Dynamic balance between vesicle transport and microtubule growth enables neurite outgrowth
Fig 5
Generation of an analytical solution for the prediction of kinetic parameters at steady state.
(A) The development of the analytical solution depends on the categorization of membrane fluxes based on their destination compartment. Such classification distinguishes four different membrane types (I-IV) (that should not be confused with the four different vesicle types we show in Fig 2B). Initial and final anterograde and retrograde transport rates (which refer to budding and fusion rates at the TGN and GC) are the sum of the transport rates of the encircled membranes types. (B) Calculation of kinetic parameter for v-SNARE V. VV/YY/UU refer to total count of SNAREs, V/Y/U describe concentration of SNAREs (per membrane area). See supplementary methods for complete derivation of analytical solution. (C) Microtubule bundle (MTB) growth is mediated by the conversion of dynamic MTs into stable MTs. Dynamic MTs nucleate de-novo, followed by their degradation or stabilization. (D) Nucleation, stabilization and degradation rates for dynamic MTs are calculated as shown. (E) To verify our analytical solution we analyzed, whether our predicted parameter sets allow neurite outgrowth with the selected velocity and without violation of model constraints. For each velocity, we selected 6 different parameter sets that differ in the number of v-SNARE V and the tethering rate at the growth cone plasma membrane (S5A Fig). Every 500 min over a simulation period of 5,000 min (~3.5days), we documented the indicated outputs. Averages and standard deviations were calculated for each velocity. As shown for a velocity of 15 μm/h, our analytical solution predicts steady state dynamics that match the anticipated model constraints (horizontal lines) with high accuracy.