Bistability in Glycolysis PDF

Bistability in Glycolysis Pathway as a Physiological Switch in Energy Metabolism Bhanu Chandra Mulukutla., Andrew Yongky., Prodromos Daoutidis, Wei-Shou Hu* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota, United States of America Abstr...

Bistability in Glycolysis Pathway as a Physiological Switch in Energy Metabolism Bhanu Chandra Mulukutla., Andrew Yongky., Prodromos Daoutidis, Wei-Shou Hu* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota, United States of America Abstract The flux of glycolysis is tightly controlled by feed-back and feed-forward allosteric regulations to maintain the body’s glucose homeostasis and to respond to cell’s growth and energetic needs. Using a mathematical model based on reported mechanisms for the allosteric regulations of the enzymes, we demonstrate that glycolysis exhibits multiple steady state behavior segregating glucose metabolism into high flux and low flux states. Two regulatory loops centering on phosphofructokinase and on pyruvate kinase each gives rise to the bistable behavior, and together impose more complex flux control. Steady state multiplicity endows glycolysis with a robust switch to transit between the two flux states. Under physiological glucose concentrations the glycolysis flux does not move between the states easily without an external stimulus such as hormonal, signaling or oncogenic cues. Distinct combination of isozymes in glycolysis gives different cell types the versatility in their response to different biosynthetic and energetic needs. Insights from the switch behavior of glycolysis may reveal new means of metabolic intervention in the treatment of cancer and other metabolic disorders through suppression of glycolysis. Citation: Mulukutla BC, Yongky A, Daoutidis P, Hu W-S (2014) Bistability in Glycolysis Pathway as a Physiological Switch in Energy Metabolism. PLoS ONE 9(6): e98756. doi:10.1371/journal.pone.0098756 Editor: Petras Dzeja, Mayo Clinic, United States of America Received January 31, 2014; Accepted May 7, 2014; Published June 9, 2014 Copyright: ß 2014 Mulukutla et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The authors have no support or funding to report. Competing Interests: The authors have declared that no competing interests exist. * E-mail: [email protected]. These authors contributed equally to this work. Introduction All three isoforms of PFK are activated by F6P and F26BP , but only PFKM and PFKL are activated by F16BP [13–15]. Glycolysis is the conduit of glucose metabolism for generating PFKFB is a bifunctional enzyme whose kinase and bisphosphatase energy and providing biosynthetic precursors for cellular materi- domains catalyze the formation and hydrolysis reaction of F26BP, als. The flux of glycolysis in cancer cells is high as compared to respectively [9,16]. Isozymes of PFKFB differ in their kinase and normal adult tissues and a vast amount of the glucose consumed is phosphatase activities as well as in their sensitivity to feedback diverted towards lactate production; a phenomenon known as the inhibition by phosphoenolpyruvate (PEP) [17–19]. Thus, each Warburg effect. This behavior is also typical of highly isozyme of PFKFB has a profoundly distinct capacity in proliferative tissues such as fetal tissues and stem cells [2,3]). In modulating PFK activity. Pyruvate kinase (PK) in mammalian contrast, quiescent cells transport glucose at low rates and systems is encoded by two genes that can produce two isoforms catabolize most glucose to carbon dioxide [4,5]. The Warburg each. Except for the PKM1 isoform, the other three isoforms effect was previously attributed to defective oxidative phosphor- of PK, PKM2, PKL and PKR, are activated by F16BP to varying ylation [1,6] until it was realized that the pathway was not extents. The M2 isoform of PK, in addition to activation by impaired in most tumor cells (see review ). F16BP, is also under the control of a host of allosteric modulators The differences in glycolysis activity observed across various cell including serine, succinylaminoimidazolecarboxamide ribose-5- types is accomplished through different levels of regulation. At phosphate (SAICAR) and phenylalanine among others [20–22]. one such level is the allosteric feed-back and feed-forward The sensitivity of the M2 isoform to such wide ranging modulators regulations exerted by the intermediate metabolites on its allows it to act, in-part, as the cell’s nutrient sensing machinery enzymes. Pivotal roles are played by three enzymes, (phospho-. Different tissues and cell types express different isoform fructokinase (PFK), pyruvate kinase (PK) and phosphofructoki- combinations of these enzymes, thus giving rise to a suitable nase/fructose-2,6-bisphosphatase (PFKFB)) through their inhibi- glycolytic flux behavior that caters to the biosynthetic and tion or activation by three reaction intermediates (fructose-1,6- energetic needs of the cell type in question. bisphosphate (F16BP), fructose-2,6-bisphosphate (F26BP), and The expression of isoforms of glycolytic enzymes and their phosphoenolpyruvate (PEP)) in glycolysis. These enzymes have regulation is tightly linked to control of cell growth. The multiple isoforms (PFKL/M/P, PKM1/M2/L/R and PFKFB1-4) make-up of the glycolytic isoforms in quiescent tissues strictly which are subjected to contrasting allosteric regulations [9–11]. restrains its flux, thus restricting the provision of the carbon for Each isoform, therefore, affects the glycolytic activity in a distinct growth and proliferation. There is increasing evidence that loss of manner. the growth control as in the case of tumor formation caused by mutations in proto-oncogenes and tumor suppressors, is accom- PLOS ONE | www.plosone.org 1 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis panied by alteration in the expression of specific glycolytic Results isozymes leading to metabolic reprogramming [24,25]. For example, HK2 is only expressed in limited number of adult In the following sections we will first present the steady state tissues but is expressed at high levels in cancer cells. HK2 binds to behavior of the F6P-node, and then discuss the effect of the outer mitochondrial membrane and inhibits the release of regulatory behavior of F6P-node on the glycolysis flux. This is cytochrome C to suppress apoptosis and promotes cell survival followed by description and analysis of the effect of a second in cancer cells [26,27]. Analogously, the embryonic isoform of regulatory loop acting on the glycolysis pathway. Lastly, the pyruvate kinase, PKM2, is found to be expressed in few adult combined effect of the two loops will be discussed. tissues, but is known to be highly expressed across wide range of tumor cells. Interestingly, knockdown of PKM2 in cancer cells, Bistability