Automated computation of low-energy pathways for complex rearrangements in proteins: application to the conformational switch of Ras p21

Free Energy Simulations of Receptor-Binding Domain Opening of the SARS-CoV-2 Spike Indicate a Barrierless Transition with Slow Conformational Motions

Infection by sarbecoviruses begins with the attachment of the homotrimeric viral "spike" protein to the angiotensin-converting enzyme 2 receptor on the surface of mammalian cells. This requires one or more receptor-binding domains (RBDs) to be in the open (up) position. Here, we present the results of long molecular dynamics simulations with umbrella sampling (US) to compute a one-dimensional free energy profile of RBD opening/closing and the associated transition times. After ≃3.58μs of simulation time per US window (∼229 μs in total), which was required to approach trajectory decorrelation, the computed free energy profile was found to be without large barriers. This suggests that the RBD diffuses between the open and closed positions without significant energetic hindrance. This interpretation appears consistent with experiments but is at odds with some previous simulations. Modeling the RBD motion as diffusive dynamics along the computed free energy profile, we find that the overall time required for the transition is only about 2 μs, which is 5 orders of magnitude shorter than experimentally measured transition times. We speculate that the most likely reason for the transition time mismatch is our use of very short glycans, which was required to make the simulations performed here feasible. Despite the long simulation times, the final free energy profile is not fully converged with statistical errors of ≃1.16 kcal/mol, which were found to be consistent with the slow time decay in the autocorrelation of the conformational motions of the protein. The simulation lengths that would be required to obtain fully converged results remain unknown, but the present calculations would benefit from at least an order-of-magnitude extension.

Activation and Inactivation of the FLT3 Kinase: Pathway Intermediates and the Free Energy of Transition

The aberrant expression of kinases is often associated with pathologies such as cancer and autoimmune diseases. Like other types of enzymes, kinases can adopt active and inactive states, where a shift toward more stable active state often leads to disease. Dozens of kinase inhibitors are, therefore, used as drugs. Most of these bind to either the inactive or active state. In this work, we study the transitions between these two states in FLT3, an important drug target in leukemias. Kinases are composed of two lobes (N- and C-terminal lobes) with the catalytic site in-between. Through projection of the largest motions obtained through molecular dynamics (MD) simulations, we show that each of the end-states (active or inactive) already possess the ability for transition as the two lobes rotate which initiates the transition. A targeted simulation approach known as essential dynamics sampling (EDS) was used to speed up the transition between the two protein states. Coupling the EDS to implicit-solvent MD was performed to estimate the free energy barriers of the transitions. The activation energies were found in good agreement with previous estimates obtained for other kinases. Finally, we identified FLT3 intermediates that assumed configurations that resemble that of the c-Src nonreceptor tyrosine kinase. The intermediates show better binding to the drug ponatinib than c-Src and the inactive state of FLT3. This suggests that targeting intermediate states can be used to explain the drug-binding patterns of kinases and for rational drug design.

Nucleotide Dependent Switching in Rho GTPase: Conformational Heterogeneity and Competing Molecular Interactions

Ras superfamily of GTPases regulate myriad cellular processes through a conserved nucleotide (GTP/GDP) dependent switching mechanism. Unlike Ras family of GTPases, for the Rho GTPases, there is no clear evidence for the existence of “sub-states” such as state 1 & state 2 in the GTP bound form. To explore the nucleotide dependent conformational space of the Switch I loop and also to look for existence of state 1 like conformations in Rho GTPases, atomistic molecular dynamics and metadynamics simulations on RhoA were performed. These studies demonstrate that both the nucleotide-free state and the GDP bound “OFF” state have very similar conformations, whereas the GTP bound “ON” state has unique conformations with signatures of two intermediate states. The conformational free energy landscape for these systems suggests the presence of multiple intermediate states. Interestingly, the energetic penalty of exposing the non-polar residues in the GTP bound form is counter balanced by the favourable hydrogen bonded interactions between the γ-phosphate group of GTP with the highly conserved Tyr34 and Thr37 residues. These competing molecular interactions lead to a tuneable energy landscape of the Switch I conformation, which can undergo significant changes based on the local environment including changes upon binding to effectors.

