Predicting the reaction coordinates of millisecond light-induced conformational changes in photoactive yellow protein

Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory

The transition path ensemble is of special interest in reaction coordinate identification as it consists of reactive trajectories that start from the reactant state and end in the product one. As a theoretical framework for describing the transition path ensemble, the transition path theory has been introduced more than 10 years ago, and so far, its applications have only been illustrated in several low-dimensional systems. Given the transition path ensemble, expressions for calculating flux, current (a vector field), and principal curves are derived here in the space of collective variables from the transition path theory, and they are applicable to time series obtained from molecular dynamics simulations of high-dimensional systems, i.e., the position coordinates as a function of time in the transition path ensemble. The connection of the transition path theory is made to a density-weighted average flux, a quantity proposed in a previous work to appraise the relevance of a coordinate to the reaction coordinate [Li, W. J. Chem. Phys. 2022, 156, 054117]. Most importantly, as an extension of the existing quantities, time-lagged quantities such as flux and current are also proposed. The main insights and objects provided by these time-lagged quantities are illustrated in the application to the alanine peptide in vacuum.

Explaining reaction coordinates of alanine dipeptide isomerization obtained from deep neural networks using Explainable Artificial Intelligence (XAI)

A method for obtaining appropriate reaction coordinates is required to identify transition states distinguishing product and reactant in complex molecular systems. Recently, abundant research has been devoted to obtaining reaction coordinates using artificial neural networks from deep learning literature, where many collective variables are typically utilized in the input layer. However, it is difficult to explain the details of which collective variables contribute to the predicted reaction coordinates owing to the complexity of the nonlinear functions in deep neural networks. To overcome this limitation, we used Explainable Artificial Intelligence (XAI) methods of the Local Interpretable Model-agnostic Explanation (LIME) and the game theory-based framework known as Shapley Additive exPlanations (SHAP). We demonstrated that XAI enables us to obtain the degree of contribution of each collective variable to reaction coordinates that is determined by nonlinear regressions with deep learning for the committor of the alanine dipeptide isomerization in vacuum. In particular, both LIME and SHAP provide important features to the predicted reaction coordinates, which are characterized by appropriate dihedral angles consistent with those previously reported from the committor test analysis. The present study offers an AI-aided framework to explain the appropriate reaction coordinates, which acquires considerable significance when the number of degrees of freedom increases.

Worldwide Protein Data Bank (wwPDB): A virtual treasure for research in biotechnology

The Research Collaboratory for Structural Bioinformatics Protein Data Bank (RSCB PDB) provides a wide range of digital data regarding biology and biomedicine. This huge internet resource involves a wide range of important biological data, obtained from experiments around the globe by different scientists. The Worldwide Protein Data Bank (wwPDB) represents a brilliant collection of 3D structure data associated with important and vital biomolecules including nucleic acids (RNAs and DNAs) and proteins. Moreover, this database accumulates knowledge regarding function and evolution of biomacromolecules which supports different disciplines such as biotechnology. 3D structure, functional characteristics and phylogenetic properties of biomacromolecules give a deep understanding of the biomolecules' characteristics. An important advantage of the wwPDB database is the data updating time, which is done every week. This updating process helps users to have the newest data and information for their projects. The data and information in wwPDB can be a great support to have an accurate imagination and illustrations of the biomacromolecules in biotechnology. As demonstrated by the SARS-CoV-2 pandemic, rapidly reliable and accessible biological data for microbiology, immunology, vaccinology, and drug development are critical to address many healthcare-related challenges that are facing humanity. The aim of this paper is to introduce the readers to wwPDB, and to highlight the importance of this database in biotechnology, with the expectation that the number of scientists interested in the utilization of Protein Data Bank's resources will increase substantially in the coming years.

