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A Markov state model is a powerful tool that can be used to track the evolution of populations of configurations in an atomistic representation of a protein. For a coarse-grained linear chain model with discontinuous interactions, the transition rates among states that appear in the Markov model when the monomer dynamics is diffusive can be determined by computing the relative entropy of states and their mean first passage times, quantities that are unchanged by the specification of the energies of the relevant states. In this paper, we verify the folding dynamics described by a diffusive linear chain model of the crambin protein in three distinct solvent systems, each differing in complexity: a hard-sphere solvent, a solvent undergoing multi-particle collision dynamics, and an implicit solvent model. The predicted transition rates among configurations agree quantitatively with those observed in explicit molecular dynamics simulations for all three solvent models. These results suggest that the local monomer-monomer interactions provide sufficient friction for the monomer dynamics to be diffusive on timescales relevant to changes in conformation. Factors such as structural ordering and dynamic hydrodynamic effects appear to have minimal influence on transition rates within the studied solvent densities., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys.140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call "Hamiltonian dielectric solvent" (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation. [ABSTRACT FROM AUTHOR]

The question whether the dynamics of hydrated proteins changes with temperature on crossing the glass transition temperature like that found in conventional glassformers is an interesting one. Recently, we have shown that a change of temperature dependence of the mean square displacement (MSD) at Tg is present in proteins solvated with bioprotectants, such as sugars or glycerol with or without the addition of water, coexisting with the dynamic transition at a higher temperature Td. The dynamical change at Tg is similar to that in conventional glassformers at sufficiently short times and low enough temperatures, where molecules are mutually caged by the intermolecular potential. This is a general and fundamental property of glassformers which is always observed at or near Tg independent of the energy resolution of the spectrometer, and is also the basis of the dynamical change of solvated proteins at Tg. When proteins are solvated with bioprotectants they show higher Tg and Td than the proteins hydrated by water alone, due to the stabilizing action of excipients, thus the observation of the change of T-dependence of the MSD at Tg is unobstructed by the methyl-group rotation contribution at lower temperatures [S. Capaccioli, K. L. Ngai, S. Ancherbak, and A. Paciaroni, J. Phys. Chem. B 116, 1745 (2012)]. On the other hand, in the case of proteins hydrated by water alone unambiguous evidence of the break at Tg is hard to find, because of their lower Tg and Td. Notwithstanding, in this paper, we provide evidence for the change at Tg of the T-dependence of proteins hydrated by pure water. This evidence turns out from (i) neutron scattering experimental investigations where the sample has been manipulated by either full or partial deuteration to suppress the methyl-group rotation contribution, and (ii) neutron scattering experimental investigations where the energy resolution is such that only motions with characteristic times shorter than 15 ps can be sensed, thus shifting the onset of both the methyl-group rotation and the dynamic transition contribution to higher temperatures. We propose that, in general, coexistence of the break of the elastic intensity or the MSD at Tg with the dynamic transition at Td in hydrated and solvated proteins. Recognition of this fact helps to remove inconsistency and conundrum encountered in interpreting data of hydrated proteins that thwart progress in understanding the origin of the dynamic transition. [ABSTRACT FROM AUTHOR]

The existence of lipid rafts is a controversial issue. The affinity of cholesterol for saturated lipids is manifested in macroscopic phase separation in model membranes, and is believed to be the thermodynamic driving force for raft formation. However, there is no clear reason to explain the small (nanometric) size of raft domains in cell membranes. In a recent paper Yethiraj and Weisshaar [Biophys. J. 93, 3113 (2007)] proposed that the effect of neutral integral membrane proteins may prevent from the formation of large lipid domains. In this paper we extend this approach by studying the effect of the protein size, as well as the lipid-protein interaction. Depending on these factors, two different mechanisms for nanodomain stabilization are shown to be possible for static proteins. The application of these results to a biological context is discussed. [ABSTRACT FROM AUTHOR]

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived. [ABSTRACT FROM AUTHOR]

In the preceding paper by Stork and Tavan, [J. Chem. Phys. 126, 165105 (2007)], the authors have reformulated an electrostatic theory which treats proteins surrounded by dielectric solvent continua and approximately solves the associated Poisson equation [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)]. The resulting solution comprises analytical expressions for the electrostatic reaction field (RF) and potential, which are generated within the protein by the polarization of the surrounding continuum. Here the field and potential are represented in terms of Gaussian RF dipole densities localized at the protein atoms. Quite like in a polarizable force field, also the RF dipole at a given protein atom is induced by the partial charges and RF dipoles at the other atoms. Based on the reformulated theory, the authors have suggested expressions for the RF forces, which obey Newton’s third law. Previous continuum approaches, which were also built on solutions of the Poisson equation, used to violate the reactio principle required by this law, and thus were inapplicable to molecular dynamics (MD) simulations. In this paper, the authors suggest a set of techniques by which one can surmount the few remaining hurdles still hampering the application of the theory to MD simulations of soluble proteins and peptides. These techniques comprise the treatment of the RF dipoles within an extended Lagrangian approach and the optimization of the atomic RF polarizabilities. Using the well-studied conformational dynamics of alanine dipeptide as the simplest example, the authors demonstrate the remarkable accuracy and efficiency of the resulting RF-MD approach. [ABSTRACT FROM AUTHOR]

The biological function of proteins is encoded in their structure and expressed through the mediation of their dynamics. This paper presents a study on the correlation between local fluctuations, binding, and biological function for two sample proteins, starting from the Langevin Equation for Protein Dynamics (LE4PD). The LE4PD is a microscopic and residue-specific coarse-grained approach to protein dynamics, which starts from the static structural ensemble of a protein and predicts the dynamics analytically. It has been shown to be accurate in its prediction of NMR relaxation experiments and Debye-Waller factors. The LE4PD is solved in a set of diffusive modes which span a vast range of time scales of the protein dynamics, and provides a detailed picture of the mode-dependent localization of the fluctuation as a function of the primary structure of the protein. To investigate the dynamics of protein complexes, the theory is implemented here to treat the coarse-grained dynamics of interacting macromolecules. As an example, calculations of the dynamics of monomeric and dimerized HIV protease and the free Insulin Growth Factor II Receptor (IGF2R) domain 11 and its IGF2R:IGF2 complex are presented. Either simulation-derived or experimentally measured NMR conformers are used as input structural ensembles to the theory. The picture that emerges suggests a dynamical heterogeneous protein where biologically active regions provide energetically comparable conformational states that are trapped by a reacting partner in agreement with the conformationselection mechanism of binding. [ABSTRACT FROM AUTHOR]

