Supplemental Information. Cand1-Mediated Adaptive Exchange Mechanism. Enables Variation in F-Box Protein Expression

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1 Molecular Cell, Volume 69 upplemental Information -Mediated Adaptive Exchange Mechanism Enables Variation in F-Box Protein Expression Xing Liu, Justin M. Reitsma, Jennifer L. Mamrosh, Yaru Zhang, Ronny traube, and Raymond J. Deshaies

2 Buffer nm nm kp Fluorecence (a.u.) Fluorecence (a.u.) nm kp nm kp nm kp β Rbx GT GT G nm kp2 H1 koff, fast: 6 x 1-3 s-1 koff, slow: 3.3 x 1-4 s nm kp koff: 2.8 x 1-4 s nm kp nm kp2. Fluorecence (a.u.) Fluorecence (a.u.) 2 Fluorecence (a.u.) 1 6 or β GT GT input PD F Rbx H (µm) kp2 1 GT or H1 kp2 Rbx1 GT / Rbx1 GT 1..3 Fluorecence (a.u.) Fluorecence (a.u.) 1 Fluorecence (a.u.) 8 nm.8 4 nm 2 nm 1 nm 1.8 Fluorecence (a.u.) Fluorecence (a.u.) 1.8 C E 4 nm 3 nm 1. B D 1 nm nm Fluorecence (a.u.) Fluorecence (a.u.) A Buffer β-trcp β-trcp (split n).4.2. Rbx1 Figure 1 1 1

3 l tro d1 on Can C sh sh B primer 1 IP: FLAG FLAG HR (3 bp) Drug resistance gene Terminator Ponceau tain D Cand2 * 3 HR (3 bp) Homologous Recombination Template E Different DKO Cell Lines WT (min) WT Cand2 DKO 13 Ponceau tain Half Lives of upon TNFα Treatment 4 F (min) Cand2 KO WT (min) KO DKO WT 1 DKO (min) DMO MLN 4924 DKO - WT - DKO - MLN min TNFα β-trcp p β-trcp/p WT DKO Cand2 KO H Ubp 2 WT GT Rbx1 Dcn1&Ubc12 GT GT p WT DKO DKO MLN4924 MLN4924 IP: 3xFLAG Dcn1 GT Rbx1 Ubc12 GT K Lysate Input 4 O 492 DM MLN J KO 7 WT t1/2 of (min) G I primer 2 sgrna b Cand2 O O 2K 1K nd and T a W C C 3 3 HR (3 bp) HR (3 bp) 3 C Exon 1 sgrna a t1/2 of (min) A IP: 3xFLAG (plit n) GT Dcn1 Ubc12 Rbx1 WB: Dcn1 WB: Ubc12 Figure 2 Dcn1 (plit n) GT GT Ubc12 Rbx1 WB: Ubc12

4 A Dcn GT.2 Rbx GT B Dcn1 - Dcn1 3s 2m m - 3s 2m m FAM channel (µm) TAMRA channel C Dcn1 (plit n) /GTDcn1 GT Predicted Actual Buffer D s 2m 3s 2m FAM channel TAMRA channel β-trcp Neddylation. FAM & TAMRA WB: β-trcp TAMRA & FAM. 2.. E (min) GTRbx1 kp2 Dcn1-1 2 (µm) Rbx1 GT /GTRbx1: Rbx1 /GTRbx1: PD: Dcn1 /GTRbx1: Rbx1 G MLN GT 2 (min) 2 3 Ctrl 2 3 Ctrl β-trcp GT Gel 1 Gel 1 β-trcp 2 β-trcp GT GT Gel 2 Gel 2 1 β-trcp chase added J 1 (hr) p β-trcp β-trcp/ 1 p IP: 3xFLAG Dissociation of β-trcp p complex 1 t1/2:.9 hr K 1 with chase 1 Time (min) no chase β-trcp β-trcp/pikbα no chase I Replicates 1 GT t1/2=14 min 7 no chase % Phosphorylation 1 H Replicates 1 no chase F 132 GT 1 (hr) β-trcp koff: 3.3 x 1 s - -1 / Time (hr) Figure 3 8 1

5 A exchange cycle 4a 1b 7 F-box binding to substrate binding to F-box 2b 2 7b a 4a DCN binding 9b 2c 9 2a 9a 7d 9b 8b 6a 6 8 8a 8b 6a 1c 1a 7c 1b 1e 1 1a 1b N8 N8 N8 N8 1d 14 7e neddylation B deneddylation CN CN CN product inhibition by CN N a CN N8 CN N8 N8 1f 12 12a 1 C CN Ub Ub Ub E2 N8 substrate degradation detailed balance relations CN 13a CN Rbx1 Rbx1 13 Rbx1 CN 13b Rbx1 CN CN 13c CN Rbx1 Rbx1

6 A B x D nM N8 CN CN 1 1 N8 N8 Dcn1 41nM 1 CN 88s kp1 1 kp1 Dcn1 C ub 1 21nM 2 8nM Dcn1 Dcn1 ub 2 234nM DC N1 DC N1 DC N1 DC DC N1 N1 F Input WT DKO WT DKO Tet - - E PD: GTRbx1 - Tet WT DKO WT DKO WT DKO WT DKO - Control β-trcp β-trcp β-trcp Fold increase of β-trcp. 6.6 (dark) Cand2.2 G Input IP: 3xFLAG PD: GTRbx1 WT DKO WT DKO WT DKO WT DKO WT DKO WT DKO Tet Rbx1 6.2 GT β-trcp β-trcp (dark) Loading Controls. Fold increase of Figure 3xFLAG 1 21nM 172nM N8 1 41nM Rbx1 GT

7 A B (min) WT (min) HA DKO Fbxo6 β-trcp WT Fbxo6 DKO 1 Fbxo6 WT DKO WT DKO Fbxo C Fbxo6 D DKO - F Control Fbxo6 E HA FT In IP G FT WT In IP DKO FT In IP FT (L) (L) HA 3xFLAG IP: HAFbxl16 ( sponge) IP: HAFbxo6Δ ( sponge) () 3xFLAG () 3xFLAG HA In IP I DKO FT In IP FT (L) HA IP: HAkp2ΔLRR ( sponge) () 3xFLAG F-box Protein % Bound % Bound (WT) (DKO) HA Fbxo6ΔF-box.. HA Fbxl16.. HA kp HA kp2δlrr WT In IP DKO FT In IP FT (L) 3xFLAG 3xFLAG IP: HAkp2 ( sponge) Fbxo6 DKO 3xFLAG WT 6 xo Fb 3xFLAG DKO IP HA Fbxo6 WT l nta re Pa β-trcp In H J HA WT 3xFLAG IP: 3xFLAG ( sponge) HA WT - Figure 6 () 3xFLAG HA

