Thermodynamics of Macromolecular Association in Heterogeneous Crowding Environments: Theoretical and Simulation Studies with a Simplified Model.
The cytoplasm of a cell is crowded with many different kinds of macromolecules. The macromolecular crowding affects the thermodynamics and kinetics of biological reactions in a living cell, such as protein folding, association, and diffusion. Theoretical and simulation studies using simplified models focus on the essential features of the crowding effects and provide a basis for analyzing experimental data. In most of the previous studies on the crowding effects, a uniform crowder size is assumed, which is in contrast to the inhomogeneous size distribution of macromolecules in a living cell. Here, we evaluate the free energy changes upon macromolecular association in a cell-like inhomogeneous crowding system via a theory of hard-sphere fluids and free energy calculations using Brownian dynamics trajectories. The inhomogeneous crowding model based on 41 different types of macromolecules represented by spheres with different radii mimics the physiological concentrations of macromolecules in the cytoplasm of Mycoplasma genitalium. The free energy changes of macromolecular association evaluated by the theory and simulations were in good agreement with each other. The crowder size distribution affects both specific and nonspecific molecular associations, suggesting that not only the volume fraction but also the size distribution of macromolecules are important factors for evaluating in vivo crowding effects. This study relates in vitro experiments on macromolecular crowding to in vivo crowding effects by using the theory of hard-sphere fluids with crowder-size heterogeneity.
Biomolecular interactions modulate macromolecular structure and dynamics in atomistic model of a bacterial cytoplasm.
Biological macromolecules function in highly crowded cellular environments. The structure and dynamics of proteins and nucleic acids are well characterized in vitro, but in vivo crowding effects remain unclear. Using molecular dynamics simulations of a comprehensive atomistic model cytoplasm we found that protein-protein interactions may destabilize native protein structures, whereas metabolite interactions may induce more compact states due to electrostatic screening. Protein-protein interactions also resulted in significant variations in reduced macromolecular diffusion under crowded conditions, while metabolites exhibited significant two-dimensional surface diffusion and altered protein-ligand binding that may reduce the effective concentration of metabolites and ligands in vivo. Metabolic enzymes showed weak non-specific association in cellular environments attributed to solvation and entropic effects. These effects are expected to have broad implications for the in vivo functioning of biomolecules. This work is a first step towards physically realistic in silico whole-cell models that connect molecular with cellular biology.
Water Orientation at Ceramide/Water Interfaces Studied by Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy and Molecular Dynamics Simulation.
Lipid/water interaction is essential for many biological processes. The water structure at the nonionic lipid interface remains little known, and there is no scope of a priori prediction of water orientation at nonionic interfaces, either. Here, we report our study combining advanced nonlinear spectroscopy and molecular dynamics simulation on the water orientation at the ceramide/water interface. We measured χ(2) spectrum in the OH stretch region of ceramide/isotopically diluted water interface using heterodyne-detected vibrational sum-frequency generation spectroscopy and found that the interfacial water prefers an overall hydrogen-up orientation. Molecular dynamics simulation indicates that this preferred hydrogen-up orientation of water is determined by a delicate balance between hydrogen-up and hydrogen-down orientation induced by lipid–water and intralipid hydrogen bonds. This mechanism also suggests that water orientation at neutral lipid interfaces depends highly on the chemical structure of the lipid headgroup, in contrast to the charged lipid interfaces where the net water orientation is determined solely by the charge of the lipid headgroup.
Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms.
This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.
GENESIS: a hybrid‐parallel and multi‐scale molecular dynamics simulator with enhanced sampling algorithms for biomolecular and cellular simulations.