in the F6P-node such as the human lung cancer cell line H1299, and replacing it Phosphofructokinase (PFK) is a pivotal enzyme in glycolysis and with PKM1 was demonstrated to result in a metabolic phenotype exists in three distinct isoforms. The muscle (PFKM) and the liver change involving decreased glucose uptake and increased oxida- (PFKL) isozymes are under allosteric feedback activation by tive phosphorylation. Further, reprogramming of somatic F16BP to a varying extent [13,14,34], whereas the platelet isozyme cells to induced pluripotent stem cells (iPSCs) has also been shown (PFKP) is not. It is well known that feedback activation can to incur metabolic reprogramming; the change from a low give rise to ultrasensitivity and even bistability. To assess the effect glycolytic flux state of somatic cells to a high flux state of rapidly of the allosteric regulation of F16BP on the PFK flux, we dividing iPSC cells is accompanied by a switch in the isozyme constructed a mechanistic model around the F6P-node encom- expression of HK and PFK enzymes. passing the reactions catalyzed by the enzymes PFK and aldolase An additional layer of flux regulation of glycolysis is exerted by (ALDO) (Figure 1A). The values of kinetic parameters for each signaling pathways. Through signaling pathways, contrasting enzyme were obtained from various literatures in which the values glycolysis flux behavior is accomplished without changing the have been experimentally determined [12,14,36]. The simulated isoforms [7,23]; instead the action of signaling pathways alters the steady state behavior is thus only affected by the relative kinetic behavior of the target enzyme. Tyrosine kinase signaling abundance levels of the two enzymes involved. The relative has been shown to change the kinetic behavior of PKM2 isoform enzyme levels were obtained from their corresponding transcript through modulation of its allosteric regulations [28,29]. Similarly, levels in cultured cells and assuming that the protein level is signaling events triggered by glucagon in hepatocytes alter the proportional to the transcript. Furthermore, the concentra- kinetics of the liver isozyme of PK. Protein kinases A/B/C tions of DHAP and GAP were held at constant levels of 0.04 mM (PKA, PKB and PKC) have been shown to affect the kinetics of and 0.02 mM, respectively. PFKFB isoforms. In the absence of feedback activation by F16BP as is the case for The composition of isozymes in glycolysis, through multiple PFKP, the steady state flux resembles a Michaelis-Menten type of kinetics (Figure S1). In contrast, the activation by F16BP on PFK layers of regulation, is pivotal to the flux control and plays a key as in the case of the isozyme PFKL (or PFKM) ([12,14]), causes the role in growth control and physiological balance. Over the last steady state flux of PFK at different F6P concentrations (Figure 1B) four decades, the kinetic behavior of isoforms of individual to bear the hallmark of bistability. In the region bound by F6P glycolytic enzymes has been examined in detail. However, a concentrations from 0.09 mM to 0.3 mM, three types of steady holistic understanding of the effect of different combinations of state can be seen, two of which are stable (low flux states and high such isoforms on the flux behavior of the complete glycolysis flux states) and the ones in the middle are unstable. The pathway is yet to be attained. We have taken a systems biology physiological concentration of F6P in rat liver tissue has been approach to study the flux states of glycolysis pathway. Using a reported to be ,0.1 mM. Outside the region, only one steady mathematical model that employs mechanistic rate equations for state for a given F6P concentration is observed; below 0.09 mM enzyme kinetics, we demonstrate that glycolysis exhibits a classical the PFK steady state flux exists only in the low state, whereas multiple steady state behavior in terms of its flux with respect to above 0.3 mM it exists only at the high state. Eigenvalue analysis the glucose concentration. The multiplicity of steady states confirmed the stability of each steady state. It should be noted that segregate cell metabolism into distinct states: high glycolytic flux the above specified concentration ranges for bistable behavior are states and low glycolytic flux states. Such bistable behavior is an subject to the model parameters (kinetic constants and enzyme output of complex allosteric regulations which in turn depend on levels) of the F6P-node. the type of glycolytic isozymes expressed. We show that the In the bistable region, the flux can be either at a low or a high presence of the muscle or the liver isozyme of PFK or/and the L, state depending on the previous state of the system. The in- R or M2 isoform of PK is necessary for multistability in glycolytic between states are unstable in nature; these states are never flux. We substantiated the modeling insights with gene expression realized experimentally. When the concentration of F6P is varied data from various tissues as well as experimental data from HeLa slowly, the PFK flux changes along the stable steady state lines. cells. Further, we discuss the factors that affect the bistable nature Starting at a low flux state, as the F6P concentration increases, the of the glycolysis such as the level and the K/P ratio of enzyme flux increases along the low flux steady state line until the F6P PFKFB. concentration reaches 0.3 mM (‘‘switch-up’’ concentration, Similar kinds of bistable behavior have been shown to act like a Figure 1B), and then the system undergoes a sharp transition to robust switch in many regulatory circuits including oocyte cell a high flux state. Further increase in F6P moves the system farther maturation , transition from quiescent to proliferative modes up along the high flux steady state line. Conversely, if the system is in mammalian cells , transition between multiple phospho- initially at a high flux state, as the F6P concentration decreases, the form stable states in multisite phosphorylation systems , flux remains at the high state until the F6P concentration among many others. The dissection of glycolytic flux as a bistable decreases to 0.09 mM (‘‘switch-down’’ concentration, Figure 1B) switch will provide new insights on the regulation of cell where it rapidly descends to the low state. Once the system is metabolism and possibly allow for a new perspective in identifying switched from the low flux state to the high flux state, or vice versa, ways to modulate metabolic activities for therapeutic purposes. it does not switch back to the original state by small fluctuations of PLOS ONE | www.plosone.org 2 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis Figure 1. Multiplicity of steady states in kinetics of fructose-6-phosphate node (F6P-node). (A) Feedback activation of phosphofructokinase (PFK) by fructose-1,6-bisphosphate (F16BP) (B) Bistability in the kinetics of PFK due to feedback regulation by F16BP. The simulation was performed using only two enzymes PFK and aldolase (ALDO). F6P was varied and the steady state PFK flux was solved algebraically. Activation of PFK by F16BP was set at KPFK,fbp = 0.65 mM. (C) Allosteric regulations in the F6P-node. (D) Modulation of bistability span by K/P ratio of PFKFB. The bifunctional enzyme PFKFB was integrated with PFK and ALDO to construct a three enzyme system. Simulations were performed at varying K/P value of PFKFB while keeping all other conditions the same as in (B). doi:10.1371/journal.pone.0098756.g001 F6P concentration at the switch-concentration. The system is thus lower switch-up F6P concentration than the muscle isoform marked by well separated high flux and low flux states, and very PFKFB1 (K/P,0.4). In addition, hormonal or growth factor distinctive ‘‘switch-up’’ and ‘‘switch-down’’ F6P concentrations. mediated regulations can modulate the K/P ratio of PFKFB All three isozymes of PFK are activated by F26BP. The bi- isozymes (see review ). Such a regulation thus equips cells with functional enzyme PFKFB catalyzes both the formation and an acute way to modulate the F6P-node steady state behavior, degradation of F26BP (Figure 1C). The steady state concentration without undergoing a switch in their isozyme composition (chronic of F26BP is thus not affected by the expression level of PFKFB but effect). by the balance between the relative activities of the kinase (K) and the bisphosphatase (P) domains of PFKFB. Thus, the flux through Bistable Behavior in Glycolysis PFK is indirectly influenced by the K to P activity ratio of PFKFB, In the following discussions, we extend our analysis to the entire also termed as the K/P ratio. glycolysis pathway. For the purpose of this study, we will be We examined the regulation of the PFK flux by incorporating focusing on the regulations of PFK, PFKFB and PK. Feedback PFKFB into the model of the F6P-node. The experimentally inhibition of HK by G6P and feed-forward activation of PFK by determined values of kinetic parameters for PFKFB were also F26BP were considered and kept active in all the simulations obtained from literature [39,40]. The K/P ratio of PFKFB alters discussed later. The known regulations for PFK, PFKFB and PK the steady state behavior of PFK flux as shown in Figure 1D. can be grouped into two regulatory loops: Loop 1 and Loop 2. Bistability is present for a wide range of K/P ratios. However, at a Loop 1 consists of the feedback activation of PFK by F16BP and very high level of K/P ratios (.10), the bistable behavior activation of PFK by F26BP. Loop 2 encompasses three disappears and the PFK flux exhibits a saturation type of kinetics. regulations consisting of the feed-forward activation of PK by Thus, changes in the K/P ratio of the PFKFB result in the F16BP, the feed-back inhibition of PFKFB by PEP and activation modulation of the steady state PFK flux. of PFK by F26BP. The three allosteric regulations in Loop 2, Different isozymes of PFKFB have widely different K/P ratios when active simultaneously, yield feedback activation effect on the (Table 1), giving rise to different steady state behaviors of F6P- activity of the glycolysis pathway. node. The brain isoform of PFKFB3 (with K/P,700) will have a PLOS ONE | www.plosone.org 3 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis Table 1. Kinetic properties and the allosteric regulations of glycolytic enzymes expressed in mammalian cells. Isozyme Isozyme (Protein Tissue Enzyme (Gene) Product) Expression Metabolite Regulation References Activators/ Inhibitors Substrates Phosphofructokinase PFKM PFKM Muscle ATP F16BP (PFK) (Ka = 0.35 mM); F26BP; AMP; F6P PFKL PFKL Liver ATP F16BP [12,14] (Ka = 0.65 mM); F26BP; AMP; F6P PFKP PFKP Platelet ATP F26BP; AMP; F6P Pyruvate Kinase PKLR PKL Liver; ATP F16BP (Ka (PK) Pancreatic (Ki = 0.05mM) = 0.01 mM); Islets; Kidney PEP (Km = 0.6 mM) PKR Erythrocytes ATP F16BP (Ka = 0.04 mM); (Ki = 0.12mM) PEP (Km = 1.2 mM) PKM PKM1 Muscle; ATP PEP (Km Heart; (Ki = 2.5mM) = 0.08 mM) Brain PKM2 Fetal; Tumor ATP F16BP (Ka Cells; Cultured (Ki = 3.5mM) = 0.04 mM); Cells PEP (Km = 0.4 mM) 6-Phosphofructo-2- PFKFB1 Liver Liver (K/P glucagon X5P [9,19,61] kinase/fructose-2,6- = 1.5–2.5) (PKA), PEP (glucose induced bisphosphatase (PFKFB) effect) Muscle Muscle PEP insulin [9,19,61] (K/P = 0.4) PFKFB2 H1-H4 Heart PEP AKT/PKB; [9,19,61] (K/P = 1.8) PKA; PKC; AMPK PFKFB3 Ubiquitous Brain; PEP - [9,19,61] Placenta (K/P = 3.1) Inducible Tumor PEP AMPK [9,19,61] (K/P = 710) PFKFB4 T Testis PEP - [9,19,61] (K/P = 4.1) doi:10.1371/journal.pone.0098756.t001 The presence or absence of the allosteric regulations considered We will show that the bistable behavior imparted by the in Loop 1 and Loop 2 is determined by the isozymes that allosteric regulation at F6P-node is extended to glycolysis pathways constitute the pathway. Loop 1 is operational with the muscle or through Loop 1. Subsequently, we will also show that the allosteric liver isoforms of PFK (PFKM or PFKL), but not with the platelet regulation of Loop 2 also gives rise to bistability. However, Loop 2 isoform (PFKP) as the latter lacks the feedback activation by encompasses a larger segment of glycolysis. Therefore the bistable F16BP. Loop 2 is mainly seen with the expression of liver (PKL) or behavior of Loop 2 will only be shown as glycolysis flux, rather the red blood cell (PKR) or the M2 isoform of PK (PKM2) which than as an isolated node. are strongly activated by F16BP, but not with the M1 isoform The glycolysis flux with neither Loop 1 nor Loop 2 regulations (PKM1). Depending on the make-up of the isozymes, the glycolysis is shown in Figure 2A. This case reflects a combination of PFKP pathway in a tissue or a cell may have allosteric regulations of (thus Loop 1 inoperative) and PKM1 (Loop 2 inactive), such as in Loop 1, Loop 2, both or neither. This is illustrated in the oocyte or zygote in which PFKP and PKM1 are the dominant expression profile of glycolytic isozymes compiled from published isozymes expressed (Table S1). The simulation was performed by RNAseq transcriptome data of developing human embryos , omitting both the terms corresponding to the F16BP feedback HeLa cells , mouse adult tissues and transformed cells activation in the equation for PFK (KPFK,fbp) and the F16BP feed- (Tables S1 and S2). forward activation in the equation for PK (KPK,fbp). In addition, the K/P ratio of PFKFB was set to 10. The simulated steady state PLOS ONE | www.plosone.org 4 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis glycolysis flux exhibits no bistability at any K/P ratio (Figure 2A glucose concentration. The