Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Intrinsic disorder and conformational coexistence in auxin coreceptors

AUXIN/INDOLE 3-ACETIC ACID (Aux/IAA) transcriptional repressor proteins and the TRANSPORT INHIBITOR RESISTANT 1/AUXIN SIGNALING F-BOX (TIR1/AFB) proteins to which they bind act as auxin coreceptors. While the structure of TIR1 has been solved, structural characterization of the regions of the Aux/IAA protein responsible for auxin perception has been complicated by their predicted disorder. Here, we use NMR, CD and molecular dynamics simulation to investigate the N-terminal domains of the Aux/IAA protein IAA17/AXR3. We show that despite the conformational flexibility of the region, a critical W-P bond in the core of the Aux/IAA degron motif occurs at a strikingly high (1:1) ratio of cis to trans isomers, consistent with the requirement of the cis conformer for the formation of the fully-docked receptor complex. We show that the N-terminal half of AXR3 is a mixture of multiple transiently structured conformations with a propensity for two predominant and distinct conformational subpopulations within the overall ensemble. These two states were modeled together with the C-terminal PB1 domain to provide the first complete simulation of an Aux/IAA. Using MD to recreate the assembly of each complex in the presence of auxin, both structural arrangements were shown to engage with the TIR1 receptor, and contact maps from the simulations match closely observations of NMR signal-decreases. Together, our results and approach provide a platform for exploring the functional significance of variation in the Aux/IAA coreceptor family and for understanding the role of intrinsic disorder in auxin signal transduction and other signaling systems.

Computational methods for exploring protein conformations

Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.

Enhanced sampling and free energy calculations for protein simulations

Molecular dynamics simulation is a powerful computational technique to study biomolecular systems, which complements experiments by providing insights into the structural dynamics relevant to biological functions at atomic scale. It can also be used to calculate the free energy landscapes of the conformational transitions to better understand the functions of the biomolecules. However, the sampling of biomolecular configurations is limited by the free energy barriers that need to be overcome, leading to considerable gaps between the timescales reached by MD simulation and those governing biological processes. To address this issue, many enhanced sampling methodologies have been developed to increase the sampling efficiency of molecular dynamics simulations and free energy calculations. Usually, enhanced sampling algorithms can be classified into methods based on collective variables (CV-based) and approaches which do not require predefined CVs (CV-free). In this chapter, the theoretical basis of free energy estimation is briefly reviewed first, followed by the reviews of the most common CV-based and CV-free methods including the presentation of some examples and recent developments. Finally, the combination of different enhanced sampling methods is discussed.

Tyrosine metabolism: identification of a key residue in the acquisition of prephenate aminotransferase activity by 1β aspartate aminotransferase

Alternative routes for the post-chorismate branch of the biosynthetic pathway leading to tyrosine exist, the 4-hydroxyphenylpyruvate or the arogenate route. The arogenate route involves the transamination of prephenate into arogenate. In a previous study, we found that, depending on the microorganisms possessing the arogenate route, three different aminotransferases evolved to perform prephenate transamination, that is, 1β aspartate aminotransferase (1β AAT), N-succinyl-l,l-diaminopimelate aminotransferase, and branched-chain aminotransferase. The present work aimed at identifying molecular determinant(s) of 1β AAT prephenate aminotransferase (PAT) activity. To that purpose, we conducted X-ray crystal structure analysis of two PAT competent 1β AAT from Arabidopsis thaliana and Rhizobium meliloti and one PAT incompetent 1β AAT from R. meliloti. This structural analysis supported by site-directed mutagenesis, modeling, and molecular dynamics simulations allowed us to identify a molecular determinant of PAT activity in the flexible N-terminal loop of 1β AAT. Our data reveal that a Lys/Arg/Gln residue in position 12 in the sequence (numbering according to Thermus thermophilus 1β AAT), present only in PAT competent enzymes, could interact with the 4-hydroxyl group of the prephenate substrate, and thus may have a central role in the acquisition of PAT activity by 1β AAT.

