Water's potential role: Insights from studies of the p53 core domain

Soluble proteins with amyloidogenic propensity such as the tumor suppressor protein p53 have high proportion of incompletely desolvated backbone H bonds (HB). Such bonds are vulnerable to water attack, thus potentially leading to the misfolding of these proteins. However, it is still not clear how the surrounding solvent influences the protein native states. To address this, systematic surveys by molecular dynamics simulations and entropy analysis were performed on the p53 core domain in this work. We examined seven wild/mutant X-ray structures and observed two types of water-network hydration in three "hot hydration centers" (DNA- or small molecule- binding surfaces of the p53 core domain). The "tight" water, resulting from the local collective hydrogen-bond interactions, is probably fundamental to the protein structural stability. The second type of water is highly "dynamical" and exchanges very fast within the bulk solution, which is unambiguously assisted by the local protein motions. An entropy mapping of the solvent around the protein and a temperature perturbation analysis further present the main features of the p53 hydration network. The particular environment created by different water molecules around the p53 core domain also partly explains the structural vulnerabilities of this protein.     

Collective dynamics of EcoRI-DNA complex by elastic network model and molecular dynamics simulations

Anisotropic network model (ANM) is used to analyze the collective motions of restriction enzyme EcoRI in free form and in complex with DNA. For comparison, three independent molecular dynamics (MD) simulations, each of 1.5 ns duration, are also performed for the EcoRI-DNA complex in explicit water. Although high mobility (equilibrium fluctuations) of inner and outer loops that surround the DNA is consistent in both methods and experiments, MD runs sample different conformational subspaces from which reliable collective dynamics cannot be extracted. However, ANM employed on different conformations from MD simulations indicates very similar collective motions. The stems of the inner loops are quite immobile even in the free enzyme and form a large, almost fixed, pocket for DNA binding. As a result, the residues that make specific and non-specific interactions with the DNA exhibit very low fluctuations in the free enzyme. The vibrational entropy difference between the EcoRI complex and free protein + unkinked DNA is positive (favorable), which may partially counteract the unfavorable enthalpy difference of DNA kink formation. Dynamic domains in EcoRI complex and cross-correlations between residue fluctuations indicate possible means of communication between the distal active sites.     

Structure and in silico simulations of a cold-active esterase reveals its prime cold-adaptation mechanism

Here we determined the structure of a cold active family IV esterase (EstN7) cloned from Bacillus cohnii strain N1. EstN7 is a dimer with a classical α/β hydrolase fold. It has an acidic surface that is thought to play a role in cold-adaption by retaining solvation under changed water solvent entropy at lower temperatures. The conformation of the functionally important cap region is significantly different to EstN7''s closest relatives, forming a bridge-like structure with reduced helical content providing greater access to the active site through more than one substrate access tunnel. However, dynamics do not appear to play a major role in cold adaption. Molecular dynamics at different temperatures, rigidity analysis, normal mode analysis and geometric simulations of motion confirm the flexibility of the cap region but suggest that the rest of the protein is largely rigid. Rigidity analysis indicates the distribution of hydrophobic tethers is appropriate to colder conditions, where the hydrophobic effect is weaker than in mesophilic conditions due to reduced water entropy. Thus, it is likely that increased substrate accessibility and tolerance to changes in water entropy are important for of EstN7''s cold adaptation rather than changes in dynamics.     

Temperature-dependent folding pathways of Pin1 WW domain: an all-atom molecular dynamics simulation of a Gō model

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded beta-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small beta-protein at its folding transition temperature has a well-established hairpin 1 made of beta1 and beta2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of beta2 and beta3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.     

