A Comparison of Three Perturbation Molecular Dynamics Methods for Modeling Conformational Transitions

Exploring Free Energies of Specific Protein Conformations Using the Martini Force Field

Coarse-grained (CG) level molecular dynamics simulations are routinely used to study various biomolecular processes. The Martini force field is currently the most widely adopted parameter set for such simulations. The functional form of this and several other CG force fields enforces secondary protein structure support by employing a variety of harmonic potentials or restraints that favor the protein's native conformation. We propose a straightforward method to calculate the energetic consequences of transitions between predefined conformational states in systems in which multiple factors can affect protein conformational equilibria. This method is designed for use within the Martini force field and involves imposing conformational transitions by linking a Martini-inherent elastic network to the coupling parameter λ. We demonstrate the applicability of our method using the example of five biomolecular systems that undergo experimentally characterized conformational transitions between well-defined structures (Staphylococcal nuclease, C-terminal segment of surfactant protein B, LAH4 peptide, and β2-adrenergic receptor) as well as between folded and unfolded states (GCN4 leucine zipper protein). The results show that the relative free energy changes associated with protein conformational transitions, which are affected by various factors, such as pH, mutations, solvent, and lipid membrane composition, are correctly reproduced. The proposed method may be a valuable tool for understanding how different conditions and modifications affect conformational equilibria in proteins.

Development of Kinase-Centric Drugs: A Computational Perspective

Kinases are prominent drug targets in the pharmaceutical and research community due to their involvement in signal transduction, physiological responses, and upon dysregulation, in diseases such as cancer, neurological and autoimmune disorders. Several FDA-approved small-molecule drugs have been developed to combat human diseases since Gleevec was approved for the treatment of chronic myelogenous leukemia. Kinases were considered "undruggable" in the beginning. Several FDA-approved small-molecule drugs have become available in recent years. Most of these drugs target ATP-binding sites, but a few target allosteric sites. Among kinases that belong to the same family, the catalytic domain shows high structural and sequence conservation. Inhibitors of ATP-binding sites can cause off-target binding. Because members of the same family have similar sequences and structural patterns, often complex relationships between kinases and inhibitors are observed. To design and develop drugs with desired selectivity, it is essential to understand the target selectivity for kinase inhibitors. To create new inhibitors with the desired selectivity, several experimental methods have been designed to profile the kinase selectivity of small molecules. Experimental approaches are often expensive, laborious, time-consuming, and limited by the available kinases. Researchers have used computational methodologies to address these limitations in the design and development of effective therapeutics. Many computational methods have been developed over the last few decades, either to complement experimental findings or to forecast kinase inhibitor activity and selectivity. The purpose of this review is to provide insight into recent advances in theoretical/computational approaches for the design of new kinase inhibitors with the desired selectivity and optimization of existing inhibitors.

Adaptive Stochastic Optimization to Improve Protein Conformation Sampling

We have long known that characterizing protein structures structure is key to understanding protein function. Computational approaches have largely addressed a narrow formulation of the problem, seeking to compute one native structure from an amino-acid sequence. Now AlphaFold2 is shown to be able to reveal a high-quality native structure for many proteins. However, researchers over the years have argued for broadening our view to account for the multiplicity of native structures. We now know that many protein molecules switch between different structures to regulate interactions with molecular partners in the cell. Elucidating such structures de novo is exceptionally difficult, as it requires exploration of possibly a very large structure space in search of competing, near-optimal structures. Here we report on a novel stochastic optimization method capable of revealing very different structures for a given protein from knowledge of its amino-acid sequence. The method leverages evolutionary search techniques and adapts its exploration of the search space to balance between exploration and exploitation in the presence of a computational budget. In addition to demonstrating the utility of this method for identifying multiple native structures, we additionally provide a benchmark dataset for researchers to continue work on this problem.

Tackling Hysteresis in Conformational Sampling: How to Be Forgetful with MEMENTO

The structure of proteins has long been recognized to hold the key to understanding and engineering their function, and rapid advances in structural biology and protein structure prediction are now supplying researchers with an ever-increasing wealth of structural information. Most of the time, however, structures can only be determined in free energy minima, one at a time. While conformational flexibility may thus be inferred from static end-state structures, their interconversion mechanisms─a central ambition of structural biology─are often beyond the scope of direct experimentation. Given the dynamical nature of the processes in question, many studies have attempted to explore conformational transitions using molecular dynamics (MD). However, ensuring proper convergence and reversibility in the predicted transitions is extremely challenging. In particular, a commonly used technique to map out a path from a starting to a target conformation called steered MD (SMD) can suffer from starting-state dependence (hysteresis) when combined with techniques such as umbrella sampling (US) to compute the free energy profile of a transition. Here, we study this problem in detail on conformational changes of increasing complexity. We also present a new, history-independent approach that we term "MEMENTO" (Morphing End states by Modelling Ensembles with iNdependent TOpologies) to generate paths that alleviate hysteresis in the construction of conformational free energy profiles. MEMENTO utilizes template-based structure modelling to restore physically reasonable protein conformations based on coordinate interpolation (morphing) as an ensemble of plausible intermediates, from which a smooth path is picked. We compare SMD and MEMENTO on well-characterized test cases (the toy peptide deca-alanine and the enzyme adenylate kinase) before discussing its use in more complicated systems (the kinase P38α and the bacterial leucine transporter LeuT). Our work shows that for all but the simplest systems SMD paths should not in general be used to seed umbrella sampling or related techniques, unless the paths are validated by consistent results from biased runs in opposite directions. MEMENTO, on the other hand, performs well as a flexible tool to generate intermediate structures for umbrella sampling. We also demonstrate that extended end-state sampling combined with MEMENTO can aid the discovery of collective variables on a case-by-case basis.

