Detecting Functional Dynamics in Proteins with Comparative Perturbed-Ensembles Analysis.

The ability to perform long, accurate molecular dynamics (MD) simulations involving proteins and other biological macromolecules could in principle lead to important scientific advances and provide a powerful new tool for drug discovery. A wide range of biologically interesting phenomena, however, occur over time scales on the order of a millisecond - several orders of magnitude beyond the duration of the longest current MD simulations. Our research group is currently building a specialized, massively parallel machine, called Anton, which should soon be capable of executing millisecond-scale MD simulations of proteins at an atomic level of detail. Antonpsilas highly accelerated execution of such simulations is attributable in large part to specialized logic for the high-speed calculation of pairwise interactions between particles and/or gridpoints separated by no more than some specified cutoff radius.In particular, each of Anton's 512 ASICs, which are implemented using 90-nm technology,includes a "high-throughput interaction subsystem" incorporating 32 highly specialized pipelines running at 800 MHz. During every cycle, each of these pipelines produces a pairwise-interaction result that would require approximately 50 arithmetic operations to calculate on a general-purpose processor. Novel algorithms and architectural features are used to greatly reduce the requirements for inter- and intra-chip communication, allowing Anton to feed these pipelines and collect their results at a speed sufficient to take advantage of the machine's computational power. The ASIC also includes a "flexible subsystem" based on eight programmable "geometry cores", each containing eight arithmetic pipelines. This talk will provide an overview of our work on parallel algorithms and machine architectures for high-speed MD simulation, with special attention to the respective roles of specialized vs. general-purpose hardware, and to the techniques used to minimize communication at various levels within the system.

Proteins are essential units of life that govern several functions. Understanding their behavior is closely related to their conformations, native folds, and change in conformations. Thus, the dynamic information of protein becomes essential to understand its properties at the molecular level. The molecular dynamics (MD) simulation approach provides atomistic-level dynamic information about proteins. However, more extended or complex MD simulations of protein are challenging to analyze and to gather meaningful confirmation from several snapshots of the dynamic system. To achieve it, i.e., analyzing MD simulation data, Markov State Model (MSM) is a powerful tool that has a statistical background. It represents the MD simulation system as a combination of finite memoryless states, i.e., states that are not dependent on prior states and transition probability among such states. MSM applications have grown from peptides to membrane protein simulations. The present book chapter sheds light on MD simulation’s role in protein dynamics and why MSM is required. The brief theoretical aspects of MSM techniques are demonstrated. Lastly, the chapter discusses the application of MSM in different protein folding and dynamics.

