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Title: Nonlinearity of Mechanochemical Motions in Motor Proteins}
Article:
Abstract:
The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors— myosin V and kinesin KIF1A— and performed numerical investigations of their conformational relaxation properties within the coarse-grained elastic network approximation. We have found that the linearity assumption is deficient for ligand-induced conformational motions and can even be violated for characteristic thermal fluctuations. The deficiency is particularly pronounced in KIF1A where the normal mode description fails completely in describing functional mechanochemical motions. These results indicate that important assumptions of the theory of protein dynamics may need to be reconsidered. Neither a single normal mode nor a superposition of such modes yields an approximation of strongly nonlinear dynamics.
Introduction:
Protein machines, which may represent enzymes, ion pumps or molecular motors, play a fundamental role in biological cells and understanding of their activity is a major challenge. Operation of these machines is based on slow conformational motions powered by external energy supply, often with ligands( such as ATP). In molecular motors, binding of ATP and its subsequent hydrolysis induce functional mechanochemical motions, essential for their operation. These motions, which follow after an energetic activation, are conformational relaxation processes. Large-scale conformational changes may take place in proteins as a result of ligand binding[1]. Despite the large magnitude of such changes, they are nonetheless often considered in the framework of the linear response theory[2] and the normal mode approximation[3]–[7]. The normal mode analysis is furthermore broadly employed in the elastic-network studies of proteins[7]–[18]. However, there is no general justification to assume that relaxation processes in proteins are linear and this assumption has to be verified for particular macromolecules. It is known that relaxation processes in complex dynamical systems may be strongly nonlinear and deviate much from simple exponential relaxation. As an example borrowed from a distant field, we can mention the Belousov-Zhabotinsky reaction which exhibits a great variety of spatiotemporal patterns( pacemakers, rotating spiral waves) that are however only complicated transients accompanying relaxation to the equilibrium state[19],[20]. Conformational relaxation in single protein molecules may also be a complicated process, comprising qualitatively different kinds of mechanochemical motions. While partial unfolding and refolding, associated with ligand binding, are known for some protein machines, such as the enzyme adenylate kinase[21], usually functional conformational motions in molecular machines and, specifically, in motor proteins are elastic. This means that the pattern of contacts between the residues in a protein is not changed upon ligand binding and preserved during the relaxation process, as generally assumed in the elastic network modeling( ENM). Here, we provide detailed analysis of conformational relaxation processes, associated with ligand binding and hydrolysis, in two motor proteins— myosin V[22],[23] and kinesin KIF1A[24]. Our investigations, performed in the framework of the ENM approximation, reveal that nonlinearity is characteristic for both macromolecules and the normal mode description is not really applicable for any of them. For KIF1A, a monomeric motor protein from the kinesin superfamily, nonlinear effects are found to dominate completely functional mechanochemical motions which turn out to be qualitatively different from the normal mode predictions. Despite the nonlinearity, well-defined conformational relaxation paths, robust against perturbations, have been found in both motor proteins.
Discussion:
The normal mode description is broadly used in structural studies of proteins. The analysis of thermal fluctuations and the interpretation of the respective experimental structural data are traditionally performed assuming that fluctuations are linear and, hence, correspond to thermal excitation of various normal modes( see, e. g.,[3],[4]). The linear response of a protein macromolecule to structural perturbations, such as ligand binding, is an often used assumption[2]. To a large extent, the elastic-network analysis of ligand-induced macromolecular motions is based on determining normal modes in the elastic networks of the considered proteins( see, e. g.,[7]). The patterns of atomic displacements in such normal modes are further compared with the experimentally measured atomic displacements in the same proteins that are induced by a change of the chemical state, such as binding of an ATP molecule[7],[14]–[17]. Large overlaps with only a few slowest normal modes are seen as the evidence for the applicability of the elastic-network ansatz, whereas the wide distribution of overlaps is considered as the indication that the elastic network description fails for a particular macromolecule. Specifically, strong overlaps between ligand-induced conformational changes and atomic displacements in the few slowest modes have been found for scallop myosin and-ATPase, while such overlaps were absent for kinesin KIF1A[18]. Our numerical investigations of elastic conformational motions in two motor proteins( myosin V and KIF1A) have revealed however that in both of them the nonlinearities play an essential role. While slow conformational relaxation motions in myosin can still be qualitatively characterized in terms of the normal modes, the normal mode description breaks down completely for KIF1A. The observed breakdown of the normal mode description does not however mean that conformational motions become irregular. We have seen that ordered and robust mechanochemical motions are characteristic for both protein motors, even though they cannot be described in terms of the linear response. We want to emphasize that, when