Active Brownian particles climb up activity gradient to reach the fuel source
Methods: Stochastic differential equations, Fokker-Planck equation, and Brownian dynamics simulation
Active matter is ubiquitous in Biology. Examples include cytoskeletal molecular motors performing directed motion on filaments inside a cell, nucleic acid motors involved in transcription process inside nucleus, and even microscopic living objects such as the Escherichia coli bacteria which generates motion using helical flagella. The defining characteristic of active matter is that it is intrinsically nonequilibrium. The constituents of active matter generate motion by consuming energy from their local environment. A model system of active matter, which has been a subject of considerable attention, is an assembly of active Brownian particles (ABPs). In addition to the solvent-induced Brownian motion, active particles undergo self-propulsion resulting in persistent character of particle trajectories. It is the self-propulsion feature of ABPs, generally termed as the activity, which captures the nonequilibrium nature of active matter.
When the activity is spatially distributed, ABPs exhibit behavior very similar to chemotaxis : they climb up the activity gradient to reach the fuel source. Very recently, we have developed a model that explains the chemotaxis-like behavior of active particles . Activity gradients strongly bias the probability of active particle to reach the fuel source and can be captured in a simple stochastic model. However, it is conceivable that the source repels the active particle via repulsive interaction. The goal of the project is to include a repulsive interaction between the fuel source and the active particle in addition to the activity gradients and investigate the target finding probability of the particle. The project will be divided into theory and simulations. The theoretical part would require using stochastic methods such as Fokker-Planck equation and stochastic differential equations. The simulations part would require Brownian dynamics simulations using either existing simulations packages or self-written code.
Schematic of the inhomogeneous active system. The surface of the yellow spherical shell r = r0 represents the target, for instance fuel or energy source for active particles. The fuel distribution in the spherical geometry is shown in red, the gradient of which represents the decaying activity profile away from the source. Active particles are shown as gray-white spheres together with their embedded orientation vector. The size of the vector represents the local self-propulsion speed of the particle. Particles are confined within r0 ≤ r ≤ R. Due to the activity gradient, particles drift towards the target which is located at higher activity (fuel) in striking resemblance to chemotaxis.