Intrinsic K-Ras dynamics: A novel molecular dynamics data analysis method shows causality between residue pair motions

K-Ras is the most frequently mutated oncogene in human cancers, but there are still no drugs that directly target it in the clinic. Recent studies utilizing dynamics information show promising results for selectively targeting mutant K-Ras. However, despite extensive characterization, the mechanisms by which K-Ras residue fluctuations transfer allosteric regulatory information remain unknown. Understanding the direction of information flow can provide new mechanistic insights for K-Ras targeting. Here, we present a novel approach –conditional time-delayed correlations (CTC) – using the motions of all residue pairs of a protein to predict directionality in the allosteric regulation of the protein fluctuations. Analyzing nucleotide-dependent intrinsic K-Ras motions with the new approach yields predictions that agree with the literature, showing that GTP-binding stabilizes K-Ras motions and leads to residue correlations with relatively long characteristic decay times. Furthermore, our study is the first to identify driver-follower relationships in correlated motions of K-Ras residue pairs, revealing the direction of information flow during allosteric modulation of its nucleotide-dependent intrinsic activity: active K-Ras Switch-II region motions drive Switch-I region motions, while α-helix-3L7 motions control both. Our results provide novel insights for strategies that directly target mutant K-Ras.

A stochastic roadmap method to model protein structural transitions

Evidence is emerging that the role of protein structure in disease needs to be rethought. Sequence mutations in proteins are often found to affect the rate at which a protein switches between structures. Modeling structural transitions in wildtype and variant proteins is central to understanding the molecular basis of disease. This paper investigates an efficient algorithmic realization of the stochastic roadmap simulation framework to model structural transitions in wildtype and variants of proteins implicated in human disorders. Our results indicate that the algorithm is able to extract useful information on the impact of mutations on protein structure and function.

Calculation of Point-to-Point Short-Time and Rare Trajectories with Boundary Value Formulation

Sampling rare, short-time, and reactive trajectories is of considerable interest in molecular simulations. These trajectories, which are also called "activated", hop between stable states separated by energy or entropy barriers. Simulations of activated trajectories with random sampling of initial conditions are inefficient, since most initial conditions lead to trajectories that do not pass the barrier in short times. A boundary value formulation is proposed that selects these rare trajectories, making the sampling of point-to-point reactive trajectories more effective. Earlier boundary value formulations by one of us focused on computations of approximate trajectories. In the proposed method, trajectories are accurate even when we employ a relatively large integration step (by a factor of about 100 compared to initial value methods). The boundary value solutions to short-time reactive trajectories tend to be unique and have significant statistical weights compared to other reactive trajectories of the microcanonical ensemble. Three numerical examples are considered:  a transition in the Mueller potential, a conformational change in alanine dipeptide, and an isomerization in a Lennard-Jones cluster.

Transition Networks for the Comprehensive Characterization of Complex Conformational Change in Proteins

Functionally relevant transitions between native conformations of a protein can be complex, involving, for example, the reorganization of parts of the backbone fold, and may occur via a multitude of pathways. Such transitions can be characterized by a transition network (TN), in which the experimentally determined end state structures are connected by a dense network of subtransitions via low-energy intermediates. We show here how the computation of a TN can be achieved for a complex protein transition. First, an efficient hierarchical procedure is used to uniformly sample the conformational subspace relevant to the transition. Then, the best path which connects the end states is determined as well as the rate-limiting ridge on the energy surface which separates them. Graph-theoretical algorithms permit this to be achived by computing the barriers of only a small number out of the many subtransitions in the TN. These barriers are computed using the Conjugate Peak Refinement method. The approach is illustrated on the conformational switch of Ras p21. The best and the 12 next-best transition pathways, having rate-limiting barriers within a range of 10 kcal/mol, were identified. Two main energy ridges, which respectively involve rearrangements of the switch I and switch II loops, show that switch I must rearrange by threading Tyr32 underneath the protein backbone before the rate-limiting switch II rearrangement can occur, while the details of the switch II rearrangement differ significantly among the low-energy pathways.

