How well can simulation predict protein folding kinetics and thermodynamics?

Unveiling the molecular interaction of hepatitis B virus inhibitor, entecavir with human serum albumin through computational, microscopic and spectroscopic approaches

Molecular docking, molecular dynamics (MD) simulation, atomic force microscopy (AFM) and multi-spectroscopic techniques were selected to unveil the molecular association between the hepatitis B virus (HBV) inhibitor, entecavir (ETR), and the major blood plasma transporter, human serum albumin (HSA). The entire docking and simulation analyses recognized ETR binding to subdomain IIA (Site I) of HSA through hydrogen bonds, hydrophobic and van der Waals forces while maintaining the complex's stability throughout the 100 ns. A gradual lessening in the Stern-Volmer quenching constant (K sv ) with rising temperatures registered ETR-induced quenching of HBV fluorescence as static quenching, thus advising complexation between ETR and HSA. The further advocation of this conclusion was seen from a larger value of the biomolecular quenching rate constant ((kq ) > 1010 M-1s-1), changes in the spectra (UV-Vis absorption) of HSA following ETR inclusion and ETR-induced swelling of HSA in the AFM results. The ETR appeared to bind to HSA with moderate affinity (K a = 1.87 - 1.19 × 10 4   M-1) at 290, 300 and 310 K. Significant alterations in the protein's secondary and tertiary structures, including changes in the protein's Tyr/Trp microenvironment, were also detected by circular dichroism and three-dimensional fluorescence spectra when the protein was bound to ETR. The findings of the drug displacement study backed the docking results of Site I as ETR's preferred binding site in HSA.Communicated by Ramaswamy H. Sarma.

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and ab initio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500 ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

Folding@home: Achievements from over 20 years of citizen science herald the exascale era

Simulations of biomolecules have enormous potential to inform our understanding of biology but require extremely demanding calculations. For over 20 years, the Folding@home distributed computing project has pioneered a massively parallel approach to biomolecular simulation, harnessing the resources of citizen scientists across the globe. Here, we summarize the scientific and technical advances this perspective has enabled. As the project's name implies, the early years of Folding@home focused on driving advances in our understanding of protein folding by developing statistical methods for capturing long-timescale processes and facilitating insight into complex dynamical processes. Success laid a foundation for broadening the scope of Folding@home to address other functionally relevant conformational changes, such as receptor signaling, enzyme dynamics, and ligand binding. Continued algorithmic advances, hardware developments such as graphics processing unit (GPU)-based computing, and the growing scale of Folding@home have enabled the project to focus on new areas where massively parallel sampling can be impactful. While previous work sought to expand toward larger proteins with slower conformational changes, new work focuses on large-scale comparative studies of different protein sequences and chemical compounds to better understand biology and inform the development of small-molecule drugs. Progress on these fronts enabled the community to pivot quickly in response to the COVID-19 pandemic, expanding to become the world's first exascale computer and deploying this massive resource to provide insight into the inner workings of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus and aid the development of new antivirals. This success provides a glimpse of what is to come as exascale supercomputers come online and as Folding@home continues its work.

Exploring the Folding Mechanism of Dimeric Superoxide Dismutase

The Cu/Zn Human Superoxide Dismutase (SOD1) is a dimeric metalloenzyme whose genetic mutations are directly related to amyotrophic lateral sclerosis (ALS), so understanding its folding mechanism is of fundamental importance. Currently, the SOD1 dimer formation is studied via molecular dynamics simulations using a simplified structure-based model and an all-atom model. Results from the simplified model reveal a mechanism dependent on distances between monomers, which are limited by constraints to mimic concentration dependence. The stability of intermediates (during the int state) is significantly affected by this distance, as well as by the presence of two folded monomers prior to dimer formation. The kinetics of interface formation are also highly dependent on the separation distance. The folding temperature of the dimer is about 4.2% higher than that of the monomer, a value not too different from experimental data. All-atom simulations on the apo dimer give binding free energy between monomers similar to experimental values. An intermediate state is evident for the apo form at a separation distance between monomers slightly larger than the native distance which has little formed interface between monomers. We have shown that this intermediate is stabilized by non-native intra- and intercontacts.

Energetics and structure of alanine-rich α-helices via adaptive steered molecular dynamics

The energetics and hydrogen bonding profiles of the helix-to-coil transition were found to be an additive property and to increase linearly with chain length, respectively, in alanine-rich α-helical peptides. A model system of polyalanine repeats was used to establish this hypothesis for the energetic trends and hydrogen bonding profiles. Numerical measurements of a synthesized polypeptide Ac-Y(AEAAKA)kF-NH2 and a natural α-helical peptide a2N (1-17) provide evidence of the hypothesis's generality. Adaptive steered molecular dynamics was employed to investigate the mechanical unfolding of all of these alanine-rich polypeptides. We found that the helix-to-coil transition is primarily dependent on the breaking of the intramolecular backbone hydrogen bonds and independent of specific side-chain interactions and chain length. The mechanical unfolding of the α-helical peptides results in a turnover mechanism in which a 310-helical structure forms during the unfolding, remaining at a near constant population and thereby maintaining additivity in the free energy. The intermediate partially unfolded structures exhibited polyproline II helical structure as previously seen by others. In summary, we found that the average force required to pull alanine-rich α-helical peptides in between the endpoints-namely the native structure and free coil-is nearly independent of the length or the specific primary structure.