stability of those steady states was and Figure S2); the steady state flux approaches its maximum level verified by eigenvalue analysis. at a relatively low glucose concentration. In both the loops described above, F26BP plays a regulatory The case that only Loop 1 is active occurs when either PFKL or role through its allosteric control over PFK. The level of F26BP PFKM and PKM1 are the dominant isoforms expressed. Such a can be modulated by the K/P ratio of PFKFB. We have shown combination of isozymes is seen mainly in various sections of brain above that modulation of K/P affects the bistability behavior in tissue including cerebellum, cortex and frontal lobe (Table S2). the F6P-node alone (Figure 1D). This effect of flux modulation The simulation was performed by setting KPFK,fbp = 0.65 mM through K/P is also translated to the entire glycolysis flux (for PFKL [12,14]) and omitting the F16BP feed-forward (Figure 2E). The simulations were performed using exactly the activation term in the rate equation for PK. The K/P ratio of same conditions as those used in Figure 2D, except for the K/P PFKFB was set to 10. All the enzyme levels (including both PFK value which was varied. The multiple steady state region shifts as and PK) and all other kinetic constants were kept at the same K/P ratio of PFKFB changes. At higher values the multiple steady values as in Figure 2A. As shown in Figure 2B, incorporation of state region is lost and the flux behaves like typical saturation type Loop 1 (which is equivalent to introducing the F6P-node to of kinetics. Reducing K/P has the effect of shifting the multiple glycolysis), elevates the glycolysis flux to a much higher level and a steady state region to higher concentration range of glucose. At region of bistability is seen. very low levels of K/P the multiple steady state region moves Similarly, the effect of the Loop 2 alone is shown in Figure 2C. outside of the normal physiological range of glucose (.10 mM). This is the case when PFKP is the dominating PFK isozyme with To evaluate the robustness of the multiple steady state behavior, PKL, PKR or PKM2 as the PK isozyme. Large and small intestine sensitivity analysis on the multiplicity of steady states was express such a combination of isozymes (Table S2). The simula- performed by changing the levels of each enzyme (over a range tion was performed by omitting the F16BP feedback activation of two orders of magnitude) while holding all the other kinetic term in the equation for PFK and setting KPK,fbp = 0.04 mM (for parameter values constant. The results show that for all enzymes, PKM2 ). The K/P ratio of PFKFB was set to 10. All the the multiplicity of steady states can be seen to exist over a wide enzyme levels (including both PFK and PK) and all other kinetic range of enzyme levels except for HK (Figure S3). It has been constants were kept at the same values as in Figures 2A-B. In this reported that such a tight control of HK, either at enzyme level or through allosteric regulation, is required in order for the glycolysis case the extent of the maximal flux is somewhat lower than the flux to reach a steady state. Changing the concentration of the case of Loop 1 alone. A bistable region is seen with both the enzyme in the ranges shown in Figure S3 maintains the presence switch-up and the switch-down concentrations of glucose shifted of the bistable behavior but shifts the switch-up and the switch- toward a higher level of glucose. down concentrations. When both the loops are active, such as in case of hESCs, HeLa We further examined the sensitivity of the steady state behavior cells (Table S1) and mouse transformed cell lines (MEL and to a number of model parameters whose value was kept constant 10T1/2) (Table S2), the glycolysis flux has multi-stable behavior in this study, including the cellular redox state ([NAD]/[NADH]), (Figure 2D). The simulation was performed by setting KPFK,fbp the ratio of mitochondrial pyruvate and lactate concentrations = 0.65 mM (for PFKL) and KPK,fbp = 0.04 mM (for PKM2). The ([PYR]m/[LAC]) and the ratio of mitochondrial pyruvate and K/P ratio of PFKFB was set to 10. All the enzyme levels (including alanine concentrations ([PYR]m/[ALA]). For [NAD]/[NADH], both PFK and PK) and all other kinetic constants were kept at the multiplicity of steady states was observed over a wide range of the same values as in Figures 2A–C. Three stable steady states and two ratio (0.5 to 700) (Figure S4A). At very low [NAD]/[NADH] unstable steady states can be seen for this case. The maximum flux ratios (#1), glycolytic flux has three steady states as compared to is the same as that of Loop 1 alone while the multiple steady state five steady states seen at higher [NAD]/[NADH] ratios ($9). The region resembles the composite of the stability curves for Loop 1 data suggest that [NAD]/[NADH] ratio has a marginal effect at and Loop 2 (Figures 2B and 2C). very low values. The effects of [PYR]m/[LAC] and [PYR]m/ The results show that the steady state glycolytic flux may be at a [ALA] were probed by maintaining [PYR]m constant (at 0.1 mM) high flux or a low flux state depending on the presence or absence and varying either [LAC] or [ALA] (Figure S4B and S4C). of the regulatory Loop 1 and Loop 2. Without Loop 1 and Loop 2 Multiplicity of steady states was observed across the range in which active, in the physiological range of glucose concentration (5– lactate and alanine were varied. No effect on the steady state flux 10 mM) glycolysis flux is at a low flux state (Figure 2A). With Loop profile was observed when lactate was varied. Whereas, at higher 1 active alone, it will be at a high flux state (Figure 2B). To switch concentrations of alanine, the switch-up concentration moves to a low flux state from a high flux state, the glucose concentration closer to upper bounds of (or in some cases beyond) the typical will need to decrease to a low level that is rarely seen range of physiological glucose concentrations. physiologically; whereas if the initial flux is at a low state, as soon as the glucose level reaches a physiological level of 5 mM the flux Effect of Isozyme Composition on Steady State Behavior will switch to a high state. The steady state behavior with Loop 2 of Glycolysis active alone is rather different from the case of Loop 1 active Many isoforms of the same enzyme are expressed at different alone; the flux in the physiological glucose concentration range is levels in the same tissue cell. The presence of different isoforms at a low state with a switch up concentration at the high end edge with different allosteric regulations makes the steady state flux of physiological concentration (Figure 2C). Even if the flux is behavior deviate from that seen with a single isoform. We initially at a high state, it will switch