Mathematical model for promotion of wound closure with ATP release.

To computationally investigate the recent experimental finding such that extracellular ATP release caused by exogeneous mechanical forces promote wound closure, we introduce a mathematical model, the Cellular Potts Model (CPM), which is a popular discretized model on a lattice, where the movement of a "cell" is determined by a Monte Carlo procedure. In the experiment, it was observed that there is mechanosensitive ATP release from the leading cells facing the wound gap and the subsequent extracellular Ca2+ influx. To model these phenomena, the Reaction-Diffusion equations for extracellular ATP and intracellular Ca2+ concentrations are adopted and combined with CPM, where we also add a polarity term because the cell migration is enhanced in the case of ATP release. From the numerical simulations using this hybrid model, we discuss effects of the collective cell migration due to the ATP release and the Ca2+ influx caused by the mechanical forces and the consequent promotion of wound closure.

Non-Markov-Type Analysis and Diffusion Map Analysis for Molecular Dynamics Trajectory of Chignolin at a High Temperature.

We apply the non-Markov-type analysis of state-to-state transitions to nearly microsecond molecular dynamics (MD) simulation data at a folding temperature of a small artificial protein, chignolin, and we found that the time scales obtained are consistent with our previous result using the weighted ensemble simulations, which is a general path-sampling method to extract the kinetic properties of molecules. Previously, we also applied diffusion map (DM) analysis, which is one of a manifold of learning techniques, to the same trajectory of chignolin in order to cluster the conformational states and found that DM and relaxation mode analysis give similar results for the eigenvectors. In this paper, we divide the same trajectory into shorter pieces and further apply DM to such short-length trajectories to investigate how the obtained eigenvectors are useful to characterize the conformational change of chignolin.

Multiscale Aspects of Molecular Motions: From Molecular Vibrations, Conformational Changes of Biomolecules to Cellular Dynamics.

Molecular aspects of living systems are important because it is the most basic aspects of life as exemplified in biochemistry and structural biology. Since molecules move due to interactive forces between atoms, physics plays an important role to understand the dynamic phenomena of living systems. Here we review our multiscale approaches for computationally treating different levels of molecular motions: vibrational dynamics of molecules, conformational change of biomolecules, and cellular dynamics using statistical-mechanics-based models.

Path Ensembles for Pin1-Catalyzed Cis-Trans Isomerization of a Substrate Calculated by Weighted Ensemble Simulations.

Pin1 enzyme protein recognizes specifically phosphorylated serine/threonine (pSer/pThr) and catalyzes the slow interconversion of the peptidyl-prolyl bond between cis and trans forms. Structural dynamics between the cis and trans forms are essential to reveal the underlying molecular mechanism of the catalysis. In this study, we apply the weighted ensemble (WE) simulation method to obtain comprehensive path ensembles for the Pin1-catalyzed isomerization process. Associated rate constants for both cis-to-trans and trans-to-cis isomerization are calculated to be submicroseconds time scales, which are in good agreement with the calculated free energy landscape where the cis form is slightly less favorable. The committor-like analysis indicates the shift of the transition state toward trans form (at the isomerization angle ω ∼ 110°) compared to the intrinsic position for the isolated substrate (ω ∼ 90°). The calculated structural ensemble clarifies a role of both the dual-histidine motif, His59/His157, and the basic residues, Lys63/Arg68/Arg69, to anchor both sides of the peptidyl-prolyl bond, the aromatic ring in Pro, and the phosphate in pSer, respectively. The rotation of the torsion angle is found to be facilitated by relaying the hydrogen-bond partner of the main-chain oxygen in pSer from Cys113 in the cis form to Arg68 in the trans form, through Ser154 at the transition state, which is really the cause of the shift in the transition state. The role of Ser154 as a driving force of the isomerization is confirmed by additional WE and free energy calculations for S154A mutant where the isomerization takes place slightly slower and the free energy barrier increases through the mutation. The present study shows the usefulness of the WE simulation for substantial path samplings between the reactant and product states, unraveling the molecular mechanism of the enzyme catalysis.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions.

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Conformational change of a biomolecule studied by the weighted ensemble method: Use of the diffusion map method to extract reaction coordinates.

