Supplemental Information Supplemental Data (Figures S1-S4, legends, Movie S1 and Tables S1-S5) Extended Experimental Procedures Supplemental References
Figure S1
Figure S2
Figure S3
Figure S4
Supplemental Figure Legends Figure S1. Summary of the comprehensive data, related to Experimental Procedures. (A) An example of time-series data of the phosphoproteome and metabolome in glycolysis, the TCA cycle and glycogen metabolism. The white boxes include metabolite time courses of three insulin doses (blue: 0.01 nm, green: 1 nm and red: 100 nm). The green boxes can include time courses of the phosphopeptide of the indicated molecules in response to 1 nm insulin stimulation. See Table S3 for the abbreviations of the enzyme names. (B) Relationships of the numbers appearing in the main text. Figure S2. Transcript and protein level of G6Pase, related to Figure 1. (A) Changed transcripts of two responsible metabolic enzymes. Two probes (blue and red) were found for G6Pase. See Table S3 for the gene names and functions. (B) The protein level of G6Pase detected by Western blotting (right). Here, 10 nm of insulin was used. Figure S3. An index for the determination of quantitatively changed metabolites, related to Figure 2. (A) The definition of quantitatively changed metabolite; S 1 / S 0 > 1. S 1 is the area surrounded by metabolite time courses of three insulin doses (blue: 0.01 nm (control), green: 1 nm and red:100 nm insulin). S 0 is an area that has a width of 2standard deviation calculated from triplicates of each time point along the time course of the control. This area represents the response within random variation. (B) Two-fold S 1 is equal to the sum of the area between the blue / green, blue / red and green / red. This area represents quantitative changes that are induced by insulin stimuli. Thus, S 1 / S 0 is an index for quantifying how much the metabolite of interest is changed by the insulin stimulus compared with random variation. (C) An increase or decrease of a metabolite is determined by whether the
increase content of S 1 is greater than the decrease. An increase or decrease content of S 1 is the area in which the metabolite time course of a higher dose of insulin is higher or lower than that of a lower dose of insulin, respectively. (D) Examples of S 1 / S 0 values in the metabolomic data. Figure S4. Analyses of the kinetic model, related to Figure 6. (A) Variable selection with 100 nm insulin. Red indicates the threshold for the variable selection (RSS=0.001). The five essential variables above the threshold are the same as the variable selection preformed with 1 nm insulin (Figure 6D). (B-G) Contribution of isocitrate, F6P and 2-oxoglutarate (B), PEP (C), citrate (D), malate (E), phosphorylation of PFKL at S775 (F), F2,6BP (G) to the time courses of F1,6BP. Red; 100 nm insulin, green; 1 nm insulin, blue; 0.01 nm insulin (basal level). The time course of F1,6BP with (dashed lines) or without (solid lines) holding the concentration of the indicated molecules. Holding PEP, citrate or malate at the basal level (0.01 nm insulin) resulted in increase of F1,6BP, whereas holding phosphorylation of PFKL at S775 or F2,6BP at the basal level resulted in decrease of F1,6BP, indicating that the former three negatively regulate F1,6P production, whereas the latter three positively regulate it (Figure 6E). (H), (I) and (J) Reaction rates (v) of PFKL, FBPase and ALDO. Blue, green and red solid lines: The time courses of the reaction rates with 0.01 nm, 1 nm and 100 nm insulin. (K) Time derivative of F1,6BP. Blue, green and red: 0.01 nm, 1 nm and 100 nm insulin, respectively. (L) Comparison of reaction rates presented in (H-J). Solid, dashed and dotted lines represent the time courses of the reaction rate of PFKL, FBPase and ALDO, respectively. Blue, green and red correspond to 0.01 nm, 1 nm and 100 nm insulin. PFKL is an enzyme that produces F1,6BP, whereas FBPase and ALDO are enzymes that consume F1,6BP. The reaction rates of PFKL and FBPase are dominant factors in the F1,6BP time course over time.