Cold adaptation of enzyme reaction rates

A major issue for organisms living at extreme temperatures is to preserve both stability and activity of their enzymes. Cold-adapted enzymes generally have a reduced thermal stability, to counteract freezing, and show a lower enthalpy and a more negative entropy of activation compared to mesophilic and thermophilic homologues. Such a balance of thermodynamic activation parameters can make the reaction rate decrease more linearly, rather than exponentially, as the temperature is lowered, but the structural basis for rate optimization toward low working temperatures remains unclear. In order to computationally address this problem, it is clear that reaction simulations rather than standard molecular dynamics calculations are needed. We have thus carried out extensive computer simulations of the keto-enol(ate) isomerization steps in differently adapted citrate synthases to explore the structure-function relationships behind catalytic rate adaptation to different temperatures. The calculations reproduce the absolute rates of the psychrophilic and mesophilic enzymes at 300 K, as well as the lower enthalpy and more negative entropy of activation of the cold-adapted enzyme, where the latter simulation result is obtained from high-precision Arrhenius plots. The overall catalytic effect originates from electrostatic stabilization of the transition state and enolate and the reduction of reorganization free energy. The simulations, however, show psychrophilic, mesophilic, and hyperthermophilic citrate synthases to have increasingly stronger electrostatic stabilization of the transition state, while the energetic penalty in terms of internal protein interactions follows the reverse order with the cold-adapted enzyme having the most favorable energy term. The lower activation enthalpy and more negative activation entropy observed for cold-adapted enzymes are found to be associated with a decreased protein stiffness. The origin of this effect is, however, not localized to the active site but to other regions of the protein structure.     

Structure and dynamics of parallel beta-sheets, hydrophobic core, and loops in Alzheimer's A beta fibrils

We explore the relative contributions of different structural elements to the stability of Abeta fibrils by molecular-dynamics simulations performed over a broad range of temperatures (298 K to 398 K). Our fibril structures are based on solid-state nuclear magnetic resonance experiments of Abeta(1-40) peptides, with sheets of parallel beta-strands connected by loops and stabilized by interior salt bridges. We consider models with different interpeptide interfaces, and different staggering of the N- and C-terminal beta-strands along the fibril axis. Multiple 10-20 ns molecular-dynamics simulations show that fibril segments with 12 peptides are stable at ambient temperature. The different models converge toward an interdigitated side-chain packing, and present water channels solvating the interior D23/K28 salt bridges. At elevated temperatures, we observe the early phases of fibril dissociation as a loss of order in the hydrophilic loops connecting the two beta-strands, and in the solvent-exposed N-terminal beta-sheets. As the most dramatic structural change, we observe collective sliding of the N- and C-terminal beta-sheets on top of each other. The interior C-terminal beta-sheets in the hydrophobic core remain largely intact, indicating that their formation and stability is crucial to the dissociation/elongation and stability of Abeta fibrils.     

Use of multistate Bennett acceptance ratio method for free-energy calculations from enhanced sampling and free-energy perturbation

Multistate Bennett acceptance ratio (MBAR) works as a method to analyze molecular dynamics (MD) simulation data after the simulations have been finished. It is widely used to estimate free-energy changes between different states and averaged properties at the states of interest. MBAR allows us to treat a wide range of states from those at different temperature/pressure to those with different model parameters. Due to the broad applicability, the MBAR equations are rather difficult to apply for free-energy calculations using different types of MD simulations including enhanced conformational sampling methods and free-energy perturbation. In this review, we first summarize the basic theory of the MBAR equations and categorize the representative usages into the following four: (i) perturbation, (ii) scaling, (iii) accumulation, and (iv) full potential energy. For each, we explain how to prepare input data using MD simulation trajectories for solving the MBAR equations. MBAR is also useful to estimate reliable free-energy differences using MD trajectories based on a semi-empirical quantum mechanics/molecular mechanics (QM/MM) model and ab initio QM/MM energy calculations on the MD snapshots. We also explain how to use the MBAR software in the GENESIS package, which we call mbar_analysis, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.     

