Why the tumor cell metabolism is not that abnormal

The cell energy metabolism is a multifactorial and evolving process that we address with a theoretical approach in order to decipher the functioning of the core system of the glycolysis-OXPHOS relationship. The model is based on some key experimental observations and well established facts. It emphasizes the role of lactate as a substrate, as well as the central role of pyruvate in the regulation of the metabolism. The simulations show how imposed environmental constraints and imposed energy requirements push the cell to adapt its metabolism to sustain its needs. The results highlight the cooperativeness of the two metabolic modes and allows to revisit the notions of metabolic switch and metabolic reprogramming. Our results thus tend to show that the Warburg effect is not an inherent characteristic of the tumor cell, but a spontaneous and transitory adaptation mechanism to a disturbed environment. This means that the tumor cell metabolism is not fundamentally different from that of a normal cell. This has implications on the way therapies are being considered. The quest to normalize the tumor acidity could be a good strategy. Author Summary Cancer cells metabolism focuses the interest of the cancer research community. Although this process is intensely studied experimentally, there exists very few theoretical models that tackle this issue. One main reason is the extraordinary complexity of the metabolism that involves many inter-related regulation networks which makes it illusory to recreate computationally this complexity. In this study we propose a simplified model of the metabolism which focuses on the interrelation of the three main energetic metabolites that are oxygen, glucose and lactate with the aim to better understand the dynamic of the core system of the glycolysis-OXPHOS relationship. However simple, the model highlights the main rules that allow the cell to dynamically adapt its metabolism to its changing environment. It moreover allows to address this impact at the tissue scale. Simulations performed in a spheroid exhibit non-trivial spatial heterogeneity of the energy metabolism. It further reveals that the metabolic features that are commonly assigned to cancer cells are not necessarily due to cell intrinsic abnormality. They can emerge spontaneously because of the disregulated over-acidic environment.


Introduction 32
The energy metabolism of cancer cells has been the subject of extensive research for over fty years, yet the 33 mechanisms governing tumors metabolism are not clearly understood. The Warburg eect, which now seems 34 accepted as a key feature of many types of cancer, is considered by some as one possible fundamental cause 35 of cancer [1,2]. Some dene this eect as a high lactate production despite sucient oxygen supply [1,3]. 36 However according to Warburg's original observations in the 1920s, the eect is limited to the production by 37 the tumor of a large amount of lactate (independently of the oxygen presence) [46]. This lactate production 38 is induced by a high glycolytic activity and increased glucose uptake. This creates around the cells, and 39 especially within solid tumors, a whole microenvironment, characterized by an acidic pH, favoring tumor 40 cells invasion. One recurring question remains "how do these extreme conditions benet the cell ?" [79]. 41 Understanding the impact of the microenvironment on ATP production may be part of the answer. The cell metabolism is highly complex since it is a multifactorial mechanisms that involves many dierent 47 interacting processes with many dierent actors. Moreover it is an evolving process and although crucial, 48 this aspect is rarely considered and often overlooked. In this context, a theoretical model is a powerful and 49 ecient way to make sense of this complexity and to address the temporality. It allows to test the pertinence 50 of some new hypotheses and to exhibit some emergent properties that cannot be intuited, so as to provide a 51 better understanding of the intimate functioning of the metabolic machinery and also to provide new insights 52 to guide future research. 53 54 Several models have been proposed to describe the cell energy metabolism [1014] but some can be too 55 complex to be easily reused and tested by experimentation. We therefore focused more specically on models 56 that describe the production of ATP according to the conditions surrounding the cell. Extracellular oxy-57 gen and glucose concentrations, lactate production and quantication of the extracellular pH (by protons 58 secretion) are the conditions that have been mainly considered in modelling. The availability of glucose and 59 oxygen respectively inuences the activity of glycolysis and oxydative phosphorylation (OXPHOS). Casciari 88 The model of cell energy metabolism may appear over-oversimplied considering the huge complexity 89 of the ne