8 A B Figure 7

9 UPPLEMENTAL FIGURE LEGEND Figure 1. Properties of complex assembly and disassembly (related to Figure 1). (A) k obs for binding to. The change in donor fluorescence versus time was measured in a stopped-flow fluorimeter upon addition of varying concentrations of FlAsH H1 to nm AMC Rbx1. Indicated concentrations are after 1:1 (v:v) mixing of the two solutions in the stopped-flow fluorimeter. ignal changes were fit to two phase exponential curves, and the fast-phase rates were used as k obs. These values are plotted against [] in Fig 1B. (B) k obs for binding to preassembled with kp2. imilar to Fig 1A, except 1 nm kp2 was preincubated with nm AMC. ignal changes were fit to two phase exponential curves, and the fast-phase rates were used as k obs. These values are plotted against [] in Fig 1C. (C) k obs for dissociation by kp2. The change in donor fluorescence versus time was measured in a stopped-flow fluorimeter upon addition of varying concentrations of kp2 to 1 nm FlAsH H1 AMC Rbx1. Indicated concentrations are after 1:1 (v:v) mixing of the two solutions in the stopped-flow fluorimeter. ignal changes were fit to single exponential curves. These values are plotted against [ kp2] in Fig 1E. (D) Replacing the first helix of with the tetracysteine tag increased the k off of from Rbx1. Fluorescence emission at 44 nm (donor emission) was detected every 2 seconds after the addition of 1 x excess FlAsH H1 (acceptor protein) to AMC Rbx1 pre-incubated with unlabeled or H1. FRET was observed following spontaneous dissociation of non-fluorescent from AMC Rbx1. ignal changes were fit to exponential curves with a fixed end point of 7% initial donor fluorescence. AMC Rbx1 was fit to a one phase curve. H1 AMC Rbx1 was fit to a two phase curve, with k off, slow similar to the k off of AMC Rbx1 and k off, fast about 2 times faster. (E) H1 Rbx1 is less stable than Rbx1. kp2, GT Rbx1, or H1 at indicated concentrations were used in the GT pulldown (PD) assay. Relative level of recovered is shown as : GT Rbx1 ratio. Based on this result and the known K D of Fbxw7, the K D of H1 is simulated to be ~4. times higher than the K D of. In this and other experiments employing recombinant, it migrates faster than expected because it is expressed by the split-n-coexpress (split n) method of Li et al (2). (F) β-trcp removes from when it is in complex with full length but not with loop regions deleted. The change in donor fluorescence versus time was measured in a

10 stopped-flow apparatus upon addition of 7 nm β-trcp or ΔΔ β-trcp to 2 nm FlAsH H1 AMC Rbx1. (G) Deletion of β-hairpin in or loop regions in enables formation of a stable complex comprising,, and. In vitro pull-down assays containing the indicated proteins were performed to demonstrate the formation of stable complexes consisting of Rbx1, and GT when and/or was mutated to delete structural elements that are predicted to clash in the Rbx1 complex. The indicated proteins were mixed in equimolar amounts and bound to glutathione-4b resin. Proteins associated with the resin were fractionated by D-PAGE and detected by silver stain. Figure 2. Degradation defects in, Cand2, and /2 double knockout cells (related to Figure 2). Complex of Dcn1 (related to Figure 3). (A) Cand2 complex was detected only when was depleted. IP-WB analysis of and Cand2 complexes in control (shcontrol) and knock-down (sh) cells that are stably expressing the shrna (Pierce et. al., 213). Cells were treated with 1 µg/ml tetracycline for 1 hour 24 hours before collection to induce expression of FLAG integrated at the FRT site (Flp-In system). (B) trategy for construction of /2 knockout cell lines. A pair of chimeric single-guide RNAs (sgrna) guiding CRIPR Cas9 (D1A) nickases were designed to target the first exon of the or Cand2 gene for mutagenesis. A homologous recombination (HR) template containing a drug resistance gene plus a translational terminator and two 3-bp homology arms that were identical to the genomic sequences flanking the first exon is depicted. Primer 1 and primer 2 were used to generate PCR products of the mutated genomic region for sequencing and confirming the complete inactivation of and Cand2 genes. Note that primer 2 probed the region outside of the 3-bp HR region on the genomic DNA. (C) Confirmation of and Cand2 single KO cell lines. WB analysis showing the loss of or Cand2 proteins in the corresponding KO cell lines. * marks a non-specific band, which serves as a loading control. (D) Confirmation of /2 DKO cell lines. WB analysis showing the loss of and Cand2 proteins in four DKO cell lines. DKO13, 22, 36 are independent cell lines confirmed by sequencing results. The filter stained with Ponceau prior to probing is shown as a loading control. These lines initially displayed slower growth than the wild type (WT) cells, but the growth rate gradually increased after a few passages and became similar to the WT cells by the time their genotypes were confirmed.

11 (E) degradation is defective in DKO13 cells. WB analysis of levels in WT and DKO13 cells at indicated time points after TNFα treatment. DKO13 shows an degradation defect similar to the DKO22 and DKO36 lines shown in Fig 2A. (F) but not Cand2 is required for proper degradation of. WB analysis of degradation in response to TNFα treatment in WT, /2 DKO, Cand2 single knockout (Cand2 KO) and KO cells. Half-lives of in this analysis are shown in the graph. (G) Inhibiting neddylation stabilizes in both WT and DKO cells and enables quantification of the rate of phosphorylation. WB analysis of degradation in response to TNFα treatment in WT and DKO cells pretreated with either.1% DMO or 1 µm MLN4924 for 1 hr. Half-lives of in this analysis are shown in the graph. (H) Inhibiting neddylation strongly inhibits ubiquitination. Expression of 3xFLAG IkBα cdna integrated at the FRT site was induced with tetracycline for 24 hours and then 3xFLAG IkBα was immunopreciptiated from cell lysate with anti-flag following pre-treatment of the cells with either.1% DMO or 1 µm MLN4924 for 1 hr before 1-min TNFα treatment. IPs were evaluated by WB analysis with antibodies against p. (I) p binds β-trcp with equal efficiency in WT and DKO cells. WT and DKO cells expressing tetracycline-induced 3xFLAG and treated with 1 µm MLN4924 for 1 hr to block p ubiquitination were lysed and subjected to IP with anti-flag followed by WB analysis with the indicated antibodies to evaluate interaction between p and β-trcp. This is essentially the same as the experiment in Fig 2G, except that ubiquitination of p was suppressed by MLN4924, instead of by treating the IPs with deububiquitinating enzyme Usp2. MLN4924 or Usp2 were used to collapse all p species into a single band to facilitate quantification. (J) forms a complex with Dcn1 and Ubc12 only in the presence of. Reciprocal pulldown assays were set up as indicated. Each protein was included at 1 µm. Proteins adsorbed to the glutathione beads were fractionated by D-PAGE and stained by Coomassie blue or subjected to WB with the indicated antibodies. (K) Binding of alters the conformation of the Dcn1 binding site on. The C-terminal domains of from PDB files of 4PO and 1U6G were aligned in PyMOL, and the front and back views of the aligned Dcn1 are shown. is in magenta and Dcn1 is in blue; in complex with is in green, and in complex with Dcn1 is in yellow. Figure 3. and neddylation (related to Figure 3). Development of the computational model (related to Figure 4 and Method 1).

