Path integral Monte Carlo with importance sampling for excitons interacting with an arbitrary phonon bath

The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance of the Monte Carlo simulation. We show that by choosing the population-normalized estimator for the reduced density matrix, an efficient and physically-meaningful sampling function can be obtained. In addition, the nonadiabatic phonon probability density is obtained as a byproduct during the sampling procedure. For importance sampling, we adopted the Metropolis-adjusted Langevin algorithm. The analytic expression for the gradient of the target probability density function associated with the population-normalized estimator cannot be obtained in closed form without a matrix power series. An approximated gradient that can be efficiently calculated is explored to achieve better computational scaling and efficiency. Application to a simple one-dimensional model system from the previous literature confirms the correctness of the method developed in this manuscript. The displaced harmonic model system within the single exciton manifold shows the numerically exact temperature dependence of the coherence and population of the excitonic system. The sampling scheme can be applied to an arbitrary anharmonic environment, such as multichromophoric systems embedded in the protein complex. The result of this study is expected to stimulate further development of real time propagation methods that satisfy the detailed balance condition for exciton populations.Comment: 16 pages, 5 figure

Quantum Dynamics in Biological Systems

In the first part of this dissertation, recent efforts to understand quantum mechanical effects in biological systems are discussed. Especially, long-lived quantum coherences observed during the electronic energy transfer process in the Fenna-Matthews-Olson complex at physiological condition are studied extensively using theories of open quantum systems. In addition to the usual master equation based approaches, the effect of the protein structure is investigated in atomistic detail through the combined application of quantum chemistry and molecular dynamics simulations. To evaluate the thermalized reduced density matrix, a path-integral Monte Carlo method with a novel importance sampling approach is developed for excitons coupled to an arbitrary phonon bath at a finite temperature. In the second part of the thesis, simulations of molecular systems and applications to vibrational spectra are discussed. First, the quantum dynamics of a molecule is simulated by combining semiclassical initial value representation and density funcitonal theory with analytic derivatives. A computationally-tractable approximation to the sum-of-states formalism of Raman spectra is subsequently discussed

Simplified Sum-Over-States Approach for Predicting Resonance Raman Spectra. Application to Nucleic Acid Bases

Resonance Raman spectra provide a valuable probe into molecular excited-state structures and properties. Moreover, resonance enhancement is of importance for the chemical contribution to surface-enhanced Raman scattering. In this work, we introduce a simplified sum-over-states scheme for computing Raman spectra and Raman excitation profiles. The proposed sum-over-states approach uses derivatives of electronic excitation energies and transition dipole moments, which can be efficiently computed from time-dependent density functional theory. We analyze and interpret the resonance Raman spectra and Raman excitation profiles of nucleic acid bases using the present approach. Contributions of individual excited states under strictly resonant and non-resonant conditions are investigated, and smooth interpolation between both limiting cases is obtained.Chemistry and Chemical Biolog

The Many Hats of Sonic Hedgehog Signaling in Nervous System Development and Disease.

Sonic hedgehog (Shh) signaling occurs concurrently with the many processes that constitute nervous system development. Although Shh is mostly known for its proliferative and morphogenic action through its effects on neural stem cells and progenitors, it also contributes to neuronal differentiation, axonal pathfinding and synapse formation and function. To participate in these diverse events, Shh signaling manifests differently depending on the maturational state of the responsive cell, on the other signaling pathways regulating neural cell function and the environmental cues that surround target cells. Shh signaling is particularly dynamic in the nervous system, ranging from canonical transcription-dependent, to non-canonical and localized to axonal growth cones. Here, we review the variety of Shh functions in the developing nervous system and their consequences for neurodevelopmental diseases and neural regeneration, with particular emphasis on the signaling mechanisms underlying Shh action

Characterization and Quantification of the Role of Coherence in Ultrafast Quantum Biological Experiments Using Quantum Master Equations, Atomistic Simulations, and Quantum Process Tomography

Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.Chemistry and Chemical Biolog

BMP gradients steer nerve growth cones by a balancing act of LIM kinase and Slingshot phosphatase on ADF/cofilin

Bone morphogenic proteins (BMPs) are involved in axon pathfinding, but how they guide growth cones remains elusive. In this study, we report that a BMP7 gradient elicits bidirectional turning responses from nerve growth cones by acting through LIM kinase (LIMK) and Slingshot (SSH) phosphatase to regulate actin-depolymerizing factor (ADF)/cofilin-mediated actin dynamics. Xenopus laevis growth cones from 4–8-h cultured neurons are attracted to BMP7 gradients but become repelled by BMP7 after overnight culture. The attraction and repulsion are mediated by LIMK and SSH, respectively, which oppositely regulate the phosphorylation-dependent asymmetric activity of ADF/cofilin to control the actin dynamics and growth cone steering. The attraction to repulsion switching requires the expression of a transient receptor potential (TRP) channel TRPC1 and involves Ca2+ signaling through calcineurin phosphatase for SSH activation and growth cone repulsion. Together, we show that spatial regulation of ADF/cofilin activity controls the directional responses of the growth cone to BMP7, and Ca2+ influx through TRPC tilts the LIMK-SSH balance toward SSH-mediated repulsion

Atomistic study of the long-lived quantum coherences in the Fenna-Matthews-Olson complex

A remarkable amount of theoretical research has been carried out to elucidate the physical origins of the recently observed long-lived quantum coherence in the electronic energy transfer process in biological photosynthetic systems. Although successful in many respects, several widely used descriptions only include an effective treatment of the protein-chromophore interactions. In this work, by combining an all-atom molecular dynamics simulation, time-dependent density functional theory, and open quantum system approaches, we successfully simulate the dynamics of the electronic energy transfer of the Fenna-Matthews-Olson pigment-protein complex. The resulting characteristic beating of populations and quantum coherences is in good agreement with the experimental results and the hierarchy equation of motion approach. The experimental absorption, linear and circular dichroism spectra and dephasing rates are recovered at two different temperatures. In addition, we provide an extension of our method to include zero-point fluctuations of the vibrational environment. This work thus presents one of the first steps to explain the role of excitonic quantum coherence in photosynthetic light-harvesting complexes based on their atomistic and molecular description.Comment: 24 pages, 6 figure

First-Principles Semiclassical Initial Value Representation Molecular Dynamics

A method for carrying out semiclassical initial value representation calculations using first-principles molecular dynamics (FP-SC-IVR) is presented. This method can extract the full vibrational power spectrum of carbon dioxide from a single trajectory providing numerical results that agree with experiment even for Fermi resonant states. The computational demands of the method are comparable to those of classical single-trajectory calculations, while describing uniquely quantum features such as the zero-point energy and Fermi resonances. By propagating the nuclear degrees of freedom using first-principles Born-Oppenheimer molecular dynamics, the stability of the method presented is improved considerably when compared to dynamics carried out using fitted potential energy surfaces and numerical derivatives.Comment: 5 pages, 2 figures, made stylistic and clarity change