Principal component analysis for protein folding dynamics

Protein folding is considered here by studying the dynamics of the folding of the triple β-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.     

Molecular-dynamics simulation of phenylalanine transfer RNA. II. Amplitudes, anisotropies, and anharmonicities of atomic motions

The atomic motions from a molecular-dynamics simulation of yeast tRNA^Phe are analyzed and compared with those observed in protein simulations. In general, the tRNA motions are of larger amplitude, they are more anisotropic, and they arise from potentials of mean force that are more anharmonic than in the protein case. In both cases, the amplitudes are largest for atoms on the surface of the molecules. On the other hand, the most anisotropic and anharmonic atomic motions are generally found in the interior of the tRNA, while they are found on the surface of the protein. These differences are discussed in terms of the differences in structure between nucleic acids and proteins.     

Molecular dynamics of ferrocytochrome c: Anharmonicity of atomic displacements

The atomic position distributions obtained from a 32-ps molecular-dynamics simulation of tuna ferrocytochrome c at 297 K are analyzed in terms of their second, third, and fourth moments. Non-Gaussian relations among these moments are found for the majority of atoms in the molecule, indicating anharmonicity in the effective potential functions for the atomic motions. Many atoms exhibit only slightly anharmonic mobility during the 32-ps period, but about half of the atoms exhibit sizeable anharmonicity. For a typical atom, the anharmonic effects are largest for motions in the direction along which the largest displacements occur. Two classes of significantly anharmonic atoms are apparent: those whose effective potentials are distorted toward a square-well shape and those whose effective potentials have secondary minima corresponding to conformational substates.     

Anisotropy and anharmonicity of atomic fluctuations in proteins: analysis of a molecular dynamics simulation

Positional probability density functions (pdf) for the atomic fluctuations are determined from a molecular dynamics simulation for hen egg-white lysozyme. Most atoms are found to have motions that are highly anisotropic but only slightly anharmonic. The largest deviations from harmonic motion are in the direction of the largest rms fluctuations in the local principal axis frame. Backbone atoms tend to be more nearly harmonic than sidechain atoms. The atoms with the largest anharmonicities tend to have pdfs with multiple peaks, each of which is close to harmonic. Several model pdfs are evaluated on the basis of how well they fit probability densities from the dynamics simulations when parameterized in terms of the moments of the distribution. Gram-Charlier and Edgeworth perturbation expansions, which have been successful in describing the motions of small molecules in crystals, are shown to be inadequate for the distributions found in the dynamics of proteins. Multipeaked distribution functions are found to be more appropriate.     

Subdiffusive-Brownian crossover in membrane proteins: a generalized Langevin equation-based approach

In this work, we propose a generalized Langevin equation-based model to describe the lateral diffusion of a protein in a lipid bilayer. The memory kernel is represented in terms of a viscous (instantaneous) and an elastic (noninstantaneous) component modeled through a Dirac δ function and a three-parameter Mittag-Leffler type function, respectively. By imposing a specific relationship between the parameters of the three-parameter Mittag-Leffler function, the different dynamical regimes—namely ballistic, subdiffusive, and Brownian, as well as the crossover from one regime to another—are retrieved. Within this approach, the transition time from the ballistic to the subdiffusive regime and the spectrum of relaxation times underlying the transition from the subdiffusive to the Brownian regime are given. The reliability of the model is tested by comparing the mean-square displacement derived in the framework of this model and the mean-square displacement of a protein diffusing in a membrane calculated through molecular dynamics simulations.     

Influence of RNA Binding on the Structure and Dynamics of the Lassa Virus Nucleoprotein

Lassa virus protects its viral genome through the formation of a ribonucleoprotein complex in which the nucleoprotein (NP) encapsidates the single-stranded RNA genome. Crystal structures provide evidence that a conformational change must occur to allow for RNA binding. In this study, the mechanism by which NP binds to RNA and how the conformational changes in NP are achieved was investigated with molecular-dynamics simulations. NP was structurally characterized in an open configuration when bound to RNA and in a closed form in the absence of RNA. Our results show that when NP is bound to RNA, the protein is highly dynamic and the system undergoes spontaneous deviations away from the open-state configuration. The equilibrium simulations are supported by free-energy calculations that quantify the influence of RNA on the free-energy surface, which governs NP dynamics. We predict that the globally stable states are qualitatively in agreement with the observed crystal structures, but that both open and closed conformations are thermally accessible in the presence of RNA. The free-energy calculations also provide a prediction of the location of the transition state for RNA binding and identify an intermediate metastable state that exhibits correlated motions that could promote RNA binding.     

