Program
Nanoscience and Microsystems Engineering
College
Engineering
Student Level
Doctoral
Start Date
7-11-2019 2:00 PM
End Date
7-11-2019 3:45 PM
Abstract
We study the motion of random walkers with residence time bias between first and subsequent visits to a site, as a model for synthetic molecular walkers based on catalytic DNA known as molecular spiders [3, 2, 1, 5]. Previous studies have discovered exceptionally long superdiffusive transients, which would be relevant in experiments and applications. The mechanism of the transient superdiffusion was explained via the emergence of a boundary between the new and the previously visited sites, and the tendency of the multi-legged spider to cling to this boundary, provided there is a residence time bias between the first and the subsequent visits to a site. Detailed results were obtained for a two-legged spider with hand-over-hand gait in one dimension. The key insight is that the spider alternates between being on the visited/new boundary (and moving forward ballistically) and drifting in the sea of previously visited sites; with each period this sea becomes bigger, hence the eventual breakdown of superdiffusion. Approaches for improving the transient and perhaps asymptotic behavior of molecular spiders include modified chemistry, different walker body and leg geometry, and the use of walker teams. Walker teams are inspired by nature's molecular motor teams [6]. Rank et al. [4] provided a detailed analysis of teams of two-legged molecular spiders, on parallel one-dimensional tracks, connected by a "leash", i.e., a kinematic constraint that no two spiders can be more than a certain distance apart. They showed that teams of two, three, and four spiders successively outperform a single spider, for a range of leash lengths and chemical kinetics. Here we ask: can we separate the effects of having a team of walkers from the effects of each walker having multiple legs? Our model system uses single-legged walkers, each on its own one-dimensional track, connected by a leash. Each track is prepared with fresh substrates for x >= 0, and consumed products for x < 0; walkers start at x = 0. Using both kinetic Monte Carlo simulation and an analytical approach, we recapitulate the method of [4]. Even though a single one-legged walker does not exhibit directional, superdiffusive motion, we find that a team of one-legged walkers on parallel tracks, connected by a flexible tether, does enjoy a superdiffusive transient. Furthermore, the one-legged walker teams exhibit a greater expected number of steps per boundary period and are able to diffuse more quickly through the product sea, leading to longer periods of superdiffusion. References [1] T. Antal and P. L. Krapivsky. Molecular spiders with memory. Physical Review E, 76(021121), 2007. [2] K. Lund, A. J. Manzo, N. Dabby, N. Michelotti, A. Johnson-Buck, J. Nangreave, S. Taylor, R. Pei, M. N. Stojanovic, N. G. Walter, E. Winfree, and H. Yan. Molecular robots guided by presciptive landscapes. Nature, 465(7295), 2010. [3] R. Pei, S. K. Taylor, D. Stefanovic, S. Rudchenko, T. E. Mitchell, and M. N. Stojanovic. Behavior of polycatalytic assemblies in a substrate-displaying matrix. Journal of the American Chemical Society, 128(39), 2006. [4] M. Rank, L. Reese, and E. Frey. Cooperative effects enhance the transport properties of molecular spider teams. Physical Review E, 87(3):032706, 2013. [5] O. Semenov, M. J. Olah, and D. Stefanovic. Mechanism of diffusive transport in molecular spider models. Physical Review E, 83(021117), 2011. [6] A. Vilfan, E. Frey, F. Schwabl, M. Thormählen, Y. Song, and E. Mandelkow. Dynamics and cooperativity of microtubule decoration by the motor protein kinesin. Journal of Molecular Biology, 312(5):1011 - 1026, 2001.
Simulation of Tethered One-Legged Molecular Walkers on Independent 1-D Tracks
We study the motion of random walkers with residence time bias between first and subsequent visits to a site, as a model for synthetic molecular walkers based on catalytic DNA known as molecular spiders [3, 2, 1, 5]. Previous studies have discovered exceptionally long superdiffusive transients, which would be relevant in experiments and applications. The mechanism of the transient superdiffusion was explained via the emergence of a boundary between the new and the previously visited sites, and the tendency of the multi-legged spider to cling to this boundary, provided there is a residence time bias between the first and the subsequent visits to a site. Detailed results were obtained for a two-legged spider with hand-over-hand gait in one dimension. The key insight is that the spider alternates between being on the visited/new boundary (and moving forward ballistically) and drifting in the sea of previously visited sites; with each period this sea becomes bigger, hence the eventual breakdown of superdiffusion. Approaches for improving the transient and perhaps asymptotic behavior of molecular spiders include modified chemistry, different walker body and leg geometry, and the use of walker teams. Walker teams are inspired by nature's molecular motor teams [6]. Rank et al. [4] provided a detailed analysis of teams of two-legged molecular spiders, on parallel one-dimensional tracks, connected by a "leash", i.e., a kinematic constraint that no two spiders can be more than a certain distance apart. They showed that teams of two, three, and four spiders successively outperform a single spider, for a range of leash lengths and chemical kinetics. Here we ask: can we separate the effects of having a team of walkers from the effects of each walker having multiple legs? Our model system uses single-legged walkers, each on its own one-dimensional track, connected by a leash. Each track is prepared with fresh substrates for x >= 0, and consumed products for x < 0; walkers start at x = 0. Using both kinetic Monte Carlo simulation and an analytical approach, we recapitulate the method of [4]. Even though a single one-legged walker does not exhibit directional, superdiffusive motion, we find that a team of one-legged walkers on parallel tracks, connected by a flexible tether, does enjoy a superdiffusive transient. Furthermore, the one-legged walker teams exhibit a greater expected number of steps per boundary period and are able to diffuse more quickly through the product sea, leading to longer periods of superdiffusion. References [1] T. Antal and P. L. Krapivsky. Molecular spiders with memory. Physical Review E, 76(021121), 2007. [2] K. Lund, A. J. Manzo, N. Dabby, N. Michelotti, A. Johnson-Buck, J. Nangreave, S. Taylor, R. Pei, M. N. Stojanovic, N. G. Walter, E. Winfree, and H. Yan. Molecular robots guided by presciptive landscapes. Nature, 465(7295), 2010. [3] R. Pei, S. K. Taylor, D. Stefanovic, S. Rudchenko, T. E. Mitchell, and M. N. Stojanovic. Behavior of polycatalytic assemblies in a substrate-displaying matrix. Journal of the American Chemical Society, 128(39), 2006. [4] M. Rank, L. Reese, and E. Frey. Cooperative effects enhance the transport properties of molecular spider teams. Physical Review E, 87(3):032706, 2013. [5] O. Semenov, M. J. Olah, and D. Stefanovic. Mechanism of diffusive transport in molecular spider models. Physical Review E, 83(021117), 2011. [6] A. Vilfan, E. Frey, F. Schwabl, M. Thormählen, Y. Song, and E. Mandelkow. Dynamics and cooperativity of microtubule decoration by the motor protein kinesin. Journal of Molecular Biology, 312(5):1011 - 1026, 2001.
