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Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: History
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Subjects: Biotechnology & Applied Microbiology
Contributor: David Lao-Martil

Saccharomyces cerevisiae is a model organism in eukaryote cell research and the workhorse for the biotechnology industry. In nature and the industrial setup, environmental perturbations act as stressing factors which challenge regulation of metabolic flux and can also lead to reduced performance in industrial applications.

  • yeast
  • central metabolism
  • stress response
  • metabolic regulation
  • kinetic model
  • in vivo kinetics
  • parameter estimation
  • complexity
  • uncertainty
  • population heterogeneity

1. Introduction

Kinetic metabolic models are mathematical representations of a biological system that consider kinetic expressions such as rate constants. They describe the network structure, kinetic rate expressions and contain values for the parameters in these expressions[1]. Thus, these descriptions are well-suited to model time-dependent dynamics. A detailed explanation of the main components in a kinetic metabolic model can be seen in Box 1. Despite the progress attained with them, a consensus version with a full coverage of CCM has not yet been achieved.

2. Glycolytic Response to Glucose Perturbations in Yeast Fermentations

Saccharomyces cerevisiae is one of the most used microorganisms in biotechnology. S. cerevisiae is a prominent cell factory involved in food, beverages, and biofuels industries[2][3]. On top of its favorable physiology and robustness, genetic engineering has allowed to introduce new pathways and improve existing ones, generating new strains that have widened its range of applications [4][5]. Nonetheless, scaling up to commercial production is a challenging stage in which developed strains may emerge as inefficient [6]. Long circulation times and nonideal mixing result in substrate gradients in the industrial fermenter, affecting most cell factories, including S. cerevisiae[7][8][9][10]. The yeast cell sees these gradients as stressing factors to which it continuously adapts, often deteriorating process yields and giving relevance to the development of stress tolerant strains [11][12][13][14].
Extracellular substrate gradients alter intracellular fluxes in CCM. Carbon flux shifts between the different pathways composing CCM during these temporal transitions [12]. This can become a challenge for the cell, which struggles to keep the different pathways composing CCM balanced[13], as was shown in [14]for a yeast strain with a defective trehalose cycle, where sudden exposure to a high glucose concentration resulted in growth arrest. Glycolysis is found at the core of this network. This pathway digests intracellular glucose into pyruvate and produces energy in the form of ATP and glycolytic intermediates that support anabolic reactions [15].
How glycolysis contributes to the metabolic processes inside the cell depends on multiple factors. The presence or absence of oxygen determines if pyruvate is used for respiration or fermentation[16][17]. Still, this conspicuously simple explanation is challenged at high-substrate concentrations, where the maximum respiratory capacity is reached and fermentation takes place even if oxygen is present[18][19], in what is known as ‘overflow metabolism’ or Crabtree effect[14]. In addition, the substrate that is used as carbon source (such as glucose or fructose) and the ability of a strain to metabolize it also affects glycolytic kinetics and process yields[20][21][22][23][24][25][26][51,52,53,54,55,56,57]. Furthermore, the cellular state determines how glycolytic intermediates are used as biomass precursors[15][27] . For instance, at changing growth rates, different usage of these precursors can be observed[28][29]. Finally, availability of cofactors cannot always be taken for granted. A higher substrate uptake rate might be an evolutionary advantage, but it results in a demand for NADH recycling that respiration cannot achieve and thus fermentation becomes active[30][31].
The response of glycolysis to dynamic glucose perturbations is controlled by different regulatory layers. The first mechanism is the storage of glycogen and trehalose when glucose uptake exceeds the glycolytic processing capacity [32]. On top of this, allosteric and post-translation regulation take place [33]. Hexokinase (HXK) is allosterically inhibited by trehalose-6-phosphate (T6P), pyruvate kinase (PYK) is activated by fructose-1,6-bis-phosphate (FBP) and multiple metabolites act on phosphofructokinase (PFK)[34][35][36] . Simultaneously, the cAMP-protein kinase A (PKA) pathway is activated upon glucose perturbation and starts a regulation cascade in CCM [37] and possible targets for Post-Translational Modifications (PTMs) have been found in multiple enzymes along the CCM[38]. Finally, to adapt to different growth conditions, yeast cells use different enzyme isoforms. For instance, hexokinases and glucokinases are balanced to adapt to different glucose concentrations [39] and the regulation of intracellular pH is compartment-specific, carried out by different ATPases [40].