Reduced Model and Simulation of Neuron with Passive Dendritic Cable: An Eigenfunction Expansion Approach

The neuron models with passive dendritic cables are often used for detailed cortical network simulations (Protopapas et al., 1998; Suarez et al., 1995). For this, the compartment model based on finite volume or finite difference discretization was used. In this paper, we propose an eigenfunction expansion approach combined with singular perturbation and demonstrate that the proposed scheme can achieve an order of magnitude accuracy improvement with the same number of equations. Moreover, it is also shown that the proposed scheme converges much faster to attain a given accuracy. Hence, for a network simulation of the neurons with passive dendritic cables, the proposed scheme can be an attractive alternative to the compartment model, that leads to a low order model with much higher accuracy or that converges faster for a given accuracy.     

Cluster Formation of Anchored Proteins Induced by Membrane-Mediated Interaction

Computer simulations were used to study the cluster formation of anchored proteins in a membrane. The rate and extent of clustering was found to be dependent upon the hydrophobic length of the anchored proteins embedded in the membrane. The cluster formation mechanism of anchored proteins in our work was ascribed to the different local perturbations on the upper and lower monolayers of the membrane and the intermonolayer coupling. Simulation results demonstrated that only when the penetration depth of anchored proteins was larger than half the membrane thickness, could the structure of the lower monolayer be significantly deformed. Additionally, studies on the local structures of membranes indicated weak perturbation of bilayer thickness for a shallowly inserted protein, while there was significant perturbation for a more deeply inserted protein. The origin of membrane-mediated protein-protein interaction is therefore due to the local perturbation of the membrane thickness, and the entropy loss—both of which are caused by the conformation restriction on the lipid chains and the enhanced intermonolayer coupling for a deeply inserted protein. Finally, in this study we addressed the difference of cluster formation mechanisms between anchored proteins and transmembrane proteins.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Microsecond simulations of the folding/unfolding thermodynamics of the Trp‐cage miniprotein

We study the unbiased folding/unfolding thermodynamics of the Trp‐cage miniprotein using detailed molecular dynamics simulations of an all‐atom model of the protein in explicit solvent using the Amberff99SB force field. Replica‐exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 μs/replica timescale. The total simulation time used in the calculations exceeds 100 μs. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, ΔG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The ΔG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure‐induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T_f = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Informative and misinformative interactions in a school of fish

Quantifying distributed information processing is crucial to understanding collective motion in animal groups. Recent studies have begun to apply rigorous methods based on information theory to quantify such distributed computation. Following this perspective, we use transfer entropy to quantify dynamic information flows locally in space and time across a school of fish during directional changes around a circular tank, i.e., U-turns. This analysis reveals peaks in information flows during collective U-turns and identifies two different flows: an informative flow (positive transfer entropy) from fish that have already turned to fish that are turning, and a misinformative flow (negative transfer entropy) from fish that have not turned yet to fish that are turning. We also reveal that the information flows are related to relative position and alignment between fish and identify spatial patterns of information and misinformation cascades. This study offers several methodological contributions and we expect further application of these methodologies to reveal intricacies of self-organisation in other animal groups and active matter in general.     

The differences in the development of Rayleigh-Taylor instability in 2D and 3D geometries

Results are presented from theoretical analysis and numerical simulations aimed to clarify specific features of Rayleigh-Taylor instability in 2D and 3D geometries. Two series of simulations, one with an isolated single-mode perturbation of the interface and the other with a random density perturbation, were performed. It is shown that the relative evolutions of integral characteristics for the first and the second series are different in 2D and 3D geometries. An attempt is made to interpret this result in the framework of the previously developed evolutionary approach based on the concept of the “critical age” of the perturbation (where, by the age is meant the product of the wavenumber and amplitude). The critical age corresponds to the destruction of the main mushroom-like structure formed during the development of Rayleigh-Taylor instability due to the onset of the secondary Kelvin-Helmholtz instability.     