Incorporating Machine Learning into Established Bioinformatics Frameworks

The exponential growth of biomedical data in recent years has urged the application of numerous machine learning techniques to address emerging problems in biology and clinical research. By enabling the automatic feature extraction, selection, and generation of predictive models, these methods can be used to efficiently study complex biological systems. Machine learning techniques are frequently integrated with bioinformatic methods, as well as curated databases and biological networks, to enhance training and validation, identify the best interpretable features, and enable feature and model investigation. Here, we review recently developed methods that incorporate machine learning within the same framework with techniques from molecular evolution, protein structure analysis, systems biology, and disease genomics. We outline the challenges posed for machine learning, and, in particular, deep learning in biomedicine, and suggest unique opportunities for machine learning techniques integrated with established bioinformatics approaches to overcome some of these challenges.

Update and Potential Opportunities in CBP [Cyclic Adenosine Monophosphate (cAMP) Response Element-Binding Protein (CREB)-Binding Protein] Research Using Computational Techniques

CBP [cyclic adenosine monophosphate (cAMP) response element-binding protein (CREB)-binding protein] is one of the most researched proteins for its therapeutic function. Several studies have identified its vast functions and interactions with other transcription factors to initiate cellular signals of survival. In cancer and other diseases such as Alzheimer's, Rubinstein-taybi syndrome, and inflammatory diseases, CBP has been implicated and hence an attractive target in drug design and development. In this review, we explore the various computational techniques that have been used in CBP research, furthermore we identified computational gaps that could be explored to facilitate the development of highly therapeutic CBP inhibitors.

Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling

Fitting mathematical models with a direct connection to experimental observables to the outputs of molecular simulations can be a powerful tool for extracting important physical information from them. In this study, we present two new approaches that use stochastic time series modeling to predict long-time-scale behavior and macroscopic properties from molecular simulation, which can be generalized to other molecular systems where complex diffusion occurs. In our previous work, we studied long molecular dynamics (MD) simulation trajectories of a cross-linked H_II phase lyotropic liquid crystal (LLC) membrane, where we observed subdiffusive solute transport behavior characterized by intermittent hops separated by periods of entrapment. In this work, we use our models to parameterize the behavior of the same systems, so we can generate characteristic trajectory realizations that can be used to predict solute mean-squared displacements (MSDs), solute flux, and solute selectivity in macroscopic length pores. First, using anomalous diffusion theory, we show how solute dynamics can be modeled as a fractional diffusion process subordinate to a continuous time random walk. From the MD simulations, we parameterize the distribution of dwell times, hop lengths between dwells, and correlation between hops. We explore two variations of the anomalous diffusion modeling approach. The first variation applies a single set of parameters to the solute displacements and the second applies two sets of parameters based on the solute's radial distance from the closest pore center. Next, we present an approach that generalizes Markov state models, treating the configurational states of the system as a Markov process where each state has distinct transport properties. For each state and transition between states, we parameterize the distribution and temporal correlation structure of positional fluctuations as a means of characterization and to allow us to predict solute MSDs. We show that both stochastic models reasonably reproduce the MSDs calculated from MD simulations. However, qualitative differences between MD and Markov state-dependent model-generated trajectories may in some cases limit their usefulness. With these parameterized stochastic models, we demonstrate how one can estimate the flux of a solute across a macroscopic length pore and, based on these quantities, the membrane's selectivity toward each solute. This work therefore helps to connect microscopic, chemically dependent solute motions that do not follow simple diffusive behavior with long-time-scale behavior, in an approach generalizable to many types of molecular systems with complex dynamics.

Combined approach of homology modeling, molecular dynamics, and docking: computer-aided drug discovery

With the continuous development in software, algorithms, and increase in computer speed, the field of computer-aided drug design has been witnessing reduction in the time and cost of the drug designing process. Structure based drug design (SBDD), which is based on the 3D structure of the enzyme, is helping in proposing novel inhibitors. Although a number of crystal structures are available in various repositories, there are various proteins whose experimental crystallization is difficult. In such cases, homology modeling, along with the combined application of MD and docking, helps in establishing a reliable 3D structure that can be used for SBDD. In this review, we have reported recent works, which have employed these three techniques for generating structures and further proposing novel inhibitors, for cytoplasmic proteins, membrane proteins, and metal containing proteins. Also, we have discussed these techniques in brief in terms of the theory involved and the various software employed. Hence, this review can give a brief idea about using these tools specifically for a particular problem.