to a low state when glucose evaluated the effect of the isoform mixtures on the glycolytic flux. decreases to a physiological level below 10 mM. In each case, the total level of the isoform mix for each enzymatic With both Loop 1 and Loop 2 active, the flux is at a high state step was kept at the same level as the one used in the original in the physiological range of glucose. Interestingly, from a high model (with single isoform for each enzymatic step). The steady flux state the system can switch only to the low state, bypassing the state behaviors of single PFK isoforms (PFKM, PFKL or PFKP) as intermediate stable steady states. The intermediate stable steady well as mixed expression of these isoforms, in conjunction with states can be reached only from a low flux state by increasing PKM2 are shown in Figure S5. In all cases, the steady state PLOS ONE | www.plosone.org 5 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis PLOS ONE | www.plosone.org 6 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis Figure 2. Multiplicity of steady states in the glycolysis flux. (A) Steady state glycolysis flux with neither Loop 1 nor Loop 2 active. The isozyme set consisting of PFKP (no activation by F16BP) and PKM1 (no activation by F16BP) were used in the simulation. The steady state flux exhibits classical Michaelis-Menten kinetics. (B) Steady state glycolysis flux with only Loop 1 active. When only Loop 1 is active, the glycolysis flux exhibits bistability. The isozyme set PFKL (KPFK,fbp = 0.65 mM) and PKM1 were used in the simulation. (C) Steady state glycolysis flux with only Loop 2 active. When only Loop 2 is active, the glycolysis flux also exhibits bistability. The isozyme set PFKP and PKM2 (KPK,fbp = 0.04 mM) were used in the simulation. (D) Steady state glycolysis flux with both Loop 1 and Loop 2 active. The isozyme set PFKL and PKM2 were used in the simulation. When both Loop 1 and Loop 2 are active, multiplicity of steady state resembling superposition of (B) and (C) is observed. For A–D the K/P of PFKFB was set at 10. (E) The effect of K/P modulation on the multiplicity of steady state in glycolysis. In this simulation PFKL and PKM2 were used, while K/P was varied. doi:10.1371/journal.pone.0098756.g002 behavior of the isoform mix takes the shape of that conferred by ratio is subjected to hormonal regulation, providing a mechanism the mixture’s dominant isoform. As shown in Figures 2A–D, the of rapid change in steady state behavior without resorting to presence of only a single isoform in any active Loop precisely fixes synthesizing new isoform of PFKFB. However, since PFKFB the switch-up and the switch-down glucose concentrations. catalyzes both the synthesis and hydrolysis of F26BP, the level of Interestingly, co-expression of the dominant isoform with smaller its expression does not alter the steady state level of F26BP, and fractions of other isoforms allows for the movement of the switch- does not have an effect on glycolysis flux, which has been up and switch-down glucose concentrations within the physiolog- confirmed by the use of the mathematical model (Figure 4A, ical range, thus equipping cells with yet another way to control the glycolytic steady state plots with 100%, 50%, 20%, and 10% span of the bistable region (Figures S5D–F). PFKFB superimpose on each other). Survey of PFKFB transcript level in different tissues reveals a wide range of expression Bistability in Cultured Cells (Figure S6). This diverse range of expression level, although does We employed HeLa cells to examine the bistability in glycolysis not change the steady state behavior, does have a profound effect flux. HeLa cells initially grown on microcarriers in high glucose on the dynamics. (HG) medium were split into two cultures with either low glucose (LG) (0.6 mM) or high glucose (HG) (25 mM) (see Materials and Methods). The cell concentration was kept low such that glucose would not be depleted in the LG condition due to the uptake by the cells. Cells were then allowed to reach steady states in LG and HG conditions, which were the low flux state (0.05 mmol/109 cells/h) and high flux state (0.31 mmol/109 cells/h), respectively. Cells from both these conditions were then re-suspended in medium containing varying glucose concentrations and the specific rates of glucose consumption and lactate production were monitored. When exposed to 25 mM glucose, cells showed high specific glucose consumption rate of ,0.31 mmol/109 cells/h regardless whether they were previously at a low flux or a high flux state (Figure 3A). When exposed to 0.6 mM glucose, cells from both HG and LG showed low specific glucose consumption rate of 0.05 mmol/109 cells/h. However, when exposed to intermediate glucose concentrations of 2 mM, 3 mM and 4.5 mM, contrasting specific rates were observed for the cells from HG and LG conditions. Cells that were previously cultured in HG maintained high specific glucose consumption rate (0.31 mmol/109 cells/h), whereas cells that were previously cultured in LG had low specific glucose consumption rate (0.05 mmol/109 cells/h). The flux in the intermediate glucose concentration range is thus dependent on the prior state or history of the cell. Since a high flux of glucose is accompanied by a high lactate flux and vice versa, the bistable behavior of glucose flux should be reflected in lactate flux. This is indeed seen when lactate efflux was measured (Figure 3B). The experimental results thus show the characteristic of bistability in HeLa cell glucose metabolism: cells which were at a high flux state (previously in HG) have to experience glucose levels below the ‘‘switch-down’’ concentration to reach the low flux state while cells from a low flux state (previously in LG) have to experience glucose levels higher than the ‘‘switch-up’’ concen- tration to reach the high flux state. PFKFB Modulates the Response Time of Metabolic State Figure 3. Bistability in cultured HeLa cells. Cells initially cultured in Switch high glucose (¤) or low glucose (%) exhibit different rates of (A) There exist four different isoforms of PFKFB with different K/P specific glucose consumption and (B) specific lactate production when ratio (Table 1). Different isoform can thus confer different steady exposed to varying glucose concentrations. state glycolysis flux behavior (Figure 2E). Additionally the K/P doi:10.1371/journal.pone.0098756.g003 PLOS ONE | www.plosone.org 7 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis The level of PFKFB affects the response time when glycolytic flux switches from a low state to a high state. This is illustrated by the simulated dynamic response of glycolytic flux upon increasing the glucose concentration corresponding to a low state to one at a high flux state. The K/P ratio of PFKFB used in the simulation