Mapping the Conformation Space of Wildtype and Mutant H-Ras with a Memetic, Cellular, and Multiscale Evolutionary Algorithm

An important goal in molecular biology is to understand functional changes upon single-point mutations in proteins. Doing so through a detailed characterization of structure spaces and underlying energy landscapes is desirable but continues to challenge methods based on Molecular Dynamics. In this paper we propose a novel algorithm, SIfTER, which is based instead on stochastic optimization to circumvent the computational challenge of exploring the breadth of a protein's structure space. SIfTER is a data-driven evolutionary algorithm, leveraging experimentally-available structures of wildtype and variant sequences of a protein to define a reduced search space from where to efficiently draw samples corresponding to novel structures not directly observed in the wet laboratory. The main advantage of SIfTER is its ability to rapidly generate conformational ensembles, thus allowing mapping and juxtaposing landscapes of variant sequences and relating observed differences to functional changes. We apply SIfTER to variant sequences of the H-Ras catalytic domain, due to the prominent role of the Ras protein in signaling pathways that control cell proliferation, its well-studied conformational switching, and abundance of documented mutations in several human tumors. Many Ras mutations are oncogenic, but detailed energy landscapes have not been reported until now. Analysis of SIfTER-computed energy landscapes for the wildtype and two oncogenic variants, G12V and Q61L, suggests that these mutations cause constitutive activation through two different mechanisms. G12V directly affects binding specificity while leaving the energy landscape largely unchanged, whereas Q61L has pronounced, starker effects on the landscape. An implementation of SIfTER is made available at http://www.cs.gmu.edu/~ashehu/?q=OurTools. We believe SIfTER is useful to the community to answer the question of how sequence mutations affect the function of a protein, when there is an abundance of experimental structures that can be exploited to reconstruct an energy landscape that would be computationally impractical to do via Molecular Dynamics.

pH-induced stability switching of the bacteriophage HK97 maturation pathway

Many viruses undergo large-scale conformational changes during their life cycles. Blocking the transition from one stage of the life cycle to the next is an attractive strategy for the development of antiviral compounds. In this work, we have constructed an icosahedrally symmetric, low-energy pathway for the maturation transition of bacteriophage HK97. By conducting constant-pH molecular dynamics simulations on this pathway, we identify which residues are contributing most significantly to shifting the stability between the states along the pathway under differing pH conditions. We further analyze these data to establish the connection between critical residues and important structural motifs which undergo reorganization during maturation. We go on to show how DNA packaging can induce spontaneous reorganization of the capsid during maturation.

Decipher the mechanisms of protein conformational changes induced by nucleotide binding through free-energy landscape analysis: ATP binding to Hsp70

ATP regulates the function of many proteins in the cell by transducing its binding and hydrolysis energies into protein conformational changes by mechanisms which are challenging to identify at the atomic scale. Based on molecular dynamics (MD) simulations, a method is proposed to analyze the structural changes induced by ATP binding to a protein by computing the effective free-energy landscape (FEL) of a subset of its coordinates along its amino-acid sequence. The method is applied to characterize the mechanism by which the binding of ATP to the nucleotide-binding domain (NBD) of Hsp70 propagates a signal to its substrate-binding domain (SBD). Unbiased MD simulations were performed for Hsp70-DnaK chaperone in nucleotide-free, ADP-bound and ATP-bound states. The simulations revealed that the SBD does not interact with the NBD for DnaK in its nucleotide-free and ADP-bound states whereas the docking of the SBD was found in the ATP-bound state. The docked state induced by ATP binding found in MD is an intermediate state between the initial nucleotide-free and final ATP-bound states of Hsp70. The analysis of the FEL projected along the amino-acid sequence permitted to identify a subset of 27 protein internal coordinates corresponding to a network of 91 key residues involved in the conformational change induced by ATP binding. Among the 91 residues, 26 are identified for the first time, whereas the others were shown relevant for the allosteric communication of Hsp70 s in several experiments and bioinformatics analysis. The FEL analysis revealed also the origin of the ATP-induced structural modifications of the SBD recently measured by Electron Paramagnetic Resonance. The pathway between the nucleotide-free and the intermediate state of DnaK was extracted by applying principal component analysis to the subset of internal coordinates describing the transition. The methodology proposed is general and could be applied to analyze allosteric communication in other proteins.

The precise biophysical characterization of the mechanisms of the protein conformational changes controlled by a nucleotide remains a challenge in biology. Molecular dynamics simulations of proteins in different nucleotide-binding states contain information on the nucleotide-dependent conformational dynamics. However, it is difficult to extract relevant information about the conformation-induced mechanism from the raw molecular dynamics data. Herein, we addressed this issue for the major ATP-dependent molecular chaperones Hsp70 s, which contribute to crucial cellular processes and are involved in several neurodegenerative diseases and in cancer. To function, Hsp70 undergoes several conformational changes controlled by the state of its nucleotide-binding domain. We demonstrated that the analysis of the effective free-energy landscape of the protein projected along the amino-acid sequence and computed from the molecular dynamics simulations of Hsp70 in different nucleotide-binding states, holds the key to identify the key residues of the conformational induced pathway. Identification of the key residues involved in the propagation of the structural changes induced by ATP binding offer alternative druggable specific sites other than the ligand binding clefts. The methodology developed for Hsp70 is general and can be adapted to any ligand induced conformational change in proteins.

