Transitions in microtubule C-termini conformations as a possible dendritic signaling phenomenon

Abstract

We model the dynamical states of the C-termini of tubulin dimers that comprise neuronal microtubules. We use molecular dynamics and other computational tools to explore the time-dependent behavior of conformational states of a C-terminus of tubulin within a microtubule and assume that each C-terminus interacts via screened Coulomb forces with the surface of a tubulin dimer, with neighboring C-termini and also with any adjacent microtubule-associated protein 2 (MAP2). Each C-terminus can either bind to the tubulin surface via one of the several positively charged regions or can be allowed to explore the space available in the solution surrounding the dimer. We find that the preferential orientation of each C-terminus is away from the tubulin surface but binding to the surface may also take place, albeit at a lower probability. The results of our model suggest that perturbations generated by the C-termini interactions with counterions surrounding a MAP2 may propagate over distances greater than those between adjacent microtubules. Thus, the MAP2 structure is able to act as a kind of biological wire (or a cable) transmitting local electrostatic perturbations resulting in ionic concentration gradients from one microtubule to another. We briefly discuss the implications the current dynamic modeling may have on synaptic activation and potentiation.

Appendix A

The choice of model parameters

• The basic units in our simulation were selected as follows:

  • Mass: 1 amu=1 D=1.66×10⁻²⁷ kg

  • Time: 1 ps (1×10⁻¹² s)

  • Charge: 1 e⁻ (1.6×10⁻¹⁹ C)

  • Length: 1 nm (hence, velocity is 1 nm/ps)

  • Energy: kJ/mol

  • Force: kJ/(mol · nm)

• The mass of the molecular chain of beads is estimated as 2 kD (summing up the amino acids of the C-terminus of a given human tubulin isotype), or 2000 unit masses. For simplicity we assume identical beads, i.e. for N-beads model the weight of each bead is 2 kD/N. We actually take N = 11, however the first bead is totally attached to the surface.

• The net charge of the C-terminus is assumed to be −10e, again taken from the same isotype of tubulin.

• The nominal length of the C-terminus is taken to be L=4.5 nm.

• The Lennard–Jones parameters are:

  • ε=1 (however recall the truncation)

  • σ=0.45 (in nm units)

  • R _c=2.0^1/6σ

• FENE parameters:

  • K=20–30

  • R _c=1.5σ

• Harmonic angle force parameters:

  • K _{θ a} =40 (the force constant)

  • θ₀=135° or 3π/4

• Dihedral harmonic angle force parameters:

  • K _{θ d} =4 (the force constant)

  • ϕ₀=0° (or π)

  • n=2 multiplication factor

• The friction coefficient used: Γ=0.03

• The noise was taken from a (3D) uniform distribution [−W,...,W] W=20;

Note that the friction coefficient, Γ, enters the equation of motion as part of the fluctuation-dissipation terms in the Langevin dynamics. We use the random and friction forces to represent a virtual solution without explicitly taking into account the particles in the solution. The actual parameters of the simulation are determined from the (room) temperature, the Lennard–Jones constants and the bead mass. The friction is determined as a function of the system’s time unit and the time steps of the numerical integration. In our case, we were interested in maintaining the higher vibrational frequencies, so the decay time was kept longer (determined from friction). The amplitude of the stochastic force then follows the Langevin constraints.

External force representation

The external force is simulated as a traveling localized wave with a certain amplitude, as follows: F(z(i), t)= amp sech(b(z(i)– vt))² where z( i) is the z-position of the ith bead

Figure 8 shows the actual force on each one of the beads. The parameters of the wave were taken to be:

• v=0.8 [nm/ps]

• amp=6 [kJ mol⁻¹ nm⁻¹]

• b=0.25