The transition between active and inactive conformations of Abl kinase studied by rock climbing and Milestoning

Evolutionary sequence and structural basis for the distinct conformational landscapes of Tyr and Ser/Thr kinases

Protein kinases are molecular machines with rich sequence variation that distinguishes the two main evolutionary branches - tyrosine kinases (TKs) from serine/threonine kinases (STKs). Using a sequence co-variation Potts statistical energy model we previously concluded that TK catalytic domains are more likely than STKs to adopt an inactive conformation with the activation loop in an autoinhibitory folded conformation, due to intrinsic sequence effects. Here we investigate the structural basis for this phenomenon by integrating the sequence-based model with structure-based molecular dynamics (MD) to determine the effects of mutations on the free energy difference between active and inactive conformations, using a thermodynamic cycle involving many (n = 108) protein-mutation free energy perturbation (FEP) simulations in the active and inactive conformations. The sequence and structure-based results are consistent and support the hypothesis that the inactive conformation DFG-out Activation Loop Folded, is a functional regulatory state that has been stabilized in TKs relative to STKs over the course of their evolution via the accumulation of residue substitutions in the activation loop and catalytic loop that facilitate distinct substrate binding modes in trans and additional modes of regulation in cis for TKs.

Evolutionary sequence and structural basis for the distinct conformational landscapes of Tyr and Ser/Thr kinases

Protein kinases are molecular machines with rich sequence variation that distinguishes the two main evolutionary branches - tyrosine kinases (TKs) from serine/threonine kinases (STKs). Using a sequence co-variation Potts statistical energy model we previously concluded that TK catalytic domains are more likely than STKs to adopt an inactive conformation with the activation loop in an autoinhibitory "folded" conformation, due to intrinsic sequence effects. Here we investigated the structural basis for this phenomenon by integrating the sequence-based model with structure-based molecular dynamics (MD) to determine the effects of mutations on the free energy difference between active and inactive conformations, using a novel thermodynamic cycle involving many (n=108) protein-mutation free energy perturbation (FEP) simulations in the active and inactive conformations. The sequence and structure-based results are consistent and support the hypothesis that the inactive conformation "DFG-out Activation Loop Folded", is a functional regulatory state that has been stabilized in TKs relative to STKs over the course of their evolution via the accumulation of residue substitutions in the activation loop and catalytic loop that facilitate distinct substrate binding modes in trans and additional modes of regulation in cis for TKs.

Evolutionary sequence and structural basis for the distinct conformational landscapes of Tyr and Ser/Thr kinases

Protein kinases are molecular machines with rich sequence variation that distinguishes the two main evolutionary branches - tyrosine kinases (TKs) from serine/threonine kinases (STKs). Using a sequence co-variation Potts statistical energy model we previously concluded that TK catalytic domains are more likely than STKs to adopt an inactive conformation with the activation loop in an autoinhibitory "folded" conformation, due to intrinsic sequence effects. Here we investigated the structural basis for this phenomenon by integrating the sequence-based model with structure-based molecular dynamics (MD) to determine the effects of mutations on the free energy difference between active and inactive conformations, using a novel thermodynamic cycle involving many (n=108) protein-mutation free energy perturbation (FEP) simulations in the active and inactive conformations. The sequence and structure-based results are consistent and support the hypothesis that the inactive conformation "DFG-out Activation Loop Folded", is a functional regulatory state that has been stabilized in TKs relative to STKs over the course of their evolution via the accumulation of residue substitutions in the activation loop and catalytic loop that facilitate distinct substrate binding modes in trans and additional modes of regulation in cis for TKs.

Exploring Kinase Asp-Phe-Gly (DFG) Loop Conformational Stability with AlphaFold2-RAVE

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular, cancers. The ubiquitousness and structural similarities of kinases make specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved Asp-Phe-Gly (DFG) motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticeably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learned order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations (Meller, A.; Bhakat, S.; Solieva, S.; Bowman, G. R. Accelerating Cryptic Pocket Discovery Using AlphaFold. J. Chem. Theory Comput. 2023, 19, 4355-4363).

