Enhanced reaction kinetics in biological cells

The cell cytoskeleton is a striking example of " active " medium driven out-of-equilibrium by ATP hydrolysis 1. Such activity has been shown recently to have a spectacular impact on the mechanical and rheological properties of the cellular medium : a generic tracer particle freely diffuses as in a standard equilibrium medium, but also intermittently binds with random interaction times to motor proteins, which perform active ballistic excursions along cytoskeletal filaments. Here, we propose for the first time an analytical model of transport limited reactions in active media, and show quantitatively how active transport can enhance reactivity for large enough tracers like vesicles. We derive analytically the average interaction time with motor proteins which optimizes the reaction rate, and reveal remarkable universal features of the optimal configuration. We discuss why active transport may be beneficial in various biological examples: cell cytoskeleton, membranes and lamellipodia, and tubular structures like axons 1. Various motor proteins such as kinesins or myosins are able to convert the chemical fuel provided by ATP into mechanical work by interacting with the semiflexible oriented filaments (mainly F–actin and microtubules) of the cytoskeleton 1. As many molecules or larger cellular organelles like vesicles, lysosomes or mitochondria, hereafter referred to as tracer particles, can randomly bind and unbind to motors, the overall transport of a tracer in the cell can be described as alternating phases of standard diffusive transport, and phases of active directed transport powered by motor proteins 1,15,16. Active transport in cells has been extensively studied both experimentally, for instance by single particle tracking methods 11,12 , and theoretically by evaluating the mean displacement of a tracer 13,17 , or stationary concentration profiles 14. On the other hand, most of cell functions are regulated by coordinated chemical reactions which involve low concentrations of reactants (such as ribosomes or vesicles carrying targeted proteins), and which are therefore limited by transport. However, up to now a general quantitative analysis of the impact of active transport on reaction kinetics in cells, and more generally in generic active media, is still missing, even if a few specific examples have been tackled 18. In this letter, we propose an analytical model which allows us to determine for the first time the kinetic constant of