Assessing the Performance of Traveling-salesman based Automated Path Searching (TAPS) on Complex Biomolecular Systems

Though crucial for understanding the function of large biomolecular systems, locating the minimum free energy paths (MFEPs) between their key conformational states is far from trivial due to their high-dimensional nature. Most existing path-searching methods require a static collective variable space as input, encoding intuition or prior knowledge of the transition mechanism. Such information is, however, hardly available a priori and expensive to validate. To alleviate this issue, we have previously introduced a Traveling-salesman based Automated Path Searching method (TAPS) and demonstrated its efficiency on simple peptide systems. Having implemented a parallel version of this method, here we assess the performance of TAPS on three realistic systems (tens to hundreds of residues) in explicit solvents. We show that TAPS successfully located the MFEP for the ground/excited state transition of the T4 lysozyme L99A variant, consistent with previous findings. TAPS also helped identifying the important role of the two polar contacts in directing the loop-in/loop-out transition of the mitogen-activated protein kinase kinase (MEK1), which explained previous mutant experiments. Remarkably, at a minimal cost of 126 ns sampling, TAPS revealed that the Ltn40/Ltn10 transition of lymphotactin needs no complete unfolding/refolding of its β-sheets and that five polar contacts are sufficient to stabilize the various partially unfolded intermediates along the MFEP. These results present TAPS as a general and promising tool for studying the functional dynamics of complex biomolecular systems.

The molecular pH-response mechanism of the plant light-stress sensor PsbS

Plants need to protect themselves from excess light, which causes photo-oxidative damage and lowers the efficiency of photosynthesis. Photosystem II subunit S (PsbS) is a pH sensor protein that plays a crucial role in plant photoprotection by detecting thylakoid lumen acidification in excess light conditions via two lumen-faced glutamates. However, how PsbS is activated under low-pH conditions is unknown. To reveal the molecular response of PsbS to low pH, here we perform an NMR, FTIR and 2DIR spectroscopic analysis of Physcomitrella patens PsbS and of the E176Q mutant in which an active glutamate has been replaced. The PsbS response mechanism at low pH involves the concerted action of repositioning of a short amphipathic helix containing E176 facing the lumen and folding of the luminal loop fragment adjacent to E71 to a 310-helix, providing clear evidence of a conformational pH switch. We propose that this concerted mechanism is a shared motif of proteins of the light-harvesting family that may control thylakoid inter-protein interactions driving photoregulatory responses.

Frontiers in Multiscale Modeling of Photoreceptor Proteins

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

A community proposal to integrate structural bioinformatics activities in ELIXIR (3D-Bioinfo Community)

Structural bioinformatics provides the scientific methods and tools to analyse, archive, validate, and present the biomolecular structure data generated by the structural biology community. It also provides an important link with the genomics community, as structural bioinformaticians also use the extensive sequence data to predict protein structures and their functional sites. A very broad and active community of structural bioinformaticians exists across Europe, and 3D-Bioinfo will establish formal platforms to address their needs and better integrate their activities and initiatives. Our mission will be to strengthen the ties with the structural biology research communities in Europe covering life sciences, as well as chemistry and physics and to bridge the gap between these researchers in order to fully realize the potential of structural bioinformatics. Our Community will also undertake dedicated educational, training and outreach efforts to facilitate this, bringing new insights and thus facilitating the development of much needed innovative applications e.g. for human health, drug and protein design. Our combined efforts will be of critical importance to keep the European research efforts competitive in this respect.

Here we highlight the major European contributions to the field of structural bioinformatics, the most pressing challenges remaining and how Europe-wide interactions, enabled by ELIXIR and its platforms, will help in addressing these challenges and in coordinating structural bioinformatics resources across Europe. In particular, we present recent activities and future plans to consolidate an ELIXIR 3D-Bioinfo Community in structural bioinformatics and propose means to develop better links across the community. These include building new consortia, organising workshops to establish data standards and seeking community agreement on benchmark data sets and strategies. We also highlight existing and planned collaborations with other ELIXIR Communities and other European infrastructures, such as the structural biology community supported by Instruct-ERIC, with whom we have synergies and overlapping common interests.

Atomistic insight into the kinetic pathways for Watson-Crick to Hoogsteen transitions in DNA

DNA predominantly contains Watson-Crick (WC) base pairs, but a non-negligible fraction of base pairs are in the Hoogsteen (HG) hydrogen bonding motif at any time. In HG, the purine is rotated ∼180° relative to the WC motif. The transitions between WC and HG may play a role in recognition and replication, but are difficult to investigate experimentally because they occur quickly, but only rarely. To gain insight into the mechanisms for this process, we performed transition path sampling simulations on a model nucleotide sequence in which an AT pair changes from WC to HG. This transition can occur in two ways, both starting with loss of hydrogen bonds in the base pair, followed by rotation around the glycosidic bond. In one route the adenine base converts from WC to HG geometry while remaining entirely within the double helix. The other route involves the adenine leaving the confines of the double helix and interacting with water. Our results indicate that this outside route is more probable. We used transition interface sampling to compute rate constants and relative free energies for the transitions between WC and HG. Our results agree with experiments, and provide highly detailed insights into the mechanisms of this important process.