The term molecular mechanics (MM) refers to the use of simple potential-energy functions (e.g., harmonic oscillator or Coulombic potentials) to model molecular systems. Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, and ligand-docking simulations. Typically, molecular mechanics models consist of spherical atoms connected by springs which represent bonds. Internal forces experienced in the model structure are described using simple mathematical functions. For example, Hooke’s law is commonly used to describe bonded interactions, and the nonbonded atoms might be treated as inelastic hard spheres or may interact according to a Lennard-Jones potential. Using these simple models, a molecular dynamics simulation numerically solves Newton’s equations of motion, thus allowing structural fluctuations to be observed with respect to time. Dynamic simulation methods are widely used to obtain information on the time evolution of conformations of proteins and other biological macromolecules1–4 and also kinetic and thermodynamic information. Simulations can provide fine detail concerning the motions of individual particles as a function of time. They can be utilized to quantify the properties of a system at a precision and on a time scale that is otherwise inaccessible, and simulation is, therefore, a valuable tool in extending our understanding of model systems. Theoretical consideration of a system additionally allows one to investigate the specific contributions to a property through “computational alchemy”,5 that is, modifying the simulation in a way that is nonphysical but nonetheless allows a model’s characteristics to be probed. One particular example is the artificial conversion of the energy function from that representing one system to that of another during a simulation. This is an important technique in free-energy calculations.6 Thus, molecular dynamics simulations, along with a range of complementary computational approaches, have become valuable tools for investigating the basis of protein structure and function. This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool. This review then covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role. The range of studies in which MD has played a considerable or pivotal role is immense, and this review cannot do justice to them; MD simulations of biomedical importance were recently reviewed.4 Particular emphasis will be placed on the study of dynamic aspects of protein recognition, an area where molecular dynamics has scope to provide broad and far-ranging insights. This review concludes with a brief discussion of the future potential offered to advancement of the biological and biochemical sciences and the remaining issues that must be overcome to allow the full extent of this potential to be realized. 1.1. Historical Background MD methods were originally conceived within the theoretical physics community during the 1950s. In 1957, Alder and Wainwright7 performed the earliest MD simulation using the so-called hard-sphere model, in which the atoms interacted only through perfect collisions. Rahman8 subsequently applied a smooth, continuous potential to mimic real atomic interactions. During the 1970s, as computers became more widespread, MD simulations were developed for more complex systems, culminating in 1976 with the first simulation of a protein9,10 using an empirical energy function constructed using physics-based first-principles assumptions. MD simulations are now widely and routinely applied and especially popular in the fields of materials science11,12 and biophysics. As will be discussed later in this review, a variety of experimental conditions may be simulated with modern theories and algorithms. The initial simulations only considered single molecules in vacuo. Over time, more realistic or at least biologically relevant simulations could be performed. This trend is continuing today. The initial protein MD simulation, of the small bovine pancreatic trypsin inhibitor (BPTI), covered only 9.2 ps of simulation time. Modern simulations routinely have so-called equilibration periods much longer than that, and production simulations of tens of nanoseconds are routine, with the first microsecond MD simulation being reported in 1998.13 In addition, the original BPTI simulation included only about 500 atoms rather than the 104-106 atoms that are common today. While much of this advancement results from an immense increase in availability of computing power, major theoretical and methodological developments also contribute significantly. The number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. A single review cannot do justice to the recent applications of MD. Using data from ISI Web of Science, the authors estimate that during 2005 at least 800 articles will be published that discuss molecular dynamics and proteins. The historical counts are shown in Figure 1. Open in a separate window Figure 1 Articles matching ISI Web of Science query “TS=(protein) AND TS=(molecular dynamics)”.

Protein Dynamics at the Picosecond-Nanosecond Time Scale: a Complementary Study by Dielectric Spectroscopy, Neutron Spectroscopy and MD Simulation

Atomistic details of protein dynamics and the role of hydration water

We present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical molecular-dynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A so-called fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a soluble protein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method.

Protein dynamics is a manifestation of the complex trajectories of these biomolecules on a multidimensional rugged potential energy surface (PES) driven by thermal energy. At present, computational methods such as atomistic molecular dynamics (MD) simulations can describe thermal protein conformational changes in fully solvated environments over millisecond timescales. Despite these advances, a quantitative assessment of protein dynamics remains a complicated topic, intricately linked to issues such as sampling convergence and the identification of appropriate reaction coordinates/structural features to describe protein conformational states and motions. Here, we present the cumulative variance of atomic coordinate fluctuations (CVCF) along trajectories as an intuitive PES sensitive metric to assess both the extent of sampling and protein dynamics captured in MD simulations. We first examine the sampling problem in model one- (1D) and two-dimensional (2D) PES to demonstrate that the CVCF when traced as a function of the sampling variable (time in MD simulations) can identify local and global equilibria. Further, even far from global equilibrium, a situation representative of standard MD trajectories of proteins, the CVCF can distinguish different PES and therefore resolve the resultant protein dynamics. We demonstrate the utility of our CVCF analysis by applying it to distinguish the dynamics of structurally homologous proteins from the ubiquitin family (ubiquitin, SUMO1, SUMO2) and ubiquitin protein-protein interactions. Our CVCF analysis reveals that differential side-chain dynamics from the structured part of the protein (the conserved β-grasp fold) present distinct protein PES to distinguish ubiquitin from SUMO isoforms. Upon binding to two functionally distinct protein partners (UBCH5A and UEV), intrinsic ubiquitin dynamics changes to reflect the binding context even though the two proteins have similar binding modes, which lead to negligible (sub-angstrom scale) structural changes.

