1 Quantitative determinants of aerobic glycolysis identify flux through the enzyme 2 GAPDH as a limiting step 3 4 Alexander A Shestov1*, Xiaojing Liu1*, Zheng Ser1, Ahmad Cluntun2, Yin P Hung3, Lei 5 Huang4, Dongsung Kim2, Anne Le5, Gary Yellen3, John G Albeck6, Jason W 6 Locasale1,2,4** 7 8 1Division of Nutritional Sciences, Cornell University, Ithaca NY 14850 9 2Field of Biochemistry and Molecular Cell Biology, Department of Molecular Biology 10 and Genetics Cornell University, Ithaca NY 14850 11 3Department of Neurobiology, Harvard Medical School, Boston MA 02115 12 4Field of Computational Biology, Department of Biological Statistics and Computational 13 Biology, Cornell University, Ithaca NY 14850 14 5Department of Pathology and Oncology, Johns Hopkins University School of Medicine, 15 Baltimore, MD 21231 16 6Department of Molecular Cell Biology, University of California Davis, Davis CA 95616 17 * Equal contribution 18 ** Correspondence: [email protected] 19 20 Abstract 21 Aerobic glycolysis or the Warburg Effect (WE) is characterized by the increased 22 metabolism of glucose to lactate. It remains unknown what quantitative changes to the 23 activity of metabolism are necessary and sufficient for this phenotype. We developed a 24 computational model of glycolysis and an integrated analysis using metabolic control 25 analysis (MCA), metabolomics data, and statistical simulations. We identified and 26 confirmed a novel mode of regulation specific to aerobic glycolysis where flux through 27 GAPDH, the enzyme separating lower and upper glycolysis, is the rate-limiting step in 28 the pathway and the levels of fructose (1,6) bisphosphate (FBP), are predictive of the rate 29 and control points in glycolysis. Strikingly, negative flux control was found and 30 confirmed for several steps thought to be rate-limiting in glycolysis. Together these 31 findings enumerate the biochemical determinants of the WE, and suggest strategies for 32 identifying the contexts in which agents that target glycolysis might be most effective. 33 34 Impact Statement 35 A computational model of the Warburg Effect is developed that reveals new mechanisms 36 for the regulation of glycolysis. These findings could lead to the definition of biomarkers 37 that determine the responses to targeting glycolysis in malignancy. 38 39 40 41 42 43 44 45 46
1 47 48 49 50 Introduction 51 52 Proliferating cells increase their glucose consumption and secrete lactate as
53 opposed to completely oxidizing the glucose in the mitochondria(Warburg, Wind et al.
54 1927) and is known as aerobic glycolysis or the Warburg Effect. Currently, this altered
55 metabolism is exploited for diagnostics and is subject to multiple drug development
56 efforts(Koppenol, Bounds et al. 2011; Vander Heiden 2011; Hamanaka and Chandel
57 2012). Numerous studies have identified genes such as KRAS, PIK3CA, and cMYC and
58 microenvironments such as hypoxia and hypoglycemia that promote aerobic glycolysis
59 but a complete understanding of the necessary and sufficient biochemical alterations
60 associated with this phenotype is unknown. Furthermore successful translation for
61 biomedical applications is limited by understanding the contexts in which therapies that
62 target glycolysis might be effective.
63 Computational modeling has a successful history in the study of
64 metabolism(Rapoport, Heinrich et al. 1976; Fell 1992; Schilling, Schuster et al. 1999;
65 Cascante, Boros et al. 2002). Genome-scale stoichiometric models of metabolism have
66 been developed to study the effects of drug targets in human metabolism and have had
67 success in predicting the WE(Molenaar, van Berlo et al. 2009; Vazquez, Liu et al. 2010;
68 Folger, Jerby et al. 2011; Shlomi, Benyamini et al. 2011). However a comprehensive
69 quantitative understanding of the WE requires knowledge of enzyme activities and
70 metabolic control.
71 Therefore, we collected and integrated multiple forms of data into a modeling
72 framework involving flux balances of glycolysis, detailed chemical kinetics based on
2 73 reaction mechanisms and parameters measured, physico-chemical constraints from
74 thermodynamics and mass conservation, metabolic control analysis, and Monte Carlo
75 sampling of parameter space. We next use mass spectrometry and isotope tracing to
76 probe concentrations and fluxes through the pathway and their responses to several
77 perturbations. Together we elaborate the determinants of aerobic glycolysis and identify
78 and confirm novel points of regulation in glycolysis that have remained unidentified for
79 over 50 years since the discovery of the pathway.
80
81 Results
82 Biochemical kinetic model of aerobic glycolysis
83 We investigated the kinetics of the glycolytic pathway from glucose uptake to
84 oxidation of pyruvate in the mitochondria or export of lactate out of the cytosol. We
85 modeled each step of the pathway according to enzymatic mechanism and known modes
86 of allosteric control resulting in a set of differential equations (Fig 1A, Materials and
87 Methods, Supplementary File 1). While it is not possible to model every possible
88 interaction explicitly, the aim is to capture enough of the pathway so that a large range of
89 experimentally realized measurements can be obtained and relationships between
90 variables can be observed.
91 Since glycolysis is the most extensively studied biochemical pathway, there is a
92 wealth of information on the kinetic parameters and enzyme expression that govern the
93 equations. Nevertheless, it is also not impossible to capture cellular physiology in any
94 biochemical model with single values of kinetic parameters(Daniels, Chen et al. 2008).
95 This difficulty arises from tremendous amount of heterogeneity within cells at multiple
3 96 levels. The origins of this heterogeneity vary from genetic variation observed across
97 cancer types, tumor types, differences in signaling mechanisms that affect post-
98 translational modifications in each cell, and the differences in microenvironmental
99 pressures (e.g. the oxygen availability) that each cell within a given tumor experiences, as
100 well as the inherent cell to cell variation common to all cells(Marusyk, Almendro et al.
101 2012). Therefore we developed an integrated algorithm to evaluate the statistics of the
102 kinetics of glycolysis that accounts for the possible variation within metabolism (Fig 1B,
103 Supplementary Information).
104 First the model is constrained using mass conservation constraints that conserve
105 the balance of glucose, redox state, and energy status. Next thermodynamic constraints
106 are used to constrain fluxes according to the free energy of the reactions determined by
107 Haldane relationships. These physical constraints are combined with the kinetic
108 mechanisms that define each step of glycolysis and the chemical reactions involving the
109 redox-associated metabolites NAD+, and NADH and energy-associated metabolites ATP,
110 ADP, and AMP. Next, the model is constrained to expression data so that protein
111 concentrations are subsumed in the Vmax values and chosen from typical concentrations
112 in cancer cells, measured kinetic parameters, and measured concentrations of nutrients
113 such as glucose, oxygen, and total intracellular adeno-nucleotide concentration.
114 At this stage, the model is subjected to a thorough statistical analysis. A Monte-
115 Carlo simulation is conducted for which the parameters within the model are randomized
116 and resulting differential equations solved. The distributions for each parameter are
117 chosen to capture observed ranges of variation. After each simulation, numerical stability
118 and the thermodynamics are assessed and all simulations that are unstable or appear
4 119 thermodynamically infeasible (i.e. a positive net flux through glycolysis is required) are
120 rejected. In each simulation, concentrations, fluxes, metabolic control coefficients, and
121 thermodynamic quantities are computed and recorded. This statistical analysis explores
122 the space of glycolysis in the context of the Warburg Effect. By assessing the statistics,
123 inferences can be made on the determinants of the Warburg Effects and its context
124 dependence to pharmacological intervention and nutrient environment. We first utilized
125 a recently developed a NADH/NAD+ fluorescent reporter(Hung, Albeck et al. 2011) and
126 measured the ratio of NADH/NAD+ across a population of cells where some experience
127 hypoxia and others glucose deprivation (Fig 1C). This variation in nutrient availability
128 across individual cells occurs in epithelial cell cultures due to differences in diffusion and
129 available cell surface area(Sheta, Trout et al. 2001). The distribution is plotted for three
130 media concentrations ranging from extreme hypoglycemia to the hyperglycemic
131 conditions typically used in cell culture (0.5 mM, 5.5mM, and 25mM).
132 The distribution of resulting fluxes (Fig 1D) was first found consistent with
133 known measurements. An analysis of the simulation revealed a distribution of NAD+
134 levels and NADH/NAD+ redox potential consistent with those observed experimentally
135 (Figs 1E,F). ATP levels peaked around 3mM with little variation (Fig 1G) and the
136 ATP/ADP energy state is observed to be bimodal (Fig 1H). Concentrations along the
137 glycolytic pathway varied with means similar to those measured in normal tissues with
138 fructose-1,6-bisphosphate (FBP) being most variable (Fig 1I). Together, these findings
139 indicate that these simulations capture the range of measured cellular concentrations and
140 provide confidence for further assessment of the behavior within the model.
