A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations

Bias-Exchange Metadynamics Simulations: An Efficient Strategy for the Analysis of Conduction and Selectivity in Ion Channels

Conduction through ion channels possesses two interesting features: (i) different ionic species are selected with high-selectivity and (ii) ions travel across the channel with rates approaching free-diffusion. Molecular dynamics simulations have the potential to reveal how these processes take place at the atomic level. However, analysis of conduction and selectivity at atomistic detail is still hampered by the short time scales accessible by computer simulations. Several algorithms have been developed to "accelerate" sampling along the slow degrees of freedom of the process under study and thus to probe longer time scales. In these algorithms, the slow degrees of freedom need to be defined in advance, which is a well-known shortcoming. In the particular case of ion conduction, preliminary assumptions about the number and type of ions participating in the permeation process need to be made. In this study, a novel approach for the analysis of conduction and selectivity based on bias-exchange metadynamics simulations was tested. This approach was compared with umbrella sampling simulations, using a model of a Na(+)-selective channel. Analogous conclusions resulted from both techniques, but the computational cost of bias-exchange simulations was lower. In addition, with bias-exchange metadynamics it was possible to calculate free energy profiles in the presence of a variable number and type of permeating ions. This approach might facilitate the definition of the set of collective variables required to analyze conduction and selectivity in ion channels.

Changes in the folding landscape of the WW domain provide a molecular mechanism for an inherited genetic syndrome

WW domains are small domains present in many human proteins with a wide array of functions and acting through the recognition of proline-rich sequences. The WW domain belonging to polyglutamine tract-binding protein 1 (PQBP1) is of particular interest due to its direct involvement in several X chromosome-linked intellectual disabilities, including Golabi-Ito-Hall (GIH) syndrome, where a single point mutation (Y65C) correlates with the development of the disease. The mutant cannot bind to its natural ligand WBP11, which regulates mRNA processing. In this work we use high-field high-resolution NMR and enhanced sampling molecular dynamics simulations to gain insight into the molecular causes the disease. We find that the wild type protein is partially unfolded exchanging among multiple beta-strand-like conformations in solution. The Y65C mutation further destabilizes the residual fold and primes the protein for the formation of a disulphide bridge, which could be at the origin of the loss of function.

Free energy surface of an intrinsically disordered protein: comparison between temperature replica exchange molecular dynamics and bias-exchange metadynamics

Intrinsically disordered proteins (IDPs), which are expected to be largely unstructured under physiological conditions, make up a large fraction of eukaryotic proteins. Molecular dynamics simulations have been utilized to probe structural characteristics of these proteins, which are not always easily accessible to experiments. However, exploration of the conformational space by brute force molecular dynamics simulations is often limited by short time scales. Present literature provides a number of enhanced sampling methods to explore protein conformational space in molecular simulations more efficiently. In this work, we present a comparison of two enhanced sampling methods: temperature replica exchange molecular dynamics and bias exchange metadynamics. By investigating both the free energy landscape as a function of pertinent order parameters and the per-residue secondary structures of an IDP, namely, human islet amyloid polypeptide, we found that the two methods yield similar results as expected. We also highlight the practical difference between the two methods by describing the path that we followed to obtain both sets of data.

Fusing simulation and experiment: The effect of mutations on the structure and activity of the influenza fusion peptide

During the infection process, the influenza fusion peptide (FP) inserts into the host membrane, playing a crucial role in the fusion process between the viral and host membranes. In this work we used a combination of simulation and experimental techniques to analyse the molecular details of this process, which are largely unknown. Although the FP structure has been obtained by NMR in detergent micelles, there is no atomic structure information in membranes. To answer this question, we performed bias-exchange metadynamics (BE-META) simulations, which showed that the lowest energy states of the membrane-inserted FP correspond to helical-hairpin conformations similar to that observed in micelles. BE-META simulations of the G1V, W14A, G12A/G13A and G4A/G8A/G16A/G20A mutants revealed that all the mutations affect the peptide’s free energy landscape. A FRET-based analysis showed that all the mutants had a reduced fusogenic activity relative to the WT, in particular the mutants G12A/G13A and G4A/G8A/G16A/G20A. According to our results, one of the major causes of the lower activity of these mutants is their lower membrane affinity, which results in a lower concentration of peptide in the bilayer. These findings contribute to a better understanding of the influenza fusion process and open new routes for future studies.

