Figure 1.
Cartoon of model interactions.
The transmembrane death receptor Fas natively adopts a closed conformation, but can open to allow the binding of FADD, an adaptor molecule that facilitates apoptotic signal transduction. Open Fas can self-stabilize via stem helix and globular interactions, which is enhanced by receptor clustering through association with the ligand FasL.
Figure 2.
Schematic of cluster-stabilization reactions.
Examples of ligand-independent cluster-stabilization reactions involving unstable () and stable (
) open receptors of molecularities two (A), three (B), and four (C). Higher-order reactions follow the same pattern. Ligand-dependent reactions are identical except that FasL (
) must be added to each reacting state.
Figure 3.
Steady-state activation curves.
The steady-state active Fas concentration shows bistability and hysteresis as a function of the FasL concentration
(stable, solid lines; unstable, dashed lines). At low receptor concentrations
, the bistability is reversible, but irreversibility emerges for
sufficiently high, representing a committed cell death decision. All parameters set at baseline values unless otherwise noted.
Figure 4.
Steady-state activation surface.
The steady-state surface for the active Fas concentration as a function of the FasL and total Fas concentrations
and
, respectively, is folded, indicating the existence of singularities, across which the system's steady-state behavior switches between monostability and bistability (stable, blue; unstable, red). All parameters set at baseline values unless otherwise noted.
Figure 5.
Steady state diagram identifying the regions of parameter space supporting monostability (colored) or bistability (gray) as a function of the FasL and total Fas concentrations and
, respectively. The monostable region is colored as a heat map corresponding to the steady-state active Fas concentration
. Irreversible bistability is indicated by the extension of the bistable region to the axis
.
Figure 6.
The activation (red) and deactivation (blue) thresholds characterizing the bistable regime (green) are defined as the concentrations
of FasL at which the steady-state active Fas concentration
(black) switches discontinuously from one branch to the other (stable, solid line; unstable, dashed line).
Figure 7.
Sensitivity analysis of bistability thresholds.
The robustness of the bistability thresholds is investigated by measuring the effects of perturbating the model parameters about baseline values. For each threshold-parameter pair, a normalized sensitivity is computed by linear regression. Top, sensitivities for the FasL thresholds
; bottom, sensitivities for the corresponding Fas thresholds
at FasL concentrations
, respectively.
Figure 8.
The fraction of parameter sets that exhibit bistability as a function of the sampling variability
follows the exponential form
, where
is the asymptotic bistable fraction. The fitted value of
suggests that this robustness remains substantial even as
.
Figure 9.
Cell-level cluster integration.
The apoptotic signals of all Fas clusters are integrated to produce a normalized cell activation . The resulting hysteresis curve on
as a function of the FasL concentration
is graded due to the heterogeneity of the bistability thresholds
across the clusters (top). Despite this variability, a strong linear dependence persists between
(bottom; the valid region
is shown in green).
Figure 10.
Model discrimination using hyperactive mutants.
The wildtype response curve, giving the steady-state active wildtype Fas fraction as a function of the FasL concentration
(stable, solid lines; unstable, dashed lines), of the cluster model varies with the mutant population fraction
, reflecting receptor interactions absent in the crosslinking model. The total receptor concentration is fixed at
. All parameters set at baseline values unless otherwise noted.
Figure 11.
Model discrimination using steady-state invariants.
Steady-state invariants are fit to synthetic data generated from each model. For each model-data pair, the invariant error is minimized over the model parameter space. The results suggest that invariant minimization can correctly identify the model from the data.