Anomalous Vapor and Ice Nucleation in Water at Negative Pressures: A Classical Density Functional Theory Study.

In contrast to the abundance of work on the anomalous behavior of water, the relationship between the water's thermodynamic anomalies and kinetics of phase transition from metastable water is relatively unexplored. In this work, we have employed classical density functional theory to provide a unified and coherent picture of nucleation (both vapor and ice) from metastable water at negative pressure conditions. Our results suggest a peculiar nonmonotonic temperature dependence of vapor-liquid surface tension at temperatures where vapor-liquid coexistence is metastable with respect to the ice phase. The vapor nucleation barrier on isochoric cooling also shows a nonmonotonic temperature dependence. We further report that, for low density isochores, the temperature of the minimum vapor nucleation barrier (TΔΩv/min*) does not coincide with the temperature of maximum density (TMD) where metastability is maximum. The difference between the TΔΩv/min* and the TMD, however, decreases with increasing the density of the isochore. The vapor nucleation barrier along isobars shows an interesting crossover behavior in the vicinity of the Widom line on lowering the temperature. Our results on the ice nucleation suggest an anomalous retracing behavior of the nucleation barrier along isotherms at negative pressures and theoretically validate the recent findings that the reentrant ice(Ih)-liquid coexistence line can induce a drastic change in the kinetics of ice nucleation. Thus, this study establishes a direct connection between the metastable water's thermodynamic anomalies and the (vapor and ice) nucleation kinetics. In addition, this study provides deeper insights into the origin of the isothermal compressibility maximum on isochoric cooling.

Structural and dynamical heterogeneity of water trapped inside Na+-pumping KR2 rhodopsin in the dark state.

Photoisomerization in the retinal leads to a channel opening in rhodopsins that triggers translocation or pumping of ions/protons. Crystal structures of rhodopsins contain several structurally conserved water molecules. It has been suggested that water plays an active role in facilitating the ion pumping/translocation process by acting as a lubricant in these systems. In this paper, we systematically investigate the localization, structure, dynamics, and energetics of the water molecules along the channel for the resting/dark state of KR2 rhodopsin. By employing several microseconds long atomistic molecular dynamics simulation of this trans-membrane protein system, we demonstrate the presence of five distinct water containing pockets/cavities separated by gateways controlled by protein side-chains. There exists a strong hydrogen bonded network involving these buried water molecules and functionally important key residues. We present evidence of significant structural and dynamical heterogeneity in the water molecules present in these cavities, with very rare exchange between them. The exchange time scale of such buried water with the bulk has an extremely wide range, from tens of nanoseconds to >1.5 µs. The translational and rotational dynamics of buried water are found to be strongly dependent on the protein cavity size and local interactions with a classic signature of trapped diffusion and rotational anisotropy.

Proteostasis collapse is a driver of cell aging and death.

What molecular processes drive cell aging and death? Here, we model how proteostasis-i.e., the folding, chaperoning, and maintenance of protein function-collapses with age from slowed translation and cumulative oxidative damage. Irreparably damaged proteins accumulate with age, increasingly distracting the chaperones from folding the healthy proteins the cell needs. The tipping point to death occurs when replenishing good proteins no longer keeps up with depletion from misfolding, aggregation, and damage. The model agrees with experiments in the worm Caenorhabditis elegans that show the following: Life span shortens nonlinearly with increased temperature or added oxidant concentration, and life span increases in mutants having more chaperones or proteasomes. It predicts observed increases in cellular oxidative damage with age and provides a mechanism for the Gompertz-like rise in mortality observed in humans and other organisms. Overall, the model shows how the instability of proteins sets the rate at which damage accumulates with age and upends a cell's normal proteostasis balance.

How Do Chaperones Protect a Cell's Proteins from Oxidative Damage?

