Stochastic models of polymerization-based axonal actin transport.

Recent advances in live cell imaging of F-actin structures, combined with pulse-chase imaging and computational modeling have suggested that actin is transported along the axon via biased polymerization of metastable actin fibers (actin trails). This mechanism is distinct from motor driven polymer transport, such as for neurofilaments and can be best described as molecular hitchhiking, where G-actin molecules are intermittently incorporated into actin fibers which grow preferentially in the anterograde direction. In this paper, we discuss how various axonal and actin trail parameters like axon diameter, trail nucleation rates, basal G-actin concentration, and trail length influence the transport rate. These predictions can help guide future experiments to verify this novel protein transport mechanism. We introduce a simplified, analytically solvable model of actin transport which relates these parameters to experimentally measurable quantities. We also discuss why a simple diffusion-based transport mechanism cannot explain bulk actin transport in the axon.

Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators.

In this paper, we present an experimental setup and an associated mathematical model to study the synchronization of two self-sustained, strongly coupled, mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely, damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes; coupled by placing them on a common base, free to move along a horizontal direction. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base, coupling the two. In our system, the mass of the oscillating pendula forms a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound "clockwork" slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied in the experiments. The simulation results showed a rapid increase in the phase difference between the two oscillators beyond a certain threshold of parameter mismatch. Our simple model of the escapement mechanism did not reproduce a complete 180° out of phase state. However, the numerical simulations show that increased mismatch in parameters leads to a synchronized state with a large phase difference.

Processive flow by biased polymerization mediates the slow axonal transport of actin.

Classic pulse-chase studies have shown that actin is conveyed in slow axonal transport, but the mechanistic basis for this movement is unknown. Recently, we reported that axonal actin was surprisingly dynamic, with focal assembly/disassembly events ("actin hotspots") and elongating polymers along the axon shaft ("actin trails"). Using a combination of live imaging, superresolution microscopy, and modeling, in this study, we explore how these dynamic structures can lead to processive transport of actin. We found relatively more actin trails elongated anterogradely as well as an overall slow, anterogradely biased flow of actin in axon shafts. Starting with first principles of monomer/filament assembly and incorporating imaging data, we generated a quantitative model simulating axonal hotspots and trails. Our simulations predict that the axonal actin dynamics indeed lead to a slow anterogradely biased flow of the population. Collectively, the data point to a surprising scenario where local assembly and biased polymerization generate the slow axonal transport of actin without involvement of microtubules (MTs) or MT-based motors. Mechanistically distinct from polymer sliding, this might be a general strategy to convey highly dynamic cytoskeletal cargoes.