Evaluation of a fast implicit solvent model for molecular dynamics simulations

Kinetics from Implicit Solvent Simulations of Biomolecules as a Function of Viscosity

Kinetic properties of alanine dipeptide, the B1 domain of streptococcal protein G, and ubiquitin are compared between explicit solvent and implicit solvent simulations with the generalized Born molecular volume (GBMV) method. The results indicate that kinetics from explicit solvent simulations and experiments can be matched closely when the implicit solvent simulations are combined with Langevin dynamics and a friction coefficient near 10 ps(-1). Smaller and larger friction coefficients accelerate and slow down conformational sampling. It is found that local conformational exploration without the crossing of significant barriers can be accelerated by a factor of 4-5; however, the acceleration of barrier crossings is limited to about a factor of 2. The use of a Nosé-Hoover thermostat instead of Langevin dynamics greatly enhances local conformational sampling but slows down the crossing of barriers by at least an order of magnitude because of the lack of solute-solvent stochastic collisions.

Effective Approximation of Molecular Volume Using Atom-Centered Dielectric Functions in Generalized Born Models

The generalized Born (GB) theory is a prime choice for implicit treatment of solvent that provides a favorable balance between efficiency and accuracy for reliable simulation of protein conformational equilibria. In GB, the dielectric boundary is a key physical property that needs to be properly described. While it is widely accepted that the molecular surface (MS) should provide the most physical description, most existing GB models are based on van der Waals (vdW)-like surfaces for computational simplicity and efficiency. A simple and effective approximation to molecular volume is explored here using atom-centered dielectric functions within the context of a generalized Born model with simple switching (GBSW). The new model, termed GBSW/MS2, is as efficient as the original vdW-like-surface-based GBSW model, but is able to reproduce the Born radii calculated from the "exact" Poisson-Boltzmann theory with a correlation of 0.95. More importantly, examination of the potentials of mean force of hydrogen-bonding and charge-charge interactions demonstrates that GBSW/MS2 correctly captures the first desolvation peaks, a key signature of true MS. Physical parameters including atomic input radii and peptide backbone torsion were subsequently optimized on the basis of solvation free energies of model compounds, potentials of mean force of their interactions, and conformational equilibria of a set of helical and β-hairpin model peptides. The resulting GBSW/MS2 protein force field reasonably recapitulates the structures and stabilities of these model peptides. Several remaining limitations and possible future developments are also discussed.

A hydrodynamic view of the first-passage folding of Trp-cage miniprotein

We study folding of Trp-cage miniprotein in the conditions when the native state of the protein is stable and unfolding events are improbable, which corresponds to physiological conditions. Using molecular dynamics simulations with an implicit solvent model, an ensemble of folding trajectories from unfolded (practically extended) states of the protein to the native state was generated. To get insight into the folding kinetics, the free energy surface and kinetic network projected on this surface were constructed. This, "conventional" analysis of the folding reaction was followed by a recently proposed hydrodynamic description of protein folding (Chekmarev et al. in Phys Rev Lett 100(1):018107, 2008), in which the process of the first-passage folding is viewed as a stationary flow of a folding "fluid" from the unfolded to native state. This approach is conceptually different from the previously used approaches and thus allows an alternative view of the folding dynamics and kinetics of Trp-cage, the conclusions about which are very diverse. In agreement with most previous studies, we observed two characteristic folding pathways: in one pathway (I), the collapse of the hydrophobic core precedes the formation of the [Formula: see text]-helix, and in the other pathway (II), these events occur in the reverse order. We found that although pathway II is complicated by a repeated partial protein unfolding, it contributes to the total folding flow as little as ≈10%, so that the folding kinetics remain essentially single-exponential.

Equilibration of Protein States: A Time Dependent Free-Energy Disconnectivity Graph

The process of equilibration of protein states in a three-stranded antiparallel β-sheet miniprotein is studied using a time-dependent free energy disconnectivity graph. To determine the rates of transitions, the molecular dynamics simulation results of a recent work (Kalgin, I. V.; J. Phys. Chem. B 2013, 117, 6092) are employed. The vertices of the graph are the free energies of characteristic states of the protein, and the edges are the transition state free energies. To determine the latter, the "complete" partition function (Eyring, 1935) is used, which includes the translational partition function corresponding to the ballistic motion of the system along the reaction coordinate. The distance along the reaction coordinate that enters the translational partition function is taken to be proportional to the observation time and thus measures the number of representative points that cross the transition state surface during given time. As the time increases, the free energy barriers between the clusters of characteristic conformations (native-like, helical, and β-sheet conformations of different degree of organization) decrease and (local) equilibrium between the clusters is established. With time, these clusters are grouped into larger clusters, extending the equilibrium to a larger portion of protein states.

