Figure 4. Mathematical model of the SCF cycle.

(A) Simplified scheme illustrating the main processes and interactions considered in the mathematical model (see Fig S4 for a detailed reaction scheme). Lines with unidirectional arrows represent irreversible reactions. FB1 stands for Skp1•β-TrCP whereas FB2 represents a pool of auxiliary Skp1•F-box proteins that compete for access to Cul1•Rbx1. Both F-box proteins form SCF ligases with Cul1•Rbx1 that undergo the same cycle of processes including F-box exchange, neddylation, deneddylation, substrate binding and substrate degradation.

(B–F) Model simulations and predictions. Simulations labeled in orange color were used to estimate unknown parameters. Remaining simulations represent model predictions. Error bars for predictions were obtained from a profile likelihood analysis (Fig S5A). Experimental results are shown as thin bars. To simulate inhibition of Nedd8 conjugation by MLN4924 we set k_nedd=0. As a result the fraction of Cul1•Rbx1 bound to Cand1 increased while the fraction of Cul1•Rbx1 bound to Skp1•FBP decreased (Reitsma et al. 2017) (B). If Cand proteins are absent (DKO) the latter fraction is predicted to increase to 100% in agreement with observations. The model confirms (C, upper panel) that re-expression of Cand1 (13% of WT level) in a DKO cell line reduces the half-life (t_1/2) for IκBα degradation back to WT levels (Fig 2C). The half-life for substrate degradation is predicted to exhibit a U-shaped dependence on the cellular Cand1 concentration with an extended valley where t_1/2 ≈20min remains approximately constant (C, lower panel). Dashed lines indicate the Cand1 concentration in WT (black) and DKO cells with Cand1 re-expressed to 13% of WT level (red). When substrate is added the fraction of β-TrCP bound to Cul1 increases ~1.7-fold (D) from its steady state level (46%) as observed in WT cells (Fig 2F). Cul1 overexpression is predicted to reduce the fraction of neddylated Cul1 (E) in agreement with observations. Also, Cul1 overexpression should have no effect on the half-life for IκBα degradation in WT, but should reduce t_1/2 in DKO cells back to WT level (F). In contrast, overexpression of β-TrCP is predicted to have no effect on t_1/2 in DKO cells (F).