Figure 1.
Overview of the signaling proteins and interactions considered in the model.
Panel A is a simplified version of Fig. 2, which follows and goes beyond the diagram shown here by illustrating the functional components of proteins responsible for interactions. Selected protein complexes considered in the model are illustrated in Panels B–D. (A) Proteins are represented by boxes. In the model, five proteins, , APC, Axin,
, and
, are considered explicitly, whereas
, PP2A (not shown), and other proteins are considered implicitly.
, which mediates phosphorylation of APC, and PP2A, which mediates dephosphorylation of APC, are assumed to be constitutively associated with Axin. In the model, their activities are engaged when Axin is in complex with APC. Interactions included in the model are represented by arrows; numbering of arrows is the same as in Fig. 2. The arrows labeled 1–6 represent reversible direct binding interactions. The arrows labeled 7–10 represent catalytic (phosphorylation) interactions (and enzyme-substrate relationships). All phosphorylation events are taken to be reversed by phosphatases. The interaction represented by Arrow 1 is constitutive. The interaction represented by Arrow 2 depends on sequential phosphorylation of APC by
and
(Arrows 9 and 10). The interactions represented by Arrows 2 and 3 are mutually exclusive, because they involve the same binding site in
, i.e., Axin and APC compete for binding to this site. The interaction between APC and Axin represented by Arrow 4 is missing for typical truncated forms of APC (i.e., forms of APC, such as APC1338, missing SAMP repeats). Arrows 5 and 6 represent recruitment of
and
to Axin. Arrows 7–10 represent phosphorylation reactions mediated by Axin-associated kinases. (B) A binary complex of APC and
connected through two distinct protein-protein interfaces. The interactions represented by Arrows 1 and 2 are allowed to occur simultaneously. (C) A complex wherein
is directly bound to Axin via the interaction represented by Arrow 3. Recall that this interaction cannot occur if
is bound to APC via the interaction represented by Arrow 2. (D) A complex containing a linear (vs. cyclic) ternary complex of APC, Axin, and
. This linear complex is allowed to close and form a cyclic complex via the interaction represented by Arrow 3. Note that the complex depicted here cannot form when APC is truncated such that the interaction represented by Arrow 4 is missing. The model is further described in Fig. 2 and Text S1.
Figure 2.
Site-specific details of the proteins and interactions considered in the model.
Proteins, interactions, and the functional components that mediate interactions are represented according to the conventions of Chylek et al. [42]. The numbering of arrows is the same as in Fig. 1. The double-arrowed lines represent reversible binding interactions. The lines ending with an open circle represent enzyme-substrate relationships and point to sites of phosphorylation. In the model, sites Ser-33, Ser-37, and Thr-41, which are
substrates, are lumped together as a single site labeled S33/37.
site Ser-45, which is a
substrate, is labeled S45. In the model, the seven 20-aa repeats of APC are lumped into two distinct sites labeled 1 and 3. For further information about the model, see Materials and Methods. A complete and executable specification of the model is provided in the Supporting Information as a plain-text BioNetGen input file (Text S2). Note that there is a correspondence between the arrows shown here and the rules of the model (Text S1). Model parameter values are summarized in Table 1.
Table 1.
Model parameter 1.
Figure 3.
Summary of APC constructs considered in simulated transfections and in the experimental study of Munemitsu et al. [31].
The 12 constructs used by Munemitsu et al. [31] are divided into six classes based on their structures. Proteins within the same class are functionally equivalent according to our model. A representative of Class A (APC-A) contains all three protein binding sites considered in the model for full-length APC. This class is regarded as equivalent to full-length APC. A representative of Class B (APC-B) contains 15-aa repeats and the first 20-aa repeat. This class is regarded as equivalent to APC1338, the truncated form of APC found in SW480 cells. A representative of Class C (APC-C) corresponds to a fragment that contains only the 15-aa repeats. A representative of Class D (APC-D) corresponds to a fragment that contains only the first 20-aa repeat. A representative of Class E (APC-E) corresponds to a fragment that contains the 20-aa and SAMP repeats. A representative of Class F (APC-F) corresponds to a nonfunctional fragment that contains none of the three APC sites included in the model.
Figure 4.
Comparison of simulated and observed effects of transfection of SW480 cells with APC constructs.