Classifying protein kinase conformations with machine learning

Protein kinases are key actors of signaling networks and important drug targets. They cycle between active and inactive conformations, distinguished by a few elements within the catalytic domain. One is the activation loop, whose conserved DFG motif can occupy DFG-in, DFG-out, and some rarer conformations. Annotation and classification of the structural kinome are important, as different conformations can be targeted by different inhibitors and activators. Valuable resources exist; however, large-scale applications will benefit from increased automation and interpretability of structural annotation. Interpretable machine learning models are described for this purpose, based on ensembles of decision trees. To train them, a set of catalytic domain sequences and structures was collected, somewhat larger and more diverse than existing resources. The structures were clustered based on the DFG conformation and manually annotated. They were then used as training input. Two main models were constructed, which distinguished active/inactive and in/out/other DFG conformations. They considered initially 1692 structural variables, spanning the whole catalytic domain, then identified ("learned") a small subset that sufficed for accurate classification. The first model correctly labeled all but 3 of 3289 structures as active or inactive, while the second assigned the correct DFG label to all but 17 of 8826 structures. The most potent classifying variables were all related to well-known structural elements in or near the activation loop and their ranking gives insights into the conformational preferences. The models were used to automatically annotate 3850 kinase structures predicted recently with the Alphafold2 tool, showing that Alphafold2 reproduced the active/inactive but not the DFG-in proportions seen in the Protein Data Bank. We expect the models will be useful for understanding and engineering kinases.

Myristoyl's dual role in allosterically regulating and localizing Abl kinase

c-Abl kinase, a key signaling hub in many biological processes ranging from cell development to proliferation, is tightly regulated by two inhibitory Src homology domains. An N-terminal myristoyl modification can bind to a hydrophobic pocket in the kinase C-lobe, which stabilizes the autoinhibitory assembly. Activation is triggered by myristoyl release. We used molecular dynamics simulations to show how both myristoyl and the Src homology domains are required to impose the full inhibitory effect on the kinase domain and reveal the allosteric transmission pathway at residue-level resolution. Importantly, we find myristoyl insertion into a membrane to thermodynamically compete with binding to c-Abl. Myristoyl thus not only localizes the protein to the cellular membrane, but membrane attachment at the same time enhances activation of c-Abl by stabilizing its preactivated state. Our data put forward a model in which lipidation tightly couples kinase localization and regulation, a scheme that currently appears to be unique for this non-receptor tyrosine kinase.

Exploring kinase DFG loop conformational stability with AlphaFold2-RAVE

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular cancers. The ubiquitousness and structural similarities of kinases makes specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved DFG motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence, and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learnt order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations.

Efficient Interrogation of the Kinetic Barriers Demarcating Catalytic States of a Tyrosine Kinase with Optimal Physical Descriptors and Mixture Models

Computer simulations are increasingly used to access thermo-kinetic information underlying structural transformation of protein kinases. Such information are necessary to probe their roles in disease progression and interactions with drug targets. However, the investigations are frequently challenged by forbiddingly high computational expense, and by the lack of standard protocols for the design of low dimensional physical descriptors that encode system features important for transitions. Here, we consider the demarcating characteristics of the different states of Abelson tyrosine kinase associated with distinct catalytic activity to construct a set of physically meaningful, orthogonal collective variables that preserve the slow modes of the system. Independent sampling of each metastable state is followed by the estimation of global partition function along the appropriate physical descriptors using the modified Expectation Maximized Molecular Dynamics method. The resultant free energy barriers are in excellent agreement with experimentally known rate-limiting dynamics and activation energy computed with conventional enhanced sampling methods. We discuss possible directions for further development and applications.

