Single molecule conformational dynamics of adenylate kinase: energy landscape, structural correlations, and transition state ensembles

We developed a coarse grained two-well model to study the single molecule protein conformational dynamics in microscopic detail at the residue level, overcoming the often encountered computational bottleneck. In particular, we explored the underlying conformational energy landscape of adenylate kinase, a crucial protein for signal transduction in the cell, and identified two major kinetic pathways for the conformational switch between open and closed states through either the intermediate state or the transient state. Based on the parameters fitted to the room-temperature experimental data, we predicted open and closed kinetic rates at the whole temperature ranges from 10 to 50 degrees C, which agree well with the experimental turnover numbers. After uncovering the underlying mechanism for conformational dynamics and exploring the structural correlations, we found the crucial dynamical interplay between the nucleoside monophosphate binding domain (NMP) and the ATP-binding domain (LID) in controlling the conformational switch. The key residues and contacts responsible for the conformational transitions are identified by following the time evolution of the two-dimensional spatial contact maps and characterizing the transition state as well as intermediate structure ensembles through phi value analysis. Our model provides a general framework to study the conformational dynamics of biomolecules and can be applied to many other systems.     

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.     

Dominant folding pathways of a peptide chain from ab initio quantum-mechanical simulations

Using the dominant reaction pathways method, we perform an ab initio quantum-mechanical simulation of a conformational transition of a peptide chain. The method we propose makes it possible to investigate the out-of-equilibrium dynamics of these systems, without resorting to an empirical representation of the molecular force field. It also allows to study rare transitions involving rearrangements in the electronic structure. By comparing the results of the ab initio simulation with those obtained by employing a standard force field, we discuss its capability to describe the nonequilibrium dynamics of conformational transitions.     

Conformational maps of medium-sized rings

A graphical method of quantitative conformational analysis of medium-sized rings that unites earlier concepts is proposed. This method was used to obtain conformational maps of 6–8-membered rings that make it possible to unequivocally determine the conformations of real rings and to show all possible pathways of conformational transitions without depiction of the individual conformations. This approach made it possible to ascertain previously unknown conformations and pathways of conformational transitions.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 542–559, April, 1988.     

Flexibility of enzymatic transitions as a hallmark of optimized enzyme steady-state kinetics and thermodynamics

We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.     

Insights into the dynamics of HIV-1 protease: a kinetic network model constructed from atomistic simulations

The conformational dynamics in the flaps of HIV-1 protease plays a crucial role in the mechanism of substrate binding. We develop a kinetic network model, constructed from detailed atomistic simulations, to determine the kinetic mechanisms of the conformational transitions in HIV-1 PR. To overcome the time scale limitation of conventional molecular dynamics (MD) simulations, our method combines replica exchange MD with transition path theory (TPT) to study the diversity and temperature dependence of the pathways connecting functionally important states of the protease. At low temperatures the large-scale flap opening is dominated by a small number of paths; at elevated temperatures the transition occurs through many structurally heterogeneous routes. The expanded conformation in the crystal structure 1TW7 is found to closely mimic a key intermediate in the flap-opening pathways at low temperature. We investigated the different transition mechanisms between the semi-open and closed forms. The calculated relaxation times reveal fast semi-open ? closed transitions, and infrequently the flaps fully open. The ligand binding rate predicted from this kinetic model increases by 38-fold from 285 to 309 K, which is in general agreement with experiments. To our knowledge, this is the first application of a network model constructed from atomistic simulations together with TPT to analyze conformational changes between different functional states of a natively folded protein.     