Lessons from computer simulations of Ras proteins in solution and in membrane

BACKGROUND

A great deal has been learned over the last several decades about the function of Ras proteins in solution and membrane environments. While much of this knowledge has been derived from a plethora of experimental techniques, computer simulations have also played a substantial role.

SCOPE OF REVIEW

Our goal here is to summarize the contribution of molecular simulations to our current understanding of normal and aberrant Ras function. We focus on lessons from molecular dynamics simulations in aqueous and membrane environments.

MAJOR CONCLUSIONS

The central message is that a close interaction between theory and simulation on the one hand and cell-biological, spectroscopic and other experimental approaches on the other has played, and will likely continue to play, a vital role in Ras research.

GENERAL SIGNIFICANCE

Atomistic insights emerging from detailed simulations of Ras in solution and in bilayers may be the key to unlock the secret that to date prevented development of selective anti-Ras inhibitors for cancer therapy.

Molecular mechanism of allosteric communication in Hsp70 revealed by molecular dynamics simulations

Investigating ligand-regulated allosteric coupling between protein domains is fundamental to understand cell-life regulation. The Hsp70 family of chaperones represents an example of proteins in which ATP binding and hydrolysis at the Nucleotide Binding Domain (NBD) modulate substrate recognition at the Substrate Binding Domain (SBD). Herein, a comparative analysis of an allosteric (Hsp70-DnaK) and a non-allosteric structural homolog (Hsp110-Sse1) of the Hsp70 family is carried out through molecular dynamics simulations, starting from different conformations and ligand-states. Analysis of ligand-dependent modulation of internal fluctuations and local deformation patterns highlights the structural and dynamical changes occurring at residue level upon ATP-ADP exchange, which are connected to the conformational transition between closed and open structures. By identifying the dynamically responsive protein regions and specific cross-domain hydrogen-bonding patterns that differentiate Hsp70 from Hsp110 as a function of the nucleotide, we propose a molecular mechanism for the allosteric signal propagation of the ATP-encoded conformational signal.

Allostery, or the capability of proteins to respond to ligand binding events with a variation in structure or dynamics at a distant site, is a common feature for biomolecular function and regulation in a large number of proteins. Intra-protein connections and inter-residue coordinations underlie allosteric mechanisms and react to binding primarily through a finely tuned modulation of motions and structures at the microscopic scale. Hence, all-atom molecular dynamics simulations are suitable to investigate the molecular basis of allostery. Moreover, understanding intra-protein communication pathways at atomistic resolutions offers unique opportunities in rational drug design. Proteins of the Hsp70 family are allosteric molecular chaperones involved in maintaining cellular protein homeostasis. These proteins are involved in several types of cancer, neurodegenerative diseases, aging and infections and are therefore pharmaceutically relevant targets. In this work we have analyzed, by multiple molecular dynamics simulations, the long-range dynamical and conformational effects of ligands bound to Hsp70, and found relevant differences in comparison to the known non-allosteric structural homolog Hsp110. The resulting model of the mechanism of allosteric propagation offers the opportunity of identifying on-pathway allosteric druggable sites, which we propose could guide rational drug-design efforts targeting Hsp70.

Isomerization mechanism of the HcRed fluorescent protein chromophore

To understand how the protein achieves fluorescence, the isomerization mechanism of the HcRed chromophore is studied both under vacuum and in the solvated red fluorescent protein. Quantum mechanical (QM) and quantum mechanical/molecular mechanical (QM/MM) methods are applied both for the ground and the first excited state. The photoinduced processes in the chromophore mainly involve torsions around the imidazolinone-bridge bond (τ) and the phenoxy-bridge bond (φ). Under vacuum, the isomerization of the cis-trans chromophore essentially proceeds by τ twisting, while the radiationless decay requires φ torsion. By contrast, the isomerization of the cis-trans chromophore in HcRed occurs via simultaneous τ and φ twisting. The protein environment significantly reduces the barrier of this hula twist motion compared with vacuum. The excited-state isomerization barrier via the φ rotation of the cis-coplanar conformer in HcRed is computed to be significantly higher than that of the trans-non-coplanar conformer. This is consistent with the experimental observation that the cis-coplanar-conformation of the chromophore is related to the fluorescent properties of HcRed, while the trans-non-planar conformation is weakly fluorescent or non-fluorescent. Our study shows how the protein modifies the isomerization mechanism, notably by interactions involving the nearby residue Ile197, which keeps the chromophore coplanar and blocks the twisting motion that leads to photoinduced radiationless decay.