12 (A) Confirmation of the estimated K D of x 1-8 M for Dcn1 binding to Rbx1. Assays were similar to Fig 3C but lower concentrations of, and GT Dcn1 were used. Proteins adsorbed to the glutathione beads were fractionated by D-PAGE and stained by Coomassie blue or subjected to WB with the antibody. Fold increase of recovered from the pulldown assay calculated by the K D values (Predicted) and measured from the experiments (Actual) are shown. (B-C) Negative controls for Fig 3F. (B) A mixture of.2 µm FAM and.2 µm TAMRA with or without.2 µm Dcn1 was incubated with.1 µm each of Nedd8, Ubc12, and NAE for indicated time period. FAM and TAMRA signals were detected by a Typhoon scanner. (C) x kp2 and DKO lysate indicated in Fig 3E was replaced with.1 µm each of Nedd8, Ubc12, and NAE, and no FBP was added. (D) Neddylation promotes the formation of CF during the exchange process., Dcn1 and GT Rbx1 were pre-incubated with glutathione beads and then mixed 1:1 (v:v) with protein solution containing β-trcp and Ubc12 or Ubc12~Nedd8. At indicated time points after mixing, beads were washed and eluted, and immobilized proteins were fractionated by D- PAGE and detected by WB. Final concentrations of the protein components were the same as in Fig 3G. (E) Dcn1 stabilizes the Rbx1 complex in the presence of FBP. Pulldown analysis of recombinant (1 µm) bound to recombinant GT Rbx1 (. µm) in the presence of kp2 (2 µm) and increasing concentrations of Dcn1 (-2 µm). Protein samples were fractionated by D-PAGE and stained with Coomassie Blue. Normalized levels of recovered were calculated as the ratio of to GT Rbx1. (F) WB estimation of phosphorylation rate. WT cells were treated with 1 µm MLN4924 for 1 hr to inhibit the ubiquitination and degradation of p, and then sampled at indicated time points after TNFα treatment. The t 1/2 of phosphorylation is estimated to be 14 min. (G-H) Concentration of endogenous is 1 times higher than endogenous β-trcp. WB quantification of the endogenous (G) and β-trcp (H) concentrations in WT cells, with recombinant GT (G) and GT β-trcp (H) spiked into cell lysate as the internal standards. Three biological replicates were analyzed on two individual gels as technical replicates. The concentration of was estimated to be 6 ± 66 nm (D, n=6). The concentration of β-trcp was estimated to be 64 ± 6 nm (D, n=6). In other experiments, sample titration was performed to confirm that the band intensities measured here were within the linear range of the instrument.

13 (I-K) p and β-trcp form a very stable complex in cells. IP-WB analysis of the dissociation rate of the p β-trcp complex in cell lysate is shown in (I). DKO cell lysate containing 3xFLAG tagged p with or without added recombinant β-trcp chase protein (~1x of endogenous β-trcp level) was incubated at room temperature for indicated times. Dissociation of β-trcp from p was calculated as ratios of β-trcp to p signals in anti- FLAG IPs, and these ratios were used to estimate k off (J) based on a fit to a single exponential. Lysate input for (I) is shown in (K). The amount of recombinant β-trcp chase protein added was in large excess of total endogenous FBP complexes as judged by relative signals for and. In addition, the level of endogenous β-trcp in the lysate remained constant throughout a1-hr incubation at room temperature with or without added chase protein. Figure 4. Detailed reaction scheme of the CF cycle model (related to Figure 4 and Method 1). (A) The scheme depicts the state variables and the reactions in the network as listed in Method 1 (Tables T2-T13 ). and denote either Fb1 and 1 (relating to β-trcp and p) or Fb2 and 2 (relating to auxiliary substrate receptors and their substrates). Lines with unidirectional arrows represent irreversible reactions. Reactions labeled by the same number (but different lower case letters) have the same kinetic parameters (Tables T3-T13 of Method 1). Note that for better visibility some states are drawn twice in the network. (B) Reactions describing product inhibition of CN by unneddylated species. We assume that states in which is not neddylated and its associated FBP is not bound to substrate, can bind CN leading to the formation of complexes which are devoid of CF ligase activity. (C) Illustration of the detailed balance relations for the thermodynamic cycles involving and FBP (lower cycle, K 1 K 4 = K 2 K 3 ), and and Dcn1 (upper cycle, K 8 K = K 3 K 9 ) (see Method 1 for details). Figure. Parameter identifiability analysis, response matrix, computation of protein fractions and cycle time (related to Figure 4, Figure 7 and Method 1). Experimental tests of the mathematical model predictions (related to Figure ). (A) Profile likelihood as a function of estimated parameters (Table T1 of Method 1). Circles were determined by numerically computing the profile likelihood according to Eq. (1). Red circles represent the optimal parameter values that minimize χ 2 as defined in Eq. (9). olid lines are smooth interpolations of the data points. Horizontal dotted lines represent thresholds

14 as defined in Eq. (11) that were used to derive 9% confidence intervals, either pointwise (lower line) or simultaneous (upper line). (B) Matrix of response coefficients as defined by Eq. (12) (see Method 1). Parameters on the horizontal axis were increased by 1% and the relative change of different observable quantities (vertical axis) was computed. Positive / negative response coefficients indicate a positive / negative correlation between parameter and observable quantity. Absolute values larger (smaller) than 1 indicate a high (low) sensitivity with respect to the corresponding parameter. The greater the absolute value of a response coefficient, the more sensitive the respective quantity is to changes in the corresponding parameter. Parameters are defined in Table T1 of Method 1. The abbreviation b2 means bound to. (C) The scheme illustrates the computation of the coefficients defined in Eqs. (13) and (14) which determine the contribution of the encircled protein complexes to the protein fractions.b2. and.b2. as defined in Table T14 of Method 1. Note that these complexes are unstable (since they contain both and FBP), and thus cannot be detected in our pull-down assays. Fb and may denote Fb1 (β-trcp) and 1 or Fb2 (auxiliary Rs) and 2. (D) Illustration of the computation of the cycle time according to Eq. (21). Concentrations represent steady state concentrations of free (unbound) proteins obtained from simulations using parameters for WT cells (Table T2-T13, T1 of Method 1). Numbers in the table summarize the values of the on and off rate constants as well as the corresponding net rate constants (red color) computed from Eqs. (1) - (2). (E) Confirmation of β-trcp overproduction in Fig C by WB analysis. Fold increase in total β- TrCP levels are indicated. (dark): more intense exposure of β-trcp blot. A 9-fold increase in total β-trcp level in both WT and DKO cells was observed in a replicate experiment. (F) Overexpression of 3xFLAG reduces levels of unassembled cellular β-trcp, and Cand2. As depicted in Fig D, WT and DKO cells were treated with or without tetracycline to induce expression of a stably integrated 3xFLAG transgene, and then lysed in the presence of excess GT Rbx1 to capture unassembled β-trcp,,, and Cand2. Lysates were subjected to pulldown with glutathione beads, and bound fractions were subjected to WB with the indicated antibodies. One set of representative results from two replicate experiments are shown. These are the underlying data for the graph in Fig E. (G) Overproduction of β-trcp modestly reduces the efficiency of its assembly with. As depicted in Fig F, WT and DKO cells with 3xFLAG-tagged endogenous were treated with or without tetracycline to induce expression of a stably integrated β-trcp transgene, and then