141 Evaluation of the Warburg Effect and its relationship to metabolic variables
5 142 Having developed a model of glycolysis and its regulation, we assessed the relationship
143 of aerobic glycolysis to other characteristics of glycolysis. The distribution of values (Fig
144 2A) of the Warburg Effect ranged from less than one (primarily oxidative metabolism) to
145 over 95% of glucose being converted to lactate thus spanning a large range of values.
146 The dynamic range over which the Warburg Effect was observed in our model allowed us
147 to investigate to other variables in metabolism. We correlated the calculated value of the
148 Warburg Effect with metabolite concentrations of intermediates in glycolysis. From an
149 analysis of these correlations, a pattern within glycolysis emerges. The levels of
150 intermediates in beginning steps in glycolysis positively correlate with the Warburg
151 Effect, the levels leading up to the oxidation of glyceraldehyde-3-phopshate (GAP) by
152 GAPDH negatively correlate with the Warburg Effect, and those following GAPDH
153 positively correlate with the Warburg Effect (Fig 2B) suggesting together that a
154 bottleneck exists in the pathway that determines the extent of fermentation. An analysis
155 of the correlation of enzyme expression with the Warburg Effect revealed that the
156 enzyme expression for any single step within glycolysis did not completely correlate with
157 the Warburg Effect. However, across glycolysis, GAPDH, the enzyme that carries out
158 oxidative phosphorylation of glyceraldehyde-3-phosphate to yield NADH and 1,3-
159 diphosphoglycerate most strongly correlated with aerobic glycolysis (Fig 2C). Notably
160 many of the correlations although significant, appear not very strong indicating that the
161 expression of individual enzymes are not sufficient for induction of aerobic glycolysis.
162 The model also captures many of the activities that are known to correlate with aerobic
163 glycolysis. These include glucose transport, pyruvate kinase, and lactate dehydrogenase
164 activities. Interestingly the expression of enzymes such as hexokinase and
6 165 phosphofructokinase were either uncorrelated or negatively correlated with the extent of
166 aerobic glycolysis likely indicating their role in creating bottlenecks at other points along
167 the pathway. Together these findings identify enzyme expression patterns that determine
168 the extent of the Warburg Effect.
169 We next investigated the relationship between the Warburg Effect and other
170 physiological variables including the NADH/NAD+ redox status, NAD+ levels, the
171 energy state defined as the ATP/ADP ratio, lactate, oxygen levels, and phosphocreatine
172 levels (Fig 2D). Oxygen concentration, ATP, and phosphocreatine levels positively
173 correlated with the Warburg Effect and NADH/NAD+ redox status and NADH levels in
174 the cytosol negatively correlated with the Warburg Effect suggesting that positive and
175 negative feedback inherent to the circuitry of glycolysis contributes to buffering the
176 Warburg Effect. Together, these results identify multiple relationships between the
177 extent of aerobic glycolysis and measurable variables in metabolism.
178 Flux control and metabolic relationships in glycolysis
179 After assessing how metabolic parameters and concentrations within glycolysis
180 determine the flux to lactate, we next investigated how each node within glycolysis exerts
181 its control on the Warburg Effect and then the relationships between variables within
182 glycolysis. Metabolic Control Analysis (MCA) provides a mathematical framework to
183 evaluate the extent that a change in metabolic activity affects a given flux. In MCA a
184 pure rate-limiting step occurs when the flux control coefficient (FCC) (Supplementary
185 Information) is one at that step and zero at all other steps. In most cases, values of FCCs
186 are distributed with gradual values across a pathway. We therefore carried out a
187 metabolic control analysis using MCA within our statistical algorithm to investigate the
7 188 influence of each node in glycolysis on lactate flux across the ensemble of statistical
189 realizations of glycolysis (Fig 3A). We first computed the distribution of FCCs for
190 Lactate production for each step in the pathway (Fig 3B). It was found that for each step
191 within glycolysis, the average control exerted was near zero. Steps early in glycolysis
192 involving enzymes Hexokinase (HK), Phosphoglucoisomerase (PGI), and
193 Phosphofructokinase (PFK) exhibit both positive and negative control and GAPDH on
194 average exhibits the most positive control on the flux through the pathway. In addition to
195 steps within glycolysis, ATPase activity exerts the most influence over lactate production
196 with oxygen consumption having less of an affect. Together these results both confirm
197 the long-standing hypothesis that ATPase activity is the most prominent rate-determining
198 step in glycolysis but also suggest that GAPDH can often exert a large control on the flux
199 to lactate. In addition, an analysis of the statistics indicates that depending on the
200 context, any point along the pathway can exert large flux control on lactate production
201 with some steps (e.g. pyruvate kinase) less likely to exert control over the Warburg Effect
202 than others. Although the finding that pyruvate kinase typically does not exert substantial
203 control over glycolysis may appear surprising, this findings is consistent with studies that
204 have observed only modest changes in glycolytic flux due to changes in pyruvate kinase
205 activity(Christofk, Vander Heiden et al. 2008; Israelsen, Dayton et al. 2013).
206 To further investigate the contexts in which steps along glycolysis can be limiting,
207 we correlated the FCCs with one another and carried out a hierarchical clustering that
208 revealed modules of co-occurring flux control (Fig 3C). It was found that enzymes
209 residing in proximal regions of upper glycolysis tend to have positively correlated flux
210 control. However, for lower glycolysis the flux control is uncorrelated suggesting that
8 211 when a step is limiting in lower glycolysis it can be more readily disrupted. This
212 behavior is in contrast with that of upper glycolysis where limiting steps co-occur.
213 Furthermore an analysis of ATPase and Oxygen consumption activities reveals their
214 control to be related to the control of enzymes clustered at different points in glycolysis
215 (Fig 3C) indicating that flux control exerted by these ancillary fluxes are tied to different
216 regions of glycolysis. Since these simulations yield for each realization of glycolysis, a
217 set of concentrations, fluxes and flux control coefficients, relationships between flux
218 control coefficients and measurable concentrations can be obtained. An analysis of these
219 relationships using hierarchical clustering (Fig 3D) revealed a bi-modal relationship in
220 glycolysis where increases in metabolites in upper glycolysis led to steps in lower
221 glycolysis exerting flux control and increases in lower glycolysis resulted in enzymes in
222 upper glycolysis exerting flux control. Further analysis of FCCs and metabolic
223 parameters (Fig 3E, Fig 3F) revealed additional relationships. Together, these findings
224 yield a comprehensive map of the flux control in glycolysis and its connections to
225 metabolic variables.
226 Experimental flux control in glycolysis
227 Surprisingly, in several instances, negative flux control is observed for several enzymes
228 that have been previously thought to be the rate-limiting steps. Negative flux control
229 implies that inhibiting the enzyme would actually increase the rate of flux of glucose to
230 lactate. Given the surprising findings on flux control in glycolysis, we sought to
231 experimentally investigate these predictions and further explore the biological
232 ramifications. We therefore considered systematic perturbations to glycolysis in cancer
233 cells.
9 234 We first devised a combined flux profiling and metabolite profiling method using
235 13C isotope tracing from glucose (Fig 4A). Cells were incubated with U -13C glucose and
236 media were extracted at different time points and subjected to high resolution LC-MS
237 analysis(Liu, Ser et al. 2014). The linearity of the time course allows for an exact
238 measurement of the flux from glucose to lactate. We next carried out direct
239 measurements of glycolysis state and flux control by perturbing glycolysis acutely with
240 pharmacological agents and subsequently measuring metabolite levels and the flux from
241 glucose to lactate. Genetic manipulations such as RNA interference were not possible
242 since the measurement of dose-dependent acute effects was necessary. In each case, the
243 compounds considered have been reported to exhibit direct inhibition of the enzyme in
244 question and to our knowledge do not directly inhibit other enzymes in glycolysis.
245 Nevertheless the general specificity of these compounds is not established and off target
246 effects that exist are likely reduced by considering acute treatments using these agents.
247 We considered inhibiting glycolysis at three separate points along the pathway
248 that are predicted to have widely variable flux control of the pathway. In the beginning
249 of glycolysis we used 3PO, a compound that targets PFK2 thus inhibiting the
250 phosphofructokinase step(Schoors, De Bock et al. 2014). Next we considered
251 iodoacetate (IA), a compound that targets GADPH(Campbell-Burk, Jones et al. 1987).
252 Finally we used FX11, a compound that targets LDH was considered(Granchi, Roy et al.
253 2011).