regulation mechanisms at work. We did not consider the role of glycolysis in the biosynthesis 90 of amino-acid either. We want to stress the point that at this stage our goal was to focus on the global 91 behavior of energy metabolism to be able to address its repercussions at the tissue scale and to highlight 92 spatial metabolic heterogeneity in a spheroid. To understand the nature of the Warburg eect, it is necessary to dene the energy mechanisms that govern 97 the cell. One of the questions that may arise is whether the Warburg eect appears as an inherent tumor 98 cell characteristic or, on the contrary, as a transitory behavior of the cell's metabolism in response to the 99 environmental constraints. In other words is it appropriate to continue to describe this phenomenon as a 100 metabolic switch [21,22]? When considering the metabolism of a cell, many parameters must be taken into 101 account, as several metabolic pathways are involved. Here we focus on the glycolysis-OXPHOS system, as 102 well as on the place of lactate within it. It is nevertheless important to remember that other pathways such 103 as β-oxidation of fatty acids or glutaminolysis can contribute to increase the reaction intermediates and thus 104 increase the energy production capacity. 105 106 In order to dene our model, we think that it is useful to recall some fundamental concepts of the 107 metabolism of these two pathways. Here glucose is considered as the main source of energy in the cell. This 108 molecule is catabolized during a sequence of three essential processes in order to produce ATP. The rst 109 reaction, glycolysis, transforms glucose into pyruvate as follows: 110 Glucose + 2 NAD + + 2 ADP + 2 P i −→ 2 Pyruvate + 2 NADH + 2 H + + 2 ATP + 2 H 2 O (1) NAD + is rate limiting for glycolysis, in the reaction catalysed by Glyceraldehyde 3-phosphate dehydro-111 genase (GAPDH). But in the overall process of fermentation / respiration, the NAD + pool is relled through 112 LDH, or oxydative phosphorylation. If the ratio NAD + / NADH is too low the glycolysis will be inhibited. 113 Many metabolic reactions modify this ratio and more generally the redox state of the cell. Here the goal is 114 not to model the set of mechanisms that can lead to change the ratio NAD + / NADH. At the moment we 115 therefore consider that NAD + is not limiting for the processes we seek to observe, although it is important 116 to be aware that this can have a signicant impact on energy metabolism. 117 Pyruvate can be reduced to lactate with lactate dehydrogenase (LDH) but the reaction will not produce 118 more ATP. Pyruvate can also be decarboxylated by the pyruvate dehydrogenase in Acetyl-CoA (Fig.1). This 119 decarboxylation takes place in the mitochondria.  Figure  conditions. Figure 2B, shows a cell with a Warburg phenotype. As in gure 2A, this cell uses both glycolysis 160 and OXPHOS, but the glycolytic ux is higher (or the ATP demand is lower), reducing the need to produce 161 ATP by the mitochondria. Pyruvate accumulates, shifting the ux to lactate production. These mechanisms To estimate the rate of ATP production per cell, it is required: (i) to evaluate the cell consumption 168 rates of glucose, oxygen and lactate which are the three limiting substrates for energy production and (ii ) 169 to understand how these dierent consumption rates vary depending on the environmental conditions. Healthy cell -The majority of the glycolytic ux is redirected in the mitochondria, and little or no pyruvate is converted to lactate; B. Warburg eect -The glycolytic ux is higher than the level that allows the balance between the production of pyruvate and its consumption. As a result, the pyruvate is partly converted into lactate and protons are secreted and progressively acidify the medium; C. Lactic acidosis -When the pH is low the glycolytic ux drops. There is not enough pyruvate to supply the OXPHOS, so the net ux of lactate enters the cell and is converted back into pyruvate. the more glucose there is, the less oxygen is consumed (Fig 3A). In our model (Fig 3B), ATP is the factor 193 that links oxygen to glucose: the more glucose is used to produce ATP, the less oxygen is consumed. This 194 new hypothesis releases a strong constraint on the system and allows for more exibility with the potential 195 for generating more metabolic behaviors. In vivo, OXPHOS is not directly limited by ATP (however the 196 reduction of ADP pool reduces its activity). But TCA enzymes like isocitrate dehydrogenase or oxoglutarate 197 dehydrogenase are inhibited by ATP and NADH. By limiting these steps there is less NADH produced that 198 can be used later for OXPHOS. Also, the less oxygen there is, the more glucose consumption increases. 199 Indeed, when the cell lacks oxygen, HIF is stabilized and upregulates the expression of glycolytic enzymes 200 [3234]. This model improvement makes things more natural (i.e. more emergent).