Local motion analysis reveals impact of the dynamic cytoskeleton on intracellular subdiffusion

Intracellular transport is a complex interplay of ballistic transport along filaments and of diffusive motion, reliably delivering material and allowing for cell differentiation, migration, and proliferation. The diffusive regime, including subdiffusive, Brownian, and superdiffusive motion, is of particular interest for inferring information about the dynamics of the cytoskeleton morphology during intracellular transport. The influence of dynamic cytoskeletal states on intracellular transport are investigated in Dictyostelium discoideum cells by single particle tracking of fluorescent nanoparticles, to relate quantitative motion parameters and intracellular processes before and after cytoskeletal disruption. A local mean-square displacement (MSD) analysis separates ballistic motion phases, which we exclude here, from diffusive nanoparticle motion. In this study, we focus on intracellular subdiffusion and elucidate lag-time dependence, with particular focus on the impact of cytoskeleton compartments like microtubules and actin filaments. This method proves useful for binary motion state distributions. Experimental results are compared to simulations of a data-driven Langevin model with finite velocity correlations that captures essential statistical features of the local MSD algorithm. Specifically, the values of the mean MSD exponent and effective diffusion coefficients can be traced back to negative correlations of the motion's increments. We clearly identify both microtubules and actin filaments as the cause for intracellular subdiffusion and show that actin-microtubule cross talk exerts viscosifying effects at timescales larger than 0.2 s. Our findings might give insights into material transport and information exchange in living cells, which might facilitate gaining control over cell functions.     

A principal component analysis of the dynamics of subdomains and binding sites in human serum albumin

The conformational dynamics of human serum albumin (HSA) was investigated by principal component analysis (PCA) applied to three molecular dynamics trajectories of 200 ns each. The overlap of the essential subspaces spanned by the first 10 principal components (PC) of different trajectories was about 0.3 showing that the PCA based on a trajectory length of 200 ns is not completely convergent for this protein. The contributions of the relative motion of subdomains and of the subdomains (internal) distortion to the first 10 PCs were found to be comparable. Based on the distribution of the first 3 PC, 10 protein conformers are identified showing relative root mean square deviations (RMSD) between 2.3 and 4.6 Å. The main PCs are found to be delocalized over the whole protein structure indicating that the motions of different protein subdomains are coupled. This coupling is considered as being related to the allosteric effects observed upon ligand binding to HSA. On the other hand, the first PC of one of the three trajectories describes a conformational transition of the protein domain I that is close to that experimentally observed upon myristate binding. This is a theoretical support for the older hypothesis stating that changes of the protein onformation favorable to binding can precede the ligand complexation. A detailed all atoms PCA performed on the primary Sites 1 and 2 confirms the multiconformational character of the HSA binding sites as well as the significant coupling of their motions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 561–572, 2014.     

Cooperative ligand reorientations in cytochrome c3: a molecular dynamics simulation.

Molecular dynamics simulations of a tetraheme cytochrome c3 were performed to investigate dynamic aspects of the motion of the axial heme iron ligands. It was found that persistent transitions between alternate axial imidazole orientations of the histidine incorporated in the CXXCH heme binding sequence occurred via correlated motions. The correlated motions involved virtually all of the atoms comprising the polypeptide backbone of the heme binding sequence as well as the histidine imidazole side-chain.     

Dynamics of proteins predicted by molecular dynamics simulations and analytical approaches: application to alpha-amylase inhibitor

The dynamics of alpha-amylase inhibitors has been investigated using molecular dynamics (MD) simulations and two analytical approaches, the Gaussian network model (GNM) and anisotropic network model (ANM). MD simulations use a full atomic approach with empirical force fields, while the analytical approaches are based on a coarse-grained single-site-per-residue model with a single-parameter harmonic potential between sufficiently close (r 相似文献   

Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme

A method is presented to describe the internal motions of proteins obtained from molecular dynamics or Monte Carlo simulations as motions of normal mode variables. This method calculates normal mode variables by projecting trajectories of these simulations onto the axes of normal modes and expresses the trajectories as a linear combination of normal mode variables. This method is applied to the result of the molecular dynamics and the Monte Carlo simulations of human lysozyme. The motion of the lowest frequency mode extracted from the simulations represents the hinge bending motion very faithfully. Analysis of the obtained motions of the normal mode variables provides an explanation of the anharmonic aspects of protein dynamics as due first to the anharmonicity of the actual potential energy surface near a minimum and second to trans-minimum conformational changes.     