Statistical Uncertainty Analysis for Small-Sample, High Log-Variance Data: Cautions for Bootstrapping and Bayesian Bootstrapping

Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive, and even significant computing resources may result in a small number of independent estimates spread over many orders of magnitude. Such small-sample, high "log-variance" data are not readily amenable to analysis using the standard uncertainty (i.e., "standard error of the mean") because unphysical negative limits of confidence intervals result. Bootstrapping, a natural alternative guaranteed to yield a confidence interval within the minimum and maximum values, also exhibits a striking systematic bias of the lower confidence limit in log space. As we show, bootstrapping artifactually assigns high probability to improbably low mean values. A second alternative, the Bayesian bootstrap strategy, does not suffer from the same deficit and is more logically consistent with the type of confidence interval desired. The Bayesian bootstrap provides uncertainty intervals that are more reliable than those from the standard bootstrap method but must be used with caution nevertheless. Neither standard nor Bayesian bootstrapping can overcome the intrinsic challenge of underestimating the mean from small-size, high log-variance samples. Our conclusions are based on extensive analysis of model distributions and reanalysis of multiple independent atomistic simulations. Although we only analyze rate constants, similar considerations will apply to related calculations, potentially including highly nonlinear averages like the Jarzynski relation.

Computational Estimation of Microsecond to Second Atomistic Folding Times

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the microsecond scale. Here, we report the folding of atomistic, implicitly solvated protein systems with folding times τ ranging from ∼10 μs to ∼100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τf = 0.8-9 μs), NTL9 at water-like viscosity (τf = 0.2-2 ms), and Protein G at low viscosity (τf = 3-200 ms). In all cases, the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

Fast pressure-jump all-atom simulations and experiments reveal site-specific protein dehydration-folding dynamics

As theory and experiment have shown, protein dehydration is a major contributor to protein folding. Dehydration upon folding can be characterized directly by all-atom simulations of fast pressure drops, which create desolvated pockets inside the nascent hydrophobic core. Here, we study pressure-drop refolding of three λ-repressor fragment (λ_6-85) mutants computationally and experimentally. The three mutants report on tertiary structure formation via different fluorescent helix-helix contact pairs. All-atom simulations of pressure drops capture refolding and unfolding of all three mutants by a similar mechanism, thus validating the nonperturbative nature of the fluorescent contact probes. Analysis of simulated interprobe distances shows that the α-helix 1-3 pair distance displays a slower characteristic time scale than the 1-2 or 3-2 pair distance. To see whether slow packing of α-helices 1 and 3 is reflected in the rate-limiting folding step, fast pressure-drop relaxation experiments captured refolding on a millisecond time scale. These experiments reveal that refolding monitored by 1-3 contact formation indeed is much slower than when monitored by 1-2 or 3-2 contact formation. Unlike the case of the two-state folder [three-α-helix bundle (α₃D)], whose drying and core formation proceed in concert, λ_6-85 repeatedly dries and rewets different local tertiary contacts before finally forming a solvent-excluded core, explaining the non-two-state behavior observed during refolding in molecular dynamics simulations. This work demonstrates that proteins can explore desolvated pockets and dry globular states numerous times before reaching the native conformation.

In silico and in vivo analysis to identify the antidiabetic activity of beta sitosterol in adipose tissue of high fat diet and sucrose induced type-2 diabetic experimental rats

Adipose tissue is the primary site of storage for excess energy as triglyceride and it helps in synthesizing a number of biologically active compounds that regulate metabolic homeostasis. Consumption of high dietary fat increases stored fat mass and is considered as a main risk factor for metabolic diseases. Beta-sitosterol (β-sitosterol) is a plant sterol. It has the similar chemical structure like cholesterol. Clinical and experimental studies have shown that β-sitosterol has anti-diabetic, hypolipidemic, anti-cancer, anti-arthritic, and hepatoprotective role. However, effect of β-sitosterol on insulin signaling molecules and glucose oxidation has not been explored. Hence in the present study we aimed to discover the protective role of β-sitosterol on the expression of insulin signaling molecules in the adipose tissue of high-fat diet and sucrose-induced type-2 diabetic experimental rats. Effect dose of β-sitosterol (20 mg/kg b.wt, orally for 30 days) was given to high fat diet and sucrose-induced type-2 diabetic rats to study its anti-diabetic activity. Results of the study showed that the treatment with β-sitosterol to diabetes-induced rats normalized the altered levels of blood glucose, serum insulin and testosterone, lipid profile, oxidative stress markers, antioxidant enzymes, insulin receptor (IR), and glucose transporter 4 (GLUT4) proteins. Our present findings indicate that β-sitosterol improves glycemic control through activation of IR and GLUT4 in the adipose tissue of high fat and sucrose-induced type-2 diabetic rats. Insilico analysis also coincides with invivo results. Hence it is very clear that β-sitosterol can act as potent antidiabetic agent.

