Spatial redistribution of neurosecretory vesicles upon stimulation accelerates their directed transport to the plasma membrane

Through the integration of results from an imaging analysis of intracellular trafficking of labelled neurosecretory vesicles in chromaffin cells, we develop a Markov state model to describe their transport and binding kinetics. Our simulation results indicate that a spatial redistribution of neurosecretory vesicles occurs upon secretagogue stimulation leading vesicles to the plasma membrane where they undergo fusion thereby releasing adrenaline and noradrenaline. Furthermore, we find that this redistribution alone can explain the observed up-regulation of vesicle transport upon stimulation and its directional bias towards the plasma membrane. Parameter fitting indicates that in the deeper compartment within the cell, vesicle transport is asymmetric and characterised by a bias towards the plasma membrane.

We can now express C and L in terms of G as follows, Now we can combine (8), (13) to get the steady state solution for G in terms ofḠ, This is the steady state for the population size in state G. As mentioned in section Minimal 4-state model it converges toḠ in the limit when the rate µ is large. This complements the steady state abundances (9),(12) and (13).

S2 Governing Equations.
We provide below the full system of coupled differential equations describing the Markov state model visualised in Fig 5A and Fig 5B above.
S3 Steady state distributions, absolute values and uncertainty

S4 Modification of the model introducing crowding
In [2] it was also reported that transition rates from the pool of free vesicles into directed transport accelerate three-fold upon stimulation (Fig 2A). This effect can't be predicted by our model which relies on the assumption of constant transition rates. In this supplementary section we present a modification of our model visualised in Fig 5A and Fig 5B suggesting that specifically the central cytoskeleton network in control cells is limited by its carrying capacity. We show that this hypothetical mechanism is consistent with the observations (Fig 2A). We hypothesise that the observed increase in the average free-to-directed transition rate upon stimulation is a consequence of the global decrease in vesicle abundance occurring at stimulation. We therefore suggest that in control transitions are slowed down by crowding of vesicles undergoing directed transport. Table S1. Parameter values We use Hill functions (for a repressor [3]) to model the limiting effect of carrying capacities on all other transition rates into directed transport by the following correction factors, It obviously appears problematic to include steady state abundances in stimulation in the correction factors. To remove these dependencies one might rewrite the correction factors as a classical Hill function with two constants, namely α i (R i ) = µ i /(1 + R i /ν i ) (for R i > R ζstim i ) and analogous expressions for β i . Nevertheless, such rewriting of the correction is not required to run the simulations and it would render our choice of parameters less transparent. We therefore keep the notation used in (14). Note that applying the correction factors (14) to the transition rates (5) would also slow down transitions from the pool of caged vesicles into transport states. Reported transition rates from caged into directed motion (averaged among spatial compartments), however, only exhibit minor variation between control and stimulation ( Fig 2B). We speculate that for caged vesicles the speed-up in response to less crowding along transport fibres upon stimulation might be compensated by faster turnover of the actomyosin cortex upon stimulation [4] which could prevent a large fraction of caged vesicles from binding to fibre-motor-protein complexes.
As a consequence we keep the peripheral caged-to-directed transition rates unmodified, while rescaling all rates listed in (5) as follows In the absence of more detailed data, and since we only seek to provide a proof of concept for the idea that crowding can explain the 3-fold speed-up of transitions from free to directed (Fig 2A) we choose a single constant for the repression coefficients (see Table S1).
We fit a single, spatially uniform, repressor coefficient (Table 1) in a way such thatat steady state -the average free-to-directed transition rate is 0.126 min −1 in control (0.29 min −1 in stimulation) as compared to 0.27 min −1 (control) (0.3 min −1 in stimulation) for the model with constant transition rates. The model with non-linear transition rates modelling crowding therefore allows to reproduce the 3-fold speed-up of transitions from free into directed motion (Fig S4D) observed experimentally (Fig 2A).
Note that we do not reassess the directional parameters ρ i , i = 1, 2, 3 with the modified transition rates. With these parameters the modified model predicts the ratio of outward vs inward transport (Fig S4C) as well as the increase of total transport (Fig S4B) almost equally well as the original model.
The correction factors with the uniform repressor coefficients listed in Table 1 are close to one in the central compartment, indicating that crowding in control is stronger in the periphery of the cell (the exact correction factors are visualised in supplementary Fig S3). This reflects that most variation of vesicle abundance between control and stimulation is in the periphery of the cell, since the steady state distribution of vesicles in control is predominantly characterised by an accumulation of vesicles close to the cortex (see steady state distributions in absolute numbers shown in supplementary Fig S1).
We reiterate that the modification of this model through carrying capacities of the transport network is entirely speculative. We report it in the supplementary material setion of this study to illustrate that even the observed increase in the transition rate free → directed (Fig 2A) in stimulated cells, which cannot be explained by spatial redistribution alone, in principle can be explained as a purely mechanistic effect and doesn't require a specific biochemical feedback. Nevertheless, more experimental data would be required to make a definite statement.