15 lysed in the presence of excess GT Rbx1 to suppress -mediated exchange and capture unassembled β-trcp complexes. Lysates were subjected to IP with anti-flag followed by pull-down with glutathione beads. Bound fractions were subjected to WB with the indicated antibodies. One set of representative results from two replicate experiments are shown. These are the underlying data for the graph in Fig G. Figure 6. FBP-dependent sequestration of inhibits proliferation of DKO cells (related to Figure 6). (A-B) Fbxo6 overexpression further slows degradation rate in the DKO cells. These are the underlying data for the graph in Fig 6A. Cells were infected with lentiviruses to overproduce Fbxo6 and were subjected to TNFα treatment three days after the viral infection. (B) WB analysis of β-trcp, HA Fbxo6, and in the cell lysates from panel (A). Relative protein levels are indicated below each blot. (C) Overproduction of HA Fbxo6 decreases the endogenous CF β-trcp. 3xFLAG was immunoprecipitated from WT and DKO cells overexpressing HA Fbxo6 in the presence of recombinant GT Rbx1 ( sponge). Co-immunoprecipitated β-trcp and HA Fbxo6 were analyzed by WB. (D) Overexpression of Fbxo6 alters the morphology of DKO cells. Live cell images were acquired at 2x magnification seven days after viral infection. (E) WB with anti-fbxo6 antibody showing HA Fbxo6 overproduction five days after infection with recombinant lentivirus. The overproduction is estimated to be 4 times of the endogenous level. (F-I) Co-IP of 3xFLAG with overexpressed HA Fbxo6 Δ (F), HA Fbxl16 (G), HA kp2 (H), and HA kp2 ΔLRR (I) in the presence of recombinant GT Rbx1 ( sponge). Cells were infected by lentiviruses to overexpress different FBPs, and the experimental procedures were similar to Fig 6D. Long (L) and short () exposures of endogenous 3xFLAG are shown. (J) Quantification of the relative percent of co-immunoprecipitated with overexpressed FBPs in (F-I), n = 2. Figure 7. FBP expression is dynamic during mouse development (related to Figure 6 and Discussion). (A) Expression of FBP genes is highly variable during development of multiple tissues, despite stable expression of core CF components. RNA-seq data from ENCODE for the indicated tissues during mouse development were normalized to E cell expression levels. Fold change for each embryonic and birth timepoint relative to E cells is presented in log1 scale. Each

16 datapoint is derived from FPKM RNA-seq values and is the average of two replicates. Grey datapoints and lines represent expression of 73 FBPs, green represents CF complex components (, Rbx1,,, and Cand2), and black represents the median fold change for all transcripts expressed in E cells (213 transcripts). (B) Expression of many FBPs is highly dynamic during development. RNA-seq data from ENCODE for mouse development was obtained as FPKM values, and averaged for two replicates. For selected FBPs, expression levels relative to total expression of 73 FBPs was calculated for each tissue and timepoint. Distinct colors represent different tissues as listed on the bottom, and bars in the same color represent different embryonic developmental timepoints from early organogenesis (leftmost; timepoint varies by tissue) to birth (rightmost). Tissues with only one timepoint represent gene expression at birth.

17 METHOD 1: Mathematical model, related to Figure 4, Figure 7, Figure 4- Protein concentrations (HEK293 cells) Table T1 protein concentration [nm] reference CN (a) Rbx Nedd8 (N8) 3373 Reitsma et al. 217 β-trcp 64 this paper 647 this paper (a) average value of CN1-CN8 excluding CN7 Total DCN concentration In humans there are DCN proteins (-) all of which bind to with similar affinity [Monda et al. (213), Keuss et al. (216)]. In addition, it seems that the DCN proteins are partially functionally redundant so that the effective pool of catalytically active DCN proteins is likely to be larger than the pool. To account for this effect in our model we defined the total DCN concentration by [DCN] = f []. (1) To estimate the scale factor f we note that in HeLa cells the total copy number of DCN proteins (-) amounts to of which the sum of and DCN2 equals [Kulak et al., 214]. Assuming that the concentrations of and DCN2 are equal and that the relative proportions of DCN proteins in HEK 293 cells are similar to those in HeLa cells we obtain f = 26892/(94931/2).4 which suggests that f 6. In the simulations we used f = 6. equestration of, CN and by other cullins, CN and do not only bind to but also to other cullins (Cul2-Cul) in cullin- RING ubiquitin ligases (CRLs) [Bennett et al., 21] which reduces the amounts of, CN and that are available for binding to. To account for this effect in our model we defined effective, CN and concentrations through [] eff = f,wt [] [] eff = f,wt [DCN] [CN] eff = f CN,WT [CN] (2) (3) (4)

18 where [], [DCN] and [CN] are defined in Table T1 and Eq. (1). ince DCN proteins bind cullins with similar affinity (within a factor of ~1) [Monda et al. (213), Keuss et a. (216)] we assumed that the scale factor f,wt is proportional to the relative abundance of, i.e. f,wt = [] [Rbx1] [Cul] = 22nM 1724nM 48nM.23. Here we used the concentration of Rbx1 (cf. Table T1) as a measure for the concentration of -Cul4 all of which form stable heterodimers with Rbx1 [Lydeard et al., 213]. The concentration of Cul was extrapolated from the value reported in [Bennett et al., 21] according to [] [Cul] = [Cul] [] Bennett 22nM 317nM 48nM. Bennett 32nM For simplicity, we used the same scale factor for CN as for DCN defined in Eq. (), i.e. () f CN,WT = f,wt.23. (6) However, previous measurements have shown that if neddylation is inhibited the fraction of associated with is.4/.7.4 (Fig. 6 in [Bennett et al., 21]) suggesting that more than half of the total pool is associated with under cellular conditions. Hence, we set f,wt =.4 in Eq. (2). tate variables and initial conditions Table T2 lists the state variables together with their initial values as used in our simulations. F- box proteins (Fb) bind to via the adaptor protein. Due to the 1:1 stoichiometry between and F-box proteins the total concentration of substrate receptors ( F-box dimers) is bounded by the availability of proteins, i.e. [FbT] [] = 217nM. In principle, it is conceivable that the amount of F-box heterodimers is lower than the total amount of. However, to reduce the number of parameters that have to be estimated by comparing model simulations with experiments (cf. Parameter estimation) we set [FbT] = []. Model reaction and rate constants We modeled the CRL cycle as a mass-action network. The network states together with the elementary reactions are depicted in Figs. 4A and 4B. The state variables together with their default initial values are defined in Table T2. Reversible reactions were parametrized by k on and k off rate constants while irreversible reactions were parametrized by (pseudo) first-order rate constants. The latter may represent an effective k cat (as for neddylation and deneddylation) or a specific degradation rate (as in the case of substrate degradation). Reactions with the same set of parameters are labelled by the same digit (1-16). Individual reactions within a group of reactions with the same set of parameters are distinguished by a lower case letter (a,b,c, ). In our model we considered two sets of F-box proteins, β-trcp (Fb1) and auxiliary (background) substrate receptors (Fb2). In Fig. 4A and 4B only reactions involving Fb1 are shown. For each reaction involving Fb1 or 1 there exists a corresponding reaction for Fb2 or 2 which is listed in the tables below without an explicit reaction number.

