Stochastic Modeling and Optimal Control for Colloidal Organization, Navigation, and Machines

Colloidal suspensions consisting of particles undergoing Brownian motion are ubiquitous in scientific research and emerging technologies. Longstanding challenges in strategic control of complex colloidal systems are to investigate the principle of optimal control, overcome the curse of dimensionality, design efficient algorithms, and develop generalizable control strategies. In the first part of this dissertation, we present methods and results from three case studies to illustrate how these challenges are addressed from the perspectives of modeling and optimal control. Single-agent optimal navigation in complex mazes. We investigate the optimal navigation principle of a self-propelled colloidal particle in complex mazes. We construct approximate Markov chain model and use the Markov decision process framework to obtain the general principle of optimal navigation. Multiple-agent cooperation and coordination for colloidal machines. Using self-propelled Janus motors as the model system, we illustrate a new paradigm for cargo capture and transport based on multiple-agent feedback control. The control algorithm can coordinate multiple motors to cooperate on forming a reconfigurable machine for cargo capture and transport. Low-dimensional modeling and ensemble control. Optimal control in a high dimensional self-assembly processes with limited actuations presents a challenge in both modelling and controller design. We use colloidal crystallization in an electric field as a model system to illustrate the methodologies of low-dimensional modeling and control for self-assembly processes. We use a nonlinear machine learning algorithm to characterize the dimensionality and parametrize the low-dimension manifold on which the system evolves. A low-dimensional Smoluchowski model is constructed and calibrated to illustrate the dynamic pathways of the assembly process. The resulting model is further leveraged to perform optimal control of the assembly process. In the second part of dissertation, we report three additional relevant research projects on colloidal interaction, dynamics, and control. The first project extends ensemble control from finite-size systems to infinite-size systems using feedback control in sedimentation. The second project develops a computational method to model depletion interactions between general geometric objects The third project develops modified Stokesian dynamics methods to investigate the colloidal rod motion near a planar wall with hydrodynamic interactions

Molecular Dynamics Simulation of Ligand Dissociation from Liver Fatty Acid Binding Protein

The mechanisms of how ligands enter and leave the binding cavity of fatty acid binding proteins (FABPs) have been a puzzling question over decades. Liver fatty acid binding protein (LFABP) is a unique family member which accommodates two molecules of fatty acids in its cavity and exhibits the capability of interacting with a variety of ligands with different chemical structures and properties. Investigating the ligand dissociation processes of LFABP is thus a quite interesting topic, which however is rather difficult for both experimental approaches and ordinary simulation strategies. In the current study, random expulsion molecular dynamics simulation, which accelerates ligand motions for rapid dissociation, was used to explore the potential egress routes of ligands from LFABP. The results showed that the previously hypothesized “portal region” could be readily used for the dissociation of ligands at both the low affinity site and the high affinity site. Besides, one alternative portal was shown to be highly favorable for ligand egress from the high affinity site and be related to the unique structural feature of LFABP. This result lends strong support to the hypothesis from the previous NMR exchange studies, which in turn indicates an important role for this alternative portal. Another less favored potential portal located near the N-terminal end was also identified. Identification of the dissociation pathways will allow further mechanistic understanding of fatty acid uptake and release by computational and/or experimental techniques