Mechanism of the electroneutral sodium/proton antiporter PaNhaP from transition-path shooting

Na⁺/H⁺ antiporters exchange sodium ions and protons on opposite sides of lipid membranes. The electroneutral Na⁺/H⁺ antiporter NhaP from archaea Pyrococcus abyssi (PaNhaP) is a functional homolog of the human Na⁺/H⁺ exchanger NHE1, which is an important drug target. Here we resolve the Na⁺ and H⁺ transport cycle of PaNhaP by transition-path sampling. The resulting molecular dynamics trajectories of repeated ion transport events proceed without bias force, and overcome the enormous time-scale gap between seconds-scale ion exchange and microseconds simulations. The simulations reveal a hydrophobic gate to the extracellular side that opens and closes in response to the transporter domain motion. Weakening the gate by mutagenesis makes the transporter faster, suggesting that the gate balances competing demands of fidelity and efficiency. Transition-path sampling and a committor-based reaction coordinate optimization identify the essential motions and interactions that realize conformational alternation between the two access states in transporter function.

Cation-proton antiporters mediate selective ion exchange across cellular membranes to control pH, salt concentration and cell volume. Here the authors present a transition-path sampling method that overcomes the timescale gap between simulations (µs) and transport processes (s), which allows them to resolve the Na⁺ and H⁺ transport cycle of the Na⁺/H⁺ antiporter NhaP from Pyrococcus abyssi.

Allostery in Its Many Disguises: From Theory to Applications

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

Orthogonal order parameters to model the reaction coordinate of an enzyme catalyzed reaction

The choice of suitable collective variables in formulating an optimal reaction coordinate is a challenging task for activated transitions between a pair of stable states especially when dealing with biochemical changes such as enzyme catalyzed reactions. A detailed benchmarking study is carried out on the choice of collective variables that can distinguish between the stable states unambiguously. We specifically address the issue if these variables may be directly used to model the optimal reaction coordinate, or if it would be better to use their orthogonalized counterparts. The proposed computational scheme is applied to the rate determining intramolecular proton transfer step in the enzyme human carbonic anhydrase II. The optimum reaction coordinate is determined with and without orthogonalization of the collective variables pertinent to a key conformational fluctuation and the actual proton transfer step at the active site of the enzyme. Suitability of the predicted reaction coordinates in different processes is examined in terms of the free energy profile projected along the reaction coordinate, the rate constant of transition and the underlying molecular mechanism of barrier crossing. Our results indicate that a better agreement with earlier simulation and experimental data is obtained when the orthogonalized collective variables are used to model the reaction coordinate.

Unbiased Atomistic Insight into the Mechanisms and Solvent Role for Globular Protein Dimer Dissociation

Association and dissociation of proteins are fundamental processes in nature. Although simple to understand conceptually, the details of the underlying mechanisms and role of the solvent are poorly understood. Here, we investigate the dissociation of the hydrophilic β-lactoglobulin dimer by employing transition path sampling. Analysis of the sampled path ensembles reveals a variety of mechanisms: (1) a direct aligned dissociation (2) a hopping and rebinding transition followed by unbinding, and (3) a sliding transition before unbinding. Reaction coordinate and transition-state analysis predicts that, besides native contact and neighboring salt-bridge interactions, solvent degrees of freedom play an important role in the dissociation process. Bridging waters, hydrogen-bonded to both proteins, support contacts in the native state and nearby lying transition-state regions, whereas they exhibit faster dynamics in further lying transition-state regions, rendering the proteins more mobile and assisting in rebinding. Analysis of the structure and dynamics of the solvent molecules reveals that the dry native interface induces enhanced populations of both disordered hydration water near hydrophilic residues and tetrahedrally ordered hydration water nearby hydrophobic residues. Although not exhaustive, our sampling of rare unbiased reactive molecular dynamics trajectories enhances the understanding of protein dissociation via complex pathways including (multiple) rebinding events.