3. The Development of Metabolic Models Has Resulted in Understanding of Key Glycolytic Properties

Many breakthroughs in metabolic modeling used genome scale models. Nonetheless, stoichiometry alone does not define function and the response to glucose perturbations is a dynamic process where stoichiometry cannot explain mechanisms that act at different time scales or the appearance of bistability, among others [1][41]. As a result, kinetic models enable a deeper understanding of glycolytic properties. Due to the abundant data available for S. cerevisiae fermentations, models of the glycolytic networks have reached a high level of maturity for this organism.
The first kinetic models developed focused on understanding glycolytic oscillations in nongrowing yeast cells [42][43][44][45][46][47][48][49][50]. Most enzymatic reactions were lumped into a few (except [42][49]) but they acknowledged the important role of enzyme PFK and showed sensitivity to different glucose, oxygen, and acetaldehyde concentrations. Later works focused on understanding control properties and glycolytic response upon a single glucose perturbation experiment[51][52][53][54]  and thanks to a progressive increase in experimental data available, more detailed models were developed [55][56][57][58] Much of the focus was on understanding how mutant strains lacking a functional trehalose cycle would undergo growth arrest upon the glucose perturbation [32][35]. This was found to be due to a glycolytic imbalance between upper and lower glycolysis and attributed first to an ATP turbo metabolism [54][82]. Later, ref. [57]explained the role that the trehalose cycle plays in the glycolytic response and highlighted how the intracellular concentrations of metabolites at a given time point modulate the outcome.
In this process, models have become more interconnected with other pathways, allowing for a more complete understanding of the glycolytic response. Ref. [58]introduced glycolytic byproduct branch reactions that were necessary to reproduce the steady state. Other works modeled pathways that are directly linked to yeast glycolysis. For instance, detailed descriptions of the glycerol synthesis, trehalose cycle and PPP were developed in [59][60][61], respectively. Later, a PPP model was connected to glycolysis in[62], and another model of glycolysis together with TCA was developed in [63]. These networks were used to understand the control properties of glycolysis, pointing to glucose transporter (GLT) and PFK for being the enzymes with the highest controlling coefficients [51][52][64][65][66]and to study the effect of genome duplications [67]. For a complete overview of metabolic models developed to understand dynamic perturbations, see Table 1.
Furthermore, the regulation exerted by cofactors has gradually become more evident, resulting in a more complex understanding of glycolysis. The depletion of inorganic phosphate concentration that was shown to be crucial in [57][18] had been overlooked in previous works where it was assumed to be constant over time. Simultaneously, the sum of adenosine nucleotides has been assumed to be a conserved moiety [55] but under some experimental conditions this is not the case [68][69], which can be relevant considering that controlling enzyme PFK is allosterically regulated by ATP and AMP.
Table 1. Properties of S. cerevisiae models developed to understand dynamic glucose perturbation response: glycolysis (GLYCO), tricarboxylic acid cycle (TCA), pentose phosphate pathway (PPP), trehalose cycle (TRE). Number of ‘+’ sign according to how advantageous the property is. Cofactor conservation moieties are sumAXP and sumNADX. N/A when reactions were not modeled, or data were not shown in article. Refs. [56][63]fitted different parameter sets to multiple data sets. Other models used a unique parameter set. From the literature pool of articles obtained in the systematic reviewing process, only the works which include glycolysis are displayed.
  Rizzi et al.[70] Teusink et al. [54] Teusink et al. [58] van Eunen et al. [56]
Contribution to glycolytic understanding Dynamic models can accurately describe glucose perturbation. ATP surplus can cause the observed overactivation of initial glycolytic steps in DTps1 mutant strains. In vivo behavior cannot be predicted with in vitro kinetics. Implementation of allosteric regulation and in vivo measured parameter values is necessary to reproduce GP data.
GLYCO Individual + branch reactions (++) Lumped reactions (+) Individual + branch reactions (++) Individual + branch reactions (++)
TRE N/A N/A N/A T6P regulation (+)
TCA Individual reactions (++) N/A N/A N/A
PPP N/A N/A N/A N/A
Cofactors Conservation moiety (+) Conservation moiety (+) Conservation moiety (+) Conservation moiety (+)
Parameters Computational, in vivo (++) Computational, toy model (+) Computational, in vivo (++) Experimental and computational, in vivo (++)
Data Single GP experiment (++) Single GP, toy data (+) SS data point (+) Single GP experiment and multiple SS (+++)
   Smallbone et al. [55]  Van Heerden et al. [57]  Messiha et al. [62]  Kesten et al. [63]
Contribution to glycolytic understanding Broad quantification of enzymatic kinetic constants in in vivo-like conditions. Glycolytic dynamics combined with cell heterogeneity determine cell fate. Feasibility of constructing larges network models by merging smaller pathway models. Cooperativity PYK-PYR and ADH-PDH bypass play a major role in the onset of the Crabtree effect.
GLYCO Individual + branch reactions + isozymes (+++) Individual + branch reactions (++) Individual + branch reactions (++) Individual + branch reactions (++)
TRE N/A T6P regulation (+) N/A N/A
TCA N/A N/A N/A Individual reactions (++)
PPP N/A N/A Individual reactions (++) N/A
Cofactors Conservation moiety (+) Conservation moiety + dynamic Pi (++) Conservation moiety (+) Conservation moiety (+)
Parameters Experimental, in vivo (++) Experimental, in vivo (++) Experimental, in vivo (++) Computational, in vivo (++)
Data N/A Single GP experiment (++) Single GP experiment (++) Single GP experiment (++)