Classification of GTP-dependent K-Ras4B active and inactive conformational states

Classifying reliably active and inactive molecular conformations of wildtype (WT) and mutated oncogenic proteins is a key, ongoing challenge in molecular cancer studies. Here, we probe the GTP-bound K-Ras4B conformational dynamics using long-time atomistic molecular dynamics (MD) simulations. We extract and analyze the detailed underlying free energy landscape of WT K-Ras4B. We use two key reaction coordinates, labeled d₁ and d₂ (i.e., distances coordinating the P_β atom of the GTP ligand with two key residues, T35 and G60), shown to correlate closely with activities of WT and mutated K-Ras4B. However, our new K-Ras4B conformational kinetics study reveals a more complex network of equilibrium Markovian states. We show that a new reaction coordinate is required to account for the orientation of acidic K-Ras4B sidechains such as D38 with respect to the interface with binding effector RAF1 and rationalize the activation/inactivation propensities and the corresponding molecular binding mechanisms. We use this understanding to unveil how a relatively conservative mutation (i.e., D33E, in the switch I region) can lead to significantly different activation propensities compared with WT K-Ras4B. Our study sheds new light on the ability of residues near the K-Ras4B-RAF1 interface to modulate the network of salt bridges at the binding interface with the RAF1 downstream effector and, thus, to influence the underlying GTP-dependent activation/inactivation mechanism. Altogether, our hybrid MD-docking modeling approach enables the development of new in silico methods for quantitative assessment of activation propensity changes (e.g., due to mutations or local binding environment). It also unveils the underlying molecular mechanisms and facilitates the rational design of new cancer drugs.

Milestoning simulation of ligand dissociation from the glycogen synthase kinase 3β

As drug-binding kinetics has become an important factor to be considered in modern drug discovery, this work evaluated the ability of the Milestoning method in computing the absolute dissociation rate of a ligand from the serine-threonine kinase, glycogen synthase kinase 3β, which is a target for designing drugs to treat diseases such as neurodegenerative disorders and diabetes. We found that the Milestoning method gave good agreement with experiment with modest computational costs. Although the time scale for dissociation lasted tens of seconds, the collective molecular dynamics simulations total less than 1μs. Computing the committor function helped to identify the transition states (TSs), in which the ligand moved substantially away from the binding pocket. The glycine-rich loop with a serine residue attaching to its tips was found to undergo large movement from the bound to the TSs and might play a role in controlling drug-dissociation kinetics.

Perspective: Path Sampling Methods Applied to Enzymatic Catalysis

This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.

Protein Flexibility and Dissociation Pathway Differentiation Can Explain Onset of Resistance Mutations in Kinases

Understanding how mutations render a drug ineffective is a problem of immense relevance. Often the mechanism through which mutations cause drug resistance can be explained purely through thermodynamics. However, the more perplexing situation is when two proteins have the same drug binding affinities but different residence times. In this work, we demonstrate how all-atom molecular dynamics simulations using recent developments grounded in statistical mechanics can provide a detailed mechanistic rationale for such variances. We discover dissociation mechanisms for the anti-cancer drug Imatinib (Gleevec) against wild-type and the N368S mutant of Abl kinase. We show how this point mutation triggers far-reaching changes in the protein's flexibility and leads to a different, much faster, drug dissociation pathway. We believe that this work marks an efficient and scalable approach to obtain mechanistic insight into resistance mutations in biomolecular receptors that are hard to explain using a structural perspective.

Evaluation of residue variability in a conformation-specific context and during evolutionary sequence reconstruction narrows drug resistance selection in Abl1 tyrosine kinase