Erratum: "Biotin-painted proteins have thermodynamic stability switched by kinetic folding routes" [J. Chem. Phys. The correction appropriately cites the paper in which the FKBP3 structure deposition is described. II D "FKBP3 biotin painting progressively increases the folding temperature" in the article[1] incorrectly describes the full FKBP3 structure (PDB code 2MPH[2]) as being an x-ray crystallographic structure. [Extracted from the article]

Nuclear magnetic resonance (NMR) order parameter S 2 for spin pairs in protein is an important quantity for deducing protein static and dynamic three-dimensional structures from NMR experimental data. In the previous paper it has been shown that contribution from low frequency motions to the order parameter can be calculated reliably from normal mode analysis carried out in dihedral angle space for spin pairs for which a number of intervening dihedral angles (NIVDA) is 10 or less. However, it has been known that for spin pairs with NIVDA=0, high frequency motions also affect the value of the order parameter. In this paper we show that the effect of high frequency motions can be accounted for by a correction term to be added to the value obtained from normal mode analysis in dihedral angle space. A factor of the correction term determined by high frequency motions can be calculated by the usual normal mode analysis for a small peptide fragment which has the same local conformation as in protein. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

It is not an understatement to say that the interplay between water and protein is a fundamental aspect of life. The vitality of an organism depends on the functionality of its biological machinery, and this, in turn, is mediated in water. Yet, we understand surprisingly little about the nature of the interface between bulk water and the protein. On the one hand, we know that the nature of the bulk water is dominated by the existence of H-bonding and H-bonded networks. On the other hand, the protein surface, where much of the bioactivity is centered, is a complex landscape of hydrophilic and hydrophobic elements. So how does the interface between these two entities work and how do they influence each other? The question is important because if one understands how a particular protein interface influences the dynamics of the water, it then becomes an easily accessible marker for similar behavior in other protein systems. The dielectric relaxation of hydrated proteins with different structures, lysozyme, collagen, and phycocyanin, has been reviewed in this paper. The dynamics of hydrated water was analyzed in terms of orientation and the ionic defect migration model. This approach enables to characterize the microscopic relaxation mechanism of the dynamics of hydration water on the different structures of the protein. In addition, our model is also capable of characterizing not only hydrated proteins but also polymer-water systems. [ABSTRACT FROM AUTHOR]

Recently, dynamic analysis methods in signal processing have been applied to the analysis of molecular dynamics (MD) trajectories of biopolymers. In the context of a relaxation mode analysis (RMA) method, based on statistical physics, it is explained why the signal-processing methods work well for the simulation trajectories of biopolymers. A distinctive difference between the RMA method and the signal-processing methods is the introduction of an additional parameter, called an evolution time parameter. This parameter enables us to better estimate the relaxation modes and rates, although it increases computational difficulty. In this paper, we propose a simple and effective extension of the RMA method, which is referred to as the positive definite RMA method, to introduce the evolution time parameter robustly. In this method, an eigenvalue problem for the time correlation matrix of physical quantities relevant to slow relaxation in a system is first solved to find the subspace in which the matrix is numerically positive definite. Then, we implement the RMA method in the subspace. We apply the method to the analysis of a 3-μs MD trajectory of a heterotrimer of an erythropoietin protein and two of its receptor proteins, and we demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, the second in a series devoted to molecular modeling of protein aggregation, a mesoscale model of proteins together with extensive discontinuous molecular dynamics simulation is used to study the phenomenon in a confined medium. The medium, as a model of a crowded cellular environment, is represented by a spherical cavity, as well as cylindrical tubes with two aspect ratios. The aggregation process leads to the formation of β sheets and eventually fibrils, whose deposition on biological tissues is believed to be a major factor contributing to many neuro-degenerative diseases, such as Alzheimer’s, Parkinson’s, and amyotrophic lateral sclerosis diseases. Several important properties of the aggregation process, including dynamic evolution of the total number of the aggregates, the mean aggregate size, and the number of peptides that contribute to the formation of the β sheets, have been computed. We show, similar to the unconfined media studied in Paper I [S. Zheng et al., J. Chem. Phys. 145, 134306 (2016)], that the computed properties follow dynamic scaling, characterized by power laws. The existence of such dynamic scaling in unconfined media was recently confirmed by experiments. The exponents that characterize the power-law dependence on time of the properties of the aggregation process in spherical cavities are shown to agree with those in unbounded fluids at the same protein density, while the exponents for aggregation in the cylindrical tubes exhibit sensitivity to the geometry of the system. The effects of the number of amino acids in the protein, as well as the size of the confined media, have also been studied. Similarities and differences between aggregation in confined and unconfined media are described, including the possibility of no fibril formation, if confinement is severe. [ABSTRACT FROM AUTHOR]

The osmotic pressure of dilute electrolyte solutions containing charged macro-ions as well as counterions can be computed directly from the particle distribution via the well-known cell model. Originally derived within the Poisson-Boltzmann mean-field approximation, the cell model considers a single macro-ion centered into a cell, together with counterions needed to neutralize the total cell charge, while it neglects the phenomena due to macro-ion correlations. While extensively applied in coarse-grained Monte Carlo (MC) simulations of continuum solvent systems, the cell model, in its original formulation, neglects the macro-ion shape anisotropy and details of the surface charge distribution. In this paper, by comparing one-body and two-body coarse-grained MC simulations, we first establish an upper limit for the assumption of neglecting correlations between macro-ions, and second, we validate the approximation of using a non-spherical macro-ion. Next, we extend the cell model to all-atom molecular dynamics simulations and show that protein concentration-dependent osmotic pressures can be obtained by confining counterions in a virtual, spherical subspace defining the protein number density. Finally, we show the possibility of using specific interaction parameters for the protein-ion and ion-ion interactions, enabling studies of protein concentration-dependent ion-specific effects using merely a single protein molecule.

