Negative friction memory induces persistent motion

We investigate the mean-square displacement (MSD) for random motion governed by the generalized Langevin equation for memory functions that contain two different time scales: In the first model, the memory kernel consists of a delta peak and a single-exponential and in the second model of the sum of two exponentials. In particular, we investigate the scenario where the long-time exponential kernel contribution is negative. The competition between positive and negative friction memory contributions produces an enhanced transient persistent regime in the MSD, which is relevant for biological motility and active matter systems. Graphical abstract

ADVANCES IN F0F1-ATP SYNTHASE BIOLOGICAL PROTEIN NANOMOTOR: FROM MECHANISMS AND STRATEGIES TO POTENTIAL APPLICATIONS

Movement and shape changes are fundamental aspects of all living organisms. This biological motility results from the biological nanomotors, in particular protein nanomotors. Cells contain a variety of protein nanomotors that rotate (e.g., F0F1-ATP synthase or bacterial flagellar motors) or move in a linear fashion (e.g., the kinesin, myosin and dynein motors). F0F1-ATP synthase is one of the ideal nanomotors or energy providing systems for micro/nanomachines because of its small size, smart and perfect structure, and ultra-high energy transfer efficiency. Therefore, in this paper, we have reviewed the structure, mechanism, and potential applications of the F0F1-ATP synthase nanomotor. In all organisms, the F0F1-ATP synthase consists of two distinct nanomotors, F0 and F1. The F0 moiety is embedded in the membrane and is a detergent soluble unit while the F1 moiety protrudes from the membrane and is a water soluble unit. F0F1-ATP synthase operates as two stepper motor/generators coupled by a common shaft and an electrochemical-to-mechanical-to-chemical energy transducer with an astounding 360° rotary motion of subunits. F0F1-ATP synthase nanomotor may enable the creation of a new class of sensors, mechanical force transducers, actuators, and nanomechanical devices. Thus, the F0F1-ATP synthase nanomotor field has expanded into a wide variety of science.