A New Multiscale Approach For Dynamic Modeling And Simulation Of Micro-nano Biomolecular Systems Characterized By A Low Reynolds Number

Abstract

In this dissertation, a new multiscale computational framework was developed in order to model and simulate motility of micro-nano-sized objects in fluid environments, characterized with a low Reynolds number. Especially, it has been used for studying the dynamic behavior of biomolecular systems such as motor proteins inside cells.Long simulation run time is one of the most important issues in modeling of cellular and biomolecular systems at the nanoscale due to the multiple time and length scales involved in the dynamics of these systems. These multiscale features are caused by either structure-structure (e.g. flexibility in biological structure or contact) or structure-fluid interactions (e.g. biological structure and surrounding fluid environment) which appear as disproportionality between physical parameters involved in their dynamics. In order to address this issue, the mostly used models, based on the famous overdamped Langevin equation, omit inertial properties in the equations of motion; that leads to a first order model which is inconsistent with the Newton's second law. However, a new dynamic multiscale approach was proposed that uses the concept of the method of multiple scales (MMS) and brings all terms of the equations of motion into proportion with each other that helps to retain the inertia terms. This holds consistency of the model with the governing physical laws, Newton's second law, and experimental observations. In addition, numerical integration's step-size can be increased from commonly used sub-femto seconds to sub-milli seconds. Therefore, simulation run time is reduced significantly in compared with other approaches.The proposed approach was examined in different cases including the dynamics of small objects (microbeads) in an optical trapping process, and locomotion of motor proteins likes myosin V and kinesin-1 in cells. The experimental observations, obtained from the study of trapped small beads in optical tweezers, verify the new multiscale model and show the proposed model can correctly predict the physical characteristics at the nanoscale. In addition, the simulation run-time using the proposed multiscale models was significantly reduced in compared with the original and the first order models. Then, the multiscale model was used for modeling and simulation of motor proteins. The simulation results obtained by the proposed multiscale model show a dynamic behavior of myosin V and kinesin which is more consistent with experimental observations in compared with other overdamped models.In this dissertation, a new online constraint embedding method was invoked in order to facilitate numerical simulation of motor proteins mechanical model, as a multibody system, with on-fly constraints including, 1) holonomic constraints due to use of Euler parameters for describing configuration of proteins and 2) non-holonomic constraints because of contact-impact between proteins and the substrates.