19 Table T2 state variable IC (a) state variable IC state variable IC (b) 22 nm N8- CN (b) 121 nm Fb1 Fb1 (b) 32 nm Fb2 Fb2 CN (b) 378 nm Fb1 1 Fb1 1 FbT (c) 217 nm Fb2 2 Fb2 2 Fb1 (b,d) 64 nm Fb1 Fb2 (e,f) 243 nm Fb2 Fb1 Fb1 1 Fb1 1 Fb2 Fb2 2 Fb2 2 Fb1 1 N8- N8- Fb1 Fb2 2 N8- Fb2 Fb1 CN CN N8- Fb1 1 Fb2 CN 1 (-P) N8- Fb2 2 CN 2 (auxiliary) N8- Fb1 CN Fb1 CN N8- Fb2 CN Fb2 CN (a) initial condition, (b) measured, (c) [FbT] = [], (d) β-trcp, (e) [Fb2] = [FbT] - [Fb1], (f) auxiliary substrate receptors F-box binding to The assembly of a functional F-box (CF) complex requires binding of a F-box heterodimer to. Here, we did not model the formation of F-box dimers explicitly, but considered them as preformed stable entities [chulman et al., 2]. In general, there are ~69 different CF complexes in humans. In our model we considered only two types of F-box proteins denoted by Fb1 and Fb2. This allows us to analyze the time scale for the degradation of a specific substrate (mediated by Fb1) in the presence of auxiliary substrate receptors (Rs). The latter compete with Fb1 for access to, and they are collectively denoted by Fb2. In a previous study the assembly of ~ F-box proteins with has been quantified under different conditions [Reitsma et al., 217]. Under normal conditions occupancy ranged from % to 7% indicating a highly non-equilibrium steady state in vivo that is driven by neddylation, F- box exchange and substrate availability. Even in the absence of neddylation occupancy ranged between % and 3% suggesting that there exists some variation in the expression level and/or the binding affinity of for different F-box proteins. For the Fbxw7 receptor biochemical studies yielded a dissociation constant of.22pm which increased by ~6 orders of magnitude to 6nM in the presence of [Pierce et al., 213]. This dramatic increase is mainly driven by a corresponding increase in the k off while the k on remained almost constant. In fact, modulating the off rate constant has been proposed as one of the main mechanisms through which cells may adjust their cellular CF repertoire [Reitsma et al, 217].

20 To allow β-trcp (Fb1) to exhibit a different binding affinity from background Rs we fix k on at the values obtained for Fbxw7 and express the off rate constants for Fb1 and Fb2 in terms of those for Fbxw7 as k Fb1 off,i Fbxw7 = f Fb1 k off,i and k Fb2 off,i = f Fb2 k Fbxw7 off,i, i = 1,2 (7) where k Fbxw7 off,1 = s 1 and k Fbxw7 off,2 = 1.3s 1 denote the off rate constants of Fbxw7 from the binary and ternary complexes (involving ), respectively [Pierce et al., 213]. The values of the two scale parameters f Fb1 and f Fb2 were estimated by comparing model predictions with experiments (cf. Parameter estimation and Table T1). Table T3 No. Reactions involving Fb1 1 Fb1 Fb1 1a Fb1 Fb1 1b Fb1 1 Fb1 1 1c Fb1 1 Fb1 1 1d N8- Fb1 N8- Fb1 1e N8- Fb1 1 N8- Fb1 1 1f N8- CN Fb1 N8- Fb1 CN 2 Fb1 Fb1 2a Fb1 Fb1 2b Fb1 1 Fb1 1 2c Fb1 1 Fb1 1 (a) measured for Fbxw7 [Pierce et al., 213] k on (a) [(M s) 1 ] k off [s 1 ] f Fb f Fb1 1.3 Table T4 Reactions involving Fb2 Fb2 Fb2 Fb2 Fb2 Fb2 2 Fb2 2 Fb2 2 Fb2 2 N8- Fb2 N8- Fb2 N8- Fb2 2 N8- Fb2 2 N8- CN Fb2 N8- Fb2 CN Fb2 Fb2 Fb2 Fb2 Fb2 2 Fb2 2 Fb2 2 Fb2 2 k on [(M s) 1 ] k off [s 1 ] f Fb f Fb2 1.3

21 As suggested by our experiments (Fig. 2H) we modeled the assembly of CF complexes by a random-order binding mechanism (Fig. 4A), i.e. F-box receptor proteins may first bind to species and then bind substrate or vice versa. In fact, previous simulations indicated that an exchange factor becomes dispensable if binding occurs in a sequential order, i.e. if substrate only binds to F-box proteins if the latter are already bound to [traube et al., 217]. binding to The exchange of F-box proteins on is catalyzed by which acts as a substrate receptor exchange factor [Pierce et al., 213]. Experiments suggest that exerts its catalytic function similar to guanine nucleotide exchange factors (GEFs), i.e. through formation of a ternary ( Fb) complex. In the absence of F-box proteins spontaneous dissociation of from a complex is extremely slow (k off,3 = 1 s 1 ) but binding of F-box to dramatically increases the dissociation constant for in the ternary complex (reaction 4). On thermodynamic grounds (cf. Detailed balance relations) the increase of the dissociation constant for upon binding of F-box to must be the same as the increase of the dissociation constant for F-box upon binding of to F-box, i.e (cf. Fig. 4C) K 2 K 1 = K 4 K 3 = τ (8) where K i = k off,i /k on,i denotes the dissociation constant of reaction i. ubstituting the known values for K 1 (.22pM) and K 2 (6nM) we obtain τ which is comparable with values obtained for the GEF-mediated GDP/GTP exchange [Goody & Hofmann-Goody, 22]. To compute the remaining dissociation constants we measured the rate constants for the association between and (k on,3 ) and that between kp2 and (k on,4 ) (cf. Fig. 1). In this way we obtained K 3 =.pm and (using Eq. 8) K 4 = (K 2 /K 1 )K μM. The latter also determines the dissociation rate constant k off,4 as k off,4 = k on,4 (K 2 /K 1 ) K 3 2.9s 1. Reactions and 6 describe the binding of to when is already bound to. Our pulldown assay with immobilized on GT beads showed (Fig. 3C and 3D) that in the presence of the K D of in the ternary complex is reduced by a factor α = 1/36 =.278 (cf. Fig. 4C). To ensure that the K D for in the ternary complex is reduced by the same factor we multiplied the k off for reaction and 6 by α and kept k on the same as for reactions 3 and 4 (Table T). ubstrate binding to F-box protein We assumed that substrate binds with equal affinity to free F-box proteins as well as to F-box proteins that are already bound to ( Fb). In general, our model allows for two substrates that may differ in their binding parameters. In particular simulations 1 represents the phosphorylated form of (-P) while 2 plays the role of auxiliary (background) substrate which is always present in cells. The off rate constant ( k off ~1 s 1 ) for the dissociation of -P from β-trcp -P is very small (cf. Fig. E) comparable