Out-of-Equilibrium Biophysical Chemistry: The Case for Multidimensional, Integrated Single-Molecule Approaches

Out-of-equilibrium processes are ubiquitous across living organisms and all structural hierarchies of life. At the molecular scale, out-of-equilibrium processes (for example, enzyme catalysis, gene regulation, and motor protein functions) cause biological macromolecules to sample an ensemble of conformations over a wide range of time scales. Quantifying and conceptualizing the structure–dynamics to function relationship is challenging because continuously evolving multidimensional energy landscapes are necessary to describe nonequilibrium biological processes in biological macromolecules. In this perspective, we explore the challenges associated with state-of-the-art experimental techniques to understanding biological macromolecular function. We argue that it is time to revisit how we probe and model functional out-of-equilibrium biomolecular dynamics. We suggest that developing integrated single-molecule multiparametric force–fluorescence instruments and using advanced molecular dynamics simulations to study out-of-equilibrium biomolecules will provide a path towards understanding the principles of and mechanisms behind the structure–dynamics to function paradigm in biological macromolecules.

Large-Scale Conformational Changes and Protein Function: Breaking the in silico Barrier

Large-scale conformational changes are essential to link protein structures with their function at the cell and organism scale, but have been elusive both experimentally and computationally. Over the past few years developments in cryo-electron microscopy and crystallography techniques have started to reveal multiple snapshots of increasingly large and flexible systems, deemed impossible only short time ago. As structural information accumulates, theoretical methods become central to understand how different conformers interconvert to mediate biological function. Here we briefly survey current in silico methods to tackle large conformational changes, reviewing recent examples of cross-validation of experiments and computational predictions, which show how the integration of different scale simulations with biological information is already starting to break the barriers between the in silico, in vitro, and in vivo worlds, shedding new light onto complex biological problems inaccessible so far.

Water-mediated interactions enable smooth substrate transport in a bacterial efflux pump

BACKGROUND

Efflux pumps of the Resistance-Nodulation-cell Division superfamily confer multi-drug resistance to Gram-negative bacteria. The most-studied polyspecific transporter belonging to this class is the inner-membrane trimeric antiporter AcrB of Escherichia coli. In previous studies, a functional rotation mechanism was proposed for its functioning, according to which the three monomers undergo concerted conformational changes facilitating the extrusion of substrates. However, the molecular determinants and the energetics of this mechanism still remain unknown, so its feasibility must be proven mechanistically.

METHODS

A computational protocol able to mimic the functional rotation mechanism in AcrB was developed. By using multi-bias molecular dynamics simulations we characterized the translocation of the substrate doxorubicin driven by conformational changes of the protein. In addition, we estimated for the first time the free energy profile associated to this process.

RESULTS

We provided a molecular view of the process in agreement with experimental data. Moreover, we showed that the conformational changes occurring in AcrB enable the formation of a layer of structured waters on the internal surface of the transport channel. This water layer, in turn, allows for a fairly constant hydration of the substrate, facilitating its diffusion over a smooth free energy profile.

CONCLUSIONS

Our findings reveal a new molecular mechanism of polyspecific transport whereby water contributes by screening potentially strong substrate-protein interactions.

GENERAL SIGNIFICANCE

We provided a mechanistic understanding of a fundamental process related to multi-drug transport. Our results can help rationalizing the behavior of other polyspecific transporters and designing compounds avoiding extrusion or inhibitors of efflux pumps.

GPCRs: What Can We Learn from Molecular Dynamics Simulations?

Advances in the structural biology of G-protein Coupled Receptors have resulted in a significant step forward in our understanding of how this important class of drug targets function at the molecular level. However, it has also become apparent that they are very dynamic molecules, and moreover, that the underlying dynamics is crucial in shaping the response to different ligands. Molecular dynamics simulations can provide unique insight into the dynamic properties of GPCRs in a way that is complementary to many experimental approaches. In this chapter, we describe progress in three distinct areas that are particularly difficult to study with other techniques: atomic level investigation of the conformational changes that occur when moving between the various states that GPCRs can exist in, the pathways that ligands adopt during binding/unbinding events and finally, the influence of lipids on the conformational dynamics of GPCRs.

Mechanistic Insights into the Reaction of Chlorination of Tryptophan Catalyzed by Tryptophan 7-Halogenase

Tryptophan 7-halogenase catalyzes chlorination of free tryptophan to 7-chlorotryptophan, which is the first step in the antibiotic pyrrolnitrin biosynthesis. Many biologically and pharmaceutically active natural products contain chlorine and thus, an understanding of the mechanism of its introduction into organic molecules is important. Whilst enzyme-catalyzed chlorination is accomplished with ease, it remains a difficult task for the chemists. Therefore, utilizing enzymes in the synthesis of chlorinated organic compounds is important, and providing atomistic mechanistic insights about the reaction mechanism of tryptophan 7-halogenase is vital and timely. In this work, we examined a mechanism for the reaction of tryptophan chlorination, performed by tryptophan 7-halogenase, by calculating potential energy and free energy surfaces using two different Combined Quantum Mechanical/Molecular Mechanical (QM/MM) methods both employing Density Functional Theory (DFT) for the QM region. Both computational strategies agree on the nature of the rate-limiting step and provided close results for the reaction barriers of the two reaction steps. The calculations for both the potential energy and the free energy profiles showed very similar geometric features and hydrogen bonding interactions for the characterized stationary points.