Supplemental Movie Legend Movie S1. Static signal flow of acute insulin action, related to Figure 5. The global landscape of the static signal flow of acute insulin action in phosphorylation and metabolic networks (Figure 5). Interactive three-dimensional visualization for Figure 5 in *.gml format is also downloadable from our website (http://www.kurodalab.org/info/signalflow/). We recommend VANTED-HIVE (http://vanted.ipk-gatersleben.de/addons/hive/) (Junker et al., 2006; Rohn et al., 2011) to open the *.gml file for viewing the trans-omic signal flow in 3D visualization. Top layer; insulin-signaling pathway, Middle layer; metabolic enzymes, Bottom layer; metabolites. Orange in the top layer; phosphorylated proteins, Orange lines from the top to middle layers; phosphorylation of metabolic enzymes by protein kinases. White lines from the middle to bottom layers; enzymatic reaction. Red and blue lines from the bottom to middle layers; allosteric regulation (red; activator, blue; inhibitor). Supplemental Table Legends Table S1. Multiple time-series omic data of acute insulin action, related to Figure 1. The time-series metabolomic data includes the 304 metabolites after three different insulin stimuli: 0.01 nm, 1 nm and 100 nm. Unit of the metabolite concentration is nmol / 1.7 x 10 7 FAO cell. Note that glycogen, F2,6BP and lipids are measured in different units (glycogen: ng / 6cm dish; F2,6BP: a.u.; lipid: peak area values (a.u.) ). The S 1 / S 0 values of the measured 304 metabolites are also presented. The time-series phosphoproteomic data of the phosphorylated responsible metabolic enzymes and responsible protein kinases were measured after 1 nm of insulin stimulus. Unit of phosphorylation intensity is arbitrary, normalized to one at 10 min. The microarray data is the time series after 10 nm of insulin stimulus presented in Figure S2.
Table S2. Constituents of the six rapid-equilibrium metabolite pool and correlation coefficients of metabolite pairs in the rapid-equilibrium metabolite pools related to Figure 2. Hub metabolites that were excluded from the calculation of the correlations are shown in this table. p-values of the Pearson s correlation coefficients for the metabolite pairs are also included. Table S3. The list of the phosphorylated responsible metabolic enzymes and their responsible protein kinases, related to Figure 3. The phosphorylated responsible metabolic enzymes and their responsible protein kinases are identified in step (iii) and (iv) in the main text, respectively. Phosphorylation of the protein kinases themselves (Figures 3B and C) are presented in detail. Red: all of the significantly changed phosphorylation exhibited an increase (>1.5-fold) in response to the insulin stimulus; blue: all of the significantly changed phosphorylation exhibited a decrease (< 2/3-fold) in the response to the insulin stimulus; green: all of the significantly changed phosphorylation exhibited either an increase or decrease in response to the insulin stimulus. Conventional abbreviations, gene name and definition of enzymes are also included. Table S4. Complete network topology of the allosteric regulation, related to Figure 4. This table is the original data of the dot-plot matrix shown in Figure 4B. Table S5. All the parameters and initial conditions of the kinetic model presented in Figure 6.
