MSMBuilder: Statistical Models for Biomolecular Dynamics

Comparative Analyses of the Conformational Dynamics Between the Soluble and Membrane-Bound Cytokine Receptors

Cytokine receptors receive extracellular cues by binding with cytokines to transduce a signaling cascade leading to gene transcription in cells. Their soluble isoforms, functioning as decoy receptors, contain only the ectodomain. Whether the ectodomains of cytokine receptors at the membrane exhibit different conformational dynamics from their soluble forms is unknown. Using Stimulation-2 (ST2) as an example, we performed microsecond molecular dynamics (MD) simulations to study the conformational dynamics of the soluble and the membrane-bound ST2 (sST2 and ST2). Combined use of accelerated and conventional MD simulations enabled extensive sampling of the conformational space of sST2 for comparison with ST2. Using the interdomain loop conformation as the reaction coordinate, we built a Markov State Model to determine the slowest implied timescale of the conformational transition in sST2 and ST2. We found that the ectodomain of ST2 undergoes slower conformational relaxation but exhibits a faster rate of conformational transition in a more restricted conformational space than sST2. Analyses of the relaxed conformations of ST2 further suggest important contributions of interdomain salt-bridge interactions to the stabilization of different ST2 conformations. Our study elucidates differential conformational properties between sST2 and ST2 that may be exploited for devising strategies to selectively target each isoform.

Computational insight into the interaction of oxaliplatin with insulin

In an organism, cisplatin and its derivatives are known to interact with proteins besides their principal DNA target. These off-target interactions have major therapeutic consequences including undesired side effects, loss of bioavailability and emergence of resistance. Insulin is one of the prototypical protein targets of platinum drugs as it has been seen to be involved in bioavailability reduction and might also determine resistance in certain cancer lines. However, despite the interest in understanding the nature of the oxaliplatin-insulin adducts, no 3D models have been achieved so far. In this study, we apply our recent computational multiscale protocol optimized for bioinorganic interactions to provide structural insights into these systems. To do so, the initial structures are predicted by blind protein-metalloligand docking calculations optimized to account for a metal-containing species, and then refined using a Molecular Dynamics (MD) and Quantum Mechanics/Molecular Mechanics (QM/MM) integrated protocol. The results are consistent with experimental information obtained from fragment analysis, and also provide novel structural information like conformational changes occurring upon binding and potential effects on the biological functions of the protein. This study opens an avenue towards applying similar strategies to a wide ensemble of metallodrug-protein/peptide systems for which no structural data are available.

Multi-state recognition pathway of the intrinsically disordered protein kinase inhibitor by protein kinase A

In the nucleus, the spatiotemporal regulation of the catalytic subunit of cAMP-dependent protein kinase A (PKA-C) is orchestrated by an intrinsically disordered protein kinase inhibitor, PKI, which recruits the CRM1/RanGTP nuclear exporting complex. How the PKA-C/PKI complex assembles and recognizes CRM1/RanGTP is not well understood. Using NMR, SAXS, fluorescence, metadynamics, and Markov model analysis, we determined the multi-state recognition pathway for PKI. After a fast binding step in which PKA-C selects PKI's most competent conformations, PKI folds upon binding through a slow conformational rearrangement within the enzyme's binding pocket. The high-affinity and pseudo-substrate regions of PKI become more structured and the transient interactions with the kinase augment the helical content of the nuclear export sequence, which is then poised to recruit the CRM1/RanGTP complex for nuclear translocation. The multistate binding mechanism featured by PKA-C/PKI complex represents a paradigm on how disordered, ancillary proteins (or protein domains) are able to operate multiple functions such as inhibiting the kinase while recruiting other regulatory proteins for nuclear export.

Structural insights into tetraspanin CD9 function

Tetraspanins play critical roles in various physiological processes, ranging from cell adhesion to virus infection. The members of the tetraspanin family have four membrane-spanning domains and short and large extracellular loops, and associate with a broad range of other functional proteins to exert cellular functions. Here we report the crystal structure of CD9 and the cryo-electron microscopic structure of CD9 in complex with its single membrane-spanning partner protein, EWI-2. The reversed cone-like molecular shape of CD9 generates membrane curvature in the crystalline lipid layers, which explains the CD9 localization in regions with high membrane curvature and its implications in membrane remodeling. The molecular interaction between CD9 and EWI-2 is mainly mediated through the small residues in the transmembrane region and protein/lipid interactions, whereas the fertilization assay revealed the critical involvement of the LEL region in the sperm-egg fusion, indicating the different dependency of each binding domain for other partner proteins.

Tetraspanins play critical roles in various physiological processes, ranging from cell adhesion to virus infection. Here authors report the crystal structure of CD9 and the cryo-electron microscopic structure of CD9 in complex with its single membrane-spanning partner protein, EWI-2.

Dynamical model of the CLC-2 ion channel reveals conformational changes associated with selectivity-filter gating

This work reports a dynamical Markov state model of CLC-2 "fast" (pore) gating, based on 600 microseconds of molecular dynamics (MD) simulation. In the starting conformation of our CLC-2 model, both outer and inner channel gates are closed. The first conformational change in our dataset involves rotation of the inner-gate backbone along residues S168-G169-I170. This change is strikingly similar to that observed in the cryo-EM structure of the bovine CLC-K channel, though the volume of the intracellular (inner) region of the ion conduction pathway is further expanded in our model. From this state (inner gate open and outer gate closed), two additional states are observed, each involving a unique rotameric flip of the outer-gate residue GLUex. Both additional states involve conformational changes that orient GLUex away from the extracellular (outer) region of the ion conduction pathway. In the first additional state, the rotameric flip of GLUex results in an open, or near-open, channel pore. The equilibrium population of this state is low (∼1%), consistent with the low open probability of CLC-2 observed experimentally in the absence of a membrane potential stimulus (0 mV). In the second additional state, GLUex rotates to occlude the channel pore. This state, which has a low equilibrium population (∼1%), is only accessible when GLUex is protonated. Together, these pathways model the opening of both an inner and outer gate within the CLC-2 selectivity filter, as a function of GLUex protonation. Collectively, our findings are consistent with published experimental analyses of CLC-2 gating and provide a high-resolution structural model to guide future investigations.