A comparative molecular dynamics study of thermophilic and mesophilic ribonuclease HI enzymes

We studied a pair of homologous thermophilic and mesophilic ribonuclease HI enzymes by molecular dynamics simulations. Each protein was subjected to three 5 ns simulations in explicit water at both 310 K and 340 K. The thermophilic enzyme showed larger overall positional fluctuations at both temperatures, while only the mesophilic enzyme at the higher temperature showed significant instability. When the temperature is changed, the relative flexibility of different local segments on the two proteins changed differently. Principal component analysis showed that the simulations of the two proteins explored largely overlapping regions in the conformational space. However, at 340 K, the collective structure variations of the thermophilic protein are different from those of the mesophilic protein. Our results, although not in accordance with the view that hyperthermostability of proteins may originate from their conformational rigidity, are consistent with several recent experimental and simulation studies which showed that thermophilic proteins may be conformationally more flexible than their mesophilic counterparts. The decorrelation between conformational rigidity and hyperthermostability may be attributed to the temperature dependence and long range nature of electrostatic interactions that play more important roles in the structural stability of thermophilic proteins.     

Collective aspects of conformons and the electron transfer chain

A set of interacting harmonic oscillators is used as a model to define a low frequency collective mode in protein molecules. Such a mode may arise from electron-phonon interactions in second order perturbation theory. The mathematical scheme is analogous to those used in the theory of carcadian rhythms and in the theory of superconductivity. This collective mode may receive energy from electrons in the electron transfer chain (conformon) and pass the energy on to other similar modes. The low frequency of the mode leads to slow reactions, in agreement with experimental data. The model is compatible with some general characteristics of the electron transfer chain and its constituents: high thermodynamic efficiency, redox pools, redox switches, entatic states and conformational free energy transfer.     

Distinct allosteric pathways in imidazole glycerol phosphate synthase from yeast and bacteria

Understanding the relationship between protein structures and their function is still an open question that becomes very challenging when allostery plays an important functional role. Allosteric proteins, in fact, exploit different ranges of motions (from sidechain local fluctuations to long-range collective motions) to effectively couple distant binding sites, and of particular interest is whether allosteric proteins of the same families with similar functions and structures also necessarily share the same allosteric mechanisms. Here, we compared the early dynamics initiating the allosteric communication of a prototypical allosteric enzyme from two different organisms, i.e., the imidazole glycerol phosphate synthase (IGPS) enzymes from the thermophilic bacteria and the yeast, working at high and room temperatures, respectively. By combining molecular dynamics simulations and network models derived from graph theory, we found rather distinct early allosteric dynamics in the IGPS from the two organisms, involving significatively different allosteric pathways in terms of both local and collective motions. Given the successful prediction of key allosteric residues in the bacterial IGPS, whose mutation disrupts its allosteric communication, the outcome of this study paves the way for future experimental studies on the yeast IGPS that could foster therapeutic applications by exploiting the control of IGPS enzyme allostery.     

Role of dynamics in the autoinhibition and activation of the exchange protein directly activated by cyclic AMP (EPAC)

The exchange protein directly activated by cAMP (EPAC) is a key receptor of cAMP in eukaryotes and controls critical signaling pathways. Currently, no residue resolution information is available on the full-length EPAC dynamics, which are known to be pivotal determinants of allostery. In addition, no information is presently available on the intermediates for the classical induced fit and conformational selection activation pathways. Here these questions are addressed through molecular dynamics simulations on five key states along the thermodynamic cycle for the cAMP-dependent activation of a fully functional construct of EPAC2, which includes the cAMP-binding domain and the integral catalytic region. The simulations are not only validated by the agreement with the experimental trends in cAMP-binding domain dynamics determined by NMR, but they also reveal unanticipated dynamic attributes, rationalizing previously unexplained aspects of EPAC activation and autoinhibition. Specifically, the simulations show that cAMP binding causes an extensive perturbation of dynamics in the distal catalytic region, assisting the recognition of the Rap1b substrate. In addition, analysis of the activation intermediates points to a possible hybrid mechanism of EPAC allostery incorporating elements of both the induced fit and conformational selection models. In this mechanism an entropy compensation strategy results in a low free-energy pathway of activation. Furthermore, the simulations indicate that the autoinhibitory interactions of EPAC are more dynamic than previously anticipated, leading to a revised model of autoinhibition in which dynamics fine tune the stability of the autoinhibited state, optimally sensitizing it to cAMP while avoiding constitutive activation.     

