Computer Science ETDs

Publication Date



We present a stochastic model and numerical simulation framework for a synthetic nanoscale walker that can be used to transport materials and information at superdiffusive rates in artificial molecular systems. Our \emph{multivalent random walker} model describes the motion of a walker with a rigid, inert body and flexible, enzymatic legs. A leg can bind to and irreversibly modify surface-bound chemical substrate sites arranged as nanoscale tracks. As the legs attach to, modify, and detach from the sites, the walker moves along these tracks. Walkers are symmetrical and the tracks they walk on are unoriented, yet we show that under appropriate kinetic constraints the walkers can transform the chemical free energy in the surface sites into directional motion, and can do ordered work against an external load force. This shows that multivalent random walkers are a new type of molecular motor, useful for directional transport in nanoscale systems. We model the motion of multivalent random walkers as a continuous-time discrete-state Markov process. States in the process correspond to the chemical state of the legs and surface sites, and transitions represent discrete chemical changes of legs binding to, unbinding from, and modifying the surface sites. The Markov property holds because we let the mechanical motion of the body and unattached legs come to equilibrium in between successive chemical steps, thus the transitions depend only on the current chemical state of the surface sites and attached legs. This coarse-grained model of walker motion allows us to use both equilibrium and non-equilibrium Markov chain Monte Carlo simulation techniques. The Metropolis-Hastings algorithm approximates the motion of a walker's body and legs at a mechanical equilibrium, while the kinetic Monte Carlo algorithm simulates the transient chemical dynamics of the walker stepping across the surface sites. Using these numerical techniques, we find that MVRWs move superdiffusively in the direction of unmodified substrate sites when there is a residence time bias between modified and unmodified sites. This superdiffusive motion persists when opposed by external load forces, showing that multivalent random walkers are \emph{molecular motors} that can transform chemical free energy into ordered mechanical work. To produce these results we devised a distributed object-oriented framework for parallel simulation and analysis of the MVRW model. We use an object-relational mapping to persistently maintain all simulation-related objects as tuples in a relational database. We present a new object-relational mapping technique called the \emph{natural entity framework} which disambiguates the semantics of object identity and uniqueness in the relational and object-oriented programming models. Using the natural entity framework we are able to guarantee the uniqueness of mappings between data stored as objects in the relational database and external data stored in non-transactionally-secured HDF5 data files.




Molecular motors, Molecular walkers, Kinetic Monte Carlo, Metropolis-Hastings, Superdiffusive Transport, Object-Relational Mapping

Document Type


Degree Name

Computer Science

Level of Degree


Department Name

Department of Computer Science

First Advisor

Darko, Stefanovic

First Committee Member (Chair)

Cris, Moore

Second Committee Member

Lance, Williams

Third Committee Member

Milan, Stojanovic

Project Sponsors

National Science Foundation