Diverse polymorphism of G-quadruplexes as a kinetic phenomenon

Knowledge of forces that drive conformational transitions of G-quadruplexes is crucial for understanding the molecular basis of several key cellular processes. It can only be acquired by combining structural, thermodynamic and kinetic information. Existing biophysical and structural evidences on polymorphism of intermolecular G-quadruplexes have shown that the formation of a number of these structures is a kinetically controlled process. Reported kinetic models that have been used to describe the association of single strands into quadruplex structures seem to be inappropriate since the corresponding model-predicted activation energies turn out to be negative. By contrast, we propose here a novel kinetic model that successfully describes experimentally monitored folding/unfolding transitions of G-quadruplexes and gives positive activation energies for all elementary steps, including those describing association of two single strands into bimolecular quadruplex structures. It is based on a combined thermodynamic and kinetic investigation of polymorphic behavior of bimolecular G-quadruplexes formed from d(G4T4G4) and d(G4T4G3) strands in the presence of Na(+) ions, monitored by spectroscopic (UV, CD) and calorimetric (DSC) techniques. According to our experiment and model analysis the topology of the measured G-quadruplexes is clearly flexible with the conformational forms that respond to the rate of temperature change at which global unfolding/folding transitions occur.     

Determination of the activation energy of chlorocyclohexane conformational transitions by infrared spectra

Chlorocyclohexane is used to demonstrate that it is possible to determine the height of the barrier between conformational isomers by following the kinetics of conformational transitions by infrared spectra. For this, crystallization of the sample has to be prevented by a suitable solvent.     

Physical mechanisms and biological significance of supramolecular protein self-assembly

In living cells, chemical reactions of metabolism, information processing, growth and development are organized in a complex network of interactions. At least in part, the organization of this network is accomplished as a result of physical assembly by supramolecular scaffolds. Indeed, most proteins function in cells within the context of multimeric or supramolecular assemblies. With the increasing availability of atomic structures and molecular thermodynamics, it is possible to recast the problem of non-covalent molecular self-assembly from a unified perspective of structural thermodynamics and kinetics. Here, we present a generalized theory of self-assembly based on Wegner's kinetic model and use it to delineate three physical mechanisms of self-assembly: as limited by association of assembly units (nucleation), by association of monomers (isodesmic), and by conformational reorganization of monomers that is coupled to assembly (conformational). Thus, we discuss actin, tubulin, clathrin, and the capsid of icosahedral cowpea chlorotic mottle virus with respect to assembly of architectural scaffolds that perform largely mechanical functions, and pyruvate dehydrogenase, and RING domain proteins PML, arenaviral Z, and BRCA1:BARD1 with regard to assembly of supramolecular enzymes with metabolic and chemically directive functions. In addition to the biological functions made possible by supramolecular self-assembly, such as mesoscale mechanics of architectural scaffolds and metabolic coupling of supramolecular enzymes, we show that the physical mechanisms of self-assembly and their structural bases are biologically significant as well, having regulatory roles in both formation and function of the assembled structures in health and disease.     

The application of quantum chemistry and condensed matter theory in studying amino-acids, protein folding and anticancer drug technology

The adaptation of methods from quantum chemistry and condensed matter theory for studying biological molecules has proved fruitful in developing our understanding of the electronic and conformational structure and thereby the functionality of amino-acids and proteins. Professor Suhai has been at the forefront of these developments and has made contributions in many areas of this vast field of research. In this article, we focus on three such areas, namely, (1) amino acids, (2) bacteriorhodopsin and (3) anti-cancer drugs involving especially Ru and Rh. We show how advances in density functional theory (DFT) have been used to calculate the electronic structure and density in amino-acids so that they can be compared with X-ray diffraction studies. We also demonstrate how ideas from the theory of phase transitions in condensed matter may be applied for studying phase transitions in bacteriorhodopsin, DNA and proteins. Finally, we highlight some of the recent work done in bringing DFT together with quantum chemistry modelling in studying metallopharmaceutical complexes and conformations of peptides.     

A skewed-momenta method to efficiently generate conformational-transition trajectories

We present a novel computational method, the skewed-momenta method (Skew'M), which applies a bias to the Maxwell distribution of initial momenta used to generate ensembles of trajectories. As a result, conformational transitions are accentuated and kinetic properties are calculated more effectively. The connection to the related puddle jumping method is discussed. A reweighting scheme permits the exact calculation of kinetic properties. Applications are presented for the rapid calculation of rate constants for molecular isomerization, and for the efficient reconstruction of free-energy profiles using a straightforward modification of the Jarzynski identity.     