Early events in helix unfolding under external forces: a milestoning analysis

Initial events of helix breakage as a function of load are considered using molecular dynamics simulations and milestoning analysis. A helix length of ∼100 amino acids is considered as a model for typical helices found in molecular machines and as a model that minimizes end effects for early events of unfolding. Transitions of individual amino acids (averaged over the helix's interior residues) are examined and its surrounding hydrogen bonds are considered. Dense kinetic networks are constructed that, with milestoning analysis, provide the overall kinetics of early breakage events. Network analysis and selection of MaxFlux pathways illustrate that load impacts unfolding mechanisms in addition to time scales. At relatively high (100 pN) load levels, the principal intermediate is the 3(10)-helix, while at relatively low (10 pN) levels the π-helix is significantly populated, albeit not as an unfolding intermediate. Coarse variables are examined at different levels of resolution; the rate of unfolding illustrates remarkable stability under changes in the coarsening. Consistent prediction of about ∼5 ns for the time of a single amino-acid unfolding event are obtained. Hydrogen bonds are much faster coarse variables (by about 2 orders of magnitude) compared to backbone torsional transition, which gates unfolding and thereby provides the appropriate coarse variable for the initiation of unfolding. Results provide an atomic description of "catch-bond" behavior, based on alternative pathways, in which unfolding of a simple protein structural element occurs over longer timescales for intermediate (10 pN) loads than for zero (0 pN) or large (100 pN) loads.

The Ras protein superfamily: evolutionary tree and role of conserved amino acids

The Ras superfamily is a fascinating example of functional diversification in the context of a preserved structural framework and a prototypic GTP binding site. Thanks to the availability of complete genome sequences of species representing important evolutionary branch points, we have analyzed the composition and organization of this superfamily at a greater level than was previously possible. Phylogenetic analysis of gene families at the organism and sequence level revealed complex relationships between the evolution of this protein superfamily sequence and the acquisition of distinct cellular functions. Together with advances in computational methods and structural studies, the sequence information has helped to identify features important for the recognition of molecular partners and the functional specialization of different members of the Ras superfamily.

Interconversion of two GDP-bound conformations and their selection in an Arf-family small G protein

ADP-ribosylation factor (Arf) and other Arf-family small G proteins participate in many cellular functions via their characteristic GTP/GDP conformational cycles, during which a nucleotide(∗)Mg(2+)-binding site communicates with a remote N-terminal helix. However, the conformational interplay between the nucleotides, the helix, the protein core, and Mg(2+) has not been fully delineated. Herein, we report a study of the dynamics of an Arf-family protein, Arl8, under various conditions by means of NMR relaxation spectroscopy. The data indicated that, when GDP is bound, the protein core, which does not include the N-terminal helix, reversibly transition between an Arf-family GDP form and another conformation that resembles the Arf-family GTP form. Additionally, we found that the N-terminal helix and Mg(2+), respectively, stabilize the aforementioned former and latter conformations in a population-shift manner. Given the dynamics of the conformational changes, we can describe the Arl8 GTP/GDP cycle in terms of an energy diagram.

Structural mechanism of the ATP-induced dissociation of rigor myosin from actin

Myosin is a true nanomachine, which produces mechanical force from ATP hydrolysis by cyclically interacting with actin filaments in a four-step cycle. The principle underlying each step is that structural changes in separate regions of the protein must be mechanically coupled. The step in which myosin dissociates from tightly bound actin (the rigor state) is triggered by the 30 Å distant binding of ATP. Large conformational differences between the crystal structures make it difficult to perceive the coupling mechanism. Energetically accessible transition pathways computed at atomic detail reveal a simple coupling mechanism for the reciprocal binding of ATP and actin.

