Realistic and verifiable coherent control of excitonic states in a light harvesting complex

We explore the feasibility of coherent control of excitonic dynamics in light harvesting complexes, analyzing the limits imposed by the open nature of these quantum systems. We establish feasible targets for phase and phase/amplitude control of the electronically excited state populations in the Fenna-Mathews-Olson (FMO) complex and analyze the robustness of this control with respect to orientational and energetic disorder, as well as decoherence arising from coupling to the protein environment. We further present two possible routes to verification of the control target, with simulations for the FMO complex showing that steering of the excited state is experimentally verifiable either by extending excitonic coherence or by producing novel states in a pump-probe setup. Our results provide a first step toward coherent control of these complex biological quantum systems in an ultrafast spectroscopy setup.Comment: 12 pages, 8 figure

Application of machine learning techniques to the description of open quantum systems.

Doctoral Degree. University of KwaZulu-Natal, Durban.This work focuses on using classical machine learning (ML) models to study the quantum dynamics of excitation energy transfer (EET) within strongly coupled open quantum systems relevant to light harvesting complexes (LHCs). Direct evidence for long-lived quantum coherence has been found to play an important role in EET processes during the first step of photosynthesis in certain LHCs where excitation energy is transmitted from the antenna pigments to the reaction center in which photochemical reactions are initiated [1–3]. The numerically exact method used to simulate the dynamics in this work is the hierarchical equations of motion (HEOM) adapted by Ishizaki and Fleming to suit the quantum biological regime [4–6]. In the case of an open quantum system, such as a photosynthetic pigment-protein complex, evolving over time we can generate a set of time dependent observables that depict the coherent movement of electronic excitations through the system by solving a suitable set of quantum dynamic equations such as the HEOM. We have focused on solving two problems, the first being the inverse problem. That is, the objective is to determine whether a trained ML model can perform Hamiltonian tomography by using the time dependence of the observables as inputs. We demonstrate the capability of the convolutional neural network (CNN) to solve the inverse problem. That is, the trained CNN can accurately describe the system under study by predicting the parameters of the system Hamiltonian when given the aforementioned time dependent data. The models developed can predict Hamiltonian parameters such as excited state energies and inter-site couplings of a system up to 99.28% accuracy. The second use of the same data set of observables involves time-series analysis. Although various analytical solutions for the dynamics of open quantum systems such as the HEOM have been developed, these often require immense computational resources. We demonstrate that models such as SARIMA, CatBoost, Prophet, convolutional and recurrent neural networks can predict the long-time dynamics provided that the initial short-time dynamics is given. Our results suggest that SARIMA can serve as a computationally inexpensive yet accurate way to predict long-time dynamics.Author's publications are listed on page iii of the thesis

Hybrid QM/classical models: Methodological advances and new applications

Hybrid methods that combine quantum mechanical descriptions with classical models are very popular in molecular modeling. Such a large diffusion reflects their effectiveness, which over the years has allowed the quantum mechanical description to extend its boundaries to systems of increasing size and to processes of increasing complexity. Despite this success, research in this field is still very active and a number of advances have been made recently, further extending the range of their applications. In this review, we describe such advances and discuss how hybrid methods may continue to improve in the future. The various formulations proposed so far are presented here in a coherent way to underline their common methodological aspects. At the same time, the specificities of the different classical models and of their coupling with the quantum mechanical domain are highlighted and discussed, with special attention to the computational and numerical aspects

State Estimation for diffusion systems using a Karhunen-Loeve-Galerkin Reduced-Order Model

This thesis focuses on generating a continuous estimate of state using a small number of sensors for a process modeled by the diffusion partial differential equation(PDE). In biological systems the diffusion of oxygen in tissue is well described by the diffusion equation, also known by biologists as Fick\u27s first law. Mass transport of many other materials in biological systems are modeled by the diffusion PDE such as CO2, cell signaling factors, glucose and other biomolecules. Estimating the state of a PDE is more formidable than that of a system described by ordinary differential equations (ODEs). While the state variables of the ODE system are finite in number, the state variables of the PDE are distributed in the spatial domain and infinite in number. Reduction of the number of state variables to a finite small number which is tractable for estimation will be accomplished through use of the Karhunen-Loeve-Galerkin method for model order reduction. The model order reduction is broken into two steps, (i) determine an appropriate set of basis functions and (ii) project the PDE onto the set of candidate basis functions. The Karhunen-Loeve expansion is used to decompose a set of observations of the system into the principle modes composing the system dynamics. The observations may be obtained through numerical simulation or physical experiments that encompass all dynamics that the reduced-order model will be expected to reproduce. The PDE is then projected onto a small number of basis functions using the linear Galerkin method, giving a small set of ODEs which describe the system dynamics. The reduced-order model obtained from the Karhunen-Loeve-Galerkin procedure is then used with a Kalman filter to estimate the system state. Performance of the state estimator will be investigated using several numerical experiments. Fidelity of the reduced-order model for several different numbers of basis functions will be compared against a numerical solution considered to be the true solution of the continuous problem. The efficiency of the empirical basis compared to an analytical basis will be examined. The reduced-order model will then be used in a Kalman filter to estimate state for a noiseless system and then a noisy system. Effects of sensor placement and quantity are evaluated. A test platform was developed to study the estimation process to track state variables in a simple non-biological system. The platform allows the diffusion of dye through gelatin to be monitored with a camera. An estimate of dye concentration throughout the entire volume of gelatin will be accomplished using a small number of point sensors, i.e. pixels selected from the camera. The estimate is evaluated against the actual diffusion as captured by the camera. This test platform will provide a means to empirically study the dynamics of diffusion-reaction systems and associated state estimators