The accumulation of protein damage in aging organisms is thought to contribute to many aging-related diseases. Yet the properties determining which proteins are most susceptible remain poorly understood. Are certain conformations more vulnerable? Which chaperones are the main guardians? We address these questions with a system-wide model of E. coli proteostasis. By predicting how proteins with different folding properties respond to each chaperone's concentration, the model computes "damage fingerprints" that identify unfolded conformations as the major damage target. What matters most is not a protein's stability or difficulty of folding, but its dwell time in an unfolded state. The main guardian chaperone is DnaK because its client proteins spend more time unfolded than clients of GroEL, providing a mechanism for why the cell's capacity to handle stress is more sensitive to DnaK levels. Also, we find that chaperones are protectors, not recyclers. This model describes how cells resist stress and indicates that designing chaperone-targeting drugs may require whole-cell, system-wide modeling.

Bacterial proteostasis balances energy and chaperone utilization efficiently.

Chaperones are protein complexes that help to fold and disaggregate a cell's proteins. It is not understood how four major chaperone systems of Escherichia coli work together in proteostasis: the recognition, sorting, folding, and disaggregating of the cell's many different proteins. Here, we model this machine. We combine extensive data on chaperoning, folding, and aggregation rates with expression levels of proteins and chaperones measured at different growth rates. We find that the proteostasis machine recognizes and sorts a client protein based on two biophysical properties of the client's misfolded state (M state): its stability and its kinetic accessibility from its unfolded state (U state). The machine is energy-efficient (the sickest proteins use the most ATP-expensive chaperones), comprehensive (it can handle any type of protein), and economical (the chaperone concentrations are just high enough to keep the whole proteome folded and disaggregated but no higher). The cell needs higher chaperone levels in two situations: fast growth (when protein production rates are high) and very slow growth (to mitigate the effects of protein degradation). This type of model complements experimental knowledge by showing how the various chaperones work together to achieve the broad folding and disaggregation needs of the cell.

Solid-liquid transition in polydisperse Lennard-Jones systems.

We study melting of a face-centered crystalline solid consisting of polydisperse Lennard-Jones spheres with Gaussian polydispersity in size. The phase diagram reproduces the existence of a nearly temperature invariant terminal polydispersity (δ(t) =/~ 0.11), with no signature of reentrant melting. The absence of reentrant melting can be attributed to the influence of the attractive part of the potential upon melting. We find that at terminal polydispersity the fractional density change approaches zero, which seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction the system undergoes a sharp transition from crystalline solid to the disordered amorphous or fluid state with increasing polydispersity. This has been quantified by second- and third-order rotational invariant bond orientational order, as well as by the average inherent structure energy. The translational order parameter also indicates a similar sharp structural change at δ =/~ 0.09 in case of T(*) = 1.0, φ = 0.58. The free energy calculation further supports the sharp nature of the transition. The third-order rotationally invariant bond order shows that with increasing polydispersity, the local cluster favors a more icosahedral arrangement and the system loses its local crystalline symmetry. Interestingly, the value of structure factor S(k) of the amorphous phase at δ =/~ 0.10 (just beyond the solid-liquid transition density at T(*) = 1) becomes 2.75, which is below the value of 2.85 required for freezing given by the empirical Hansen-Verlet rule of crystallization, well known in the theory of freezing.

Kinetic proofreading at single molecular level: aminoacylation of tRNA(Ile) and the role of water as an editor.

