Figure 1.
Illustration of model processes and associated rates that are shared between models.
(A) PEX5 (green oval) associated with cargo (orange square) binds to available binding sites on a peroxisomal importomer (blue irregular shape) at a rate . There are
binding sites per importomer; here we illustrate
. (B) If unoccupied, the RING complex site is immediately occupied by another PEX5 on the importomer. (C) The RING complex (purple rectangle) will ubiquitinate an associated PEX5 at rate
. We generally allow only one ubiquitinated PEX5 per importomer. For (A), (B), and (C) the AAA complex is shown, and will participate in PEX5 export as described in Fig. 2.
Figure 2.
Illustration of translocation and export models and associated rates.
(A) PEX5 (green oval) associated with cargo (orange square) binds to available binding sites on a peroxisomal importomer (blue irregular shape) at a rate . In uncoupled translocation, associated cargo is translocated spontaneously after binding to the importomer. (B) If translocation is uncoupled, then export of ubiquitinated PEX5 by the AAA complex at rate
does not have a relationship with cargo translocation. (C) In directly coupled translocation, the cargo translocation occurs as the ubiquitinated PEX5 is removed from the importomer by the AAA complex at rate
. The PEX5 is shown simultaneously both cargo-loaded and ubiquitinated — this figure is meant to be illustrative; see Methods for discussion. (D) In cooperatively coupled translocation, the removal of PEX5 by the AAA complex (
) can only occur when coupled to the cargo translocation of a distinct PEX5-cargo in the same importomer. This always leaves at least one PEX5 associated with each importomer.
Figure 3.
Uncoupled and directly coupled cargo translocation.
Both uncoupled and directly coupled translocation models have identical PEX5 and ubiquitination behavior and so they are reported together. (A) cytosolic PEX5-cargo concentration vs. cargo addition rate, . Different numbers of binding sites per importomer are shown from
(orange triangles) to
(green diamonds), as shown in the legend; the legend also applies to (B), (C), and (D). The dashed black line is the measured cytosolic PEX5 concentration of
[43]. This is consistent with
when
. (B) Peroxisomal PEX5 fraction vs.
. (C) Fraction of peroxisomal PEX5 that is ubiquitinated vs. PEX5 cargo addition rate,
. (D) Ubiquitin per peroxisome vs.
. A characteristic increase of ubiquitination with
is seen that is largely independent of the number of binding sites
. Vertical bars represent the standard deviation of observed values; error bars are smaller than point sizes.
Figure 4.
Cooperatively coupled cargo translocation.
(A) Cytosolic PEX5-cargo concentration vs. PEX5 cargo addition rate, . The dashed black line is the measured cytosolic PEX5 concentration of
[43]. Inset shows the fraction of importomers that are fully occupied by PEX5 vs. PEX5 cargo addition rate, with five PEX5 sites per importomer and cooperative coupling. (B) peroxisomal PEX5 fraction vs.
for cooperatively coupled cargo translocation. (C) Fraction of peroxisomal PEX5 that is ubiquitinated vs.
. (D) ubiquitin per peroxisome vs.
. A characteristic decrease of ubiquitination with
is seen that is largely independent of the number of binding sites
. Different number of binding sites per importomer are shown from
(red circles) to
(green diamonds), as shown in the legend in (B). Cooperative coupling cannot function with
, so that is not shown. Subsequent figures use
(blue squares). Note that the vertical scale of ubiquitin per peroxisome in (D) is much larger than in Fig. 3.
Figure 5.
Ubiquitin thresholds for cooperative coupling.
(A) Example time dependence of total peroxisomal ubiquitin for cargo addition rate , with the default number of peroxisomes (
) and importomers per peroxisome (
). The characteristic timescale for fluctuations in the ubiquitination level is several seconds. Two possible threshold values are illustrated with dashed lines. (B) The average interval of time spent below a given threshold vs.
for thresholds as indicated by the legend, which also applies to (C). (C) The average interval of time spent above a given threshold vs.
.
Figure 6.
Peroxisome number variation for cooperative coupling.
Here we investigate the effects of varying the number of peroxisomes (, as indicated by legend in (A)) when the other parameters are kept constant (with
sites per importomer). (A) Peroxisomal PEX5 fraction vs.
for cooperatively coupled cargo translocation. (B) Ubiquitin per peroxisome vs.
. Horizontal black dashed line represents a possible ubiquitin threshold for peroxisome degradation.
Figure 7.
Export complex number variation for cooperative coupling.
For cooperatively coupled systems with ,
, and
we vary the number of export complexes
, which directly scales the PEX5 export rate,
. (A) Peroxisomal PEX5 fraction vs. stoichiometry of export complexes to importomers (
). As shown in the legend, we consider different fixed rates of cargo addition,
; this legend also applies to (B). (B) Ubiquitin per peroxisome vs.
, for the same set of
.
Table 1.
Model parameter definitions and values.