254 In each case (Figs 4B-D) differential, complex, nonlinear responses of metabolite
255 levels to inhibiting glycolysis were observed. The exception was treatment with IA (Fig
256 4C) which exhibited an expected accumulation of intermediates upstream of GAPDH and
10 257 depletion of intermediates downstream of the target. We next measured the directly the
258 flux control coefficients for each compound. An analysis of the flux control (Figs 4E-G)
259 revealed several interesting responses. Strikingly, as predicted by the model, a negative
260 flux control was observed for targeting PFK implying that inhibiting this step in these
261 circumstances increases the glycolytic flux and Warburg Effect (Fig 4E). The largest
262 flux control was observed with inhibition of GAPDH (Fig 4F). Inhibition of LDH as
263 predicted also resulted in little flux control (Fig 4G). Together these findings confirm the
264 mechanisms of flux control of glycolysis predicted by the model and demonstrate the
265 novel regulation of glycolytic flux that can be differentially perturbed by
266 pharmacological compounds.
267 FBP status and signatures of glycolysis state
268 We have thus far observed experimentally the dynamic behavior of flux control in
269 glycolysis including both positive and negative flux control in the pathway and a high
270 variability of flux control depending on the point of inhibition in the pathway ranging
271 from large decreases, increases, and little effects on pathway flux. Having established the
272 complex relationships between glycolytic flux and susceptibility to specific targeted
273 inhibition of the pathway, we sought to investigate whether there was any predictive
274 capacity and new mechanisms of biochemical regulation related to these findings.
275 We noticed that Fructose-(1,6)-bisphosphate (FBP) levels exhibited highly
276 dynamic and counterintuitive behavior with each drug perturbation. An analysis of
277 metabolite levels across a series of 14 conditions in triplicate involving pharmacological
278 perturbations of PFK2, LDH, and GAPDH at different concentrations and two separate
279 vehicle treatments (Fig 5A) revealed large magnitude, dynamic responses in FBP levels.
11 280 We next investigated the extent that FBP levels could characterize the metabolic state of
281 glycolysis. The simulated PDF of FBP levels exhibited a bimodal distribution (Fig 5B)
282 consisting of a state of low FBP where the concentration was in the high micromolar
283 range. In addition there existed a state of FBP where the concentration was several
284 orders of magnitude high in the millimolar range. When demarcating the experiments
285 into two groups (high and low FBP) we correlated the levels with lactate flux
286 experimentally (Fig 5C, Fig 5E) and found the results to match those observed
287 computationally (Fig 5D, Fig 5F). In addition correlations in these two states with the
288 remainder of the concentrations of glycolytic intermediates agreed well with experiments.
289 Together these findings suggest in addition to the model being able to capture a diverse
290 set of experimental metabolic conditions, the FBP status in cells was able to determine
291 the state of glycolysis and its rate-limiting steps.
292 A unified model of aerobic glycolysis
293 Together the combined computational model, metabolite profiling, and flux
294 analysis points to a different picture of glycolysis (Figure 6). When the levels of FBP are
295 low, metabolite levels of glycolytic intermediates tend to be more evenly distributed
296 across the pathway. In this circumstance, flux through the pathway is controlled largely
297 through the initial steps in glycolysis involving hexokinase and phosphofructokinase.
298 Bottlenecks downstream of these canonical rate-limiting steps are not affecting flux
299 through the pathway. Under these conditions, FBP is also not allosterically activating
300 pyruvate kinase. In contrast, when the levels of FBP are high, there is a disconnect in the
301 relative concentration of glycolytic intermediates that is marked by a separation between
302 upper and lower glycolysis at the GAPDH step. In this case, there is an accumulation of
12 303 intermediates in upper glycolysis, most notably FBP and a depletion of intermediates
304 downstream of GAPDH. Under these circumstances, GAPDH exerts control as the most
305 rate-determining step in the pathway since increased activity through GAPDH will serve
306 then to create a balance along the pathway by pulling the metabolites from upper
307 glycolysis into lower glycolysis. Under these conditions, the beginning steps of
308 glycolysis can exert negative control on the pathway since inhibiting them will result in
309 even greater increases in the intermediates in upper glycolysis. This state has analogies
310 with a recently observed state of glycolysis observed in yeast where an accumulation of
311 FBP leads to cellular toxicity(van Heerden, Wortel et al. 2014). Notably in this case, in
312 order to balance the fluxes in higher and lower glycolysis, an imbalance in the
313 concentrations of metabolites in upper and lower glycolysis results.
314 Discussion
315 Together our analysis yields a comprehensive, quantitative framework for
316 understanding glycolysis and its regulation in the context of the Warburg Effect.
317 Historically, glycolysis is also thought to have a rate-limiting step at several points in the
318 pathway(Chance and Hess 1956; Wu 1965). These points correspond to positions in the
319 pathway where large free energy differences arise including the ATP-coupled enzymes
320 Hexokinase, Phosphofructokinase, and Pyruvate Kinase(Rose and Warms 1966;
321 Rapoport, Heinrich et al. 1976; Hue and Rider 1987). Surprisingly, we identified a strong
322 context-dependence with both positive and negative control in glycolysis at each of these
323 steps. In the case of inhibiting flux through PFK, the observed negative control in
324 conditions implies that inhibiting this point in the pathway leads to increased rates of
13 325 fermentation providing a possible explanation for why its efficacy may be more prevalent
326 in stromal cells(Schoors, De Bock et al. 2014).
327 Unexpectedly, GAPDH was found to be a recurrent rate-controlling step in
328 aerobic glycolysis. This finding, first documented to our knowledge in parasitic bacteria
329 feeding on high glucose(Bakker, Michels et al. 1999), is in contrast to the longstanding
330 notion that GAPDH is not a limiting flux through glycolysis with the activity of enzymes
331 such as hexokinase, phosphofructokinase, and pyruvate kinase thought to be limiting. In
332 the case of GAPDH, the bottleneck occurs due to its unique placement in the pathway
333 where it can be regulated by ATP, NAD+, and the levels of glucose-derived intermediates
334 in the pathway that affects the thermodynamics of glycolysis. There are multiple
335 mechanisms that lead to this finding. ATP consumption has previously been reported to
336 control the rate of glycolysis and this effect likely occurs to some extent through
337 GAPDH(Racker 1976; Locasale and Cantley 2011; Lunt and Vander Heiden 2011).
338 NAD+ regeneration that is mediated by the malate-aspartate shuttle and lactate
339 dehydrogenase also affects flux through glycolysis(DeBerardinis, Lum et al. 2008;
340 Locasale and Cantley 2011). In addition, the activity of the pathway upstream and
341 downstream of GAPDH changes the balance of the levels of intermediates in glycolysis
342 and results in driving the thermodynamics of the reactions out of equilibrium also can
343 result in greater flux control(Noor, Bar-Even et al. 2014). Each of these mechanisms
344 separately or together acts to allow for GAPDH to exert flux control over the glycolytic
345 pathway.
346 Enzymes along glycolysis that are believed to control flux have many
347 documented regulatory mechanisms. For example pyruvate kinase and
14 348 phosphofructokinase have numerous small molecule effectors and post-translational
349 modifications that affect their activities(Mor, Cheung et al. 2011; Chaneton and Gottlieb
350 2012; Keller, Tan et al. 2012; Yi, Clark et al. 2012). It is notable that GAPDH also is
351 subject to multiple forms of regulation including post-translational modifications such as
352 nitrosylation and reactive oxygen species (ROS) that interacts with the catalytic cysteine
353 in GAPDH to inhibit its activity(Gaupels, Kuruthukulangarakoola et al. 2011; Tristan,
354 Shahani et al. 2011; Moellering and Cravatt 2013). In the context of ROS, it is tempting
355 to speculate that alterations in ROS could lead to selective modulation of glycolytic flux
356 as has been suggested to occur with pyruvate kinase(Anastasiou, Poulogiannis et al.
357 2011). While ROS-mediated inhibition is unlikely in conditions of exponential growth, it
358 may be more apparent in physiological conditions of hypoxia and glucose deprivation
359 with high concentrations of ROS. Another critical aspect of the flux control that GAPDH
360 exerts over the glycolytic pathway is high expression of GAPDH in cells undergoing
361 aerobic glycolysis. Indeed, reports of quantitative protein abundance in mammalian cells
362 have identified enzymes in the pathway glycolysis as the most highly expressed
363 collective of proteins in cells(Moghaddas Gholami, Hahne et al. 2013). Interestingly, it
364 was found that within glycolysis, GAPDH is often the mostly highly concentrated protein
365 in glycolysis suggesting that the role of this high expression in these cases is to support
366 the increased amount of glycolytic flux in these cells. Nevertheless, although
367 mechanisms that regulate phosphofructokinase and pyruvate kinase for example have
368 been shown to mediate cell growth and proliferation, whether regulatory mechanisms of
369 GAPDH have functional roles in cell growth and proliferation related to aerobic
370 glycolysis is not known.