Dynamical structures of intrinsically disordered proteins (IDPs) and multi-domain proteins that include large ID regions between the domains are unable to be determined by such conventional methods as X-ray crystallography and electron microscopy. Small-angle X-ray scattering (SAXS) is suitable to determine low-resolution structures of proteins and protein complexes in solution, but the structural data on protein dynamics are averaged over the structural ensemble in protein solution. To overcome this problem, we have developed a novel method, named MD-SAXS, of the combined use of SAXS and molecular dynamics (MD) simulation to analyze protein dynamics in solution of multi-subunit protein complexes and multi-domain proteins toward the structural characterization of IDPs. Here we show validity of the method through the structural characterization of restriction Endonuclease EcoO109I.

Molecular dynamics (MD) simulation is a rigorous theoretical tool that when used efficiently could provide reliable answers to questions pertaining to the structure-function relationship of proteins. Data collated from protein dynamics can be translated into useful statistics that can be exploited to sieve thermodynamics and kinetics crucial for the elucidation of mechanisms responsible for the modulation of biological processes such as protein-ligand binding and protein-protein association. Continuous modernization of simulation tools enables accurate prediction and characterization of the aforementioned mechanisms and these qualities are highly beneficial for the expedition of drug development when effectively applied to structure-based drug design (SBDD). In this review, current all-atom MD simulation methods, with focus on enhanced sampling techniques, utilized to examine protein structure, dynamics, and functions are discussed. This review will pivot around computer calculations of protein-ligand and protein-protein systems with applications to SBDD. In addition, we will also be highlighting limitations faced by current simulation tools as well as the improvements that have been made to ameliorate their efficiency.

Molecular dynamics simulations of intrinsically disordered protein regions enable biophysical interpretation of variant effect predictors.

Molecular Dynamics (MD) simulation of biomolecules provides important insights into conformational changes and dynamic behavior, revealing critical information about folding and interactions with other molecules. The collection of simulations stored in computers across the world holds immense potential to serve as training data for future Machine Learning models that will transform the prediction of structure, dynamics, drug interactions, and more. Ideally, there should exist an open access repository that enables scientists to submit and store their MD simulations of proteins and protein-drug interactions, and to find, retrieve, analyze, and visualize simulations produced by others. However, despite the ubiquity of MD simulation in structural biology, no such repository exists; as a result, simulations are instead stored in scattered locations without uniform metadata or access protocols. Here, we introduce MDRepo, a robust infrastructure that provides a relatively simple process for standardized community contribution of simulations, activates common downstream analyses on stored data, and enables search, retrieval, and visualization of contributed data. MDRepo is built on top of the open-source CyVerse research cyber-infrastructure, and is capable of storing petabytes of simulations, while providing high bandwidth upload and download capabilities and laying a foundation for cloud-based access to its stored data.

Hydrogen deuterium exchange mass spectrometry (HDX-MS) is a powerful technique for studying protein dynamics, which is an important factor governing protein functions. However, the process of hydrogen/deuterium exchange (HDX) of proteins is highly complex and the underlying mechanism has not yet been fully elucidated. Meanwhile, molecular dynamics (MD) simulation is a computational technique that can be used to elucidate HDX behaviour on proteins and facilitate interpretation of HDX-MS data. This article aims to summarize the current understandings on the mechanism of HDX and its correlation with MD simulation, to discuss the recent developments in the techniques of HDX-MS and MD simulation and to extend the perspectives of these two techniques in protein dynamics study.