The carbon monoxide dehydrogenase accessory protein CooJ is a histidine-rich multidomain dimer containing an unexpected Ni(II)-binding site

Activation of nickel enzymes requires specific accessory proteins organized in multiprotein complexes controlling metal transfer to the active site. Histidine-rich clusters are generally present in at least one of the metallochaperones involved in nickel delivery. The maturation of carbon monoxide dehydrogenase in the proteobacterium Rhodospirillum rubrum requires three accessory proteins, CooC, CooT, and CooJ, dedicated to nickel insertion into the active site, a distorted [NiFe₃S₄] cluster coordinated to an iron site. Previously, CooJ from R. rubrum (RrCooJ) has been described as a nickel chaperone with 16 histidines and 2 cysteines at its C terminus. Here, the X-ray structure of a truncated version of RrCooJ, combined with small-angle X-ray scattering data and a modeling study of the full-length protein, revealed a homodimer comprising a coiled coil with two independent and highly flexible His tails. Using isothermal calorimetry, we characterized several metal-binding sites (four per dimer) involving the His-rich motifs and having similar metal affinity (K_D = 1.6 μm). Remarkably, biophysical approaches, site-directed mutagenesis, and X-ray crystallography uncovered an additional nickel-binding site at the dimer interface, which binds Ni(II) with an affinity of 380 nm Although RrCooJ was initially thought to be a unique protein, a proteome database search identified at least 46 bacterial CooJ homologs. These homologs all possess two spatially separated nickel-binding motifs: a variable C-terminal histidine tail and a strictly conserved H(W/F)X ₂HX ₃H motif, identified in this study, suggesting a dual function for CooJ both as a nickel chaperone and as a nickel storage protein.

Focused conformational sampling in proteins

A detailed understanding of the conformational dynamics of biological molecules is difficult to obtain by experimental techniques due to resolution limitations in both time and space. Computer simulations avoid these in theory but are often too short to sample rare events reliably. Here we show that the progress index-guided sampling (PIGS) protocol can be used to enhance the sampling of rare events in selected parts of biomolecules without perturbing the remainder of the system. The method is very easy to use as it only requires as essential input a set of several features representing the parts of interest sufficiently. In this feature space, new states are discovered by spontaneous fluctuations alone and in unsupervised fashion. Because there are no energetic biases acting on phase space variables or projections thereof, the trajectories PIGS generates can be analyzed directly in the framework of transition networks. We demonstrate the possibility and usefulness of such focused explorations of biomolecules with two loops that are part of the binding sites of bromodomains, a family of epigenetic "reader" modules. This real-life application uncovers states that are structurally and kinetically far away from the initial crystallographic structures and are also metastable. Representative conformations are intended to be used in future high-throughput virtual screening campaigns.

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as "the protein folding problem," has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.

Hamiltonian Monte Carlo with Constrained Molecular Dynamics as Gibbs Sampling

Compared to fully flexible molecular dynamics, simulations of constrained systems can use larger time steps and focus kinetic energy on soft degrees of freedom. Achieving ergodic sampling from the Boltzmann distribution, however, has proven challenging. Using recent generalizations of the equipartition principle and Fixman potential, here we implement Hamiltonian Monte Carlo based on constrained molecular dynamics as a Gibbs sampling move. By mixing Hamiltonian Monte Carlo based on fully flexible and torsional dynamics, we are able to reproduce free energy landscapes of simple model systems and enhance sampling of macrocycles.

Characterization of the three-dimensional free energy manifold for the uracil ribonucleoside from asynchronous replica exchange simulations

Replica exchange molecular dynamics has emerged as a powerful tool for efficiently sampling free energy landscapes for conformational and chemical transitions. However, daunting challenges remain in efficiently getting such simulations to scale to the very large number of replicas required to address problems in state spaces beyond two dimensions. The development of enabling technology to carry out such simulations is in its infancy, and thus it remains an open question as to which applications demand extension into higher dimensions. In the present work, we explore this problem space by applying asynchronous Hamiltonian replica exchange molecular dynamics with a combined quantum mechanical/molecular mechanical potential to explore the conformational space for a simple ribonucleoside. This is done using a newly developed software framework capable of executing >3,000 replicas with only enough resources to run 2,000 simultaneously. This may not be possible with traditional synchronous replica exchange approaches. Our results demonstrate 1.) the necessity of high dimensional sampling simulations for biological systems, even as simple as a single ribonucleoside, and 2.) the utility of asynchronous exchange protocols in managing simultaneous resource requirements expected in high dimensional sampling simulations. It is expected that more complicated systems will only increase in computational demand and complexity, and thus the reported asynchronous approach may be increasingly beneficial in order to make such applications available to a broad range of computational scientists.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

