arXiv subjects

Hiroshi Fujisaki

Publications and source records attributed to Hiroshi Fujisaki.

At least 19 recordsLinked to original sources

arXiv2022

Numerical simulation using cellular Potts model for wound closure with ATP release and the mechanobioligical effects

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 Pots 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 intracellular Ca$^{2+}$ influx. To model these phenomena, the Reaction-Diffusion equations for ATP and Ca$^{2+}$ 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 his hybrid model, we discuss effects of the collective cell migration due to the ATP release and the Ca${}^{2+}$ influx caused by the mechanical forces and the consequent promotion of wound closure.

physics.bio-ph↗

arXiv2020

Modular Arithmetic Erasure Channels and Their Multilevel Channel Polarization

This study proposes \emph{modular arithmetic erasure channels} (MAECs), a novel class of erasure-like channels with an input alphabet that need not be binary. This class contains the binary erasure channel (BEC) and some other known erasure-like channels as special cases. For MAECs, we provide recursive formulas of Arıkan-like polar transform to simulate channel polarization. In other words, we show that the synthetic channels of MAECs are equivalent to other MAECs. This is a generalization of well-known recursive formulas of the polar transform for BECs. Using our recursive formulas, we also show that a recursive application of the polar transform for MAECs results in \emph{multilevel channel polarization,} which is an asymptotic phenomenon that is characteristic of non-binary polar codes. Specifically, we establish a method to calculate the limiting proportions of the partially noiseless and noisy channels that are generated as a result of multilevel channel polarization for MAECs. In the particular case of MAECs, this calculation method solves an open problem posed by Nasser (2017) in the study of non-binary polar codes.

cs.IT↗

arXiv2019

Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions

Polar transforms are central operations in the study of polar codes. This paper examines polar transforms for non-stationary memoryless sources on possibly infinite source alphabets. This is the first attempt of source polarization analysis over infinite alphabets. The source alphabet is defined to be a Polish group, and we handle the Arıkan-style two-by-two polar transform based on the group. Defining erasure distributions based on the normal subgroup structure, we give recursive formulas of the polar transform for our proposed erasure distributions. As a result, the recursive formulas lead to concrete examples of multilevel source polarization with countably infinite levels when the group is locally cyclic. We derive this result via elementary techniques in lattice theory.

cs.IT↗

arXiv2018

Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels

This study examines multilevel channel polarization for a certain class of erasure channels that the input alphabet size is an arbitrary composite number. We derive limiting proportions of partially noiseless channels for such a class. The results of this study are proved by an argument of convergent sequences, inspired by Alsan and Telatar's simple proof of polarization, and without martingale convergence theorems for polarization process.

cs.IT↗

arXiv2013

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 (MSES) technique suggested by Moritsugu and coworkers (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 computed more efficiently than the original system. We simulate this combined system (original + CG system) using (underdamped) 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 able to sample the configuration and path space more efficiency. We need to correct the bias caused by the coupling, however, by employing the Hamiltonian replica exchange where we prepare many path replica 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.

physics.bio-ph↗

arXiv2010

Non-Markovian theory of vibrational energy relaxation and its applications to biomolecular systems

Energy transfer (relaxation) phenomena are ubiquitous in nature. At a macroscopic level, the phenomenological theory of heat (Fourier law) successfully describes heat transfer and energy flow. However, its microscopic origin is still under debate. This is because the phenomena can contain many-body, multi-scale, nonequilibrium, and even quantum mechanical aspects, which present significant challenges to theories addressing energy transfer phenomena in physics, chemistry and biology. In this paper, we describe our recent theoretical attempts to treat vibrational energy relaxation (VER) in biomolecular systems, including peptide, porphyrin, and protein. First we construct a reduced model using (instantaneous) normal mode analysis, and further add anharmonic coupling between vibrational modes. Using such a model combined with time-dependent perturbation theory for the anharmonic coupling, we derive non-Markovian VER formulas, which are applicable to small timescales such as sub picoseconds. We apply the VER formulas with full atomistic detail to various biomolecular systems, discuss the VER timescales and mechanisms, and compare with experiment if possible. We finally mention further theoretical prospects of the energy transfer phenomena in physics, chemistry, and biology.

physics.bio-ph↗

arXiv2010

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.

physics.bio-ph↗

arXiv2008

Quantum and classical vibrational relaxation dynamics of N-methylacetamide on ab initio potential energy surfaces

