Hamiltonian potentials to investigate energy transduction in nano-scale kinesin motors
Gunjan Singh Thakur, Megan Valentine and Igor Mezic
Mechanical Department, University of California at Campus, Campus, CA 93106-5070
Tel 805.893.2430 E-mail:
Summary: We construct a Hamiltonian potential which encodes the consensus mechanism for kinesin translocation, and use molecular dynamics simulations to demonstrate the unidirectional stepping of simple motors.
Intracellular transport is essential for appropriate cellular morphology and function. Kinesin superfamily motors are the key players in the microtubule based transport. These proteins, and are also very important for other cellular processes such as mitosis, meiosis, etc. The kinesin motor has two conserved N-terminal catalytic motor domains (called "heads") and walks processively toward the plus-end of microtubules, hydrolyzing one ATP per 8-nm step. The motor domain is followed by a 12 to 15 amino acid residue neck linker that leads to the coiled-coil stalk, which is in turn attached like a tether to the cargo.
Molecular dynamics (MD) simulations approaches using all the experimentally available data are possible; however the complexity of the system allows us only to model at time scales which are far smaller than the scale at which the motor operates. Moreover, deriving appropriate potential functions, , that are meaningfully detailed presents significant challenges [4]. In this work we present a new approach using a coarse grained MD model. Using programmable Hamiltonian potentials [1] we perform MD simulations on Lammps to demonstrate the motility of the motor proteins.
a) b)
Fig. 1. Schematic representation of the simulated kKinesin motor protein,with represented with its two heads and the a coiled-coil stalk, attached to a microtubule (represented as a straight-line segment of green and yellow beads). The binary molecules (red and green) are the representationof a ATP molecules. a) Head 1 is attached to the microtubule with the neck-liner in a docked configuration and and ATP attached to the headbound to the motor head. This neck linker docking biasespushedthe free the head 2, shown with an ADP molecule (red bead) attached bound, forward. b) A short time later, After a few step in the translocation mechanism , we have find head 2 attached with to the microtubule in a rigor state, with a disordered neck-linker, and waiting for an ATP molecule to bind in order for the cyclic process to continue.
We first construct an abstract model of the kinesin motor protein and the microtubule. The neck linker, motor head coiled-coil stalk and microtubule are schematically represented as flexible chains with different elasticity, each having specific sites through which they interact. This model is coupled with a three dimensional viscous environment with a prescribed number of ATP molecules performing Brownian dynamics. The interaction between various active sites in this system is specified via Hamiltonian potentials constructed to encode various biochemical reaction steps.
Using the programmable Hamiltonian potential approach, we demonstrate qualitatively correct unidirectional trans locomotion of the kinesin motor protein. We anticipate that this new framework will be useful in testing hypotheses of molecular-level regulation of motor protein function by chemistry and mechanics.
[1] Thakur GS, Mezic I, Programmable potentials (in preparation).
[2] Valentine MT, Gilbert SP, “To step or not to step? How biochemistry and mechanics influence processivity in Kinesin and Eg5”, Ccurr. Oopinion in Ccell Bio., 19, 75-81 (2007).