15 371 Two states of glycolysis were observed with different extents of flux control,
372 tendencies for aerobic glycolysis, and concentration patterns along glycolysis. Notably
373 the FBP levels have implications on the activity of pyruvate kinase that is also
374 allosterically activated by FBP. At low FBP concentration, pyruvate kinase is not
375 activated by FBP but this occurs only in the high FBP state. This finding could have
376 implications in understanding the contexts in which pharmacologically activating
377 pyruvate kinase may have efficacy. Furthermore, it remains to be seen if any signature of
378 these metabolite states could manifest in the alterations of peripheral metabolism
379 involving pathways whose fluxes emanate from glycolysis. If this were the case, then a
380 tempting possibility would be that these states of glycolysis could be predicted from
381 measurements of peripheral metabolites that could be excreted into circulation allowing
382 for the possibility of developing serum biomarkers for the status of glycolysis in tumors.
383 Finally, the surge of interest in metabolism and its contribution to pathogenesis
384 has created an expectation that therapeutics that target glucose metabolism will be
385 clinically successful. Targeting glycolysis in metabolism has raised interest but is limited
386 by the development of biomarkers that could determine the contexts in which targeting
387 glucose metabolism in malignancy would be efficacious(Vander Heiden 2011; Galluzzi,
388 Kepp et al. 2013; Vander Heiden 2013). From our model analysis, the consequences of
389 inhibiting glycolysis appear enormously complex which would limit the ability of
390 biomarker development due to the nonlinear mechanisms that determine the response of
391 the pathway to a drug perturbation. Nevertheless, with the development of these
392 predictive models that can capture diverse behaviors of glycolysis and thus make
16 393 predictions about drug response, it is worth considering whether they may have
394 predictive capacity in pre-clinical and clinical settings.
395 Acknowledgements
396 We are grateful to Chi V Dang, Navdeep Chandel, Dimitris Anastasiou, and members of
397 the Locasale lab for helpful comments.
398 Funding
399 YPH is supported by an Albert J. Ryan fellowship and a Stuart H. Q. and Victoria Quan
400 predoctoral fellowship in neurobiology. JWL is supported by awards R00CA168997 and
401 R01AI110613 from the National Institutes of Health and a Future Leader award from the
402 International Life Sciences Institute.
403 Competing interests 404 405 A patent related to this work has been filed. 406
407 References
408 Barber, R. D., D. W. Harmer, et al. (2005). "GAPDH as a housekeeping gene: analysis of 409 GAPDH mRNA expression in a panel of 72 human tissues." Physiol Genomics 410 21(3): 389-395. 411 Campbell-Burk, S. L., K. A. Jones, et al. (1987). "31P NMR saturation-transfer 412 measurements in Saccharomyces cerevisiae: characterization of phosphate 413 exchange reactions by iodoacetate and antimycin A inhibition." Biochemistry 414 26(23): 7483-7492. 415 Cascante, M., L. G. Boros, et al. (2002). "Metabolic control analysis in drug discovery 416 and disease." Nat Biotechnol 20(3): 243-249. 417 Chance, B. and B. Hess (1956). "On the control of metabolism in ascites tumor cell 418 suspensions." Ann N Y Acad Sci 63(5): 1008-1016. 419 Daniels, B. C., Y. J. Chen, et al. (2008). "Sloppiness, robustness, and evolvability in 420 systems biology." Curr Opin Biotechnol 19(4): 389-395. 421 Fell, D. A. (1992). "Metabolic control analysis: a survey of its theoretical and 422 experimental development." Biochem J 286 ( Pt 2): 313-330. 423 Folger, O., L. Jerby, et al. (2011). "Predicting selective drug targets in cancer through 424 metabolic networks." Mol Syst Biol 7: 501. 425 Galluzzi, L., O. Kepp, et al. (2013). "Metabolic targets for cancer therapy." Nat Rev Drug 426 Discov 12(11): 829-846.
17 427 Granchi, C., S. Roy, et al. (2011). "Discovery of N-hydroxyindole-based inhibitors of 428 human lactate dehydrogenase isoform A (LDH-A) as starvation agents against 429 cancer cells." J Med Chem 54(6): 1599-1612. 430 Hamanaka, R. B. and N. S. Chandel (2012). "Targeting glucose metabolism for cancer 431 therapy." J Exp Med 209(2): 211-215. 432 Hue, L. and M. H. Rider (1987). "Role of fructose 2,6-bisphosphate in the control of 433 glycolysis in mammalian tissues." Biochem J 245(2): 313-324. 434 Koppenol, W. H., P. L. Bounds, et al. (2011). "Otto Warburg's contributions to current 435 concepts of cancer metabolism." Nat Rev Cancer 11(5): 325-337. 436 Liu, X., Z. Ser, et al. (2014). "Development and quantitative evaluation of a high- 437 resolution metabolomics technology." Anal Chem 86(4): 2175-2184. 438 Marusyk, A., V. Almendro, et al. (2012). "Intra-tumour heterogeneity: a looking glass for 439 cancer?" Nat Rev Cancer 12(5): 323-334. 440 Molenaar, D., R. van Berlo, et al. (2009). "Shifts in growth strategies reflect tradeoffs in 441 cellular economics." Mol Syst Biol 5: 323. 442 Rapoport, T. A., R. Heinrich, et al. (1976). "The regulatory principles of glycolysis in 443 erythrocytes in vivo and in vitro. A minimal comprehensive model describing 444 steady states, quasi-steady states and time-dependent processes." Biochem J 445 154(2): 449-469. 446 Rose, I. A. and J. V. Warms (1966). "Control of glycolysis in the human red blood cell." 447 J Biol Chem 241(21): 4848-4854. 448 Schilling, C. H., S. Schuster, et al. (1999). "Metabolic pathway analysis: basic concepts 449 and scientific applications in the post-genomic era." Biotechnol Prog 15(3): 296- 450 303. 451 Schoors, S., K. De Bock, et al. (2014). "Partial and transient reduction of glycolysis by 452 PFKFB3 blockade reduces pathological angiogenesis." Cell Metab 19(1): 37-48. 453 Schoors, S., K. De Bock, et al. (2014). "Partial and Transient Reduction of Glycolysis by 454 PFKFB3 Blockade Reduces Pathological Angiogenesis." Cell Metab 19(1): 37- 455 48. 456 Shlomi, T., T. Benyamini, et al. (2011). "Genome-scale metabolic modeling elucidates 457 the role of proliferative adaptation in causing the Warburg effect." PLoS Comput 458 Biol 7(3): e1002018. 459 van Heerden, J. H., M. T. Wortel, et al. (2014). "Lost in transition: start-up of glycolysis 460 yields subpopulations of nongrowing cells." Science 343(6174): 1245114. 461 Vander Heiden, M. G. (2011). "Targeting cancer metabolism: a therapeutic window 462 opens." Nat Rev Drug Discov 10(9): 671-684. 463 Vazquez, A., J. Liu, et al. (2010). "Catabolic efficiency of aerobic glycolysis: the 464 Warburg effect revisited." BMC Syst Biol 4: 58. 465 Warburg, O., F. Wind, et al. (1927). "The Metabolism of Tumors in the Body." J Gen 466 Physiol 8(6): 519-530. 467 Wu, R. (1965). "Rate-Limiting Factors in Glycolysis and Inorganic Orthophosphate 468 Transport in Rat Liver and Kidney Slices." J Biol Chem 240: 2373-2381. 469 470 471 472
18 473 Figure 1 – A quantitative model and statistical simulation method captures the 474 diversity of metabolic states observed in tumor and proliferating cells 475 476 A.) Schematic of the glycolysis model with chemical reactions and allosteric points of 477 regulation described. Abbreviations: GLC – glucose, G6P – glucose-6-phosphate, F6P – 478 fructose-6-phosphate, FBP – fructose-1,6,-bisphosphate, F26BP – fructose-2,6,- 479 bisphosphate, GAP – glcyceraldehyde-3-phosphate, DHAP – dihydroxyacetone 480 phosphate, BPG – 1,3 bisphosphoglycerate, 3PG – 3-phosphoglycerate, 2PG – 2- 481 phosphoglycerate, PEP – phosphoenolpyruvate, PYR – pyruvate, SER – Serine, GLY – 482 glycine, Lac – Lactate, MAL – Malate, ASP – Aspartate, Pi – Inorganic phosphate, CI – 483 Creatine, PCI – Phosphphocreatine, GTR – Glucose transporter, HK – Hexokinase, PGI – 484 Phosphoglucoisomerase, PFK – Phosphofructokinase, ALD – Aldolase, TPI – 485 Triosephosphoisomerase, GAPDH – Glyceraldehyde-phosphate dehydrogenase, PGK – 486 phosphoglycerate kinase, PGM – Phosphoglycerate mutase, ENO – Enolase, PK – 487 Pyruvate kinase, LDH – Lactate dehydrogenase, MCT – Monocarboxylate transporter, 488 PDH – Pyruvate dehydrogenase, CK – Creatine kinase. B.) Overview of the algorithm 489 and simulation method. C.) Measured values of the NADH/NAD+ ratio across a 490 population of MCF10A breast epithelial cells. Three values of glucose concentration are 491 considered (0.5mM – blue, 5.5mM green, and 25mM red). D.) Calculated fluxes 492 (mM/hr) for glycolysis rate (Glycolysis) define as the rate of glucose to pyruvate, 493 pyruvate to lactate flux (LDH), rate of oxygen consumption (OxPhos), rate of NADH 494 turnover (NADH), and ATP turnover (ATPase). E.) Calculated Probability Density 495 Function (PDF) of NAD+ concentrations. F.) Calculated Probability Density Function 496 (PDF) of NADH/NAD+ ratio. G.) Calculated Probability Density Function (PDF) of 497 ATP concentrations. H.) Calculated Probability Density Function (PDF) of ATP/ADP 498 ratio. I.) Box plots showing the distribution of concentrations computed from the 499 simulation for each intermediate in glycolysis. 500 501 Figure 2 - Evaluation of the statistics of the Warburg Effect and relationships to 502 other variables in metabolism 503 504 A.) Probability Density Function (PDF) of the Warburg Effect (WE) defined as the ratio 505 of flux through LDH to that of flux into the mitochondria. B.) Pearson correlations of 506 intermediate metabolite levels in glycolysis with the extent of the Warburg Effect (WE). 507 C.) Pearson correlations of the expression levels of glycolytic enzymes with the extent of 508 the Warburg Effect (WE). D.) Pearson correlations of coupled metabolic parameters with 509 the extent of the Warburg Effect (WE). 510 511 Figure 3 - Metabolic control analysis and its relationship to metabolic variables 512 513 A.) Schematic of workflow for global sensitivity analysis. After the model is constructed 514 and feasible solutions obtained, each realization of glycolysis is subjected to Metabolic 515 Control Analysis (MCA). The resulting analysis is then subject to a statistical evaluation. 516 B.) (left) Box plots of flux control coefficient (FCC) for lactate production for each 517 enzymatic step in glycolysis (FCC = dlnJlac/dln Ei) where Jlac is the rate of pyruvate th 518 conversion to lactate and Ei is the i enzyme in glycolysis for each step of glycolysis.