the dynamics is nonlinear, neither a single normal mode, nor a combination of many such modes can reproduce the motions. Thus, the normal mode description fails completely in this case and the problem is not that many normal modes must be taken into account. Actually, as we have shown, even for KIF1A, one normal mode would be sufficient to describe long-time relaxation within the harmonic domain— however, this domain is restricted to a tiny neighbourhood of the equilibrium state. Thermal fluctuations have not been explicitly included into our dynamical ENM simulations. However, such fluctuations are effectively generating random conformational perturbations. In our study, relaxation processes starting from random conformational perturbations have indeed been considered. In myosin V, one well-defined nonlinear conformational relaxation trajectory, leading to the equilibrium state, has been identified. Starting from an arbitrary initial conformation( but still without unfolding), rapid convergence to this special trajectory takes place. While the motion corresponding to the special attractive trajectory is initially nonlinear, it becomes harmonical later and a substantial part of the ordered conformational relaxation process is within the harmonic domain of the equilibrium state. Similar behavior has been previously noted by us[29] for scallop myosin and-ATPase, but its detailed analysis has not yet been performed. The situation is more complex for the monomeric kinesin KIF1A. Instead of a unique deep energy valley leading to the reference ADP-bound state, two such valleys, both leading to the equilibrium state, are present. These valleys correspond to two kinds of ordered conformational motions possible in the protein. The first of them is relatively wide and, when thermal conformational fluctuations are excited, they would typically proceed along it. However, the conformational relaxation motion starting from the ATP-bound state follows a different path, which corresponds to the second energy valley branching from the typical fluctuation path already at very small deviations from the equilibrium state. Note that the branching takes place as the change in the distance between the molecular labels Glu233 and Ala286 is still less than an angstrom, which is much smaller than the intensity of typical thermal fluctuations for such a distance. Thus, the nonlinear effects in KIF1A are strong even for the typical thermal fluctuations. Remarkably, such second relaxation path is also stable with respect to perturbations, i. e. structurally robust. Our numerical investigations reveal that motion along this path can be divided into two qualitatively different stages. At the first of them, sliding of the switch I loop is observed, whereas at the second stage a transition from the loop to the-helix is realized. Structural reorganization, corresponding to this transition, is not possible until the sliding motion is completed, lifting a restriction through the backbone chain. Recent crystallographic studies suggest that the switch I loop/helix plays an important role in control of the motor function through interaction with and switch II[33]. Thus, in contrast to myosin, a single ATP binding event induces in KIF1A a complex, but ordered conformational motion characterized by two qualitatively different consequent phases. As we conjecture, this special dynamical property of KIF1A may be needed for the processive motion of this single-headed molecular motor[24]. In myosin V, conformational motions driven by random thermal fluctuations are similar in their properties to the relaxation motion from the nucleotide-free state. This may facilitate exploitation of such fluctuation motions for the motor operation, as suggested by recent single-molecule experiments[34]. In KIF1A, where the energy valley splits into two branches, typical thermal conformational fluctuations are qualitatively different from the relaxation motion starting from the previous ATP-bound state. The latter motion is entropically hindered for thermal fluctuations and cannot be reversed through them. This may turn out to be important for the understanding of the operation of the monomeric kinesin as a molecular motor. Latest experimental techniques permit simultaneous observation of stepping motion and conformational changes of a motor[35]. The coarse-grained modeling, including our present study, can contribute further suggestions for the design( e. g., by determining positions for fluorescent labeling) of such experiments. Finally, we note that our study has been based on the elastic network approximation for proteins. More detailed descriptions, such as, e. g., G-like models, can also be used to consider conformational relaxation processes[36]. We expect that similar behavior will then be observed.
Biological cells use a variety of molecular machines representing enzymes , ion channels or pumps , and motors . Motor proteins are nanometer-size devices generating forces and actively moving or rotating under the supply of chemical energy through ATP hydrolysis . They are crucial for many cell functions and promising for nanotechnology of the future . Although such motors represent single molecules , their operation cycles cannot be followed in detail in simulations even on the best modern supercomputers and some approximations need to be employed . It is often assumed that conformational dynamics of motor proteins is well described within a linear response approximation and corresponds to excitation of normal modes . We have checked this assumption for two motor proteins , myosin V and kinesin KIF1A . Our results show that , while both these biomolecules respond by well-defined motions to energetic excitations , these motions are essentially nonlinear . The effect is particularly pronounced in KIF1A where relaxation proceeds through a sequence of qualitatively different conformational changes , which may facilitate complex functional motions without additional control mechanisms .