where k G is the Michaelis constant for glucose consumption and V max G is the maximum uptake rate of 207 glucose at saturation. First, the less oxygen there is, the more V max G increases (observation 2 ). Additionally, 208 the more acidic the medium, the more V max G decreases (observation 3 ). This is also true when the pH 209 becomes alkaline [35]. V max G is thus expressed by the combination of these two eects as follows: where U max G is the physiological uptake limit of glucose and p O G is a constant for glucose uptake variations 211 according to the oxygen level. The pH-related term has a Gaussian form, which (i) varies from close to 0, 212 when the pH is acidic, to 1 when it is physiological (pH ≈ 7.3), (ii) reaches a maximum at pH max , which 213 is the pH corresponding to the maximum glucose uptake and (iii) decreases after. p pH max G is the maximum 214 expression of glucose uptake when the pH is optimum and σ is a constant that tunes the spread in the 215 Gaussian term of the glucose uptake.

216
Oxygen uptake rate, U O

217
As for glucose and according to observation 1, the oxygen uptake is described with a Michaelis-Menten 218 function: where k O is the Michaelis constant for oxygen consumption and V max O is the maximum uptake rate of 220 oxygen at saturation.   gradient between the outside and the inside of the cell is required to transport lactate [37]. The parameter 246 V max L is therefore taken as a Hill function that decreases with increasing pH.
Pyruvate fate and Lactate secretion 248 The change in intracellular concentration of pyruvate is written as: Finally, pyruvate converted to lactate corresponds to the "surplus" pyruvate, [P yr] T arget being the basal 252 concentration in the cell. Since this is a surplus, this term should not be negative: The functions dened in (eq.8-12) are tted and parameterized from experimental data. Table 1  From the previous uptakes, the production rate of ATP can be calculated (see eq.6). Several models 265 do not take into account the need for ATP as a mechanism to regulate the uptakes of the main substrates. 266 However, it is expensive for the cell to overproduce ATP [38] as it is disadvantageous to under-produce ATP Glucose uptake at pH 7.3; B. Glucose uptake at pH 6.6; C. Oxygen uptake at pH 7.3; D. Oxygen uptake at pH 6.6. Normalized ATP production rate in multiple conditions: E. ATP Production rate at pH 7.3; F. ATP Production rate at pH 6.6; G. Heatmap of ATP production rate at pH 7.3 (left) and 6.6 (right) with a logarithmic scale. For each ATP level a cellular state can be associated. Typically low levels of ATP correspond to quiescent cells (reduced metabolism) whereas high levels of ATP are associated to proliferating cells. to the cell energetic demand. We note that for the higher energetic demands, the glucose uptake saturates. 297 This is why the drop in glucose concentration is the same for the medium and high ATP demands (both 298 are beyond the saturation level). For the low energetic demand, OXPHOS is low, since there is no need for 299 more ATP. This low OXPHOS is insucient to absorb all the pyruvate produced through glycolysis. As a 300 consequence, the excess pyruvate is transformed into lactate, which is excreted thus increasing the acidity.  and comes out of the cell with a proton until the pH is stabilized signing the equilibrium between OXPHOS 317 and glycolysis. As soon as anoxia is reached, OXPHOS stops and pyruvate is entirely converted into lactate. 318 Lactate is excreted and this leads to a second acidic drop. 319 For the high ATP demand, we note a sharp drop of pyruvate since OXPHOS consumes more pyruvate than 320 glycolysis can produce. As soon as oxygen disappears, OXPHOS stops and the pyruvate pool is relled. 321 During the initial oxygen decrease, the glucose uptake increases transiently until saturation (limited uptake 322 capability). This dramatically increases the acidity that ultimately results in the glucose uptake collapse. In this section we aim to specically highlight the heterogeneity that exists in a spheroid due to the 362 gradients of the main substrate from the periphery to the core (Fig. 6, upper graph). These gradients  Figure 6A clearly shows that the glycolysis contribution is much higher in the centre where the oxygen 373 level is low (Fig. 6, upper graph). As a consequence, the pH is lower in the centre and is directly correlated 374 to the glucose uptake gradient ( Fig. 6D and 6B). In the other hand, the gradient of oxygen uptake is steeper 375 from the centre to the periphery since the consumption of oxygen is higher