Cooperative Membrane Binding of HIV-1 Matrix Proteins.

The HIV-1 assembly process begins with a newly synthesized Gag polyprotein being targeted to the inner leaflet of the plasma membrane of the infected cells to form immature viral particles. Gag-membrane interactions are mediated through the myristoylated (Myr) N-terminal matrix (MA) domain of Gag, which eventually multimerize on the membrane to form trimers and higher order oligomers. The study of the structure and dynamics of peripheral membrane proteins like MA has been challenging for both experimental and computational studies due to the complex transient dynamics of protein-membrane interactions. Although the roles of anionic phospholipids (PIP2, PS) and the Myr group in the membrane targeting and stable membrane binding of MA are now well-established, the cooperative interactions between the MA monomers and MA-membrane remain elusive in the context of viral assembly and release. Our present study focuses on the membrane binding dynamics of a higher order oligomeric structure of MA protein (a dimer of trimers), which has not been explored before. Employing time-lagged independent component analysis (tICA) to our microsecond-long trajectories, we investigate conformational changes of the matrix protein induced by membrane binding. Interestingly, the Myr switch of an MA monomer correlates with the conformational switch of adjacent monomers in the same trimer. Together, our findings suggest complex protein dynamics during the formation of the immature HIV-1 lattice; while MA trimerization facilitates Myr insertion, MA trimer-trimer interactions in the immature lattice can hinder the same.

Molecular dynamics simulations of HIV-1 matrix-membrane interactions at different stages of viral maturation.

Although the structural rearrangement of the membrane-bound matrix (MA) protein trimers upon HIV-1 maturation has been reported, the consequences of MA maturation on the MA-lipid interactions are not well understood. Long-timescale molecular dynamics simulations of the MA multimeric assemblies of immature and mature virus particles with our realistic asymmetric membrane model have explored MA-lipid interactions and lateral organization of lipids around MA complexes. The number of stable MA-phosphatidylserine and MA-phosphatidylinositol 4,5-bisphosphate (PIP2) interactions at the trimeric interface of the mature MA complex is observed to be greater compared to that of the immature MA complex. Our simulations identified an alternative PIP2-binding site in the immature MA complex where the multivalent headgroup of a PIP2 lipid with a greater negative charge binds to multiple basic amino acid residues such as ARG3 residues of both the MA monomers at the trimeric interface and highly basic region (HBR) residues (LYS29, LYS31) of one of the MA monomers. Our enhanced sampling simulations have explored the conformational space of phospholipids at different binding sites of the trimer-trimer interface of MA complexes that are not accessible by conventional unbiased molecular dynamics. Unlike the immature MA complex, the 2' acyl tail of two PIP2 lipids at the trimeric interface of the mature MA complex is observed to sample stable binding pockets of MA consisting of helix-4 residues. Together, our results provide molecular-level insights into the interactions of MA trimeric complexes with membrane and different lipid conformations at the specific binding sites of MA protein before and after viral maturation.

Conformational transitions of the HIV-1 Gag polyprotein upon multimerization and gRNA binding.

During the HIV-1 assembly process, the Gag polyprotein multimerizes at the producer cell plasma membrane, resulting in the formation of spherical immature virus particles. Gag-genomic RNA (gRNA) interactions play a crucial role in the multimerization process, which is yet to be fully understood. We performed large-scale all-atom molecular dynamics simulations of membrane-bound full-length Gag dimer, hexamer, and 18-mer. The inter-domain dynamic correlation of Gag, quantified by the heterogeneous elastic network model applied to the simulated trajectories, is observed to be altered by implicit gRNA binding, as well as the multimerization state of the Gag. The lateral dynamics of our simulated membrane-bound Gag proteins, with and without gRNA binding, agree with prior experimental data and help to validate our simulation models and methods. The gRNA binding is observed to affect mainly the SP1 domain of the 18-mer and the matrix-capsid linker domain of the hexamer. In the absence of gRNA binding, the independent dynamical motion of the nucleocapsid domain results in a collapsed state of the dimeric Gag. Unlike stable SP1 helices in the six-helix bundle, without IP6 binding, the SP1 domain undergoes a spontaneous helix-to-coil transition in the dimeric Gag. Together, our findings reveal conformational switches of Gag at different stages of the multimerization process and predict that the gRNA binding reinforces an efficient binding surface of Gag for multimerization, and also regulates the dynamic organization of the local membrane region itself.

Cooperative Membrane Binding of HIV-1 Matrix Proteins.