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

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

Equipartition terms in transition path ensemble: Insights from molecular dynamics simulations of alanine dipeptide

Transition path ensemble consists of reactive trajectories and possesses all the information necessary for the understanding of the mechanism and dynamics of important condensed phase processes. However, quantitative description of the properties of the transition path ensemble is far from being established. Here, with numerical calculations on a model system, the equipartition terms defined in thermal equilibrium were for the first time estimated in the transition path ensemble. It was not surprising to observe that the energy was not equally distributed among all the coordinates. However, the energies distributed on a pair of conjugated coordinates remained equal. Higher energies were observed to be distributed on several coordinates, which are highly coupled to the reaction coordinate, while the rest were almost equally distributed. In addition, the ensemble-averaged energy on each coordinate as a function of time was also quantified. These quantitative analyses on energy distributions provided new insights into the transition path ensemble.

Stability and growth mechanism of self-assembling putative antifreeze cyclic peptides

Cyclic peptides (CPs) that self-assemble in nanotubes can be candidates for use as antifreeze proteins. Based on the cyclic peptide sequence cyclo-[(l-LYS-d-ALA-l-LEU-d-ALA)₂], which can stack into nanotubes, we propose a putative antifreeze cyclic peptide (AFCP) sequence, cyclo-[(l-LYS-d-ALA)₂-(l-THR-d-ALA)₂], containing THR-ALA-THR ice binding motifs. Using molecular dynamics simulations we investigate the stability of these cyclic peptides and their growth mechanism. Both nanotube sequences get more stable as a function of size. The relative stability of the AFCP sequence CPNT increases at sizes greater than a dimer by forming intermolecular THR side chain H-bonds. We find that, like the naturally occurring AF protein from spruce budworm (Choristoneura fumiferana), the THR distances of the AFCP's ice binding motif match the ice prism plane O-O distances, thus making the AFCP a suitable AF candidate. In addition, we investigated the nanotube growth process, i.e. the association/dissociation of a single CP to an existing AFCP nanotube, by Transition Path Sampling. We found a general dock-lock mechanism, in which a single CP first docks loosely before locking into place. Moreover, we identified several qualitatively different mechanisms for association, involving different metastable intermediates, including a state in which the peptide was misfolded inside the hydrophobic core of the tube. Finally, we find evidence for a mechanism involving non-specific association followed by 1D diffusion. Under most conditions, this will be the dominant pathway. The results yield insights into the mechanisms of peptide assembly, and might lead to an improved design of self-assembling antifreeze proteins.

Incorporating Fast Protein Dynamics into Enzyme Design: A Proposed Mutant Aromatic Amine Dehydrogenase

In recent years, there has been encouraging progress in the engineering of enzymes that are designed to catalyze reactions not accelerated by natural enzymes. We tested the possibility of reengineering an existing enzyme by introducing a fast protein motion that couples to the reaction. Aromatic amine dehydrogenase is a system that has been shown to use a fast substrate motion as part of the reaction mechanism. We identified a mutation that preserves this fast motion but also introduces a favorable fast motion near the active site that did not exist in the native enzyme. Transition path sampling was used for the analysis of the atomic details of the mechanism.

Combined probes of X-ray scattering and optical spectroscopy reveal how global conformational change is temporally and spatially linked to local structural perturbation in photoactive yellow protein

Real-time probing of structural transitions of a photoactive protein is challenging owing to the lack of a universal time-resolved technique that can probe the changes in both global conformation and light-absorbing chromophores of the protein. In this work, we combine time-resolved X-ray solution scattering (TRXSS) and transient absorption (TA) spectroscopy to investigate how the global conformational changes involved in the photoinduced signal transduction of photoactive yellow protein (PYP) is temporally and spatially related to the local structural change around the light-absorbing chromophore. In particular, we examine the role of internal proton transfer in developing a signaling state of PYP by employing its E46Q mutant (E46Q-PYP), where the internal proton transfer is inhibited by the replacement of a proton donor. The comparison of TRXSS and TA spectroscopy data directly reveals that the global conformational change of the protein, which is probed by TRXSS, is temporally delayed by tens of microseconds from the local structural change of the chromophore, which is probed by TA spectroscopy. The molecular shape of the signaling state reconstructed from the TRXSS curves directly visualizes the three-dimensional conformations of protein intermediates and reveals that the smaller structural change in E46Q-PYP than in wild-type PYP suggested by previous studies is manifested in terms of much smaller protrusion, confirming that the signaling state of E46Q-PYP is only partially developed compared with that of wild-type PYP. This finding provides direct evidence of how the environmental change in the vicinity of the chromophore alters the conformational change of the entire protein matrix.

