Model for kinetics of wild-type and mutant kinesins

Mechanism of processive movement of monomeric and dimeric kinesin molecules

Kinesin molecules are motor proteins capable of moving along microtubule by hydrolyzing ATP. They generally have several forms of construct. This review focuses on two of the most studied forms: monomers such as KIF1A (kinesin-3 family) and dimers such as conventional kinesin (kinesin-1 family), both of which can move processively towards the microtubule plus end. There now exist numerous models that try to explain how the kinesin molecules convert the chemical energy of ATP hydrolysis into the mechanical energy to "power" their processive movement along microtubule. Here, we attempt to present a comprehensive review of these models. We further propose a new hybrid model for the dimeric kinesin by combining the existing models and provide a framework for future studies in this subject.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

Background

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined.

For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided.

Results

Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa.

Conclusions

We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Processive hand-over-hand motion of homodimeric nanomotors induced by interaction between two monomeric components and thermal noise

A simple homodimeric nanowalker is presented that is capable of moving processively along an extended periodic track. The unidirectional motion is based on a mechanism that makes use of the interaction between the two monomers and the thermal noise. The effect of the neck linker, which plays a critical role in the previously proposed design, plays an unimportant role in the present system. Except the requirement of a fixed binding orientation of the monomer relative to the track at the minimum of the potential well, the system has no other requirement for the form of the interaction potential between the motor and the track, which is critical to the unidirectional movement of the monomeric motor. Using detailed analyses and numerical simulations, it is shown that the homodimeric nanowalker walks hand over hand along the track with a high efficiency and a high stall force.

Processivity of single-headed kinesin motors

The processive movement of single-headed kinesins is studied by using a ratchet model of non-Markov process, which is built on the experimental evidence that the strong binding of kinesin to microtubule in rigor state induces a large apparent change in the local microtubule conformation. In the model, the microtubule plays a crucial active role in the kinesin movement, in contrast to the previous belief that the microtubule only acts as a passive track for the kinesin motility. The unidirectional movement of single-headed kinesin is resulted from the asymmetric periodic potential between kinesin and microtubule while its processivity is determined by its binding affinity for microtubule in the weak ADP state. Using the model, various experimental results for monomeric kinesin KIF1A, such as the mean step size, the step-size distribution, the long run length and the mean velocity versus load, can be well explained quantitatively. This local conformational change of the microtubule may also play important roles in the processive movement of conventional two-headed kinesins. An experiment to verify the model is suggested.

Limping of Homodimeric Kinesin Motors

Conventional kinesin, a homodimeric motor protein that transports cargo in various cells, walks limpingly along microtubule. Here, based on our previously proposed partially coordinated hand-over-hand model, we present a new mechanism for the limping behaviors of both wild-type and mutant kinesin homodimers. The limping is caused by different vertical forces acting on the heads in two successive steps during the processive movement of the dimer. From the model, various theoretical results, such as the dependences of the mean dwell time and dwell time ratio on the coiled-coil length and on the external load as well as the effect of vertical force on velocity, are in good agreement with previous experimental results. We predict that a high degree of limping will correlate strongly with a high sensitivity of ATP turnover rate to upwards force.

Model for unidirectional movement of axonemal and cytoplasmic dynein molecules

A model for the unidirectional movement of dynein is presented based on the structural observations and biochemical experimental results available. In this model, the binding affinity of dynein for microtubule (MT) is independent of its nucleotide state and the change between strong and weak MT-binding is determined naturally by the variation of relative orientation between the stalk and MT, as the stalk rotates following nucleotide-state transition. Thus the enigmatic communication from the adenosine triphosphate (ATP)-binding site in the globular domain to the far MT-binding site in the tip of the stalk, which is a prerequisite in conventional models, is not required. Using the present model, the previous experimental results such as the effect of ATP and adenosine diphosphate (ADP) bindings on dissociation of dynein from MT, the movement of single-headed axonemal dyneins at saturating ATP concentration, the load dependence of step-size for the movement of two-headed cytoplasmic dyneins and the dependence of stall force on ATP concentration can be well explained.

Mechanochemical couplings of kinesin motors

Kinesins are molecular motors capable of moving processively along microtubule in a stepwise manner by hydrolyzing ATP. Numerous experimental results on various aspects of their dynamical behaviours are available in literature. Although a number of models of tightly coordinated mechanism have been proposed to explain some experimental results, up to now no good explanation has been given to all these experimental results by using a single model. We have recently proposed such a model of partially coordinated hand-over-hand moving mechanism. In this paper, we use this model to study in detail various aspects of the dynamical properties of single kinesin molecules. We show that kinesin dimers walk hand-over-hand along microtubules in a partially coordinated rather than a tightly coordinated manner. The degree of coordination depends on the ratio of the two heads' ATPase rates that are in turn determined by both internal elastic force and external load. We have tested this model using various available experimental results on different samples and obtained a good agreement between the theory and the experiments.

A hand-over-hand diffusing model for myosin-VI molecular motors

Single molecules of dimeric myosin-VI have been demonstrated to be able to move processively towards the pointed end of actin filament with a mean step size of approximately 36 nm. Here we present a hand-over-hand diffusing mechanism for this unidirectional movement. Based on this mechanism, its dynamical behaviors such as the step-size distribution, dwell-time distributions and mean dwell time at various ATP and ADP concentrations and under various loads are studied in detail. The calculated results show good agreement with previous experimental results. The processive movement of mutant myosin-V with its neck domains truncated to only one IQ motif can also be explained by using this hand-over-hand diffusing model.