The HIV-1 assembly process begins with a newly synthesized Gag polyprotein being targeted to the inner leaflet of the plasma membrane of the infected cells to form immature viral particles. Gag-membrane interactions are mediated through the myristoylated(Myr) N-terminal matrix (MA) domain of Gag which eventually multimerize on the membrane to form trimers and higher-order oligomers. The study of the structure and dynamics of peripheral membrane proteins like MA has been challenging for both experimental and computational studies due to the complex dynamics of protein-membrane interactions. Although the roles of anionic phospholipids (PIP2, PS) and the Myr group in the membrane targeting and stable membrane binding of MA are now well-established, the cooperative interactions between MA monomers and MA-membrane still remain elusive. Our present study focuses on the membrane binding dynamics of a higher-order oligomeric structure of MA protein (a dimer of trimers), which has not been explored before. Employing time-lagged independent component analysis (tICA) to our microsecond-long trajectories, we investigate conformational changes of the matrix protein induced by membrane binding. Interestingly, the Myr switch of a MA monomer correlates with the conformational switch of adjacent monomers in the same trimer. Together, our findings suggest that MA trimerization facilitates Myr insertion, but MA trimer-trimer interactions in the lattice of immature HIV-1 particles can hinder the same. Additionally, local lipid density patterns of different lipid species provide a signature of the initial stage of lipid-domain formation upon membrane binding of the protein complex.

Conformational transitions of the HIV-1 Gag polyprotein upon multimerization and gRNA binding.

During the HIV-1 assembly process, the Gag polyprotein multimerizes at the producer cell plasma membrane, resulting in the formation of spherical immature virus particles. Gag-gRNA interactions play a crucial role in the multimerization process, which is yet to be fully understood. We have performed large-scale all-atom molecular dynamics simulations of membrane-bound full-length Gag dimer, hexamer, and 18-mer. The inter-domain dynamic correlation of Gag, quantified by the heterogeneous elastic network model (hENM) applied to the simulated trajectories, is observed to be altered by implicit gRNA binding, as well as the multimerization state of the Gag. The lateral dynamics of our simulated membrane-bound Gag proteins, with and without gRNA binding, agree with prior experimental data and help to validate our simulation models and methods. The gRNA binding is observed to impact mainly the SP1 domain of the 18-mer and the MA-CA linker domain of the hexamer. In the absence of gRNA binding, the independent dynamical motion of the NC domain results in a collapsed state of the dimeric Gag. Unlike stable SP1 helices in the six-helix bundle, without IP6 binding, the SP1 domain undergoes a spontaneous helix-to-coil transition in the dimeric Gag. Together, our findings reveal conformational switches of Gag at different stages of the multimerization process and predict that the gRNA binding reinforces an efficient binding surface of Gag for multimerization, as well as regulates the dynamic organization of the local membrane region itself. Significance: Gag(Pr 55 Gag ) polyprotein orchestrates many essential events in HIV-1 assembly, including packaging of the genomic RNA (gRNA) in the immature virion. Although various experimental techniques, such as cryo-ET, X-ray, and NMR, have revealed structural properties of individual domains in the immature Gag clusters, structural and biophysical characterization of a full-length Gag molecule remains a challenge for existing experimental techniques. Using atomistic molecular dynamics simulations of the different model systems of Gag polyprotein, we present here a detailed structural characterization of Gag molecules in different multimerization states and interrogate the synergy between Gag-Gag, Gag-membrane, and Gag-gRNA interactions during the viral assembly process.

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.

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.

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.

Dynamics of linear molecules in water: Translation-rotation coupling in jump motion driven diffusion.

We study by computer simulations, and by theory, the coupled rotational and translational dynamics of three important linear diatomic molecules, namely, carbon monoxide (CO), nitric oxide (NO), and cyanide ion (CN-) in water. Translational diffusion of these molecules is found to be strongly coupled to their own rotational dynamics which, in turn, are coupled to similar motions of the surrounding water. In particular, we find that coupled orientational jump motions play an important role in all three cases. While CO and NO show similar features, CN- exhibits certain differences. Our results agree well with the known experimental values of the diffusion coefficient. We examined the validity of hydrodynamic predictions and found them to be inadequate, particularly for rotational diffusion. A mode coupling theory approach is developed and applied to understand the complexity of translation-rotation coupling.

Ions' motion in water.