GENESIS (Generalized‐Ensemble Simulation System) is a new software package for molecular dynamics (MD) simulations of macromolecules. It has two MD simulators, called ATDYN and SPDYN. ATDYN is parallelized based on an atomic decomposition algorithm for the simulations of all‐atom force‐field models as well as coarse‐grained Go‐like models. SPDYN is highly parallelized based on a domain decomposition scheme, allowing large‐scale MD simulations on supercomputers. Hybrid schemes combining OpenMP and MPI are used in both simulators to target modern multicore computer architectures. Key advantages of GENESIS are (1) the highly parallel performance of SPDYN for very large biological systems consisting of more than one million atoms and (2) the availability of various REMD algorithms (T‐REMD, REUS, multi‐dimensional REMD for both all‐atom and Go‐like models under the NVT, NPT, NPAT, and NPγT ensembles). The former is achieved by a combination of the midpoint cell method and the efficient three‐dimensional Fast Fourier Transform algorithm, where the domain decomposition space is shared in real‐space and reciprocal‐space calculations. Other features in SPDYN, such as avoiding concurrent memory access, reducing communication times, and usage of parallel input/output files, also contribute to the performance. We show the REMD simulation results of a mixed (POPC/DMPC) lipid bilayer as a real application using GENESIS. GENESIS is released as free software under the GPLv2 licence and can be easily modified for the development of new algorithms and molecular models.
Complete Atomistic Model of a Bacterial Cytoplasm for Integrating Physics, Biochemistry, and Systems Biology Journal of Molecular Graphics and Modelling.
A model for the cytoplasm of Mycoplasma genitalium is presented that integrates data from a variety of sources into a physically and biochemically consistent model. Based on gene annotations, core genes expected to be present in the cytoplasm were determined and a metabolic reaction network was reconstructed. The set of cytoplasmic genes and metabolites from the predicted reactions were assembled into a comprehensive atomistic model consisting of proteins with predicted structures, RNA, protein/RNA complexes, metabolites, ions, and solvent. The resulting model bridges between atomistic and cellular scales, between physical and biochemical aspects, and between structural and systems views of cellular systems and is meant as a starting point for a variety of simulation studies.
"REIN: Replica-exchange INterface for simulating protein dynamics and function"
Replica-exchange molecular dynamics (REMD) method is one of the enhanced conformational sampling algorithms widely applied in computational biophysics and biochemistry. In the method, molecular dynamics (MD) simulations for multiple replicas of a target system are performed simultaneously and independently. Every few steps, temperatures or other parameters are exchanged between a pair of replicas according to the modified Metropolis criteria. Replica-Exchange INterface (REIN) is interface software for REMD simulations. It utilizes existing MD software without modification and performs the exchanges of replicas. In this article, we introduce the software design of REIN and demonstrate its applicability through benchmark simulations of alanine pentapeptide in explicit water, as well as the free-energy analysis of N-glycan and Tom20-presequence complex in solution.
"Multidimensional umbrella sampling and replica-exchange molecular dynamics simulations for structure prediction of transmembrane helix dimers"
Structural information of a transmembrane (TM) helix dimer is useful in understanding molecular mechanisms of important biological phenomena such as signal transduction across the cell membrane. Here, we describe an umbrella sampling (US) scheme for predicting the structure of a TM helix dimer in implicit membrane using the interhelical crossing angle and the TM–TM relative rotation angles as the reaction coordinates. This scheme conducts an efficient conformational search on TM–TM contact interfaces, and its robustness is tested by predicting the structures of glycophorin A (GpA) and receptor tyrosine kinase EphA1 (EphA1) TM dimers. The nuclear magnetic resonance (NMR) structures of both proteins correspond to the global free-energy minimum states in their free-energy landscapes. In addition, using the landscape of GpA as a reference, we also examine the protocols of temperature replica-exchange molecular dynamics (REMD) simulations for structure prediction of TM helix dimers in implicit membrane. A wide temperature range in REMD simulations, for example, 250–1000 K, is required to efficiently obtain a free-energy landscape consistent with the US simulations. The interhelical crossing angle and the TM–TM relative rotation angles can be used as reaction coordinates in multidimensional US and be good measures for conformational sampling of REMD simulations.