Free-energy profiles of membrane insertion of the M2 transmembrane peptide from influenza A virus

The insertion of the M2 transmembrane peptide from influenza A virus into a membrane has been studied with molecular-dynamics simulations. This system is modeled by an atomically detailed peptide interacting with a continuum representation of a membrane bilayer in aqueous solution. We performed replica-exchange molecular-dynamics simulations with umbrella-sampling techniques to characterize the probability distribution and conformation preference of the peptide in the solution, at the membrane interface, and in the membrane. The minimum in the calculated free-energy surface of peptide insertion corresponds to a fully inserted, helical peptide spanning the membrane. The free-energy profile also shows that there is a significant barrier for the peptide to enter into this minimum in a nonhelical conformation. The sequence of the peptide is such that hydrophilic amino acid residues at the ends of the otherwise primarily hydrophobic peptide create a trapped, U-shaped conformation with the hydrophilic residues associated with the aqueous phase and the hydrophobic residues embedded in the membrane. Analysis of the free energy shows that the barrier to insertion is largely enthalpic in nature, whereas the membrane-spanning global minimum is favored by entropy.     

Temperature-dependent structural and functional features of a hyperthermostable enzyme using elastic neutron scattering

The dynamic behavior of an endoglucanase from the hyperthermophilic microorganism Pyrococcus furiosus was investigated using elastic neutron scattering. The temperature dependence of the atomic motions was correlated with conformational and functional characteristics of the enzyme. The onset of biological function at temperatures higher than approximately 25 degrees C (the hyperthermostable enzyme is essentially inactive at room temperature) was associated with a dynamical transition in the anharmonic motions domain. This transition from the nonactive to the enzymatically active conformation involved structurally similar conformational substates in the energy landscape. From the mean-square displacement of the protein atoms, the molecular flexibility and the effective force constants were calculated at different temperature zones. The results showed that the activity increases at higher temperatures where the intramolecular bonds are weakened and the overall rigidity of the protein is decreased. Further temperature increase resulted in significantly increased atomic fluctuations featuring heat denaturation of the protein.     

Molecular dynamics of ferrocytochrome c: Time dependence of the atomic displacements

The thermal motions of the atoms in a dynamical simulation of ferrocytochrome c are geometrically decomposed into local and highly collective components, and the contributions of these components to the net motion are determined for different intervals of time. It is found that the atomic displacement magnitudes and anisotropies are governed by local motions for times <10^?12s, but that the highly collective motions tend to be dominant at longer times. Variations in this behavior are noted among different groups of atoms. Orientational correlations between the preferred directions of atomic displacement and elements of the protein structure are analyzed as a function of time scale. Finally, several sinificant implications of these results with respect to protein structure and function are considered.     

Computational studies on the conformations of some large‐ring cyclodextrins (CDn,n = 20, 21, 22, 23)

Computational studies were carried out on the conformations of large‐ring cyclodextrins with degree of polymerization from 20 to 23. Principal component analysis (PCA) was applied for postprocessing of trajectories from conformational search, based on 100.0 ns molecular dynamics simulations. The dominant PCA modes for concerted motions of the macroring atoms were monitored in a lower‐dimensions subspace. The first six lowest indexed principal components contribute more than 90% of the total atomic motions in all cases, with about 70% (CD21) to 83% (CD22) contribution coming from the three highest‐eigenvalue principal components. Representative average geometries of the cyclodextrin macrorings were also obtained for the whole simulation and for the ten 10.0 ns time intervals of the simulation. We concluded that resemblance exists of the representative conformations of these four cyclodextrins with the circularized three‐turn single helical structure proposed for CD21 from small‐angle X‐ray scattering, as well as with the representative conformations of CD26. Chirality, 2011. © 2011 Wiley‐Liss, Inc.     

Anomalous diffusion of proteins due to molecular crowding

We have studied the diffusion of tracer proteins in highly concentrated random-coil polymer and globular protein solutions imitating the crowded conditions encountered in cellular environments. Using fluorescence correlation spectroscopy, we measured the anomalous diffusion exponent alpha characterizing the dependence of the mean-square displacement of the tracer proteins on time, r(2)(t) approximately t(alpha). We observed that the diffusion of proteins in dextran solutions with concentrations up to 400 g/l is subdiffusive (alpha < 1) even at low obstacle concentration. The anomalous diffusion exponent alpha decreases continuously with increasing obstacle concentration and molecular weight, but does not depend on buffer ionic strength, and neither does it depend strongly on solution temperature. At very high random-coil polymer concentrations, alpha reaches a limit value of alpha(l) approximately 3/4, which we take to be the signature of a coupling between the motions of the tracer proteins and the segments of the dextran chains. A similar, although less pronounced, subdiffusive behavior is observed for the diffusion of streptavidin in concentrated globular protein solutions. These observations indicate that protein diffusion in the cell cytoplasm and nucleus should be anomalous as well, with consequences for measurements of solute diffusion coefficients in cells and for the modeling of cellular processes relying on diffusion.     