Over the decades, a great deal of attention has been focused on the solvation and transport properties of small rigid monatomic ions such as Na+, K+, Li+, Cl-, and Br- due to their importance in physical chemistry. Much less attention has been devoted to polyatomic ions although many polyatomic ions (such as nitrate, acetate, sulfate, and ammonium) are of great importance in biological and chemical processes. While the translational diffusion of smaller rigid ions shows the remarkable nonmonotonic dependence on inverse ion size (known as the "breakdown of Walden product"), the intermediate- to large-sized polyatomic ions (such as nitrate, acetate, and sulfate) exhibit different anomalies pointed out only recently. In this Perspective article, we provide an overview of how rotational diffusion and translational diffusion of these ions themselves are coupled to translational and rotational motions of water molecules. We discuss how diffusion of polyatomic ions is different from that of monatomic ions due to the rotational self-motion of the former that enhances diffusion in specific cases because of symmetry. While a continuum hydrodynamic model fails to describe the motion of polyatomic ions, we discuss how a mode-coupling theory approach can capture many aspects of this coupling between the solute ion and solvent water. We discuss how ionic mobility in water and other dipolar solvents are intimately connected to the dipolar solvation dynamics, in particular to its ultrafast component. We point out how the usual thinking on the relation between the diffusion and entropy needs to be modified in the case of ion diffusion.

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.

Effects of metastable phases on surface tension, nucleation, and the disappearance of polymorphs.

In nature, we often find that multiple solid phases form from the same solution. Zeolites present the best-known example. The preferential formation of one solid form over the other, at specific temperatures, is often explained by invoking a competition between thermodynamic and kinetic control. A quantitative theory, however, could not be developed because of the lack of accurate values of relevant surface tension terms, although some estimates of thermodynamic functions (like enthalpy and entropy) are becoming available. Motivated by the observation that wetting of the interface between two stable phases by multiple metastable phases of intermediate order can reduce the surface tension significantly [T. R. Kirkpatrick, D. Thirumalai, and P. G. Wolynes, Phys. Rev. A 40(2), 1045 (1989)], we develop a statistical mechanical approach based on a Landau-Ginzburg type free energy landscape to calculate the surface tension under various free energy situations. We analyze the trapping of a metastable phase in the presence of a thermodynamically stable phase. The interplay between free energy differences and the surface tension is partly captured in classical nucleation theory. We provide an explanation of the quickly disappearing polymorphs (QDPMs) that often melt back to the liquid (or the sol) phase. To this aim, we have presented the failure of classical nucleation theory and the importance of considering a multidimensional nucleation theory. Simple model calculations are performed to show that the surface tension between two coexisting stable phases (melt and the stable crystalline forms) depends significantly on the number, relative depths, and arrangements of the free energy minima of the metastable phases. Even a change in the curvature of the free energy surfaces induced by the change in temperature (T) can play a role in determining the sequence of the formation of phases. Finally, we show that our model systems could describe some of the real polymorphic systems, like phosphates and zeolites.

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.

Rotational dynamics of polyatomic ions in aqueous solutions: From continuum model to mode-coupling theory, aided by computer simulations.

Due to the presence of the rotational mode and the distributed surface charges, the dynamical behavior of polyatomic ions in water differs considerably from those of the monatomic ions. However, their fascinating dynamical properties have drawn scant attention. We carry out theoretical and computational studies of a series of well-known polyatomic ions, namely, sulfate, nitrate, and acetate ions. All three ions exhibit different rotational diffusivity, with that of the nitrate ion being considerably larger than the other two. They all defy the hydrodynamic laws of size dependence. Study of the local structure around the ions provides valuable insight into the origin of these differences. We carry out a detailed study of the rotational diffusion of these ions by extensive computer simulation and by using the theoretical approaches of the dielectric friction developed by Fatuzzo-Mason (FM) and Nee-Zwanzig (NZ), and subsequently generalized by Alavi and Waldeck. A critical element of the FM-NZ theory is the decomposition of the total rotational friction, ζRot, into Stokes and dielectric parts. The study shows a dominant role of dielectric friction in the sense that if the ions are made neutral, the nature of diffusion changes and the values become much larger. Our analyses further reveal that the decomposition of total friction into the Stokes and dielectric friction breaks down for sulfate ions but remains semi-quantitatively valid for nitrate and acetate ions. We discuss the relationship between translational and rotational dielectric friction on rigid spherical ions. We develop a self-consistent mode-coupling theory (SC-MCT) formalism that could provide a unified view of rotational friction of polyatomic ions in polar medium. Our SC-MCT shows that the breakdown can be attributed to the change in the microscopic structural features. The mode-coupling theory helps in elucidating the role of coupling between translational and rotational motion of these ions. In fact, these two motions self-consistently determine the value of each other. The reference interaction site model-based MCT suggests an interesting relation between the torque-torque and the force-force time correlation function with the proportionality constant being determined by the geometry and the charge distribution of the polyatomic molecule. We point out several parallelisms between the theories of translational and rotation friction calculations of ions in polar liquids.

