of the static dielectric constant (SDC) of confined water has been addressed and unearthed. While the low value is partly due to the different dielectric boundaries, a significant role is played by the "electrically dead layer" (EDL). As the observed dielectric constant is the harmonic mean of the grid-wise SDCs, the first layer, having the smallest SDC, makes a disproportionately large contribution. This enhanced contribution, in turn, arises from the orientationally ordered surface water molecules. They exhibit reduced fluctuations in collective dipole moment, as the molecules remain partly caged due to water-surface interactions. This phenomenon is found to be universal. We study the structure and dynamics of the water molecules which characterize the EDL. We demonstrate that while the EDL remains alive at a molecular level, with a finite residence time, it displays time scales not substantially different compared to the distant water layers.

Fluctuation theory of immune response: A statistical mechanical approach to understand pathogen induced T-cell population dynamics.

In this period of intense interest in human immunity, we attempt here to quantify the immune response against pathogen invasion through T-cell population dynamics. Borrowing concepts from equilibrium statistical mechanics, we introduce a new description of the immune response function (IMRF) in terms of fluctuations in the population number of relevant biological cells (effector and regulatory T-cells). We use a coarse-grained chemical reaction network model (CG-CRNM) to calculate the number fluctuations and show that the response function derived as such can, indeed, capture the crossover observed in a T-cell driven immune response. We employ the network model to learn the effect of vitamin-D as an immunomodulator. We solve our CG-CRNM using a stochastic Gillespie algorithm. Depending on the effector T-cell concentration, we can classify immune regulation regimes into three categories: weak, strong, and moderate. The IMRF is found to behave differently in these three regimes. A damped cross-regulatory behavior found in the dynamics of effector and regulatory T-cell concentration in the diseased states correlates well with the same found in a cohort of patients with specific malignancies and autoimmune diseases. Importantly, the crossover from the weakly regulated steady state to the other (the strongly regulated) is accompanied by a divergence-like growth in the fluctuation of both the effector and the regulatory T-cell concentration, characteristic of a dynamic phase transition. We believe such steady-state IMRF analyses could help not only to phase-separate different immune stages but also aid in the valuable connection between autoimmunity, optimal vitamin-D, and consequences of immunosuppressive stress and malignancy.

How different are the dynamics of nanoconfined water?

We unravel the combined effects of confinement and surface interactions by studying the position dependent, time-resolved dynamic response functions in nano-containers of different shapes. Spectroscopic signatures are additionally studied through solvation dynamics by placing ionic and dipolar probes at varying distances from the enclosing surface. We find that the confined water molecules exhibit exotic dynamical features and stark differences from that in the bulk liquid. We employ atomistic molecular dynamics simulation to obtain the solvation time correlation function, non-Gaussian parameter, and non-linear response function that reveal the existence of heterogeneous and non-exponential dynamics with a strong sensitivity to both the size and the shape of the enclosure. Importantly, the slower long-time decay constant exhibits a non-monotonic spatial dependence. The initial ultrafast component is reminiscent of the same in the bulk, but it is found to have a different origin in the present systems. We perform shell-wise analyses to understand the microscopic origin of these observations and the range of the propagation of the surface induced effects.

Study of entropy-diffusion relation in deterministic Hamiltonian systems through microscopic analysis.

Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study and any derivation of an algebraic relation between the two do not seem to exist. Here, we explore the nature of this entropy-diffusion relation in three deterministic systems where an accurate estimate of both can be carried out. We study three deterministic model systems: (a) the motion of a single point particle with constant energy in a two-dimensional periodic potential energy landscape, (b) the same in the regular Lorentz gas where a point particle with constant energy moves between collisions with hard disk scatterers, and (c) the motion of a point particle among the boxes with small apertures. These models exhibit diffusive motion in the limit where ergodicity is shown to exist. We estimate the self-diffusion coefficient of the particle by employing computer simulations and entropy by quadrature methods using Boltzmann's formula. We observe an interesting crossover in the diffusion-entropy relation in some specific regions, which is attributed to the emergence of correlated returns. The crossover could herald a breakdown of the Rosenfeld-like exponential scaling between the two, as observed at low temperatures. Later, we modify the exponential relation to account for the correlated motions and present a detailed analysis of the dynamical entropy obtained via the Lyapunov exponent, which is rather an important quantity in the study of deterministic systems.

Role of local order in anomalous ion diffusion: Interrogation through tetrahedral entropy of aqueous solvation shells.

Small rigid ions perturb the water structure around them significantly. At constant viscosity, alkali cations (Li+, Na+, and so on) exhibit an anomalous non-monotonic dependence of diffusivity on ion-size, in stark violation of the Stokes-Einstein expression. Although this is a well-known problem, we find that an entropic view of the problem can be developed, which provides valuable insight. The local entropy experienced by the solute ion is relevant here, which leads to the connection with local viscosity, discussed earlier by many. Due to the strong interactions with ions, the translational and rotational entropy of solvation water decreases sharply; however, an opposite effect comes from the disruption of the tetrahedral network structure of water near the charges. We compute the tetrahedral order of water molecules (qtet) around the ion and suitably defined tetrahedral entropy [S(qtet)] that is a contribution to the excess entropy of the system. Our results reveal that although the structural properties of the second shell become nearly identical to the bulk, S(qtet) of the second shell is found to play an important role in giving rise to the non-monotonic ion-size dependence. The detailed study of the static and dynamic fluctuations in qtet and the number of hydration water molecules provides interesting insights into correlation between the structure and dynamics; the smallest static fluctuation of qtet for the first hydration shell water molecules of Li+ is indicative of the iceberg picture. The study of fluctuation properties of qtet and the coordination number also reveals the role of the second hydration layer and could explain the anomalous behavior of the Rb+ ion.

Ion pair correlations due to interference between solvent polarizations induced in water.

Motions of two distinct ions can get correlated because the polarization induced by the ions can propagate through intervening water and can interfere with each other. This important aspect, which is not included in the continuum model based theories, has not been studied adequately. We calculate the effective force between two oppositely charged and similarly charged ions fixed in water as a function of separation distance R. At short separations, R less than 1.5 nm, the effective force vastly differs from the 1/εsR2 dependence advocated by the screened Coulomb's force law (SCFL), where εs is the static dielectric constant of the medium. This breakdown of the SCFL is shown to be due to the persistent interference between the polarizations created by the two charges in a manner similar to the vortex-antivortex pair formation in the XY model Hamiltonian. The distance dependence of dielectric constants, εs(R), extracted from our simulation exhibits interesting features and can be used in future modeling. In addition, we show that the force-force time autocorrelation between two neighboring ions decays differently at short separation and analyze the friction on the ion pair at different separation distances.