304 B. Cummins et al.
XY00 10012011 21 FCFP
(a) (b) (c)00 10012011 21FC^0010012011 21 FCFP
(d) (e) (f) (g)00 10012011 21FC^0010012011 21 FPONFP
(h) (i) (j) (k)Fig. 1.(a) Two dimensional network. The pairs (b)-(c), (d)-(e), (f)-(g), (h)-(i) and (j)-
(k) provide examples of STG (first panel in each pair) and their associated augmented
Morse graphs (second panel in each pair). See beginning of Sect. 3 for description of
labeling of nodes in STG (panels (b), (d), (f), (h), (j)) See latter part of Sect. 2 for a
description of labeling of nodes in Morse graphs (panels (c), (e), (g), (i), (k)).
For example, 00 is the domain where bothXandY are below their respective
lowest thresholds, and 21 is where they are above their respective highest thresh-
olds. We use these domain labels to represent the nodes in STG, and the arrows
between them represent the flow between domains in phase space (Figs. 1 (b),
(d), (f), (h), (j)). From STGs, we calculate the corresponding Morse graph for
each parameter, shown in Figs. 1 (c), (e), (g), (i), (k).
(2) Comparing dynamics across networks.We use DSGRN to find a net-
work that exhibits robustly cyclic dynamics in a neighborhood of a given net-
work. The network in Fig. 2 (a, top) is a potential network driving cell cycle
progression in yeast [ 21 ]. The backbone of the network, which includes all mole-
cules except CdH1, is a subnetwork of Fig. 4 (c) in [ 21 ]. This backbone network
shows highly prevalent oscillatory dynamics in form of a Morse graph with sta-
ble FC. Experimental evidence showed that in the network where all cyclins
are knocked out, the system does not oscillate, but approaches an equilibrium.