Arup Chakraborty Research Group

    Molecular Motors:  

    Most molecular motors convert chemical energy into mechanical work through a cycle involving nucleotide hydrolysis. These motors differ profoundly from macroscopic motors for their dynamics is dominated by Brownian motion. For purposes of classification, a nomenclature has evolved to describe two extreme cases of what is actually a continuum of intermediates: Brownian ratchet vs. power stroke {Wang, 2001 #11}. A Brownian ratchet refers to the situation where the load is driven directly by thermal fluctuations and its diffusive motion is rectified by a chemical reaction with a large free energy drop. A typical example is a load driven by polymerization {Mogilner, 2003 #18}. A power stroke refers to a situation where the motion of the load is driven directly by the chemical reaction(s), generally through an elastic coupling. Power strokes generate mechanical force using the energy acquired during progressive substrate binding, each step of which driven by relatively small Brownian fluctuations (Å-sized) with modest free energy drops. This progressive binding is diffusive, biased by attractive intermolecular forces, a process that has been called the ‘Binding Zipper’ {Oster, 2000 #5}.

Power stroke motors generally run in a continuous cycle by using a ‘fuel’ molecule, usually ATP. The fuel ligand ends up tightly bound. In order to release the ligand so that the cycle can be repeated, it is cleaved into two in a manner that will allow products to diffuse out of the catalytic pocket, which can then relax and bind a new fuel ligand. Some motors have characteristics of both types of mechanisms {Dimroth, 1999 #5924; Xing, 2003 #8297}. This paper deals with the catalytic site of power stroke molecular motors.

There are two general classes of ATPase motors, grouped according to the structure of their catalytic sites. The RecA class share common structural motifs, including a central b-sheet whose loops grasp the nucleotide: the Walker A (or P-loop) and Walker B structures {reviewed in Ye, 2004 #21}. Amongst these motors are the helicases, AAA motors, proteases, and the F₁ ATPase. A second class of motors whose catalytic sites resemble that if the G-proteins include myosin and kinesin. In these motors, the mechanism of force generation is different, involving binding to a polymer ‘track’ (actin or microtubules), and the energy of the nucleotide hydrolysis cycle is used to regulate the affinity of the track binding site {Vale, 2000 #23}. Here we restrict our attention to the RecA class of motor proteins.

Within each class of motors, several other criteria are employed. Motors that move on tracks (e.g. DNA, RNA, or peptide chains) may be classified according to their ‘processivity’: how many steps, or hydrolysis cycles, they undergo before dissociating from their track. ‘Tightly coupled’ motors move, on average, one step per hydrolysis cycle {Howard, 2001 #24; Wang, 2002 #4}.

There are two measures of motor protein efficiency. The thermodynamic efficiency can be measured when a motor is processive, tightly coupled, and operating against a conservative load close to its stall force. Frequently, the only load that can be imposed experimentally on a motor is viscous drag. In this situation the Stokes efficiency measures the ratio of energy dissipation rate to the hydrolysis rate {Wang, 2002 #4}. This quantity measures how close the motor force is to a constant force, and is related to motor performance since the dissipation increases with the square of the velocity. Many motors operate near 100% thermodynamic efficiency near stall, and some molecular motors approach a Stokes efficiency of 100% because they output a nearly constant force or torque {Oster, 2000 #6; Wang, 2002 #4}. Recently quantitative Fokker-Planck models have been created to explain the high Stokes efficiency of ATP synthase{Oster, 2000 #6}.

Although constrained and forced molecular dynamics studies have been used to elucidate some features of nucleotide binding {Bockmann, 2003 #14; Bockmann, 2001 #15; Bockmann, 2002 #16}, the size of molecular motors makes unconstrained, atomistic molecular dynamics studies infeasible. Thus there is a need for general principles that govern how nucleotide binding is efficiently translated into mechanical work. Here we present a coarse grained model that bridges the gap between detailed atomistic molecular dynamic simulations and Fokker-Planck models that capture the binding process by a phenomenological potential function. RecA type motors hold the nucleotide by loops emanating from the central b-sheet. The actual force is generated by the sliding of the P-loop over the nucleotide. This motion is ‘levered up’ to larger, nanometer size motions in different ways. Here we investigate a ‘cartoon’ version of the ATP binding process by coarse-graining the P-loop as a polymer chain and modeling ATP as a static surface with reactive sites. This allows us to examine a molecular motor model that can operate in a cycle that converts binding energy into mechanical work and release the bound nucleotide by ‘hydrolyzing’ it into two subunits that can be released.

This model illuminates how binding depends on geometric and chemical matching between the catalytic site and the ligand, the proper binding progression for an efficient power stroke, the requirements for the release of spent substrates, and the role of solvent effects and on free energy changes during the binding process. Our results are in general agreement with the binding zipper model and provide insight into how the P-loop binding to ATP generates a mechanical force. We anticipate that these insights into how a power stroke functions in biological motors can steer coarse-grained models for the design of biomimetic synthetic motors.

    "Minimal Models for How Proteins Convert Chemical Energy Into Mechanical Work", Eide, J., Chakrbaorty, A., Oster, G. Submitted Biophys. J. (2004)

Molecular Crowding Effects in the T-cell Signaling Pathway:

Other Publications:

    At Stanford: "Molecular Cloning and Sequence Analysis of the Complestation biosynthetic gene cluster", Chiu, H.T., Hubbard, B., Shah, A., Eide, J., Fredenburg, R.A., Walsh, C., Khosla, C. PNAS 98, 8548 (2001)