Complex Folding Landscape of Apomyoglobin at Acidic pH Revealed by Ultrafast Kinetic Analysis of Core Mutants

Under mildly acidic conditions (pH 4-4.5) apomyoglobin (apoMb) adopts a partially structured equilibrium state ( M-state) that structurally resembles a kinetic intermediate encountered at a late stage of folding to the native structure at neutral pH. We have previously reported that the M-state is formed rapidly (<1 ms) via a multistate process and thus offers a unique opportunity for exploring early stages of folding by both experimental and computational techniques. In order to gain structural insight into intermediates and barriers at the residue level, we studied the folding/unfolding kinetics of 12 apoMb mutants at pH 4.2 using fluorescence-detected ultrafast mixing techniques. Global analysis of the submillisecond folding/unfolding kinetics vs urea concentration for each variant, based on a sequential four-state mechanism ( U ⇔ I ⇔ L ⇔ M), allowed us to determine elementary rate constants and their dependence on urea concentration for most transitions. Comparison of the free energy diagrams constructed from the kinetic data of the mutants with that of wild-type apoMb yielded quantitative information on the effects of mutations on the free energy (ΔΔ G) of both intermediates and the first two kinetic barriers encountered during folding. Truncation of conserved aliphatic side chains on helices A, G, and H gives rise to a stepwise increase in ΔΔ G as the protein advances from U toward M, consistent with progressive stabilization of native-like contacts within the primary core of apoMb. Helix-helix contacts in the primary core contribute little to the first folding barrier ( U ⇔ I) and thus are not required for folding initiation but are critical for the stability of the late intermediate, L, and the M-state. Alanine substitution of hydrophobic residues at more peripheral helix-helix contact sites of the native structure, which are still absent or unstable in the M-state, shows both positive (destabilizing) and negative (stabilizing) ΔΔ G, indicating that non-native contacts are formed initially and weakened or lost as a result of subsequent structural rearrangement steps.

Current Therapeutic Molecules and Targets in Neurodegenerative Diseases Based on in silico Drug Design

Abstract: Background

As the number of elderly persons increases, neurodegenerative diseases are becoming ubiquitous. There is currently a great need for knowledge concerning management of old-age neurodegenerative diseases; the most important of which are: Alzheimer’s disease, Parkinson’s disease, Amyotrophic Lateral Sclerosis, and Huntington’s disease.

Objective

To summarize the potential of computationally predicted molecules and targets against neurodegenerative diseases.

Method

Review of literature published since 1997 against neurodegenerative diseases, utilizing as keywords: in silico, Alzheimer’s disease, Parkinson’s disease, Amyotrophic Lateral Sclerosis ALS, and Huntington’s disease was conducted.

Results and Conclusion

Due to the costs associated with experimentation and current ethical law, performing experiments directly on living organisms has become much more difficult. In this scenario, in silico techniques have been successful and have become powerful tools in the search to cure disease. Researchers use the Computer Aided Drug Design pipeline which: 1) generates 3-dimensional structures of target proteins through homology modeling 2) achieves stabilization through molecular dynamics simulation, and 3) exploits molecular docking through large compound libraries. Next generation sequencing is continually producing enormous amounts of raw sequence data while neuroimaging is producing a multitude of raw image data. To solve such pressing problems, these new tools and algorithms are required. This review elaborates precise in silico tools and techniques for drug targets, active molecules, and molecular docking studies, together with future prospects and challenges concerning possible breakthroughs in Alzheimer’s, Parkinson’s, Amyotrophic Lateral Sclerosis, and Huntington’s disease.

Atomistic Peptide Folding Simulations Reveal Interplay of Entropy and Long-Range Interactions in Folding Cooperativity

Understanding how proteins fold has remained a problem of great interest in biophysical research. Atomistic computer simulations using physics-based force fields can provide important insights on the interplay of different interactions and energetics and their roles in governing the folding thermodynamics and mechanism. In particular, generalized Born (GB)-based implicit solvent force fields can be optimized to provide an appropriate balance between solvation and intramolecular interactions and successfully recapitulate experimental conformational equilibria for a set of helical and β-hairpin peptides. Here, we further demonstrate that key thermodynamic properties and their temperature dependence obtained from replica exchange molecular dynamics simulations of these peptides are in quantitative agreement with experimental results. Useful lessons can be learned on how the interplay of entropy and sequentially long-range interactions governs the mechanism and cooperativity of folding. These results highlight the great potential of high-quality implicit solvent force fields for studying protein folding and large-scale conformational transitions.

Intramolecular Diffusion in α-Synuclein: It Depends on How You Measure It

Intramolecular protein diffusion, the motion of one part of the polypeptide chain relative to another part, is a fundamental aspect of protein folding and may modulate amyloidogenesis of disease-associated intrinsically disordered proteins. Much work has determined such diffusion coefficients using a variety of probes, but there has been an apparent discrepancy between measurements using long-range probes, such as fluorescence resonance energy transfer, and short-range probes, such as Trp-Cys quenching. In this work, we make both such measurements on the same protein, α-synuclein, and confirm that such discrepancy exists. Molecular dynamics simulations suggest that such differences result from a diffusion coefficient that depends on the spatial distance between probes. Diffusional estimates in good quantitative agreement with experiment are obtained by accounting for the distinct distance ranges probed by fluorescence resonance energy transfer and Trp-Cys quenching.

