A possible mechanism for neurofilament slowing down in myelinated axon: Phosphorylation-induced variation of NF kinetics

Abstract

Neurofilaments(NFs) are the most abundant intermediate filaments that make up the inner volume of axon, with possible phosphorylation on their side arms, and their slow axonal transport by molecular motors along microtubule tracks in a "stop-and-go" manner with rapid, intermittent and bidirectional motion. The kinetics of NFs and morphology of axon are dramatically different between myelinate internode and unmyelinated node of Ranvier. The NFs in the node transport as 7.6 times faster as in the internode, and the distribution of NFs population in the internode is 7.6 folds as much as in the node of Ranvier. We hypothesize that the phosphorylation of NFs could reduce the on-track rate and slow down their transport velocity in the internode. By modifying the '6-state' model with (a) an extra phosphorylation kinetics to each six state and (b) construction a new '8-state' model in which NFs at off-track can be phosphorylated and have smaller on-track rate, our model and simulation demonstrate that the phosphorylation-induced decrease of on-track rate could slow down the NFs average velocity and increase the axonal caliber. The degree of phosphorylation may indicate the extent of velocity reduction. The Continuity equation used in our paper predicts that the ratio of NFs population is inverse proportional to the ratios of average velocity of NFs between node of Ranvier and internode. We speculate that the myelination of axon could increase the level of phosphorylation of NF side arms, and decrease the possibility of NFs to get on-track of microtubules, therefore slow down their transport velocity. In summary, our work provides a potential mechanism for understanding the phosphorylation kinetics of NFs in regulating their transport and morphology of axon in myelinated axons, and the different kinetics of NFs between node and internode.

Fig 1. Distribution of NFs along axon in the ‘6-state’ model with kinetics of phosphorylation and dephosphorylation.

Fig 2. The dependence of velocity boost on the rate ratio between phosphorylation and dephosphorylation r = γ_ph: γ_de.

The x-axis is the velocity ratio n between the node V(fast) and internode V(slow) without the phosphorylation kinetics. The y-axis is the velocity ratio between node V(node) and internode V(internode) with the phosphorylation kinetics.

Fig 3. The probability of NFs at each state by reconstruction of velocity along node and internode by numerical solution of PDE.

Fig 4. The distribution of NFs in each state at dynamical equilibrium by velocity reconstruction in the ‘8-state’ model.

Fig 5. Distribution of NFs along axon by reconstruction of on-track rate in the ‘8-state’ model.

Fig 6. The velocity acceleration in the node depends on the parameter of r and increase folds of γon2.

The x axis are the increase folds of the on-track rate ${\mathrm{\gamma }}_{\mathrm{o}\mathrm{n}}^2$ for both the node and internode, increasing from ${\mathrm{\gamma }}_{\mathrm{o}\mathrm{n}}^2=0.00498s^{-1}$ to ${\mathrm{\gamma }}_{\mathrm{o}\mathrm{n}}^2=0.0498s^{-1}$ by ten folds.

Fig 7. The ratio of velocity between node and internode changes with the rate ratio of phospohorylation and dephosphorylatoin r = γ_ph: γ_de in the internode.

The ${\mathrm{\gamma }}_{\mathrm{o}\mathrm{n}}^2$ in the internode is fixe as b = 0.00498 s⁻¹.

Fig 8. NFs kinetics between states of phosphorylation and dephosphorylation.

Fig 9. The distribution of γ_de, γ_ph along the axon.

Fig 10. Schematic diagram of the ‘8-state’ model.

Fig 11. Distribution of on-track rates γon1,γon2 along node and internode for ‘8-state’ model.