Cooperativity and modularity in protein folding

A simple statistical mechanical model proposed by Wako and Saitô has explained the aspects of protein folding surprisingly well. This model was systematically applied to multiple proteins by Muñoz and Eaton and has since been referred to as the Wako-Saitô-Muñoz-Eaton (WSME) model. The success of the WSME model in explaining the folding of many proteins has verified the hypothesis that the folding is dominated by native interactions, which makes the energy landscape globally biased toward native conformation. Using the WSME and other related models, Saitô emphasized the importance of the hierarchical pathway in protein folding; folding starts with the creation of contiguous segments having a native-like configuration and proceeds as growth and coalescence of these segments. The Φ-values calculated for barnase with the WSME model suggested that segments contributing to the folding nucleus are similar to the structural modules defined by the pattern of native atomic contacts. The WSME model was extended to explain folding of multi-domain proteins having a complex topology, which opened the way to comprehensively understanding the folding process of multi-domain proteins. The WSME model was also extended to describe allosteric transitions, indicating that the allosteric structural movement does not occur as a deterministic sequential change between two conformations but as a stochastic diffusive motion over the dynamically changing energy landscape. Statistical mechanical viewpoint on folding, as highlighted by the WSME model, has been renovated in the context of modern methods and ideas, and will continue to provide insights on equilibrium and dynamical features of proteins.

Picosecond Photobiology: Watching a Signaling Protein Function in Real Time via Time-Resolved Small- and Wide-Angle X-ray Scattering

The capacity to respond to environmental changes is crucial to an organism's survival. Halorhodospira halophila is a photosynthetic bacterium that swims away from blue light, presumably in an effort to evade photons energetic enough to be genetically harmful. The protein responsible for this response is believed to be photoactive yellow protein (PYP), whose chromophore photoisomerizes from trans to cis in the presence of blue light. We investigated the complete PYP photocycle by acquiring time-resolved small and wide-angle X-ray scattering patterns (SAXS/WAXS) over 10 decades of time spanning from 100 ps to 1 s. Using a sequential model, global analysis of the time-dependent scattering differences recovered four intermediates (pR0/pR1, pR2, pB0, pB1), the first three of which can be assigned to prior time-resolved crystal structures. The 1.8 ms pB0 to pB1 transition produces the PYP signaling state, whose radius of gyration (Rg = 16.6 Å) is significantly larger than that for the ground state (Rg = 14.7 Å) and is therefore inaccessible to time-resolved protein crystallography. The shape of the signaling state, reconstructed using GASBOR, is highly anisotropic and entails significant elongation of the long axis of the protein. This structural change is consistent with unfolding of the 25 residue N-terminal domain, which exposes the β-scaffold of this sensory protein to a potential binding partner. This mechanistically detailed description of the complete PYP photocycle, made possible by time-resolved crystal and solution studies, provides a framework for understanding signal transduction in proteins and for assessing and validating theoretical/computational approaches in protein biophysics.

Transition-State Theory, Dynamics, and Narrow Time Scale Separation in the Rate-Promoting Vibrations Model of Enzyme Catalysis