Diseases with readily available therapies may eventually prevail against the specific treatment by the acquisition of resistance. The constitutively active Abl1 tyrosine kinase known to cause chronic myeloid leukemia is an example, where patients may experience relapse after small inhibitor drug treatment. Mutations in the Abl1 tyrosine kinase domain (Abl1-KD) are a critical source of resistance and their emergence depends on the conformational states that have been observed experimentally: the inactive state, the active state, and the intermediate inactive state that resembles Src kinase. Understanding how resistant positions and amino acid identities are determined by selection pressure during drug treatment is necessary to improve future drug development or treatment decisions. We carry out in silico site-saturation mutagenesis over the Abl1-KD structure in a conformational context to evaluate the in situ and conformational stability energy upon mutation. Out of the 11 studied resistant positions, we determined that 7 of the resistant mutations favored the active conformation of Abl1-KD with respect to the inactive state. When, instead, the sequence optimization was modeled simultaneously at resistant positions, we recovered five known resistant mutations in the active conformation. These results suggested that the Abl1 resistance mechanism targeted substitutions that favored the active conformation. Further sequence variability, explored by ancestral reconstruction in Abl1-KD, showed that neutral genetic drift, with respect to amino acid variability, was specifically diminished in the resistant positions. Since resistant mutations are susceptible to chance with a certain probability of fixation, combining methodologies outlined here may narrow and limit the available sequence space for resistance to emerge, resulting in more robust therapeutic treatments over time.

Mapping the conformational energy landscape of Abl kinase using ClyA nanopore tweezers

Protein kinases play central roles in cellular regulation by catalyzing the phosphorylation of target proteins. Kinases have inherent structural flexibility allowing them to switch between active and inactive states. Quantitative characterization of kinase conformational dynamics is challenging. Here, we use nanopore tweezers to assess the conformational dynamics of Abl kinase domain, which is shown to interconvert between two major conformational states where one conformation comprises three sub-states. Analysis of kinase-substrate and kinase-inhibitor interactions uncovers the functional roles of relevant states and enables the elucidation of the mechanism underlying the catalytic deficiency of an inactive Abl mutant G321V. Furthermore, we obtain the energy landscape of Abl kinase by quantifying the population and transition rates of the conformational states. These results extend the view on the dynamic nature of Abl kinase and suggest nanopore tweezers can be used as an efficient tool for other members of the human kinome.

Quantitative characterization of kinase conformational dynamics remains challenging. Here, the authors show that protein nanopore tweezers allow analyzing the conformational energy landscape and ligand binding of the Abl kinase domain.

Practical Protocols for Efficient Sampling of Kinase-Inhibitor Binding Pathways Using Two-Dimensional Replica-Exchange Molecular Dynamics

Molecular dynamics (MD) simulations are increasingly used to study various biological processes such as protein folding, conformational changes, and ligand binding. These processes generally involve slow dynamics that occur on the millisecond or longer timescale, which are difficult to simulate by conventional atomistic MD. Recently, we applied a two-dimensional (2D) replica-exchange MD (REMD) method, which combines the generalized replica exchange with solute tempering (gREST) with the replica-exchange umbrella sampling (REUS) in kinase-inhibitor binding simulations, and successfully observed multiple ligand binding/unbinding events. To efficiently apply the gREST/REUS method to other kinase-inhibitor systems, we establish modified, practical protocols with non-trivial simulation parameter tuning. The current gREST/REUS simulation protocols are tested for three kinase-inhibitor systems: c-Src kinase with PP1, c-Src kinase with Dasatinib, and c-Abl kinase with Imatinib. We optimized the definition of kinase-ligand distance as a collective variable (CV), the solute temperatures in gREST, and replica distributions and umbrella forces in the REUS simulations. Also, the initial structures of each replica in the 2D replica space were prepared carefully by pulling each ligand from and toward the protein binding sites for keeping stable kinase conformations. These optimizations were carried out individually in multiple short MD simulations. The current gREST/REUS simulation protocol ensures good random walks in 2D replica spaces, which are required for enhanced sampling of inhibitor dynamics around a target kinase.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Activation of Abl1 Kinase Explored Using Well-Tempered Metadynamics Simulations on an Essential Dynamics Sampled Path