Validation of Molecular Simulation: An Overview of Issues

Computer simulation of molecular systems enables structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic, or supra-molecular level. To interpret results of such simulations appropriately, the quality of the calculated properties must be evaluated. This depends on the way the simulations are performed and on the way they are validated by comparison to values Q^exp of experimentally observable quantities Q. One must consider 1) the accuracy of Q^exp , 2) the accuracy of the function Q(r^N ) used to calculate a Q-value based on a molecular configuration r^N of N particles, 3) the sensitivity of the function Q(r^N ) to the configuration r^N , 4) the relative time scales of the simulation and experiment, 5) the degree to which the calculated and experimental properties are equivalent, and 6) the degree to which the system simulated matches the experimental conditions. Experimental data is limited in scope and generally corresponds to averages over both time and space. A critical analysis of the various factors influencing the apparent degree of (dis)agreement between simulations and experiment is presented and illustrated using examples from the literature. What can be done to enhance the validation of molecular simulation is also discussed.

Comparison of Five Protein Engineering Strategies for Stabilizing an α/β-Hydrolase

A review of the previous stabilization of α/β-hydrolase fold enzymes revealed many different strategies, but no comparison of strategies on the same enzyme. For this reason, we compared five strategies to identify stabilizing mutations in a model α/β-hydrolase fold enzyme, salicylic acid binding protein 2, to reversible denaturation by urea and to irreversible denaturation by heat. The five strategies included one location agnostic approach (random mutagenesis using error-prone polymerase chain reaction), two structure-based approaches [computational design (Rosetta, FoldX) and mutation of flexible regions], and two sequence-based approaches (addition of proline at locations where a more stable homologue has proline and mutation to consensus). All strategies identified stabilizing mutations, but the best balance of success rate, degree of stabilization, and ease of implementation was mutation to consensus. A web-based automated program that predicts substitutions needed to mutate to consensus is available at http://kazlab.umn.edu .

Amyloid β Fibril Elongation by Monomers Involves Disorder at the Tip

The growth of amyloid fibrils from Aβ_1-42 peptide, one of the key pathogenic players in Alzheimer's disease, is believed to follow a nucleation-elongation mechanism. Fibril elongation is often described as a "dock-lock" procedure, where a disordered monomer adsorbs to an existing fibril in a relatively fast process (docking), followed by a slower conformational transition toward the ordered state of the template (locking). Here, we use molecular dynamics simulations of an ordered pentamer of Aβ42 at fully atomistic resolution, which includes solvent, to characterize the elongation process. We construct a Markov state model from an ensemble of short trajectories generated by an advanced sampling algorithm that efficiently diversifies a subset of the system without any bias forces. This subset corresponds to selected dihedral angles of the peptide chain at the fibril tip favored to be the fast growing one experimentally. From the network model, we extract distinct locking pathways covering time scales in the high microsecond regime. Slow steps are associated with the exchange of hydrophobic contacts, between nonnative and native intermolecular contacts as well as between intra- and intermolecular ones. The N-terminal segments, which are disordered in fibrils and typically considered inert, are able to shield the lateral interfaces of the pentamer. We conclude by discussing our findings in the context of a refined dock-lock model of Aβ fibril elongation, which involves structural disorder for more than one monomer at the growing tip.

How fast fast-folding proteins fold in silico

In reported microcanonical molecular dynamics simulations, fast-folding proteins CLN025 and Trp-cage autonomously folded to experimentally determined native conformations. However, the folding times of these proteins derived from the simulations were more than 4-10 times longer than their experimental values. This article reports autonomous folding of CLN025 and Trp-cage in isobaric-isothermal molecular dynamics simulations with agreements within factors of 0.69-1.75 between simulated and experimental folding times at different temperatures. These results show that CLN025 and Trp-cage can now autonomously fold in silico as fast as in experiments, and suggest that the accuracy of folding simulations for fast-folding proteins begins to overlap with the accuracy of folding experiments. This opens new prospects of developing computer algorithms that can predict both ensembles of conformations and their interconversion rates for a protein from its sequence for artificial intelligence on how and when a protein acts as a receiver, switch, and relay to facilitate various subcellular-to-tissue communications. Then the genetic information that encodes proteins can be better read in the context of intricate biological functions.