Molecular dynamics simulation strategies for designing carbon-nanotube-based targeted drug delivery

The carbon nanotube (CNT)-based target-specific delivery of drugs, or other molecular cargo, has emerged as one of the most promising biomedical applications of nanotechnology. To achieve efficient CNT-based drug delivery, the interactions between the drug, CNT and biomolecular target need to be properly optimized. Recent advances in the computer-aided molecular design tools, in particular molecular dynamics (MD) simulation studies, offer an appropriate low-cost approach for such optimization. This review highlights the various potential MD approaches for the simulation of CNT interactions with cell membranes while emphasizing various methods of cellular internalization and toxicities of CNTs to build new strategies for designing rational CNT-based targeted drug delivery to circumvent the limitations associated with the various clinically available nonspecific therapeutic agents.

Dynamic, structural and thermodynamic basis of insulin-like growth factor 1 kinase allostery mediated by activation loop phosphorylation

Despite the importance of kinases' catalytic activity regulation in cell signaling, detailed mechanisms underlying their activity regulation are poorly understood. Herein, using insulin-like growth factor 1 receptor kinase (IGF-1RK) as a model, the mechanisms of kinase regulation by its activation loop (A-loop) phosphorylation were investigated through molecular dynamics (MD) and alchemical free energy simulations. Analyses of the simulation results and free energy landscapes determined for the entire catalytic cycle of the kinase revealed that A-loop phosphorylation affects each step in the IGF-1RK catalytic cycle, including conformational change, substrate binding/product release and catalytic phosphoryl transfer. Specifically, the conformational equilibrium of the kinase is shifted by 13.2 kcal mol-1 to favor the active conformation after A-loop phosphorylation, which increases substrate binding affinity of the activated kinase. This free energy shift is achieved primarily via destabilization of the inactive conformation. The free energy of the catalytic reaction is also changed by 3.3 kcal mol-1 after the phosphorylation and in the end, facilitates product release. Analyses of MD simulations showed that A-loop phosphorylation produces these energetic effects by perturbing the side chain interactions around each A-loop tyrosine. These interaction changes are propagated to the remainder of the kinase to modify the orientations and dynamics of the αC-helix and A-loop, and together yield the observed free energy changes. Since many protein kinases share similar interactions identified in this work, the mechanisms of kinase allostery and catalysis unraveled here can be applicable to them.

Minimum action transition paths connecting minima on an energy surface

Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.

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

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

Adaptive Steered Molecular Dynamics of the Long-Distance Unfolding of Neuropeptide Y

Neuropeptide Y (NPY) has been found to adopt two stable conformations in vivo: (1) a monomeric form called the PP-fold in which a polyproline tail is folded onto an α-helix via a β-turn and (2) a dimeric form of the unfolded proteins in which the α-helices interact with each other via side chains. The transition pathway and rates between the two conformations remain unknown and are important to the nature of the binding of the protein. Toward addressing this question, the present work suggests that the unfolding of the PP-fold is too slow to play a role in NPY monomeric binding unless the receptor catalyzes it to do so. Specifically, the dynamics and structural changes of the unfolding of a monomeric NPY protein have been investigated in this work. Temperature accelerated molecular dynamics (MD) simulations at 500 K under constant (N,V,E) conditions suggests a hinge-like unraveling of the tail rather than a random unfolding. The free energetics of the proposed unfolding pathway have been described using an adaptive steered MD (SMD) approach at various temperatures. This approach generalizes the use of Jarzynski's equality through a series of stages that allows for better convergence along nonlinear and long-distance pathways. Results acquired using this approach provide a potential of mean force (PMF) with narrower error bars and are consistent with some of the earlier reports on the qualitative behavior of NPY binding.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Many proteins are nanomachines that perform mechanical or chemical work by changing their three-dimensional shape and cycle between multiple conformational states. Computer simulations of such conformational transitions provide mechanistic insights into protein function but such simulations have been challenging. In particular, it is not clear how to quantitatively compare current simulation methods or to assess their accuracy. To that end, we present a general and flexible computational framework for quantifying transition paths—by measuring mutual geometric similarity—that, compared with existing approaches, requires minimal a-priori assumptions and can take advantage of full atomic detail alongside heuristic information derived from intuition. Using our Path Similarity Analysis (PSA) framework in parallel with several existing quantitative approaches, we examine transitions generated for a toy model of a transition and two biological systems, the enzyme adenylate kinase and diphtheria toxin. Our results show that PSA enables the quantitative comparison of different path sampling methods and aids the identification of potentially important atomistic motions by exploiting geometric information in transition paths. The method has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing macromolecular conformational transitions.

Computational study of correlated domain motions in the AcrB efflux transporter

As active part of the major efflux system in E. coli bacteria, AcrB is responsible for the uptake and pumping of toxic substrates from the periplasm toward the extracellular space. In combination with the channel protein TolC and membrane fusion protein AcrA, this efflux pump is able to help the bacterium to survive different kinds of noxious compounds. With the present study we intend to enhance the understanding of the interactions between the domains and monomers, for example, the transduction of mechanical energy from the transmembrane domain into the porter domain, correlated motions of different subdomains within monomers, and cooperative effects between monomers. To this end, targeted molecular dynamics simulations have been employed either steering the whole protein complex or specific parts thereof. By forcing only parts of the complex towards specific conformational states, the risk for transient artificial conformations during the simulations is reduced. Distinct cooperative effects between the monomers in AcrB have been observed. Possible allosteric couplings have been identified providing microscopic insights that might be exploited to design more efficient inhibitors of efflux systems.