is 10, corresponding to a condition in which a shift from a low flux state to a high flux state is possible in the physiological glucose concentration range. The system is initially at a low flux steady state in the bistable region. The glucose concentration is then increased to a level at which only high flux steady state is possible (Figure 4A). Given sufficient amount of time, the system will settle at a new high flux state. However, if the glucose concentration is switched back to the original level in the bistable region after a brief period of time (Figure 4B), two outcomes are possible: the system may remain at the high flux steady state, or returns to the low flux steady state. With a high PFKFB level, the flux changes faster to the higher flux state and settles at a new steady state before the glucose concentration is returned to the original level in the bistable region (Figure 4C). It remains at the high flux state even after glucose is returned to the bistable region. In contrast, at a lower PFKFB level the response is sluggish when glucose concentration is given a step change. Upon switching glucose concentration to the original level, the flux returns to the original low flux state (Figure 4C). The response time to a switch to the new high flux steady state is clearly dependent on the level of PFKFB. Discussion In this study we demonstrate that in the physiological range of glucose concentration the glycolysis flux exhibits multiple steady state behavior. The multiple steady states arise from the regulatory loops centering at PFK and PK. The presence of M/L isoforms PFK and the M2 isoform of PK, which are all subjected to activation by their respective effectors, give rise to steady state multiplicity. The sets of isoforms, (PFKM/PFKL and PKM2) and (PFKP and PKM1), confer contrasting multiple steady state and the saturation type steady state behaviors to glycolysis flux, respec- tively (Figure 5). With the latter set of isozymes, the flux is at a low flux state under physiological glucose concentrations. In contrast, the bistable region conferred by the former set of isozymes can span the physiological concentration range of glucose. The model thus predicts that the flux will be at a high flux state under physiological conditions. Only upon a long period of exposure to a very low glucose concentration (,,1 mM) will the glyolysis flux switch to a low flux state. A high flux state is also associated with a high lactate production as shown by the model simulation (Figure S7). Figure 4. Effect of PFKFB levels on the transient response of In the bistable region, the stable steady state at which the glycolysis activity to pulse input in glucose concentration. (A) glycolysis resides at a particular glucose concentration is dictated Steady state behavior of glycolysis at different levels of PFKFB. All by the trajectory along which the system moves. Cells which are steady state glycolytic plots for different PFKFB levels including 100%, originally at a high flux state will remain at high flux state until the 50%, 20% and 10% superimpose on each other. (B) Glucose pulse input. This figure shows the pulse input in glucose concentration made at 50h glucose concentration is reduced to a level below the switch-down for duration of 1.5h and an amplitude sufficient enough to increase concentration; whereas cells which are originally at a low flux glucose concentration from low flux state (a) to high flux region (b). (C) state, will stay at low flux state until the glucose concentration is Response of the glycolysis to pulse input in glucose concentration for increased beyond the switch-up concentration. Using HeLa cells systems with different PFKFB levels. Systems were stationed at low flux we demonstrated this effect of cell’s ‘‘history’’ in terms of the fluxes state (a) when the pulse input was initiated. Systems with 100% and of both glucose consumption and lactate production (Figure 3). 50% PFKFB switch to the high state (b) in the given glucose pulse time. On the contrary, the response of the systems with 20% and 10% PFKFB Metabolic switch between low and high flux states to meet the is not fast enough to switch to the high state and therefore return to changing bioenergetic demands caused by oncogenic or develop- the low state when glucose is switched back to original concentration. mental events may be brought about by expression of a different doi:10.1371/journal.pone.0098756.g004 set of isozymes (see review [2,3,7]). Mature oocyte and zygote exhibit the oxidative type of metabolism. As zygote differen- PLOS ONE | www.plosone.org 8 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis Figure 5. Glycolytic behaviors observed in mammalian cells. Two types of glycolytic steady state kinetics were observed. These include steady state behavior with no multiplicity of states or those with multiplicity of states. The type of glycolytic isozymes expressed forms the basis for presence or absence of multiplicity of states in glycolysis activity. In case of non-proliferating cell, isozyme combination comprising of PFKP, PKM1 and PFKFB with K/P = 0.5 was used whereas in case of proliferating cell, isozyme combination including PFKM, PKM2 and PFKFB with K/P = 10 was employed. doi:10.1371/journal.pone.0098756.g005 tiates and reaches the late blastocyst state, the metabolic PFKFB affects the activity of PFK through its reaction product phenotype changes to predominantly glycolytic. Such a change F26BP. Different isoforms of PFKFB have different K/P ratios in the metabolic phenotype from the oxidative state of quiescent that give rise to different steady state behavior of glycolysis oocyte and zygote to glycolytic state of the blastocyst is associated (Figure 2E). An isoform with a high K/P ratio yields a higher level with changes in glycolytic isozymes from PKM1, PFKP and of F26BP at steady state, exerts a stronger activation of PFK and PFKFB2 to PKM2, PFKM/PFKL and PFKFB3/PFKFB4 moves the switch-up glucose concentration to lower levels. With isozymes (Table S1). The concurrent switch in the isozyme hormonal actions that change the K/P of PFKFB, the steady state pattern and the flux behavior observed in the above scenario behavior of glycolysis can be altered quickly without resorting to matches that presented by our model simulations (Figure 5). changes in the isoform expression. Since PFKFB catalyzes both It should be noted that most cells express a mixture of isoforms forward and reverse reaction of F26BP synthesis, the level of its rather than a single one [45–50]. Such pattern is also observed in expression does not alter the steady state level of F26BP, and does the tissues described above (oocyte, zygote and blastocyst), where not have an effect on glycolysis flux. But the response time to reach other isoforms