Local motions in a benchmark of allosteric proteins

Allosteric proteins have been studied extensively in the last 40 years, but so far, no systematic analysis of conformational changes between allosteric structures has been carried out. Here, we compile a set of 51 pairs of known inactive and active allosteric protein structures from the Protein Data Bank. We calculate local conformational differences between the two structures of each protein using simple metrics, such as backbone and side-chain Cartesian displacement, and torsion angle change and rearrangement in residue-residue contacts. Thresholds for each metric arise from distributions of motions in two control sets of pairs of protein structures in the same biochemical state. Statistical analysis of motions in allosteric proteins quantifies the magnitude of allosteric effects and reveals simple structural principles about allostery. For example, allosteric proteins exhibit substantial conformational changes comprising about 20% of the residues. In addition, motions in allosteric proteins show strong bias toward weakly constrained regions such as loops and the protein surface. Correlation functions show that motions communicate through protein structures over distances averaging 10-20 residues in sequence space and 10-20 A in Cartesian space. Comparison of motions in the allosteric set and a set of 21 nonallosteric ligand-binding proteins shows that nonallosteric proteins also exhibit bias of motion toward weakly constrained regions and local correlation of motion. However, allosteric proteins exhibit twice as much percent motion on average as nonallosteric proteins with ligand-induced motion. These observations may guide efforts to design flexibility and allostery into proteins.     

Intracellular transport dynamics of endosomes containing DNA polyplexes along the microtubule network

We have explored the transport of DNA polyplexes enclosed in endosomes within the cellular environment by multiple particle tracking (MPT). The polyplex-loaded endosomes demonstrate enhanced diffusion at short timescales (t<7 s) with their mean-square displacement (MSD) Deltax(t)2 scaling as t1.25. For longer time intervals they exhibit subdiffusive transport and have an MSD scaling as t0.7. This crossover from an enhanced diffusion to a subdiffusive regime can be explained by considering the action of motor proteins that actively transport these endosomes along the cellular microtubule network and the thermal bending modes of the microtubule network itself.     

Temperature dependence of dynamics of hydrated myoglobin. Comparison of force field calculations with neutron scattering data

Molecular dynamics is used to probe the atomic motions of the carboxy-myoglobin protein as a function of temperature. Simulations of 150 picoseconds in length are carried out on the protein at 20, 60, 100, 180, 220, 240, 260, 280, 300, 320 and 340 K. The simulations attempt to mimic neutron scattering experiments very closely by including a partial hydration shell around the protein. Theoretical elastic, quasielastic and inelastic neutron scattering data are derived from the trajectories and directly compared with experiment. Compared to experiment, the simulation-derived elastic scattering curves show a decrease in intensity as a function of the scattering wavevector, q2. The inelastic and quasielastic spectra show that the inelastic peak is shifted to lower frequency than the experimental value, while quasielastic behavior is in good agreement with experiment. This suggests that the theoretical model is too flexible in the harmonic limit (low temperature), but accurately reproduces high-temperature behavior. Time correlation functions of the intermediate scattering function are determined. At low temperature there is one fast decay process, and at high temperatures there is an additional slow relaxation process that is due to quasielastic scattering. The average atomic fluctuations show that the protein behaves harmonically at low temperatures. At approximately 210 K, a glass-like transition in atomic fluctuations is seen. Above the transition temperature, the atomic fluctuations exhibit both harmonic and anharmonic behavior. Comparison of protein mobility behavior with experiment indicate the fluctuations derived from simulations are larger in the harmonic region. However, the anharmonic region agrees very well with experiment. The anharmonicity is large at all temperatures, with a gradual monotonic increase from 0.5 at 20 K to greater than 0.7 at 340 K without a noticeable change at the glass transition temperature. Heavy-atom dihedral transitions are monitored as a function of temperature. Trends in the type of dihedral transitions that occur with temperature are clearly visible. Dihedral transitions involving backbone atoms occur only above the glass transition temperature. The overall protein behavior results suggest that at low temperatures there is purely vibrational motion with one fast decay process, and above the glass transition temperature there is more anharmonic motion with a fast and a slower relaxation process occurring simultaneously.(ABSTRACT TRUNCATED AT 400 WORDS)     

Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm^?1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a resealed version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the resealing factor, termed the “normal mode resealing factor,” has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis. © 1995 Wiley-Liss, Inc.