An in-depth assessment into simultaneous monitoring of dissolved reactive phosphorus (DRP) and low-molecular-weight organic phosphorus (LMWOP) in aquatic environments using diffusive gradients in thin films (DGT)

Long-term laborious and thus costly monitoring of phosphorus (P) fractions is required in order to provide reasonable estimates of the levels of bioavailable phosphorus for eutrophication studies. A practical solution to this problem is the application of passive samplers, known as Diffusive Gradient in Thin films (DGTs), providing time-average concentrations. DGT, with the phosphate adsorbent Fe-oxide based binding gel, is capable of collecting both orthophosphate and low molecular weight organic phosphorus (LMWOP) compounds, such as adenosine monophosphate (AMP) and myo-inositol hexakisphosphate (IP6). The diffusion coefficient (D) is a key parameter relating the amount of analyte determined from the DGT to a time averaged ambient concentration. D at 20 °C for AMP and IP6 were experimentally determined to be 2.9 × 10(-6) cm(2) s(-1) and 1.0 × 10(-6) cm(2) s(-1), respectively. Estimations by conceptual models of LMWOP uptake by DGTs indicated that this fraction constituted more than 75% of the dissolved organic phosphorus (DOP) accumulated. Since there is no one D for LMWOP, a D range was estimated through assessment of D models. The models tested for estimating D for a variety of common LMWOP molecules proved to be still too uncertain for practical use. The experimentally determined D for AMP and IP6 were therefore used as upper and lower D, respectively, in order to estimate minimum and maximum ambient concentrations of LMWOP. Validation of the DGT data was performed by comparing concentrations of P fractions determined in natural water samples with concentration of P fractions determined using DGT. Stream water draining three catchments with different land-use (forest, mixed and agriculture) showed clear differences in relative and absolute concentrations of dissolved reactive phosphorus (DRP) and dissolved organic P (DOP). There was no significant difference between water sample and DGT DRP (p > 0.05). Moreover, the upper and lower limit D for LMWOP proved reasonable as water sample determined DOP was found to lie in-between the limits of DGT LMWOP concentrations, indicating that on average DOP consists mainly of LMWOP. "Best fit" D was determined for each stream in order to practically use the DGTs for estimating time average DOP. Applying DGT in a eutrophic lake provided insight into P cycling in the water column.

Designing and exploring active N'-[(5-nitrofuran-2-yl) methylene] substituted hydrazides against three Trypanosoma cruzi strains more prevalent in Chagas disease patients

Chagas disease affects around 8 million people worldwide and its treatment depends on only two nitroheterocyclic drugs, benznidazole (BZD) and nifurtimox (NFX). Both drugs have limited curative power in chronic phase of disease. Nifuroxazide (NF), a nitroheterocyclic drug, was used as lead to design a set of twenty one compounds in order to improve the anti-Trypanosoma cruzi activity. Lipinski's rules were considered in order to support drug-likeness designing. The set of N'-[(5-nitrofuran-2-yl) methylene] substituted hydrazides was assayed against three T. cruzi strains, which represent the discrete typing units more prevalent in human patients: Y (TcII), Silvio X10 cl1 (TcI), and Bug 2149 cl10 (TcV). All the derivatives, except one, showed enhanced trypanocidal activity against the three strains as compared to BZD. In the Y strain 62% of the compounds were more active than NFX. The most active compound was N'-((5-nitrofuran-2-yl) methylene)biphenyl-4-carbohydrazide (C20), which showed IC50 values of 1.17 ± 0.12 μM; 3.17 ± 0.32 μM; and 1.81 ± 0.18 μM for Y, Silvio X10 cl1, and Bug 2149 cl10 strains, respectively. Cytotoxicity assays with human fibroblast cells have demonstrated high selectivity indices for several compounds. Exploratory data analysis indicated that primarily topological, steric/geometric, and electronic properties have contributed to the discrimination of the set of investigated compounds. The findings can be helpful to drive the designing, and subsequently, the synthesis of additional promising drugs against Chagas disease.

Folding of a β-sheet miniprotein: probability fluxes, streamlines, and the potential for the driving force

In this work we continue the study of the first-passage folding of an antiparallel β-sheet miniprotein (beta3s) that was initiated in the previous work [Kalgin et al. J. Phys. Chem. B, 2014, 118, 4287]. We consider a larger ensemble of folding trajectories, which allows us to gain a closer insight into the folding dynamics. In particular, we calculate the potential for the driving force of folding in a reduced space of collective variables. The potential has two components. One component (Φ) is responsible for the source and sink of the folding flow, which are formed, respectively, in the regions of the unfolded and native states of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the sides of the reaction channel and provides the canalization of the folding flow between the source and sink. We show that both components obey Poisson's equations with the corresponding source/sink terms. The resulting components have a very simple form: the Φ-surface consists of two well-defined peaks of different signs, which correspond, respectively, to the source and sink of the folding flow, and the Ψ-surface consists of two ridges of different signs that connect the source and sink of the flow.

