Figure 1.
Canonical model and variations.
(A1) The canonical model describes the convergence of two signaling pathways (elements A and B) onto target (T). A single stimulus (S) activates both A and B. Then, A and B positively regulate the activation of T. (A2) For the canonical model, the stimulus-response curves are transient in both model variants M and A (S = 1). (B–E) Various network motifs derived from the canonical model. (B1) Two types of coherent feed-forward loop (FFL). (B2) Positive feed-back loop between A and B (i.e., mutual excitation, ME). (B3) Negative feed-back loop between A and B (i.e., mutual inhibition, MI). (C1) Positive auto-regulation loop of A (i.e., auto-excitation, AE). (C2) Negative auto-regulation loop of A (i.e., auto-inhibition, AI). (D1) Negative feedback between A and B (NF (B-A)). (D2) Negative feedback from T to A and B (NF (T-A/B)). (E) Positive feedback from T to A and B (PF (T-A/B)).
Figure 2.
A schematic of NB synergism (A) and additive synergism (B).
Response for AE curve = effect of drug 1 alone+effect of drug 2 alone. The maximal difference between peak value and endpoints of NB curves determines the maximum NB synergism. The maximal difference between NB and AE curves determines maximum additive synergism.
Figure 3.
Histograms of NB synergism (A) and additive synergism (B) degrees from 91 parameter pairs for Variant M (grey bars) and Variant A (green bars) (S = 1).
(C) Variation of the parameter pair KTA/kbasal_A in Variant M shows that additive synergism can exist in the absence of NB synergism. kbasal_A increases from 0 to 90% as KTA concurrently decreases from 90 to 0%. (D) Variation of KB/KT in Variant A shows that NB synergism can exist in the absence of additive synergism (red box, concave-down NB curve is below AE curve).
Figure 4.
For Variant M (S = 1), the histograms of synergism degrees from 91 parameter pairs were compared between standard parameter values and varied parameter values.
(A) The stimulus and response curves of A (see Eq. 1) and B (see Eq. 2) with standard parameter values (A1) and with parameters altered to give slower B dynamics (orange trace), or delayed B dynamics (green trace), with dynamics of A unchanged (black trace) (A2). (B) The histograms of NB synergism (B1) and additive synergism (B2) degrees with standard parameter values (grey bars) and with parameters altered to give slower B dynamics (orange bars) or delayed B dynamics (green bars). (C) The histograms of NB synergism (C1) and additive synergism (C2) degrees with standard parameter values (grey bars), with kST increased by 25% (red bars), and with kST reduced by 25% (pink bars). (D) The histograms of NB synergism (D1) and additive synergism (D2) degrees with standard values (grey bars), KT increased by 25% (dark brown bars), and KT reduced by 25% (light brown bars).
Figure 5.
Simulations with Variant M generated NB curves and AE curves for three pairs of parameters, which show strong NB synergism (kdA/kdB) (A), moderate NB synergism (kdA/kST) (B), and weak NB (kdA/KT) (C).
S = 1 in the left column, and S = 10 in the right column.
Figure 6.
Simulations of three parameter pairs with Variant M generated dose-effect curves that describe the relationships between NB synergism and stimulus strength (A), and between additive synergism and stimulus strength (B).
The strength of stimulus (S) was varied from 1 to 40.
Figure 7.
Summary of the degrees of NB and additive synergism observed for all motifs for S = 1 and S = 10.
Degrees of synergism are plotted for kdA/kdB (A), kdA/kST (B), and kdA/KT (C). Motif abbreviations are as in Fig. 1. Vertical dashed lines delineate each motif and its associated synergism degrees (four for each combination of a motif and a parameter pair). For each motif and parameter pair, the degrees of additive synergism are plotted as blue and light green bars, and the degrees of additive synergism are plotted as black and grey bars, for S = 1 and S = 10 respectively. Negative values represent degrees of antagonism. In a few cases, the NB and AE curves were intertwined (e.g., Fig. S1B1) and exhibited both additive synergism and additive antagonism. For those cases only positive values (synergism) are plotted. The values of some data are too small to be easily visualized.
Figure 8.
The model of Song et al. [26] and simulations.
(A1) The feedback loops described by the model. (A2) After 5 pulses of 5-HT treatment, CREB1 and CREB2 switch from a LOW state to a HIGH state. (B) The NB curve and AE curve for the parameter pair Vx/kdy. This pair shows strong NB synergism, and additive synergism.