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TY  - THES
AU  - Di Cairano, Loris
TI  - Generalized Langevin equation-based approach for investigating complex biological systems
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2021-11852
SP  - 1 Online-Ressource : Illustrationen
PY  - 2021
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2022
N1  - Dissertation, RWTH Aachen University, 2021
AB  - In this thesis, we propose several theoretical approaches based on the generalized Langevin equation (GLE) for describing the dynamics of biological systems. We focus our attention on two particular topics relevant to molecular signaling: the protein diffusion in lipid membrane and the study of collective oscillations of vibrational modes within a protein also known as Fröhlich condensation. Regarding the protein diffusion in lipid membrane, we develop a GLE-based model for the lateral diffusion of a protein describing the lipid membrane as a linear viscoelastic fluid. The main contribution to this field is to provide a suitable modelling of the time-dependent friction function entering the GLE which allows to describe the memory effects due to the protein-membrane interactions and, therefore, to describe the main viscoelastic properties of the lipid membrane.More precisely, the friction function is represented in terms of a viscous (instantaneous) and an elastic (non instantaneous) component modeled respectively through a Dirac delta function and a three-parameter Mittag-Leffler type function. By imposing a specific relationship between the parameters of the three-parameters 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 Squared Displacement (MSD) derived by this model and the MSD obtained through molecular dynamics simulations. In the context of Fröhlich condensation, which is a biological conjectured effect where all the internal vibrational modes of a protein condensate into the lowest frequency mode when the system is pumped externally, we provide an alternative approach based on second quantization which allows to derive a GLE for the protein vibrational modes. More precisely, we adopted the same Hamiltonian operator in second quantization proposed by Wu and Austin for describing the Fröhlich system composed by protein, external source and heat bath. However, in order to get a well-defined GLE, we slightly modify the Wu-Austin Hamiltonian adding a further term which produces a zero mean noise term, which is not possible otherwise. The main contribution to this field consists in introducing a non perturbative quantum procedure. In particular, starting from the Heisenberg equations of motion for protein, heat bath and source operators, we formally solve the heat bath and source equations and we plug the solution into the protein equation getting an operator GLE. Projecting such a GLE onto a coherent state-basis, we get a c-number GLE which can be solved as a stochastic Ito equation. The c-number GLE written in the coherent state-basis naturally allows us to provide observables for quantifying the degree of coherence of the vibrational modes that, to the best of our knowledge, has never been done in this context.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2021-11852
UR  - https://publications.rwth-aachen.de/record/837200
ER  -