"Surface-tension replica-exchange molecular dynamics method for enhanced sampling of biological membrane systems"
Conformational sampling is fundamentally important for simulating complex bio-molecular systems. The generalized-ensemble algorithm, especially the temperature replica-exchange molecular dynamics method (T-REMD), is one of the most powerful methods to explore structures of bio-molecules such as proteins, nucleic acids, carbohydrates, and also of lipid membranes. T-REMD simulations have focused on soluble proteins rather than membrane proteins or lipid bilayers, because explicit membranes do not keep their structural integrity at high temperature. Here, we propose a new generalized-ensemble algorithm for membrane systems, which we call the surface-tension REMD method. Each replica is simulated in the NPγT ensemble, and surface tensions in a pair of replicas are exchanged at certain intervals to enhance conformational sampling of the target membrane system. We test the method on two biological membrane systems: a fully hydrated DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine) lipid bilayer and a WALP23–POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) membrane system. During these simulations, a random walk in surface tension space is realized. Large-scale lateral deformation (shrinking and stretching) of the membranes takes place in all of the replicas without collapse of the lipid bilayer structure. There is accelerated lateral diffusion of DPPC lipid molecules compared with conventional MD simulation, and a much wider range of tilt angle of the WALP23 peptide is sampled due to large deformation of the POPC lipid bilayer and through peptide-lipid interactions. Our method could be applicable to a wide variety of biological membrane systems.
"Efficient lookup table using a linear function of inverse distance squared"
The major bottleneck in molecular dynamics (MD) simulations of biomolecules exist in the calculation of pairwise nonbonded interactions like Lennard-Jones and long-range electrostatic interactions. Particle-mesh Ewald (PME) method is able to evaluate long-range electrostatic interactions accurately and quickly during MD simulation. However, the evaluation of energy and gradient includes time-consuming inverse square roots and complementary error functions. To avoid such time-consuming operations while keeping accuracy, we propose a new lookup table for short-range interaction in PME by defining energy and gradient as a linear function of inverse distance squared. In our lookup table approach, densities of table points are inversely proportional to squared pair distances, enabling accurate evaluation of energy and gradient at small pair distances. Regardless of the inverse operation here, the new lookup table scheme allows fast pairwise nonbonded calculations owing to efficient usage of cache memory.
"Reaching new levels of realism in modeling biological macromolecules in cellular environments"
An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction–diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.
"Energetics of the Presequence-Binding Poses in Mitochondrial Protein Import Through Tom20"
Tom20 is located at the outer membrane of mitochondria and functions as a receptor for the N-terminal presequence of mitochondrial-precursor proteins. Recently, three atomic structures of the Tom20-presequence complex were determined using X-ray crystallography and classified into A-, M-, and Y-poses in terms of their presequence-binding modes. Combined with biochemical and NMR data, a dynamic-equilibrium model between the three poses has been proposed. To investigate this mechanism in further detail, we performed all-atom molecular dynamics (MD) simulations and replica-exchange MD (REMD) simulations of the Tom20-presequence complex in explicit water. In the REMD simulations, one major distribution and another minor one were observed in the converged free-energy landscape at 300 K. In the major distribution, structures similar to A- and M-poses exist, whereas those similar to Y-pose are located in the minor one, suggesting that A-pose in solution is more stable than Y-pose. A k-means clustering algorithm revealed a new pose not yet obtained by X-ray crystallography. This structure has double salt bridges between Arg14′ in the presequence and Glu78 or Glu79 in Tom20 and can explain the binding affinity of the complex in previous pull-down assay experiments. Structural clustering and analyses of contacts between Tom20 and the presequence suggest smooth conformational changes from Y- to A-poses through low activation barriers. M-pose lies between Y- and A-poses as a metastable state. The REMD simulations thus provide insights into the energetics of the multiple-binding forms and help to detail the progressive conformational states in the dynamic-equilibrium model based on the experimental data.
"Reduced Native State Stability in Crowded Cellular Environment Due to Protein–Protein Interactions"
The effect of cellular crowding environments on protein structure and stability is a key issue in molecular and cellular biology. The classical view of crowding emphasizes the volume exclusion effect that generally favors compact, native states. Here, results from molecular dynamics simulations and NMR experiments show that protein crowders may destabilize native states via protein–protein interactions. In the model system considered here, mixtures of villin head piece and protein G at high concentrations, villin structures become increasingly destabilized upon increasing crowder concentrations. The denatured states observed in the simulation involve partial unfolding as well as more subtle conformational shifts. The unfolded states remain overall compact and only partially overlap with unfolded ensembles at high temperature and in the presence of urea. NMR measurements on the same systems confirm structural changes upon crowding based on changes of chemical shifts relative to dilute conditions. An analysis of protein–protein interactions and energetic aspects suggests the importance of enthalpic and solvation contributions to the crowding free energies that challenge an entropic-centered view of crowding effects.
