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@PHDTHESIS{DiCairano:837200,
      author       = {Di Cairano, Loris},
      othercontributors = {Carloni, Paolo and Hartmann, Carsten and Stamm, Benjamin},
      title        = {{G}eneralized {L}angevin equation-based approach for
                      investigating complex biological systems},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2021-11852},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2021},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University 2022; Dissertation, RWTH Aachen University, 2021},
      abstract     = {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.},
      cin          = {137810 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)137810_20140620$ / $I:(DE-82)130000_20140620$},
      pnm          = {CSD-SSD - Center for Simulation and Data Science (CSD) -
                      School for Simulation and Data Science (SSD)
                      (CSD-SSD-20190612) / Doktorandenprogramm
                      (PHD-PROGRAM-20170404)},
      pid          = {G:(DE-Juel1)CSD-SSD-20190612 /
                      G:(DE-HGF)PHD-PROGRAM-20170404},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2021-11852},
      url          = {https://publications.rwth-aachen.de/record/837200},
}