Computing ensembles of transitions with molecular dynamics simulations

A molecular understanding of conformational change is important for connecting structure and function. Without the ability to sample on the meaningful large-scale conformational changes, the ability to infer biological function and to understand the effect of mutations and changes in environment is not possible. Our Dynamic Importance Sampling method (DIMS), part of the CHARMM simulation package, is a method that enables sampling over ensembles of transition intermediates. This chapter outlines the context for the method and the usage within the program.

Structure-affinity properties of a high-affinity ligand of FKBP12 studied by molecular simulations of a binding intermediate

With a view to explaining the structure-affinity properties of the ligands of the protein FKBP12, we characterized a binding intermediate state between this protein and a high-affinity ligand. Indeed, the nature and extent of the intermolecular contacts developed in such a species may play a role on its stability and, hence, on the overall association rate. To find the binding intermediate, a molecular simulation protocol was used to unbind the ligand by gradually decreasing the biasing forces introduced. The intermediate was subsequently refined with 17 independent stochastic boundary molecular dynamics simulations that provide a consistent picture of the intermediate state. In this state, the core region of the ligand remains stable, notably because of the two anchoring oxygen atoms that correspond to recurrent motifs found in all FKBP12 ligand core structures. Besides, the non-core regions participate in numerous transient intermolecular and intramolecular contacts. The dynamic aspect of most of the contacts seems important both for the ligand to retain at least a part of its configurational entropy and for avoiding a trapped state along the binding pathway. Since the transient and anchoring contacts contribute to increasing the stability of the intermediate, as a corollary, the dissociation rate constant of this intermediate should be decreased, resulting in an increase of the affinity constant . The present results support our previous conclusions and provide a coherent rationale for explaining the prevalence in high-affinity ligands of (i) the two oxygen atoms found in carbonyl or sulfonyl groups of dissimilar core structures and of (ii) symmetric or pseudo-symmetric mobile groups of atoms found as non-core moieties. Another interesting aspect of the intermediate is the distortion of the flexible 80 s loop of the protein, mainly in its tip region, that promotes the accessibility to the bound state.

Conformational Transition Pathways of Epidermal Growth Factor Receptor Kinase Domain from Multiple Molecular Dynamics Simulations and Bayesian Clustering

The epidermal growth factor receptor (EGFR) is aberrantly activated in various cancer cells and an important target for cancer treatment. Deep understanding of EGFR conformational changes between the active and inactive states is of pharmaceutical interest. Here we present a strategy combining multiply targeted molecular dynamics simulations, unbiased molecular dynamics simulations, and Bayesian clustering to investigate transition pathways during the activation/inactivation process of EGFR kinase domain. Two distinct pathways between the active and inactive forms are designed, explored, and compared. Based on Bayesian clustering and rough two-dimensional free energy surfaces, the energy-favorable pathway is recognized, though DFG-flip happens in both pathways. In addition, another pathway with different intermediate states appears in our simulations. Comparison of distinct pathways also indicates that disruption of the Lys745-Glu762 interaction is critically important in DFG-flip while movement of the A-loop significantly facilitates the conformational change. Our simulations yield new insights into EGFR conformational transitions. Moreover, our results verify that this approach is valid and efficient in sampling of protein conformational changes and comparison of distinct pathways.

Assessing the Accuracy of Two Enhanced Sampling Methods Using EGFR Kinase Transition Pathways: The Influence of Collective Variable Choice

Structurally elucidating transition pathways between protein conformations gives deep mechanistic insight into protein behavior but is typically difficult. Unbiased molecular dynamics (MD) simulations provide one solution, but their computational expense is often prohibitive, motivating the development of enhanced sampling methods that accelerate conformational changes in a given direction, embodied in a collective variable. The accuracy of such methods is unclear for complex protein transitions, because obtaining unbiased MD data for comparison is difficult. Here, we use long-time scale, unbiased MD simulations of epidermal growth factor receptor kinase deactivation as a complex biological test case for two widely used methods-steered molecular dynamics (SMD) and the string method. We found that common collective variable choices, based on the root-mean-square deviation (RMSD) of the entire protein, prevented the methods from producing accurate paths, even in SMD simulations on the time scale of the unbiased transition. Using collective variables based on the RMSD of the region of the protein known to be important for the conformational change, however, enabled both methods to provide a more accurate description of the pathway in a fraction of the simulation time required to observe the unbiased transition.

Modeling conformational transitions in kinases by molecular dynamics simulations: achievements, difficulties, and open challenges

Protein kinases work because their flexibility allows to continuously switch from inactive to active form. Despite the large number of structures experimentally determined in such states, the mechanism of their conformational transitions as well as the transition pathways are not easily to capture. In this regard, computational methods can help to shed light on such an issue. However, due to the intrinsic sampling limitations, much efforts have been done to model in a realistic way the conformational changes occurring in protein kinases. In this review we will address the principal biological achievements and structural aspects in studying kinases conformational transitions and will focus on the main challenges related to computational approaches such as molecular modeling and MD simulations.