Molecular modeling of peptides

This article presents a review of the field of molecular modeling of peptides. The main focus is on atomistic modeling with molecular mechanics potentials. The description of peptide conformations and solvation through potentials is discussed. Several important computer simulation methods are briefly introduced, including molecular dynamics, accelerated sampling approaches such as replica-exchange and metadynamics, free energy simulations and kinetic network models like Milestoning. Examples of recent applications for predictions of structure, kinetics, and interactions of peptides with complex environments are described. The reliability of current simulation methods is analyzed by comparison of computational predictions obtained using different models with each other and with experimental data. A brief discussion of coarse-grained modeling and future directions is also presented.

Simulations and experiments in protein folding

The interplay between simulations and experiments of protein folding has largely contributed to the elucidation of many important aspects of the phenomenon. In this chapter, I briefly describe the experiments which provide information on the kinetics of the protein folding process, and help to characterize the folding transition state. Then, I show how to probe the kinetics of protein folding using molecular dynamics simulations, how to compare the simulations with the experiments and how to help and rationalize the latter, ultimately offering a molecular picture of the process. After the production of suitable molecular dynamics simulation data in the form of trajectories, the procedure involves sequentially the identification of the stable states of the protein, the identification of the transition pathways connecting the stable states, the identification of the transition state conformations, comparison with experimental results, and finally, the identification of the molecular determinants or reaction coordinates of the folding process, that is, the features that clearly help distinguishing the transition state from the stable states.

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm²) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies.

A relationship between the transient structure in the monomeric state and the aggregation propensities of α-synuclein and β-synuclein

α-Synuclein is an intrinsically disordered protein whose aggregation is implicated in Parkinson's disease. A second member of the synuclein family, β-synuclein, shares significant sequence similarity with α-synuclein but is much more resistant to aggregation. β-Synuclein is missing an 11-residue stretch in the central non-β-amyloid component region that forms the core of α-synuclein amyloid fibrils, yet insertion of these residues into β-synuclein to produce the βSHC construct does not markedly increase the aggregation propensity. To investigate the structural basis of these different behaviors, quantitative nuclear magnetic resonance data, in the form of paramagnetic relaxation enhancement-derived interatomic distances, are combined with molecular dynamics simulations to generate ensembles of structures representative of the solution states of α-synuclein, β-synuclein, and βSHC. Comparison of these ensembles reveals that the differing aggregation propensities of α-synuclein and β-synuclein are associated with differences in the degree of residual structure in the C-terminus coupled to the shorter separation between the N- and C-termini in β-synuclein and βSHC, making protective intramolecular contacts more likely.

Structural transitions and energy landscape for Cowpea Chlorotic Mottle Virus capsid mechanics from nanomanipulation in vitro and in silico

Physical properties of capsids of plant and animal viruses are important factors in capsid self-assembly, survival of viruses in the extracellular environment, and their cell infectivity. Combined AFM experiments and computational modeling on subsecond timescales of the indentation nanomechanics of Cowpea Chlorotic Mottle Virus capsid show that the capsid's physical properties are dynamic and local characteristics of the structure, which change with the depth of indentation and depend on the magnitude and geometry of mechanical input. Under large deformations, the Cowpea Chlorotic Mottle Virus capsid transitions to the collapsed state without substantial local structural alterations. The enthalpy change in this deformation state ΔHind = 11.5-12.8 MJ/mol is mostly due to large-amplitude out-of-plane excitations, which contribute to the capsid bending; the entropy change TΔSind = 5.1-5.8 MJ/mol is due to coherent in-plane rearrangements of protein chains, which mediate the capsid stiffening. Direct coupling of these modes defines the extent of (ir)reversibility of capsid indentation dynamics correlated with its (in)elastic mechanical response to the compressive force. This emerging picture illuminates how unique physico-chemical properties of protein nanoshells help define their structure and morphology, and determine their viruses' biological function.

First passage analysis of the folding of a β-sheet miniprotein: is it more realistic than the standard equilibrium approach?

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed ”streamlines”, the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations.

Evolution- and structure-based computational strategy reveals the impact of deleterious missense mutations on MODY 2 (maturity-onset diabetes of the young, type 2)

