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Journal of Biomechanical Engineering | Volume 130 | Issue 4 | Research Paper
Research Papers

Mechanical Model of the Tubulin Dimer Based on Molecular Dynamics Simulations

[+] Author and Article Information
Søren Enemark1

Department of Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italysoren.enemark@polimi.it

Marco A. Deriu

Department of Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; Department of Mechanical Engineering,  Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Monica Soncini, Alberto Redaelli

Department of Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

1

Corresponding author.

J Biomech Eng 130(4), 041008 (Jun 03, 2008) (7 pages) doi:10.1115/1.2913330 History: Received April 15, 2007; Revised February 26, 2008; Published June 03, 2008
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The basic unit in microtubules is αβ-tubulin, a heterodimer consisting of an α- and a β-tubulin monomer. The mechanical characteristics of the dimer as well as of the individual monomers may be used to obtain new insight into the microtubule tensile properties. In the present work, we evaluate the elastic constants of each monomer and the interaction force between them by means of molecular dynamics simulations. Molecular models of α-, β-, and αβ-tubulins were developed starting from the 1TUB.pdb structure from the RCSB database. Simulations were carried out in a solvated environment by using explicit water molecules. In order to measure the monomers’ elastic constants, simulations were performed by mimicking experiments carried out with atomic force microscopy. A different approach was used to determine the interaction force between the α- and β-monomers by using 16 different monomer configurations based on different intermonomer distances. The obtained results show an elastic constant value for α-tubulin of 3.8–3.9N∕m, while for the β-tubulin, the elastic constant was measured to be 3.3–3.6N∕m. The maximum interaction force between the monomers was estimated to be 11.9nN. A mechanical model of the tubulin dimer was then constructed and, using the results from MD simulations, Young’s modulus was estimated to be 0.6GPa. A fine agreement with Young’s modulus values from literature (0.1–2.5GPa) is found, thus validating this approach for obtaining molecular scale mechanical characteristics. In perspective, these outcomes will allow exchanging atomic level description with key mechanical features enabling microtubule characterization by continuum mechanics approach.
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References

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Figures

Grahic Jump Location
+The αβ-tubulin dimer together with GTP, GDP, and Mg2+ (inserts)
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The αβ-tubulin dimer together with GTP, GDP, and Mg2+ (inserts)
Figure 1

The αβ-tubulin dimer together with GTP, GDP, and Mg2+ (inserts)

Grahic Jump Location
+Scheme of mechanical test for the monomer. The CM of reference group (R) is frozen while the CM of pull group (P) is connected to one end of a spring. A constant rate displacement is imposed to the other end of the spring (S).
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Scheme of mechanical test for the monomer. The CM of reference group (R) is frozen while the CM of pull group (P) is connected to one end of a spring. A constant rate displacement is imposed to the other end of the spring (S).
Figure 2

Scheme of mechanical test for the monomer. The CM of reference group (R) is frozen while the CM of pull group (P) is connected to one end of a spring. A constant rate displacement is imposed to the other end of the spring (S).

Grahic Jump Location
+The solvated, energy minimized, and equilibrated structure (left) was used to set up the configurations with different individual intermonomer distances (right)
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The solvated, energy minimized, and equilibrated structure (left) was used to set up the configurations with different individual intermonomer distances (right)
Figure 3

The solvated, energy minimized, and equilibrated structure (left) was used to set up the configurations with different individual intermonomer distances (right)

Grahic Jump Location
+Ramachandran plot of the αβ-tubulin dimer after the second EM in water. Dark gray, gray, light gray, and white regions mark the favored, accepted, largely accepted, and nonaccepted regions, respectively.
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Ramachandran plot of the αβ-tubulin dimer after the second EM in water. Dark gray, gray, light gray, and white regions mark the favored, accepted, largely accepted, and nonaccepted regions, respectively.
Figure 4

Ramachandran plot of the αβ-tubulin dimer after the second EM in water. Dark gray, gray, light gray, and white regions mark the favored, accepted, largely accepted, and nonaccepted regions, respectively.

Grahic Jump Location
+Potential energy (dark gray) and temperature (light gray) behavior of the dimer in the first 50ps of a MD simulation over 800ps. Between 0ps and 35ps, the structure was heated to 300K by an external heat bath. The heating was followed by an equilibration over the rest of the simulation time as shown in the insert.
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Potential energy (dark gray) and temperature (light gray) behavior of the dimer in the first 50ps of a MD simulation over 800ps. Between 0ps and 35ps, the structure was heated to 300K by an external heat bath. The heating was followed by an equilibration over the rest of the simulation time as shown in the insert.
Figure 5

Potential energy (dark gray) and temperature (light gray) behavior of the dimer in the first 50ps of a MD simulation over 800ps. Between 0ps and 35ps, the structure was heated to 300K by an external heat bath. The heating was followed by an equilibration over the rest of the simulation time as shown in the insert.

Grahic Jump Location
+(a) MD simulation for the α-tubulin model. In the upper right part, the results for the pulling tests at three different velocities are shown, while the lower left part shows the curves for the compression. (b) MD simulation for the β-tubulin model. In the upper right part, the results for the pulling tests at three different velocities are shown, while the lower left part shows the curves for compression.
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(a) MD simulation for the α-tubulin model. In the upper right part, the results for the pulling tests at three different velocities are shown, while the lower left part shows the curves for the compression. (b) MD simulation for the β-tubulin model. In the upper right part, the results for the pulling tests at three different velocities are shown, while the lower left part shows the curves for compression.
Figure 6

(a) MD simulation for the α-tubulin model. In the upper right part, the results for the pulling tests at three different velocities are shown, while the lower left part shows the curves for the compression. (b) MD simulation for the β-tubulin model. In the upper right part, the results for the pulling tests at three different velocities are shown, while the lower left part shows the curves for compression.

Grahic Jump Location
+Potential energy, Vint, of the interaction between the two monomers as a function of the displacement, Δr, from the 800ps equilibrated configuration.
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Potential energy, Vint, of the interaction between the two monomers as a function of the displacement, Δr, from the 800ps equilibrated configuration.
Figure 7

Potential energy, Vint, of the interaction between the two monomers as a function of the displacement, Δr, from the 800ps equilibrated configuration.

Grahic Jump Location
+Interaction force between the two intradimer monomers as a function of the displacement. Points are obtained from inserting the distances for which the measurements were done into the first derivative of the potential energy polynomial.
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Interaction force between the two intradimer monomers as a function of the displacement. Points are obtained from inserting the distances for which the measurements were done into the first derivative of the potential energy polynomial.
Figure 8

Interaction force between the two intradimer monomers as a function of the displacement. Points are obtained from inserting the distances for which the measurements were done into the first derivative of the potential energy polynomial.

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