Electrostatic Forces Control the Negative Allosteric Regulation in a Disordered Protein Switch

The transcriptional adaptor zinc-binding 1 (TAZ1) domain of the transcriptional coactivator CBP/P300 and two disordered peptides, HIF-1α and CITED2, form a delicate protein switch that regulates cellular hypoxic response. In hypoxia, HIF-1α binds TAZ1 to control the transcription of adaptive genes critical for the recovery from hypoxic stress. CITED2 acts as the negative feedback regulator to rapidly displace HIF-1α and efficiently attenuate the hypoxic response. Though CITED2 and HIF-1α have the same dissociation constant (K_d = 10 nM) in their binary complexes with TAZ1, CITED2 is much more competitive than HIF-1α upon binding the same target TAZ1 in ternary ( Berlow et al. Nature 2017 , 543 , 447 - 451 ). Here we demonstrate that a simple coarse-grained model can recapitulate this negative allosteric effect and provide detailed physical insights into the displacement mechanism. We find that long-range electrostatic forces are essential for the efficient displacement of HIF-1α by CITED2. The strong electrostatic interactions between CITED2 and TAZ1, along with the unique binding mode, make CITED2 much more competitive than HIF-1α in binding TAZ1.

From molecular energy landscapes to equilibrium dynamics via landscape analysis and markov state models

Molecular dynamics (MD) simulation software allows probing the equilibrium structural dynamics of a molecule of interest, revealing how a molecule navigates its structure space one structure at a time. To obtain a broader view of dynamics, typically one needs to launch many such simulations, obtaining many trajectories. A summarization of the equilibrium dynamics requires integrating the information in the various trajectories, and Markov State Models (MSM) are increasingly being used for this task. At its core, the task involves organizing the structures accessed in simulation into structural states, and then constructing a transition probability matrix revealing the transitions between states. While now considered a mature technology and widely used to summarize equilibrium dynamics, the underlying computational process in the construction of an MSM ignores energetics even though the transition of a molecule between two nearby structures in an MD trajectory is governed by the corresponding energies. In this paper, we connect theory with simulation and analysis of equilibrium dynamics. A molecule navigates the energy landscape underlying the structure space. The structural states that are identified via off-the-shelf clustering algorithms need to be connected to thermodynamically-stable and semi-stable (macro)states among which transitions can then be quantified. Leveraging recent developments in the analysis of energy landscapes that identify basins in the landscape, we evaluate the hypothesis that basins, directly tied to stable and semi-stable states, lead to better models of dynamics. Our analysis indicates that basins lead to MSMs of better quality and thus can be useful to further advance this widely-used technology for summarization of molecular equilibrium dynamics.

How to learn from inconsistencies: Integrating molecular simulations with experimental data

Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.

Integrated Computational Approaches and Tools forAllosteric Drug Discovery

Understanding molecular mechanisms underlying the complexity of allosteric regulationin proteins has attracted considerable attention in drug discovery due to the benefits and versatilityof allosteric modulators in providing desirable selectivity against protein targets while minimizingtoxicity and other side effects. The proliferation of novel computational approaches for predictingligand-protein interactions and binding using dynamic and network-centric perspectives has ledto new insights into allosteric mechanisms and facilitated computer-based discovery of allostericdrugs. Although no absolute method of experimental and in silico allosteric drug/site discoveryexists, current methods are still being improved. As such, the critical analysis and integration ofestablished approaches into robust, reproducible, and customizable computational pipelines withexperimental feedback could make allosteric drug discovery more efficient and reliable. In this article,we review computational approaches for allosteric drug discovery and discuss how these tools can beutilized to develop consensus workflows for in silico identification of allosteric sites and modulatorswith some applications to pathogen resistance and precision medicine. The emerging realization thatallosteric modulators can exploit distinct regulatory mechanisms and can provide access to targetedmodulation of protein activities could open opportunities for probing biological processes and insilico design of drug combinations with improved therapeutic indices and a broad range of activities.

Adaptive Markov state model estimation using short reseeding trajectories

In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on slow time scales. A promising approach to enhanced sampling of MSMs is to use "adaptive" methods, in which new MD trajectories are "seeded" preferentially from previously identified states. Here, we investigate the performance of various MSM estimators applied to reseeding trajectory data, for both a simple 1D free energy landscape and mini-protein folding MSMs of WW domain and NTL9(1-39). Our results reveal the practical challenges of reseeding simulations and suggest a simple way to reweight seeding trajectory data to better estimate both thermodynamic and kinetic quantities.