Heterozygous mutations in the central glycolytic enzyme glucokinase (GCK) can result in an autosomal dominant inherited disease, namely maturity-onset diabetes of the young, type 2 (MODY 2). MODY 2 is characterised by early onset: it usually appears before 25 years of age and presents as a mild form of hyperglycaemia. In recent years, the number of known GCK mutations has markedly increased. As a result, interpreting which mutations cause a disease or confer susceptibility to a disease and characterising these deleterious mutations can be a difficult task in large-scale analyses and may be impossible when using a structural perspective. The laborious and time-consuming nature of the experimental analysis led us to attempt to develop a cost-effective computational pipeline for diabetic research that is based on the fundamentals of protein biophysics and that facilitates our understanding of the relationship between phenotypic effects and evolutionary processes. In this study, we investigate missense mutations in the GCK gene by using a wide array of evolution- and structure-based computational methods, such as SIFT, PolyPhen2, PhD-SNP, SNAP, SNPs&GO, fathmm, and Align GVGD. Based on the computational prediction scores obtained using these methods, three mutations, namely E70K, A188T, and W257R, were identified as highly deleterious on the basis of their effects on protein structure and function. Using the evolutionary conservation predictors Consurf and Scorecons, we further demonstrated that most of the predicted deleterious mutations, including E70K, A188T, and W257R, occur in highly conserved regions of GCK. The effects of the mutations on protein stability were computed using PoPMusic 2.1, I-mutant 3.0, and Dmutant. We also conducted molecular dynamics (MD) simulation analysis through in silico modelling to investigate the conformational differences between the native and the mutant proteins and found that the identified deleterious mutations alter the stability, flexibility, and solvent-accessible surface area of the protein. Furthermore, the functional role of each SNP in GCK was identified and characterised using SNPeffect 4.0, F-SNP, and FASTSNP. We hope that the observed results aid in the identification of disease-associated mutations that affect protein structure and function. Our in silico findings provide a new perspective on the role of GCK mutations in MODY2 from an evolution-based structure-centric point of view. The computational architecture described in this paper can be used to predict the most appropriate disease phenotypes for large-genome sequencing projects and to provide individualised drug therapy for complex diseases such as diabetes.

Variational Optimization of an All-Atom Implicit Solvent Force Field to Match Explicit Solvent Simulation Data

The development of accurate implicit solvation models with low computational cost is essential for addressing many large-scale biophysical problems. Here, we present an efficient solvation term based on a Gaussian solvent-exclusion model (EEF1) for simulations of proteins in aqueous environment, with the primary aim of having a good overlap with explicit solvent simulations, particularly for unfolded and disordered states - as would be needed for multiscale applications. In order to achieve this, we have used a recently proposed coarse-graining procedure based on minimization of an entropy-related objective function to train the model to reproduce the equilibrium distribution obtained from explicit water simulations. Via this methodology, we have optimized both a charge screening parameter and a backbone torsion term against explicit solvent simulations of an α-helical and a β-stranded peptide. The performance of the resulting effective energy function, termed EEF1-SB, is tested with respect to the properties of folded proteins, the folding of small peptides or fast-folding proteins, and NMR data for intrinsically disordered proteins. The results show that EEF1-SB provides a reasonable description of a wide range of systems, but its key advantage over other methods tested is that it captures very well the structure and dimension of disordered or weakly structured peptides. EEF1-SB is thus a computationally inexpensive (~ 10 times faster than Generalized-Born methods) and transferable approximation for treating solvent effects.

Molecular docking and molecular dynamics study on the effect of ERCC1 deleterious polymorphisms in ERCC1-XPF heterodimer

Excision repair cross complementation group 1 (ERCC1) is an important protein in the nucleotide excision repair (NER) pathway, which is responsible for removing DNA adducts induced by platinum based compounds. The heterodimer ERCC1-XPF is one of two endonucleases required for NER. Genetic variations or polymorphisms in ERCC1 gene alter DNA repair capacity. Reduced DNA repair (NER) capacity may result in tumors and enhances cisplatin chemotherapy in cancer patients, which functions by causing DNA damage. Therefore, ERCC1 variants have the potential to be used as a strong candidate biomarker in cancer treatments. In this study we identified five variants V116M, R156Q, A199T, S267P, and R322C of ERCC1 gene as highly deleterious. Further structural and functional analysis has been conducted for ERCC1 protein in the presence of three variants V116M, R156Q, and A199T. Occurrence of theses variations adversely affected the regular interaction between ERCC1 and XPF protein. Analysis of 20 ns molecular dynamics simulation trajectories reveals that the predicted deleterious variants altered the ERCC1-XPF complex stability, flexibility, and surface area. Notably, the number of hydrogen bonds in ERCC1-XPF mutant complexes decreased in the molecular dynamic simulation periods. Overall, this study explores the link between the ERCC1 deleterious variants and cisplatin chemotherapy for various cancers with the help of molecular docking and molecular dynamic approaches.

Absolute hydration free energies of blocked amino acids: implications for protein solvation and stability

Most proteins perform their function in aqueous solution. The interactions with water determine the stability of proteins and the desolvation costs of ligand binding or membrane insertion. However, because of experimental restrictions, absolute solvation free energies of proteins or amino acids are not available. Instead, solvation free energies are estimated based on side chain analog data. This approach implies that the contributions to free energy differences are additive, and it has often been employed for estimating folding or binding free energies. However, it is not clear how much the additivity assumption affects the reliability of the resulting data. Here, we use molecular dynamics-based free energy simulations to calculate absolute hydration free energies for 15 N-acetyl-methylamide amino acids with neutral side chains. By comparing our results with solvation free energies for side chain analogs, we demonstrate that estimates of solvation free energies of full amino acids based on group-additive methods are systematically too negative and completely overestimate the hydrophobicity of glycine. The largest deviation of additive protocols using side chain analog data was 6.7 kcal/mol; on average, the deviation was 4 kcal/mol. We briefly discuss a simple way to alleviate the errors incurred by using side chain analog data and point out the implications of our findings for the field of biophysics and implicit solvent models. To support our results and conclusions, we calculate relative protein stabilities for selected point mutations, yielding a root-mean-square deviation from experimental results of 0.8 kcal/mol.