Conformational ensembles and sampled energy landscapes: Analysis and comparison

We present novel algorithms and software addressing four core problems in computational structural biology, namely analyzing a conformational ensemble, comparing two conformational ensembles, analyzing a sampled energy landscape, and comparing two sampled energy landscapes. Using recent developments in computational topology, graph theory, and combinatorial optimization, we make two notable contributions. First, we present a generic algorithm analyzing height fields. We then use this algorithm to perform density‐based clustering of conformations, and to analyze a sampled energy landscape in terms of basins and transitions between them. In both cases, topological persistence is used to manage (geometric) frustration. Second, we introduce two algorithms to compare transition graphs. The first is the classical earth mover distance metric which depends only on local minimum energy configurations along with their statistical weights, while the second incorporates topological constraints inherent to conformational transitions. Illustrations are provided on a simplified protein model (BLN69), whose frustrated potential energy landscape has been thoroughly studied. The software implementing our tools is also made available, and should prove valuable wherever conformational ensembles and energy landscapes are used. © 2015 Wiley Periodicals, Inc.     

Artificial Accelerators of the Molecular Chaperone Hsp90 Facilitate Rate‐Limiting Conformational Transitions

The molecular chaperone Hsp90 undergoes an ATP‐driven cycle of conformational changes in which large structural rearrangements precede ATP hydrolysis. Well‐established small‐molecule inhibitors of Hsp90 compete with ATP‐binding. We wondered whether compounds exist that can accelerate the conformational cycle. In a FRET‐based screen reporting on conformational rearrangements in Hsp90 we identified compounds. We elucidated their mode of action and showed that they can overcome the intrinsic inhibition in Hsp90 which prevents these rearrangements. The mode of action is similar to that of the co‐chaperone Aha1 which accelerates the Hsp90 ATPase. However, while the two identified compounds influence conformational changes, they target different aspects of the structural transitions. Also, the binding site determined by NMR spectroscopy is distinct. This study demonstrates that small molecules are capable of triggering specific rate‐limiting transitions in Hsp90 by mechanisms similar to those in protein cofactors.     

Crowding alters the folding kinetics of a β-hairpin by modulating the stability of intermediates

Crowded environments inside cells exert significant effects on protein structure, stability, and function, but their effects on (pre)folding dynamics and kinetics, especially at molecular levels, remain ill-understood. Here, we examine the latter for, as an initial candidate, a small de novo β-hairpin using extensive all-atom molecular dynamics simulations for crowder volume fractions φ up to 40%. We find that crowding does not introduce new folding intermediates or misfolded structures, although, as expected, it promotes compact structures and reduces the accessible conformational space. Furthermore, while hydrophobic-collapse-mediated folding is slightly enhanced, the turn-directed zipper mechanism (dominant in crowder-free situations) increases many-fold, becoming even more dominant. Interestingly, φ influences the stability of the folding intermediates (FI(1) and FI(2)) in an apparently counterintuitive manner, which can be understood only by considering specific intrachain interactions and intermediate (and hierarchical) structural transitions. For φ values <20%, native-turn formation is enhanced, and FI(1), characterized by a hairpin structure but slightly mismatched hydrophobic contacts, increases in frequency, thus enhancing eventual folding. However, higher φ values impede native-turn formation, and FI(2), which lacks native turns, re-emerges and increasingly acts as a kinetic trap. The change in the stability of these intermediates with φ strongly correlates with the hierarchical folding stages and their kinetics. The results show that crowding assists intermediate structural changes more by impeding backward transitions than by promoting forward transitions and that a delicate competition between reduction in configuration space and introduction of kinetic traps along the folding route is key to understanding folding kinetics under crowded conditions.     