Mechanism of extracellular ion exchange and binding-site occlusion in a sodium/calcium exchanger

Na⁺/Ca²⁺ exchangers utilize the Na⁺ electrochemical gradient across the plasma membrane to extrude intracellular Ca²⁺, and play a central role in Ca²⁺ homeostasis. Here, we elucidate their mechanisms of extracellular ion recognition and exchange through a structural analysis of the exchanger from Methanococcus jannaschii (NCX_Mj) bound to Na⁺, Ca²⁺ or Sr²⁺ in various occupancies and in an apo state. This analysis defines the binding mode and relative affinity of these ions, establishes the structural basis for the anticipated 3Na⁺:1Ca²⁺ exchange stoichiometry, and reveals the conformational changes at the onset of the alternating-access transport mechanism. An independent analysis of the dynamics and conformational free-energy landscape of NCX_Mj in different ion-occupancy states, based on enhanced-sampling molecular-dynamics simulations, demonstrates that the crystal structures reflect mechanistically relevant, interconverting conformations. These calculations also reveal the mechanism by which the outward-to-inward transition is controlled by the ion-occupancy state, thereby explaining the emergence of strictly-coupled Na⁺/Ca²⁺ antiport.

Mapping the Dynamics Landscape of Conformational Transitions in Enzyme: The Adenylate Kinase Case

Conformational transition describes the essential dynamics and mechanism of enzymes in pursuing their various functions. The fundamental and practical challenge to researchers is to quantitatively describe the roles of large-scale dynamic transitions for regulating the catalytic processes. In this study, we tackled this challenge by exploring the pathways and free energy landscape of conformational changes in adenylate kinase (AdK), a key ubiquitous enzyme for cellular energy homeostasis. Using explicit long-timescale (up to microseconds) molecular dynamics and bias-exchange metadynamics simulations, we determined at the atomistic level the intermediate conformational states and mapped the transition pathways of AdK in the presence and absence of ligands. There is clearly chronological operation of the functional domains of AdK. Specifically in the ligand-free AdK, there is no significant energy barrier in the free energy landscape separating the open and closed states. Instead there are multiple intermediate conformational states, which facilitate the rapid transitions of AdK. In the ligand-bound AdK, the closed conformation is energetically most favored with a large energy barrier to open it up, and the conformational population prefers to shift to the closed form coupled with transitions. The results suggest a perspective for a hybrid of conformational selection and induced fit operations of ligand binding to AdK. These observations, depicted in the most comprehensive and quantitative way to date, to our knowledge, emphasize the underlying intrinsic dynamics of AdK and reveal the sophisticated conformational transitions of AdK in fulfilling its enzymatic functions. The developed methodology can also apply to other proteins and biomolecular systems.

Permeability across lipid membranes

Molecular permeation through lipid membranes is a fundamental biological process that is important for small neutral molecules and drug molecules. Precise characterization of free energy surface and diffusion coefficients along the permeation pathway is required in order to predict molecular permeability and elucidate the molecular mechanisms of permeation. Several recent technical developments, including improved molecular models and efficient sampling schemes, are illustrated in this review. For larger penetrants, explicit consideration of multiple collective variables, including orientational, conformational degrees of freedom, are required to be considered in addition to the distance from the membrane center along the membrane normal. Although computationally demanding, this method can provide significant insights into the molecular mechanisms of permeation for molecules of medical and pharmaceutical importance. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

A Flexible Domain-Domain Hinge Promotes an Induced-fit Dominant Mechanism for the Loading of Guide-DNA into Argonaute Protein in Thermus thermophilus