19 519 (right) Box plots of flux control coefficient (FCC) for lactate production for Oxygen 520 consumption (OxPhos) and ATP consumption (ATP). C.) Pearson correlations between 521 lactate FCC values for each step in glycolysis. Heat map is colored ranging from the 522 minimum value (green) to the maximum value (purple). D.) Pearson correlations 523 between metabolite concentrations in glycolysis and lactate FCC values for each step in 524 glycolysis. Heat map is colored ranging from the minimum value (green) to the 525 maximum value (purple). E.) Pearson correlations between metabolic parameters and 526 lactate FCC values for each step in glycolysis. Heat map is colored ranging from the 527 minimum value (green) to the maximum value (purple). F.) Pearson correlations 528 between ratios and lactate FCC values for each step in glycolysis. 529 530 Figure 4 – Experimental flux control coefficients 531 532 A.) Schematic of experimental flux control analysis. Cells are pre-incubated with 13C 533 glucose and treated with differing concentrations of inhibitors that target glycolysis at 534 different points in the pathway. Media and intracellular metabolites are collected, subject 535 to (liquid chromatography high resolution mass spectrometry) LC-HRMS, and subjected 536 to flux analysis. B.) Results obtained from treatment with 3PO an inhibitor of PFK2. C.) 537 Results obtained from treatment with IA an inhibitor of GAPDH. D.) Results obtained 538 from treatment with FX11 and inhibitor of LDH. For B-D, the plot on the left shows the 539 measured glucose to lactate flux as a function of the inhibitor concentration (left) and 540 estimated fraction of enzyme inhibited (right). 541 542 Figure 5 – FBP levels predict distinct mechanisms in glycolysis 543 544 A.) Variation of metabolite levels across glycolysis over 14 conditions in triplicate 545 resulting in 42 independent experiments involving cells growing in basal conditions and 546 those with differing extents of inhibition of glycolysis from results in Figure 4. B.) 547 Simulated distribution of FBP levels in glycolysis. C.) Correlation of lactate flux with 548 measured glycolytic intermediates for low FBP levels. The left panel shows data for FBP 549 and right panel reports the values of the Spearman correlation coefficients for each 550 metabolite. D.) Simulated correlation of lactate flux with metabolite levels of glycolytic 551 intermediates in conditions of low FBP levels. E.) Correlation of lactate flux with 552 measured glycolytic intermediates for high FBP levels. The left panel shows data for 553 FBP and right panel reports the values of the Spearman correlation coefficients for each 554 metabolite. F.) Simulated correlation of lactate flux with metabolite levels of glycolytic 555 intermediates in conditions of low FBP levels. 556 557 Figure 6 – A unified model of aerobic glycolysis 558 559 A unified picture of flux control in aerobic glycolysis. (left) Under conditions where 560 there is an accumulation of intermediates in upper glycolysis and depletion of 561 intermediates in lower glycolysis a bottleneck exists at the step involving GAPDH. This 562 bottle neck is due to the status of energy and redox metabolism and the thermodynamics 563 of the pathway that together mediate the flux through GAPDH. As a result, inhibiting 564 flux through glycolysis is most sensitive to a perturbation in GAPDH activity. (right)
20 565 Under conditions where the metabolites in glycolysis are distributed more evenly with 566 levels together being either high or low, no such bottleneck exists. Instead flux through 567 glycolysis leading to lactate production is most determined by the canonical pacemaking 568 steps in glycolysis involving PFK and HK. The relative levels of glycolytic intermediates 569 are denoted by the size of the text. 570
571 Supplementary File 1
572 Equations and parameters used for the glycolysis model
573
21 574 Materials and Methods 575 576 Kinetic model of glycolysis 577 578 The model includes a compartment involving enzymes in glycolysis and additional 579 compartments involving with reactions that are coupled to glycolysis. The following 580 compartments are considered in addition to the enzymes in glycolysis are considered: 581 582 1.) Glucose uptake through the glucose transporter 583 2.) Lactate dehydrogenase (LDH) activity and lactate transport through 584 the monocarboxylate transporter (MCT) 585 3.) Oxygen consumption, transport and activity of oxidative 586 phosphorylation (OxPhos) 587 4.) ATP-buffering mechanisms involving adenylate Kinase, creatine 588 Kinase, and ATPase activity, 589 5.) NADH/NAD+ mediated mitochondrial shuttles including the Malate- 590 Aspartate Shuttle and the Glycerol-3-Phosphate Shuttle. 591 592 More generally glycogen metabolism, pentose phosphate pathway and alanine 593 biosynthesis could also be included but are omitted since the conclusions drawn in this 594 study do not depend on their activities. A schematic representation of the kinetic model 595 and resulting network is shown in Fig 2A. 596 597 We first introduce notation and other conventions. Each symbol indicates the respective 598 concentration. A subscript “0” refers to the steady-state value. Reaction rate are 599 expressed in millimoles per hour per unit intracellular volume. Together with initial state
600 vectors , of metabolites and fluxes respectively. 601 The dynamics of the system are therefore formulated as initial value problem for ordinary 602 differential equations (ODE). Starting parameter values based on published data are 603 listed below. Reaction rates are defined through a consideration of the respective enzyme 604 mechanisms with forming feed forward and feed back regulation giving rise to allosteric 605 activation and inhibition. 606 607 Therefore, the model is designed to describe: a) steady-state and dynamic behavior of the J 608 cell energy metabolism states, including the Warburg effect (W = Lac ), energy state JOx 609 (ATP/ADP ratio), redox state (NADH/NAD+ ratio) together with glucose, lactate and 610 oxygen supply through exchange fluxes from the intercellular and extracellular 611 compartment, b) steady states and time courses of all variables of metabolic network, and 612 c) effects of metabolic parameters perturbations on the overall system output. Cellular 613 energy homeostasis through ATP is supported by several mechanisms with different 614 relaxation times and regulation mechanisms: a) directly by glycolysis that converts 615 glucose into intracellular pyruvate, b) mitochondrial respiration through consumption of 616 pyruvate and oxygen via the TCA cycle, and c) the buffering effect of creatine kinase that 617 facilitates the reversible reaction of phosphocreatine (PCr) with ADP to produce creatine 618 (Cr) and ATP, and d) adenylate kinase activity that catalyzes interconversion of adenine
22 619 nucleotides: 2ADP ⇔ ATP + AMP and e) the additional NADH pool produced in 620 cytosol and transported to mitochondrion by different shuttle mechanisms. For oxygen 621 consumption, we assumed that mitochondrial respiration (O2 consumption) depends on 622 cellular pyruvate and oxygen concentrations and that respiratory chain activity is 623 activated by ADP concentration. 624 The state of the system is represented by the state vector of time-dependent metabolite 625 concentrations Cn, (n=1,…, N) and includes 27 state variables whose names, balance 626 equations and steady-state values are presented below. The model also includes 3 mass 627 conservations laws, which reduces the number of state variables. 628 629 The temporal profile of the system is governed by the set of ODE based on model 630 bionetwork that distinguish media and cellular domains. For the metabolite i in the 631 intracellular compartment, the general form is: 632
633 ∑ ∑ , (7)
634
635 where the intracellular concentration of species i is is the net transport flux for
636 boundary species i between media and cell; , are normalized reaction fluxes
637 that produce (j) or utilize (k) cellular species i; and are corresponding 638 stoichiometric coefficients. For extracellular boundary metabolites in the media, the 639 dynamic mass balance has the following general form: 640
641 , (8)
642 643 where the concentration of extracellular (e) species is and rie is the ratio of cell 644 volume to media volume. To ensure that steady states are obtained during perturbations 645 of parameters without loss of generality we assume that the media boundary metabolites 646 have constant concentrations. The transport of boundary species is taken to be either 647 facilitated (glucose, lactate, serine, glycine) or passive (oxygen). For passive diffusion of 648 oxygen the equation for the net transport flux is: 649 ( ) 650 , (9) 651
652 where is the effective rate constant for passive diffusion, and and are 653 medium and intracellular oxygen concentrations. For facilitated transport, the equation 654 for the net transport flux is: 655
( )
656 , (10)
657
658 where is the extracellular concentration for species i, maximal transport
659 rate, and is the Michaelis-Menten constant for transport. NADH transport from 660 cytosol to mitochondria is mediated by malate-aspartate and glycerol phosphate shuttles.