than glucose and its initial con-376 centration is lower making it more sensitive to depletion (Fig. 6C). The net lactate secretion exhibits an 377 interesting prole (Fig. 6E) with a mid layer of lower secretion. This is explained by a high OXPHOS activity 378 requiring pyruvate at the outer layer. This leads to a lower level of secreted lactate since glycolysis is slightly 379 diminished from the periphery. At the other end, in the centre, OXPHOS is highly diminished since oxygen 380 level is low. This reduces the need for pyruvate (by OXPHOS), therefore excess pyruvate is converted into 381 lactate. The net lactate secretion thus reaches almost the same level at the heart of the spheroid than at its 382 periphery. Finally, ATP is globally maintained around its basal level, except at the centre where the oxygen 383 is low and OXPHOS is reduced (Fig. 6F). We note that glycolysis is not able to sustain the ATP level. 384 This would typically induce a transition towards a reduced metabolism such as quiescence. However, the cell 385 usually reduces its energetic needs much before it lacks ATP, since HIF triggers the entry into quiescence as 386 soon as the oxygen level is too low.  Figure 6E, that shows the net lactate production, exhibits a non-homogeneous 390 Warburg eect. Its intensity -dened by the importance of the glycolysis contribution (Fig. 6A)  The cell metabolism is highly complex since it is a multifactorial mechanisms that involves many dierent 399 interacting processes with many dierent actors. Moreover it is an evolving process and although crucial, 400 this aspect is rarely considered and often overlooked. contextual (acidity-dependent). Therefore it is not an inherent characteristic of the tumor cell, but a sponta-454 neous and transitory adaptation mechanism not fundamentally dierent from a normal cell. In response to 455 Upadhyay et al. [54], this eect appears more as an epiphenomenon that plays no causal role in tumorigenesis. can also be misleading. According to some denitions, metabolic reprogramming can refer to "the ability 472 of cancer cells to alter their metabolism in order to support the increased energy demand due to continuous 473 growth, rapid proliferation, and other characteristics of neoplastic cells" [41]. However, this denition is 474 too vague and appears inadequate since our model responds to it, by allowing the cell to adapt, without The main diculty encountered when building a theoretical model is its parameterization. Not all parameters 522 come from the same experiments. They are obtained for dierent cell lines and with dierent protocols which 523 implies some variability on each parameters. The choice of the parameters used in this study is thus based 524 on a consensus. As a consequence, our aim was limited to observe the qualitative emergence of dierent 525 metabolic behaviors depending on some imposed conditions related to the environment and cell energetic 526 needs. To reach a quantitative accuracy, it would be necessary to acquire more fundamental data on the 527 consumption rates of the cells for the dierent substrates and to establish energetic proles in a standardized 528 way, at the level of several cell lines, as indicated by Zu and Guppy [53]. 529 We are aware of the tremendous complexity of the cell metabolic machinery. However we deliberately chose 530 to simplify it, by focusing on the interactions of three main metabolites (glucose, oxygen, lactate) allowing 531 to reduce the computational cost with the idea to look at their impact at the tissue scale. As a consequence, 532 we proposed a relatively simple model -for which we already explained some of the limitations above -and 533 we have additionally ruled out the following mechanisms:  4. There are multiple sources of acidity and we only considered the acidity from the transport of lactate. 544 While it helps to focus on the specic eect of lactic acidosis it may neglect other important acidity 545 sources like CO 2 546 5. The balance between biosynthesis of amino-acid and energy production has not been considered. 547 The consequence of these limitations on the results, is that we highlight major behaviors and qualitative 548 tendencies. More precise models would not dramatically change the results but would allow to reach a 549 quantitative description and test ne regulation mechanisms.  In order to keep the level of pyruvate constant, the pyruvate production must be equal to the pyruvate 769 consumption (eq.14). To nd the level of glycolytic ATP contribution that does not require any lactate, we 770 use (eq.14) that gives :