Molecular Mechanism of Brassinosteroid Perception by the Plant Growth Receptor BRI1

Brassinosteroids (BRs) are essential phytohormones, which bind to the plant receptor, BRI1, to regulate various physiological processes. The molecular mechanism of the perception of BRs by the ectodomain of BRI1 remains not fully understood. It also remains elusive why a substantial difference in biological activity exists between the BRs. In this work, we study the binding mechanisms of the two most bioactive BRs, brassinolide (BLD) and castasterone (CAT), using molecular dynamics simulations. We report free-energy landscapes of the binding processes of both ligands, as well as detailed ligand binding pathways. Our results suggest that CAT has a lower binding affinity compared to BLD due to its inability to form hydrogen-bonding interactions with a tyrosine residue in the island domain of BRI1. We uncover a conserved nonproductive binding state for both BLD and CAT, which is more stable for CAT and may further contribute to the bioactivity difference. Finally, we validate past observations about the conformational restructuring and ordering of the island domain upon BLD binding. Overall, this study provides new insights into the fundamental mechanism of the perception of the two most bioactive BRs, which may create new avenues for genetic and agrochemical control of their signaling cascade.

FSATOOL: A useful tool to do the conformational sampling and trajectory analysis work for biomolecules

Reliable conformational sampling and trajectory analysis are always important to the study of the folding or binding mechanisms of biomolecules. Generally, one has to prepare many complicated parameters and follow a lot of steps to obtain the final data. The whole process is too complicated to new users. In this article, we provide a convenient and user-friendly tool that is compatible to AMBER, called fast sampling and analysis tool (FSATOOL). FSATOOL has some useful features. First and the most important, the whole work is extremely simplified into two steps, one is the fast sampling procedure and the other is the trajectory analysis procedure. Second, it contains several powerful sampling methods for the simulation on graphics process unit, including our previous mixing replica exchange molecular dynamics method. The method combines the advantages of the biased and unbiased simulations. Finally, it extracts the dominant transition pathways automatically from the folding network by Markov state model. Users do not need to do the tedious intermediate steps by hand. To illustrate the usage of FSATOOL in practice, we perform one simulation for a RNA hairpin in explicit solvent. All the results are presented. © 2019 Wiley Periodicals, Inc.

Revealing Molecular Determinants of hERG Blocker and Activator Binding

The Kv11.1 potassium channel, encoded by the human ether-a-go-go-related gene (hERG), plays an essential role in the cardiac action potential. hERG blockade by small molecules can induce "torsade de pointes" arrhythmias and sudden death; as such, it is an important off-target to avoid during drug discovery. Recently, a cryo-EM structure of the open channel state of hERG was reported, opening the door to in silico docking analyses and interpretation of hERG structure-activity relationships, with a view to avoiding blocking activity. Despite this, docking directly to this cryo-EM structure has been reported to yield binding modes that are unable to explain known mutagenesis data. In this work, we use molecular dynamics simulations to sample a range of channel conformations and run ensemble docking campaigns at the known hERG binding site below the selectivity filter, composed of the central cavity and the four deep hydrophobic pockets. We identify a hERG conformational state allowing discrimination of blockers vs nonblockers from docking; furthermore, the binding pocket agrees with mutagenesis data, and blocker binding modes fit the hERG blocker pharmacophore. We then use the same protocol to identify a binding pocket in the hERG channel pore for hERG activators, again agreeing with the reported mutagenesis. Our approach may be useful in drug discovery campaigns to prioritize candidate compounds based on hERG liability via virtual docking screens.

Opening dynamics of HIV-1 gp120 upon receptor binding is dictated by a key hydrophobic core

HIV-1 entry is mediated firstly by the molecular recognition between the viral glycoprotein gp120 and its receptor CD4 on host T-cells. As a key antigen that can be targeted by neutralizing antibodies, gp120 has been a focus for extensive studies with efforts to understand its structural properties and conformational dynamics upon receptor binding. An atomistic-level revelation of gp120 opening dynamics activated by CD4, however, is still unknown. Here, by constructing a Markov State Model (MSM) based on hundreds of Molecular Dynamics (MD) simulations with an aggregated simulation time of ∼20 microseconds (μs), we identify the key metastable states of gp120 during its opening dynamics upon CD4 binding. The MSM provides a clear dynamic model whereby the identified metastable states coexist and can reach an equilibrium. More importantly, a hydrophobic core flanked by variable loops (V1V2 and V3) and the β20/21 region plays an essential role in triggering the gp120 opening. Any destabilizing effects introduced into the hydrophobic core, therefore, can be expected to promote transition of gp120 to an open state. Moreover, the variable loops demonstrate high flexibilities in fully open gp120. In particular, the V3 region is capable of exploring both closed and open conformations, even with the V1/V2 loops largely adopting an open form. In addition, the bridging sheet formation in gp120 is likely induced by the incoming co-receptor/antibody recognitions, since the V1/V2 structure is highly heterogeneous so that the bridging-sheet formed conformation is not the most populated state. Our studies provide deep insights into the dynamic features of gp120 and its molecular recognitions to the broadly neutralizing antibodies, which guides future attempts to design more effective gp120 immunogens.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

Base-flipping dynamics from an intrahelical to an extrahelical state exerted by thymine DNA glycosylase during DNA repair process

Thymine DNA glycosylase (TDG) is a DNA repair enzyme that excises a variety of mismatched or damaged nucleotides (nts), e.g. dU, dT, 5fC and 5caC. TDG is shown to play essential roles in maintaining genome integrity and correctly programming epigenetic modifications through DNA demethylation. After locating the lesions, TDG employs a base-flipping strategy to recognize the damaged nucleobases, whereby the interrogated nt is extruded from the DNA helical stack and binds into the TDG active site. The dynamic mechanism of the base-flipping process at an atomistic resolution, however, remains elusive. Here, we employ the Markov State Model (MSM) constructed from extensive all-atom molecular dynamics (MD) simulations to reveal the complete base-flipping process for a G.T mispair at a tens of microsecond timescale. Our studies identify critical intermediates of the mispaired dT during its extrusion process and reveal the key TDG residues involved in the inter-state transitions. Notably, we find an active role of TDG in promoting the intrahelical nt eversion, sculpturing the DNA backbone, and penetrating into the DNA minor groove. Three additional TDG substrates, namely dU, 5fC, and 5caC, are further tested to evaluate the substituent effects of various chemical modifications of the pyrimidine ring on base-flipping dynamics.