Argonaute proteins (Ago) are core components of the RNA Induced Silencing Complex (RISC) that load and utilize small guide nucleic acids to silence mRNAs or cleave foreign DNAs. Despite the essential role of Ago in gene regulation and defense against virus, the molecular mechanism of guide-strand loading into Ago remains unclear. We explore such a mechanism in the bacterium Thermus thermophilus Ago (TtAgo), via a computational approach combining molecular dynamics, bias-exchange metadynamics, and protein-DNA docking. We show that apo TtAgo adopts multiple closed states that are unable to accommodate guide-DNA. Conformations able to accommodate the guide are beyond the reach of thermal fluctuations from the closed states. These results suggest an induced-fit dominant mechanism for guide-strand loading in TtAgo, drastically different from the two-step mechanism for human Ago 2 (hAgo2) identified in our previous study. Such a difference between TtAgo and hAgo2 is found to mainly originate from the distinct rigidity of their L1-PAZ hinge. Further comparison among known Ago structures from various species indicates that the L1-PAZ hinge may be flexible in general for prokaryotic Ago's but rigid for eukaryotic Ago's.

Spectral gap optimization of order parameters for sampling complex molecular systems

In modern-day simulations of many-body systems, much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CVs) or reaction coordinates. A vast array of enhanced-sampling methods are based on the identification and biasing of these low-dimensional order parameters, whose fluctuations are important in driving rare events of interest. Here, we describe a new algorithm for finding optimal low-dimensional CVs for use in enhanced-sampling biasing methods like umbrella sampling, metadynamics, and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. The algorithm is called spectral gap optimization of order parameters (SGOOP). Through multiple practical examples, we show how this postprocessing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs.

Using Local States To Drive the Sampling of Global Conformations in Proteins

Conformational changes associated with protein function often occur beyond the time scale currently accessible to unbiased molecular dynamics (MD) simulations, so that different approaches have been developed to accelerate their sampling. Here we investigate how the knowledge of backbone conformations preferentially adopted by protein fragments, as contained in precalculated libraries known as structural alphabets (SA), can be used to explore the landscape of protein conformations in MD simulations. We find that (a) enhancing the sampling of native local states in both metadynamics and steered MD simulations allows the recovery of global folded states in small proteins; (b) folded states can still be recovered when the amount of information on the native local states is reduced by using a low-resolution version of the SA, where states are clustered into macrostates; and (c) sequences of SA states derived from collections of structural motifs can be used to sample alternative conformations of preselected protein regions. The present findings have potential impact on several applications, ranging from protein model refinement to protein folding and design.

A kinetic model for molecular diffusion through pores

The number of pathogens developing multiple drug resistance is ever increasing. The impact on healthcare systems is huge and the need for novel antibiotics as well a new way to develop them is urgent, especially against Gram-negative bacteria. The first defense of these bacteria is the outer membrane, where unspecific protein channels (porins) modulate nutrients passive diffusion. Also polar antibiotics enter through this path and down-regulation and/or mutation of porins are very common in drug resistant strains. Our inability to come up with novel effective antibiotics mostly relies upon the insufficient comprehension of the key molecular features enabling better penetration through porins. Molecular dynamics simulations offer an extraordinary tool in the study of the dynamics of biological systems; however, one of the major drawbacks of this method is that its use is currently restricted to study time scales of the order of microsecond. Enhanced sampling methods like Metadynamics have been recently used to investigate the diffusion of antibiotics through bacterial porins. The main limitation is that dynamical properties cannot be estimated because of the different potential that the systems under study are experiencing. Recently, the scope of Metadynamics has been extended. By applying an a posteriori analysis one can obtain rates of transitions and rate-limiting steps of the process under study, directly comparable with kinetic data extracted from electrophysiology experiments. In this work, we apply this method to the study of the permeability of Escherichia coli's OmpF with respect to Meropenem, finding good agreement with the residence time obtained analyzing experimental current noise. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

All-Atom Structural Models of the Transmembrane Domains of Insulin and Type 1 Insulin-Like Growth Factor Receptors