23 661 We modeled the NAD+-mediated mitochondrial shuttle flux from NADH to NAD+ by 662 assuming that the total shuttle flux is balanced with the NADH-generation reactions 663 involving LDH and PHGDH. 664 665 (11) 666 667 668 When possible, in order to minimize the number of parameters we utilized a “one-step 669 binding enzyme mechanism” with a rate law of the form(Segel 1975): 670
∏ ∏
( ) 671 ( ) , (12) ∏ ∏
672 673 where ( ) is a control function that accounts for the effects of activation , or 674 inhibition . A general form for the control function is(Liebermeister and Klipp 2006; 675 Liebermeister and Klipp 2006): 676 [ ] ⁄ ([ ] ) 677 ( ) , (13)
⁄([ ] ) { 678 where [ ] and [ ] are the concentrations of the activator or inhibitor, and are the 679 corresponding activation and inhibition constants. With this convention, there are 4 (or 5 680 including the control function) independent parameters for every metabolic flux with a 681 one-step binding mechanism. For fluxes with no allosteric regulation, ( ) . 682 683 For all metabolic fluxes involving NAD+/NADH oxidoreductase activity, we utilized a 684 more complex rate law than that of a one step binding reaction(Cornish-Bowden 2012). 685 We chose to consider a more complicated rate-law since our initial observations indicated 686 that a one-step binding mechanism produced numerical instabilities in the solutions. We 687 therefore considered a general rate law corresponding to a random bi-bi mechanism (for 688 LDH and PHGDH) and a random ter-bi reaction for GAPDH. For example, in its general 689 form the rate law for LDH is: 690
691 (14)
692 693 694 However, it has also been suggested that the enzymatic reaction for oxidoreductase 695 activity proceeds in an ordered fashion resulting in a rate law of the form: 696
24
697 (15)
698 699 When considering this mechanism, it was found that statistical evaluation of the model 700 was robust to changes in the choice of rate law. 701 702 703 The rate equations for each metabolic reaction and metabolic parameters values are given 704 below. Taking into account additional thermodynamic constraints by invoking the 705 Haldane equation that relates the forward and reverse fluxes and their Vmax values 706 allowed for a further reduction in the number of independent parameters to three 707 parameters per reaction flux. The Haldane equation has the form: 708
709 , (16)
710 711 where is the reaction apparent equilibrium constant:
712 ( ) , and is standard reaction Gibbs free energy. values for 713 glycolytic reactions are listed below. 714 715 We first used two independent sets of experimental data from a compendium of steady- 716 state metabolite concentrations of liver cells and steady-state fluxes of DB1 melanoma 717 cells evaluated using a cultured bioreactor(Konig, Bulik et al. 2012; Shestov, Mancuso et 718 al. 2013). The model was further validated by a comparison of measurements of redox 719 status, assessment of ATP, ADP, and AMP concentrations. Together those data were able 720 to generate a thermodynamically feasible and experimentally observable model of 721 glycolysis that was then used as the starting point for exhaustive Monte Carlo simulations 722 and coupled metabolic control analysis. 723 724 Monte carlo simulations for global sensitivity analysis 725 726 The specific aim of this work is to enumerate the variables within and coupled to 727 glycolysis that determine the extent of aerobic glycolysis. We therefore developed a 728 novel algorithm to assess these features. The algorithm involves a global sensitivity 729 analysis based on a Monte Carlo method. The Monte Carlo analysis allows for sampling 730 of parameter space over a broad range of simultaneous variations of parameters (enzyme 731 expression levels) followed by statistical assessment of the resulting solution. The idea 732 of this method is to inject uncertainty of the parameters in the model by randomly 733 selecting parameters values from uniform probability distributions. This was achieved by 734 a Monte Carlo method using a randomly drawn set of parameters. The range of 735 parameters chosen with uniform sampling was within two orders of magnitudes of each 736 Vmax (which is proportional to enzyme activity level and was in the range of 10 times 737 less and 10 times greater than the initial Vmax value). Such a sampling was chosen to be 738 large enough to cover all feasible solutions of aerobic glycolysis. The sampling was 739 carried out using a Latin Hypercube sampling method(Oguz, Laomettachit et al. 2013).
25 740 For each chosen set of random parameter vectors the model was simulated between 2000 741 and 5000 times and its output was calculated. Briefly we divided the range of the i-th 742 normalized parameter into n (n=2000-5000) subintervals of equal size. Then we 743 randomly sample n values (e.g pi, i=1,…,n), one from each subinterval, for the i-th 744 parameter. We next randomly permuted the n values for each parameter to get the 745 parameter vector. We then evaluated the following: the Warburg effect value, energy and 746 redox states, metabolite steady state concentrations and fluxes and Flux Control 747 Coefficients (FCCs). The flux control coefficient that an enzyme Ei exerts on the lactate 748 flux JLac is defined as(Heinrich and Rapoport 1974; Fell 1992; Shestov, Barker et al. 749 2013): 750
¶ln JLac 751 FCCi = (17) ¶ln Ei 752 753 To compute the FCC values numerically, we considered a perturbation 0.01 times of the 754 enzyme value and then evaluated the change in flux. 755 756 To statistically evaluate the output parameter sensitivity we quantitatively compared the 757 probability distribution functions for model output parameters and correlated those 758 parameters with each other. The model was implemented in Matlab as a system of 27 759 ordinary differential equations (ODEs) with an ODE solver designed for stiff ODE 760 systems. 761 762 Cell culture and metabolite extraction 763 764 HCT116 cells were cultured with a growth medium, which contains RPMI 1640, 10 % 765 ells were 766 obtained as a gift from Lewis Cantley’s laboratory. Cells were cultured in 37 °C with 5 5 767 5% CO2. For treatments, cells were seeded in 6-well plate at a density of 2×10 to 5×10 768 cells per well. After overnight incubation, full growth media were removed and cells 769 were washed with 2 ml PBS before the addition of RPMI media (without glucose), 770 supplemented with 10% dialyzed and heat inactivated FBS, 100 U/ml penicillin, 100 771 -glucose, or 5 mM 13C-U-glucose 772 (Cambridge Isotope Laboratory). For drug treatments and flux measurements, full 773 growth media were replaced with fresh growth media, containing either 0.1% DMSO, or 774 the concentration of the indicated drug. Media were then collected at 30, 60, 90, and 120 775 minutes after incubation. From 20µl media, 80µl of ice cold H2O was added, together 776 with 400µl ice cold methanol (Fisher, Optima LC/MS grade). After vigorous vortexing, 777 the solution was then centrifuged at 20 000g at 4°C for 10min and then the supernatant 778 was dried under vacuum. At 120 minutes, the media were removed as completely as 779 possible, and then 6-well plates were immediately placed on dry ice, followed by the 780 addition of 1 ml extraction solvent, 80% MeOH/H2O (Fisher, Optima LC/MS Grade), 781 which was pre-cooled in -80 °C freezer for at least 1 hour. The dishes were then 782 transferred to the -80 °C freezer. The plates were left for 15 min and then cells were 783 scraped into the solvent on dry ice and then transferred to two 1.7 ml eppendorf tubes, 784 and centrifuged with the speed of 20 000 g at 4 °C for 10 min. Metabolite extracts are