Extended Experimental Procedures Cell culture and treatments Rat hepatoma FAO cells were seeded at a density of 1.8 10 6 cells per 10 cm dish and were then cultured in RPMI 1640 supplemented with 10% (v/v) fetal bovine serum for 2 days before starvation. The cells were starved in the presence of 0.01 nm insulin (Sigma) in RPMI 1640 with 10 nm dexamethasone (Wako) for 12 hours. The medium was then changed twice every 2 hours before the stimulation. The reason for the addition of the 0.01 nm insulin during starvation was to mimic the in vivo basal secretion during fasting (Kubota et al., 2012; Polonsky et al., 1988). The cells were stimulated by replacing the medium with the starvation medium containing the indicated doses of insulin, and were used for phosphoproteome and metabolome measurements. HEK293 cells were cultured in DMEM with 10% (v/v) fetal bovine serum. The indicated plasmids harboring cdnas of wild-type and mutants of mouse PFKL were transfected into HEK293 cells using Lipofectamine 2000 (Invitrogen) according to the manufacturer s instructions. After being in culture for 20 hours, the cells were harvested as described in the next section, and used for PFKL assay. Phosphoproteome measurement The cells stimulated with 1 nm insulin were washed with ice-cold PBS (phosphate-buffered saline) twice and were lysed using TRIzol (Invitrogen). The aliquots, including the protein fraction, were washed with 95 % EtOH with 0.3 M guanidine hydrochloride and dissolved in buffer (100 mm Tris [ph 8.8] and 7 M guanidine hydrochloride) that contained reference protein (casein). After digestion with lysil endopeptidase, the peptides were alkylated with iodoacetamide. The peptide mixtures were loaded into an Fe-charged column (Fe-IMAC) and washed with Fe-IMAC washing buffers (0.1% trifluoroacetic acid [TFA], 60% acetonitrile [ACN] and 0.1% TFA, 2% ACN) (Matsumoto et al.,
2009). Bound peptides were eluted with 1% phosphate. Then, the peptide mixtures were immediately subjected to a reverse-phase chromatography column and washed with reverse-phase chromatography washing buffer (0.1% TFA, 2% ACN). Bound peptides were eluted with elution buffer (0.1% TFA, 60% ACN) and lyophilized. The peptide for each time point was labeled with 4-plex itraq (Applied Biosystems) as described by the manufacturer (10 minutes, itraq-114; 0 minutes, itraq-115; 5 minutes, itraq-116; and 45 minutes, itraq-117; or 10 minutes, itraq-114; 2 minutes, itraq- 115; 30 minutes, itraq-116; 60 minutes, itraq-117). After labeling, the peptides were mixed 1:1:1:1 and lyophilized. The peptides were dissolved in 50 μl 0.1% TFA, 2% ACN. The peptides were then desalted and lyophilized. The peptides were analyzed by a nanolc-ms/ms system, which comprised of a quadrupole-tof (time of flight) hybrid mass spectrometer (QSTAR elite; AB/MDS- Sciex) and nanolc (liquid chromatography) (Paradigm MS2; Michrom BioResources) (Matsumoto et al., 2009). The peptide separation was conducted using in-house-pulled fused silica capillaries (0.1mm id, 15 cm length, 0.05mm tip id) packed with 3 mm C18 L-column. Metabolome measurement The cells stimulated with 0.01 nm, 1 nm, or 100 nm insulin were washed with 5% mannitol twice and incubated for 10 minutes in methanol with 25 μm L-methionine sulfone. Then Milli-Q water (500 μl) was added, 600 μl of the solution was transferred, and 400 μl chloroform was added and mixed well. The solution was centrifuged at 20,000 g for 15 min at 4 C, and the separated 400-μL aqueous layer was centrifugally filtered through a Millipore 5 kda cutoff filter to remove the proteins. The filtrate (320 μl) was lyophilized and dissolved in 50 μl Milli-Q water containing reference compounds (200 μm each of trimesate and 3-aminopyrrolidine) and then injected into the capillary electrophoresis timeof-flight mass spectrometry (CE-TOFMS) system (Agilent Technologies) (Soga, 2006; Soga et al.,
2009). For lipidomics, the stimulated cells were washed with PBS twice, and MeOH (1 ml) was added. Then, chloroform (250 μl) with 0.8 μm internal standards (d18:1/12:0 sphingomyelin and 14:0/14:0 phosphatidylcholine) was added to 500 μl of the solution and mixed well. The solution was incubated for 15 minutes at room temperature. Finally, Milli-Q water (50 μl) was added. The solution was incubated for 15 minutes at 4 C, and centrifuged at 1,000 g for 10 minutes at room temperature. The supernatant was collected and injected into two types of liquid chromatography-tandem mass spectrometry (LC-MS/MS) systems (2 μl). LC MS/MS analysis was performed using Triple Quad 5500 System (AB SCIEX, Foster City, CA, USA) for acyl CoA and acyl carnitine, or Triple TOF 5600 System (AB SCIEX ) for free fatty acid with an Agilent 1290 Infinity LC system (Agilent Technologies, Loveland, CO, USA). The reverse-phase LC separation was achieved by ACQUITY UPLC HSS column (particle size, 1.8 μm, 50 2.1 mm i.d., Waters Corporation, Milford, MA, USA) at 45 C. The mobile phase was prepared by mixing solvents (A) acetonitrile/methanol/water (20/20/60; 5mM ammonium formate) and (B) isopropanol (5mM ammonium formate) at a flow rate of 300 μl / min. The level of F2,6BP was independently quantified as described (van Schaftingen et al., 1982). Microarray analysis Total RNA was extracted using the Qiagen RNeasy Mini Kit (Qiagen). Labeled crna was synthesized from 700 ng total RNA using the standard protocol of the Agilent Low RNA Input Linear Amplification Kit (Agilent Technologies). Samples were then hybridized to the Agilent Rat Whole Genome Microarrays (Agilent Technologies, #G4131F). The arrays were washed and scanned using Agilent Microarray Scanner (Agilent Technologies).