Dynamics of the excised base release in thymine DNA glycosylase during DNA repair process

Thymine DNA glycosylase (TDG) initiates base excision repair by cleaving the N-glycosidic bond between the sugar and target base. After catalysis, the release of excised base is a requisite step to terminate the catalytic cycle and liberate the TDG for the following enzymatic reactions. However, an atomistic-level understanding of the dynamics of the product release process in TDG remains unknown. Here, by employing molecular dynamics simulations combined with the Markov State Model, we reveal the dynamics of the thymine release after the excision at microseconds timescale and all-atom resolution. We identify several key metastable states of the thymine and its dominant releasing pathway. Notably, after replacing the TDG residue Gly142 with tyrosine, the thymine release is delayed compared to the wild-type (wt) TDG, as supported by our potential of mean force (PMF) calculations. These findings warrant further experimental tests to potentially trap the excised base in the active site of TDG after the catalysis, which had been unsuccessful by previous attempts. Finally, we extended our studies to other TDG products, including the uracil, 5hmU, 5fC and 5caC bases in order to compare the product release for different targeting bases in the TDG–DNA complex.

Driven to near-experimental accuracy by refinement via molecular dynamics simulations

Protein model refinement has been an essential part of successful protein structure prediction. Molecular dynamics simulation-based refinement methods have shown consistent improvement of protein models. There had been progress in the extent of refinement for a few years since the idea of ensemble averaging of sampled conformations emerged. There was little progress in CASP12 because conformational sampling was not sufficiently diverse due to harmonic restraints. During CASP13, a new refinement method was tested that achieved significant improvements over CASP12. The new method intended to address previous bottlenecks in the refinement problem by introducing new features. Flat-bottom harmonic restraints replaced harmonic restraints, sampling was performed iteratively, and a new scoring function and selection criteria were used. The new protocol expanded conformational sampling at reduced computational costs. In addition to overall improvements, some models were refined significantly to near-experimental accuracy.

Nonlinear discovery of slow molecular modes using state-free reversible VAMPnets

The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simplest molecular systems, and their data-driven discovery directly from molecular simulation trajectories has been a central focus of the molecular simulation community to both unveil the important physical mechanisms and drive enhanced sampling. In this work, we introduce state-free reversible VAMPnets (SRV) as a deep learning architecture that learns nonlinear CV approximants to the leading slow eigenfunctions of the spectral decomposition of the transfer operator that evolves equilibrium-scaled probability distributions through time. Orthogonality of the learned CVs is naturally imposed within network training without added regularization. The CVs are inherently explicit and differentiable functions of the input coordinates making them well-suited to use in enhanced sampling calculations. We demonstrate the utility of SRVs in capturing parsimonious nonlinear representations of complex system dynamics in applications to 1D and 2D toy systems where the true eigenfunctions are exactly calculable and to molecular dynamics simulations of alanine dipeptide and the WW domain protein.

The dynamic conformational landscape of the protein methyltransferase SETD8

Elucidating the conformational heterogeneity of proteins is essential for understanding protein function and developing exogenous ligands. With the rapid development of experimental and computational methods, it is of great interest to integrate these approaches to illuminate the conformational landscapes of target proteins. SETD8 is a protein lysine methyltransferase (PKMT), which functions in vivo via the methylation of histone and nonhistone targets. Utilizing covalent inhibitors and depleting native ligands to trap hidden conformational states, we obtained diverse X-ray structures of SETD8. These structures were used to seed distributed atomistic molecular dynamics simulations that generated a total of six milliseconds of trajectory data. Markov state models, built via an automated machine learning approach and corroborated experimentally, reveal how slow conformational motions and conformational states are relevant to catalysis. These findings provide molecular insight on enzymatic catalysis and allosteric mechanisms of a PKMT via its detailed conformational landscape.

Our cells contain thousands of proteins that perform many different tasks. Such tasks often involve significant changes in the shape of a protein that allow it to interact with other proteins or ligands. Understanding these shape changes can be an essential step for predicting and manipulating how proteins work or designing new drugs. Some changes in protein shape happen quickly, whereas others take longer. Existing experimental approaches generally only capture some, but not all, of the different shapes an individual protein adopts.

A family of proteins known as protein lysine methyltransferases (PKMTs) help to regulate the activities of other proteins by adding small tags called methyl groups to specific positions on their target proteins. PKMTs play important roles in many life processes including in activating genes, maintaining stem cells and controlling how organs develop.

It is important for cells to properly control the activity of PKMTs because too much, or too little, activity can promote cancers and neurological diseases. For example, genetic mutations that increase the levels of a PKMT known as SETD8 appear to promote the progression of some breast cancers and childhood leukemia. There is a pressing need to develop new drugs that can inhibit SETD8 and other PKMTs in human patients. However, these efforts are hindered by the lack of understanding of exactly how the shape of PKMT proteins change as they operate in cells.