The power of transition-state theory (TST) for understanding enzymes is evidenced by its recent use in the design and synthesis of highly active de novo enzymes. However, dynamics can influence reaction kinetics, and some studies of rate-promoting vibrations even claim that dynamical theories instead of TST are needed to understand enzymatic reaction mechanisms. For the rate-promoting vibration (RPV) model of enzyme catalysis [Antoniou et al., J. Chem. Phys. 2004, 121, 6442], a reactive flux correlation function analysis shows that dynamical effects do slow the kinetics. However, the RPV model also shows extremely long-lived correlations because the RPV and the bath are not directly coupled. Additionally, earlier studies of the RPV model show a narrow time scale separation due to a small 5kT barrier. Thus earlier findings based on the RPV model may have little bearing on the properties of real enzymes. The intrinsic reaction coordinate (IRC) reveals that the RPV is an important component of the reaction coordinate at early and late stages of the pathway, but the RPV is not an important component of the reaction coordinate direction at the transition state. The unstable eigenmode from harmonic TST (which coincides with the IRC at the saddle point) gives a larger transmission coefficient than the coordinate used in the correlation functions of Antoniou et al. Thus while TST cannot predict the transmission coefficient, the RPV model suggests that TST can provide mechanistic insights on elementary steps in enzyme catalysis. Finally, we propose a method for using the transition-state ensemble as predicted from harmonic TST to distinguish promoting vibrations from other more mundane bath variables.

Free energy landscape of activation in a signalling protein at atomic resolution

The interconversion between inactive and active protein states, traditionally described by two static structures, is at the heart of signaling. However, how folded states interconvert is largely unknown due to the inability to experimentally observe transition pathways. Here we explore the free energy landscape of the bacterial response regulator NtrC by combining computation and NMR, and discover unexpected features underlying efficient signaling. We find that functional states are defined purely in kinetic and not structural terms. The need of a well-defined conformer, crucial to the active state, is absent in the inactive state, which comprises a heterogeneous collection of conformers. The transition between active and inactive states occurs through multiple pathways, facilitated by a number of nonnative transient hydrogen bonds, thus lowering the transition barrier through both entropic and enthalpic contributions. These findings may represent general features for functional conformational transitions within the folded state.

Hierarchical Conformational Analysis of Native Lysozyme Based on Sub-Millisecond Molecular Dynamics Simulations

Hierarchical organization of free energy landscape (FEL) for native globular proteins has been widely accepted by the biophysics community. However, FEL of native proteins is usually projected onto one or a few dimensions. Here we generated collectively 0.2 milli-second molecular dynamics simulation trajectories in explicit solvent for hen egg white lysozyme (HEWL), and carried out detailed conformational analysis based on backbone torsional degrees of freedom (DOF). Our results demonstrated that at micro-second and coarser temporal resolutions, FEL of HEWL exhibits hub-like topology with crystal structures occupying the dominant structural ensemble that serves as the hub of conformational transitions. However, at 100ns and finer temporal resolutions, conformational substates of HEWL exhibit network-like topology, crystal structures are associated with kinetic traps that are important but not dominant ensembles. Backbone torsional state transitions on time scales ranging from nanoseconds to beyond microseconds were found to be associated with various types of molecular interactions. Even at nanoseconds temporal resolution, the number of conformational substates that are of statistical significance is quite limited. These observations suggest that detailed analysis of conformational substates at multiple temporal resolutions is both important and feasible. Transition state ensembles among various conformational substates at microsecond temporal resolution were observed to be considerably disordered. Life times of these transition state ensembles are found to be nearly independent of the time scales of the participating torsional DOFs.

Mapping allostery through computational glycine scanning and correlation analysis of residue-residue contacts

Understanding allosteric mechanisms is essential for the physical control of molecular switches and downstream cellular responses. However, it is difficult to decode essential allosteric motions in a high-throughput scheme. A general two-pronged approach to performing automatic data reduction of simulation trajectories is presented here. The first step involves coarse-graining and identifying the most dynamic residue-residue contacts. The second step is performing principal component analysis of these contacts and extracting the large-scale collective motions expressed via these residue-residue contacts. We demonstrated the method using a protein complex of nuclear receptors. Using atomistic modeling and simulation, we examined the protein complex and a set of 18 glycine point mutations of residues that constitute the binding pocket of the ligand effector. The important motions that are responsible for the allostery are reported. In contrast to conventional induced-fit and lock-and-key binding mechanisms, a novel "frustrated-fit" binding mechanism of RXR for allosteric control was revealed.

The water-catalyzed mechanism of the ring-opening reaction of glucose

The transition path sampling simulations of the water-assisted ring-opening reaction of α- and β-glucose anomers allow us to elucidate the molecular details of the process.