Investigations of α-helix↔β-sheet transition pathways in a miniprotein using the finite-temperature string method

A parallel implementation of the finite-temperature string method is described, which takes into account the invariance of coordinates with respect to rigid-body motions. The method is applied to the complex α-helix↔β-sheet transition in a β-hairpin miniprotein in implicit solvent, which exhibits much of the complexity of conformational changes in proteins. Two transition paths are considered, one derived from a linear interpolant between the endpoint structures and the other derived from a targeted dynamics simulation. Two methods for computing the conformational free energy (FE) along the string are compared, a restrained method, and a tessellation method introduced by E. Vanden-Eijnden and M. Venturoli [J. Chem. Phys. 130, 194103 (2009)]. It is found that obtaining meaningful free energy profiles using the present atom-based coordinates requires restricting sampling to a vicinity of the converged path, where the hyperplanar approximation to the isocommittor surface is sufficiently accurate. This sampling restriction can be easily achieved using restraints or constraints. The endpoint FE differences computed from the FE profiles are validated by comparison with previous calculations using a path-independent confinement method. The FE profiles are decomposed into the enthalpic and entropic contributions, and it is shown that the entropy difference contribution can be as large as 10 kcal/mol for intermediate regions along the path, compared to 15-20 kcal/mol for the enthalpy contribution. This result demonstrates that enthalpic barriers for transitions are offset by entropic contributions arising from the existence of different paths across a barrier. The possibility of using systematically coarse-grained representations of amino acids, in the spirit of multiple interaction site residue models, is proposed as a means to avoid ad hoc sampling restrictions to narrow transition tubes.

Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics-inspired method

Background

Many proteins tune their biological function by transitioning between different functional states, effectively acting as dynamic molecular machines. Detailed structural characterization of transition trajectories is central to understanding the relationship between protein dynamics and function. Computational approaches that build on the Molecular Dynamics framework are in principle able to model transition trajectories at great detail but also at considerable computational cost. Methods that delay consideration of dynamics and focus instead on elucidating energetically-credible conformational paths connecting two functionally-relevant structures provide a complementary approach. Effective sampling-based path planning methods originating in robotics have been recently proposed to produce conformational paths. These methods largely model short peptides or address large proteins by simplifying conformational space.

Methods

We propose a robotics-inspired method that connects two given structures of a protein by sampling conformational paths. The method focuses on small- to medium-size proteins, efficiently modeling structural deformations through the use of the molecular fragment replacement technique. In particular, the method grows a tree in conformational space rooted at the start structure, steering the tree to a goal region defined around the goal structure. We investigate various bias schemes over a progress coordinate for balance between coverage of conformational space and progress towards the goal. A geometric projection layer promotes path diversity. A reactive temperature scheme allows sampling of rare paths that cross energy barriers.

Results and conclusions

Experiments are conducted on small- to medium-size proteins of length up to 214 amino acids and with multiple known functionally-relevant states, some of which are more than 13Å apart of each-other. Analysis reveals that the method effectively obtains conformational paths connecting structural states that are significantly different. A detailed analysis on the depth and breadth of the tree suggests that a soft global bias over the progress coordinate enhances sampling and results in higher path diversity. The explicit geometric projection layer that biases the exploration away from over-sampled regions further increases coverage, often improving proximity to the goal by forcing the exploration to find new paths. The reactive temperature scheme is shown effective in increasing path diversity, particularly in difficult structural transitions with known high-energy barriers.

Discover binding pathways using the sliding binding-box docking approach: application to binding pathways of oseltamivir to avian influenza H5N1 neuraminidase

Drug binding and unbinding are transient processes which are hardly observed by experiment and difficult to analyze by computational techniques. In this paper, we employed a cost-effective method called "pathway docking" in which molecular docking was used to screen ligand-receptor binding free energy surface to reveal possible paths of ligand approaching protein binding pocket. A case study was applied on oseltamivir, the key drug against influenza a virus. The equilibrium pathways identified by this method are found to be similar to those identified in prior studies using highly expensive computational approaches.

Transitions to catalytically inactive conformations in EGFR kinase

The epidermal growth factor receptor (EGFR) is a key protein in cellular signaling, and its kinase domain (EGFR kinase) is an intensely pursued target of small-molecule drugs. Although both catalytically active and inactive conformations of EGFR kinase have been resolved crystallographically, experimental characterization of the transitions between these conformations remains difficult. Using unbiased, all-atom molecular dynamics simulations, we observed EGFR kinase spontaneously transition from the active to the so-called "Src-like inactive" conformation by way of two sets of intermediate conformations: One corresponds to a previously identified locally disordered state and the other to previously undescribed "extended" conformations, marked by the opening of the ATP-binding site between the two lobes of the kinase domain. We also simulated the protonation-dependent transition of EGFR kinase to another ["Asp-Phe-Gly-out" ("DFG-out")] inactive conformation and observed similar intermediate conformations. A key element observed in the simulated transitions is local unfolding, or "cracking," which supports a prediction of energy landscape theory. We used hydrogen-deuterium (H/D) exchange measurements to corroborate our simulations and found that the simulated intermediate conformations correlate better with the H/D exchange data than existing active or inactive EGFR kinase crystal structures. The intermediate conformations revealed by our simulations of the transition process differ significantly from the existing crystal structures and may provide unique possibilities for structure-based drug discovery.