Molecular evolution of protein conformational changes revealed by a network of evolutionarily coupled residues

An improved understanding of protein conformational changes has broad implications for elucidating the mechanisms of various biological processes and for the design of protein engineering experiments. Understanding rearrangements of residue interactions is a key component in the challenge of describing structural transitions. Evolutionary properties of protein sequences and structures are extensively studied; however, evolution of protein motions, especially with respect to interaction rearrangements, has yet to be explored. Here, we investigated the relationship between sequence evolution and protein conformational changes and discovered that structural transitions are encoded in amino acid sequences as coevolving residue pairs. Furthermore, we found that highly coevolving residues are clustered in the flexible regions of proteins and facilitate structural transitions by forming and disrupting their interactions cooperatively. Our results provide insight into the evolution of protein conformational changes and help to identify residues important for structural transitions.

Relation between the conformational heterogeneity and reaction cycle of Ras: molecular simulation of Ras

Ras functions as a molecular switch by cycling between the active GTP-bound state and the inactive GDP-bound state. It is known experimentally that there is another GTP-bound state called state 1. We investigate the conformational changes and fluctuations arising from the difference in the coordinations between the switch regions and ligands in the GTP- and GDP-bound states using a total of 830 ns of molecular-dynamics simulations. Our results suggest that the large fluctuations among multiple conformations of switch I in state 1 owing to the absence of coordination between Thr-35 and Mg(2+) inhibit the binding of Ras to effectors. Furthermore, we elucidate the conformational heterogeneity in Ras by using principal component analysis, and propose a two-step reaction path from the GDP-bound state to the active GTP-bound state via state 1. This study suggests that state 1 plays an important role in signal transduction as an intermediate state of the nucleotide exchange process, although state 1 itself is an inactive state for signal transduction.

The distinct conformational dynamics of K-Ras and H-Ras A59G

Ras proteins regulate signaling cascades crucial for cell proliferation and differentiation by switching between GTP- and GDP-bound conformations. Distinct Ras isoforms have unique physiological functions with individual isoforms associated with different cancers and developmental diseases. Given the small structural differences among isoforms and mutants, it is currently unclear how these functional differences and aberrant properties arise. Here we investigate whether the subtle differences among isoforms and mutants are associated with detectable dynamical differences. Extensive molecular dynamics simulations reveal that wild-type K-Ras and mutant H-Ras A59G are intrinsically more dynamic than wild-type H-Ras. The crucial switch 1 and switch 2 regions along with loop 3, helix 3, and loop 7 contribute to this enhanced flexibility. Removing the gamma-phosphate of the bound GTP from the structure of A59G led to a spontaneous GTP-to-GDP conformational transition in a 20-ns unbiased simulation. The switch 1 and 2 regions exhibit enhanced flexibility and correlated motion when compared to non-transitioning wild-type H-Ras over a similar timeframe. Correlated motions between loop 3 and helix 5 of wild-type H-Ras are absent in the mutant A59G reflecting the enhanced dynamics of the loop 3 region. Taken together with earlier findings, these results suggest the existence of a lower energetic barrier between GTP and GDP states of the mutant. Molecular dynamics simulations combined with principal component analysis of available Ras crystallographic structures can be used to discriminate ligand- and sequence-based dynamic perturbations with potential functional implications. Furthermore, the identification of specific conformations associated with distinct Ras isoforms and mutants provides useful information for efforts that attempt to selectively interfere with the aberrant functions of these species.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Simulating oligomerization at experimental concentrations and long timescales: A Markov state model approach

Here, we present a novel computational approach for describing the formation of oligomeric assemblies at experimental concentrations and timescales. We propose an extension to the Markovian state model approach, where one includes low concentration oligomeric states analytically. This allows simulation on long timescales (seconds timescale) and at arbitrarily low concentrations (e.g., the micromolar concentrations found in experiments), while still using an all-atom model for protein and solvent. As a proof of concept, we apply this methodology to the oligomerization of an Abeta peptide fragment (Abeta(21-43)). Abeta oligomers are now widely recognized as the primary neurotoxic structures leading to Alzheimer's disease. Our computational methods predict that Abeta trimers form at micromolar concentrations in 10 ms, while tetramers form 1000 times more slowly. Moreover, the simulation results predict specific intermonomer contacts present in the oligomer ensemble as well as putative structures for small molecular weight oligomers. Based on our simulations and statistical models, we propose a novel mutation to stabilize the trimeric form of Abeta in an experimentally verifiable manner.