NESS06SM reduces body weight with an improved profile relative to SR141716A

We have recently synthesized a new series of 4,5-dihydrobenzo-oxa-cycloheptapyrazole derivatives with the aim to discover novel CB1 antagonist agents characterized by anti-obesity activity comparable to that of SR141716A but with reduced adverse effects such as anxiety and depression. Within the novel class, the CB1 antagonist 8-chloro-1-(2,4-dichlorophenyl)-N-piperidin-1-yl-4,5-dihydrobenzo-1H-6-oxa-cyclohepta(1,2-c)pyrazole-3-carboxamide (NESS06SM) has been selected as lead compound. We found that NESS06SM is a CB1 neutral antagonist, characterized by poor blood-brain barrier permeability. Moreover, NESS06SM chronic treatment determined both anti-obesity effect and cardiovascular risk factor improvement in C57BL/6N Diet Induced Obesity (DIO) mice fed with fat diet (FD mice). In fact, the mRNA gene expression in Central Nervous System (CNS) and peripheral tissues by real time PCR, showed a significant increase of orexigenic peptides and a decrease of anorexigenic peptides elicited by NESS06SM treatment, compared to control mice fed with the same diet. Moreover, in contrast to SR141716A treatment, the chronic administration of NESS06SM did not change mRNA expression of both monoaminergic transporters and neurotrophins highly related with anxiety and mood disorders. Our results suggest that NESS06SM reduces body weight and it can restore the disrupted expression profile of genes linked to the hunger-satiety circuit without altering monoaminergic transmission probably avoiding SR141716A side effects. Therefore the novel CB1 neutral antagonist could represent a useful candidate agent for the treatment of obesity and its metabolic complications.

New insights into the folding of a β-sheet miniprotein in a reduced space of collective hydrogen bond variables: application to a hydrodynamic analysis of the folding flow

A new analysis of the 20 μs equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel β-sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted principal component analysis (PCA); i.e., to make structured conformations more pronounced, only the formed bonds are included in determining the principal components. It is shown that a three-dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin), is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed, and it is complemented by a hydrodynamic analysis. The latter, making use of "passive tracers" in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortices which correspond to repeated local rearrangement, not only around minima of the free energy surface but also in flat regions between minima. The vortices revealed by the hydrodynamic analysis are apparently not evident in folding pathways generated by transition-path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is determined. Interestingly, the transition rates show an approximate exponential correlation with distance in the hydrogen bond subspace. Comparison with the many published studies shows good agreement with the present analysis for the parts that can be compared, supporting the robust character of our understanding of this "hydrogen atom" of protein folding.

Methylations of tryptophan-modified naphthoquinone affect its inhibitory potential toward Aβ aggregation

Aggregation of amyloid beta (Aβ) is the hallmark of Alzheimer's disease (AD). Small molecules inhibiting Aβ can be valuable therapeutics for AD. We have previously reported that 1,4-naphthoquinon-2-yl-l-tryptophan (NQTrp), reduces aggregation and oligomerization of Aβ in vitro and in vivo. In silico analysis further showed that certain functional groups of NQTrp, not in the aromatic rings, are also involved in binding and inhibiting Aβ. To better understand the exact mode of action and identify the groups crucial for NQTrp inhibitory activity, we conducted structure-activity analysis. Four derivatives of NQTrp were studied in silico: a D-isomer, two single-methylated and one double-methylated derivative. In silico results showed that the NQTrp groups involved in hydrogen bonds are the anilinic NH (i.e., the NH linker between the quinone and tryptophan moieties), the quinonic carbonyls, and the carboxylic acid. These predictions were supported by in vitro results. Our results should aid in designing improved small-molecule inhibitors of Aβ aggregation for treating AD.

Mechanical transition from α-helical coiled coils to β-sheets in fibrin(ogen)

We characterized the α-to-β transition in α-helical coiled-coil connectors of the human fibrin(ogen) molecule using biomolecular simulations of their forced elongation and theoretical modeling. The force (F)-extension (X) profiles show three distinct regimes: (1) the elastic regime, in which the coiled coils act as entropic springs (F < 100-125 pN; X < 7-8 nm); (2) the constant-force plastic regime, characterized by a force-plateau (F ≈ 150 pN; X ≈ 10-35 nm); and (3) the nonlinear regime (F > 175-200 pN; X > 40-50 nm). In the plastic regime, the three-stranded α-helices undergo a noncooperative phase transition to form parallel three-stranded β-sheets. The critical extension of the α-helices is 0.25 nm, and the energy difference between the α-helices and β-sheets is 4.9 kcal/mol per helical pitch. The soft α-to-β phase transition in coiled coils might be a universal mechanism underlying mechanical properties of filamentous α-helical proteins.