Effects of protonation state of Asp181 and position of active site water molecules on the conformation of PTP1B

In protein tyrosine phosphatase 1B (PTP1B), the flexible WPD loop adopts a closed conformation (WPDclosed ) in the active state of PTP1B, bringing the catalytic Asp181 close to the active site pocket, while WPD loop is in an open conformation (WPDopen ) in the inactive state. Previous studies showed that Asp181 may be protonated at physiological pH, and ordered water molecules exist in the active site. In the current study, molecular dynamics simulations are employed at different Asp181 protonation states and initial positions of active site water molecules, and compared with the existing crystallographic data of PTP1B. In WPDclosed conformation, the active site is found to maintain its conformation only in the protonated state of Asp181 in both free and liganded states, while Asp181 is likely to be deprotonated in WPDopen conformation. When the active site water molecule network that is a part of the free WPDclosed crystal structure is disrupted, intermediate WPD loop conformations, similar to that in the PTPRR crystal structure, are sampled in the MD simulations. In liganded PTP1B, one active site water molecule is found to be important for facilitating the orientation of Cys215 and the phosphate ion, thus may play a role in the reaction. In conclusion, conformational stability of WPD loop, and possibly catalytic activity of PTP1B, is significantly affected by the protonation state of Asp181 and position of active site water molecules, showing that these aspects should be taken into consideration both in MD simulations and inhibitor design.

The Uptake Mechanism of the Cell-Penetrating pVEC Peptide

Peptide based drug design efforts have gained renewed interest with the discovery of cargo-carrying or cell-penetrating peptides. Understanding the translocation mechanism of these peptides and identifying the residues or elements that contribute to uptake can provide valuable clues toward the design of novel peptides. To this end, we have performed steered molecular dynamics (SMD) simulations on the pVEC peptide from murine vascular endothelial-cadherin protein and its two variants. Translocation was found to occur in three stages, adsorption via the cationic residues, inclusion of the whole peptide inside the membrane accompanied by formation of a water defect, and exit of both peptide and water molecules from the bilayer. Our simulation results suggest that the precise order in which the hydrophobic, cationic, and the polar regions are located in the amphipathic pVEC peptide contributes to its uptake mechanism. These results present new opportunities for the design of novel cell-penetrating and antimicrobial peptides.

Unrestrained computation of free energy along a path

We apply the adaptive biasing potential (ABP) method to optimize the principal curve defining a conformational transition between two known end states and to subsequently compute the one-dimensional potential of mean force as a function of arc length along the principal curve. This approach allows the use of the ABP method in a collective variable space of arbitrary dimension and offers several advantages over line-search methods. First, configurations are neither generated along an initial path for the transition nor equilibrated during evolution of the path. Second, and most importantly, the powerful sampling provided by the ABP serves to accelerate the dynamics during the optimization and computation of the free energy. Finally, the free energy is formulated as a potential of mean force that captures changes in the reaction channel along the principal curve, in contrast to the free energy profile evaluated from the local free-energy gradient in restrained path optimization methods. We first demonstrate the ABP formulation of path optimization using a two-dimensional potential surface and then with a more complex system of Src protein tyrosine kinase. The method is shown to be efficient and robust in the case of rugged, free-energy landscapes.

Analysis and elimination of a bias in targeted molecular dynamics simulations of conformational transitions: application to calmodulin

The popular targeted molecular dynamics (TMD) method for generating transition paths in complex biomolecular systems is revisited. In a typical TMD transition path, the large-scale changes occur early and the small-scale changes tend to occur later. As a result, the order of events in the computed paths depends on the direction in which the simulations are performed. To identify the origin of this bias, and to propose a method in which the bias is absent, variants of TMD in the restraint formulation are introduced and applied to the complex open ↔ closed transition in the protein calmodulin. Due to the global best-fit rotation that is typically part of the TMD method, the simulated system is guided implicitly along the lowest-frequency normal modes, until the large spatial scales associated with these modes are near the target conformation. The remaining portion of the transition is described progressively by higher-frequency modes, which correspond to smaller-scale rearrangements. A straightforward modification of TMD that avoids the global best-fit rotation is the locally restrained TMD (LRTMD) method, in which the biasing potential is constructed from a number of TMD potentials, each acting on a small connected portion of the protein sequence. With a uniform distribution of these elements, transition paths that lack the length-scale bias are obtained. Trajectories generated by steered MD in dihedral angle space (DSMD), a method that avoids best-fit rotations altogether, also lack the length-scale bias. To examine the importance of the paths generated by TMD, LRTMD, and DSMD in the actual transition, we use the finite-temperature string method to compute the free energy profile associated with a transition tube around a path generated by each algorithm. The free energy barriers associated with the paths are comparable, suggesting that transitions can occur along each route with similar probabilities. This result indicates that a broad ensemble of paths needs to be calculated to obtain a full description of conformational changes in biomolecules. The breadth of the contributing ensemble suggests that energetic barriers for conformational transitions in proteins are offset by entropic contributions that arise from a large number of possible paths.

Towards the prediction of order parameters from molecular dynamics simulations in proteins

A molecular understanding of how protein function is related to protein structure requires an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy barriers and within a complex energy landscape. This makes it very difficult to reliably connect, for example by all-atom molecular dynamics calculations, the states, their energies, and the pathways between them. A major issue needed to improve sampling on the intermediate states is an order parameter--a reduced descriptor for the major subset of degrees of freedom--that can be used to aid sampling for the large conformational change. We present a method to combine information from molecular dynamics using non-linear time series and dimensionality reduction, in order to quantitatively determine an order parameter connecting two large-scale conformationally distinct protein states. This new method suggests an implementation for molecular dynamics calculations that may be used to enhance sampling of intermediate states.