We consider a monodispersed Rayleigh droplet beam of water droplets doped with proteins. An intense infrared laser is used to align these droplets. The arrangement has been proposed for electron- and x-ray-diffraction studies of proteins which are difficult to crystallize. This paper considers the effect of thermal fluctuations on the angular spread of alignment in thermal equilibrium, and relaxation phenomena, particularly the damping of oscillations excited as the molecules enter the field. The possibility of adiabatic alignment is also considered. We find that damping times in a high-pressure gas cell as used in x-ray-diffraction experiments are short compared with the time taken for molecules to traverse the beam and that a suitably shaped field might be used for electron-diffraction experiments in vacuum to provide adiabatic alignment, thus obviating the need for a damping gas cell. [ABSTRACT FROM AUTHOR]

In the present paper a procedure to calculate the properties of proteins in aqueous mixed solvents, particularly the excesses of the constituents of the mixed solvent near the protein molecule and the preferential binding parameters, is suggested. Expressions for the Kirkwood-Buff integrals in ternary mixtures and for the preferential binding parameter were derived and used to calculate various properties of infinitely dilute proteins in aqueous mixed solvents. The derived expressions and experimental information regarding the partial molar volumes and the preferential binding parameters were used to calculate the excesses (deficits) of water and cosolvent (in comparison with the bulk concentrations of protein-free mixed solvent) in the vicinity of ribonuclease A, ribonuclease T1, and lysozyme molecules. The calculations showed that water was in excess in the vicinity of ribonuclease A for water/glycerol and water/trehalose mixtures, and the cosolvent urea was in excess in the vicinity of ribonuclease T1 and lysozyme. The derivative of the activity coefficient of the protein with respect to the mole fraction of water was also calculated. This derivative was negative for the water/glycerol and water/trehalose mixed solvents and positive for the water/urea mixture. The mixture of lysozyme in the water/urea solvent is of particular interest, because the lysozyme at pH 7.0 is in its native state up to 9.3M urea, while at pH 2.0 it is denaturated between 2.5 and 5M and higher concentrations of urea. Our results demonstrated a striking similarity in the hydration of lysozyme at both pHs. It is worthwhile to note that the excesses of urea were only weakly composition dependent on both cases. [ABSTRACT FROM AUTHOR]

In this paper, a novel hybrid algorithm combining genetic algorithms and tabu search is presented. In the proposed hybrid algorithm, the idea of tabu search is applied to the crossover operator. We demonstrate that the hybrid algorithm can be applied successfully to the protein folding problem based on a hydrophobic–hydrophilic lattice model. The results show that in all cases the hybrid algorithm works better than a genetic algorithm alone. A comparison with other methods is also made. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new model to study proteinic systems including a many-body polarization and a hydrogen bond energy contribution is presented. This model represents an extension of an earlier water many-body model [M. Masella and J.-P. Flament, J. Chem. Phys. 107 9105 (1997)]. As in this earlier model, the new model is developed to reproduce quantum computations on small molecular aggregates, and, in this first paper, we focus our efforts in developing an accurate potential to describe interactions among all nonbonded atoms occurring in proteins, and among those atoms and six cations of biological interest: Li[SUP+], Na[SUP+], K[SUP+], Mg[SUP2+], Ca[SUP2+], and Zn[SUP2+]. Intramolecular degrees of freedom are described as in classical two-body force fields. In the present paper, the new model is applied to investigate the properties of small ion-neutral [M,L[SUBn][SUPm+] complexes and of small hydrogen-bonded systems. The results showed that this model is able to reproduce most of the theoretical quantum predictions and experimental data published until now regarding those systems. [ABSTRACT FROM AUTHOR]

The co-involvement of biological molecules and nanomaterials has increasingly come to the fore in modern-day applications. While the "bio-nano" (BN) interface presents physico-chemical characteristics that are manifestly different from those observed in isotropic bulk conditions, the underlying molecular reasons remain little understood; this is especially true of anomalies in interfacial hydration. In this paper, we leverage atomistic simulations to study differential adsorption characteristics of a small protein on the inner (concave) surface of a single-walled carbon nanotube whose diameter exceeds dimensions conducive to single-file water movement. Our findings indicate that the extent of adsorption is decided by the degree of foldedness of the protein conformational substate. Importantly, we find that partially folded substates, but not the natively folded one, induce reorganization of the protein hydration layer into an inner layer water closer to the nanotube axis and an outer layer water in the interstitial space near the nanotube walls. Further analyses reveal sharp dynamical differences between water molecules in the two layers as observed in the onset of increased heterogeneity in rotational relaxation and the enhanced deviation from Fickian behavior. The vibrational density of states reveals that the dynamical distinctions are correlated with differences in crucial bands in the power spectra. The current results set the stage for further systematic studies of various BN interfaces vis-à-vis control of hydration properties.

In this paper we further develop the concept of interatomic tunneling currents [A.A. Stuchebrukhov, J. Chem. Phys. 104, 8424 (1996)] for the description of long-range electron tunneling in proteins. Here we discuss a formulation of the theory for the case when nonorthogonality of the atomic basis set of the medium propagating electron is explicitly taken into account. This method provides an effective computational scheme for an exact, i.e., nonperturbative, evaluation (in one-electron approximation) of the superexchange electron tunneling matrix element, and allows one to determine which regions in the protein matrix are important for the tunneling process. The theory is applied for calculation of tunneling currents and the electronic matrix element in His126-Ru-modified blue copper protein azurin from a recent experimental work of Gray and co-workers. Analysis of interatomic currents reveals a nontrivial structure of the tunneling flow between donor and acceptor in the intervening protein medium in this system. [ABSTRACT FROM AUTHOR]