Well-tempered metadynamics (wT-metaD) simulations using path collective variables (CVs) have been successfully applied in recent years to explore conformational transitions in protein kinases and other biomolecular systems. While this methodology has the advantage of describing the transitions with a limited number of predefined path CVs, it requires as an input a reference path connecting the initial and target states of the system. It is desirable to automate the path generation using approaches that do not rely on the choice of geometric CVs to describe the transition of interest. To this end, we developed an approach that couples essential dynamics sampling with wT-metaD simulations. We used this newly developed procedure to explore the activation mechanism of Abl1 kinase and compute the associated free energy barriers. Through these simulations, we identified a three-step mechanism for the activation that involved two metastable intermediates that possessed a partially open activation loop and differed primarily in the “in” or “out” conformation of the aspartate residue of the DFG motif. One of these states is similar to a conformation that was detected in previous spectroscopic studies of Abl1 kinase, albeit its mechanistic role in the activation was hitherto not well understood. The present study establishes its intermediary role in the activation and predicts a rate-determining free energy barrier of 13.8 kcal/mol that is in good agreement with previous experimental and computational estimates. Overall, our study demonstrates the usability of essential dynamics sampling as a path CV in wT-metaD to conveniently study conformational transitions and accurately calculate the associated barriers.

TYROSINE KINASES: COMPLEX MOLECULAR SYSTEMS CHALLENGING COMPUTATIONAL METHODOLOGIES

Classical molecular dynamics (MD) simulations based on atomic models play an increasingly important role in a wide range of applications in physics, biology, and chemistry. Nonetheless, generating genuine knowledge about biological systems using MD simulations remains challenging. Protein tyrosine kinases are important cellular signaling enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Due to the large conformational changes and long timescales involved in their function, these kinases present particularly challenging problems to modern computational and theoretical frameworks aimed at elucidating the dynamics of complex biomolecular systems. Markov state models have achieved limited success in tackling the broader conformational ensemble and biased methods are often employed to examine specific long timescale events. Recent advances in machine learning continue to push the limitations of current methodologies and provide notable improvements when integrated with the existing frameworks. A broad perspective is drawn from a critical review of recent studies.

Computer Simulations of the Dissociation Mechanism of Gleevec from Abl Kinase with Milestoning

Gleevec (a.k.a., imatinib) is an important anticancer (e.g., chronic myeloid leukemia) chemotherapeutic drug due to its inhibitory interaction with the Abl kinase. Here, we use atomically detailed simulations within the Milestoning framework to study the molecular dissociation mechanism of Gleevec from Abl kinase. We compute the dissociation free energy profile, the mean first passage time for unbinding, and explore the transition state ensemble of conformations. The milestones form a multidimensional network with average connectivity of about 2.93, which is significantly higher than the connectivity for a one-dimensional reaction coordinate. The free energy barrier for Gleevec dissociation is estimated to be ∼10 kcal/mol, and the exit time is ∼55 ms. We examined the transition state conformations using both, the committor and transition function. We show that near the transition state the highly conserved salt bridge K217 and E286 is transiently broken. Together with the calculated free energy profile, these calculations can advance the understanding of the molecular interaction mechanisms between Gleevec and Abl kinase and play a role in future drug design and optimization studies.

Protein storytelling through physics

Every protein has a story-how it folds, what it binds, its biological actions, and how it misbehaves in aging or disease. Stories are often inferred from a protein's shape (i.e., its structure). But increasingly, stories are told using computational molecular physics (CMP). CMP is rooted in the principled physics of driving forces and reveals granular detail of conformational populations in space and time. Recent advances are accessing longer time scales, larger actions, and blind testing, enabling more of biology's stories to be told in the language of atomistic physics.

Exploring the Reaction Mechanism of HIV Reverse Transcriptase with a Nucleotide Substrate

Enzymatic reactions consist of several steps: (i) a weak binding event of the substrate to the enzyme, (ii) an induced fit or a protein conformational transition upon ligand binding, (iii) the chemical reaction, and (iv) the release of the product. Here we focus on step iii of the reaction of a DNA polymerase, HIV RT, with a nucleotide. We determine the rate and the free energy profile for the addition of a nucleotide to a DNA strand using a combination of a QM/MM model, the string method, and exact Milestoning. The barrier height and the time scale of the reaction are consistent with experiment. We show that the observables (free energies and mean first passage time) converge rapidly, as a function of the Milestoning iteration number. We also consider the substitution of an oxygen of the incoming nucleotide by a nonbridging sulfur atom and its impact on the enzymatic reaction. This substitution has been suggested in the past as a tool to examine the influence of the chemical step on the overall rate. Our joint computational and experimental study suggests that the impact of the substitution is small. Computationally, the differences between the two are within the estimated error bars. Experiments suggest a small difference. Finally, we examine step i, the weak binding of the nucleotide to the protein surface. We suggest that this step has only a small contribution to the selectivity of the enzyme. Comments are made on the impact of these steps on the overall mechanism.