26 785 prepared from three separate wells to make three replicate samples. The supernatant is 786 then transferred to new eppendorf tubes, and dried under vacuum. For analysis, each 787 extract was then re-constituted into water (15 μl for cell extract and 50 μl for medium 788 extract) and then diluted with an equal volume of 50% Methanol/Acetonitrile. Finally, 5 789 μl was injected into the column for analysis. 790 791 Flux analysis 792 793 Absolute concentrations of 13C lactate were first measured by mixing a standard of 794 unlabeled lactate with a defined concentration into the medium. For each calculated flux, 795 an estimation of the flux from glucose to lactate was obtained from the slope of the time 796 course of 13C lactate production using the time points of media collection described 797 above. Slopes were computed using Graphpad Prism with time courses determined to be 798 linear from the goodness of fit (R2>0.98 with few exceptions). For corresponding plots 799 for different agents, fraction of inhibition was computed from Ki values that were taken 800 based on previous reports(Foxall, Brindle et al. 1984; Le, Cooper et al. 2010; Telang, 801 Clem et al. 2012). 802 803 Mass spectrometry 804 805 The Q Exactive Mass Spectrometer (QE-MS) is equipped with a heated electrospray 806 ionization probe (HESI), and the relevant parameters are as listed: heater temperature, 807 120 °C; sheath gas, 30; auxiliary gas, 10; sweep gas, 3; spray voltage, 3.6 kV for positive 808 mode and 2.5 kV for negative mode. Capillary temperature was set at 320 °C, and S-lens 809 was 55. A full scan range from 60 to 900 (m/z) was used. The resolution was set at 70 810 000. The maximum injection time was 200 ms with typical injection times around 50 ms. 811 These settings resulted in a duty cycle of around 550 ms to carry out scans in both 812 positive and negative mode. Automated gain control (AGC) was targeted at 3,000,000 813 ions. 814 815 Liquid chromatography 816 817 Liquid chromatography (Ultimate 3000 UHPLC) is coupled to the QE-MS for metabolite 818 separation and detection. An Xbridge amide column (100 x 2.1 mm i.d., 3.5 μm; Waters) 819 is employed for compound separation. The mobile phase A is 20 mM ammonium acetate 820 and 15 mM ammonium hydroxide in water with 3% acetonitrile, pH 9.0, as described 821 above, and mobile phase B is acetonitrile. A linear gradient was used as follows: 0 min, 822 85% B; 1.5 min, 85% B, 5.5 min, 35% B; 10min, 35% B, 10.5 min, 35% B, 14.5 min, 823 35% B, 15 min, 85% B, and 20 min, 85% B. The flow rate was 0.15 ml/min from 0 to 10 824 min and 15 to 20 min, and 0.3 ml/min from 10.5 to 14.5 min. All solvents are LC-MS 825 Optima grade and purchased from Fisher Scientific. 826 827 NADH/NAD+ imaging 828 829 Human mammary epithelial MCF-10A cells (CRL-10317, ATCC) stably expressing 830 Peredox-NLS were generated and cultured as described(Debnath, Muthuswamy et al.
27 831 2003; Hung, Albeck et al. 2011). 2-4 days prior to imaging, ~500 cells were plated onto 832 the center of each well of a 96-well plate. On the day of the experiment, cells were placed 833 in custom DMEM/F12 (Gibco) containing no glucose and glucose (Sigma) was 834 supplemented to the levels mentioned. Fluorescence images were acquired using a Nikon 835 inverted Eclipse Ti microscope, equipped with a Nikon 20×/0.75 Plan Apo objective, 3 836 different regions of interest chosen, images sequentially acquired every 8 min with 50- 837 100 ms exposure and 2×2 binning. Using custom MATLAB algorithm previously 838 developed, we subtracted background, set a threshold for cell segmentation, and analyzed 839 the data as previously described(Hung, Albeck et al. 2011). The concentration of glucose 840 is maintained by considering a culture system in which cells are seeded at low density 841 and media is present in vast excess. An estimate of glucose maintenance in the media in 842 the low glucose condition can be considered using values the glucose uptake rate of the 843 cells(~100fmol/cell/hr), the cell number (~2000), the volume of media used (400 μL), 844 and concentration of glucose in the media (750μM, 500μM from supplementation + 845 250μM from the Horse Serum). Thus in 24 hours, we estimate that about 5nmols of 846 glucose are consumed. The media contains roughly 200 nmols of glucose which is in 847 excess of the amount consumed by the cells. 848 849 Data analysis 850 851 Raw data collected from the QE-MS is processed using Sieve 2.0 (Thermo Scientific). 852 Peak alignment and detection are performed according to the protocol described by 853 Thermo Scientific. For a targeted metabolite analysis, the method “peak alignment and 854 frame extraction” is applied. An input file of theoretical m/z and detected retention time 855 known metabolites is used for targeted metabolite analysis with data collected in both 856 positive and negative mode. m/z width is set at 10 ppm. The output file including 857 detected m/z and relative intensity in different samples is obtained after data processing. 858 For resulting simulation data, hierarchical clustering was carried out using spearman 859 ranked correlations and the Gene-e software package (Broad Institute). Box-plots 860 (25%/75% percentile, mean and median) was calculated and made with the Graphpad 861 Prism software package. 862 863 References 864 865 Anastasiou, D., G. Poulogiannis, et al. (2011). "Inhibition of pyruvate kinase M2 by reactive 866 oxygen species contributes to cellular antioxidant responses." Science 334(6060): 1278- 867 1283. 868 Bakker, B. M., P. A. Michels, et al. (1999). "What controls glycolysis in bloodstream form 869 Trypanosoma brucei?" J Biol Chem 274(21): 14551-14559. 870 Buxton, R. B. and L. R. Frank (1997). "A model for the coupling between cerebral blood flow 871 and oxygen metabolism during neural stimulation." J Cereb Blood Flow Metab 17(1): 64- 872 72. 873 Campbell-Burk, S. L., K. A. Jones, et al. (1987). "31P NMR saturation-transfer measurements in 874 Saccharomyces cerevisiae: characterization of phosphate exchange reactions by 875 iodoacetate and antimycin A inhibition." Biochemistry 26(23): 7483-7492. 876 Cascante, M., L. G. Boros, et al. (2002). "Metabolic control analysis in drug discovery and 877 disease." Nat Biotechnol 20(3): 243-249.