We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way. We find that the transition time scales thus obtained are comparable to those using previously employed hydrogen-bond distances as the order parameters. Since the DM method only uses the 3D Cartesian coordinates of a peptide, this shows that the DM method can extract the important distance information of the peptide without relying on chemical intuition. The time scales are compared well with the previous results using different techniques, non-Markovian analysis and core-set milestoning for a single long trajectory. We also find that the most significant DM coordinate turns out to extract a dihedral angle of glycine, and the previously studied relaxation modes are well correlated with the most significant DM coordinates.

Energetics and conformational pathways of functional rotation in the multidrug transporter AcrB.

The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive. Here, calculating the minimum free energy pathway of the functional rotation for the complete AcrB trimer, we describe the structural and energetic basis behind the coupling between the functional rotation and the proton translocation at atomic resolution. Free energy calculations show that protonation of Asp408 in the transmembrane portion of the drug-bound protomer drives the functional rotation. The conformational pathway identifies vertical shear motions among several transmembrane helices, which regulate alternate access of water in the transmembrane as well as peristaltic motions that pump drugs in the periplasm.

Extended Phase-Space Methods for Enhanced Sampling in Molecular Simulations: A Review.

Molecular Dynamics simulations are a powerful approach to study biomolecular conformational changes or protein-ligand, protein-protein, and protein-DNA/RNA interactions. Straightforward applications, however, are often hampered by incomplete sampling, since in a typical simulated trajectory the system will spend most of its time trapped by high energy barriers in restricted regions of the configuration space. Over the years, several techniques have been designed to overcome this problem and enhance space sampling. Here, we review a class of methods that rely on the idea of extending the set of dynamical variables of the system by adding extra ones associated to functions describing the process under study. In particular, we illustrate the Temperature Accelerated Molecular Dynamics (TAMD), Logarithmic Mean Force Dynamics (LogMFD), and Multiscale Enhanced Sampling (MSES) algorithms. We also discuss combinations with techniques for searching reaction paths. We show the advantages presented by this approach and how it allows to quickly sample important regions of the free-energy landscape via automatic exploration.

Reconstruction of semiautomated cardiac regions of interest using iodine-123 metaiodobenzylguanidine myocardial scintigraphy.

INTRODUCTION: Analysis using cardiac iodine-123 metaiodobenzylguanidine (MIBG) scintigraphy with regions of interest (ROIs) is useful for assessing myocardial sympathetic activity. However, manual placement of the cardiac ROI is sometimes difficult because myocardial MIBG uptake is reduced in patients with heart failure. A new method was developed to reconstruct the semiautomated cardiac ROI in a sympathetic denervated heart. MATERIALS AND METHODS: Using dynamic planar data, a summed image was generated and the matrix size was changed. Then, the radial count profiles originating from the center of the left ventricle were generated to extract the myocardial count profiles. An asymmetric Gaussian distribution was fitted to each profile and the epicardial border was defined by the threshold method. This program was tested in 50 patients, and its reproducibility was validated when compared with the manual tracing method. RESULTS: The semiautomated method yielded a better quality image compared with the standard image with higher counts. Cardiac ROIs were generated successfully in each patient within normal limits. The intraobserver and interobserver agreements were excellent (P<0.0001 each). This approach showed a significantly higher consistency in measuring the heart-to-mediastinum ratio as compared with the manual tracing method (P<0.05). CONCLUSION: The semiautomated method is useful in generating cardiac ROIs with high reproducibility in myocardial MIBG imaging.

Multiscale enhanced path sampling based on the Onsager-Machlup action: application to a model polymer.

We propose a novel path sampling method based on the Onsager-Machlup (OM) action by generalizing the multiscale enhanced sampling technique suggested by Moritsugu and co-workers [J. Chem. Phys. 133, 224105 (2010)]. The basic idea of this method is that the system we want to study (for example, some molecular system described by molecular mechanics) is coupled to a coarse-grained (CG) system, which can move more quickly and can be computed more efficiently than the original system. We simulate this combined system (original + CG system) using Langevin dynamics where different heat baths are coupled to the two systems. When the coupling is strong enough, the original system is guided by the CG system, and is able to sample the configuration and path space with more efficiency. We need to correct the bias caused by the coupling, however, by employing the Hamiltonian replica exchange, where we prepare many path replicas with different coupling strengths. As a result, an unbiased path ensemble for the original system can be found in the weakest coupling path ensemble. This strategy is easily implemented because a weight for a path calculated by the OM action is formally the same as the Boltzmann weight if we properly define the path "Hamiltonian." We apply this method to a model polymer with Asakura-Oosawa interaction, and compare the results with the conventional transition path sampling method.

