Domain growth kinetics in active binary mixtures.

We study motility-induced phase separation in symmetric and asymmetric active binary mixtures. We start with the coarse-grained run-and-tumble bacterial model that provides evolution equations for the density fields ρi(r⃗,t). Next, we study the phase separation dynamics by solving the evolution equations using the Euler discretization technique. We characterize the morphology of domains by calculating the equal-time correlation function C(r, t) and the structure factor S(k, t), both of which show dynamical scaling. The form of the scaling functions depends on the mixture composition and the relative activity of the species, Δ. For k → ∞, S(k, t) follows Porod's law: S(k, t) ∼ k-(d+1) and the average domain size L(t) shows a diffusive growth as L(t) ∼ t1/3 for all mixtures.

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.

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.

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.

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.

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.

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.

Effect of ethanol on insulin dimer dissociation.

Insulin-dimer dissociation is an essential biochemical process required for the activity of the hormone. We investigate this dissociation process at the molecular level in water and at the same time, in 5% and 10% water-ethanol mixtures. We compute the free energy surface of the protein dissociation processes by employing biased molecular dynamics simulation. In the presence of ethanol (EtOH), we observe a marked lowering in the free energy barrier of activation of dimer dissociation from that in the neat water, by as much as ∼50%, even in the 5% water-ethanol solution. In addition, ethanol is found to induce significant changes in the dissociation pathway. We extract the most probable conformations of the intermediate states along the minimum energy pathway in the case of all the three concentrations (EtOH mole fractions 0, 5, and 10). We explore the change in microscopic structures that occur in the presence of ethanol. Interestingly, we discover a stable intermediate state in the water-ethanol binary mixture where the centers of the monomers are separated by about 3 nm and the contact order parameter is close to zero. This intermediate is stabilized by the wetting of the interface between the two monomers by the preferential distribution of ethanol and water molecules. This wetting serves to reduce the free energy barrier significantly and thus results in an increase in the rate of dimer dissociation. We also analyze the solvation of the two monomers during the dissociation and both the proteins' departure from the native state configuration to obtain valuable insights into the dimer dissociation processes.

Insulin dimer dissociation in aqueous solution: A computational study of free energy landscape and evolving microscopic structure along the reaction pathway.

The dissociation of an insulin dimer to two monomers is an important life process. Although the monomer is the biologically active form of the hormone, it is stored in the ß-cells of the pancreas in the hexameric form. The latter, when the need comes, dissociates to dimers and the dimers in turn to monomers to maintain the endogenous delivery of the hormone. In order to understand insulin dimer dissociation at a molecular level, we perform biased molecular dynamics simulations (parallel tempering metadynamics in the well-tempered ensemble) of the dissociation of the insulin dimer in water using two order parameters and an all-atom model of the protein in explicit water. The two order parameters selected (after appropriate studies) are the distance (RMM) between the center of mass of two monomers and the number of contacts (NMM) among the backbone-Cα atoms of the two monomers. We calculated the free energy landscape as a function of these two order parameters and determined the minimum free energy pathway of dissociation. We find that the pathway involves multiple minima and multiple barriers. In the initial stage of dissociation, the distance between the monomers does not change significantly but the NMM decreases rapidly. In the latter stage of separation, the opposite occurs, that is, the distance RMM increases at nearly a constant low value of NMM. The configurations of the two monomeric proteins so formed are found to be a bit different due to the entropic reasons. Water is seen to play a key role in the dissociation process stabilizing the intermediates along the reaction path. Our study reveals interesting molecular details during the dissociation, such as the variation in the structural and relative orientational arrangement of the amino acid residues along the minimum energy path. The conformational changes of monomeric insulin in the stable dimer and in the intermediate states during dimer dissociation have been studied in detail.

Enhancement of reaction rate in small-sized droplets: A combined analytical and simulation study.

Several recent mass spectrometry experiments reveal a marked enhancement of the reaction rate of organic reactions in microdroplets. This enhancement has been tentatively attributed to the accumulation of excess charge on a surface, which in turn can give rise to a lowering of activation energy of the reaction. Here we model the reactions in droplets as a three-step process: (i) diffusion of a reactant from the core of the droplet to the surface, (ii) search by diffusion of the reactant on the surface to find a reactive partner, and finally (iii) the intrinsic reaction leading to bond breaking and product formation. We obtain analytic expressions for the mean search time (MST) to find a target located on the surface by a reactant in both two- and three-dimensional droplets. Analytical results show quantitative agreement with Brownian dynamics simulations. We find, as also reported earlier, that the MST varies as R2/D, where R is the radius of the droplet and D is the diffusion constant of the molecules in the droplet medium. We also find that a hydronium ion in the vicinity can substantially weaken the bond and hence lowers the activation barrier. We observe a similar facilitation of bond breaking in the presence of a static dipolar electric field along any of the three Cartesian axes. If the intrinsic reaction is faster compared to the mean search time involved, it becomes primarily a diffusion-controlled process; otherwise the reaction cannot be accelerated in the droplet medium. The air-droplet interface provides a different environment compared to the interior of the droplet. Hence, we might also expect a completely different mechanism and products in the case of droplet reactions.