PFKL assay The wild-type PFKL and PFKL S775A, S775D, and S775E were cloned in pcmv vector, a mammalian expression vector for tagging proteins with an N-terminal FLAG epitope (Funato et al., 2013). The transfected HEK293 cells were washed with Tris-buffered saline (TBS) twice, and lysed with lysis buffer (20 mm Tris [ph 7.5], 150 mm NaCl, 2 mm EDTA, 1 mm PMSF). Lysates were centrifuged at 20,000 g for 10 minutes at 4 C. Supernatants were incubated with anti-flag beads (Wako) for 1.5 hours at 4 C. The beads were washed with lysis buffer three times. Then, the buffer was replaced with reaction buffer (50 mm HEPES [ph7.0], 100 mm KCl, 5 mm MgCl 2, 5 mm Na 2 HPO 4, 1 mm NH 4 Cl, 1.5 mm ATP, 0.15 mm NADH and 0.1 mm AMP). The proteins were eluted from the beads with 3 FLAG peptide (Wako). The eluted proteins were mixed with 1 ml of reaction buffer with 5 mm fructose-6-phosphate, 5 units triosephosphate isomerase per milliliter, 0.5 units of aldolase per milliliter and 0.5 units of α-glycerophosphate dehydrogenase per milliliter. Absorbance at 340 nm, which reflects the amount of NADH whose consumption was the index of PFKL activity, was read at room temperature every 5 minutes (Deng et al., 2008; Funato et al., 2013). Tukey-Kramer test was performed to determine statistical significance between enzyme activities of the wild-type PFKL and three mutant PFKLs (S775A, S775D, and S775E). Procedure for Reconstruction of Trans-omic Signal Flow Step (i): identification of quantitatively changed metabolites (Figure 2) Criteria to identify quantitatively changed metabolites We defined the area between the time course curves of a metabolite as S 1 and the area within the width of 2standard deviation calculated from triplicates of each time point along the time course with 0.01 nm insulin stimulation defined as S 0 (Figures S3A and S3B). S 1 represents the magnitude of
response against insulin stimuli, whereas S 0 represents the magnitude of random variation. If the time course of the metabolite with a higher dose of insulin is higher or lower than that of a lower dose of insulin for a certain time interval, then the area within this interval represents an increase or decrease of the metabolite in response to insulin stimuli, respectively (Figure S3C). The sign of S 1 is positive or negative if the total increase area is larger or smaller than the total decrease area, respectively. If S 1 / S 0 > 1, then the metabolite of interest was defined as a quantitatively changed metabolite. In Figure S3D, we provide some examples of the time course and index (S 1 /S 0 ) of a metabolite that show that the index characterizes our intuitive impression on the degree of changes by insulin from the time course data. Note that the metabolites are uniquely distinguished by the KEGG Compound ID (Kanehisa et al., 2012) throughout the analyses. Substitution of data-missing values If no data are measured for a time point of a time course with 0.01 nm insulin stimulation, then the average of the other measured time points of the time course with 0.01 nm insulin stimulation was used to substitute the average value of this data-missing point. If a time point of a time course with 0.01 nm insulin stimulation was not measured in triplicate, then the standard deviation of this time point was estimated by multiplying the average of this time point by the average of coefficient values of the other time points of the time course with 0.01 nm insulin stimulation. For the time courses with 1 nm and 100 nm insulin stimulations, values of data-missing points were estimated by linear interpolation.