Comprehensive evaluation of lipophilicity of biogenic amines and related compounds using different chemically bonded phases and various descriptors

The retention behavior for a series of biogenic amines and related sympathomimetic drugs has been investigated in reversed-phase thin-layer chromatography using RP-2, RP-8, RP-18W, and Diol stationary phase and mixtures of phosphate buffer (pH = 7.10) and methanol in different proportions as mobile phases. Several methodologies like arithmetic mean of experimental retention values, extrapolation to zero methanol concentration procedure and principal component analysis were applied to retention data values (R(M)) in order to determine relevant parameters (mean of R(M) - mR(M), R(M0), and scores corresponding to the first principal component - PC1/R(M) respectively) encoding information on the lipophilic behavior of compounds. High similarities in lipophilicity behavior of investigated amines were highlighted by mR(M) and PC1/R(M) lipophilicity indices for all of the studied stationary phases. The experimental results were compared with some computed lipophilicity parameters expressed as distribution coefficients at working pH (logD), partition coefficients (logP(N), logP(I), and diff(logP(N-I))) concerning both neutral and fully protonated species and difference between both species, and also with various lipophilicity values (logP) generated by different commonly used software. Significant correlations were observed between the experimental lipophilicity indices mR(M) respectively PC1/R(M) and diff(logP(N-I) ) values in all cases.

7-Alkyl-3-benzylcoumarins: a versatile scaffold for the development of potent and selective cannabinoid receptor agonists and antagonists

A series of 7-alkyl-3-benzylcoumarins was designed, synthesized, and tested at cannabinoid CB(1) and CB(2) receptors in radioligand binding and cAMP accumulation studies. 7-Alkyl-3-benzylcoumarins were found to constitute a versatile scaffold for obtaining potent CB receptor ligands with high potency at either CB(1) or CB(2) and a broad spectrum of efficacies. Fine-tuning of compound properties was achieved by small modifications of the substitution pattern. The most potent compounds of the present series include 5-methoxy-3-(2-methylbenzyl)-7-pentyl-2H-chromen-2-one (19a, PSB-SB-1201), a selective CB(1)antagonist (K(i) CB(1) 0.022 μM), 5-methoxy-3-(2-methoxybenzyl)-7-pentyl-2H-chromen-2-one (21a, PSB-SB-1202), a dual CB(1)/CB(2)agonist (CB(1)K(i) 0.032 μM, EC(50) 0.056 μM; CB(2)K(i) 0.049 μM, EC(50) 0.014 μM), 5-hydroxy-3-(2-hydroxybenzyl)-7-(2-methyloct-2-yl)-2H-chromen-2-one (25b, PSB-SB-1203), a dual CB(1)/CB(2) ligand that blocks CB(1) but activates CB(2) receptors (CB(1)K(i) 0.244 μM; CB(2)K(i) 0.210 μM, EC(50) 0.054 μM), and 7-(1-butylcyclopentyl)-5-hydroxy-3-(2-hydroxybenzyl)-2H-chromen-2-one (27b, PSB-SB-1204), a selective CB(2) receptor agonist (CB(1)K(i) 1.59 μM; CB(2)K(i) 0.068 μM, EC(50) 0.048 μM).

Distribution of Reciprocal of Interatomic Distances: A Fast Structural Metric

We present a structural metric based on the Distribution of Reciprocal of Interatomic Distances (DRID) for evaluating geometrical similarity between two conformations of a molecule. A molecular conformation is described by a vector of 3N orientation-independent DRID descriptors where N is the number of molecular centroids, for example, the non-hydrogen atoms in all nonsymmetric groups of a peptide. For two real-world applications (pairwise comparison of snapshots from an explicit solvent simulation of a protease/peptide substrate complex and implicit solvent simulations of reversible folding of a 20-residue β-sheet peptide), the DRID-based metric is shown to be about 5 and 15 times faster than coordinate root-mean-square deviation (cRMSD) and distance root-mean-square deviation (dRMSD), respectively. A single core of a mainstream processor can perform about 10(8) DRID comparisons in one-half a minute. Importantly, the DRID metric has closer similarity to kinetic distance than does either cRMSD or dRMSD. Therefore, DRID is suitable for clustering molecular dynamics trajectories for kinetic analysis, for example, by Markov state models. Moreover, conformational space networks and free energy profiles derived by DRID-based clustering preserve the kinetic information.