are also expressed in small fractions (Table S1). We a new steady state upon a change in glucose concentration is evaluated the effect of mixed expression of multiple isoforms of affected by the level of PFKFB expression (Figure 4). PFK on the multiple steady state behavior. When different In a separate study, an extended version of the current isoforms of PFK are expressed, the isoforms which exhibit bistable mathematical model has been used to examine the steady state behavior, namely PFKL and PFKM, dominate over PFKP unless behavior in glycolysis, in glucose and lactate concentration ranges PFKP is present in a much larger proportion than the other that are beyond the physiological level but is of interest to isoforms (Figure S5). It is also worth noting that not all industrial bioprocessing for pharmaceutical biologics production proliferating cells and quiescent cells have the same isozyme (Mulukutla et al., in preparation). In those cases, the high levels of patterns. However, it has been reported that fast proliferating cells lactate accumulated in culture causes inhibition of PFK [54,55] typically express PFKM/PFKL, PKM2 and PFKFB3 as the major and induces a shift in the metabolism to lactate consumption isoforms; whereas quiescent cells favor PFKP, PKM1 and other (Mulukutla et al., in preparation). The extended model includes isoforms of PFKFB as the dominating isoforms [28,51,52]. the pentose phosphate pathway (PPP) and the TCA cycle. We Metabolic shift may also come about by hormonal or signaling observed that the extended model also showed multiple steady regulation, such as those that change the K/P ratio of PFKFB state behavior in glycolytic flux in the similar glucose concentra- (Figure 2E). For example, the K/P ratio of PFKFB in hepatocytes tion range and such complex glycolytic behavior also affect the can be quickly modulated by glucagon-triggered cAMP signaling dynamics of TCA cycle and PPP flux.. Furthermore, a number of factors that affect the allosteric state The mechanisms used to describe the enzyme reactions of PKM2 isozyme, including serine, SAICAR and phenylalanine, involved in the pathway and the values of the kinetic parameters can influence the transition between the two metabolic states [20– used were all taken from the reported literature. The transcrip- 22,53]. tome data of mouse myeloma cells were employed to estimate PLOS ONE | www.plosone.org 9 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis the relative abundance level of glycolysis isozymes. A survey of the NADH), metal ions influencing the kinetics of glycolytic enzymes archived transcriptome data of different tissue and cultured cells (Mg2+, K+, Ca2+ etc) and several metabolic intermediates revealed a wide range of transcript level and proportion of (mitochondrial pyruvate and extracellular lactate) were set to be isoforms for virtually all enzymes in glycolysis. Cells of constant in order to insulate glycolysis behavior from the effect of different types and arising from different tissues thus possess a their concentration fluctuations. The fixed concentrations of these varying steady state behavior. Exhaustive simulation for evaluation are tabulated in Table S4. of steady state behavior on all possible enzyme combinations is clearly not feasible. We evaluated the range of enzyme expression Model Transient Simulations level that gives multiple steady state behavior. By varying the Transient simulations of the ODE model were performed in the concentration of one enzyme while keeping all other variables Matlab (Mathworks, Inc.) computing environment using the constant we show that steady state multiplicity is seen in a wide implicit numerical ODE solver ode15. The inputs for the model range of concentration of the two pivotal enzymes, PFK and PK were the concentrations of glucose and lactate. A simulation time (Figure S3). of 500 time steps (hour) was used to ensure the steady state was The bistable behavior in glycolysis confers robustness to the reached. The intracellular concentrations of energy nucleotides response of glycolysis to changes in glucose concentration; within (ATP, ADP, AMP, NAD+, NADH), and metal ions influencing the the physiological range of glucose concentration a change in the kinetics of glycolytic enzymes (Mg2+, K+, Ca2+ etc) and several flux state is not readily realized unless via a regulatory action, metabolic intermediates (mitochondrial pyruvate and extracellular differentiation or oncogenic event. In recent years there has been lactate) were set to be constant in order to insulate glycolysis increasing interest in developing treatment strategies of suppress- behavior from the effect of their concentration fluctuations. Their ing hyperactive cellular metabolism to control cancer cell growth concentrations are tabulated in Table S4. or diabetes development. The glycolysis flux behavior revealed in this study may be exploited to negatively manipulate the Cell Culture metabolism of tumor cells by rendering Loop 1 or Loop 2 HeLa cell line, originally obtained from ATCC (Manassas, VA) inoperative. Decreasing the activation of PFK by F16BP can make was a generous gift from Dr. Kim Do-Hyung and has been Loop 1 less active. Tumor cells typically express PKM2 as the reported previously. HeLa cells were cultured in DMEM dominant pyruvate kinase isozyme. Disrupting the allosteric medium (Invitrogen, 11995-065) supplemented with 4% fetal regulations of PKM2 activity, such as by administering SAICAR bovine serum at 37uC in 5% CO2. 100 mL culture with 5 g/L of , will make Loop 2 inactive. Further, suppressing the K/P Cytodex 1 microcarriers (GE Healthcare, 17-0448-01) was carried ratio of PFKFB3 through expression of TIGAR or by the use out in 250 mL spinner flasks. HeLa cells were inoculated at 26105 of small molecule modulators such as 3-(3-pyridinyl)-1-(4-pyridi- cells/mL on Day 0. The procedure for microcarrier culture has nyl)-2-propen-1-one (3PO) can make Loop 2 inoperative. A been described previously. On Day 5, cells on microcarriers mechanistic understanding of the regulation of glycolytic flux will were washed and re-suspended at 16105 cells/mL in DMEM have a positive impact on the advances of these metabolism-based medium containing either 0.6 mM (LG) or 25 mM (HG) of therapeutic treatments. glucose. The cell concentration was intentionally kept low such that the glucose concentration in the culture could be maintained Materials and Methods at a relatively constant level without getting depleted. The two flasks were then maintained for a further 12 hours to allow the cells Mathematical Model of Glycolysis in LG condition to reach a low flux state and those in HG An ordinary differential equation (ODE) model that encom- condition to reach a high flux state. Subsequently, the cells from passes