"Recent Applications of Replica-Exchange Molecular Dynamics Simulations of Biomolecules"
Replica-exchange molecular dynamics (REMD) method is one of the enhanced conformational sampling techniques in MD simulations of proteins or other systems with rugged-energy landscapes. In REMD method, copies of original simulation system at different temperatures are simulated separately and simultaneously. Every few steps, temperatures between neighboring replicas are exchanged if the Metropolis criteria for their instantaneous potential energies are satisfied. Due to its simplicity and high efficiency in parallel computers, the method has been applied to many biological problems including protein folding, aggregation, receptor-ligand binding, and so on. In the last ten years, continuous effort to improve sampling efficiency of REMD simulations for larger biological systems has been carried out by us and other theoretical scientists. In this review article, we introduce two different approaches in REMD simulations to reduce the computational cost. One is the multicanonical replica-exchange method (MUCAREM) for reducing the number of replicas. In this method, each replica has a different multicanonical weight factor and takes a flat energy distribution to cover a wider potential energy space. Another approach is to employ implicit solvent/membrane models for representing surrounding environments of target proteins in REMD simulations. We show two applications of proteinfolding simulations in explicit solvent using the former approach and a structural prediction of a transmembrane protein dimer using the latter. Finally, we discuss possibilities of REMD method to simulate a large-scale conformational change of protein systems using massively parallel supercomputers.
"Effect of Bisecting GlcNAc and Core Fucosylation on Conformational Properties of Biantennary Complex-Type N-Glycans in Solution"
The introduction of bisecting GlcNAc and core fucosylation in N-glycans is essential for fine functional regulation of glycoproteins. In this paper, the effect of these modifications on the conformational properties of N-glycans is examined at the atomic level by performing replica-exchange molecular dynamics (REMD) simulations. We simulate four biantennary complex-type N-glycans, namely, unmodified, two single-substituted with either bisecting GlcNAc or core fucose, and disubstituted forms. By using REMD as an enhanced sampling technique, five distinct conformers in solution, each of which is characterized by its local orientation of the Manα1-6Man glycosidic linkage, are observed for all four N-glycans. The chemical modifications significantly change their conformational equilibria. The number of major conformers is reduced from five to two and from five to four upon the introduction of bisecting GlcNAc and core fucosylation, respectively. The population change is attributed to specific inter-residue hydrogen bonds, including water-mediated ones. The experimental NMR data, including nuclear Overhauser enhancement and scalar J-coupling constants, are well reproduced taking the multiple conformers into account. Our structural model supports the concept of “conformer selection”, which emphasizes the conformational flexibility of N-glycans in protein-glycan interactions.
"Conformational flexibility of N-glycans in solution studied by REMD simulations"
Protein–glycan recognition regulates a wide range of biological and pathogenic processes. Conformational diversity of glycans in solution is apparently incompatible with specific binding to their receptor proteins. One possibility is that among the different conformational states of a glycan, only one conformer is utilized for specific binding to a protein. However, the labile nature of glycans makes characterizing their conformational states a challenging issue. All-atom molecular dynamics (MD) simulations provide the atomic details of glycan structures in solution, but fairly extensive sampling is required for simulating the transitions between rotameric states. This difficulty limits application of conventional MD simulations to small fragments like di- and tri-saccharides. Replica-exchange molecular dynamics (REMD) simulation, with extensive sampling of structures in solution, provides a valuable way to identify a family of glycan conformers. This article reviews recent REMD simulations of glycans carried out by us or other research groups and provides new insights into the conformational equilibria of N-glycans and their alteration by chemical modification. We also emphasize the importance of statistical averaging over the multiple conformers of glycans for comparing simulation results with experimental observables. The results support the concept of “conformer selection” in protein–glycan recognition.