Chen, Wiewiora et al. used a technique called X-ray crystallography to generate structural models of the human SETD8 protein in the presence or absence of native or foreign ligands. These models were used to develop computer simulations of how the shape of SETD8 changes as it operates. Further computational analysis and laboratory experiments revealed how slow changes in the shape of SETD8 contribute to the ability of the protein to attach methyl groups to other proteins.

This work is a significant stepping-stone to developing a complete model of how the SETD8 protein works, as well as understanding how genetic mutations may affect the protein’s role in the body. The next step is to refine the model by integrating data from other approaches including biophysical models and mathematical calculations of the energy associated with the shape changes, with a long-term goal to better understand and then manipulate the function of SETD8.

The Effect of Cofactor Binding on the Conformational Plasticity of the Biological Receptors in Artificial Metalloenzymes: The Case Study of LmrR

The design of Artificial Metalloenzymes (ArMs), which result from the incorporation of organometallic cofactors into biological structures, has grown steadily in the last two decades and important new-to-Nature reactions have been reached. These type of exercises could greatly benefit from an understanding of the structural impact that the inclusion of organometallic moieties may have on the biological host. To date though, our understanding of this phenomenon is highly partial. This lack of knowledge is one of the elements that condition that first-generation ArMs generally display relatively poor catalytic profiles. In this work, we approach this matter by assessing the dynamics and stability of a series of ArMs resulting from the inclusion, via different anchoring strategies, of a variety of organometallic cofactors into the Lactococcal multidrug resistance regulator (LmrR) protein. To this aim, we coupled standard force field-based techniques such as Protein-Ligand Docking and Molecular Dynamics simulations with a variety of trajectory convergence analyses, capable of assessing both the stability and flexibility of the different systems under study upon the binding of cofactors. Together with the experimental evidence obtained in other studies, we provide an overview on how these changes can affect the catalytic outcomes obtained from the different ArMs. Fundamentally, our results show that the convergence analysis used in this work can assess how the inclusion of synthetic metallic cofactors in proteins can condition different structural modulations of their host. Those conformational modifications are key to the success of the desired catalytic activity and their proper identification can be wisely used to improve the quality and the rate of success of the ArMs.

Enspara: Modeling molecular ensembles with scalable data structures and parallel computing

Markov state models (MSMs) are quantitative models of protein dynamics that are useful for uncovering the structural fluctuations that proteins undergo, as well as the mechanisms of these conformational changes. Given the enormity of conformational space, there has been ongoing interest in identifying a small number of states that capture the essential features of a protein. Generally, this is achieved by making assumptions about the properties of relevant features-for example, that the most important features are those that change slowly. An alternative strategy is to keep as many degrees of freedom as possible and subsequently learn from the model which of the features are most important. In these larger models, however, traditional approaches quickly become computationally intractable. In this paper, we present enspara, a library for working with MSMs that provides several novel algorithms and specialized data structures that dramatically improve the scalability of traditional MSM methods. This includes ragged arrays for minimizing memory requirements, message passing interface-parallelized implementations of compute-intensive operations, and a flexible framework for model construction and analysis.

Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study

One of the fundamental events in protein folding is α-helix formation, which involves sequential development of a series of helical hydrogen bonds between the backbone C═O group of residues i and the -NH group of residues i + 4. While we now know a great deal about α-helix folding dynamics, a key question that remains to be answered is where the productive helical nucleation event occurs. Statistically, a helical nucleus (or the first helical hydrogen-bond) can form anywhere within the peptide sequence in question; however, the one that leads to productive folding may only form at a preferred location. This consideration is based on the fact that the α-helical structure is inherently asymmetric, due to the specific alignment of the helical hydrogen bonds. While this hypothesis is plausible, validating it is challenging because there is not an experimental observable that can be used to directly pinpoint the location of the productive nucleation process. Therefore, in this study we combine several techniques, including peptide cross-linking, laser-induced temperature-jump infrared spectroscopy, and molecular dynamics simulations, to tackle this challenge. Taken together, our experimental and simulation results support an α-helix folding mechanism wherein the productive nucleus is formed at the N-terminus, which propagates toward the C-terminal end of the peptide to yield the folded structure. In addition, our results show that incorporation of a cross-linker can lead to formation of differently folded conformations, underscoring the need for all-atom simulations to quantitatively assess the proposed cross-linking design.

How Effectively Can Adaptive Sampling Methods Capture Spontaneous Ligand Binding?

Molecular dynamics (MD) simulations that capture the spontaneous binding of drugs and other ligands to their target proteins can reveal a great deal of useful information, but most drug-like ligands bind on time scales longer than those accessible to individual MD simulations. Adaptive sampling methods―in which one performs multiple rounds of simulation, with the initial conditions of each round based on the results of previous rounds―offer a promising potential solution to this problem. No comprehensive analysis of the performance gains from adaptive sampling is available for ligand binding, however, particularly for protein–ligand systems typical of those encountered in drug discovery. Moreover, most previous work presupposes knowledge of the ligand’s bound pose. Here we outline existing methods for adaptive sampling of the ligand-binding process and introduce several improvements, with a focus on methods that do not require prior knowledge of the binding site or bound pose. We then evaluate these methods by comparing them to traditional, long MD simulations for realistic protein–ligand systems. We find that adaptive sampling simulations typically fail to reach the bound pose more efficiently than traditional MD. However, adaptive sampling identifies multiple potential binding sites more efficiently than traditional MD and also provides better characterization of binding pathways. We explain these results by showing that protein–ligand binding is an example of an exploration–exploitation dilemma. Existing adaptive sampling methods for ligand binding in the absence of a known bound pose vastly favor the broad exploration of protein–ligand space, sometimes failing to sufficiently exploit intermediate states as they are discovered. We suggest potential avenues for future research to address this shortcoming.