Proofreading/editing in protein synthesis is essential for accurate translation of information from the genetic code. In this article we present a theoretical investigation of efficiency of a kinetic proofreading mechanism that employs hydrolysis of the wrong substrate as the discriminatory step in enzyme catalytic reactions. We consider aminoacylation of tRNA(Ile) which is a crucial step in protein synthesis and for which experimental results are now available. We present an augmented kinetic scheme and then employ methods of stochastic simulation algorithm to obtain time dependent concentrations of different substances involved in the reaction and their rates of formation. We obtain the rates of product formation and ATP hydrolysis for both correct and wrong substrates (isoleucine and valine in our case, respectively), in single molecular enzyme as well as ensemble enzyme kinetics. The present theoretical scheme correctly reproduces (i) the amplitude of the discrimination factor in the overall rates between isoleucine and valine which is obtained as (1.8×10(2)).(4.33×10(2)) = 7.8×10(4), (ii) the rates of ATP hydrolysis for both Ile and Val at different substrate concentrations in the aminoacylation of tRNA(Ile). The present study shows a non-michaelis type dependence of rate of reaction on tRNA(Ile) concentration in case of valine. The overall editing in steady state is found to be independent of amino acid concentration. Interestingly, the computed ATP hydrolysis rate for valine at high substrate concentration is same as the rate of formation of Ile-tRNA(Ile) whereas at intermediate substrate concentration the ATP hydrolysis rate is relatively low. We find that the presence of additional editing domain in class I editing enzyme makes the kinetic proofreading more efficient through enhanced hydrolysis of wrong product at the editing CP1 domain.

Anisotropy induced crossover from weakly to strongly first order melting of two dimensional solids.

Melting and freezing transitions in two dimensional (2D) systems are known to show highly unusual characteristics. Most of the earlier studies considered atomic systems: the melting of 2D molecular solids is still largely unexplored. In order to understand the role of anisotropy as well as multiple energy and length scales present in molecular systems, here we report computer simulation studies of melting of 2D molecular systems. We computed a limited portion of the solid-liquid phase diagram. We find that the interplay between the strength of isotropic and anisotropic interactions can give rise to rich phase diagram consisting of isotropic liquid and two crystalline phases-honeycomb and oblique. The nature of the transition depends on the relative strength of the anisotropic interaction and a strongly first order melting turns into a weakly first order transition on increasing the strength of the isotropic interaction. This crossover can be attributed to an increase in stiffness of the solid phase free energy minimum on increasing the strength of the anisotropic interaction. The defects involved in melting of molecular systems are quite different from those known for the atomic systems.

Nucleation of a stable solid from melt in the presence of multiple metastable intermediate phases: wetting, Ostwald's step rule, and vanishing polymorphs.

In many systems, nucleation of a stable solid may occur in the presence of other (often more than one) metastable phases. These may be polymorphic solids or even liquid phases. Sometimes, the metastable phase might have a lower free energy minimum than the liquid but higher than the stable-solid-phase minimum and have characteristics in between the parent liquid and the globally stable solid phase. In such cases, nucleation of the solid phase from the melt may be facilitated by the metastable phase because the latter can "wet" the interface between the parent and the daughter phases, even though there may be no signature of the existence of metastable phase in the thermodynamic properties of the parent liquid and the stable solid phase. Straightforward application of classical nucleation theory (CNT) is flawed here as it overestimates the nucleation barrier because surface tension is overestimated (by neglecting the metastable phases of intermediate order) while the thermodynamic free energy gap between daughter and parent phases remains unchanged. In this work, we discuss a density functional theory (DFT)-based statistical mechanical approach to explore and quantify such facilitation. We construct a simple order-parameter-dependent free energy surface that we then use in DFT to calculate (i) the order parameter profile, (ii) the overall nucleation free energy barrier, and (iii) the surface tension between the parent liquid and the metastable solid and also parent liquid and stable solid phases. The theory indeed finds that the nucleation free energy barrier can decrease significantly in the presence of wetting. This approach can provide a microscopic explanation of the Ostwald step rule and the well-known phenomenon of "disappearing polymorphs" that depends on temperature and other thermodynamic conditions. Theory reveals a diverse scenario for phase transformation kinetics, some of which may be explored via modern nanoscopic synthetic methods.

Catalysis of tRNA aminoacylation: single turnover to steady-state kinetics of tRNA synthetases.