Step (ii): identification of responsible metabolic enzymes and rapid-equilibrium metabolite pools (Figure 2) Identification of responsible metabolic enzymes We comprehensively searched the data downloaded from the KEGG PATHWAY database to identify all of the enzymes with substrates or products that include at least one quantitatively changed metabolite. Such enzymes were defined as responsible metabolic enzymes. Identification of rapid-equilibrium metabolite pools Any group of metabolite pairs that resided within two enzyme steps away in the metabolic pathway and that had time courses with a correlation of r 0.8 (r: Pearson correlation coefficient) were defined as a rapid-equilibrium metabolite pool. Note that the metabolites with S 1 /S 0 values that had not been calculated because of data-missing points might be involved in the rapid-equilibrium metabolite pools. We selected pairs of metabolites with more than 12 overlapping measured data points over time among 24 time points. Note that each value of the 24 time points is the average of triplicates that may include estimation values as described in Substitution of data-missing values for step (i). Then, the correlation coefficients of the time courses of the metabolite pairs were calculated based on the overlapping time points. If a pair of metabolites in two enzyme steps away is connected only via hub metabolites such as ATP, the pair was excluded from the pool identification to filter out trivial metabolite pairs. The hub metabolites were determined in reference to previous studies of network topology (Table S2) (Alves et al., 2002). We calculated probabilities of finding the identified rapidequilibrium metabolic pools by chance. First, all the adjacent metabolite pairs residing within two enzyme steps from one another were classified into two groups: those with the correlation coefficient,
r, of the metabolite pair being r 0.8 (pool) and those with r < 0.8 (out of pool). Then, p values of these correlation coefficients were calculated based on the T-statistics. T(r) r N 2 1 r 2 (r: correlation coefficient; N: number of time points) Step (iii): identification of protein phosphorylation of the responsible metabolic enzymes (Figure 3) We prepared a matching table that bridges between the International Protein Index (IPI) (Kersey et al., 2004) and EC number to associate the phosphoproteomic data with the responsible metabolic enzymes obtained in step (ii). The matching table of the IPI and EC numbers was generated from a matching table of IPI and NCBI-GeneIDs provided by European Bioinformatics Institute (ftp://ftp.ebi.ac.uk/pub/databases/ipi/current/ipi.rat.xrefs.gz) and a matching table of NCBI-GeneID and EC numbers was downloaded from the KEGG FTP (ftp://ftp.bioinformatics.jp/kegg/pathway/organisms/rno.tar.gz). Using the matching table of IPI and EC, we compared the list of responsible metabolic enzymes obtained in step (ii) and measured phosphopeptides to find the phosphorylation of the responsible metabolic enzymes. A fold change was calculated as a ratio of the phosphorylation intensity at each time point to the phosphorylation intensity at t=0 or 2 min. A phosphopeptide whose phosphorylation intensity at more than one time point was greater than a 1.5-fold increase or less than 0.67-fold decrease was determined as a quantitatively changed phosphopeptide.
