Table 2.

Translating qualitative phenotype observations into quantitative constraints

phenotypic constraint (CRi)		mathematical interpretation	percent of sampled parameter sets that satisfice criterion
CR 1	Prior to signal perturbation, the system should exhibit a stable steady state.	${‖d/dt‖}_{all species}\le {10}^{-8}$	56.4%
CR 2	PI3P depletion induces fusion.	$\frac{\int {\left[Sec17:SNARE\right]}_{\text{PI}3\text{P}\hspace{0.33em}\text{depletion}}dt}{\int {\left[Sec17:SNARE\right]}_{\text{no}\hspace{0.33em}\text{perturbation}}dt}\le 0.1$	9.7%
CR 3	Trigger activation induces fusion.	$\frac{\int {\left[Sec17:SNARE\right]}_{\text{trigger}\hspace{0.33em}\text{activation}}dt}{\int {\left[Sec17:SNARE\right]}_{\text{no}\hspace{0.33em}\text{perturbation}}dt}\le 0.1$	24.0%
CR 4	Fusion due to PI3P depletion should be faster than that due to trigger activation.	$\frac{\int {\left[Sec17:SNARE\right]}_{\text{trigger}\hspace{0.33em}\text{activation}}dt}{\int {\left[Sec17:SNARE\right]}_{\text{PI}3\text{P}\hspace{0.33em}\text{depletion}}dt}\le 0.1$	20.2%
CR 5	In the absence of an external signal, spontaneous fusion events should be rare.	${\left.[Sec17:SNARE]\right|}_{no perturbation}\le {10}^{-6}$	6.9%
all criteria satisficed concurrently			0.1%