Activation of the edema factor of Bacillus anthracis by calmodulin: evidence of an interplay between the EF-calmodulin interaction and calcium binding

Calmodulin (CaM) is a remarkably flexible protein which can bind multiple targets in response to changes in intracellular calcium concentration. It contains four calcium-binding sites, arranged in two globular domains. The calcium affinity of CaM N-terminal domain (N-CaM) is dramatically reduced when the complex with the edema factor (EF) of Bacillus anthracis is formed. Here, an atomic explanation for this reduced affinity is proposed through molecular dynamics simulations and free energy perturbation calculations of the EF-CaM complex starting from different crystallographic models. The simulations show that electrostatic interactions between CaM and EF disfavor the opening of N-CaM domains usually induced by calcium binding. Relative calcium affinities of the N-CaM binding sites are probed by free energy perturbation, and dissociation probabilities are evaluated with locally enhanced sampling simulations. We show that EF impairs calcium binding on N-CaM through a direct conformational restraint on Site 1, by an indirect destabilization of Site 2, and by reducing the cooperativity between the two sites.     

A Comparative Molecular Dynamics Study of Thermophilic and Mesophilic Ribonuclease HI Enzymes

Abstract

We studied a pair of homologous thermophilic and mesophilic ribonuclease HI enzymes by molecular dynamics simulations. Each protein was subjected to three 5 ns simulations in explicit water at both 310 K and 340 K. The thermophilic enzyme showed larger overall positional fluctuations at both temperatures, while only the mesophilic enzyme at the higher temperature showed significant instability. When the temperature is changed, the relative flexibility of different local segments on the two proteins changed differently. Principal component analysis showed that the simulations of the two proteins explored largely overlapping regions in the conformational space. However, at 340 K, the collective structure variations of the thermophilic protein are different from those of the mesophilic protein. Our results, although not in accordance with the view that hyperthermostability of proteins may originate from their conformational rigidity, are consistent with several recent experimental and simulation studies which showed that thermophilic proteins may be conformationally more flexible than their mesophilic counterparts. The decorrelation between conformational rigidity and hyperthermostability may be attributed to the temperature dependence and long range nature of electrostatic interactions that play more important roles in the structural stability of thermophilic proteins.     

Nanosecond Motions in Proteins Impose Bounds on the Timescale Distributions of Local Dynamics

We elucidate the physics of protein dynamical transition via 10-100-ns molecular dynamics simulations at temperatures spanning 160-300 K. By tracking the energy fluctuations, we show that the protein dynamical transition is marked by a crossover from nonstationary to stationary processes that underlie the dynamics of protein motions. A two-timescale function captures the nonexponential character of backbone structural relaxations. One timescale is attributed to the collective segmental motions and the other to local relaxations. The former is well defined by a single-exponential, nanosecond decay, operative at all temperatures. The latter is described by a set of processes that display a distribution of timescales. Although their average remains on the picosecond timescale, the distribution is markedly contracted at the onset of the transition. It is shown that the collective motions impose bounds on timescales spanned by local dynamical processes. The nonstationary character below the transition implicates the presence of a collection of substates whose interactions are restricted. At these temperatures, a wide distribution of local-motion timescales, extending beyond that of nanoseconds, is observed. At physiological temperatures, local motions are confined to timescales faster than nanoseconds. This relatively narrow window makes possible the appearance of multiple channels for the backbone dynamics to operate.