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Research Papers

Modeling Flexibility in Myosin V Using a Multiscale Articulated Multi-Rigid Body Approach

[+] Author and Article Information
Mahdi Haghshenas-Jaryani

The Robotics, Biomechanics, and
Dynamic Systems Laboratory,
Department of Mechanical and
Aerospace Engineering,
University of Texas,
Arlington, TX 76019
e-mail: mahdi.haghshenasjaryani@mavs.uta.edu

Alan Bowling

Assistant Professor
The Robotics, Biomechanics, and
Dynamic Systems Laboratory,
Department of Mechanical and
Aerospace Engineering,
University of Texas,
Arlington, TX 76019
e-mail: bowling@uta.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 4, 2013; final manuscript received February 7, 2014; published online October 13, 2014. Assoc. Editor: Tae-Won Park.

J. Comput. Nonlinear Dynam 10(1), 011015 (Oct 13, 2014) (11 pages) Paper No: CND-13-1212; doi: 10.1115/1.4026819 History: Received September 04, 2013; Revised February 07, 2014

This paper presents a multiscale dynamic model for the simulation and analysis of flexibility in myosin V. A 3D finite segment model, a multirigid body model connected with torsional springs, is developed to mechanically model the biological structure of myosin V. The long simulation run time is one of the most important issues in the dynamic modeling of biomolecules and proteins due to the disproportionality between the physical parameters involved in their dynamics. In order to address this issue, the most-used models, based on the famous overdamped Langevin equation, omit the inertial terms in the equations of motion; that leads to a first order model that is inconsistent with Newton's second law. However, the proposed model uses the concept of the method of multiple scales (MMS) that brings all of the terms of the equations of motion into proportion with each other; that helps to retain the inertia terms. This keeps the consistency of the model with the physical laws and experimental observations. In addition, the numerical integration's step size can be increased from commonly used subfemtoseconds to submilliseconds. Therefore, the simulation run time is significantly reduced in comparison with other approaches. The simulation results obtained by the proposed multiscale model show a dynamic behavior of myosin V which is more consistent with experimental observations in comparison with other overdamped models.

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Figures

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Fig. 1

The 3D structure of myosin V in a ribbon presentation obtained from the RCSB protein data bank (PDB ID: 2dfs) [31]. Myosin V's neck domain is comprised of tandem elements called IQ motifs, drawn schematically as dash ellipses. It can be considered as three pairs, shown as solid ellipses, which can bend at the junctures between them.

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Fig. 2

(a) A schematic representation of myosin V with a flexible neck (not drawn to scale). The schematic shows the different rigid bodies in the model. (b) A mechanical model of myosin V's neck (not drawn to scale). The flexibility of the neck domain is modeled by rigid bodies assembled through spherical joints (filled black circles) and torsional springs (spiral shape objects). Adjacent links (bodies) have a relative motion around the axes of rotation (dashed arrows). The 3D model is shown as a planar sketch for the sake of simplicity.

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Fig. 3

Viscous friction forces acting on myosin V

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Fig. 4

Forces emulating the conformational changes and external forces

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Fig. 5

Binding charges on myosin V

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Fig. 6

Absolute value of the charge potential and the associated force

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Fig. 7

Contact forces on myosin V

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Fig. 8

Brownian motion for myosin V

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Fig. 9

Random forces acting on the head ‘H’ in Fig. 2

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Fig. 10

Oscillation of heads of the flexible mechanical model of myosin V during docking. At t = 0.08 msec, the head H docks to the binding site on the substrate (point B1 in Fig. 2); therefore, its position is fixed after that time. (a) Position of the binding site (point HE) on the head H (see Fig. 2), and (b) position of the binding site (point KE) on the head K (see Fig. 2).

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Fig. 11

Deterministic single step locomotion of the 3D mechanical model of flexible myosin V: (a) 2D view and (b) 3D view. The numbers show the sequence of myosin V's snapshots. The neck's segments are shown by three different colors (red, blue, and green). The blue and green circles on the heads are location of the binding site and the candidate contact point, respectively.

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Fig. 12

Deterministic single step locomotion of the 2D mechanical model of flexible myosin V [30]

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Fig. 13

Initial and prestroke configurations of myosin V obtained by the 3D model. The neck domains are straight at the initial condition but they will bend in response to the conformational forces. This perfectly matches with the experimental observation in Ref. [5].

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Fig. 14

Random single step locomotion of the 2D mechanical model of flexible myosin V. The black path shows the complete trajectory of the binding site (blue circle) on the trailing head during a single step.

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Fig. 15

A schematic representation of myosin V with a flexible neck (not drawn to scale). The schematic shows the different rigid bodies in the model. The 3D model is shown as a planar sketch for the sake of simplicity.

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