Minimum free energy path of ligand-induced transition in adenylate kinase.

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates.

We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the "centroid IRC," corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH(3) molecule and N(2)H(5) (-) ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH(3), the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N(2)H(5) (-), the centroid IRC is largely deviated from the "classical" IRC, and the free energy barrier is reduced by the quantum effects even more drastically.

Different inhibitory potency of febuxostat towards mammalian and bacterial xanthine oxidoreductases: insight from molecular dynamics.

Febuxostat, a drug recently approved in the US, European Union and Japan for treatment of gout, inhibits xanthine oxidoreductase (XOR)-mediated generation of uric acid during purine catabolism. It inhibits bovine milk XOR with a K(i) in the picomolar-order, but we found that it is a much weaker inhibitor of Rhodobacter capsulatus XOR, even though the substrate-binding pockets of mammalian and bacterial XOR are well-conserved as regards to catalytically important residues and three-dimensional structure, and both permit the inhibitor to be accommodated in the active site, as indicated by computational docking studies. To clarify the reason for the difference of inhibitory potency towards the two XORs, we performed molecular dynamics simulations. The results indicate that differences in mobility of hydrophobic residues that do not directly interact with the substrate account for the difference in inhibitory potency.

Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways.

For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.

Evaluation of utility of asymmetric index for count-based oxygen extraction fraction on dual-tracer autoradiographic method for chronic unilateral brain infarction.

OBJECTIVE: For diagnosing patients with ischemic cerebrovascular disease, non-invasive count-based method with (15)O(2) and H (2) (15) O positron-emission tomography (PET) data is widely used to measure asymmetric increases in oxygen extraction fraction (OEF). For shortening study time, we have proposed dual-tracer autoradiographic (DARG) protocol in which (15)O(2) gas and C(15)O(2) gas are sequentially administrated within short period. In this paper, we evaluated feasibility of the non-invasive count-based method with the DARG protocol. METHODS: Twenty-three patients [67.8 +/- 9.9 (mean +/- SD) years] with chronic unilateral brain infarction were examined by the use of measurements of asymmetric OEF elevation. As DARG protocol, (15)O(2) and C(15)O(2) gases were inhaled with 5-min interval and dynamic PET data were acquired for 8 min. Quantitative OEF (qOEF) image was computed with PET data and arterial input function. Ratio image of (15)O(2) and C(15)O(2) phases of PET data was computed as count-based OEF (cbOEF) image. The asymmetric indices (AI) of qOEF (qOEF-AI) and cbOEF (cbOEF-AI) were obtained from regions of interest symmetric placed on left and right sides of cerebral hemisphere. To optimize the summation time of PET data for the cbOEF image, qOEF and cbOEF images with various summation times were compared. RESULTS: Image quality of cbOEF image was better than that of qOEF image. The best correlation coefficient of 0.94 was obtained when the cbOEF image was calculated from 0 to 180 s of (15)O(2) summed image and 340 to 440 s of C(15)O(2) summed image. CONCLUSION: Using the appropriate summation time, we obtained the cbOEF image with good correlation with qOEF image, which suggests non-invasive cbOEF image can be used for evaluating the degree of misery perfusion in patients with chronic unilateral brain infarction. The count-based method with DARG protocol has a potential to dramatically reduce the examination time of (15)O PET study.

Mode-specific vibrational energy relaxation of amide I' and II' modes in N-methylacetamide/water clusters: intra- and intermolecular energy transfer mechanisms.

