Within a coarse-grained elastic-network model (ENM) with deterministic overdamped relaxation, Togashi, Yanagida and Mikhailov (2010) found that functional conformational motions in the motor proteins myosin V and kinesin KIF1A are strongly nonlinear: myosin V relaxes to its ATP-bound reference state along a single robust attractive pathway that is harmonic only in its final stage, while in KIF1A the energy valley guiding relaxation to the ADP-bound state is branched, with the functional ATP-to-ADP motion confined to a side branch that separates from the typical fluctuation path at sub-Ångström scale — below the amplitude of typical thermal fluctuations — and proceeds through a two-stage switch I motion (loop sliding followed by loop-to-α-helix conversion), so that the standard normal-mode description fails completely. The open problem is whether these nonlinear relaxation scenarios are genuine physical properties of the two motors rather than artifacts of the ENM approximation: do they persist in higher-resolution dynamical models (structure-based Gō-like models, all-atom molecular dynamics), under explicit finite-temperature dynamics in which thermal noise interacts with the branched landscape, and when hydrodynamic interactions and heterogeneous mobilities are included; and can the predicted pathways — above all the two-stage switch I sequence in KIF1A — be detected by single-molecule or time-resolved structural experiments. Subsequent work by the same group has remained within the deterministic ENM framework, while higher-resolution and experimental studies of these motors have addressed different questions; the core problem remains open.

Background

Molecular motor proteins convert the chemical energy of hydrolysis of ATP (adenosine triphosphate), the cell's universal chemical fuel, into mechanical work, and their operation cycles involve nucleotide-dependent conformational changes of the motor domain on millisecond timescales. Myosin V is a dimeric, actin-based motor that transports cargo processively (taking many steps without detaching) in cells; KIF1A is a neuronal kinesin-3 motor, a member of the microtubule-based kinesin superfamily, notable because a single motor domain suffices for processive motion. In both motors, the nucleotide state (ATP-, ADP- or nucleotide-free) controls conformation through two conserved segments flanking the nucleotide-binding pocket, termed switch I and switch II, which rearrange — including partial folding and unfolding of loop and helix structure — as the chemical state changes. Because full operation cycles are far beyond all-atom simulation reach, coarse-grained descriptions are used. In the elastic network model (ENM), each amino-acid residue is represented by a point particle placed at its α-carbon (the backbone carbon atom of the residue) position in a chosen reference crystal structure, and two particles are connected by a Hookean spring whenever their distance in the reference structure is below a cutoff (here 10 Å); the network then relaxes under overdamped dynamics dRi/dt=−Γ ∂U/∂Rid\mathbf{R}_i/dt=-\Gamma\,\partial U/\partial \mathbf{R}_i, where UU is the total spring energy, Γ\Gamma the mobility, and time is measured in rescaled units of (Γκ)−1(\Gamma\kappa)^{-1} with κ\kappa the spring constant. Linearizing these equations about the reference state yields the normal modes — the collective harmonic vibration patterns routinely used to interpret functional motions and thermal fluctuation data in structural biology. Togashi and Mikhailov (2007) had shown that ENM relaxation is intrinsically nonlinear even though each spring is linear, because spring orientations rotate as the network deforms, and found strongly nonlinear relaxation with ordered attractive pathways in several protein machines. Togashi, Yanagida and Mikhailov (2010) then compared two motor proteins in detail. For myosin V they built the ENM on the ATP-analog-bound structure (PDB 1W7J — PDB, the Protein Data Bank of resolved biomolecular structures; the four-character code identifies the entry — crystallized with MgADP-BeFx, an ATP analog) and followed relaxation from the nucleotide-free conformation (PDB 1OE9), finding a well-defined attractive relaxation path, robust against perturbations, that agrees with the slowest normal mode only in the final harmonic stage. For KIF1A they built the ENM on the ADP-bound structure (PDB 1I5S) and followed relaxation from the ATP-analog-bound conformation (PDB 1I6I, crystallized with MgAMPPCP, a non-hydrolyzable ATP analog), finding that the deep energy valley leading to the reference state is branched: the functional mechanochemical motion follows a side branch that separates from the path of typical relaxation and fluctuation motions while a chosen label distance (between residues Glu233 and Ala286) has changed by less than an ångström — much less than typical thermal fluctuation amplitudes — and the motion proceeds in two stages, sliding of the switch I loop followed by its conversion into an α-helix only after the sliding is completed. Hence neither a single normal mode nor any superposition of modes can represent the functional motion. The simulations were deterministic and at zero explicit temperature; thermal fluctuations entered only through amplitude estimates and through relaxation from random static perturbations; hydrodynamic interactions (the solvent-mediated coupling of moving residues) were neglected, though the authors note they can be incorporated into mesoscale elastic-network descriptions, as shown by Cressman, Togashi, Mikhailov and Kapral (2008).

Problem Statement

Determine whether the strongly nonlinear functional conformational relaxation predicted by the elastic-network model for myosin V and KIF1A is a physical property of these motors rather than an artifact of the coarse-grained ENM approximation. Concretely: (a) do the predicted relaxation scenarios — in myosin V, a single robust attractive relaxation path upon ATP binding that enters the harmonic normal-mode regime only at its final stage, and in KIF1A a branched relaxation landscape whose side branch carries the functional ATP-to-ADP motion in two stages, sliding of the switch I loop followed by its conversion into an α-helix — persist when the same nucleotide-dependent transitions (KIF1A PDB 1I6I to 1I5S; myosin V PDB 1OE9 to 1W7J) are simulated with higher-resolution dynamical models such as structure-based Gō-like models (simulation models whose attractive residue-residue interactions are taken from the native contact map of a reference structure) or all-atom molecular dynamics with explicit solvent; (b) under explicit finite-temperature Langevin dynamics — stochastic equations of motion incorporating random thermal forces — how does thermal noise sample the branched KIF1A landscape given that the branch separation occurs at sub-ångström scale below typical thermal fluctuation amplitudes — can thermally driven transitions access the functional side branch, and is the functional relaxation motion entropically hindered against thermal reversal as the elastic-network analysis suggests; (c) how do hydrodynamic interactions and heterogeneous residue mobilities, neglected in the original model, modify the relaxation timescales and the pathway selection; and (d) can the predicted nonlinear pathways — above all the two-stage switch I sequence in KIF1A and the nonlinear relaxation manifold in myosin V — be observed in single-molecule or time-resolved structural experiments? The four parts are independently resolvable rather than jointly mandatory. Parts (a) and (d) directly test whether the predicted scenario survives beyond the coarse-grained approximation, so a definite confirmation, refutation, or modification of the nonlinear relaxation scenario established by either of them — by higher-resolution simulation (a) or by experiment (d) — resolves the overall question; parts (b) and (c) are separate, independently refutable aspects — finite-temperature sampling of the branched landscape and the effect of hydrodynamic interactions and heterogeneous mobilities on the relaxation timescales and pathway selection — that further characterize the scenario and may be left open.

References

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