Allosteric mechanism of the circadian protein Vivid resolved through Markov state model and machine learning analysis

The fungal circadian clock photoreceptor Vivid (VVD) contains a photosensitive allosteric light, oxygen, voltage (LOV) domain that undergoes a large N-terminal conformational change. The mechanism by which a blue-light driven covalent bond formation leads to a global conformational change remains unclear, which hinders the further development of VVD as an optogenetic tool. We answered this question through a novel computational platform integrating Markov state models, machine learning methods, and newly developed community analysis algorithms. Applying this new integrative approach, we provided a quantitative evaluation of the contribution from the covalent bond to the protein global conformational change, and proposed an atomistic allosteric mechanism leading to the discovery of the unexpected importance of A'α/Aβ and previously overlooked Eα/Fα loops in the conformational change. This approach could be applicable to other allosteric proteins in general to provide interpretable atomistic representations of their otherwise elusive allosteric mechanisms.

OpenPathSampling: A Python Framework for Path Sampling Simulations. 1. Basics

Transition path sampling techniques allow molecular dynamics simulations of complex systems to focus on rare dynamical events, providing insight into mechanisms and the ability to calculate rates inaccessible by ordinary dynamics simulations. While path sampling algorithms are conceptually as simple as importance sampling Monte Carlo, the technical complexity of their implementation has kept these techniques out of reach of the broad community. Here, we introduce an easy-to-use Python framework called OpenPathSampling (OPS) that facilitates path sampling for (bio)molecular systems with minimal effort and yet is still extensible. Interfaces to OpenMM and an internal dynamics engine for simple models are provided in the initial release, but new molecular simulation packages can easily be added. Multiple ready-to-use transition path sampling methodologies are implemented, including standard transition path sampling (TPS) between reactant and product states and transition interface sampling (TIS) and its replica exchange variant (RETIS), as well as recent multistate and multiset extensions of transition interface sampling (MSTIS, MISTIS). In addition, tools are provided to facilitate the implementation of new path sampling schemes built on basic path sampling components. In this paper, we give an overview of the design of this framework and illustrate the simplicity of applying the available path sampling algorithms to a variety of benchmark problems.

Molecular Mechanisms of Macular Degeneration Associated with the Complement Factor H Y402H Mutation

A single nucleotide polymorphism, tyrosine at position 402 to histidine (Y402H), within the gene encoding complement factor H (FH) predisposes individuals to acquiring age-related macular degeneration (AMD) after aging. This polymorphism occurs in short consensus repeat (SCR) 7 of FH and results in decreased binding affinity of SCR6-8 for heparin. As FH is responsible for regulating the complement system, decreased affinity for heparin results in decreased regulation on surfaces of self. To understand the involvement of the Y402H polymorphism in AMD, we leverage methods from bioinformatics and computational biophysics to quantify structural and dynamical differences between SCR7 isoforms that contribute to decreased pattern recognition in SCR7^H402. Our data from molecular and Brownian dynamics simulations suggest a revised mechanism for decreased heparin binding. In this model, transient contacts not observed in structures for SCR7 are predicted to occur in molecular dynamics simulations between coevolved residues Y402 and I412, stabilizing SCR7^Y402 in a conformation that promotes association with heparin. H402 in the risk isoform is less likely to form a contact with I412 and samples a larger conformational space than Y402. We observe energy minima for sidechains of Y402 and R404 from SCR7^Y402 that are predicted to associate with heparin at a rate constant faster than energy minima for sidechains of H402 and R404 from SCR7^H402. As both carbohydrate density and degree of sulfation decrease with age in Bruch's membrane of the macula, the decreased heparin recognition of SCR7^H402 may contribute to the pathogenesis of AMD.

SAXS-guided Enhanced Unbiased Sampling for Structure Determination of Proteins and Complexes

Molecular simulations can be utilized to predict protein structure ensembles and dynamics, though sufficient sampling of molecular ensembles and identification of key biologically relevant conformations remains challenging. Low-resolution experimental techniques provide valuable structural information on biomolecule at near-native conditions, which are often combined with molecular simulations to determine and refine protein structural ensembles. In this study, we demonstrate how small angle x-ray scattering (SAXS) information can be incorporated in Markov state model-based adaptive sampling strategy to enhance time efficiency of unbiased MD simulations and identify functionally relevant conformations of proteins and complexes. Our results show that using SAXS data combined with additional information, such as thermodynamics and distance restraints, we are able to distinguish otherwise degenerate structures due to the inherent ambiguity of SAXS pattern. We further demonstrate that adaptive sampling guided by SAXS and hybrid information can significantly reduce the computation time required to discover target structures. Overall, our findings demonstrate the potential of this hybrid approach in predicting near-native structures of proteins and complexes. Other low-resolution experimental information can be incorporated in a similar manner to collectively enhance unbiased sampling and improve the accuracy of structure prediction from simulation.

t-Distributed Stochastic Neighbor Embedding Method with the Least Information Loss for Macromolecular Simulations

Dimensionality reduction methods are usually applied on molecular dynamics simulations of macromolecules for analysis and visualization purposes. It is normally desired that suitable dimensionality reduction methods could clearly distinguish functionally important states with different conformations for the systems of interest. However, common dimensionality reduction methods for macromolecules simulations, including predefined order parameters and collective variables (CVs), principal component analysis (PCA), and time-structure based independent component analysis (t-ICA), only have limited success due to significant key structural information loss. Here, we introduced the t-distributed stochastic neighbor embedding (t-SNE) method as a dimensionality reduction method with minimum structural information loss widely used in bioinformatics for analyses of macromolecules, especially biomacromolecules simulations. It is demonstrated that both one-dimensional (1D) and two-dimensional (2D) models of the t-SNE method are superior to distinguish important functional states of a model allosteric protein system for free energy and mechanistic analysis. Projections of the model protein simulations onto 1D and 2D t-SNE surfaces provide both clear visual cues and quantitative information, which is not readily available using other methods, regarding the transition mechanism between two important functional states of this protein.

Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes

Interest in atomically detailed simulations has grown significantly with recent advances in computational hardware and Markov state modeling (MSM) methods, yet outstanding questions remain that hinder their widespread adoption. Namely, how do alternative sampling strategies explore conformational space and how might this influence predictions generated from the data? Here, we seek to answer these questions for four commonly used sampling methods: (1) a single long simulation, (2) many short simulations run in parallel, (3) adaptive sampling, and (4) our recently developed goal-oriented sampling algorithm, FAST. We first develop a theoretical framework for analytically calculating the probability of discovering select states on simple landscapes, where we uncover the drastic effects of varying the number and length of simulations. We then use kinetic Monte Carlo simulations on a variety of physically inspired landscapes to characterize the probability of discovering particular states and transition pathways for each of the four methods. Consistently, we find that FAST simulations discover each target state with the highest probability, while traversing realistic pathways. Furthermore, we uncover the potential pathology that short parallel simulations sometimes predict an incorrect transition pathway by crossing large energy barriers that long simulations would typically circumnavigate. We refer to this pathology as "pathway tunneling". To protect against this phenomenon when using adaptive-sampling and FAST simulations, we introduce the FAST-string method. This method enhances sampling along the highest-flux transition paths to refine an MSMs transition probabilities and discriminate between competing pathways. Additionally, we compare the performance of a variety of MSM estimators in describing accurate thermodynamics and kinetics. For adaptive sampling, we recommend simply normalizing the transition counts out of each state after adding small pseudocounts to avoid creating sources or sinks. Lastly, we evaluate whether our insights from simple landscapes hold for all-atom molecular dynamics simulations of the folding of the λ-repressor protein. Remarkably, we find that FAST-contacts predicts the same folding pathway as a set of long simulations but with orders of magnitude less simulation time.

Protocol for Identifying Accurate Collective Variables in Enhanced Molecular Dynamics Simulations for the Description of Structural Transformations in Flexible Metal-Organic Frameworks

Various kinds of flexibility have been observed in metal-organic frameworks, which may originate from the topology of the material or the presence of flexible ligands. The construction of free energy profiles describing the full dynamical behavior along the phase transition path is challenging since it is not trivial to identify collective variables able to identify all metastable states along the reaction path. In this work, a systematic three-step protocol to uniquely identify the dominant order parameters for structural transformations in flexible metal-organic frameworks and subsequently construct accurate free energy profiles is presented. Methodologically, this protocol is rooted in the time-structure based independent component analysis (tICA), a well-established statistical modeling technique embedded in the Markov state model methodology and often employed to study protein folding, that allows for the identification of the slowest order parameters characterizing the structural transformation. To ensure an unbiased and systematic identification of these order parameters, the tICA decomposition is performed based on information from a prior replica exchange (RE) simulation, as this technique enhances the sampling along all degrees of freedom of the system simultaneously. From this simulation, the tICA procedure extracts the order parameters-often structural parameters-that characterize the slowest transformations in the material. Subsequently, these order parameters are adopted in traditional enhanced sampling methods such as umbrella sampling, thermodynamic integration, and variationally enhanced sampling to construct accurate free energy profiles capturing the flexibility in these nanoporous materials. In this work, the applicability of this tICA-RE protocol is demonstrated by determining the slowest order parameters in both MIL-53(Al) and CAU-13, which exhibit a strongly different type of flexibility. The obtained free energy profiles as a function of this extracted order parameter are furthermore compared to the profiles obtained when adopting less-suited collective variables, indicating the importance of systematically selecting the relevant order parameters to construct accurate free energy profiles for flexible metal-organic frameworks, which is in correspondence with experimental findings. The method succeeds in mapping the full free energy surface in terms of appropriate collective variables for MOFs exhibiting linker flexibility. For CAU-13, we show the decreased stability of the closed pore phase by systematically adding adsorbed xylene molecules in the framework.

Simulations of the regulatory ACT domain of human phenylalanine hydroxylase (PAH) unveil its mechanism of phenylalanine binding

Phenylalanine hydroxylase (PAH) regulates phenylalanine (Phe) levels in mammals to prevent neurotoxicity resulting from high Phe concentrations as observed in genetic disorders leading to hyperphenylalaninemia and phenylketonuria. PAH senses elevated Phe concentrations by transient allosteric Phe binding to a protein-protein interface between ACT domains of different subunits in a PAH tetramer. This interface is present in an activated PAH (A-PAH) tetramer and absent in a resting-state PAH (RS-PAH) tetramer. To investigate this allosteric sensing mechanism, here we used the GROMACS molecular dynamics simulation suite on the Folding@home computing platform to perform extensive molecular simulations and Markov state model (MSM) analysis of Phe binding to ACT domain dimers. These simulations strongly implicated a conformational selection mechanism for Phe association with ACT domain dimers and revealed protein motions that act as a gating mechanism for Phe binding. The MSMs also illuminate a highly mobile hairpin loop, consistent with experimental findings also presented here that the PAH variant L72W does not shift the PAH structural equilibrium toward the activated state. Finally, simulations of ACT domain monomers are presented, in which spontaneous transitions between resting-state and activated conformations are observed, also consistent with a mechanism of conformational selection. These mechanistic details provide detailed insight into the regulation of PAH activation and provide testable hypotheses for the development of new allosteric effectors to correct structural and functional defects in PAH.

