Multiple Molecular Spiders With a Single Localized Source—the One-Dimensional Case Extended Abstract Oleg Semenov, Mark J. Olah, and Darko Stefanovic Department of Computer Science, University of New Mexico Abstract. Molecular spiders are nanoscale walkers made with DNA enzyme legs attached to a common body. They move over a surface of DNA substrates, cleaving them and leaving behind product DNA strands, which they are able to revisit. Simple one-dimensional models of spider motion show significant su- perdiffusive motion when the leg-substrate bindings are longer-lived than the leg-product bindings. This gives the spiders potential as a faster-than-diffusion transport mechanism. However, analysis shows that single-spider motion eventu- ally decays into an ordinary diffusive motion, owing to the ever increasing size of the region of cleaved products. Inspired by cooperative behavior of natural molecular walkers, we propose a model for multiple walkers moving collectively over a one-dimensional lattice. We show that when walkers are sequentially re- leased from the origin, the collective effect is to prevent the leading walkers from moving too far backwards. Hence there is an effective outward pressure on the leading walkers that keeps them moving superdiffusively for longer times, despite the growth of the product region. 1 Introduction Molecular walkers are nanometer-sized molecules that move over surfaces with tracks of chemical sites by means of chemical reactions. They provide a means to transport chemicals by non-diffusive directed motion. Molecular walkers are ubiquitous as a transport mechanism in biological systems [12], and many of the complex regulatory cellular processes are controlled by the actions of molecular walkers such as kinesin and dynein [7]. It has been demonstrated experimentally that these cellular molecular walkers work in teams, wherein their collective action leads to behaviors not possible for a single walker [3]. In addition, theoretical models predict that collective coopera- tive or competitive behavior of walkers is fundamentally different from the behavior of individual walkers [5, 6, 8]. Inspired by the potential for walker cooperation, we propose a model describing the collective behavior of teams of molecular walkers. Our model is based on synthetic walkers called molecular spiders [10] (Sec. 2). Molecular spiders have two or more en- zymatic legs attached to a common body. The legs are deoxyribozymes—catalytic se- quences of single-stranded DNA that can cleave complementary single-stranded DNA substrates. Spiders move over a surface coated with substrates, attaching to, cleaving, and detaching from the substrate sites. Spiders leave behind product strands, which are the lower portions of the cleaved surface-bound substrates. Experiments have shown