A major unsolved problem in protein dynamics is the connection between the amino acid sequence and the propensity to fold to a unique, ordered structure. Many globular proteins fold to native states with great regularity in their tertiary structure, reminiscent of symmetry. This paper considers the relation between sequence, regular folded structure, and formal group theoretical symmetry in lattice protein models. In computer simulations of model proteins consisting of a chain of hydrophobic (H) and polar (P) units on a lattice [K. Yue and K. A. Dill, Proc. Natl. Acad. Sci. USA 92, 146 (1995)] it was observed that some chains fold to regular, ‘‘symmetric’’ structures. These structures have a small number of native states, i.e., the conformations of minimum energy have low degeneracy in this model, in which the energy depends only on the number of H–H contacts. The present work is concerned with the connection between the symmetry properties of the H–P sequence and those of the folded lattice protein. The meaning of symmetry in lattice models is discussed in terms of mathematical groups. The concepts of the lattice symmetry, the hydrophobic lattice core and its geometrical symmetry, and the core sequence and its permutation symmetry, are defined and related. With the help of a simple rescaling of the energy, the folded lattice protein is seen to have the symmetry of a microcrystal of H and P ‘‘atoms’’ arranged on a lattice. Geometrical symmetry of the folded structure is related to formal permutation symmetry properties of the H–P sequence, in order to establish the connection between sequence and fold. How these relations among symmetry, structure, and sequence might relate to folding in real proteins, including the design of sequences to fold into desired structures, is discussed. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Multisite phosphorylation plays an important role in regulating switch-like protein activity and has been used widely in mathematical models. With the development of new experimental techniques and more molecular data, molecular phosphorylation processes emerge in many systems with increasing complexity and sizes. These developments call for simple yet valid stochastic models to describe various multisite phosphorylation processes, especially in large and complex biochemical networks. To reduce model complexity, this work aims at simplifying the multisite phosphorylation mechanism by a stochastic Hill function model. Furthermore, this work optimizes regions of parameter space to match simulation results from the stochastic Hill function with the distributive multisite phosphorylation process. While traditional parameter optimization methods have been focusing on finding the best parameter vector, in most circumstances, modelers would like to find a set of parameter vectors that generate similar system dynamics and results. This paper proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill function based on a quasi-Newton stochastic optimization algorithm. Different objective functions are investigated characterizing different features of the simulation-based empirical data, among which the approximate maximum log-likelihood method is recommended for general applications. Numerical results demonstrate that with an appropriate parameter vector value, the stochastic Hill function model depicts the multisite phosphorylation process well except the initial (transient) period.

Computational techniques for accurate and efficient prediction of protein-protein complex structures are widely used for elucidating protein-protein interactions, which play important roles in biological systems. Recently, it has been reported that selecting a structure similar to the native structure among generated structure candidates (decoys) is possible by calculating binding free energies of the decoys based on all-atom molecular dynamics (MD) simulations with explicit solvent and the solution theory in the energy representation, which is called evERdock. A recent version of evERdock achieves a higher-accuracy decoy selection by introducing MD relaxation and multiple MD simulations/energy calculations; however, huge computational cost is required. In this paper, we propose an efficient decoy selection method using evERdock and the best arm identification (BAI) framework, which is one of the techniques of reinforcement learning. The BAI framework realizes an efficient selection by suppressing calculations for nonpromising decoys and preferentially calculating for the promising ones. We evaluate the performance of the proposed method for decoy selection problems of three protein-protein complex systems. Their results show that computational costs are successfully reduced by a factor of 4.05 (in the best case) compared to a standard decoy selection approach without sacrificing accuracy.

The Histone-like Nucleoid Structuring protein (H-NS) is a nucleoid-associated protein, which is involved in both gene regulation and DNA compaction. Although it is a key player in genome organization by forming bridges between DNA duplexes, the precise structure of complexes of DNA and H-NS proteins is still not well understood. In particular, it is not clear whether the structure of DNA/H-NS complexes in the living cell is similar to that of complexes deposited on mica surfaces, which may be observed by AFM microscopy. A coarse-grained model, which helps getting more insight into this question, is described and analyzed in the present paper. This model is able of describing both the bridging of bacterial DNA by H-NS in the bulk and the deposition and equilibration of the complex on a charged surface. Simulations performed with the model reveal that a slight attraction between DNA and the charged surface is sufficient to let DNA/H-NS complexes reorganize from 3D coils to planar plasmids bridged by H-NS proteins similar to those observed by AFM microscopy. They furthermore highlight the antagonistic effects of the interactions between DNA and the surface. Indeed, increasing these interactions slows down the equilibration of naked plasmids on the surface but, on the other hand, enables a faster equilibration of DNA/H-NS complexes. Based on the distribution of the lifetimes of H-NS bridges and the time evolution of the number of trans-binding protein dimers during equilibration of the complexes on the surface, it is argued that the decrease of the equilibration time of the complex upon increase of the interaction strength between DNA and the surface is ascribable to the associated decrease of the probability to form new bridges between DNA and the proteins. [ABSTRACT FROM AUTHOR]

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys.118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys.1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ i of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys.2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ i. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua. [ABSTRACT FROM AUTHOR]

In this paper, we show that ensembles of well-structured and unstructured proteins can be distinguished by borrowing concepts from non-equilibrium statistical mechanics. For this purpose, we represent proteins by two different polymer models and interpret the resulting polymer configurations as random walks of a diffusing particle in space. The first model is the trace of the C α -atoms along the protein main chain, and the second is their projections onto the protein axis. The resulting trajectories are subsequently analyzed using the theory of the generalized Langevin equation. Velocities are replaced by displacements relating consecutive points on the discrete protein axes and equilibrium ensemble averages by averages over appropriate protein structure ensembles. The resulting displacement autocorrelation functions resemble those of the velocity autocorrelation functions of simple liquids and display a minimum, which can be related to the lengths of secondary structure elements. This minimum is clearly more pronounced for well-structured proteins than for unstructured ones, and the corresponding memory function displays a slower decay, indicating a stronger "folding memory."

In large photosynthetic chromophore-protein complexes not all chromophores are coupled strongly, and thus the situation is well described by formation of delocalized states in certain domains of strongly coupled chromophores. In order to describe excitation energy transfer among different domains without performing extensive numerical calculations, one of the most popular techniques is a generalization of Förster theory to multichromophoric aggregates (generalized Förster theory) proposed by Sumi [J. Phys. Chem. B 103, 252 (1999)] and Scholes and Fleming [J. Phys. Chem. B 104, 1854 (2000)]. The aim of this paper is twofold. In the first place, by means of analytic continuation and a time convolutionless quantum master equation approach, a theory of emission lineshape of multichromophoric systems or molecular aggregates is proposed. In the second place, a comprehensive framework that allows for a clear, compact, and effective study of the multichromophoric approach in the full general version proposed by Jang, Newton, and Silbey [Phys. Rev. Lett. 92, 218301 (2004)] is developed. We apply the present theory to simple paradigmatic systems and we show on one hand the effectiveness of time-convolutionless techniques in deriving lineshape operators and on the other hand we show how the multichromophoric approach can give significant improvements in the determination of energy transfer rates in particular when the systems under study are not the purely Förster regime. The presented scheme allows for an effective implementation of the multichromophoric Förster approach which may be of use for simulating energy transfer dynamics in large photosynthetic aggregates, for which massive computational resources are usually required. Furthermore, our method allows for a systematic comparison of multichromophoric Föster and generalized Förster theories and for a clear understanding of their respective limits of validity. [ABSTRACT FROM AUTHOR]