22 to that for the dissociation of F-box from an CF complex. The on rate constant has not been measured, but is expected to lie between (M s) 1. In the simulations we used the value k on = 1 7 (M s) 1 for both -P (1) and auxiliary substrate (2). ince the latter represents a mixture of different substrates (the type and amount of which is difficult to quantify for our experimental conditions) we assumed a less extreme value for the off rate constant of 2. The reactions involving 1 and 2 are listed in Table T6 and Table T7, respectively. Table T No. Reactions k on [(M s) 1 ] k off [s 1 ] (a) (b) 1 4 Fb1 Fb1 4a Fb2 Fb2 Fb1 1 Fb1 1 Fb2 2 Fb (a) 2.9 (c) (d) α 1 6 Fb1 Fb1 6a Fb2 Fb2 Fb1 1 Fb1 1 Fb2 2 Fb2 2 (a) measured (b) measured [Pierce et al., 213], (c) computed from Eq. (8), (d) α = α 2.9 Table T6 No. Reactions involving 1 k on [(M s) 1 ] k off [s 1 ] 7 Fb1 1 Fb1 1 7a 7b 7c 7d Fb1 1 Fb1 1 Fb1 1 Fb1 1 Fb1 1 Fb1 1 Fb1 1 Fb1 1 7e N8- Fb1 1 N8- Fb1 1 (a) estimated, (b) measured 1 7 (a) (b) Table T7 No. Reactions involving 2 k on [(M s) 1 ] k off [s 1 ] Fb2 2 Fb1 2 Fb2 2 Fb2 2 Fb2 2 Fb2 2 Fb2 2 Fb2 2 Fb2 2 Fb2 2 N8- Fb2 2 N8- Fb2 2 (a) estimated 1 7 (a).1 (a)

23 binding to is a scaffold-like E3 ligase which is required for efficient neddylation [Kurz et al., 28]. Experiments have shown that forms a stable ternary complex with and [Keuss et al., 216]. In the absence of the K D for binding to is comparably low (1.8µM) [Monda et al., 213] while binding of increases the affinity of to 36-fold (Fig. 3C and 3D), i.e. the K D is lowered by a factor α = 1/36 =.278 (cf. binding to ). To generate a K D of 1.8µM we set k on = 1 6 (M s) 1 and k off = 1.8 s 1 (Table T8). When is bound to we keep k on, but lower k off by a factor α. Table T8 No. Reactions k on [(M s) 1 ] k off [s 1 ] 8 8a 8b Fb1 Fb1 Fb2 Fb2 Fb1 1 Fb1 1 Fb2 2 Fb a 9b Fb1 Fb1 Fb2 Fb2 Fb1 1 Fb1 1 Fb2 2 Fb2 2 (a) estimated, (b) adjusted so that K D = 1.8µM [Monda et al., 213], (c) α= (a) 1.8 (b) 1 6 α 1.8 (c) Detailed balance relations The CRL network contains several thermodynamic cycles two of which are depicted in Fig. 4C. ince each of these cycles comprises only of reversible equilibria there must be no net flux in each cycle at steady state. In physical terms, this means that the change in free energy for the formation of the ternary complexes ( Fb and ) must not depend on the order in which they are formed. This constraint leads to detailed balance relations between the dissociation constants in each cycle, i.e. K 1 K 4 = K 2 K 3 and K 3 K 9 = K K 8. A similar relation also holds for the cycle comprising the reactions 4, 6, 8a, and 9a which leads to K 4 K 9 = K 8 K 6. Neddylation reactions ince is required for efficient neddylation of [Kurz et al., 28] and since binding and N8 conjugation cannot occur simultaneously [Liu et al., 22] we assumed that neddylation can only occur from CF states where is bound to and is not bound to. In general, Nedd8 (N8) conjugation is catalyzed by an associated E2 enzyme (e.g. UBC12) which is recruited to the Rbx1 domain of an CF complex. However, the rate constants for E2 binding and N8 conjugation are not known. To keep the number of unknown parameters as small as possible we model neddylation by a first order process (Table T9) with effective neddylation rate constant k nedd which is treated as a variable parameter to be estimated from experiments (cf. Table T1). Also, since the concentration of N8 is much larger

24 than that of the other proteins (cf. Table T1) we assumed that N8 is not limiting for the reaction so that it can be absorbed into the definition of the rate constant. Table T9 No. Reactions k nedd [s 1 ] 1 N8-1a 1b Fb1 N8- Fb1 Fb2 N8- Fb2 Fb1 1 N8- Fb1 1 Fb2 2 N8- Fb2 2 (a) estimated.268 (a) Deneddylation reactions Deneddylation is mediated by the COP9 signalosome (CN). Consistent with measurements of the rate constants for CN-mediated deneddylation of N8- [Mosadeghi et al., 216] we assumed that CN first binds reversibly to N8- and N8- Fb (11 and 11a) and, in a second step, N8 is cleaved leading to the dissociation of CN (12 and 12a). Table T1 No. Reactions k on [(M s) 1 ] k off [s 1 ] k cat [s 1 ] 11 N8- CN N8- CN 11a N8- Fb1 CN N8- Fb1 CN N8- Fb2 CN N8- Fb2 CN 12 N8- CN CN 12a N8- Fb1 CN Fb1 CN N8- Fb2 CN Fb2 CN (a) measured [Mosadeghi et al., 216] (a).32 (a) 1.1 (a) Product inhibition of CN While neddylated is a substrate of the CN deneddylated acts as an inhibitor of CN activity [Mosadeghi et al., 216]. CN binds to both neddylated and deneddylated, but with different binding affinity. While the k on is the same for both reactions the k off for CN in complex with non-neddylated is increased by a factor of ~2. Previous biochemical analysis has shown that, in the presence of or substrate, the deneddylation rate is reduced [Emberley et al., 212]. Moreover, addition of substrate impedes stable association of CN with CF [Enchev et al., 212]. Hence, to model product inhibition of CN we assumed that CN only binds to, Fb, and Fb states (cf. Table T11).