Implicit Solvation Parameters Derived from Explicit Water Forces in Large-Scale Molecular Dynamics Simulations

Implicit solvation is a mean force approach to model solvent forces acting on a solute molecule. It is frequently used in molecular simulations to reduce the computational cost of solvent treatment. In the first instance, the free energy of solvation and the associated solvent–solute forces can be approximated by a function of the solvent-accessible surface area (SASA) of the solute and differentiated by an atom–specific solvation parameter σ_i^SASA. A procedure for the determination of values for the σ_i^SASA parameters through matching of explicit and implicit solvation forces is proposed. Using the results of Molecular Dynamics simulations of 188 topologically diverse protein structures in water and in implicit solvent, values for the σ_i^SASA parameters for atom types i of the standard amino acids in the GROMOS force field have been determined. A simplified representation based on groups of atom types σ_g^SASA was obtained via partitioning of the atom–type σ_i^SASA distributions by dynamic programming. Three groups of atom types with well separated parameter ranges were obtained, and their performance in implicit versus explicit simulations was assessed. The solvent forces are available at http://mathbio.nimr.mrc.ac.uk/wiki/Solvent_Forces.

Free Energy Guided Sampling

A free energy-guided sampling (FEGS) method is proposed for accelerating exploration of conformational space in unbiased molecular dynamics. Using the cut-based free energy profile and Markov state models, FEGS speeds up sampling of the canonical ensemble by iteratively restarting multiple short simulations in parallel from regions of the free energy surface visited rarely. This exploration stage is followed by a refinement stage in which multiple independent runs are initiated from Boltzmann distributed conformations. Notably, FEGS does not require either collective variables or reaction coordinates and can control the kinetic distance from the starting conformation. We applied FEGS to the alanine dipeptide, which has a human-comprehensible two-dimensional free energy landscape, and a three-stranded antiparallel β-sheet peptide of 20 residues whose folding/unfolding process is governed by a delicate interplay of enthalpy and entropy. For these two systems, FEGS speeds up the exploration of conformational space by 1 to 2 orders of magnitude with respect to conventional sampling and preserves the basins and barriers on the free energy profile.

Sorption behavior of charged and neutral polar organic compounds on solid phase extraction materials: which functional group governs sorption?

Numerous polar anthropogenic organic chemicals have been found in the aqueous environment. Solid phase extraction (SPE) has been applied for the isolation of these from aqueous matrices, employing various materials. Nevertheless, little is known about the influence of functional groups on the sorption of the solutes onto these materials. Therefore, the sorption interactions of (charged) polar organic solutes to neutral (HLB), cation-exchanging (MCX, WCX), and anion-exchanging (MAX, WAX) OASIS polymers have been studied. For neutral solutes HLB has the highest capacity and affinity. Van der Waals interaction, rather than hydrogen bonding, appears to be the predominant factor determining sorption. For charged molecules, MCX and MAX show by far the highest affinity and capacity. Adsorption is already efficient at low concentrations and the maximum sorption capacity equals the amount of charged functional groups on the material. The results from this study allow semiquantitative predictions if a solute will adsorb on one of the OASIS materials and which functional groups govern adsorption.

Kinetic rate constant prediction supports the conformational selection mechanism of protein binding

The prediction of protein-protein kinetic rate constants provides a fundamental test of our understanding of molecular recognition, and will play an important role in the modeling of complex biological systems. In this paper, a feature selection and regression algorithm is applied to mine a large set of molecular descriptors and construct simple models for association and dissociation rate constants using empirical data. Using separate test data for validation, the predicted rate constants can be combined to calculate binding affinity with accuracy matching that of state of the art empirical free energy functions. The models show that the rate of association is linearly related to the proportion of unbound proteins in the bound conformational ensemble relative to the unbound conformational ensemble, indicating that the binding partners must adopt a geometry near to that of the bound prior to binding. Mirroring the conformational selection and population shift mechanism of protein binding, the models provide a strong separate line of evidence for the preponderance of this mechanism in protein-protein binding, complementing structural and theoretical studies.

Protein-water interactions in MD simulations: POPS/POPSCOMP solvent accessibility analysis, solvation forces and hydration sites

The effects of solvation on molecular recognition are investigated from different perspectives, ranging from methods to analyse explicit solvent dynamical behaviour at the protein surface to methods for the implicit treatment of solvent effects associated with the conformational behaviour of biomolecules. The here presented implicit solvation method is based on an analytical approximation of the Solvent Accessible Surface Area (SASA) of solute molecules, which is computationally efficient and easy to parametrise. The parametrised SASA solvation method is discussed in the light of protein design and ligand binding studies. The POPS program for the SASA computation on single molecules and complex interfaces is described in detail. Explicit solvent behaviour is described here in the form of solvent density maps at the protein surface. We highlight the usefulness of that approach in defining the organisation of specific water molecules at functional sites and in determining hydrophobicity scores for the identification of potential interaction patches.

Force fields for homology modeling

Accurate all-atom energy functions are crucial for successful high-resolution protein structure prediction. In this chapter, we review both physics-based force fields and knowledge-based potentials used in protein modeling. Because it is important to calculate the energy as accurately as possible given the limitations imposed by sampling convergence, different components of the energy, and force fields representing them to varying degrees of detail and complexity are discussed. Force fields using Cartesian as well as torsion angle representations of protein geometry are covered. Since solvent is important for protein energetics, different aqueous and membrane solvation models for protein simulations are also described. Finally, we summarize recent progress in protein structure refinement using new force fields.