Step (iv): identification of protein kinase dependent insulin signaling to metabolic enzymes (Figure 3) We estimated responsible protein kinases for the quantitatively changed phosphorylation of the responsible metabolic enzymes identified in step (iii) using a stand-alone version of NetPhorest (http://netphorest.info/images/netphorest_source_v1.0.tgz) (Miller et al., 2008). The inputs for NetPhorest are rat protein sequences that are associated with IPI in FASTA format (ftp://ftp.ebi.ac.uk/pub/databases/ipi/current/ipi.rat.fasta.gz). We obtained posterior probabilities of an amino acid residue being recognized by a particular protein kinase. Among the candidate protein kinases, we selected a protein kinase that had the largest posterior probability value for the responsible protein kinase of the phosphorylated amino acid sequence as a responsible protein kinase. The responsible protein kinase was connected to the insulin signaling pathway if it was included in this pathway map. Step (v): identification of allosteric regulation (Figures 4A and B) We obtained the entries for the responsible metabolic enzymes from the BRENDA database (http://www.brenda-enzymes.org) (Schomburg et al., 2013) and extracted their allosteric effector (activator and inhibitor) information, as reported for mammals (Bos Taurus, Felis catus, Homo sapiens, Macaca, Mammalia, Monkey, Mus booduga, Mus musculus, Rattus norvegicus, Rattus rattus, Rattus sp., Sus scrofa, dolphin, and hamster ). We unified synonyms of allosteric effector names used in BRENDA into standard compound names using the Ligand Structure ID of BRENDA, which is retrievable over Simple Object Access Protocol (SOAP). Then, we associated the names of allosteric effectors with metabolite names that were used in KEGG, thereby producing a matching table between the names of allosteric effectors in BRENDA and the KEGG compound ID. Using this matching table,
quantitatively changed allosteric effectors were identified because the list of the quantitatively changed metabolites is available in terms of the KEGG compound ID. Consequently, we obtained quantitatively changed allosteric effectors and their targeted responsible metabolic enzymes. Step (vi): reconstruction of the static signal flow of acute insulin action in a trans-omic network (Figure 5) We integrated the results of steps (i) to (v) and reconstructed the static signal flow of acute insulin action in a trans-omic network. Phosphorylation and allosteric regulation of the responsible metabolic enzymes were integrated by using the EC numbers of the responsible metabolic enzymes. VANTED- HIVE (http://vanted.ipk-gatersleben.de/addons/hive/) (Junker et al., 2006; Rohn et al., 2011) was used for the three-dimensional visualization of the trans-omic signal flow. Step (vii): construction of the kinetic model (Figure 6) Variables F1,6BP was the only variable calculated by the kinetic model presented in Figure 6A and Table S5, whereas the other variables (metabolites) were fixed at the experimental values. The time courses between experimental time points of these fixed variables were linearly interpolated. We defined these fixed variables as boundary metabolites because they are located at the systems boundary (outer edge) of the biochemical pathway exhibited in Figure 6A. Rate law We used the formalism of Modular Rate Law particularly the common modular with complete activation/inhibition (Liebermeister et al., 2010), so that it could consider a contribution of activators, inhibitors, and phosphorylation of the enzyme to the reaction rate,
v [ A] K i I j Vmax[ S] [ ] [ ] [ ] i K A A i j KI I j Km S i j where v denotes the reaction rate, [A] i, [I] j, and [S] denote the ith activator concentration, the jth inhibitor concentration, and the substrate concentration, respectively. K A, i K I j, and K m are the activation constant for the ith activator, the inhibition constant for the jth inhibitor and the Michaelis constant for the substrate, respectively. V max represents the maximum reaction rate. Note that the term for the reverse reaction has been removed for simplification. The contribution of phosphorylation to the reaction rate is considered either an activator or an inhibitor. Consequently, the kinetic model comprises of the following three rate equations (see Table S5 for abbreviations and parameter values): v v v PFKL FBPase ALDO K K K k Mal ALDO [F2,6BP] K 2OG [F2,6BP] K [2OG] 2OG K K Mal [ppfkl] V [Mal] KpPFKL [ppfkl] K K F2,6BP [Cit] V [F2,6BP] KCit [Cit] K [F1,6BP] F2,6BP F2,6BP max F6P F1,6BP K PEP [PEP] K [F6P] [F6P] [F1,6BP] [F1,6BP] PEP max Cit K Cit [Cit] K IsoCit K IsoCit [IsoCit] The time courses of these three reaction rates and the time derivative of [F1,6BP] are presented in Figures S4H through S4L. Initial estimates of the kinetic parameters The initial estimates for the kinetic rate constants were calculated using the flux distribution predicted by a constraint-based model (Bordbar et al., 2011) in combination with the COnstraints Based Reconstruction and Analysis (COBRA) toolbox (Schellenberger et al., 2011), glycolytic fluxes measured in hepatocytes (Marin-Hernandez et al., 2006), and our comprehensive data. The initial estimates of the kinetic parameters were determined as follows. The initial estimate of v is the flux