This paper addresses the question to which extent anisotropic atomic motions in proteins impact angular-averaged incoherent neutron scattering intensities, which are typically recorded for powder samples. For this purpose, the relevant correlation functions are represented as multipole series in which each term corresponds to a different degree of intrinsic motional anisotropy. The approach is illustrated by a simple analytical model and by a simulation-based example for lysozyme, considering in both cases the elastic incoherent structure factor. The second example shows that the motional anisotropy of the protein atoms is considerable and contributes significantly to the scattering intensity. [ABSTRACT FROM AUTHOR]

Signal proteins are able to adapt their response to a change in the environment, governing in this way a broad variety of important cellular processes in living systems. While conventional molecular-dynamics (MD) techniques can be used to explore the early signaling pathway of these protein systems at atomistic resolution, the high computational costs limit their usefulness for the elucidation of the multiscale transduction dynamics of most signaling processes, occurring on experimental timescales. To cope with the problem, we present in this paper a novel multiscale-modeling method, based on a combination of the kinetic Monte-Carlo- and MD-technique, and demonstrate its suitability for investigating the signaling behavior of the photoswitch light-oxygen-voltage-2-Jα domain from Avena Sativa (AsLOV2-Jα) and an AsLOV2-Jα-regulated photoactivable Rac1-GTPase (PA-Rac1), recently employed to control the motility of cancer cells through light stimulus. More specifically, we show that their signaling pathways begin with a residual re-arrangement and subsequent H-bond formation of amino acids near to the flavin-mononucleotide chromophore, causing a coupling between β-strands and subsequent detachment of a peripheral α-helix from the AsLOV2-domain. In the case of the PA-Rac1 system we find that this latter process induces the release of the AsLOV2-inhibitor from the switchII-activation site of the GTPase, enabling signal activation through effector-protein binding. These applications demonstrate that our approach reliably reproduces the signaling pathways of complex signal proteins, ranging from nanoseconds up to seconds at affordable computational costs. [ABSTRACT FROM AUTHOR]

The paper presents an analytical theory and numerical simulations of the dipolar response of hydrated proteins in solution. We calculate the effective dielectric constant representing the average dipole moment induced at the protein by a uniform external field. The dielectric constant shows a remarkable variation among the proteins, changing from 0.5 for ubiquitin to 640 for cytochrome c. The former value implies a negative dipolar susceptibility, that is a dia-electric dipolar response and negative dielectrophoresis. It means that ubiquitin, carrying an average dipole of ≃240 D, is expected to repel from the region of a stronger electric field. This outcome is the result of a negative cross-correlation between the protein and water dipoles, compensating for the positive variance of the intrinsic protein dipole in the overall dipolar susceptibility. In contrast to the neutral ubiquitin, charged proteins studied here show para-electric dipolar response and positive dielectrophoresis. The study suggests that the dipolar response of proteins in solution is strongly affected by the coupling of the protein surface charge to the hydration water. The protein-water dipolar cross-correlations are long-ranged, extending ∼2 nm from the protein surface into the bulk. A similar correlation length of about 1 nm is seen for the electrostatic potential produced by the hydration water inside the protein. The analysis of numerical simulations suggests that the polarization of the protein-water interface is highly heterogeneous and does not follow the standard dielectric results for cavities carved in dielectrics. The polarization of the water shell gains in importance, relative to the intrinsic protein dipole, at high frequencies, above the protein Debye peak. The induced interfacial dipole can be either parallel or antiparallel to the protein dipole, depending on the distribution of the protein surface charge. As a result, the high-frequency absorption of the protein solution can be either higher or lower than the absorption of water. Both scenarios have been experimentally observed in the THz window of radiation. [ABSTRACT FROM AUTHOR]

In this paper, we present a theoretical approach to construct a fluctuating quantum model of the CO vibration in heme-CO proteins and its interaction with external laser fields. The methodology consists of mixed quantum-classical calculations for a restricted number of snapshots, which are then used to construct a parametrized quantum model. As an example, we calculate the infrared absorption spectrum of carboxy-hemoglobin, based on a simplified protein model, and found the absorption linewidth in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms of clustering in colloids, nanoparticles, and proteins is of significant interest in material science and both chemical and pharmaceutical industries. Recently, using an integral equation theory formalism, Bomont et al. [J. Chem. Phys. 132, 184508 (2010)] studied theoretically the temperature dependence, at a fixed density, of the cluster formation in systems where particles interact with a hard-core double Yukawa potential composed of a short-range attraction and a long-range repulsion. In this paper, we provide evidence that the low-q peak in the static structure factor, frequently associated with the formation of clusters, is a common behavior in systems with competing interactions. In particular, we demonstrate that, based on a thermodynamic self-consistency criterion, accurate structural functions are obtained for different choices of closure relations. Moreover, we explore the dependence of the low-q peak on the particle number density, temperature, and potential parameters. Our findings indicate that enforcing thermodynamic self-consistency is the key factor to calculate both thermodynamic properties and static structure factors, including the low-q behavior, for colloidal dispersions with both attractive and repulsive interactions. Additionally, a simple analysis of the mean number of neighboring particles provides a qualitative description of some of the cluster features. [ABSTRACT FROM AUTHOR]

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies. [ABSTRACT FROM AUTHOR]

In this paper, we present a detailed dynamics study of the catalytic core domain (CCD) of HIV-1 integrase using both polarized and nonpolarized force fields. The numerical results reveal the critical role of protein polarization in stabilizing Mg2+ coordination complex in CCD. Specifically, when nonpolarized force field is used, a remarkable drift of the Mg2+ complex away from its equilibrium position is observed, which causes the binding site blocked by the Mg2+ complex. In contrast, when polarized force field is employed in MD simulation, HIV-1 integrase CCD structure is stabilized and both the position of the Mg2+ complex and the binding site are well preserved. The detailed analysis shows the transition of α-helix to 310-helix adjacent to the catalytic loop (residues 139–147), which correlates with the dislocation of the Mg2+ complex. The current study demonstrates the importance of electronic polarization of protein in stabilizing the metal complex in the catalytic core domain of HIV-1 integrase. [ABSTRACT FROM AUTHOR]

The mechanical model based on beads and springs, which we recently proposed to study nonspecific DNA-protein interactions [J. Chem. Phys. 130, 015103 (2009)], was improved by describing proteins as sets of interconnected beads instead of single beads. In this paper, we first compare the results obtained with the updated model with those of the original one and then use it to investigate several aspects of the dynamics of DNA sampling, which could not be accounted for by the original model. These aspects include the effect on the speed of DNA sampling of the regularity and/or randomness of the protein charge distribution, the charge and location of the search site, and the shape and deformability of the protein. We also discuss the efficiency of facilitated diffusion, that is, the extent to which the combination of 1D sliding along the DNA and 3D diffusion in the cell can lead to faster sampling than pure 3D diffusion of the protein. [ABSTRACT FROM AUTHOR]