Assessment and optimization of collective variables for protein conformational landscape: GB1 β-hairpin as a case study

Collective variables (CVs), when chosen judiciously, can play an important role in recognizing rate-limiting processes and rare events in any biomolecular systems. However, high dimensionality and inherent complexities associated with such biochemical systems render the identification of an optimal CV a challenging task, which in turn precludes the elucidation of an underlying conformational landscape in sufficient details. In this context, a relevant model system is presented by a 16-residue β-hairpin of GB1 protein. Despite being the target of numerous theoretical and computational studies for understanding the protein folding, the set of CVs optimally characterizing the conformational landscape of the β-hairpin of GB1 protein has remained elusive, resulting in a lack of consensus on its folding mechanism. Here we address this by proposing a pair of optimal CVs which can resolve the underlying free energy landscape of the GB1 hairpin quite efficiently. Expressed as a linear combination of a number of traditional CVs, the optimal CV for this system is derived by employing the recently introduced time-structured independent component analysis approach on a large number of independent unbiased simulations. By projecting the replica-exchange simulated trajectories along these pair of optimized CVs, the resulting free energy landscape of this system is able to resolve four distinct well-separated metastable states encompassing the extensive ensembles of folded, unfolded, and molten globule states. Importantly, the optimized CVs were found to be capable of automatically recovering a novel partial helical state of this protein, without needing to explicitly invoke helicity as a constituent CV. Furthermore, a quantitative sensitivity analysis of each constituent in the optimized CV provided key insights on the relative contributions of the constituent CVs in the overall free energy landscapes. Finally, the kinetic pathways connecting these metastable states, constructed using a Markov state model, provide an optimum description of the underlying folding mechanism of the peptide. Taken together, this work offers a quantitatively robust approach toward comprehensive mapping of the underlying folding landscape of a quintessential model system along its optimized CV.

Predicting ligand binding affinity using on- and off-rates for the SAMPL6 SAMPLing challenge

Interest in ligand binding kinetics has been growing rapidly, as it is being discovered in more and more systems that ligand residence time is the crucial factor governing drug efficacy. Many enhanced sampling methods have been developed with the goal of predicting ligand binding rates ([Formula: see text]) and/or ligand unbinding rates ([Formula: see text]) through explicit simulation of ligand binding pathways, and these methods work by very different mechanisms. Although there is not yet a blind challenge for ligand binding kinetics, here we take advantage of experimental measurements and rigorously computed benchmarks to compare estimates of [Formula: see text] calculated as the ratio of two rates: [Formula: see text]. These rates were determined using a new enhanced sampling method based on the weighted ensemble framework that we call "REVO": Reweighting of Ensembles by Variance Optimization. This is a further development of the WExplore enhanced sampling method, in which trajectory cloning and merging steps are guided not by the definition of sampling regions, but by maximizing trajectory variance. Here we obtain estimates of [Formula: see text] and [Formula: see text] that are consistent across multiple simulations, with an average log10-scale standard deviation of 0.28 for on-rates and 0.56 for off-rates, which is well within an order of magnitude and far better than previously observed for previous applications of the WExplore algorithm. Our rank ordering of the three host-guest pairs agrees with the reference calculations, however our predicted [Formula: see text] values were systematically lower than the reference by an average of 4.2 kcal/mol. Using tree network visualizations of the trajectories in the REVO algorithm, and conformation space networks for each system, we analyze the results of our sampling, and hypothesize sources of discrepancy between our [Formula: see text] values and the reference. We also motivate the direct inclusion of [Formula: see text] and [Formula: see text] challenges in future iterations of SAMPL, to further develop the field of ligand binding kinetics prediction and modeling.

Multifidelity Analysis for Predicting Rare Events in Stochastic Computational Models of Complex Biological Systems

Rare events such as genetic mutations or cell-cell interactions are important contributors to dynamics in complex biological systems, eg, in drug-resistant infections. Computational approaches can help analyze rare events that are difficult to study experimentally. However, analyzing the frequency and dynamics of rare events in computational models can also be challenging due to high computational resource demands, especially for high-fidelity stochastic computational models. To facilitate analysis of rare events in complex biological systems, we present a multifidelity analysis approach that uses medium-fidelity analysis (Monte Carlo simulations) and/or low-fidelity analysis (Markov chain models) to analyze high-fidelity stochastic model results. Medium-fidelity analysis can produce large numbers of possible rare event trajectories for a single high-fidelity model simulation. This allows prediction of both rare event dynamics and probability distributions at much lower frequencies than high-fidelity models. Low-fidelity analysis can calculate probability distributions for rare events over time for any frequency by updating the probabilities of the rare event state space after each discrete event of the high-fidelity model. To validate the approach, we apply multifidelity analysis to a high-fidelity model of tuberculosis disease. We validate the method against high-fidelity model results and illustrate the application of multifidelity analysis in predicting rare event trajectories, performing sensitivity analyses and extrapolating predictions to very low frequencies in complex systems. We believe that our approach will complement ongoing efforts to enable accurate prediction of rare event dynamics in high-fidelity computational models.