Quantifying Nonnative Interactions in the Protein-Folding Free-Energy Landscape

Protein folding is a central problem in biological physics. Energetic roughness is an important aspect that controls protein-folding stability and kinetics. The roughness is associated with conflicting interactions in the protein and is also known as frustration. Recent studies indicate that an addition of a small amount of energetic frustration may enhance folding speed for certain proteins. In this study, we have investigated the conditions under which frustration increases the folding rate. We used a Cα structure-based model to simulate a group of proteins. We found that the free-energy barrier at the transition state (ΔF) correlates with nonnative-contact variation (ΔA), and the simulated proteins are clustered according to their fold motifs. These findings are corroborated by the Clementi-Plotkin analytical model. As a consequence, the optimum frustration regime for protein folding can be predicted analytically.

N-terminal diproline and charge group effects on the stabilization of helical conformation in alanine-based short peptides: CD studies with water and methanol as solvent

Protein folding problem remains a formidable challenge as main chain, side chain and solvent interactions remain entangled and have been difficult to resolve. Alanine-based short peptides are promising models to dissect protein folding initiation and propagation structurally as well as energetically. The effect of N-terminal diproline and charged side chains is assessed on the stabilization of helical conformation in alanine-based short peptides using circular dichroism (CD) with water and methanol as solvent. A1 (Ac-Pro-Pro-Ala-Lys-Ala-Lys-Ala-Lys-Ala-NH₂ ) is designed to assess the effect of N-terminal homochiral diproline and lysine side chains to induce helical conformation. A2 (Ac-Pro-Pro-Glu-Glu-Ala-Ala-Lys-Lys-Ala-NH₂ ) and A3 (Ac-dPro-Pro-Glu-Glu-Ala-Ala-Lys-Lys-Ala-NH₂ ) with N-terminal homochiral and heterochiral diproline, respectively, are designed to assess the effect of Glu...Lys (i, i + 4) salt bridge interactions on the stabilization of helical conformation. The CD spectra of A1, A2 and A3 in water manifest different amplitudes of the observed polyproline II (PPII) signals, which indicate different conformational distributions of the polypeptide structure. The strong effect of solvent substitution from water to methanol is observed for the peptides, and CD spectra in methanol evidence A2 and A3 as helical folds. Temperature-dependent CD spectra of A1 and A2 in water depict an isodichroic point reflecting coexistence of two conformations, PPII and β-strand conformation, which is consistent with the previous studies. The results illuminate the effect of N-terminal diproline and charged side chains in dictating the preferences for extended-β, semi-extended PPII and helical conformation in alanine-based short peptides. The results of the present study will enhance our understanding on stabilization of helical conformation in short peptides and hence aid in the design of novel peptides with helical structures. Copyright © 2017 European Peptide Society and John Wiley & Sons, Ltd.

Gating mechanism of mechanosensitive channel of large conductance: a coupled continuum mechanical-continuum solvation approach

Gating transition of the mechanosensitive channel of large conductance (MscL) represents a good example of important biological processes that are difficult to describe using atomistic simulations due to the large (submicron) length scale and long (millisecond) time scale. Here we develop a novel computational framework that tightly couples continuum mechanics with continuum solvation models to study the detailed gating behavior of E. coli-MscL. The components of protein molecules are modeled by continuum elements that properly describe their shape, material properties and physicochemical features (e.g., charge distribution). The lipid membrane is modeled as a three-layer material in which the lipid head group and tail regions are treated separately, taking into account the fact that fluidic lipid bilayers do not bear shear stress. Coupling between mechanical and chemical responses of the channel is realized by an iterative integration of continuum mechanics (CM) modeling and continuum solvation (CS) computation. Compared to previous continuum mechanics studies, the present model is capable of capturing the most essential features of the gating process in a much more realistic fashion: due mainly to the apolar solvation contribution, the membrane tension for full opening of MscL is reduced substantially to the experimental measured range. Moreover, the pore size stabilizes constantly during gating because of the intricate interactions of the multiple components of the system, implying the mechanism for sub-conducting states of MscL gating. A significant fraction ([Formula: see text]2/3) of the gating membrane strain is required to reach the first sub-conducting state of our model, which is featured with a relative conductance of 0.115 to the fully opened state. These trends agree well with experimental observations. We anticipate that the coupled CM/CS modeling framework is uniquely suited for the analysis of many biomolecules and their assemblies under external mechanical stimuli.

Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.

Molecular Dynamics Simulations of the Temperature Induced Unfolding of Crambin Follow the Arrhenius Equation

Molecular dynamics simulations have been used extensively to model the folding and unfolding of proteins. The rates of folding and unfolding should follow the Arrhenius equation over a limited range of temperatures. This study shows that molecular dynamic simulations of the unfolding of crambin between 500K and 560K do follow the Arrhenius equation. They also show that while there is a large amount of variation between the simulations the average values for the rate show a very high degree of correlation.