A number of experiments and experimentally based simulations showed that β-proteins are mechanically more stable than α-proteins. However, the theory that might explain this evidence is still lacking. In this paper we have developed a simple elastic theory, which allows to estimate critical forces for stretching both kinds of proteins. It has been shown that unfolding of β-proteins does really require notably higher forces as compared to the stretching of α-proteins. [ABSTRACT FROM AUTHOR]

S-layer proteins have a wide range of application potential due to their characteristic features concerning self-assembling, assembling on various surfaces, and forming of isoporous structures with functional groups located on the surface in an identical position and orientation. Although considerable knowledge has been experimentally accumulated on the structure, biochemistry, assemble characteristics, and genetics of S-layer proteins, no structural model at atomic resolution has been available so far. Therefore, neither the overall folding of the S-layer proteins—their tertiary structure—nor the exact amino acid or domain allocations in the lattices are known. In this paper, we describe the tertiary structure prediction for the S-layer protein SbsB from Geobacillus stearothermophilus PV72/p2. This calculation was based on its amino acid sequence using the mean force method (MF method) achieved by performing molecular dynamic simulations. This method includes mainly the thermodynamic aspects of protein folding as well as steric constraints of the amino acids and is therefore independent of experimental structure analysis problems resulting from biochemical properties of the S-layer proteins. Molecular dynamic simulations were performed in vacuum using the simulation software NAMD. The obtained tertiary structure of SbsB was systematically analyzed by using the mean force method, whereas the verification of the structure is based on calculating the global free energy minimum of the whole system. This corresponds to the potential of mean force, which is the thermodynamically most favorable conformation of the protein. Finally, an S-layer lattice was modeled graphically using CINEMA4D and compared with scanning force microscopy data down to a resolution of 1 nm. The results show that this approach leads to a thermodynamically favorable atomic model of the tertiary structure of the protein, which could be verified by both the MF Method and the lattice model. [ABSTRACT FROM AUTHOR]

An initial guess is one of the most important factors in solving self-consistent field (SCF) molecular orbital calculations for large molecules. Recently, the authors reported that the quasicanonical localized orbital (QCLO) method was useful to prove the initial guess for all-electron calculations for proteins. This paper describes a new QCLO method that takes into account protein information derived from protein structures such as salt bridges and the secondary structure of the molecule. In several test calculations using typical models, the difference between the initial guess and final atomic charges was markedly decreased, and the number of SCF iterations was reduced. We suggest that the structure-based QCLO method improves the precision of the initial guess and achievement of automatic all-electron calculations for proteins. [ABSTRACT FROM AUTHOR]

Urate oxidase from Asperigillus flavus has been shown to be a model protein for studying the effects of polyethylene glycol (PEG) on the crystallization of large proteins. Extensive experimental studies based on small angle x-ray scattering [Vivarès and Bonneté, J. Phys. Chem. B 108, 6498 (2004)] have determined the effects of salt, pH, temperature, and most importantly PEG on the crystallization of this protein. Recently, some aspects of the phase diagram have also been determined experimentally. In this paper, we use Monte Carlo techniques to predict the phase diagram for urate oxidase in solution with PEG, including the liquid-liquid and liquid-solid coexistence curves. The model used includes an electrostatic interaction, van der Waals attraction, and a polymer-induced depletion interaction [Vivarès et al., Eur. Phys. J. E 9, 15 (2002)]. Results from the simulation are compared with experimental results. [ABSTRACT FROM AUTHOR]

Annealed importance sampling assigns equilibrium weights to a nonequilibrium sample that was generated by a simulated annealing protocol [R. M. Neal, Stat. Comput. 11, 125 (2001)]. The weights may then be used to calculate equilibrium averages, and also serve as an “adiabatic signature” of the chosen cooling schedule. In this paper we demonstrate the method on the 50-atom dileucine peptide and an alanine 5-mer, showing that equilibrium distributions are attained for manageable cooling schedules. For dileucine, as naively implemented here, the method is modestly more efficient than constant temperature simulation. The alanine application demonstrates the success of the method when there is little overlap between the high (unfolded) and low (folded) temperature distributions. The method is worth considering whenever any simulated heating or cooling is performed (as is often done at the beginning of a simulation project or during a NMR structure calculation), as it is simple to implement and requires minimal additional computational expense. Furthermore, the naive implementation presented here can be improved. [ABSTRACT FROM AUTHOR]

The authors reformulate and revise an electrostatic theory treating proteins surrounded by dielectric solvent continua [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)] to make the resulting reaction field (RF) forces compatible with Newton’s third law. Such a compatibility is required for their use in molecular dynamics (MD) simulations, in which the proteins are modeled by all-atom molecular mechanics force fields. According to the original theory the RF forces, which are due to the electric field generated by the solvent polarization and act on the partial charges of a protein, i.e., the so-called qE forces, can be quite accurately computed from Gaussian RF dipoles localized at the protein atoms. Using a slightly different approximation scheme also the RF energies of given protein configurations are obtained. However, because the qE forces do not account for the dielectric boundary pressure exerted by the solvent continuum on the protein, they do not obey the principle that actio equals reactio as required by Newton’s third law. Therefore, their use in MD simulations is severely hampered. An analysis of the original theory has led the authors now to a reformulation removing the main difficulties. By considering the RF energy, which represents the dominant electrostatic contribution to the free energy of solvation for a given protein configuration, they show that its negative configurational gradient yields mean RF forces obeying the reactio principle. Because the evaluation of these mean forces is computationally much more demanding than that of the qE forces, they derive a suggestion how the qE forces can be modified to obey Newton’s third law. Various properties of the thus established theory, particularly issues of accuracy and of computational efficiency, are discussed. A sample application to a MD simulation of a peptide in solution is described in the following paper [M. Stork and P. Tavan, J. Chem. Phys., 126, 165106 (2007). [ABSTRACT FROM AUTHOR]