Aminoacyl-tRNA synthetases (aaRS) catalyze the bimolecular association reaction between amino acid and tRNA by specifically and unerringly choosing the cognate amino acid and tRNA. There are two classes of such synthetases that perform tRNA-aminoacylation reaction. Interestingly, these two classes of aminoacyl-tRNA synthetases differ not only in their structures but they also exhibit remarkably distinct kinetics under pre-steady-state condition. The class I synthetases show initial burst of product formation followed by a slower steady-state rate. This has been argued to represent the influence of slow product release. In contrast, there is no burst in the case of class II enzymes. The tight binding of product with enzyme for class I enzymes is correlated with the enhancement of rate in presence of elongation factor EF-TU. In spite of extensive experimental studies, there is no detailed theoretical analysis that can provide a quantitative understanding of this important problem. In this article, we present a theoretical investigation of enzyme kinetics for both classes of aminoacyl-tRNA synthetases. We present an augmented kinetic scheme and then employ the methods of time-dependent probability statistics to obtain expressions for the first passage time distribution that gives both the time-dependent and the steady-state rates. The present study quantitatively explains all the above experimental observations. We propose an alternative path way in the case of class II enzymes showing the tRNA-dependent amino acid activation and the discrepancy between the single-turnover and steady-state rate.

Sensitivity of nucleation phenomena on range of interaction potential.

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.

Crossover dynamics at large metastability in gas-liquid nucleation.

We have developed an alternate description of dynamics of nucleation in terms of an extended set of order parameters. The order parameters consist of an ordered set of kth largest clusters, ordered such that k= 1 is the largest cluster in the system, k= 2 is the second largest cluster, and so on. We have derived an analytic expression for the free energy for the kth largest cluster, which is in excellent agreement with the simulated results. At large supersaturation, the free energy barrier for the growth of the kth largest cluster disappears and the nucleation becomes barrierless. The major success of this extended theoretical formalism is that it can clearly explain the observed change in mechanism at large metastability [P. Bhimalapuram et al., Phys. Rev. Lett. 98, 206104 (2007)] and the associated dynamical crossover. The classical nucleation theory cannot explain this crossover. The crossover from activated to barrierless nucleation is found to occur at a supersaturation where multiple clusters cross the critical size. We attribute the crossover as the onset of the kinetic spinodal. We have derived an expression for the rate of nucleation in the barrierless regime by modeling growth as diffusion on the free energy surface of the largest cluster. The model reproduces the slower increase in the rate of growth as a function of supersaturation, as observed in experiments.

Line tension of a two dimensional gas-liquid interface.

In two dimensional (2D) gas-liquid systems, the reported simulation values of line tension are known to disagree with the existing theoretical estimates. We find that while the simulation erred in truncating the range of the interaction potential, and as a result grossly underestimated the actual value, the earlier theoretical calculation was also limited by several approximations. When both the simulation and the theory are improved, we find that the estimate of line tension is in better agreement with each other. The small value of surface tension suggests increased influence of noncircular clusters in 2D gas-liquid nucleation, as indeed observed in a recent simulation.

Gas-liquid nucleation in a two dimensional system.

We study the nucleation of liquid phase from a supersaturated vapor in two dimensions, where the particles interact through Lennard-Jones (LJ) pairwise potential. Using different Monte Carlo simulation methods, we calculate the free energy barrier for nucleation, the line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinodal limit). In two dimensions, a surprisingly large cutoff (r(c) > or = 7.0sigma, sigma is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff [typically 2.5sigma which is generally sufficient in three dimensional (3D) studies] leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. It is found that in two dimensions, the classical nucleation theory (CNT) fails to provide a reliable estimate of the free energy barrier. It underestimates the barrier by as much as 50% at the saturation ratio S = 1.1 (defined as S = P/P(C), where P(C) is the coexistence pressure) and at the reduced temperature T(*) = 0.427 (defined as T(*) = k(B)T/epsilon, where epsilon is the depth of the potential well). Interestingly, CNT has been found to overestimate the nucleation free energy barrier in 3D systems near the triple point. In fact, the agreement of the calculated nucleation rate with CNT is much worse in two dimensions than in three dimensions. The reason for the inadequacy of the CNT can be attributed to the noncircular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable noncircular nature remains even without any cutoff to make the simple CNT inaccurate.