Study on Wangzaozin-A-Inducing Cancer Apoptosis and Its Theoretical Protein Targets

Wangzaozin A is the most representative cytotoxic C-20-nonoxide compound of Isodon plants of Labiatae. The protein targets of the 2 isomers (X and X') of Wangzaozin A are, respectively, extracted from target fishing dock Web site. Each isomer has 23 targets with good energy scores. The binding modes of each isomer and its targets are, respectively, analyzed by Dock. The energy score of the binding mode between the isomer X and the inositol-1(or 4)-monophosphatase is the smallest. The apoptosis, antiproliferative, and lethal effects of human gastric cancer cells induced by Wangzaozin A are assessed by trypan blue exclusion, hoechst33258 stain in SGC-7901, and flow cytometric measurement. The mechanism of Wangzaozin-A-inducing cancer apoptosis is analyzed. Wangzaozin A inhibits the growth of human gastric cancer SGC-7901 cell lines at the lower concentration (<4.0 µmol/L) and results in the lethal effect at the relative higher concentration (>8.0 µmol/L).

Integrating atomistic molecular dynamics simulations, experiments, and network analysis to study protein dynamics: strength in unity

In the last years, we have been observing remarkable improvements in the field of protein dynamics. Indeed, we can now study protein dynamics in atomistic details over several timescales with a rich portfolio of experimental and computational techniques. On one side, this provides us with the possibility to validate simulation methods and physical models against a broad range of experimental observables. On the other side, it also allows a complementary and comprehensive view on protein structure and dynamics. What is needed now is a better understanding of the link between the dynamic properties that we observe and the functional properties of these important cellular machines. To make progresses in this direction, we need to improve the physical models used to describe proteins and solvent in molecular dynamics, as well as to strengthen the integration of experiments and simulations to overcome their own limitations. Moreover, now that we have the means to study protein dynamics in great details, we need new tools to understand the information embedded in the protein ensembles and in their dynamic signature. With this aim in mind, we should enrich the current tools for analysis of biomolecular simulations with attention to the effects that can be propagated over long distances and are often associated to important biological functions. In this context, approaches inspired by network analysis can make an important contribution to the analysis of molecular dynamics simulations.

Structural dynamics and inhibitor searching for Wnt-4 protein using comparative computational studies

Wnt-4 (wingless mouse mammary tumor virus integration site-4) protein is involved in many crucial embryonic pathways regulating essential processes. Aberrant Wnt-4 activity causes various anomalies leading to gastric, colon, or breast cancer. Wnt-4 is a conserved protein in structure and sequence. All Wnt proteins contain an unusual fold comprising of a thumb (or N-terminal domain) and index finger (or C-terminal domain) bifurcated by a palm domain. The aim of this study was to identify the best inhibitors of Wnt-4 that not only interact with Wnt-4 protein but also with the covalently bound acyl group to inhibit aberrant Wnt-4 activity. A systematic computational approach was used to analyze inhibition of Wnt-4. Palmitoleic acid was docked into Wnt-4 protein, followed by ligand-based virtual screening of nearly 209,847 compounds; conformer generation of 271 compounds resulted from extensive virtual screening and comparative docking of 10,531 conformers of 271 unique compounds through GOLD (Genetic Optimization for Ligand Docking), AutoDock-Vina, and FRED (Fast Rigid Exhaustive Docking) was subsequently performed. Linux scripts was used to handle the libraries of compounds. The best compounds were selected on the basis of having maximum interactions to protein with bound palmitoleic acid. These represented lead inhibitors in further experiments. Palmitoleic acid is important for efficient Wnt activity, but aberrant Wnt-4 expression can be inhibited by designing inhibitors interacting with both protein and palmitoleic acid.

Redesigning the type II' β-turn in green fluorescent protein to type I': implications for folding kinetics and stability

Both Type I' and Type II' β-turns have the same sense of the β-turn twist that is compatible with the β-sheet twist. They occur predominantly in two residue β-hairpins, but the occurrence of Type I' β-turns is two times higher than Type II' β-turns. This suggests that Type I' β-turns may be more stable than Type II' β-turns, and Type I' β-turn sequence and structure can be more favorable for protein folding than Type II' β-turns. Here, we redesigned the native Type II' β-turn in GFP to Type I' β-turn, and investigated its effect on protein folding and stability. The Type I' β-turns were designed based on the statistical analysis of residues in natural Type I' β-turns. The substitution of the native "GD" sequence of i+1 and i+2 residues with Type I' preferred "(N/D)G" sequence motif increased the folding rate by 50% and slightly improved the thermodynamic stability. Despite the enhancement of in vitro refolding kinetics and stability of the redesigned mutants, they showed poor soluble expression level compared to wild type. To overcome this problem, i and i + 3 residues of the designed Type I' β-turn were further engineered. The mutation of Thr to Lys at i + 3 could restore the in vivo soluble expression of the Type I' mutant. This study indicates that Type II' β-turns in natural β-hairpins can be further optimized by converting the sequence to Type I'.