Internal motions in proteins, such as oscillations of internuclear vectors u(NiHiN) of amide bonds about their equilibrium position, can be characterized by a local order parameter. This dynamic parameter can be determined experimentally by measuring the longitudinal and transverse relaxation rates of 15Ni nuclei by suitable NMR methods. In this paper, it is shown that local variations of order parameters Sii2 can be predicted from the knowledge of the structure. To this effect, the diffusive motion of the internuclear vector u(NiHiN) is described in a potential that takes into account the deviations of the angles θij between u(NiHiN) and neighboring vectors u(NjHjN) from their average value and similarly of deviations of the angles subtended between u(NiHiN) and u(XjYj), where Xj and Yj are heavy atoms in the vicinity of the u(NiHiN) vector under investigation. It is shown how the concept of vicinity can be defined by a simple cutoff threshold, i.e., by neglecting vectors u(XjYj) with distances d(Ni,Xj)>7.5 Å. The local order parameters Sii2 can be predicted from the structure using a limited set of coordinates of heavy atoms. The inclusion of a larger number of heavy atoms does not improve the predictions. Applications to calmodulin, calbindin, and interleukin 4 illustrate the success and limitations of the predictions. [ABSTRACT FROM AUTHOR]

In order to probe the fundamental principles that govern protein evolution, we use a minimalist model of proteins to provide a mapping from genotype to phenotype. The model is based on physically realistic forces of protein folding and includes an explicit definition of protein function. Thus, we can find the fitness of a sequence from its ability to fold to a stable structure and perform a function. We study the fitness landscapes of these functional model proteins, that is, the set of all sequences mapped on to their corresponding fitnesses and connected to their one mutant neighbors. Through population dynamics simulations we directly study the influence of the nature of the fitness landscape on evolution. Populations are observed to move to a steady state, the distribution of which can often be predicted prior to the population dynamics simulations from the nature of the fitness landscape and a quantity analogous to a partition function. In this paper, we develop a scheme for predicting the steady-state population on a fitness landscape, based on the nature of the fitness landscape, thereby obviating the need for explicit population dynamics simulations and providing some insight into the impact on molecular evolution of the nature of fitness landscapes. Poor predictions are indicative of fitness landscapes that consist of a series of weakly connected sublandscapes. [ABSTRACT FROM AUTHOR]

Protein refolding to its native state in vitro is a challenging problem in biotechnology, i.e., in the biomedical, pharmaceutical, and food industry. Protein aggregation and misfolding usually inhibit the recovery of proteins with their native states. These problems can be partially solved by adding a surfactant into a suitable solution environment. However, the process of this surfactant-assisted protein refolding is not well understood. In this paper, we wish to report on the first-ever simulations of surfactant-assisted protein refolding. For these studies, we defined a simple model for the protein and the surfactant and investigated how a surfactant affected the folding behavior of a two-dimensional lattice protein molecule. The model protein and model surfactant were chosen such that we could capture the important features of the folding process and the interaction between the protein and the surfactant, namely, the hydrophobic interaction. It was shown that, in the absence of surfactants, a protein in an “energy trap” conformation, i.e., a local energy minima, could not fold into the native form, which was characterized by a global energy minimum. The addition of surfactants created folding pathways via the formation of protein-surfactant complexes and thus enabled the conformations that fell into energy trap states to escape from these traps and to form the native proteins. The simulation results also showed that it was necessary to match the hydrophobicity of surfactant to the concentration of denaturant, which was added to control the folding or unfolding of a protein. The surfactants with different hydrophobicity had their own concentration range on assisting protein refolding. All of these simulations agreed well with experimental results reported elsewhere, indicating both the validity of the simulations presented here and the potential application of the simulations for the design of a surfactant on assisting protein refolding. [ABSTRACT FROM AUTHOR]

Time series analysis is applied on the collective coordinates obtained from principal component analysis of independent molecular dynamics simulations of α-amylase inhibitor tendamistat and immunity protein of colicin E7 based on the Cα coordinates history. Even though the principal component directions obtained for each run are considerably different, the dynamics information obtained from these runs are surprisingly similar in terms of time series models and parameters. There are two main differences in the dynamics of the two proteins: the higher density of low frequencies and the larger step sizes for the interminima motions of colicin E7 than those of α-amylase inhibitor, which may be attributed to the higher number of residues of colicin E7 and/or the structural differences of the two proteins. The cumulative density function of the low frequencies in each run conforms to the expectations from the normal mode analysis. When different runs of α-amylase inhibitor are projected on the same set of eigenvectors, it is found that principal components obtained from a certain conformational region of a protein has a moderate explanation power in other conformational regions and the local minima are similar to a certain extent, while the height of the energy barriers in between the minima significantly change. As a final remark, time series analysis tools are further exploited in this study with the motive of explaining the equilibrium fluctuations of proteins. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The origin of the interactions occurring in the calmodulin protein interacting with one of its target peptide and counterions, and binding four calcium dications, has been investigated in the gas phase, using the many-body model presented in Paper I [Masella and Cuniasse, J. Chem. Phys. 119, 1866 (2003)] and a classical pairwise force field. As compared to the latter force field, the many-body model is shown to provide a geometrical description of the calmodulin/target peptide structure in better agreement with the x-ray experimental one, and a better description of the Ca[SUP2+] binding sites (as compared to "small molecule" structures reported in the Cambridge Structural Database). Regarding the energy, both models provide qualitatively a similar description of the interactions occurring in the calmodulin/target peptide system. However, quantitatively, the pairwise model predicts interaction energies greater by about 25% as compared to the many-body one in the case of calmodulin/Ca[SUP2+] interactions. This is due to the inability of pairwise force fields to account for the strong anticooperative effects predicted to occur in [Ca, (carboxylate)[SUBn]][SUP2-n] systems by both the many-body model and quantum computations. Hence, the new many-body model appears to be well suited for describing proteinic systems interacting with cations, both in terms of geometry and energy. [ABSTRACT FROM AUTHOR]

Determining the role of non-native interactions in folding dynamics, kinetics, and mechanisms is a classic problem in protein folding. More recently, this question has witnessed a renewed interest in light of the hypothesis that knotted proteins require the assistance of non-native interactions to fold efficiently. Here, we conduct extensive equilibrium and kinetic Monte Carlo simulations of a simple off-lattice C-alpha model to explore the role of non-native interactions in the thermodynamics and kinetics of three proteins embedding a trefoil knot in their native structure. We find that equilibrium knotted conformations are stabilized by non-native interactions that are non-local, and proximal to native ones, thus enhancing them. Additionally, non-native interactions increase the knotting frequency at high temperatures, and in partially folded conformations below the transition temperatures. Although non-native interactions clearly enhance the efficiency of transition from an unfolded conformation to a partially folded knotted one, they are not required to efficiently fold a knotted protein. Indeed, a native-centric interaction potential drives the most efficient folding transition, provided that the simulation temperature is well below the transition temperature of the considered model system. [ABSTRACT FROM AUTHOR]

