Figure S3. (A). (B). 0. 0.1. 0.9. 1. E1 tot. MAPK activity x a x b. 0. 5. 10. 15. 0. 0.2. 0.4 n. H. Density. P(n. H. >1)=0.9996. P(n. H. >2)=0.7421. P(n. H. >3)=0.5036.
Figure S3 (A)
(B)
1 0.9 Density
MAPK activity
0.4
0.1 0
xa
5
10
15
n
(D)
0.1 0
H
y2 0.1 0
2
2
1
0.5 (x −x )/(x −x ) 2
1
b
1 0 0
1
a
0.5 y −y 2
(G)
1
1
(H)
6
3
4
2
SN Density
1 0.9 y1
3
0 0
xa x1 xmx2xb E1tot
(F)
3
Density
y1
H
(E)
Density
1 0.9 y2
Density
MAPK activity
0 0
H
(C)
MAPK activity
0.2
xb
E1tot
P(n >1)=0.9996 H P(n >2)=0.7421 H P(n >3)=0.5036 H P(nH>4)=0.3196
2
1
SN xa x1x2 xb E1tot
0
0
0.5 (x −x )/|x −x | 2
1
b
a
1
0 0
0.5 y −y 1
1
2
(A), (C) and (F) Schematic plots defining variables useful in the discussion of the adjacent histograms. (B) Histogram of Hill coefficients (nH ≡ log(81)/ log(xb /xa )) for “Single-valued” bifurcation diagrams; xa and xb are inputs (E1tot ) that correspond to 10% and 90% maximum output (MAPK activity). The quantities xa and xb are similarly defined in (C) and (F). (D) and(E) Histograms for “Oscillatory” bifurcation diagram properties. The quantities x1 and x2 in (D) and (E) are defined in (C) as input concentrations at the Hopf bifurcation points. The quantity xm is defined as xm ≡ (x1 + x2 )/2 . The quantities y1 and y2 are the minimum and maximum MAPK activity along the oscillatory solution evaluated at xm . The red bar in (E) represents the bifurcation diagrams with y2 − y1 > 1 . (G) and (H) Histograms for “Hysteretic” bifurcation diagrams properties. The quantities x1 and x2 in (G) and (H) are defined in (F) as input concentrations at the Saddle-Node bifurcation points. The red bar in (G) represents bifurcation diagrams that are discarded while computing the distributions. The quantities y1 and y2 are defined as the MAPK activities at the corresponding Saddle-Node bifurcation points.