"The Intertransmembrane Region of Kaposi’s Sarcoma-Associated Herpesvirus Modulator of Immune Recognition 2 Contributes to B7-2 Downregulation"
Kaposi’s sarcoma-associated herpesvirus (KSHV), a human tumor virus, encodes two homologous membrane-associated E3 ubiquitin ligases, modulator of immune recognition 1 (MIR1) and MIR2, to evade host immunity. Both MIR1 and MIR2 downregulate the surface expression of major histocompatibility complex class I (MHC I) molecules through ubiquitin-mediated endocytosis followed by lysosomal degradation. Since MIR2 additionally downregulates a costimulatory molecule (B7-2) and an integrin ligand (intercellular adhesion molecule 1 [ICAM-1]), MIR2 is thought to be a more important molecule for immune evasion than MIR1; however, the molecular basis of the MIR2 substrate specificity remains unclear. To address this issue, we determined which regions of B7-2 and MIR2 are required for MIR2-mediated B7-2 downregulation. Experiments with chimeras made by swapping domains between human B7-2 and CD8α, a non-MIR2 substrate, and between MIR1 and MIR2 demonstrated a significant contribution of the juxtamembrane (JM) region of B7-2 and the intertransmembrane (ITM) region of MIR2 to MIR2-mediated downregulation. Structure prediction and mutagenesis analyses indicate that Phe119 and Ser120 in the MIR2 ITM region and Asp244 in the B7-2 JM region contribute to the recognition of B7-2 by MIR2. This finding provides new insight into the molecular basis of substrate recognition by MIR family members.
"Protein Crowding Affects Hydration Structure and Dynamics"
The effect of protein crowding on the structure and dynamics of water was examined from explicit solvent molecular dynamics simulations of a series of protein G and protein G/villin systems at different protein concentrations. Hydration structure was analyzed in terms of radial distribution functions, three-dimensional hydration sites, and preservation of tetrahedral coordination. Analysis of hydration dynamics focused on self-diffusion rates and dielectric constants as a function of crowding. The results show significant changes in both structure and dynamics of water under highly crowded conditions. The structure of water is altered mostly beyond the first solvation shell. Diffusion rates and dielectric constants are significantly reduced following linear trends as a function of crowding reflecting highly constrained water in crowded environments. The reduced dynamics of diffusion is expected to be strongly related to hydrodynamic properties of crowded cellular environments while the reduced dielectric constant under crowded conditions has implications for the stability of biomolecules in crowded environments. The results from this study suggest a prescription for modeling solvation in simulations of cellular environments.
"Variable Interactions between Protein Crowders and Biomolecular Solutes Are Important in Understanding Cellular Crowding"
The effect of cellular crowding was examined from molecular dynamics simulations of chymotrypsin inhibitor 2 (CI2) in the presence of either lysozyme or bovine serum albumin (BSA) crowder molecules as a complement to recent experimental studies of the same systems (Miklos, A. C.; Sarkar, M.; Wang, Y.; Pielak, G. J. J. Am. Chem. Soc. 2011, 133, 7116). The simulations confirm a destabilization and significantly slowed diffusion of CI2 in the presence of lysozyme and indicate that this observation is a result of extensive, non-specific protein-protein interactions between CI2 and lysozyme. CI2 interacts much less with BSA crowders corresponding to a weak effect of crowding. Energetic analysis suggests an overall favorable crowding free energy in the presence of lysozyme while weaker interactions with BSA appear to be unfavorable.
"Analysis of Lipid Surface Area in Protein-Membrane Systems Combining Voronoi Tessellation and Monte Carlo Integration Methods"
All-atom molecular dynamics (MD) simulation has become a powerful research tool to investigate structural and dynamical properties of biological membranes and membrane proteins. The lipid structures of simple membrane systems in recent MD simulations are in good agreement with those obtained by experiments. However, for protein–membrane systems, the complexity of protein–lipid interactions makes investigation of lipid structure difficult. Although the area per lipid is one of the essential structural properties in membrane systems, the area in protein–membrane systems cannot be computed easily by conventional approaches like the Voronoi tessellation method. To overcome this limitation, we propose a new method combining the two-dimensional Voronoi tessellation and Monte Carlo integration methods. This approach computes individual surface areas of lipid molecules not only in bulk lipids but also in proximity to membrane proteins. We apply the method to all-atom MD trajectories of the sarcoplasmic reticulum Ca2+-pump and the SecY protein-conducting channel. The calculated lipid surface area is in agreement with experimental values and consistent with other structural parameters of lipid bilayers. We also observe changes in the average area per lipid induced by the conformational transition of the SecY channel. Our method is particularly useful for examining equilibration of lipids around membrane proteins and for analyzing the time course of protein–lipid interactions.