Employing extensive quantum-chemical calculations at the DFT/B3LYP and MP2 level, a quartic force field of isolated N-methylacetamide is constructed. Taking into account 24 vibrational degrees of freedom, the model is employed to perform numerically exact vibrational configuration interaction calculations of the vibrational energy relaxation of the amide I mode. It is found that the energy transfer pathways may sensitively depend on details of the theoretical description. Moreover, the exact reference calculations were used to study the applicability and accuracy of (i) the quasiclassical trajectory method, (ii) time-dependent second-order perturbation theory, and (iii) the instantaneous normal mode description of frequency fluctuations. Based on the results, several strategies to describe vibrational energy relaxation in biomolecular systems are discussed.

physics.chem-ph↗

arXiv2008

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. {\bf 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 an MD 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 ($\lesssim$ 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.

physics.chem-ph↗

arXiv2008

Resonant Analytic Fields Applied to Generic Multi-state Systems

Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the Schroedinger equation. First, we introduce an extension of the rotating-wave approximation for multi-state systems. Under an assumption that a smooth transition is induced by the optimal field, we obtain three types of analytic control fields and demonstrate their validity and deficiency for generic systems represented by random matrices. Through the comparison, we conclude that the analytic field based on our coarse-grained approach outperforms the other ones for generic quantum systems with a large number of states. Finally, the further extension of the analytic field is introduced for realistic chaotic systems and its validity is shown in banded random matrix systems.

nlin.CD↗

arXiv2007

Analytic Approach for Controlling Realistic Quantum Chaotic Systems

An analytic approach for controlling quantum states, which was originally applied to fully random matrix systems [T. Takami and H. Fujisaki, Phys. Rev. E 75, 036219 (2007)], is extended to deal with more realistic quantum systems with a banded random matrix (BRM). The validity of the new analytic field is confirmed by directly solving the Schroedinger equation with a BRM interaction. We find a threshold of the width of the BRM for the quantum control to be successful.

nlin.CD↗

arXiv2007

Vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c: Theoretical investigation of VER rates and pathways

Using 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 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 sub picosecond timescales, while the relaxation mechanism turns out to be sensitive to the environment of the amide I mode.

q-bio.BM↗

arXiv2007

Quantum dynamics of N-methylacetamide studied by the vibrational configuration interaction method

Vibrational energy transfer of the amide I mode of N-methylacetamide (NMA) is studied theoretically using the vibrational configuration interaction method. A quartic force field of NMA is constructed at the B3LYP/6-31G+(d) level of theory and its accuarcy is checked by comparing the resulting anharmonic frequencies with available theoretical and experimental values. Quantum dynamics calculations for the amide I mode excitation clarify the dominant energy transfer pathways, which sensitively depend on the anharmonic couplings among vibrational modes. A ratio of the anharmonic coupling to the frequency mismatch is employed to predict and interpret the dominant energy flow pathways.

q-bio.BM↗

arXiv2007

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 (2004) 3215-3216; Adv. Chem. Phys. 130A (2005) 435-458], 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 wavpacket 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.

nlin.CD↗

arXiv2006

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by Mikami and Okazaki invoking the path-integral influence functional method [J. Chem. Phys. 121 (2004) 10052]. We apply our formulas to VER of the amide I mode of a small amino-acide like molecule, N-methylacetamide, in heavy water.

q-bio.BM↗

arXiv2005

Vibrational energy relaxation in proteins

An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied using two theoretical approaches. One is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements. Both methods result in estimates of the VER time (sub ps) for a CD stretching mode in the protein at room temperature. The theoretical predictions are in accord with the experimental data of Romesberg's group. A perspective on future directions for the detailed study of time scales and mechanisms for VER in proteins is presented.

q-bio.BM↗

arXiv2004

Coarse-Grained Picture for Controlling Complex Quantum Systems

We propose a coarse-grained picture to control ``complex'' quantum dynamics, i.e., multi-level-multi-level transition with a random interaction. Assuming that optimally controlled dynamics can be described as a Rabi-like oscillation between an initial and final state, we derive an analytic optimal field as a solution to optimal control theory. For random matrix systems, we numerically confirm that the analytic optimal field steers an initial state to a target state which both contains many eigenstates.

nlin.CD↗

arXiv2004

Probing vibrational energy relaxation in proteins using normal modes

Vibrational energy relaxation (VER) of a selected mode in cytochrome c (hemeprotein) in vacuum is studied using two theoretical approaches: One is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach which describes the protein as an ensemble of normal modes coupled with nonlinear coupling elements. Both methods result in estimates of VER time (sub ps) for a CD stretching mode in the protein at room temperature, that are in accord with the experimental data of Romesberg's group. The applicability of the two methods is examined through a discussion of the validity of Fermi's golden rule on which the two methods are based.

q-bio.BM↗