predicted by the constraint-based model or the measured glycolytic fluxes. Because the units for flux were mmol / h / body in the constraint-based model and nmol / min / mg cell protein in the measured glycolytic fluxes, we converted these units into M / min using 2.4 10 11 hepatocytes / body, 3.4 10-12 L / hepatocyte, and 30 mg protein / ml. For the initial estimates of K A, K I, and K m, we used [A], [I] and [S] at t = 0, respectively. Then, substituting [A], [I], and [S] with their values at t = 0, we could obtain the initial estimate of V max by solving the equation above. Initial metabolite concentration and phosphorylation intensity The initial concentration of the metabolites and initial intensity of the phosphorylation were taken from our comprehensive measurements (Table S5). The unit for the metabolomic data nmol / 1.7 10 7 cells was converted into M using 1.3 10-12 L / FAO cell. Estimating the kinetic parameters F1,6BP was used to evaluate the fitting of the kinetic model to the experimental data. The parameters of the kinetic model were estimated by using the experimental data shown in Figure 6C in accordance with two methods in the series similar to those in our previous studies (Kubota et al., 2012; Noguchi et al., 2013); a meta-evolutionary programming method was used to approach the neighborhood of the local minimum, and the Nelder-Mead method was used to reach the local minimum. Using these methods, the parameters were estimated to minimize the value of the objective function, which was defined as the residual sum of squares between the experiment and simulation. After 200 independent estimations of the model, we selected the parameter values that resulted in the minimum value for the objective function. The parameters and equations that were used in this study are shown in Table S5. Among the best five models, we confirmed that the model had similar characteristics in terms of the time course of F1,6BP. We performed the simulations and the parameter estimations using MATLAB
software (version R2013a; MathWorks) and the Systems Biology Toolbox 2 (SBTOOLBOX2) (Schmidt and Jirstrand, 2006) for MATLAB. Kinetic simulations (Figure 6C) The time courses of F1,6BP with 0.01 nm, 1 nm, and 100 nm insulin stimulations were calculated using the kinetic model presented in Figure 6A and Table S5. Because the time courses of phosphorylation of PFKL at S775 was not measured with 0.01 nm or 100 nm insulin stimulation, we simulated the time course of phosphorylation by using a kinetic model of insulin signaling to p70s6k (Kubota et al., 2012) and used the calculated time course of phosphorylation of PFKL at S775. We first estimated the parameters for phosphorylation of PFKL by pp70s6k using the time course of phosphorylation of PFKL by pp70s6k with 0.01 nm or 1 nm insulin stimulation in experiments. Because the time course of phosphorylation of PFKL with 0.01 nm had not been measured, it was assumed that the time course of phosphorylation of PFKL with 0.01 nm insulin is a flat time course at t = 0 value with 1 nm insulin. Using the estimated parameters, we simulated time course of phosphorylation of PFKL at S775 with 0.01 nm, 1 nm, or 100 nm insulin stimulation, and used these time courses to predict behavior of F1,6BP (Figures 6C and 6E, dashed lines) and for further analyses (Figure S4). Variable selection (Figure 6D) We made a variable selection based on the residual sum of squares presented in Figure 6D that were calculated by the recursive algorithm that follows.
Definition: Suppose there is a kinetic model that includes n boundary metabolites. We call this model n variable model. Then, the time course of a boundary metabolite with 1 nm (or 100 nm) insulin stimulus is replaced with the time course with the 0.01nM insulin condition. We call this resultant model the n-1 variable model. This procedure achieves a virtual situation in which the insulin signal flow via a certain phosphorylation or allosteric regulation is turned off. Algorithm: (1) Calculate a residual sum of squares between the n variable and n-1 variable models for each variable. (2) Choose one of the n-1 variable models with the smallest residual sum of squares. (3) Return to step (1). Use the n-1 variable model chosen in step (2) as the n variable model for this iteration. Repeat this loop until all of the time courses of boundary metabolites have been replaced with those stimulated by 0.01 nm insulin. We eliminated the variables whose residual sum of squares is less than 0.001. See Table S5 for the parameters that reproduce the time courses of boundary metabolites with 0.01 nm, 1nM, or 100 nm insulin stimulation. Supplemental References Alves, R., Chaleil, R.A., and Sternberg, M.J. (2002). Evolution of enzymes in metabolism: a network perspective. J Mol Biol 320, 751-770.
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