Figure 1.
Schematic representation of a stacked Golgi apparatus that undergoes cisternal maturation.
A) ER-derived vesicles (beige) fuse with each other to yield the first, most cis, cisterna. Individual cisterna mature from position 1 to position 8, where they disintegrate into transport carriers destined for the plasma membrane and endosomes. Vesicles originating from cisterna #2 deliver cis Golgi proteins to cisterna #1 while at the same time cisterna #2 receives Golgi resident proteins from cisterna #3. B) The cisternae are categorized as cis, medial and trans based on the abundance of Golgi residence proteins, mostly glycosylating enzymes, which exhibit distinct but overlapping peaks along the Golgi stack according to their sequential role in the processing of exocytic cargo. C) Two SNARE pairs, which we term SNARE (purple) and
SNARE (green) are thought to mediate intra-Golgi transport of resident proteins. The respective v and t-SNAREs of
SNARE both decay with a steep gradient from cis to trans.
-t-SNAREs decay with a shallow gradient, while its corresponding
-v-SNARE concentration increases from cisternae 1 to 8. The graphs are schematic representations of data from [17].
Figure 2.
Self-generated concentrations of SNAREs and enzymes.
Panel A: Steady state concentration of cisternal SNARE vs the number of cisterna
for: both the loss and the vesicular transport mechanisms are enacted (solid line), only the loss mechanism operates (dashed line), only vesicular transport occurs (dotted line). All concentrations are sampled immediately before the cisternal shift event, when the number of each cisterna is incremented by one. The definitions of parameters are given in Methods. Here and in all following plots it is assumed that
and
, i.e. all concentrations are expressed in the units of initial concentrations and the time is expressed in units of the cisternal maturation period. Solid line:
and
, dashed line:
and
, dotted line:
and
, for all curves
. Panel B: Distribution of Golgi enzymes: cis (solid line), medial (dashed line) and trans (dotted line) established as a result of competition for incorporation into vesicles. Vesicular flux is controlled by the gradient of cisternal SNAREs shown by the solid line in the left panel, vesicles from the first cisterna can exit the Golgi and fuse with the ER. The parameters for the enzyme transport are
,
,
, and
.
Table 1.
Dissociation constants for binding to vesicular sites that yield the plots depicted in Fig. 3.
Figure 3.
Self-generated steady state distributions of alpha and beta SNAREs and enzymes as it is observed in the Golgi apparatus.
Panel A: t-SNARE (solid line) and v-SNARE (circles) coinciding with t-SNARE, and
t-SNARE (dashed line) and v-SNARE (dotted line) vs. the cisternal number
. Panel B: cis (solid line), medial (dashed line) and trans (dotted line) Golgi enzymes normalized by their maximum value vs number of cisterna
. The parameters are: Decay rates
are zero for all substances except for
t-SNARE for which
, the vesicular transport coefficient
, and dissociation constants for vesicular binding are
for ER v-SNARE,
for cis t- and v-SNAREs,
for trans t-SNARE,
for trans v-SNARE,
for cis enzymes,
for median enzymes, and
for trans enzymes. Initial concentrations of all substances in the first cisterna are
, and the concentration of t-SNARE in ER is 0.7.
Figure 4.
Steady state concentrations of three classes of enzymes in the unrestricted fusion scenario.
Golgi enzyme concentrations are normalized by their maximum value. The parameters are: Decay rates for the cis and trans t-SNARE are , the vesicular transport coefficient
, and dissociation constants for vesicular binding are:
for the ER v-SNARE,
for the cis t- and v-SNAREs,
for trans t-SNARE,
for trans v-SNARE,
for cis enzymes,
for medial enzymes, and
for trans enzymes. Initial concentrations of all proteins in the first cisterna are
, and the concentration of the t-SNARE in the ER is 0.7.
Figure 5.
Distribution of SNARE for large number of cisternae.
The steady state gradient has the exponentially decaying form, where
depends on two dimensionless groups of parameters,
which caracterizes the decay of the SNARE and
which characterizes the vesicular transport of SNARE:
and
(solid line) with the best fit given by
,
and
(dashed line) with the best fit given by
. Theoretical values of
determined from (11) are indistinguishable from the values obtained as the best fit for the simulations. The dotted line corresponds to the case of zero loss,
and
, and illustrates the absence of a concentration gradient. To reveal the exponential decay of the SNARE concentration, we purposefully consider a non-biologically high number of compartments and analyze the SNARE concentration away from both the cis and trans ends of the stack, where the boundary effects can play a role.
Figure 6.
Enzyme segregation depends on the open boundary condition.
Steady state distribution of the same enzymes as in Fig. 2 if the “Closed boundary conditions” on the cis end of the stack are assumed: No vesicles can exit the Golgi. The parameters are the same as in Fig. 2.