Relative levels in SW480 cells in response to transfection with the APC constructs of Fig. 3 are shown. The gray bars, which correspond to the left
, represent experimental data from Munemitsu et al. [31]. The black bars, which correspond to the right
, represent model predictions. The predicted concentrations (black bars) are each divided by the concentration of
in a normal cell (35 nM, Table 1). For all APC constructs, the same transfection efficiency is assumed. We take a transfected cell to contain 100 nM of added protein. The predicted results therefore represent the effects of 100 nM of a construct in addition to 100 nM of endogeneous APC1338. The simulation results shown here were obtained using BioNetGen input files provided in the Supporting Information: Text S3 was used for the APC-B and APC-F cases, Text S4 was used for the APC-A case, Text S5 was used for the APC-C case, Text S6 was used for the APC-D case, and Text S7 was used for the APC-E case.
Figure 5.
Concentration-dependent effects of full-length APC on .
(A) level in a normal cell is shown as a function of APC concentration. The
represents the relative amount of APC introduced exogeneously with respect to the endogeneously present 100 nM of full-length APC in a normal cell. The
represents the level of
relative to its nominal level in a normal cell (Table 1). (B)
level in an SW480 cell is shown as a function of APC concentration. The
represents the amount of APC introduced exogeneously relative to the endogeneously present 100 nM of APC1338 in an SW480 cell. The
represents the level of
relative to its nominal level in a normal cell, as in panel A. The simulation results shown here were obtained using BioNetGen input files provided in the Supporting Information: Text S2 was used for panel A and Text S4 was used for panel B.
Figure 6.
Concentration-dependent effects of APC constructs in SW480 cells.
Predicted level is shown as a function of expression level for APC-B, -C, -D, and -E. In each panel, the
represents the amount of expression relative to the endogeneous level of APC1338 (100 nM). The
represents the
level relative to the nominal level in a normal cell (35 nM, Table 1). Thus, a value of 1 on the
corresponds to a concentration of 100 nM of transfected protein, and a value of 1 on the
corresponds to a concentration of 35 nM of
. The simulation results shown here were obtained using BioNetGen input files provided in the Supporting Information: Text S3 was used for panel A, Text S5 was used for panel B, Text S6 was used for panel C, and Text S7 was used for panel D.
Figure 7.
APC1338 phosphorylation and its competition with Axin for .
(A) level is shown at different levels of APC1338 phosphorylation. Phosphorylation of APC1338 at the first 20-aa repeat is modulated by changing the values of the phosphorylation and dephosphorylation rate constants
and
. In the figure, the ratio,
corresponds to the default values of
and
in the model, which are taken to be the same (Table 1). The case where
represents an extreme, where the 20-aa repeat always remains phosphorylated. The case where
represents the opposite extreme, where APC1338 never becomes phosphorylated. (B) Competition effects on
binding arising from APC1338 phosphorylation. The
represents the fraction of Axin in complex with
. The patterns of the lines represent different phosphorylation and dephosphorylation rate constants, as labeled in panel A. The simulation results shown here were obtained using Text S3, a BioNetGen input file provided in the Supporting Information.
Figure 8.
Sequestration of away from Axin by APC1338.
(A) Predicted amount of associated either directly or indirectly with Axin is shown as a function of APC1338 concentration in the background of an SW480 cell. The horizontal axis indicates the amount of APC1338 divided by the nominal amount of APC1338 in an SW480 cell (100 nM). The vertical axis indicates the amount of Axin-associated
divided by the total amount of
at steady state, which is a function of APC1338 concentration. (B) Predicted amount of
associated either directly or indirectly with Axin is shown as a function of full-length APC concentration in the background of a normal cell. The horizontal axis indicates the amount of full-length APC divided by the nominal amount of full-length APC in a normal cell (100 nM). The vertical axis indicates the amount of Axin-associated
divided by the total amount of
at steady state, which is a function of full-length APC concentration. (C) Predicted amount of
associated directly with APC1338 as a function of relative APC1338 concentration. (D) Predicted amount of
associated directly with full-length APC as a function of relative full-length APC concentration. All results shown were obtained using the parameter values of Table 1, except as indicated. The following BioNetGen input files were used to obtain simulation results: Text S3 was used for panels A and C and Text S2 was used for panels B and D.
Figure 9.
Effects of simulated perturbations of the putative closed/cyclic core destruction complex.
Three cases are considered, as indicated in the descriptions of Text S8, S9, S10 (Supporting Information). Each of the three protein-protein interfaces, (Text S8),
(Text S9), and APC-Axin (Text S10), is ablated such that a closed/cylic structure cannot form. The relative
level in each case is compared with the nominal
level in a normal cell.