Multiscale approaches to describe multichromophoric systems in complex environments

The modeling of supramolecular aggregates is an interesting challenge in the field of computational chemistry. In this work we applied multiscale approaches by combining quantum-mechanical and classical methods for the study of multichromophoric systems embedded in complex environments. Different multichromophoric systems have been investigated by applying an excitonic strategy and a particular attention has been devoted to the reproduction of excitonic optical spectra. An interesting class of multichromophoric systems is constituted by pigment-protein light harvesting complex specialized in the sunlight energy absorption in photosynthetic organisms. A novel approach based on the integration of classical molecular dynamics with fully polarizable QM/classical methods has been presented and applied to two different light-harvesting systems

Global and target analysis of time-resolved spectra

AbstractIn biological/bioenergetics research the response of a complex system to an externally applied perturbation is often studied. Spectroscopic measurements at multiple wavelengths are used to monitor the kinetics. These time-resolved spectra are considered as an example of multiway data. In this paper, the methodology for global and target analysis of time-resolved spectra is reviewed. To fully extract the information from the overwhelming amount of data, a model-based analysis is mandatory. This analysis is based upon assumptions regarding the measurement process and upon a physicochemical model for the complex system. This model is composed of building blocks representing scientific knowledge and assumptions. Building blocks are the instrument response function (IRF), the components of the system connected in a kinetic scheme, and anisotropy properties of the components. The combination of a model for the kinetics and for the spectra of the components results in a more powerful spectrotemporal model. The model parameters, like rate constants and spectra, can be estimated from the data, thus providing a concise description of the complex system dynamics. This spectrotemporal modeling approach is illustrated with an elaborate case study of the ultrafast dynamics of the photoactive yellow protein

Estimation of Phytoplankton Chlorophyll-a Concentration in the Western Basin of Lake Erie Using Sentinel-2 and Sentinel-3 Data

Worldwide phenomena called algae bloom has been recently a serious matter for inland water bodies. Temporal and spatial variability of the bloom makes it di cult to use in-situ monitoring of the lakes. This study aimed to evaluate the potential of Sentinel-3 Ocean and Land Colour Instrument (OLCI) and Sentinel-2 Multispectral Instrument (MSI) data for monitoring algal blooms in Lake Erie. Chlorophyll-a (Chl-a) related products were tested using NOAA-Great Lakes Chl-a monitoring data over summer 2016 and 2017. Thematic water processor, fluorescence line height/maximum chlorophyll index (MCI) and S2 MCI, plug-in SNAP were assessed for their ability to estimate Chl-a concentration. We processed both Top of the Atmosphere (TOA) reflectance and radiance data. Results show that while FLH algorithms are limited to lakes with Chl-a < 8 mg m-3, MCI has the potential to be used effectively to monitor Chl-a concentration over eutrophic lakes. Sentinel-3 MCI is suggested for Chl-a > 20 mg m-3 and Sentinel-2 MCI for Chla > 8 mg m-3. The different Chl-a range limitation for the MCI products can be due to the different location of the maximum peak bands, 705 and 709 for MSI and OLCI sensors respectively. TOA radiances showed a signi cantly better correlation with in situ data compared to TOA reflectances which may be related to the poor pixel identi cation during the process of pixel flagging affected by the complexity of Case-2 water. Our fi nding suggests that Sentinel-2 MCI achieves better performance for Chl-a retrieval (R2 = 0.90). However, the FLH algorithms outperformed showing negative reflectance due to the shift of reflectance peak to longer wavelengths along with increasing Chl-a values. Although the algorithms show moderate performance for estimating Chl-a concentration; this study demonstrated that the new satellite sensors, OLCI and MSI, can play a signi ficant role in the monitoring of algae blooms for Lake Erie