The receptor tyrosine kinase superfamily comprises many cell-surface receptors including the insulin receptor (IR) and type 1 insulin-like growth factor receptor (IGF1R) that are constitutively homodimeric transmembrane glycoproteins. Therefore, these receptors require ligand-triggered domain rearrangements rather than receptor dimerization for activation. Specifically, binding of peptide ligands to receptor ectodomains transduces signals across the transmembrane domains for trans-autophosphorylation in cytoplasmic kinase domains. The molecular details of these processes are poorly understood in part due to the absence of structures of full-length receptors. Using MD simulations and enhanced conformational sampling algorithms, we present all-atom structural models of peptides containing 51 residues from the transmembrane and juxtamembrane regions of IR and IGF1R. In our models, the transmembrane regions of both receptors adopt helical conformations with kinks at Pro961 (IR) and Pro941 (IGF1R), but the C-terminal residues corresponding to the juxtamembrane region of each receptor adopt unfolded and flexible conformations in IR as opposed to a helix in IGF1R. We also observe that the N-terminal residues in IR form a kinked-helix sitting at the membrane-solvent interface, while homologous residues in IGF1R are unfolded and flexible. These conformational differences result in a larger tilt-angle of the membrane-embedded helix in IGF1R in comparison to IR to compensate for interactions with water molecules at the membrane-solvent interfaces. Our metastable/stable states for the transmembrane domain of IR, observed in a lipid bilayer, are consistent with a known NMR structure of this domain determined in detergent micelles, and similar states in IGF1R are consistent with a previously reported model of the dimerized transmembrane domains of IGF1R. Our all-atom structural models suggest potentially unique structural organization of kinase domains in each receptor.

Toward structure prediction of cyclic peptides

Cyclic peptides are a promising class of molecules that can be used to target specific protein-protein interactions. A computational method to accurately predict their structures would substantially advance the development of cyclic peptides as modulators of protein-protein interactions. Here, we develop a computational method that integrates bias-exchange metadynamics simulations, a Boltzmann reweighting scheme, dihedral principal component analysis and a modified density peak-based cluster analysis to provide a converged structural description for cyclic peptides. Using this method, we evaluate the performance of a number of popular protein force fields on a model cyclic peptide. All the tested force fields seem to over-stabilize the α-helix and PPII/β regions in the Ramachandran plot, commonly populated by linear peptides and proteins. Our findings suggest that re-parameterization of a force field that well describes the full Ramachandran plot is necessary to accurately model cyclic peptides.

The molecular mechanism of secondary sodium symporters elucidated through the lens of the computational microscope

Transport of molecules across cellular membranes is a key biological process for normal cell function. In this review we describe current state-of-the-art knowledge on molecular mechanism of secondary active transporters obtained by molecular simulations studies.

Coarse kMC-based replica exchange algorithms for the accelerated simulation of protein folding in explicit solvent

In this paper, we present a coarse replica exchange molecular dynamics (REMD) approach, based on kinetic Monte Carlo (kMC).

Structural Insights into the Calcium-Mediated Allosteric Transition in the C-Terminal Domain of Calmodulin from Nuclear Magnetic Resonance Measurements

Calmodulin is a two-domain signaling protein that becomes activated upon binding cooperatively two pairs of calcium ions, leading to large-scale conformational changes that expose its binding site. Despite significant advances in understanding the structural biology of calmodulin functions, the mechanistic details of the conformational transition between closed and open states have remained unclear. To investigate this transition, we used a combination of molecular dynamics simulations and nuclear magnetic resonance (NMR) experiments on the Ca(2+)-saturated E140Q C-terminal domain variant. Using chemical shift restraints in replica-averaged metadynamics simulations, we obtained a high-resolution structural ensemble consisting of two conformational states and validated such an ensemble against three independent experimental data sets, namely, interproton nuclear Overhauser enhancements, (15)N order parameters, and chemical shift differences between the exchanging states. Through a detailed analysis of this structural ensemble and of the corresponding statistical weights, we characterized a calcium-mediated conformational transition whereby the coordination of Ca(2+) by just one oxygen of the bidentate ligand E140 triggers a concerted movement of the two EF-hands that exposes the target binding site. This analysis provides atomistic insights into a possible Ca(2+)-mediated activation mechanism of calmodulin that cannot be achieved from static structures alone or from ensemble NMR measurements of the transition between conformations.