A mode-coupling theory analysis of the observed diffusion anomaly in aqueous polyatomic ions.

In contrast to simple monatomic alkali and halide ions, complex polyatomic ions such as nitrate, acetate, nitrite, and chlorate have not been studied in any great detail. Experiments have shown that diffusion of polyatomic ions exhibits many remarkable anomalies; notable among them is the fact that polyatomic ions with similar size show large difference in their diffusivity values. This fact has drawn relatively little interest in scientific discussions. We show here that a mode-coupling theory can provide a physically meaningful interpretation of the anomalous diffusivity of polyatomic ions in water, by including the contribution of rotational jumps on translational friction. The two systems discussed here, namely, aqueous nitrate ion and aqueous acetate ion, although have similar ionic radii, exhibit largely different diffusivity values due to the differences in the rate of their rotational jump motions. We have further verified the mode-coupling theory formalism by comparing it with experimental and simulation results that agree well with the theoretical prediction.

Rotation driven translational diffusion of polyatomic ions in water: A novel mechanism for breakdown of Stokes-Einstein relation.

While most of the existing theoretical and simulation studies have focused on simple, spherical, halide and alkali ions, many chemically, biologically, and industrially relevant electrolytes involve complex non-spherical polyatomic ions like nitrate, chlorate, and sulfate to name only a few. Interestingly, some polyatomic ions in spite of being larger in size show anomalously high diffusivity and therefore cause a breakdown of the venerable Stokes-Einstein (S-E) relation between the size and diffusivity. Here we report a detailed analysis of the dynamics of anions in aqueous potassium nitrate (KNO3) and aqueous potassium acetate (CH3COOK) solutions. The two ions, nitrate (NO3-) and acetate (CH3CO2-), with their similar size show a large difference in diffusivity values. We present evidence that the translational motion of these polyatomic ions is coupled to the rotational motion of the ion. We show that unlike the acetate ion, nitrate ion with a symmetric charge distribution among all periphery oxygen atoms shows a faster rotational motion with large amplitude rotational jumps which enhances its translational motion due to translational-rotational coupling. By creating a family of modified-charge model systems, we have analysed the rotational motion of asymmetric polyatomic ions and the contribution of it to the translational motion. These model systems help clarifying and establishing the relative contribution of rotational motion in enhancing the diffusivity of the nitrate ion over the value predicted by the S-E relation and also over the other polyatomic ions having asymmetric charge distribution like the acetate ion. In the latter case, reduced rotational motion results in lower diffusivity values than those with symmetric charge distribution. We propose translational-rotational coupling as a general mechanism of the breakdown of the S-E relation in the case of polyatomic ions.

Coupled jump rotational dynamics in aqueous nitrate solutions.

A nitrate ion (NO3-) with its trigonal planar geometry and charges distributed among nitrogen and oxygen atoms can couple to the extensive hydrogen bond network of water to give rise to unique dynamical characteristics. We carry out detailed atomistic simulations and theoretical analyses to investigate these aspects and report certain interesting findings. We find that the nitrate ions in aqueous potassium nitrate solution exhibit large amplitude rotational jump motions that are coupled to the hydrogen bond rearrangement dynamics of the surrounding water molecules. The jump motion of nitrate ions bears certain similarities to the Laage-Hynes mechanism of rotational jump motions of tagged water molecules in neat liquid water. We perform a detailed atomic-level investigation of hydrogen bond rearrangement dynamics of water in aqueous KNO3 solution to unearth two distinct mechanisms of hydrogen bond exchange that are instrumental to promote these jump motions of nitrate ions. As observed in an earlier study by Xie et al., in the first mechanism, after breaking a hydrogen bond with nitrate ion, water forms a new hydrogen bond with a water molecule, whereas the second mechanism involves just a switching of hydrogen bond between the two oxygen atoms of the same nitrate ion (W. J. Xie et al., J. Chem. Phys. 143, 224504 (2015)). The magnitude as well as nature of the reorientational jump of nitrate ion for the two mechanisms is different. In the first mechanism, nitrate ion predominantly undergoes out-of-plane rotation, while in the second mechanism, in-plane reorientation of NO3- is favourable. These have been deduced by computing the torque on the nitrate ion during the hydrogen bond switching event. We have defined and computed the time correlation function for coupled reorientational jump of nitrate and water and obtained the associated relaxation time which is also different for the two mechanisms. These results provide insight into the relation between the coupled reorientational jump dynamics of solute and solvent molecules.