The synchronization and bundling process of bacterial flagella is investigated by mesoscale hydrodynamic simulations. Systems with two to six flagella are considered, which are anchored at one end, and are driven by a constant torque. A flagellum is modelled as a linear helical structure composed of mass points with their elastic shape maintained by bonds, bending, and torsional potentials. The characteristic times for synchronization and bundling are analyzed in terms of motor torque, separation, and number of flagella. We find that hydrodynamic interactions determine the bundling behavior. The synchronization time is smaller than the bundling time, but their ratio depends strongly on the initial separation. The bundling time decreases with increasing number of flagella at a fixed radius in a circular arrangement due to multi-helix hydrodynamics.

Synthetic chemically-powered motors with various geometries have potentially new applications involving dynamics on very small scales. Self-generated concentration and fluid flow fields, which depend on geometry, play essential roles in motor dynamics. Sphere-dimer motors, comprising linked catalytic and noncatalytic spheres, display more complex versions of such fields, compared to the often-studied spherical Janus motors. By making use of analytical continuum theory and particle-based simulations we determine the concentration fields, and both the complex structure of the near-field and point-force dipole nature of the far-field behavior of the solvent velocity field that are important for studies of collective motor motion. We derive the dependence of motor velocity on geometric factors such as sphere size and dimer bond length and, thus, show how to construct motors with specific characteristics.

Diffusion is the principal transport mechanism that controls the motion of solute molecules and other species in solution; however, the random walk process that underlies diffusion is slow and often nonspecific. Although diffusion is an essential mechanism for transport in the biological realm, biological systems have devised more efficient transport mechanisms using molecular motors. Most biological motors utilize some form of chemical energy derived from their surroundings to induce conformational changes in order to carry out specific functions. These small molecular motors operate in the presence of strong thermal fluctuations and in the regime of low Reynolds numbers, where viscous forces dominate inertial forces. Thus, their dynamical behavior is fundamentally different from that of macroscopic motors, and different mechanisms are responsible for the production of useful mechanical motion.There is no reason why our interest should be confined to the small motors that occur naturally in biological systems. Recently, micron and nanoscale motors that use chemical energy to produce directed motion by a number of different mechanisms have been made in the laboratory. These small synthetic motors also experience strong thermal fluctuations and operate in regimes where viscous forces dominate. Potentially, these motors could be directed to perform different transport tasks, analogous to those of biological motors, for both in vivo and in vitro applications. Although some synthetic motors execute conformational changes to effect motion, the ma- * To whom correspondence should be addressed jority do not, and, instead, they use other mechanisms to convert chemical energy into directed motion.In this Account, we describe how synthetic motors that operate by self-diffusiophoresis make use of a self-generated concentration gradient to drive motor motion. A description of propulsion by selfdiffusiophoresis is presented for Janus particle motors comprising catalytic and noncatalytic faces. The properties of the dynamics of chemically powered motors are illustrated by presenting the results of particle-based simulations of sphere-dimer motors constructed from linked catalytic and noncatalytic spheres. The geometries of both Janus and sphere-dimer motors with asymmetric catalytic activity support the formation of concentration gradients around the motors. Because directed motion can occur only when the system is not in equilibrium, the nature of the environment and the role it plays in motor dynamics are described. Rotational Brownian motion also acts to limit directed motion, and it has especially strong effects for very 1 arXiv:1407.6338v2 [cond-mat.soft] 3 Nov 2014 small motors. We address the following question: how small can motors be and still exhibit effects due to propulsion, even if only to enhance diffusion? Synthetic motors have the potential to transform the manner in which chemical dynamical processes are carried out for a wide range of applications.

The concentration dependence of the conformations of ring polymers is investigated by lattice Monte Carlo simulations and compared with that of linear polymers. The relative radii of gyration of linear polymers follow a universal master curve as a function of the scaled concentration for various chain lengths, with a scaling relationship ⟨R g 2⟩ ∼ ϕ–0.25, which is consistent with scaling theory and neutron scattering experiments. Ring polymers of different lengths also follow a universal behavior with a broad crossover to a scaling behavior ⟨R g 2⟩ ∼ ϕ–0.59 for long chains. The scaling relationship between the concentration dependence and the chain-length dependence of the radius of gyration implies ⟨R g 2⟩ ∼ N 0.72, indicating highly collapsed conformations for long-chain ring polymers in the melt.

Peritrichous bacteria exploit bundles of helical flagella for propulsion and chemotaxis. Here, changes in the swimming direction (tumbling) are induced by a change of the rotational frequency of some flagella. Employing coarse-grained modeling and simulations, we investigate the dynamical properties of helical flagella bundles driven by mismatched motor torques. Over a broad range of distances between the flagella anchors and applied torque differences, we find a stable bundled state, which is important for a robust directional motion of a bacterium. With increasing torque difference, a phase lag in the flagellar rotations develops, followed by slippage and ultimately unbundling, which sensitively depends on the anchoring distance of neighboring flagella. In the slippage and drift states, the different rotation frequencies of the flagella generate a tilting torque on the bacterial body, which implies a change of the swimming direction as observed experimentally.