HIV-1 Protease Dimerization Dynamics Reveals a Transient Druggable Binding Pocket at the Interface

The binding mechanism of HIV-1 protease monomers leading to the catalytically competent dimeric enzyme has been investigated by means of state-of-the-art atomistic simulations. The emerging picture allows a deeper understanding of experimental observations and reveals that water molecules trapped at the interface have an important role in slowing down the kinetics of the association process. Unexpectedly, a cryptic binding pocket is identified at the interface of the complex, corresponding to a partially bound dimer that lacks enzymatic function. The pocket has a transient nature with a lifetime longer than 1 μs, and it displays very favorable druggability features. Docking as well as MM-GBSA free-energy calculations further support the possibility to target the new binding site by means of inhibitors able to prevent the complete dimerization by capturing the inactive conformation. This discovery could open the way to the rational design of a new class of anti-HIV drugs.

Calculation of Lipid-Bilayer Permeabilities Using an Average Force

Calculations of lipid bilayer permeabilities from first principles, using molecular simulations, would be valuable to rapidly assess the bioavailability of drug candidates, as well as to decipher, at the atomic level, the mechanisms that underlie the translocation of permeants. The most common theoretical approach, the solubility-diffusion model, requires determination of the free energy and the diffusivity as functions of the position of the permeant. Quantitative predictions of permeability have, however, been stymied by acute difficulties in calculating the diffusivity, inadequate sampling, and, most insidiously, systematic biases due to imperfections in the force field, simulation parameters, and the inherent limitations of the diffusive model. In the present work, we combine importance-sampling simulations employing an adaptive biasing force with a Bayesian-inference algorithm to determine the free energy and diffusivity with noteworthy precision and spatial resolution. In multimicrosecond simulations, we probe the sensitivity of the permeability estimates to different aspects of the methodology, including the truncation of short-range interactions, the thermostat, the force-field parameters of the permeant, the time scale over which the diffusivity is estimated, and the size of the simulated system. The force-field parameters and time scale dependence of the diffusivities impose the greatest uncertainties on the permeability estimates. Our simulations highlight the importance of membrane distortion due to the presence of the permeant, which may be partially suppressed if the bilayer patch is not large enough. We suggest that improvements to force fields and more robust kinetic models may be needed to reduce systematic errors below a factor of two.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

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.

Folding Thermodynamics and Mechanism of Five Trp-Cage Variants from Replica-Exchange MD Simulations with RSFF2 Force Field

To test whether our recently developed residue-specific force field RSFF2 can reproduce the mutational effect on the thermal stability of Trp-cage mini-protein and decipher its detailed folding mechanism, we carried out long-time replica-exchange molecular dynamics (REMD) simulations on five Trp-cage variants, including TC5b and TC10b. Initiated from their unfolded structures, the simulations not only well-reproduce their experimental structures but also their melting temperatures and folding enthalpies reasonably well. For each Trp-cage variant, the overall folding free energy landscape is apparently two-state, but some intermediate states can be observed when projected on more detailed coordinates. We also found different variants have the same major folding pathway, including the well formed PII-helix in the unfolded state, the formation of W6-P12/P18/P19 contacts and the α-helix before the transition state, the following formation of most native contacts, and the final native loop formation. The folding mechanism derived here is consistent with many previous simulations and experiments.