25 Table T11 No. Reactions k on [(M s) 1 ] k off [s 1 ] 13 CN CN 13a 13b 13c Fb1 CN Fb1 CN Fb2 CN Fb2 CN CN CN Fb1 CN Fb1 CN (a) 6.2 (a) Fb2 CN Fb2 CN (a) measured [Mosadeghi et al., 216] ubstrate degradation ubstrate degradation by itself is a complex process which involves recruitment of Ub-loaded E2 enzyme to the Rbx1 domain of an CF complex, subsequent multiple Ub transfers to the substrate and processing by the 26 proteasome. Here, we neglected much of this complexity and assumed that once a substrate-bound CF complex is neddylated the substrate can be degraded. The latter process was described by first order rate constant k deg which summarizes the above mentioned processes in an effective manner (Table T12). Also, for simplicity we assumed that the degradation rate constant is the same for 1 (-P) and background substrate 2. For the human 26 proteasome substrate degradation rates range from less than.1 min 1 up to.7 min 1 depending on the substrate and the number of conjugated ubiquitins [Lu et al., 216]. For CyclinB-NT with 4 conjugated ubiquitins the degradation rate is. min 1 or.83 s 1. Based on our measurements we estimated k deg =.71 s 1 (cf. Table T1). Table T12 No. Reactions k deg [s 1 ] 14 N8- Fb1 1 N8- Fb1 N8- Fb2 2 N8- Fb2 (a) estimated.71 (a) Background substrate To generate the high degree of neddylation observed experimentally we had to assume that cells contain a certain amount of CRL substrates, which is consistent with the fact that substrate favors the neddylated state of CRL ligases [Emberley et al., 212; Enchev et al., 212]. To generate auxiliary substrate we assumed a constitutive synthesis term (Table T13). ince the total amount of background CRL substrates in the cell is unknown we treated the synthesis rate as a variable parameter to be determined by comparison with experiments (cf. Table T1). In this way we obtained an estimate of 2261nM for the concentration of background substrate under steady state conditions in wildtype cells assuming that substrates are only degraded via the CRL-mediated pathway. Table T13 No. reaction 2 k synth [nm s 1 ] 1 Ø (a) (a) estimated

26 imulations were done with the ystems Biology Toolbox of MATLAB [MATLAB 21b] which was used to translate the model reactions (1-1) into a system of ordinary differential equations using mass-action kinetics. Integrations were performed with the implicit solver ode1s. Parameter estimation To validate our model we measured different quantities in wildtype (WT) cells as well as in response to different genetic perturbations (cf. Table T14). Conditions listed in bold font were used to estimate the values of unknown parameters. Altogether, our model comprises 4 state variables and 3 parameters (rate constants, protein concentrations and scale parameters) from which 22 parameters were either known from previous experiments or measured in this work. Among the 13 remaining parameters 8 parameters could be reasonably estimated or constrained leaving only parameters to be fitted by comparing model simulations with experiments. The 4 scale factors P1 P4 (Table T1) were estimated based on relative protein abundances and previous measurements of the association of with different cullins. The 4 on and off rate constants P P8 had almost no effect on the value of the measured quantities (cf. T14 and Fig. B), so we fixed them at the indicated values to reduce the number of variable parameters during the fitting procedure. Table T14 Experimental conditions and measured quantities measured quantity cell type / perturbation / condition type of experiment figure.b2. (a) WT (e) / WT MLN4924 steady state 4B.b2. (b) WT / WT MLN4924 / DKO (f) steady state 4B.b2.N8 (c) WT / WT / DKO / DKO steady state 4E β-trcp.b2. (d) WT steady state 4D WT / DKO / DKO 4C t 1/2 WT β-trcp / WT / DKO β-trcp / DKO transient 4F (a) fraction of bound to, (b) fraction of bound to, (c) fraction of bound to Nedd8, (d) fraction of β-trcp bound to, (e) WT wildtype, (f) DKO double knockout -/-, Cand2 -/- To estimate the values of the remaining parameters in Table T1 (P9-P13) we used nonlinear optimization in combination with a profile likelihood approach as described in [Raue et al., 29]. To calibrate the model we defined the weighted sum of squared residuals as an objective function 6 χ 2 (θ) (y k y k (θ)) 2 k=1 σ k 2 (9) 2 and numerically determined θ = (f Fb1, f Fb2, k nedd, k deg, k synth ) such that θ = argmin [χ 2 (θ)]. In Eq. (9) y k and σ k 2 denote the values of the measured quantities (cf. T14, bold face) and their respective measurement errors. The quantities y k (θ) are the predicted values of the measured quantities obtained from numerical simulations of our model for a particular set of parameter values. Due to limited sample size we were not able to reliably estimate the measurement errors from the data. o, for convenience, we assumed equal variances of

27 σ k 2 =.1y k (1% from the mean values) for all measurements. However, since all parameters are identifiable (see below) a different choice for the values of the variances would yield qualitatively similar results. To obtain confidence intervals for the estimated parameter values we numerically computed the profile likelihood for each parameter defined as χ 2 PL (θ i ) = min θj i [χ 2 (θ)], (1) i.e. for each value of θ i the objective function defined in Eq. (9) was re-optimized with respect to the remaining parameters θ j i. The resulting plots exhibit a parabolic shape (Fig. A) indicating that all parameters are identifiable [Raue et al., 29]. To obtain finite sample confidence intervals we defined the confidence regions {θ i : χ 2 PL (θ) χ 2 (θ ) < Δ α }, i = 1,, (11) where the threshold Δ α = χ 2 (α, df) is the α quantile (confidence level) of the χ 2 -distribution with df degrees of freedom. Pointwise confidence intervals are obtained for df = 1 while df = yields simultaneous confidence intervals for all parameters. Confidence intervals for model predictions (cf. Fig. 4) were computed by running simulations for parameters sampled from the confidence region defined by Eq. (11) with the threshold Δ α = χ 2 (.9,) (Fig. A, upper horizontal line). Table T1 List of estimated parameters parameter value expected range defined in fixed / variable P1 f 6 6 Eq. (1) fixed P2 f,wt.23 fixed P3 f CN,WT Eqs. (2) (4) P4 f,wt.4 fixed P P6 P7 P8 1 k on 1 7 (Ms) (Ms) 1 Table T6 fixed 2 k on 1 7 (Ms) (Ms) 1 Table T7 fixed 2 k off.1s s 1 Table T7 fixed k on 1 6 (Ms) (Ms) 1 Table T8 fixed P9 f Fb (a) Eq. (7) variable P1 f Fb (a) Eq. (7) variable P11 k nedd.268 s s 1 (a) Table T9 variable P12 k deg.71 s s 1 (a) Table T12 variable 2 P13 k synth 1.4 nm s nm s 1 (a) Table T13 variable (a) simultaneous confidence intervals to a 9% confidence level with 1% assumed measurement errors. Response coefficients To quantify how small changes in one of the parameters (P P13) would impact the predicted values for the measured quantities (cf. T14) we computed the matrix of response coefficients (Fig. B) according to