Exploration of Protein Conformational Change with PELE and Meta-Dynamics

Atomistic molecular simulation methods are now able to explore complex protein or protein-ligand dynamical space in a tractable way with methods such as meta-dynamics or adaptive biasing force. However, many of these methods either require a careful selection of reaction coordinates or the knowledge of an initial pathway of some kind. Thus, it is important that effective methods are developed to produce this pathway data in an efficient fashion. PELE, a proven protein-ligand sampling code, has been developed to provide rapid protein sampling in highly flexible cases, using a reduced network model eigen problem approach. The resulting method is able to rapidly sample configuration space with very general driving information. When applied to ubiquitin, PELE was able to reproduce RMSD and average force data found in molecular dynamics simulations. PELE was also applied to explore the opening/closing transition of T4 lysozyme. A meta-dynamics exploration using a low energy pathway validated that the configurations explored by PELE represent the most populated regions of phase space. PELE and meta-dynamics explorations also discovered a low free energy region where a large cross-domain helix of T4 lysozyme is broken in two. There is previous NMR evidence for the validity of this unfolded helix region.

The conformational transition pathways of ATP-binding cassette transporter BtuCD revealed by targeted molecular dynamics simulation

BtuCD is a member of the ATP-binding cassette transporters in Escherichia coli that imports vitamin B(12) into the cell by utilizing the energy of ATP hydrolysis. Crystal structures of BtuCD and its homologous protein HI1470/1 in various conformational states support the "alternating access" mechanism which proposes the conformational transitions of the substrate translocation pathway at transmembrane domain (TMD) between the outward-facing and inward-facing states. The conformational transition at TMD is assumed to couple with the movement of the cytoplasmic nucleotide-binding domains (NBDs) driven by ATP hydrolysis/binding. In this study, we performed targeted molecular dynamics (MD) simulations to explore the atomic details of the conformational transitions of BtuCD importer. The outward-facing to inward-facing (O→I) transition was found to be initiated by the conformational movement of NBDs. The subsequent reorientation of the substrate translocation pathway at TMD began with the closing of the periplasmic gate, followed by the opening of the cytoplamic gate in the last stage of the conformational transition due to the extensive hydrophobic interactions at this region, consistent with the functional requirement of unidirectional transport of the substrates. The reverse inward-facing to outward-facing (I→O) transition was found to exhibit intrinsic diversity of the conformational transition pathways and significant structural asymmetry, suggesting that the asymmetric crystal structure of BtuCD-F is an intermediate state in this process.

Computing ensembles of transitions from stable states: Dynamic importance sampling

There is an increasing dataset of solved biomolecular structures in more than one conformation and increasing evidence that large-scale conformational change is critical for biomolecular function. In this article, we present our implementation of a dynamic importance sampling (DIMS) algorithm that is directed toward improving our understanding of important intermediate states between experimentally defined starting and ending points. This complements traditional molecular dynamics methods where most of the sampling time is spent in the stable free energy wells defined by these initial and final points. As such, the algorithm creates a candidate set of transitions that provide insights for the much slower and probably most important, functionally relevant degrees of freedom. The method is implemented in the program CHARMM and is tested on six systems of growing size and complexity. These systems, the folding of Protein A and of Protein G, the conformational changes in the calcium sensor S100A6, the glucose-galactose-binding protein, maltodextrin, and lactoferrin, are also compared against other approaches that have been suggested in the literature. The results suggest good sampling on a diverse set of intermediates for all six systems with an ability to control the bias and thus to sample distributions of trajectories for the analysis of intermediate states.

Maximum Flux Transition Paths of Conformational Change

Given two metastable states A and B of a biomolecular system, the problem is to calculate the likely paths of the transition from A to B. Such a calculation is more informative and more manageable if done for a reduced set of collective variables chosen so that paths cluster in collective variable space. The computational task becomes that of computing the "center" of such a cluster. A good way to define the center employs the concept of a committor, whose value at a point in collective variable space is the probability that a trajectory at that point will reach B before A. The committor "foliates" the transition region into a set of isocommittors. The maximum flux transition path is defined as a path that crosses each isocommittor at a point which (locally) has the highest crossing rate of distinct reactive trajectories. This path is based on the same principle as the minimum resistance path of Berkowitz et al (1983), but it has two advantages: (i) the path is invariant with respect to a change of coordinates in collective variable space and (ii) the differential equations that define the path are simpler. It is argued that such a path is nearer to an ideal path than others that have been proposed with the possible exception of the finite-temperature string method path. To make the calculation tractable, three approximations are introduced, yielding a path that is the solution of a nonsingular two-point boundary-value problem. For such a problem, one can construct a simple and robust algorithm. One such algorithm and its performance is discussed.

Functional rotation of the transporter AcrB: insights into drug extrusion from simulations

The tripartite complex AcrAB-TolC is the major efflux system in Escherichia coli. It extrudes a wide spectrum of noxious compounds out of the bacterium, including many antibiotics. Its active part, the homotrimeric transporter AcrB, is responsible for the selective binding of substrates and energy transduction. Based on available crystal structures and biochemical data, the transport of substrates by AcrB has been proposed to take place via a functional rotation, in which each monomer assumes a particular conformation. However, there is no molecular-level description of the conformational changes associated with the rotation and their connection to drug extrusion. To obtain insights thereon, we have performed extensive targeted molecular dynamics simulations mimicking the functional rotation of AcrB containing doxorubicin, one of the two substrates that were co-crystallized so far. The simulations, including almost half a million atoms, have been used to test several hypotheses concerning the structure-dynamics-function relationship of this transporter. Our results indicate that, upon induction of conformational changes, the substrate detaches from the binding pocket and approaches the gate to the central funnel. Furthermore, we provide strong evidence for the proposed peristaltic transport involving a zipper-like closure of the binding pocket, responsible for the displacement of the drug. A concerted opening of the channel between the binding pocket and the gate further favors the displacement of the drug. This microscopically well-funded information allows one to identify the role of specific amino acids during the transitions and to shed light on the functioning of AcrB.