Mapping the Protein Fold Universe Using the CamTube Force Field in Molecular Dynamics Simulations

It has been recently shown that the coarse-graining of the structures of polypeptide chains as self-avoiding tubes can provide an effective representation of the conformational space of proteins. In order to fully exploit the opportunities offered by such a ‘tube model’ approach, we present here a strategy to combine it with molecular dynamics simulations. This strategy is based on the incorporation of the ‘CamTube’ force field into the Gromacs molecular dynamics package. By considering the case of a 60-residue polyvaline chain, we show that CamTube molecular dynamics simulations can comprehensively explore the conformational space of proteins. We obtain this result by a 20 μs metadynamics simulation of the polyvaline chain that recapitulates the currently known protein fold universe. We further show that, if residue-specific interaction potentials are added to the CamTube force field, it is possible to fold a protein into a topology close to that of its native state. These results illustrate how the CamTube force field can be used to explore efficiently the universe of protein folds with good accuracy and very limited computational cost.

Modelling protein behaviour using computer simulations has progressively emerged in the last 50 years as a powerful strategy in structural and molecular biology. Over this period there has been a continuing interest in pushing the boundaries of this approach in terms of the size of the systems and the timescale of the processes that can be studied. Coarse-grained models offer in principle great opportunities in this context, but it has been extremely challenging to obtain force fields of accuracy comparable to that typical of fully atomistic models. We show here that the representation of protein molecules as self-avoiding tubes within the CamTube model enables the comprehensive, accurate and very fast exploration of the conformational space of proteins in molecular dynamics simulations. We illustrate in particular how the comprehensive mapping of the protein fold universe obtained using the CamTube model offers the possibility of analysing the behaviour of proteins in a wide range of non-native states.

Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation

A Gaussian accelerated molecular dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calculation of biomolecules is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomolecular model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomolecules. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow us to identify distinct low-energy states of the biomolecules and characterize the protein-folding and ligand-binding pathways quantitatively.

Atomic-resolution dissection of the energetics and mechanism of isomerization of hydrated ATP-Mg(2+) through the SOMA string method

The atomic mechanisms of isomerization of ATP-Mg(2+) in solution are characterized using the recently developed String Method with Optimal Molecular Alignment (SOMA) and molecular-dynamics simulations. Bias-Exchange Metadynamics simulations are first performed to identify the primary conformers of the ATP-Mg(2+) complex and their connectivity. SOMA is then used to elucidate the minimum free-energy path (MFEP) for each transition, in a 48-dimensional space. Analysis of the per-atom contributions to the global free-energy profiles reveals that the mechanism of these transitions is controlled by the Mg(2+) ion and its coordinating oxygen atoms in the triphosphate moiety, as well as by the ion-hydration shell. Metadynamics simulations in path collective variables based on the MFEP demonstrate these isomerizations proceed across a narrow channel of configurational space, thus validating the premise underlying SOMA. This study provides a roadmap for the examination of conformational changes in biomolecules, based on complementary enhanced-sampling techniques with different strengths. © 2015 Wiley Periodicals, Inc.

Accelerated molecular dynamics simulations of protein folding

Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred-of-microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2-2.1 Å of the native NMR or X-ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein-folding studies.

Free energy landscape and multiple folding pathways of an H-type RNA pseudoknot

How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA.

Folding Atomistic Proteins in Explicit Solvent Using Simulated Tempering

Following a previous report on a coarse-grained protein model in implicit solvent, we applied simulated tempering (ST) with on-the-fly Helmholtz free energy (weight factors) determination to the folding or aggregation of seven proteins with the CHARMM, OPLS, and AMBER protein, and the SPC and TIP3P water force fields. For efficiency and reliability, we also performed replica exchange molecular dynamics (REMD) simulations on the alanine di- and deca-peptide, and the dimer of the Aβ16-22 Alzheimer's fragment, and used experimental data and previous simulation results on the chignolin, beta3s, Trp-cage, and WW domain peptides of 10-37 amino acids. The sampling with ST is found to be more efficient than with REMD for a much lower CPU cost. Starting from unfolded or extended conformations, the WW domain and the Trp-cage peptide fold to their NMR structures with a backbone RMSD of 2.0 and 1 Å. Remarkably, the ST simulation explores transient non-native topologies for Trp-cage that have been rarely discussed by other simulations. Our ST simulations also show that the CHARMM22* force field has limitations in describing accurately the beta3s peptide. Taken together, these results open the door to the study of the configurations of single proteins, protein aggregates, and any molecular systems at atomic details in explicit solvent using a single normal CPU. They also demonstrate that our ST scheme can be used with any force field ranging from quantum mechanics to coarse-grain and atomistic.