28 878 Chance, B. and B. Hess (1956). "On the control of metabolism in ascites tumor cell suspensions." 879 Ann N Y Acad Sci 63(5): 1008-1016. 880 Chaneton, B. and E. Gottlieb (2012). "Rocking cell metabolism: revised functions of the key 881 glycolytic regulator PKM2 in cancer." Trends Biochem Sci 37(8): 309-316. 882 Christofk, H. R., M. G. Vander Heiden, et al. (2008). "The M2 splice isoform of pyruvate kinase 883 is important for cancer metabolism and tumour growth." Nature 452(7184): 230-233. 884 Cornish-Bowden, A. (2012). Fundamentals of enzyme kinetics. Weinheim, Wiley-Blackwell. 885 Daniels, B. C., Y. J. Chen, et al. (2008). "Sloppiness, robustness, and evolvability in systems 886 biology." Curr Opin Biotechnol 19(4): 389-395. 887 DeBerardinis, R. J., J. J. Lum, et al. (2008). "The biology of cancer: metabolic reprogramming 888 fuels cell growth and proliferation." Cell Metab 7(1): 11-20. 889 Debnath, J., S. K. Muthuswamy, et al. (2003). "Morphogenesis and oncogenesis of MCF-10A 890 mammary epithelial acini grown in three-dimensional basement membrane cultures." 891 Methods 30(3): 256-268. 892 Ercan-Fang, N., M. C. Gannon, et al. (2002). "Integrated effects of multiple modulators on human 893 liver glycogen phosphorylase a." Am J Physiol Endocrinol Metab 283(1): E29-37. 894 Fell, D. A. (1992). "Metabolic control analysis: a survey of its theoretical and experimental 895 development." Biochem J 286 ( Pt 2): 313-330. 896 Folger, O., L. Jerby, et al. (2011). "Predicting selective drug targets in cancer through metabolic 897 networks." Mol Syst Biol 7: 501. 898 Foxall, D. L., K. M. Brindle, et al. (1984). "The inhibition of erythrocyte glyceraldehyde-3- 899 phosphate dehydrogenase. In situ PMR studies." Biochim Biophys Acta 804(2): 209-215. 900 Galluzzi, L., O. Kepp, et al. (2013). "Metabolic targets for cancer therapy." Nat Rev Drug Discov 901 12(11): 829-846. 902 Gaupels, F., G. T. Kuruthukulangarakoola, et al. (2011). "Upstream and downstream signals of 903 nitric oxide in pathogen defence." Curr Opin Plant Biol 14(6): 707-714. 904 Goldberg, R. N., Y. B. Tewari, et al. (2004). "Thermodynamics of enzyme-catalyzed reactions--a 905 database for quantitative biochemistry." Bioinformatics 20(16): 2874-2877. 906 Granchi, C., S. Roy, et al. (2011). "Discovery of N-hydroxyindole-based inhibitors of human 907 lactate dehydrogenase isoform A (LDH-A) as starvation agents against cancer cells." J 908 Med Chem 54(6): 1599-1612. 909 Hamanaka, R. B. and N. S. Chandel (2012). "Targeting glucose metabolism for cancer therapy." J 910 Exp Med 209(2): 211-215. 911 Heinrich, R. and T. A. Rapoport (1974). "A linear steady-state treatment of enzymatic chains. 912 General properties, control and effector strength." Eur J Biochem 42(1): 89-95. 913 Hue, L. and M. H. Rider (1987). "Role of fructose 2,6-bisphosphate in the control of glycolysis in 914 mammalian tissues." Biochem J 245(2): 313-324. 915 Hung, Y. P., J. G. Albeck, et al. (2011). "Imaging cytosolic NADH-NAD(+) redox state with a 916 genetically encoded fluorescent biosensor." Cell Metab 14(4): 545-554. 917 Israelsen, W. J., T. L. Dayton, et al. (2013). "PKM2 isoform-specific deletion reveals a 918 differential requirement for pyruvate kinase in tumor cells." Cell 155(2): 397-409. 919 Keller, K. E., I. S. Tan, et al. (2012). "SAICAR stimulates pyruvate kinase isoform M2 and 920 promotes cancer cell survival in glucose-limited conditions." Science 338(6110): 1069- 921 1072. 922 Konig, M., S. Bulik, et al. (2012). "Quantifying the contribution of the liver to glucose 923 homeostasis: a detailed kinetic model of human hepatic glucose metabolism." PLoS 924 Comput Biol 8(6): e1002577. 925 Koppenol, W. H., P. L. Bounds, et al. (2011). "Otto Warburg's contributions to current concepts 926 of cancer metabolism." Nat Rev Cancer 11(5): 325-337. 927 Le, A., C. R. Cooper, et al. (2010). "Inhibition of lactate dehydrogenase A induces oxidative 928 stress and inhibits tumor progression." Proc Natl Acad Sci U S A 107(5): 2037-2042.
29 929 Li, X., F. Wu, et al. (2011). "A database of thermodynamic properties of the reactions of 930 glycolysis, the tricarboxylic acid cycle, and the pentose phosphate pathway." Database 931 (Oxford) 2011: bar005. 932 Liebermeister, W. and E. Klipp (2006). "Bringing metabolic networks to life: convenience rate 933 law and thermodynamic constraints." Theor Biol Med Model 3: 41. 934 Liebermeister, W. and E. Klipp (2006). "Bringing metabolic networks to life: integration of 935 kinetic, metabolic, and proteomic data." Theor Biol Med Model 3: 42. 936 Liu, X., Z. Ser, et al. (2014). "Development and quantitative evaluation of a high-resolution 937 metabolomics technology." Anal Chem 86(4): 2175-2184. 938 Locasale, J. W. and L. C. Cantley (2011). "Metabolic flux and the regulation of mammalian cell 939 growth." Cell Metab 14(4): 443-451. 940 Lunt, S. Y. and M. G. Vander Heiden (2011). "Aerobic glycolysis: meeting the metabolic 941 requirements of cell proliferation." Annu Rev Cell Dev Biol 27: 441-464. 942 Marusyk, A., V. Almendro, et al. (2012). "Intra-tumour heterogeneity: a looking glass for 943 cancer?" Nat Rev Cancer 12(5): 323-334. 944 Moellering, R. E. and B. F. Cravatt (2013). "Functional lysine modification by an intrinsically 945 reactive primary glycolytic metabolite." Science 341(6145): 549-553. 946 Moghaddas Gholami, A., H. Hahne, et al. (2013). "Global proteome analysis of the NCI-60 cell 947 line panel." Cell Rep 4(3): 609-620. 948 Molenaar, D., R. van Berlo, et al. (2009). "Shifts in growth strategies reflect tradeoffs in cellular 949 economics." Mol Syst Biol 5: 323. 950 Mor, I., E. C. Cheung, et al. (2011). "Control of glycolysis through regulation of PFK1: old 951 friends and recent additions." Cold Spring Harb Symp Quant Biol 76: 211-216. 952 Noor, E., A. Bar-Even, et al. (2014). "Pathway thermodynamics highlights kinetic obstacles in 953 central metabolism." PLoS Comput Biol 10(2): e1003483. 954 Oguz, C., T. Laomettachit, et al. (2013). "Optimization and model reduction in the high 955 dimensional parameter space of a budding yeast cell cycle model." BMC Syst Biol 7: 53. 956 Racker, E. (1976). "Why do tumor cells have a high aerobic glycolysis?" J Cell Physiol 89(4): 957 697-700. 958 Rapoport, T. A., R. Heinrich, et al. (1976). "The regulatory principles of glycolysis in 959 erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady 960 states, quasi-steady states and time-dependent processes." Biochem J 154(2): 449-469. 961 Rose, I. A. and J. V. Warms (1966). "Control of glycolysis in the human red blood cell." J Biol 962 Chem 241(21): 4848-4854. 963 Schilling, C. H., S. Schuster, et al. (1999). "Metabolic pathway analysis: basic concepts and 964 scientific applications in the post-genomic era." Biotechnol Prog 15(3): 296-303. 965 Schoors, S., K. De Bock, et al. (2014). "Partial and transient reduction of glycolysis by PFKFB3 966 blockade reduces pathological angiogenesis." Cell Metab 19(1): 37-48. 967 Schoors, S., K. De Bock, et al. (2014). "Partial and Transient Reduction of Glycolysis by 968 PFKFB3 Blockade Reduces Pathological Angiogenesis." Cell Metab 19(1): 37-48. 969 Segel, I. H. (1975). Enzyme kinetics : behavior and analysis of rapid equilibrium and steady state 970 enzyme systems. New York, Wiley. 971 Shestov, A. A., B. Barker, et al. (2013). "Computational approaches for understanding energy 972 metabolism." Wiley Interdiscip Rev Syst Biol Med. 973 Shestov, A. A., A. Mancuso, et al. (2013). "Metabolic network analysis of DB1 melanoma cells: 974 how much energy is derived from aerobic glycolysis?" Adv Exp Med Biol 765: 265-271. 975 Sheta, E. A., H. Trout, et al. (2001). "Cell density mediated pericellular hypoxia leads to 976 induction of HIF-1alpha via nitric oxide and Ras/MAP kinase mediated signaling 977 pathways." Oncogene 20(52): 7624-7634.
30 978 Shlomi, T., T. Benyamini, et al. (2011). "Genome-scale metabolic modeling elucidates the role of 979 proliferative adaptation in causing the Warburg effect." PLoS Comput Biol 7(3): 980 e1002018. 981 Telang, S., B. F. Clem, et al. (2012). "Small molecule inhibition of 6-phosphofructo-2-kinase 982 suppresses t cell activation." J Transl Med 10: 95. 983 Tristan, C., N. Shahani, et al. (2011). "The diverse functions of GAPDH: views from different 984 subcellular compartments." Cell Signal 23(2): 317-323. 985 van Heerden, J. H., M. T. Wortel, et al. (2014). "Lost in transition: start-up of glycolysis yields 986 subpopulations of nongrowing cells." Science 343(6174): 1245114. 987 Vander Heiden, M. G. (2011). "Targeting cancer metabolism: a therapeutic window opens." Nat 988 Rev Drug Discov 10(9): 671-684. 989 Vander Heiden, M. G. (2013). "Exploiting tumor metabolism: challenges for clinical translation." 990 J Clin Invest 123(9): 3648-3651. 991 Vazquez, A., J. Liu, et al. (2010). "Catabolic efficiency of aerobic glycolysis: the Warburg effect 992 revisited." BMC Syst Biol 4: 58. 993 Warburg, O., F. Wind, et al. (1927). "The Metabolism of Tumors in the Body." J Gen Physiol 994 8(6): 519-530. 995 Wu, R. (1965). "Rate-Limiting Factors in Glycolysis and Inorganic Orthophosphate Transport in 996 Rat Liver and Kidney Slices." J Biol Chem 240: 2373-2381. 997 Yi, W., P. M. Clark, et al. (2012). "Phosphofructokinase 1 glycosylation regulates cell growth and 998 metabolism." Science 337(6097): 975-980. 999 1000 1001
1002
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