TY - JOUR
T1 - Effective behavior of cooperative and nonidentical molecular motors
AU - Klobusicky, Joseph J.
AU - Fricks, John
AU - Kramer, Peter R.
N1 - Funding Information:
The work of JF and PRK are partially supported by National Institutes of Health grant R01GM122082 and PRK was partially supported by a grant from the Simons foundation. The work of JK is partially supported by an National Science Foundation RTG grant 1344962. Acknowledgements
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - Molecular motors
KW - Renewal-reward theory
KW - Stochastic averaging
KW - Switched diffusion
UR - http://www.scopus.com/inward/record.url?scp=85091314045&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85091314045&partnerID=8YFLogxK
U2 - 10.1007/s40687-020-00230-7
DO - 10.1007/s40687-020-00230-7
M3 - Article
AN - SCOPUS:85091314045
SN - 2522-0144
VL - 7
JO - Research in Mathematical Sciences
JF - Research in Mathematical Sciences
IS - 4
M1 - 29
ER -