Multiscale approach to the determination of the photoactive yellow protein signaling state ensemble

The nature of the optical cycle of photoactive yellow protein (PYP) makes its elucidation challenging for both experiment and theory. The long transition times render conventional simulation methods ineffective, and yet the short signaling-state lifetime makes experimental data difficult to obtain and interpret. Here, through an innovative combination of computational methods, a prediction and analysis of the biological signaling state of PYP is presented. Coarse-grained modeling and locally scaled diffusion map are first used to obtain a rough bird's-eye view of the free energy landscape of photo-activated PYP. Then all-atom reconstruction, followed by an enhanced sampling scheme; diffusion map-directed-molecular dynamics are used to focus in on the signaling-state region of configuration space and obtain an ensemble of signaling state structures. To the best of our knowledge, this is the first time an all-atom reconstruction from a coarse grained model has been performed in a relatively unexplored region of molecular configuration space. We compare our signaling state prediction with previous computational and more recent experimental results, and the comparison is favorable, which validates the method presented. This approach provides additional insight to understand the PYP photo cycle, and can be applied to other systems for which more direct methods are impractical.

Many protein systems of biological interest undergo dynamical changes on a time scale too long to be modeled using standard computational methods. One example is photoactive yellow protein (PYP), found in several bacterial species. Blue light, potentially harmful for DNA, triggers several structural changes in PYP, eventually resulting in a conformation that changes the swimming behavior of bacteria. This conformation is difficult to investigate, as it is too short lived. In addition, understanding this “signaling state” is computationally difficult because of the long timescale of the transition. We overcome this by constructing a coarse-grained model to rapidly induce transitions to the signaling state. We then reconstruct and further sample the all-atom configurations from these coarse-grained representations. Our results are consistent with all available experimental and computational evidence.

Thermodynamics of Deca-alanine Folding in Water

The determination of the folding dynamics of polypeptides and proteins is critical in characterizing their functions in biological systems. Numerous computational models and methods have been developed for studying structure formation at the atomic level. Due to its small size and simple structure, deca-alanine is used as a model system in molecular dynamics (MD) simulations. The free energy of unfolding in vacuum has been studied extensively using the end-to-end distance of the peptide as the reaction coordinate. However, few studies have been conducted in the presence of explicit solvent. Previous results show a significant decrease in the free energy of extended conformations in water, but the α-helical state is still notably favored over the extended state. Although sufficient in vacuum, we show that end-to-end distance is incapable of capturing the full complexity of deca-alanine folding in water. Using α-helical content as a second reaction coordinate, we deduce a more descriptive free-energy landscape, one which reveals a second energy minimum in the extended conformations that is of comparable free energy to the α-helical state. Equilibrium simulations demonstrate the relative stability of the extended and α-helical states in water as well as the transition between the two states. This work reveals both the necessity and challenge of determining a proper reaction coordinate to fully characterize a given process.

Recent developments in methods for identifying reaction coordinates

In the study of rare events in complex systems with many degrees of freedom, a key element is to identify the reaction coordinates of a given process. Over recent years, a number of methods and protocols have been developed to extract the reaction coordinates based on limited information from molecular dynamics simulations. In this review, we provide a brief survey over a number of major methods developed in the past decade, some of which are discussed in greater detail, to provide an overview of the problems that are partially solved and challenges that still remain. A particular emphasis has been placed on methods for identifying reaction coordinates that are related to the committor.

The dynamics of the conformational changes in the hexopyranose ring: a transition path sampling approach

The transition paths corresponding to the conformational rearrangements in the ring of hexapyranose (α-d- and β-d-glucose) molecules were described by applying the transition path sampling method.

A comprehensive study of isomerization and protonation reactions in the photocycle of the photoactive yellow protein

A comprehensive picture of the overall photocycle was obtained to reveal a wide range of structural signals in the photoactive yellow protein.