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5–10 millihartrees and 5 cm−1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) is an extremely powerful, highly effective, and widely used approach to understanding the nature of chemical processes in atomic details for proteins. The accuracy of results from MD simulations is highly dependent on force fields. Currently, molecular mechanical (MM) force fields are mainly utilized in MD simulations because of their low computational cost. Quantum mechanical (QM) calculation has high accuracy, but it is exceedingly time consuming for protein simulations. Machine learning (ML) provides the capability for generating accurate potential at the QM level without increasing much computational effort for specific systems that can be studied at the QM level. However, the construction of general machine learned force fields, needed for broad applications and large and complex systems, is still challenging. Here, general and transferable neural network (NN) force fields based on CHARMM force fields, named CHARMM-NN, are constructed for proteins by training NN models on 27 fragments partitioned from the residue-based systematic molecular fragmentation (rSMF) method. The NN for each fragment is based on atom types and uses new input features that are similar to MM inputs, including bonds, angles, dihedrals, and non-bonded terms, which enhance the compatibility of CHARMM-NN to MM MD and enable the implementation of CHARMM-NN force fields in different MD programs. While the main part of the energy of the protein is based on rSMF and NN, the nonbonded interactions between the fragments and with water are taken from the CHARMM force field through mechanical embedding. The validations of the method for dipeptides on geometric data, relative potential energies, and structural reorganization energies demonstrate that the CHARMM-NN local minima on the potential energy surface are very accurate approximations to QM, showing the success of CHARMM-NN for bonded interactions. However, the MD simulations on peptides and proteins indicate that more accurate methods to represent protein–water interactions in fragments and non-bonded interactions between fragments should be considered in the future improvement of CHARMM-NN, which can increase the accuracy of approximation beyond the current mechanical embedding QM/MM level. [ABSTRACT FROM AUTHOR]

Protein folding in confined media has attracted wide attention over the past 15 years due to its importance to both in vivo and in vitro applications. It is generally believed that protein stability increases by decreasing the size of the confining medium, if the medium's walls are repulsive, and that the maximum folding temperature in confinement is in a pore whose size D is only slightly larger than the smallest dimension of a protein's folded state. Until recently, the stability of proteins in pores with a size very close to that of the folded state has not received the attention it deserves. In a previous paper [L. Javidpour and M. Sahimi, J. Chem. Phys. 0 is only slightly larger than the smallest dimension of a protein's folded state. Until recently, the stability of proteins in pores with a size very close to that of the folded state has not received the attention it deserves. In a previous paper [L. Javidpour and M. Sahimi, J. Chem. Phys. 135 , 125101 (2011)], we showed that, contrary to the current theoretical predictions, the maximum folding temperature occurs in larger -helices. Moreover, in very tight pores, the free energy surface becomes rough, giving rise to a new barrier for protein folding close to the unfolded state. In contrast to unbounded domains, in small nanopores proteins with an smaller α -helices. Moreover, in very tight pores, the free energy surface becomes rough, giving rise to a new barrier for protein folding close to the unfolded state. In contrast to unbounded domains, in small nanopores proteins with an α structures are entropically stabilized implying that folding rates decrease notably and that the free energy surface becomes rougher. In view of the potential significance of such results to interpretation of many sets of experimental data that could not be explained by the current theories, particularly the reported anomalously low rates of folding and the importance of entropic effects on proteins' misfolded states in highly confined environments, we address the following question in the present paper: To what extent the geometry of a confined medium affects the stability and folding rates of proteins? Using millisecond-long molecular dynamics simulations, we study the problem in three types of confining media, namely, cylindrical and slit pores and spherical cavities. Most importantly, we find that the prediction of the previous theories that the dependence of the maximum folding temperature β structures are entropically stabilized implying that folding rates decrease notably and that the free energy surface becomes rougher. In view of the potential significance of such results to interpretation of many sets of experimental data that could not be explained by the current theories, particularly the reported anomalously low rates of folding and the importance of entropic effects on proteins' misfolded states in highly confined environments, we address the following question in the present paper: To what extent the geometry of a confined medium affects the stability and folding rates of proteins? Using millisecond-long molecular dynamics simulations, we study the problem in three types of confining media, namely, cylindrical and slit pores and spherical cavities. Most importantly, we find that the prediction of the previous theories that the dependence of the maximum folding temperature T of a confined medium occurs in larger media for larger proteins is correct f in spherical geometry, whereas the opposite is true in the two other geometries that we study. Also studied is the effect of the strength of the interaction between the confined media's walls and the proteins. If the walls are only weakly or moderately attractive, a complex behavior emerges that depends on the size of the confining medium.D of a confined medium occurs in larger media for larger proteins is correct only in spherical geometry, whereas the opposite is true in the two other geometries that we study. Also studied is the effect of the strength of the interaction between the confined media's walls and the proteins. If the walls are only weakly or moderately attractive, a complex behavior emerges that depends on the size of the confining medium.

An efficient molecular dynamics (MD) algorithm is presented in this paper for biomolecular systems, which incorporates a novel variation on the fast multipole method (FMM) coupled to the reversible reference system propagator algorithm (r-RESPA). A top-down FMM is proposed which calculates multipoles recursively from the top of the box tree instead of from the bottom in Greengard’s original FMM, in an effort to be more efficient for noncubic or nonuniform systems. In addition, the use of noncubic box subdivisions of biomolecular systems is used and discussed. Reversible RESPA based on a Trotter factorization of the Liouville propagator in generating numerical integration schemes is coupled to the top-down FMM and applied to a MD study of proteins in vacuo, and is shown to be able to use a much larger time-step than the standard velocity Verlet method for a comparable level of accuracy. Furthermore, by using the FMM it becomes possible to perform MD simulations for very large biomolecules, since memory and CPU time requirements are now nearly of order of O(N) instead of O(N2). For a protein with 9513 atoms (the photosynthetic reaction center), the efficient MD algorithm leads to 20-fold reduction in CPU time for the Coulomb interaction and approximately 15-fold reduction in total CPU time over the standard velocity Verlet algorithm with a direct evaluation of Coulomb forces. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]