The enhanced extended phenomenological kinetics method to deal with timescale disparity problem among different reaction pathways

Kinetic Monte Carlo method can provide valuable mechanistic insights for catalytic systems. Nonetheless, it suffers from the notorious problem of timescale disparity due to the existence of the complex catalytic network that consists of fast events and slow events. Previously, we have proposed the extended phenomenological kinetics (XPK) method that effectively deals with the timescale disparity problem between diffusion and reaction. However, it remains a great challenge to simulate systems with timescale disparity among different reaction pathways, which is important when selectivity is the major concern. In this study, we implement the enhanced XPK method to address this problem. The new algorithm works by identifying states connected through fast transitions and compressing them into a “superstate” when the chosen states satisfy a local steadystate condition. This state compression algorithm simplifies the reaction network by concealing the fast transitions. The accuracy and efficiency of the algorithm are demonstrated by two model systems: selective catalytic hydrogenation and selective catalytic decomposition. The enhanced XPK method is expected to be beneficial to the kinetic simulations of catalytic systems, especially those with complex reaction networks.     

Permeation and gating in proteins: kinetic Monte Carlo reaction path following

We present a new Monte Carlo technique, kinetic Monte Carlo reaction path following (kMCRPF), for the computer simulation of permeation and large-scale gating transitions in protein channels. It combines ideas from Metropolis Monte Carlo (MMC) and kinetic Monte Carlo (kMC) algorithms, and is particularly suitable when a reaction coordinate is well defined. Evolution of transition proceeds on the reaction coordinate by small jumps (kMC technique) toward the nearest lowest-energy uphill or downhill states, with the jumps thermally activated (constrained MMC). This approach permits navigation among potential minima on an energy surface, finding the minimum-energy paths and determining their associated free-energy profiles. The methodological and algorithmic strategies underlying the kMCRPF method are described. We have tested it using an analytical model and applied it to study permeation through the curvilinear ClC chloride and aquaporin pores and to gating in the gramicidin A channel. These studies of permeation and gating in real proteins provide extensive procedural tests of the method.     

Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics

Parallel tempering (PT) molecular dynamics simulations have been extensively investigated as a means of efficient sampling of the configurations of biomolecular systems. Recent work has demonstrated how the short physical trajectories generated in PT simulations of biomolecules can be used to construct the Markov models describing biomolecular dynamics at each simulated temperature. While this approach describes the temperature-dependent kinetics, it does not make optimal use of all available PT data, instead estimating the rates at a given temperature using only data from that temperature. This can be problematic, as some relevant transitions or states may not be sufficiently sampled at the temperature of interest, but might be readily sampled at nearby temperatures. Further, the comparison of temperature-dependent properties can suffer from the false assumption that data collected from different temperatures are uncorrelated. We propose here a strategy in which, by a simple modification of the PT protocol, the harvested trajectories can be reweighted, permitting data from all temperatures to contribute to the estimated kinetic model. The method reduces the statistical uncertainty in the kinetic model relative to the single temperature approach and provides estimates of transition probabilities even for transitions not observed at the temperature of interest. Further, the method allows the kinetics to be estimated at temperatures other than those at which simulations were run. We illustrate this method by applying it to the generation of a Markov model of the conformational dynamics of the solvated terminally blocked alanine peptide.     

Perspective: pre-chemistry conformational changes in DNA polymerase mechanisms

In recent papers, there has been a lively exchange concerning theories for enzyme catalysis, especially the role of protein dynamics/pre-chemistry conformational changes in the catalytic cycle of enzymes. Of particular interest is the notion that substrate-induced conformational changes that assemble the polymerase active site prior to chemistry are required for DNA synthesis and impact fidelity (i.e., substrate specificity). High-resolution crystal structures of DNA polymerase β representing intermediates of substrate complexes prior to the chemical step are available. These structures indicate that conformational adjustments in both the protein and substrates must occur to achieve the requisite geometry of the reactive participants for catalysis. We discuss computational and kinetic methods to examine possible conformational change pathways that lead from the observed crystal structure intermediates to the final structures poised for chemistry. The results, as well as kinetic data from site-directed mutagenesis studies, are consistent with models requiring pre-chemistry conformational adjustments in order to achieve high fidelity DNA synthesis. Thus, substrate-induced conformational changes that assemble the polymerase active site prior to chemistry contribute to DNA synthesis even when they do not represent actual rate-determining steps for chemistry.