glucose metabolism from glucose uptake through glycolysis, each flask were washed twice with PBS and transferred to the wells lactate production, and pyruvate transport into mitochondria was of a 12-well plate containing 1 mL of medium with varying glucose constructed. The model considers mass balances for the 12 concentration. Cells were inoculated at a high enough concentra- reaction intermediates of glycolysis (Information S1, Mathematical tion (26106 cells/mL) to allow measurable changes in the medium Model for Glycolysis Flux section). The mechanistic rate equations glucose concentration due to cellular glucose uptake. Supernatants for enzyme reactions and the values of the kinetic parameters were were collected at time 0, 2, 4, and 6 hours which were then all reported previously and are described in detail in the Rate assessed for glucose and lactate levels using the Infinity Glucose Equation section of Information S1. The abbreviations of enzymes reagent (Thermo Scientific, TR15421) and YSI 2700 SELECT and reaction intermediates are listed in the Table S3. The levels of industrial analyzer (YSI Inc.), respectively. Subsequently, using each enzyme (or alternatively the Vmax) used in the ODE model linear regression, specific rates of glucose uptake and lactate are included in the Rate Equation section of Information S1. production were calculated from the glucose/lactate measurement data. Steady State Solution of the Model An algebraic model consisting of the steady state mass balance Supporting Information equations for the intermediates of all the reactions considered was derived from the ODE model. The algebraic model was used to Figure S1 Steady state behavior of F6P-node with PFKP evaluate all the possible steady states and the corresponding as the sole PFK isozyme expressed. F6P-node was simulated eigenvalues (Information S1). The solutions were obtained using using PFKP as the sole PFK isozyme, at different K/P ratios (range: 0.5–50). In all the cases, the steady state flux of the system the inbuilt numerical solver fsolve in Matlab (Mathworks, Inc.) (JPFK) followed the Michaelis-Menten type of kinetics. No computing environment. For each glucose concentration, positive multiplicity of states was observed in the range of K/P simulated. and real-valued solutions were calculated using initial guesses of (TIF) pseudorandom values drawn from the standard uniform distribu- tion. Stability analysis was performed using eigenvalue analysis on Figure S2 Steady state behavior of the glycolysis flux each steady state solution obtained. In the simulations intracellular with no loop active and with PFKP as the sole PFK concentrations of energy nucleotides (ATP, ADP, AMP, NAD+, isozyme expressed. The steady state glycolysis flux was PLOS ONE | www.plosone.org 10 June 2014 | Volume 9 | Issue 6 | e98756  Bistable Switch in Glycolysis simulated using PFKP as the sole PFK isozyme, at different K/P Figure S7 Experimental data of glycolysis rate at ratios (range: 5–100). In all the cases, the steady state flux followed varying glucose concentration. Data from continuous culture the Michaelis-Menten type of kinetics. No multiplicity of states was of mouse hybridoma cells (reference of Information S1) were observed in the range of K/P simulated. used to plot the metabolic rates as a function of glucose (TIF) concentration (A). The continuous culture data were from a total of 14 runs and reported data were all from steady states with a Figure S3 Bounds of enzyme activity within which dilution rate (or growth rate) in the range of 0.30 to 0.33 h21. (B) bistability in glycolysis is observed. Sensitivity analysis The ratio of lactate production (analogous to LDH rate) to glucose was performed on the glycolytic enzyme activity levels. Each consumption (analogous to glycolysis rate) is shown as DL/DG. A enzyme level was varied individually while holding all other sharp transition from high flux state to a low flux state can be seen parameters constant. The values shown are normalized to the (0.24 mM glucose). The overlapping region of high flux and low concentration of enzyme used in the original simulation (shown in flux state resembles that of bistability (0.17–0.24 mM). The DL/ Figure 2D). The range of enzyme activities in which bistability was DG plot is consistent with that postulated in Warburg effect. (C–D) observed for each enzyme are plotted. The majority of enzymes Simulation results corresponding to the glycolysis activity and DL/ have a large range of enzyme activity in which bistable behavior is DG shown in (A–B). observed for complete glycolysis. Only few enzymes including HK, (TIF) ALDO and GAPDH have small enzyme activity range for bistable behavior. Table S1 Composition of the transcript levels of several (TIF) glycolysis isozymes at various stages of human embry- onic development and cell lines. Figure S4 Sensitivity of the steady state behavior of (DOCX) glycolysis to the perturbations in: (A) NAD/NADH ratio (B) [Pyruvate]m/[Lactate] ratio and (C) [Pyruvate]m/[Alanine] ratio. Table S2 Composition of the transcript levels of several (TIF) glycolysis isozymes in various mouse organs and cell lines. Figure S5 Effect of single or mixtures of PFK isozymes (DOCX) on the bistability in glycolysis. (A) Single PFKM isozyme (B) Single PFKL isozyme (C) Single PFKP isozyme (D) Mixtures of Table S3 Nomenclature. varying levels of PFKM and PFKP. (E) Mixtures of varying levels (DOCX) of PFKL and PFKP. (F) Mixtures of varying levels of PFKM and Table S4 Fixed parameter values in the model. PFKL. (DOCX) (TIF) Information S1 Supplementary information. Figure S6 PFKFB expression in various tissues. Tran- (DOCX) scriptome data for mouse tissue were obtained from previously reported work (reference of Information S1). Raw files were obtained from the NCBI GEO website with accession number Acknowledgments GSE9954. The raw data were used to obtain the intensity data for We thank Dr. Alex Lange, Dr. Howard Towle and Dr. David Bernlohr, all the probes and they were normalized by using linear University of Minnesota, for reviewing the findings of the manuscript and normalization to a mean value of 500. The combined expression providing us with constructive comments. levels of PFKFB isozymes (PFKFB1-4) in those tissues were then plotted. Expression of PFKFB in muscle and adipose tissues was an Author Contributions order of magnitude different as compared to proliferating cells Conceived and designed the experiments: WSH PD. Performed the including embryonic stem cells (ES_cells) and fetus. experiments: BM AY. Analyzed the data: BM AY. Contributed reagents/ (TIF) materials/analysis tools: WSH PD. Wrote the paper: BM AY WSH. References 1. Warburg O (1956) On the origin of cancer cells. 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