Does amino acid sequence determine the properties of Aβ dimer?

The effect of random reshuffling of amino acids on the properties of dimers formed by Aβ peptides is studied using replica exchange molecular dynamics and united atom implicit solvent model. We show that thermodynamics of dimer assembly and the dimer globule-like state are not affected by sequence permutation. Furthermore, sequence reshuffling does not change the distributions of non-local interactions and, to a large extent, amino acids in the dimer volume. To rationalize these results, we demonstrate that Gaussian statistics applies surprisingly well to the end-to-end distances of the peptides in the dimer implying that non-bonded interactions between distant along the chain amino acids are effectively screened. This observation suggests that peptides in the dimer behave as ideal chains in polymer melt, in which amino acids lose their "identity" and therefore the memory of sequence position. As a result large-scale properties of the dimer become universal or sequence independent. Comparison of our simulations with the prior theoretical studies and their implications for experiments are discussed.

New functionalities in the GROMOS biomolecular simulation software

Since the most recent description of the functionalities of the GROMOS software for biomolecular simulation in 2005 many new functions have been implemented. In this article, the new functionalities that involve modified forces in a molecular dynamics (MD) simulation are described: the treatment of electronic polarizability, an implicit surface area and internal volume solvation term to calculate interatomic forces, functions for the GROMOS coarse-grained supramolecular force field, a multiplicative switching function for nonbonded interactions, adiabatic decoupling of a number of degrees of freedom with temperature or force scaling to enhance sampling, and nonequilibrium MD to calculate the dielectric permittivity or viscosity. Examples that illustrate the use of these functionalities are given.

Delineation of folding pathways of a β-sheet miniprotein

Several methods have been developed in the past few years for the analysis of molecular dynamics simulations of biological (macro)molecules whose complexity is difficult to capture by simple projections of the free-energy surface onto one or two geometric variables. The locally scaled diffusion map (LSDMap) method is a nonlinear dimensionality reduction technique for describing the dynamics of complex systems in terms of a few collective coordinates. Here, we compare LSDMap to two previously developed approaches for the characterization of the configurational landscape associated with the folding dynamics of a three-stranded antiparallel β-sheet peptide, termed Beta3s. The analysis is aided by an improved procedure for extracting pathways from the equilibrium transition network, which enables calculation of pathway-specific cut-based free energy profiles. We find that the results from LSDMap are consistent with analysis based on transition networks and allow a coherent interpretation of metastable states and folding pathways in terms of different time scales of transitions between minima on the free energy projections.

Motion of a disordered polypeptide chain as studied by paramagnetic relaxation enhancements, 15N relaxation, and molecular dynamics simulations: how fast is segmental diffusion in denatured ubiquitin?

Molecular dynamics (MD) simulations have been widely used to analyze dynamic conformational equilibria of folded proteins, especially in relation to NMR observables. However, this approach found little use in the studies of disordered proteins, where the sampling of vast conformational space presents a serious problem. In this paper, we demonstrate that the latest advances in computation technology make it possible to overcome this limitation. The experimentally validated (calibrated) MD models allow for new insights into structure/dynamics of disordered proteins. As a test system, we have chosen denatured ubiquitin in solution with 8 M urea at pH 2. High-temperature MD simulations in implicit solvent have been carried out for the wild-type ubiquitin as well as MTSL-tagged Q2C, D32C, and R74C mutants. To recalibrate the MD data (500 K) in relation to the experimental conditions (278 K, 8 M urea), the time axes of the MD trajectories were rescaled. The scaling factor was adjusted such as to maximize the agreement between the simulated and experimental (15)N relaxation rates. The resulting effective length of the trajectories, 311 μs, ensures good convergence properties of the MD model. The constructed MD model was validated against the array of experimental data, including additional (15)N relaxation parameters, multiple sets of paramagnetic relaxation enhancements (PREs), and the radius of gyration. In each case, a near-quantitative agreement has been obtained, suggesting that the model is successful. Of note, the MD-based approach rigorously predicts the quantities that are inherently dynamic, i.e., dependent on the motional correlation times. This cannot be accomplished, other than in empirical fashion, on the basis of static structural models (conformational ensembles). The MD model was further used to investigate the relative translational motion of the MTSL label and the individual H(N) atoms. The derived segmental diffusion coefficients proved to be nearly uniform along the peptide chain, averaging to D = 0.49-0.55 × 10(-6) cm(2)/s. This result was verified by direct analysis of the experimental PRE data using the recently proposed Ullman-Podkorytov model. In this model, MTSL and H(N) moieties are treated as two tethered spheres undergoing mutual diffusion in a harmonic potential. The fitting of the experimental data involving D as a single adjustable parameter leads to D = 0.45 × 10(-6) cm(2)/s, in good agreement with the MD-based analyses. This result can be compared with the range of estimates obtained from the resonance energy transfer experiments, D = 0.2-6.0 × 10(-6) cm(2)/s.