Conformational flexibility correlates with glucose tolerance for point mutations in β-glucosidases - a computational study

β-glucosidases (EC 3.2.1.21) have been described as essential to second-generation biofuel production. They act in the last step of the lignocellulosic saccharification, cleaving the β - 1,4 glycosidic bonds in cellobiose to produce two molecules of glucose. However, β-glucosidases have been described as strongly inhibited by glucose, causing an increment of cellobiose concentration. Also, cellobiose is an inhibitor of other enzymes used in this process, such as exoglucanases and endoglucanases. Hence, the engineering of thermostable and glucose-tolerant β-glucosidases has been targeted by many studies. In this study, we performed high sampling accelerated molecular dynamics for a wild glucose-tolerant GH1 β-glucosidase (Bgl1A), a wild non-tolerant (Bgl1B), and a set of glucose-tolerant Bgl1B's mutants: V302F, N301Q/V302F, F172I, V227M, G246S, T299S, and H228T. Our results suggest that point mutations promissory to induce glucose tolerance trend to enhance the mobility of the flexible loops around the active site. Mutations affected B and C loops regions, and an αβ-hairpin motif between them. Conformational clusters and free energy landscape profiles suggest that the mobility acquired by mutants allows a higher closure of the substrate channel. This closure is compatible with a higher impedance for glucose entrance and stimulus of its withdrawal. Based on mutants' structural analyses, we inferred that both the direct stereochemical effect on the glucose path and the changes in the mobility affect glucose tolerance. We hope these results be useful for the rational design of glucose-tolerant and industrially promising enzymes.Communicated by Ramaswamy H. Sarma.

Long-time methods for molecular dynamics simulations: Markov State Models and Milestoning

Molecular dynamics (MD) studies of biomolecules require the ability to simulate complex biochemical systems with an increasingly larger number of particles and for longer time scales, a problem that cannot be overcome by computational hardware advances alone. A main problem springs from the intrinsically high-dimensional and complex nature of the underlying free energy landscape of most systems, and from the necessity to sample accurately such landscapes for identifying kinetic and thermodynamic states in the configurations space, and for accurate calculations of both free energy differences and of the corresponding transition rates between states. Here, we review and present applications of two increasingly popular methods that allow long-time MD simulations of biomolecular systems that can open a broad spectrum of new studies. A first approach, Markov State Models (MSMs), relies on identifying a set of configuration states in which the system resides sufficiently long to relax and loose the memory of previous transitions, and on using simulations for mapping the underlying complex energy landscape and for extracting accurate thermodynamic and kinetic information. The Markovian independence of the underlying transition probabilities creates the opportunity to increase the sampling efficiency by using sets of appropriately initialized short simulations rather than typically long MD trajectories, which also enhances sampling. This allows MSM-based studies to unveil bio-molecular mechanisms and to estimate free energy barriers with high accuracy, in a manner that is both systematic and relatively automatic, which accounts for their increasing popularity. The second approach presented, Milestoning, targets accurate studies of the ensemble of pathways connecting specific end-states (e.g., reactants and products) in a similarly systematic, accurate and highly automatic manner. Applications presented range from studies of conformational dynamics and binding of amyloid-forming peptides, cell-penetrating peptides and the DFG-flip dynamics in Abl kinase. As highlighted by the increasing number of studies using both methods, we anticipate that they will open new avenues for the investigation of systematic sampling of reactions pathways and mechanisms occurring on longer time scales than currently accessible by purely computational hardware developments.