Structure and dynamics of the integrin LFA-1 I-domain in the inactive state underlie its inside-out/outside-in signaling and allosteric mechanisms

Lymphocyte function-associated antigen 1 (LFA-1) is an integrin that transmits information in two directions across the plasma membrane of leukocytes, in so-called outside-in and inside-out signaling mechanisms. To investigate the structural basis of these mechanisms, we studied the conformational space of the apo I-domain using replica-averaged metadynamics simulations in combination with nuclear magnetic resonance chemical shifts. We thus obtained a free energy landscape that reveals the existence of three conformational substates of this domain. The three substates include conformations similar to existing crystallographic structures of the low-affinity I-domain, the inactive I-domain with an allosteric antagonist inhibitor bound underneath α helix 7, and an intermediate affinity state of the I-domain. The multiple substates were validated with residual dipolar coupling measurements. These results suggest that the presence of three substates in the apo I-domain enables the precise regulation of the binding process that is essential for the physiological function of LFA-1.

Tuning the Attempt Frequency of Protein Folding Dynamics via Transition-State Rigidification: Application to Trp-Cage

The attempt frequency or prefactor (k0) of the transition-state rate equation of protein folding kinetics has been estimated to be on the order of 10(6) s(-1), which is many orders of magnitude smaller than that of chemical reactions. Herein we use the mini-protein Trp-cage to show that it is possible to significantly increase the value of k0 for a protein folding reaction by rigidifying the transition state. This is achieved by reducing the conformational flexibility of a key structural element (i.e., an α-helix) formed in the transition state via photoisomerization of an azobenzene cross-linker. We find that this strategy not only decreases the folding time of the Trp-cage peptide by more than an order of magnitude (to ∼100 ns at 25°C) but also exposes parallel folding pathways, allowing us to provide, to the best of our knowledge, the first quantitative assessment of the curvature of the transition-state free-energy surface of a protein.

Tackling sampling challenges in biomolecular simulations

Molecular dynamics (MD) simulations are a powerful tool to give an atomistic insight into the structure and dynamics of proteins. However, the time scales accessible in standard simulations, which often do not match those in which interesting biological processes occur, limit their predictive capabilities. Many advanced sampling techniques have been proposed over the years to overcome this limitation. This chapter focuses on metadynamics, a method based on the introduction of a time-dependent bias potential to accelerate sampling and recover equilibrium properties of a few descriptors that are able to capture the complexity of a process at a coarse-grained level. The theory of metadynamics and its combination with other popular sampling techniques such as the replica exchange method is briefly presented. Practical applications of these techniques to the study of the Trp-Cage miniprotein folding are also illustrated. The examples contain a guide for performing these calculations with PLUMED, a plugin to perform enhanced sampling simulations in combination with many popular MD codes.

Metadynamics simulations reveal a Na+ independent exiting path of galactose for the inward-facing conformation of vSGLT

Sodium-Galactose Transporter (SGLT) is a secondary active symporter which accumulates sugars into cells by using the electrochemical gradient of Na⁺ across the membrane. Previous computational studies provided insights into the release process of the two ligands (galactose and sodium ion) into the cytoplasm from the inward-facing conformation of Vibrio parahaemolyticus sodium/galactose transporter (vSGLT). Several aspects of the transport mechanism of this symporter remain to be clarified: (i) a detailed kinetic and thermodynamic characterization of the exit path of the two ligands is still lacking; (ii) contradictory conclusions have been drawn concerning the gating role of Y263; (iii) the role of Na⁺ in modulating the release path of galactose is not clear. In this work, we use bias-exchange metadynamics simulations to characterize the free energy profile of the galactose and Na⁺ release processes toward the intracellular side. Surprisingly, we find that the exit of Na⁺ and galactose is non-concerted as the cooperativity between the two ligands is associated to a transition that is not rate limiting. The dissociation barriers are of the order of 11–12 kcal/mol for both the ion and the substrate, in line with kinetic information concerning this type of transporters. On the basis of these results we propose a branched six-state alternating access mechanism, which may be shared also by other members of the LeuT-fold transporters.

