Figure 6. Mathematical modeling framework for bidirectional transport models.

Hypothetical mechanisms can be explored and quantitatively tested using mathematical models of cargo transport by kinesin and dynein motors. On a given cargo, there are N kinesin motors (Kin₁ to Kin_N) and M dynein motors (Dyn₁ to Dyn_M). Motor states are defined generically as On and Off, with different hypothetical mechanisms having different definitions of the on- and off-states (given at the right in order: microtubule tethering, mechanical activation, and steric disinhibition). For each motor, the rate constant k⁺ defines the rate that the motor switches from the off-state to the on-state, and the rate constant k defines the rate that the motor switches from the on-state to the off-state. These switching rates depend on different variables in the system (such as the force acting on that motor, the cargo position, or the activity of the opposing motors), and the switching rate magnitudes and parameter dependencies are the principal determinants of overall model behavior. The different hypothetical mechanisms presented in Figure 5 will have different dependencies for their switching rates; for example, the k⁺ dependencies for the three hypothetical mechanisms are given at the right. These models readily lend themselves to standard Monte Carlo (Gillespie Stochastic Simulation Algorithm¹⁶⁴) approaches.