Sphingosine kinase 1 (SPhK1) is a crucial signaling enzyme involved in cell proliferation, cellular survival, stimulation of angiogenesis, and apoptosis prevention. Recently, we have reported the unfolding kinetics of SPhK1 using molecular dynamics (MD) simulation, circular dichroism, and fluorescence spectroscopy. We found that SPhK1 showed a biphasic unfolding with an intermediate state (~ 4.0 M urea). We aim to understand the impact of MD simulation duration on the structure, function, and dynamics of proteins. In order to get deeper insights into the folding mechanism, an extended MD simulation is required. Here, we extended the MD simulations time scale from 100 to 300 ns on SPhK1 at increasing urea concentration to explore structural changes in the SPhK1. The results suggested a constant form of the unfolding of SPhK1 upon extending the simulation time scale at different urea concentrations. Furthermore, we showed step by step unfolding and percentage of secondary structure contents in SPhK1 under the influence of urea at each concentration. The results from the current work revealed a uniform pattern of the SPhK1 unfolding at different urea concentrations. This study provides deeper mechanistic insights into the urea-induced denaturation of SPhK1.

In the previous chapter, we saw that protein dynamics is a major candidate to explain the structure-function relationship. Experimental techniques, such as X-ray crystallography and Nuclear Magnetic Resonance (NMR), have become very powerful nowadays in providing accurate descriptions of the three-dimensional protein structure. Plenty of structures are in fact resolved every year and deposited into public databases, such as the Protein Data Bank (PDB) [21]. As of December 2020, the PDB comprises a total of about 160,000 protein structures, 89% of which obtained from X-ray crystallography, 7% from NMR, and the remaining 4% resolved with other methodologies such as Electron Microscopy (EM) and hybrid methods [22]. The knowledge of the three-dimensional protein structure is obviously an important starting point in order to investigate its mechanism of action. A thorough analysis of its dynamics subsequently allows to predict its functional behavior. Hence, how can we investigate protein dynamics?One of the most used approach is through Molecular Dynamics (MD) simulations [23, 24]. MD is based on solving the Newton’s laws of motion for a system subjected to certain forces. The initial model of the system is usually taken from experimental structures, which can be represented at various levels of detail. Once the system is built, the forces acting on every atom are computed based on the derivation of potential energies. Different forms of potentials can be used for this purpose. Often these potential energies include spring terms for bond stretching and angle distortions, Lennard-Jones terms for long-range interactions, as well as Coulomb’s laws for Van der Waals and electrostatic effects [24]. Obtained the forces acting on the systems, the equations of motion are integrated to obtain the velocities and positions of all the atoms. This is carried out by adopting numerical integration strategies, which require discretization into small time frames of the order of femtoseconds. Although MD simulations can provide detailed and often accurate predictions of the trajectories of the system, the high computational burden and the difficulty to achieve stable solutions at very large time scales often constitute serious obstacles.

Computational approaches could decrease the need for the laborious high-throughput experimental screening that is often required to improve enzymes by mutagenesis. Here, we report that using multiple short molecular dynamics (MD) simulations makes it possible to accurately model enantioselectivity for large numbers of enzyme-substrate combinations at low computational costs. We chose four different haloalkane dehalogenases as model systems because of the availability of a large set of experimental data on the enantioselective conversion of 45 different substrates. To model the enantioselectivity, we quantified the frequency of occurrence of catalytically productive conformations (near attack conformations) for pairs of enantiomers during MD simulations. We found that the angle of nucleophilic attack that leads to carbon-halogen bond cleavage was a critical variable that limited the occurrence of productive conformations; enantiomers for which this angle reached values close to 180° were preferentially converted. A cluster of 20-40 very short (10 ps) MD simulations allowed adequate conformational sampling and resulted in much better agreement to experimental enantioselectivities than single long MD simulations (22 ns), while the computational costs were 50-100 fold lower. With single long MD simulations, the dynamics of enzyme-substrate complexes remained confined to a conformational subspace that rarely changed significantly, whereas with multiple short MD simulations a larger diversity of conformations of enzyme-substrate complexes was observed.