Membrane proteins are crucial for the communication of the cell with the environment. Among these, symporters are in charge of the transport of molecules (like sugars, amino acids, osmolytes) inside the cells, exploiting the concentration gradient of an ion to perform the task. Here we investigate by atomistic simulations the transport mechanism of the Sodium-Galactose symporter. Our results allow constructing a detailed and quantitative model of the release process of the two ligands. Surprisingly, we find that the galactose is released to the cytosol independently from the ion, unambiguously indicating that the coupling in their transport mechanism is associated to the steps preceding the release process. A large family of symporters shares the same fold and potentially the same transport mechanism. As such our results are important also because they can provide insights on common mechanistic features of these transporters.

Enhanced sampling techniques in biomolecular simulations

Biomolecular simulations are routinely used in biochemistry and molecular biology research; however, they often fail to match expectations of their impact on pharmaceutical and biotech industry. This is caused by the fact that a vast amount of computer time is required to simulate short episodes from the life of biomolecules. Several approaches have been developed to overcome this obstacle, including application of massively parallel and special purpose computers or non-conventional hardware. Methodological approaches are represented by coarse-grained models and enhanced sampling techniques. These techniques can show how the studied system behaves in long time-scales on the basis of relatively short simulations. This review presents an overview of new simulation approaches, the theory behind enhanced sampling methods and success stories of their applications with a direct impact on biotechnology or drug design.

Sampling the equilibrium kinetic network of Trp-cage in explicit solvent

We employed the single replica multiple state transition interface sampling (MSTIS) approach to sample the kinetic (un)folding network of Trp-cage mini-protein in explicit water. Cluster analysis yielded 14 important metastable states in the network. The MSTIS simulation thus resulted in a full 14 × 14 rate matrix. Analysis of the kinetic rate matrix indicates the presence of a near native intermediate state characterized by a fully formed alpha helix, a slightly disordered proline tail, a broken salt-bridge, and a rotated arginine residue. This intermediate was also found in recent IR experiments. Moreover, the predicted rate constants and timescales are in agreement with previous experiments and simulations.

Structural determinants in prion protein folding and stability

Prions are responsible for a heterogeneous group of fatal neurodegenerative diseases, involving post-translational modifications of the cellular prion protein. Epidemiological studies on Creutzfeldt-Jakob disease, a prototype prion disorder, show a majority of cases being sporadic, while the remaining occurrences are either genetic or iatrogenic. The molecular mechanisms by which PrP(C) is converted into its pathological isoform have not yet been established. While point mutations and seeds trigger the protein to cross the energy barriers, thus causing genetic and infectious transmissible spongiform encephalopathies, respectively, the mechanism responsible for sporadic forms remains unclear. Since prion diseases are protein-misfolding disorders, we investigated prion protein folding and stability as functions of different milieus. Using spectroscopic techniques and atomistic simulations, we dissected the contribution of major structural determinants, also defining the energy landscape of prion protein. In particular, we elucidated (i) the essential role of the octapeptide region in prion protein folding and stability, (ii) the presence of a very enthalpically stable intermediate in prion-susceptible species, and (iii) the role of the disulfide bridge in prion protein folding.

Machine learning. Clustering by fast search and find of density peaks

Cluster analysis is aimed at classifying elements into categories on the basis of their similarity. Its applications range from astronomy to bioinformatics, bibliometrics, and pattern recognition. We propose an approach based on the idea that cluster centers are characterized by a higher density than their neighbors and by a relatively large distance from points with higher densities. This idea forms the basis of a clustering procedure in which the number of clusters arises intuitively, outliers are automatically spotted and excluded from the analysis, and clusters are recognized regardless of their shape and of the dimensionality of the space in which they are embedded. We demonstrate the power of the algorithm on several test cases.