Blind prediction of SAMPL4 cucurbit[7]uril binding affinities with the mining minima method

Accurate methods for predicting protein-ligand binding affinities are of central interest to computer-aided drug design for hit identification and lead optimization. Here, we used the mining minima (M2) method to predict cucurbit[7]uril binding affinities from the SAMPL4 blind prediction challenge. We tested two different energy models, an empirical classical force field, CHARMm with VCharge charges, and the Poisson-Boltzmann surface area solvation model; and a semiempirical quantum mechanical (QM) Hamiltonian, PM6-DH+, coupled with the COSMO solvation model and a surface area term for nonpolar solvation free energy. Binding affinities based on the classical force field correlated strongly with the experiments with a correlation coefficient (R(2)) of 0.74. On the other hand, binding affinities based on the QM energy model correlated poorly with experiments (R(2) = 0.24), due largely to two major outliers. As we used extensive conformational search methods, these results point to possible inaccuracies in the PM6-DH+ energy model or the COSMO solvation model. Furthermore, the different binding free energy components, solute energy, solvation free energy, and configurational entropy showed significant deviations between the classical M2 and quantum M2 calculations. Comparison of different classical M2 free energy components to experiments show that the change in the total energy, i.e. the solute energy plus the solvation free energy, is the key driving force for binding, with a reasonable correlation to experiment (R(2) = 0.56); however, accounting for configurational entropy further improves the correlation.

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a Cα structure-based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well-separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non-native contact interactions in different folding scenarios. These findings strongly correlate with the protein free-energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins.

How fast does a signal propagate through proteins?

As the molecular basis of signal propagation in the cell, proteins are regulated by perturbations, such as mechanical forces or ligand binding. The question arises how fast such a signal propagates through the protein molecular scaffold. As a first step, we have investigated numerically the dynamics of force propagation through a single (Ala) protein following a sudden increase in the stretching forces applied to its end termini. The force propagates along the backbone into the center of the chain on the picosecond scale. Both conformational and tension dynamics are found in good agreement with a coarse-grained theory of force propagation through semiflexible polymers. The speed of force propagation of 50Å ps⁻¹ derived from these simulations is likely to determine an upper speed limit of mechanical signal transfer in allosteric proteins or molecular machines.

Molecular dynamics simulations of amyloid fibrils: an in silico approach

Amyloid fibrils play causal roles in the pathogenesis of amyloid-related degenerative diseases such as Alzheimer's disease, type II diabetes mellitus, and the prion-related transmissible spongiform encephalopathies. The mechanism of fibril formation and protein aggregation is still hotly debated and remains an important open question in order to develop therapeutic method of these diseases. However, traditional molecular biological and crystallographic experiments could hardly observe atomic details and aggregation process. Molecular dynamics (MD) simulations could provide explanations for experimental results and detailed pathway of protein aggregation. In this review, we focus on the applications of MD simulations on several amyloidogenic protein systems. Furthermore, MD simulations could help us to understand the mechanism of amyloid aggregation and how to design the inhibitors.

Biomolecular simulation: a computational microscope for molecular biology

Molecular dynamics simulations capture the behavior of biological macromolecules in full atomic detail, but their computational demands, combined with the challenge of appropriately modeling the relevant physics, have historically restricted their length and accuracy. Dramatic recent improvements in achievable simulation speed and the underlying physical models have enabled atomic-level simulations on timescales as long as milliseconds that capture key biochemical processes such as protein folding, drug binding, membrane transport, and the conformational changes critical to protein function. Such simulation may serve as a computational microscope, revealing biomolecular mechanisms at spatial and temporal scales that are difficult to observe experimentally. We describe the rapidly evolving state of the art for atomic-level biomolecular simulation, illustrate the types of biological discoveries that can now be made through simulation, and discuss challenges motivating continued innovation in this field.

Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy

Theory, simulations and experimental results have suggested an important role of internal friction in the kinetics of protein folding. Recent experiments on spectrin domains provided the first evidence for a pronounced contribution of internal friction in proteins that fold on the millisecond timescale. However, it has remained unclear how this contribution is distributed along the reaction and what influence it has on the folding dynamics. Here we use a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, microfluidic mixing and denaturant- and viscosity-dependent protein-folding kinetics to probe internal friction in the unfolded state and at the early and late transition states of slow- and fast-folding spectrin domains. We find that the internal friction affecting the folding rates of spectrin domains is highly localized to the early transition state, suggesting an important role of rather specific interactions in the rate-limiting conformational changes.

Microsecond folding experiments and simulations: a match is made

For the past two decades, protein folding experiments have been speeding up from the second or millisecond time scale to the microsecond time scale, and full-atom simulations have been extended from the nanosecond to the microsecond and even millisecond time scale. Where the two meet, it is now possible to compare results directly, allowing force fields to be validated and refined, and allowing experimental data to be interpreted in atomistic detail. In this perspective we compare recent experiments and simulations on the microsecond time scale, pointing out the progress that has been made in determining native structures from physics-based simulations, refining experiments and simulations to provide more quantitative underlying mechanisms, and tackling the problems of multiple reaction coordinates, downhill folding, and complex underlying structure of unfolded or misfolded states.