Allosteric activation transitions in enzymes and biomolecular motors: insights from atomistic and coarse-grained simulations

The chemical step in enzymes is usually preceded by a kinetically distinct activation step that involves large-scale conformational transitions. In "simple" enzymes this step corresponds to the closure of the active site; in more complex enzymes, such as biomolecular motors, the activation step is more complex and may involve interactions with other biomolecules. These activation transitions are essential to the function of enzymes and perturbations in the scale and/or rate of these transitions are implicated in various serious human diseases; incorporating key flexibilities into engineered enzymes is also considered a major remaining challenge in rational enzyme design. Therefore it is important to understand the underlying mechanism of these transitions. This is a significant challenge to both experimental and computational studies because of the allosteric and multi-scale nature of such transitions. Using our recent studies of two enzyme systems, myosin and adenylate kinase (AK), we discuss how atomistic and coarse-grained simulations can be used to provide insights into the mechanism of activation transitions in realistic systems. Collectively, the results suggest that although many allosteric transitions can be viewed as domain displacements mediated by flexible hinges, there are additional complexities and various deviations. For example, although our studies do not find any evidence for "cracking" in AK, our results do underline the contribution of intra-domain properties (e.g., dihedral flexibility) to the rate of the transition. The study of mechanochemical coupling in myosin highlights that local changes important to chemistry require stabilization from more extensive structural changes; in this sense, more global structural transitions are needed to activate the chemistry in the active site. These discussions further emphasize the importance of better understanding factors that control the degree of co-operativity for allosteric transitions, again hinting at the intimate connection between protein stability and functional flexibility. Finally, a number of topics of considerable future interest are briefly discussed.

Protein dynamics and the enzymatic reaction coordinate

This chapter discusses progress over the past 15 years in understanding the role of protein dynamics in enzymatically catalyzed chemical reactions. Research has shown that protein motion on all timescales from femtoseconds to milliseconds can contribute to function, and in particular in some enzymes there are sub-picosecond motions, on the same timescale as barrier passage, the couple directly to chemical transformation, and are thus part of the reaction coordinate. Approaches such as transition path sampling and committor analysis have greatly enhanced our understanding of these processes.

Network approach to identify the folding transition states of peptides and proteins

Folding transition states and their structures are crucial in understanding protein folding pathways and folding dynamics. As they cannot be detected directly by experiments due to their instability, many computational methods have been proposed to solve this problem. However, each of these methods can give only one part of the transition state ensemble for a peptide or protein. Here we present a folding-network approach to identify the transition states of peptides or proteins and test it on the β-hairpin peptide trpzip2, with the result that we identify all the folding transition states of tripzip2, which may only be determined separately by other methods. This suggests that the network approach can provide more complete information about the folding transition states, at least for peptides.

Elucidating the locking mechanism of peptides onto growing amyloid fibrils through transition path sampling

We investigate the molecular mechanism of monomer addition to a growing amyloid fibril composed of the main amyloidogenic region from the insulin peptide hormone, the LVEALYL heptapeptide. Applying transition path sampling in combination with reaction coordinate analysis reveals that the transition from a docked peptide to a locked, fully incorporated peptide can occur in two ways. Both routes involve the formation of backbone hydrogen bonds between the three central amino acids of the attaching peptide and the fibril, as well as a reorientation of the central Glu side chain of the locking peptide toward the interface between two β-sheets forming the fibril. The mechanisms differ in the sequence of events. We also conclude that proper docking is important for correct alignment of the peptide with the fibril, as alternative pathways result in misfolding.

Protein conformational switches: from nature to design

Protein conformational switches alter their shape upon receiving an input signal, such as ligand binding, chemical modification, or change in environment. The apparent simplicity of this transformation--which can be carried out by a molecule as small as a thousand atoms or so--belies its critical importance to the life of the cell as well as its capacity for engineering by humans. In the realm of molecular switches, proteins are unique because they are capable of performing a variety of biological functions. Switchable proteins are therefore of high interest to the fields of biology, biotechnology, and medicine. These molecules are beginning to be exploited as the core machinery behind a new generation of biosensors, functionally regulated enzymes, and "smart" biomaterials that react to their surroundings. As inspirations for these designs, researchers continue to analyze existing examples of allosteric proteins. Recent years have also witnessed the development of new methodologies for introducing conformational change into proteins that previously had none. Herein we review examples of both natural and engineered protein switches in the context of four basic modes of conformational change: rigid-body domain movement, limited structural rearrangement, global fold switching, and folding-unfolding. Our purpose is to highlight examples that can potentially serve as platforms for the design of custom switches. Accordingly, we focus on inducible conformational changes that are substantial enough to produce a functional response (e.g., in a second protein to which it is fused), yet are relatively simple, structurally well-characterized, and amenable to protein engineering efforts.