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.

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.

Alkynes as Linchpins for the Additive Annulation of Biphenyls: Convergent Construction of Functionalized Fused Helicenes.

A new approach to fused helicenes is reported, where varied substituents are readily incorporated in the extended aromatic frame. From the alkynyl precursor, the final helical compounds are obtained under mild conditions in a two-step process, in which the final C-C bond is formed via a photochemical cyclization/ dehydroiodination sequence. The distortion of the π-system from planarity leads to unusual packing in the solid state. Computational analysis reveals that substituent incorporation perturbs geometries and electronic structures of these nonplanar aromatics.

The Missing C1-C5 Cycloaromatization Reaction: Triplet State Antiaromaticity Relief and Self-Terminating Photorelease of Formaldehyde for Synthesis of Fulvenes from Enynes.

The last missing example of the four archetypical cycloaromatizations of enediynes and enynes was discovered by combining a twisted alkene excited state with a new self-terminating path for intramolecular conversion of diradicals into closed-shell products. Photoexcitation of aromatic enynes to a twisted alkene triplet state creates a unique stereoelectronic situation, which is facilitated by the relief of excited state antiaromaticity of the benzene ring. This enables the usually unfavorable 5-endo-trig cyclization and merges it with 5-exo-dig closure. The 1,4-diradical product of the C1-C5 cyclization undergoes internal H atom transfer that is coupled with the fragmentation of an exocyclic C-C bond. This sequence provides efficient access to benzofulvenes from enynes and expands the utility of self-terminating aromatizing enyne cascades to photochemical reactions. The key feature of this self-terminating reaction is that, despite the involvement of radical species in the key cyclization step, no external radical sources or quenchers are needed to provide the products. In these cascades, both radical centers are formed transiently and converted to the closed-shell products via intramolecular H-transfer and C-C bond fragmentation. Furthermore, incorporating C-C bond cleavage into the photochemical self-terminating cyclizations of enynes opens a new way for the use of alkenes as alkyne equivalents in organic synthesis.

Alkenes as alkyne equivalents in radical cascades terminated by fragmentations: overcoming stereoelectronic restrictions on ring expansions for the preparation of expanded polyaromatics.

Chemoselective interaction of aromatic enynes with Bu3Sn radicals can be harnessed for selective cascade transformations, yielding either Sn-substituted naphthalenes or Sn-indenes. Depending on the substitution at the alkene terminus, the initial regioselective 5-exo-trig cyclizations can be intercepted at the 5-exo stage via either hydrogen atom abstraction or C-S bond scission or allowed to proceed further to the formal 6-endo products via homoallylic ring expansion. Aromatization of the latter occurs via ß-C-C bond scission, which is facilitated by 2c,3e through-bond interactions, a new stereoelectronic effect in radical chemistry. The combination of formal 6-endo-trig cyclization with stereoelectronically optimized fragmentation allows the use of alkenes as synthetic equivalents of alkynes and opens a convenient route to α-Sn-substituted naphthalenes, a unique launching platform for the preparation of extended polyaromatics.

Design of leaving groups in radical C-C fragmentations: through-bond 2c-3e interactions in self-terminating radical cascades.

Radical cascades terminated by ß-scission of exocyclic CC bonds allow for the formation of aromatic products. Whereas ß-scission is common for weaker bonds, achieving this reactivity for carbon-carbon bonds requires careful design of radical leaving groups. It has now been found that the energetic penalty for breaking a strong σ-bond can be compensated by the gain of aromaticity in the product and by the stabilizing two-center, three-electron "half-bond" present in the radical fragment. Furthermore, through-bond communication of a radical and a lone pair accelerates the fragmentation by selectively stabilizing the transition state. The stereoelectronic design of radical leaving groups leads to a new, convenient route to Sn-functionalized aromatics.

Rerouting radical cascades: intercepting the homoallyl ring expansion in enyne cyclizations via C-S scission.

The switch from 5-exo- to 6-endo-trig selectivity in the radical cyclization of aromatic enynes was probed via the combination of experimental and computational methods. This transformation occurs by kinetic self-sorting of the mixture of four equilibrating radicals via 5-exo-trig cyclization, followed by homoallyl (3-exo-trig/fragmentation) ring expansion to afford the benzylic radical necessary for the final aromatizing C-C bond fragmentation. The interception of the intermediate 5-exo-trig product via ß-scission of a properly positioned weak C-S bond provides direct mechanistic evidence for the 5-exo cyclization/ring expansion sequence. The overall cascade uses alkenes as synthetic equivalents of alkynes for the convenient and mild synthesis of Bu3Sn-functionalized naphthalenes.