28 R ij Q i/q i ref P j /P j ref (12) where P j = P j P j ref denotes the change of parameter P j relative to a reference value P j ref and Q i = Q i Q ref i represents the corresponding change of the predicted quantity Q i. Depending on whether Q i increases or decreases upon a parameter change P j the response coefficient R ij may be positive or negative, respectively. Its magnitude quantifies the fractional change of Q i upon a fractional change of P j. The fact that almost all response coefficients satisfy R ij < 1 means that our system exhibits only a weak sensitivity to most of the parameters at the respective reference point. This is particularly true for the 4 on and off rate constants P P8 DCN which have almost no effect on the predicted values of the measured quantities except for k on which weakly affects the half-life for substrate degradation in DKO cells. To reduce the number of fitting parameters we have, therefore, fixed P P8 during parameter estimation. From the entries of the response matrix for the remaining parameters (P9 P13) we can make some interesting observations: The fractions of bound to, and Nedd8 (first 2 three rows) are mainly determined by the ratio between substrate synthesis ( k synth ) and degradation (k deg ). If the substrate synthesis rate is increased the neddylated fraction of increases and more F-box proteins are recruited to leading to a reduction of the fraction of associated with. Increasing k deg has the opposite effect. However, the 2 latter also affects the half-life for degradation while k synth has only a minor effect on t 1/2. Interestingly the total concentration of F-box proteins (FbT) has a strong positive effect on the half-life for degradation in DKO cells because increasing the total pool of F-box proteins reduces the amount of available for binding to β-trcp. Protein fractions in terms of state variables To relate the measured quantities defined in Table T14 to state variables in our model (cf. Table 2) we used the following relations: The fraction of bound to Nedd8 was computed as [N8 ] [N8 Fb1] [N8 Fb2]. b2. N8 = T [N8 Fb1 1] [N8 Fb2 2] [N8 CN] T [N8 Fb1 CN] [N8 Fb2 CN] T where T denotes the total concentration of defined in Table T1. To define the fractions of bound to (.b2.) and bound to F-box (.b2.) we had to take into account that higher-order complexes involving and Fb1 or Fb2 are unstable and, thus, cannot be detected in our pull-down assays. For example, the complexes Fbi i would rapidly decay into Fbi i and or and Fbi i (Fig. C). The corresponding probabilities are given by a i = k off,2 i k off,2 i k off,4 and b i = 1 a i = k off,2 k off,4 i k off,4, i = 1,2 (13)

29 i where the rate constants k off,2 and k off,4 are defined in Tables T3-T. For the decay of complexes involving, and Fb1 or Fb2 we considered three decay channels as the dissociation of and from Fbi i or Fbi occurs with similar rates. The respective probabilities are given by c i = k off,2 i k off,2 i k off,6 k off,9, d i = k off,2 k off,6 i k off,6 k off,9, e i = 1 (c i d i ), (14) for i = 1,2 where the rate constants k off,6 and k off,9 are defined in Tables T and T8, respectively. With the help of these probabilities the protein fractions.b2. and.b2. (which we set equal to.b2.fb1.b2.fb2) are defined by. b2. = [ ] a 1([ Fb1] [ Fb1 1]) T a 2([ Fb2] [ Fb2 2]) [ ] T (a 1e 1 c 1 )([ Fb1] [ Fb1 1]) T (a 2e 2 c 2 )([ Fb2] [ Fb2 2]) T and [ Fbi] [ Fbi i] [ Fbi]. b2. Fbi = T b i([ Fbi] [ Fbi i]) T (b ie i d i )([ Fbi] [ Fbi i]) T [N8 Fbi] [N8 Fbi i] [N8 Fbi CN] T [ Fbi CN] [ Fbi CN] [ Fbi i] T for i = 1,2. The fraction of β-trcp bound to (β-trcp.b2.) is given by β TrCP. b2. =. b2. Fb1 T Fb1 T where Fb1 T equals the total β-trcp concentration listed in Table T1. imulation protocols To simulate degradation of we started simulations from steady state by adding the reaction No. reaction k phos [s 1 ] initial condition 16 -P (1) ln(2) /(6 14) []=647nM

30 which describes the phosphorylation of by kinase. Phosphorylated (-P) is generated with a half-life of 14min serving as a substrate of the CF β-trcp ligase ( Fb1). To simulate the conditions and perturbations listed in Table T14 we used the protocols defined in Table T16. Inhibition of Nedd8 conjugation as well as -/-, Cand2 -/- double knockout were simulated by setting the neddylation rate constant and the total concentration to zero, respectively. To simulate overexpression we computed a scale factor assuming that competes with other cullins for access to Rbx1. imilarly, to simulate β-trcp overexpression we computed a scale factor assuming that β-trcp competes with auxiliary Rs for access to. In the case of overexpression we also had to recompute the scale factors that account for sequestration of, CN and by other cullins. In both cases the overexpression factors (f and f β TrCP ) account for both endogenous and exogenous proteins. Table T16 perturbation protocol remark WT MLN4924 set k nedd = at t = DKO set [] = at t = set [] OE = f OE, [] WT (a) with f (b) f [Rbx1] OE, = [Rbx1] (f 1)[] WT Inhibition of Nedd8 conjugation -/-, Cand2 -/- double knockout WT / DKO and recompute scale factors in Eqs. (2) (4) f,oe (c) = [] OE [] OE [Rbx1] [] WT [Cul] overexpression in WT or DKO f,oe (d) = min (1, f,wt f,oe f,wt ) WT / DKO β-trcp set [Fb1] OE = f OE,β TrCP [Fb1] (e) WT with f (f) f β TrCP [FbT] WT OE,β TrCP = [FbT] WT (f β TrCP 1)[Fb1] WT β-trcp overexpression in WT or DKO set [FbT] OE = [FbT] WT [Fb1] OE (a) [] WT = 22nM, (b) f = 6.6 in WT and f = in DKO, (c) f CN,OE = f,oe, (d) not applicable in DKO, (e) [Fb1] WT = 64nM, (f) f β TrCP =. in WT and f β TrCP = 8 in DKO, [FbT] WT = 217nM Computation of the cycle time To compute the cycle time for the cyclic reaction chain depicted in Fig. 7 we assigned to each reversible reaction an effective forward rate constant using the concept of net rate constants [Cleland, 197]. The latter are denoted by k 1,,k 6 in Fig. D (highlighted in red color). For irreversible reactions such as neddylation (k 1 ) and deneddylation (k 12 ) the net rate constant is identical with the rate constant. Then the net rate constant k 6 is given by