In nature, bacteria have to resist several toxic threats to be able to survive, from bile acids in intestines up to antibiotics. The Escherichia coli bacterium, which usually is a commensal inhabitant of human intestines, can also acquire pathogenic properties which would harm the human body. To dispose of toxic compounds, E. coli has developed a protein machinery which is called “efflux pump”. Here, we studied the dynamics of the transporter protein AcrB, a component of the E. coli major efflux system, in complex with an antibiotic (doxorubicin). We used computer simulations to complement the existing experimental data. Our purpose was to gain more detailed insights into the pumping mechanism at the molecular level. In our simulations the drug leaves the binding pocket upon induction of functional rotation in the protein, although a complete extrusion was never observed. A peristaltic motion, which starts with a zipper-like closure of the interior of the protein, is an important step for the extrusion of the drug. Interestingly, such a peristaltic mechanism of pumping has been suggested before on the basis of structural data. The molecular details obtained in this study shall deepen the understanding of the functioning of the efflux pump.

Cooperative nature of gating transitions in K(+) channels as seen from dynamic importance sampling calculations

The growing dataset of K(+) channel x-ray structures provides an excellent opportunity to begin a detailed molecular understanding of voltage-dependent gating. These structures, while differing in sequence, represent either a stable open or closed state. However, an understanding of the molecular details of gating will require models for the transitions and experimentally testable predictions for the gating transition. To explore these ideas, we apply dynamic importance sampling to a set of homology models for the molecular conformations of K(+) channels for four different sets of sequences and eight different states. In our results, we highlight the importance of particular residues upstream from the Pro-Val-Pro (PVP) region to the gating transition. This supports growing evidence that the PVP region is important for influencing the flexibility of the S6 helix and thus the opening of the gating domain. The results further suggest how gating on the molecular level depends on intra-subunit motions to influence the cooperative behavior of all four subunits of the K(+) channel. We hypothesize that the gating process occurs in steps: first sidechain movement, then inter-S5-S6 subunit motions, and lastly the large-scale domain rearrangements.

The conformational transition pathway of ATP binding cassette transporter MsbA revealed by atomistic simulations

ATP binding cassette transporters are integral membrane proteins that use the energy released from ATP hydrolysis at the two nucleotide binding domains (NBDs) to translocate a wide variety of substrates through a channel at the two transmembrane domains (TMDs) across the cell membranes. MsbA from Gram-negative bacteria is a lipid and multidrug resistance ATP binding cassette exporter that can undergo large scale conformational changes between the outward-facing and the inward-facing conformations revealed by crystal structures in different states. Here, we use targeted molecular dynamics simulation methods to explore the atomic details of the conformational transition from the outward-facing to the inward-facing states of MsbA. The molecular dynamics trajectories revealed a clear spatiotemporal order of the conformational movements. The disruption of the nucleotide binding sites at the NBD dimer interface is the very first event that initiates the following conformational changes, verifying the assumption that the conformational conversion is triggered by ATP hydrolysis. The conserved x-loops of the NBDs were identified to participate in the interaction network that stabilizes the cytoplasmic tetrahelix bundle of the TMDs and play an important role in mediating the cross-talk between the NBD and TMD. The movement of the NBD dimer is transmitted through x-loops to break the tetrahelix bundle, inducing the packing rearrangements of the transmembrane helices at the cytoplasmic side and the periplasmic side sequentially. The packing rearrangement within each periplasmic wing of TMD that results in exposure of the substrate binding sites occurred at the end stage of the trajectory, preventing the wrong timing of the binding site accessibility.

Steered molecular dynamics simulations reveal the likelier dissociation pathway of imatinib from its targeting kinases c-Kit and Abl

Development of small molecular kinase inhibitors has recently been the central focus in drug discovery. And type II kinase inhibitors that target inactive conformation of kinases have attracted particular attention since their potency and selectivity are thought to be easier to achieve compared with their counterpart type I inhibitors that target active conformation of kinases. Although mechanisms underlying the interactions between type II inhibitors and their targeting kinases have been widely studied, there are still some challenging problems, for example, how type II inhibitors associate with or dissociate from their targeting kinases. In this investigation, steered molecular dynamics simulations have been carried out to explore the possible dissociation pathways of typical type II inhibitor imatinib from its targeting protein kinases c-Kit and Abl. The simulation results indicate that the most favorable pathway for imatinib dissociation corresponds to the ATP-channel rather than the relatively wider allosteric-pocket-channel, which is mainly due to the different van der Waals interaction that the ligand suffers during dissociation. Nevertheless, the direct reason comes from the fact that the residues composing the ATP-channel are more flexible than that forming the allosteric-pocket-channel. The present investigation suggests that a bulky hydrophobic head is unfavorable, but a large polar tail is allowed for a potent type II inhibitor. The information obtained here can be used to direct the discovery of type II kinase inhibitors.