RESUMEN
Analytical formulas for effective drift, diffusivity, run times, and run lengths are derived for an intracellular transport system consisting of a cargo attached to two cooperative but not identical molecular motors (for example, kinesin-1 and kinesin-2) which can each attach and detach from a microtubule. The dynamics of the motor and cargo in each phase are governed by stochastic differential equations, and the switching rates depend on the spatial configuration of the motor and cargo. This system is analyzed in a limit where the detached motors have faster dynamics than the cargo, which in turn has faster dynamics than the attached motors. The attachment and detachment rates are also taken to be slow relative to the spatial dynamics. Through an application of iterated stochastic averaging to this system, and the use of renewal-reward theory to stitch together the progress within each switching phase, we obtain explicit analytical expressions for the effective drift, diffusivity, and processivity of the motor-cargo system. Our approach accounts in particular for jumps in motor-cargo position that occur during attachment and detachment events, as the cargo tracking variable makes a rapid adjustment due to the averaged fast scales. The asymptotic formulas are in generally good agreement with direct stochastic simulations of the detailed model based on experimental parameters for various pairings of kinesin-1 and kinesin-2 under assisting, hindering, or no load.
RESUMEN
Efforts toward improving patient compliance in medication focus on either identifying trends in patient features or studying changes through an intervention. Our study seeks to provide an important link between these two approaches through defining trends of evolving compliance. In addition to using clinical covariates provided through insurance claims and health records, we also extracted census based data to provide socioeconomic covariates such as income and population density. Through creating quadrants based on periods of medicine intake, we derive several novel definitions of compliance. These definitions revealed additional compliance trends through considering refill histories later in a patient's length of therapy. These results suggested that the link between patient features and compliance includes a temporal component, and should be considered in policymaking when identifying compliant subgroups.