Mapping the nucleotide and isoform-dependent structural and dynamical features of Ras proteins

Ras GTPases are conformational switches controlling cell proliferation, differentiation, and development. Despite their prominent role in many forms of cancer, the mechanism of conformational transition between inactive GDP-bound and active GTP-bound states remains unclear. Here we describe a detailed analysis of available experimental structures and molecular dynamics simulations to quantitatively assess the structural and dynamical features of active and inactive states and their interconversion. We demonstrate that GTP-bound and nucleotide-free G12V H-ras sample a wide region of conformational space, and show that the inactive-to-active transition is a multiphase process defined by the relative rearrangement of the two switches and the orientation of Tyr32. We also modeled and simulated N- and K-ras proteins and found that K-ras is more flexible than N- and H-ras. We identified a number of isoform-specific, long-range side chain interactions that define unique pathways of communication between the nucleotide binding site and the C terminus.

Transition networks for modeling the kinetics of conformational change in macromolecules

The kinetics and thermodynamics of complex transitions in biomolecules can be modeled in terms of a network of transitions between the relevant conformational substates. Such a transition network, which overcomes the fundamental limitations of reaction-coordinate-based methods, can be constructed either based on the features of the energy landscape, or from molecular dynamics simulations. Energy-landscape-based networks are generated with the aid of automated path-optimization methods, and, using graph-theoretical adaptive methods, can now be constructed for large molecules such as proteins. Dynamics-based networks, also called Markov State Models, can be interpreted and adaptively improved using statistical concepts, such as the mean first passage time, reactive flux and sampling error analysis. This makes transition networks powerful tools for understanding large-scale conformational changes.

The Structural Coupling between ATPase Activation and Recovery Stroke in the Myosin II Motor

Before the myosin motor head can perform the next power stroke, it undergoes a large conformational transition in which the converter domain, bearing the lever arm, rotates approximately 65 degrees . Simultaneous with this "recovery stroke," myosin activates its ATPase function by closing the Switch-2 loop over the bound ATP. This coupling between the motions of the converter domain and of the 40 A-distant Switch-2 loop is essential to avoid unproductive ATP hydrolysis. The coupling mechanism is determined here by finding a series of optimized intermediates between crystallographic end structures of the recovery stroke (Dictyostelium discoideum), yielding movies of the transition at atomic detail. The successive formation of two hydrogen bonds by the Switch-2 loop is correlated with the successive see-saw motions of the relay and SH1 helices that hold the converter domain. SH1 helix and Switch-2 loop communicate via a highly conserved loop that wedges against the SH1-helix upon Switch-2 closing.

Analyzing large-scale structural change in proteins: comparison of principal component projection and Sammon mapping

Effective analysis of large-scale conformational transitions in macromolecules requires transforming them into a lower dimensional representation that captures the dominant motions. Herein, we apply and compare two different dimensionality reduction techniques, namely, principal component analysis (PCA), a linear method, and Sammon mapping, which is nonlinear. The two methods are used to analyze four different protein transition pathways of varying complexity, obtained by using either the conjugate peak refinement method or constrained molecular dynamics. For the return-stroke in myosin, both Sammon mapping and PCA show that the conformational change is dominated by a simple rotation of a rigid body. Also, in the case of the T-->R transition in hemoglobin, both methods are able to identify the two main quaternary transition events. In contrast, in the cases of the unfolding transition of staphylococcal nuclease or the signaling switch of Ras p21, which are both more complex conformational transitions, only Sammon mapping is able to identify the distinct phases of motion.

Structural mechanism of the recovery stroke in the myosin molecular motor

The power stroke pulling myosin along actin filaments during muscle contraction is achieved by a large rotation ( approximately 60 degrees ) of the myosin lever arm after ATP hydrolysis. Upon binding the next ATP, myosin dissociates from actin, but its ATPase site is still partially open and catalytically off. Myosin must then close and activate its ATPase site while returning the lever arm for the next power stroke. A mechanism for this coupling between the ATPase site and the distant lever arm is determined here by generating a continuous series of optimized intermediates between the crystallographic end-states of the recovery stroke. This yields a detailed structural model for communication between the catalytic and the force-generating regions that is consistent with experimental observations. The coupling is achieved by an amplifying cascade of conformational changes along the relay helix lying between the ATPase and the domain carrying the lever arm.