The mode-specific vibrational energy relaxation of the amide I' and amide II' modes in NMA-d(1)/(D(2)O)(n) (n = 0-3) clusters were studied using the time-dependent perturbation theory at the B3LYP/aug-cc-pvdz level. The amide modes were identified for each cluster based on the potential energy distribution of each mode. The vibrational population relaxation time constants were derived for the amide I' and II' modes. Results for the amide I' mode relaxation of NMA-d(1)/(D(2)O)(3) agree well with previous experimental results. The energy relaxation pathways were identified, and both intra- and intermolecular mechanisms were found to be important. The amide II' mode was identified in the energy transfer pathways from the excited amide I' mode of NMA-d(1)/(D(2)O)(n) (n = 1-3) clusters. The modes associated with methyl group deformation were found to play a role in the mechanism of energy transfer from both excited amide I' and II' modes. The kinetics of energy flow in the cluster were examined by solving a master equation describing the vibrational energy relaxation process from excited system mode as a multistep reaction with the third order Fermi resonance parameters as the reaction rate constants. The intramolecular energy transfer mechanism was found to dominate the short time energy flow dynamics, whereas the intermolecular mechanism was found to be dominant at longer times.

Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. I. Five-coordinate ferrous iron porphyrin model.

The time scales and mechanisms of mode-specific vibrational energy relaxation in imidazole ligated ferrous iron porphine were studied using a non-Markovian time-dependent perturbation theory and density functional theory calculation. Seven normal modes, including nu(4), nu(7), and five Fe out-of-plane modes (Fe-oop), were treated as the relaxing system mode coupled to all other modes forming the bath. The derived cooling time constants for the nu(4) and nu(7) modes agree well with the results of previous experimental studies. The pathways for energy transfer from each system mode were identified. The gamma(7) mode, associated with Fe-oop motion with frequency approximately 350 cm(-1), was observed to couple strongly through its overtone with the nu(7) porphine in-plane vibration. This suggests a possible mechanism for the excitation of the nu(7) mode, which is distinct from the direct excitation together with Fe-oop motion of the nu(4) mode. Four other Fe-oop motions were observed to couple to low frequency modes including those involving significant imidazole ligand motions. Through these couplings, excitation following ligand photodissociation may be efficiently transferred from the heme doming mode to the protein backbone motions essential to conformational changes associated with the protein's function.

Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment.

A computational approach to describe the energy relaxation of a high-frequency vibrational mode in a fluctuating heterogeneous environment is outlined. Extending previous work [H. Fujisaki, Y. Zhang, and J. E. Straub, J. Chem. Phys. 124, 144910 (2006)], second-order time-dependent perturbation theory is employed which includes the fluctuations of the parameters in the Hamiltonian within the vibrational adiabatic approximation. This means that the time-dependent vibrational frequencies along a molecular dynamics trajectory are obtained via a partial geometry optimization of the solute with fixed solvent and a subsequent normal mode calculation. Adopting the amide I mode of N-methylacetamide in heavy water as a test problem, it is shown that the inclusion of dynamic fluctuations may significantly change the vibrational energy relaxation. In particular, it is found that relaxation occurs in two phases, because for short times (approximately < 200 fs) the spectral density appears continuous due to the frequency-time uncertainty relation, while at longer times the discrete nature of the bath becomes apparent. Considering the excellent agreement between theory and experiment, it is speculated if this behavior can explain the experimentally obtained biphasic relaxation the amide I mode of N-methylacetamide.

Vibrational energy relaxation of isotopically labeled amide I modes in cytochrome c: theoretical investigation of vibrational energy relaxation rates and pathways.

With use of a time-dependent perturbation theory, vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c solvated with water is investigated. Contributions to the VER are decomposed into two contributions from the protein and water. The VER pathways are visualized by using radial and angular excitation functions for resonant normal modes. Key differences of VER among different amide I modes are demonstrated, leading to a detailed picture of the spatial anisotropy of the VER. The results support the experimental observation that amide I modes in proteins relax with subpicosecond time scales, while the relaxation mechanism turns out to be sensitive to the environment of the amide I mode.

Analytic approach for controlling quantum states in complex systems.

We examine random matrix systems driven by an external field in view of optimal control theory (OCT). By numerically solving OCT equations, we can show that there exists a smooth transition between two states called "moving bases" which are dynamically related to initial and final states. In our previous work [J. Phys. Soc. Jpn. 73, 3215 (2004); Adv. Chem. Phys. 130A, 435 (2005)], they were assumed to be orthogonal, but in this paper, we introduce orthogonal moving bases. We can construct a Rabi-oscillation-like representation of a wave packet using such moving bases, and derive an analytic optimal field as a solution of the OCT equations. We also numerically show that the newly obtained optimal field outperforms the previous one.