The ubiquitin ligase Ubr4 controls stability of podocin/MEC-2 supercomplexes

The PHB-domain protein podocin maintains the renal filtration barrier and its mutation is an important cause of hereditary nephrotic syndrome. Podocin and its Caenorhabditis elegans orthologue MEC-2 have emerged as key components of mechanosensitive membrane protein signalling complexes. Whereas podocin resides at a specialized cell junction at the podocyte slit diaphragm, MEC-2 is found in neurons required for touch sensitivity. Here, we show that the ubiquitin ligase Ubr4 is a key component of the podocin interactome purified both from cultured podocytes and native glomeruli. It colocalizes with podocin and regulates its stability. In C. elegans, this process is conserved. Here, Ubr4 is responsible for the degradation of mislocalized MEC-2 multimers. Ubiquitylomic analysis of mouse glomeruli revealed that podocin is ubiquitylated at two lysine residues. These sites were Ubr4-dependent and were conserved across species. Molecular dynamics simulations revealed that ubiquitylation of one site, K301, do not only target podocin/MEC-2 for proteasomal degradation, but may also affect stability and disassembly of the multimeric complex. We suggest that Ubr4 is a key regulator of podocyte foot process proteostasis.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Enhancing constant-pH simulation in explicit solvent with a two-dimensional replica exchange method

We present a new method for enhanced sampling for constant-pH simulations in explicit water based on a two-dimensional (2D) replica exchange scheme. The new method is a significant extension of our previously developed constant-pH simulation method, which is based on enveloping distribution sampling (EDS) coupled with a one-dimensional (1D) Hamiltonian exchange method (HREM). EDS constructs a hybrid Hamiltonian from multiple discrete end state Hamiltonians that, in this case, represent different protonation states of the system. The ruggedness and heights of the hybrid Hamiltonian's energy barriers can be tuned by the smoothness parameter. Within the context of the 1D EDS-HREM method, exchanges are performed between replicas with different smoothness parameters, allowing frequent protonation-state transitions and sampling of conformations that are favored by the end-state Hamiltonians. In this work, the 1D method is extended to 2D with an additional dimension, external pH. Within the context of the 2D method (2D EDS-HREM), exchanges are performed on a lattice of Hamiltonians with different pH conditions and smoothness parameters. We demonstrate that both the 1D and 2D methods exactly reproduce the thermodynamic properties of the semigrand canonical (SGC) ensemble of a system at a given pH. We have tested our new 2D method on aspartic acid, glutamic acid, lysine, a four residue peptide (sequence KAAE), and snake cardiotoxin. In all cases, the 2D method converges faster and without loss of precision; the only limitation is a loss of flexibility in how CPU time is employed. The results for snake cardiotoxin demonstrate that the 2D method enhances protonation-state transitions, samples a wider conformational space with the same amount of computational resources, and converges significantly faster overall than the original 1D method.

Efficiently computing pathway free energies: New approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes

BACKGROUND

Accurately modeling condensed phase processes is one of computation's most difficult challenges. Include the possibility that conformational dynamics may be coupled to chemical reactions, where multiscale (i.e., QM/MM) methods are needed, and this task becomes even more daunting.

METHODS

Free energy simulations (i.e., molecular dynamics), multiscale modeling, and reweighting schemes.

RESULTS

Herein, we present two new approaches for mitigating the aforementioned challenges. The first is a new chain-of-replica method (off-path simulations, OPS) for computing potentials of mean force (PMFs) along an easily defined reaction coordinate. This development is coupled with a new distributed, highly-parallel replica framework (REPDstr) within the CHARMM package. Validation of these new schemes is carried out on two processes that undergo conformational changes. First is the simple torsional rotation of butane, while a much more challenging glycosidic rotation (in vacuo and solvated) is the second. Additionally, a new approach that greatly improves (i.e., possibly an order of magnitude) the efficiency of computing QM/MM PMFs is introduced and compared to standard schemes. Our efforts are grounded in the recently developed method for efficiently computing QM-based free energies (i.e., QM-Non-Boltzmann Bennett, QM-NBB). Again, we validate this new technique by computing the QM/MM PMF of butane's torsional rotation.

CONCLUSIONS

The OPS-REPDstr method is a promising new approach that overcomes many limitations of standard pathway simulations in CHARMM. The combination of QM-NBB with pathway techniques is very promising as it offers significant advantages over current procedures.

GENERAL SIGNIFICANCE

Efficiently computing potentials of mean force is a major, unresolved, area of interest. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.