SupplementaryInformation
The glucose metabolism model which is based on a simple Michaelis-Menten kineticsis discribed. The analysis is carried out for constant supply of nutrient, that is, the external glucose concentration is constant. The Monod’s kinetic model is used to obtain an expression for the specific growth rate of cell based on the glucose cocentration. Uptake of glucose by the cells is dependent on the GLUT1, a glucose transporter, which in turn is positively regulated by HIF1 and this phenomenon is incorporated in the model using a Hill equation. The model represents the conversion of glucose to pyruvate through glycolysis. Further, at the puruvate mode the carbon flux is diverted through two routes, one going towards the Tricarboxylic acid cycle (TCA) cycle and the other towards lactate formation. The equations are based on the published litterature (Molenaar et al. 2009).It should be noted that while the oxidative phosphorylation post TCA cycle is an efficient system, the lactate formation is inefficient with lower energy output. However, the flux through the metabolism is faster in case of the inefficient process of lactate fromation as compared to the flux through the TCA cycle. The model also incorporated the negative regulation of the flux going towards mitochondrialTCA cycle by HIF concentration which is regulated by α-ketoglutarate (Parson et al. 2008), which is alsoquantified by a Hill equation. The model also captures the Crabtree effect by incoprorating the inhibition of the TCA cycle by Fructose 1,2 bisphosphate (Ruiz et al. 2008). However, in the model it is captured as a function of pyruvate.The model was simulated using Matlab ODE15s subroutine to solve the set of differential equations. To demonstrate the hypothesis, the parameter set reported in Table S1 was used.
Model Equations
Table S1 The parameter values in the model simulation.
Component Concentrations / Glce, Glc, HIF, G6P,Pyr, ,α ketoglutarate,Lactate
Maximum Rate Constants / Vmax1 = 2.27 sec-1, Vmax2= 2.65 sec-1,
Vmax3 = 754.2 sec-1, Vmax4 = 0.022 sec-1, Vmax5 = 0.007 sec-1, Vmax6 = 0.003 sec-1 , Vmax7= 10 sec-1,
Half Saturation Constants / Km1= 0.S12 nM, Km2 =0.80 nM ,
K1=Km3=420nM, Km4=4000 nM ,
Km5=0.05 nM, Km6= 3000 nM,
K2 = 100 nM, K3=5 nM,
Hill Coefficients / nh1 = 2, = 2, nh2 =2;
Equations for the given system:
External Glucose is constant:
(S1.1)
Glucose concentration dynamics based on the Michaelis-Menten kinetics and positive regulation by HIF:
(S1.2)
(S1.3)
Pyruvate concentration dynamics incoprorating the inhibition of the TCA cycle by Fructose 1,2 bisphosphate (note that in the model it is captured as a function of pyruvate) as well as the inhibition by HIF: (S1.4) (S1.5)
(S1.6)
(S1.7)
HIF dynamics incorporating the inihibition of HIF by α-ketoglutarate:
(S1.8)
Fig S1 shows the phase plane plot for various initial conditions of α-ketoglutarate and HIF. It is noted that the solution demonstarted that the system is bistable with two stable states which are dependent on the initial threshold concentratin of α-ketoglutarate. The analysis also demostrated that the bistable response was dependent on the crabtree effect and on removal of the inhibition posed by the crabtree effect only single stable steady state was observed.
Fig.S1 Phase plot for different concentration of HIF and α-ketoglutarate
Fig S2 shows the flux ratio, which is the ratio of steady state rate towrds lactate formationto that towards oxidative phosphorylation corrosponding to the two steady states S1 and S2. It clearly illustartes the threshold for the switching between the two states. For normal cells having α- ketoglutarate concentration above the threshold value steady state S1 is achieved, while the cells below threshold of α- ketoglutarate glycolytic phenotype is ensued and the cells reached the steady state S2. At steady state S2, the glycolysis accounts 95% of the total flux while for the normal state, S1, the oxidative phosphorylation accounts for 95% of the total flux.
Similarly, Fig S3 demonstrates the glucose uptake rate for the two states. The analysis demonstrated that the cells in the steady state with high flux towards lactate (S2) the glucose uptake rate is 4.5 times that of the normal cells (S1).
Fig.S2Mitochondrial Flux % of Total Flux corresponding to steady states
Fig. S3 Net Glucose uptake Flux for the two states
Figure S4 presents the possible distribution of HIF in cell for different standard deviations. We have assumed the normal distribution with mean normalized around the α-ketoglutarate value in normal cells(Bhat and Venkatesh 2005)
Fig. S4 Possible Cell Distribution with varying α- ketoglutarate concentration
Corresponding to the distribution presented in figure S4, the P values for the threshold are calculated. They represent the number of cells which lie in the glycolyic range and are presented in Figure S5. Figure S5 represents the percentage of cells in the glycolysis region as a function of standard deviation. We can see for the higher variability more cells fall into glycolytic region.
Fig.S5 Percentage of Cells in steady state S2 (aerobic glycolysis)
References:
Bhat PJ and Venkatesh KV (2005)Stochastic variation in the concentration of a repressor activatesGAL genetic switch: implications in evolution of regulatory network.FEBS Lett 579: 597–603
Molenaar D, van Berlo R, de Ridder D, Teusink B (2009) Shifts in growth strategies reflect tradeoffs in cellular economics. Mol Syst Biol 5:323-332
Parsons DW, Jones S, Zhang X, et al (2008) An Integrated Genomic Analysis of Human Glioblastoma Multiforme. Science 321(5897): 1807-1812
Ruiz R, Averet N,Araiza D,et al ( 2008)Mitochondrial Oxidative Phosphorylation Is Regulated by Fructose 1,6-Bisphosphate A possible role in crabtree effect induction? J Biolo Chem 283(43):26948–26955