4. From Glycolysis to Central Carbon Metabolism: Understanding Response to Glucose Perturbations Is Limited by Model Complexity

Development of kinetic models of metabolism has often been constrained to small systems. In S. cerevisiae models, each next step forward in the understanding of glycolysis encountered a new limitation due to the inherent complexity of the pathway.
Models studying glycolytic oscillations or single GP experiments led to an in-depth analysis of glycolytic dynamics, but to understand central carbon metabolism performance, more pathways than only glycolysis must be considered. For instance, a significant fraction of glucose-derived carbon is taken up at different points in glycolysis [31]. To account for this, a relatively simple option is to implement branches or sink reactions (developed for Escherichia coli in [18]). This led S. cerevisiae models to reproduce steady state where imbalance had been mistakenly predicted [58] Still, dynamic regulation of storage metabolism is more complex than a sink reaction [57][71]and later models gradually added complexity to the trehalose cycle kinetics to avoid the imbalance from happening upon dynamic perturbation [56][57]. A similar situation could happen for other closely linked pathways such as the TCA or PPP, which have mostly been lumped into a single reaction, even though a few exceptions exist[70][63][59][62]. Simultaneously, other approaches such as linlog kinetics have aimed at attaining high model complexity but with simplified expressions using less parameters [72][73][74].
Furthermore, factors such as growth rate, compartmentation, or transport of metabolites other than glucose, regulate glycolytic response but have barely been considered. First, the growth rate determines how sink reactions behave [31], but most models focus only on a unique growth rate of 0.1 h−1. Since the effect of this variable has not been explicitly considered, models simulating different growth rates had no other alternative than to fit a different parameter set each time [56] Second, compartmentation and transport reactions have barely been considered and, for instance, this is relevant in trehalose regulation since it is known to accumulate in compartments other than the cytosol[75][76]. Third, transport of metabolites such as gases oxygen (O2) and carbon dioxide (CO2) could allow models to explain differences between respiratory and fermentative behavior [33][77][22]but neither has been implemented.
On top of this, other variables affect individual enzyme kinetics, and have neither been considered. First, cytosolic pH decays upon extracellular glucose perturbation, affecting multiple intracellular processes, including enzyme kinetics [35]. Second, PTMs are a fast response mechanism and multiple target sites have been found throughout CCM [78]. Third, different enzyme isoforms are expressed under different growth regimes. Examples of this are the differential expression of GLK/HXK and Glyceraldehyde 3-phosphate dehydrogenase (GAPDH) genes ([79] and [80], respectively).
Finally, a key challenge is the representation of variables that are not part of the carbon flux, such as cofactors. Most models have kept them constant or adopted moiety conservation cycles [81], such as the sum of intracellular adenine nucleotides ([ATP] + [ADP] + [AMP] = [AXP]) or inorganic phosphate [55]. Nonetheless, under intense glucose perturbations, both variables behave in a dynamic manner[56][82][68][83] and alter glycolytic response. An example of this is the ATP paradox, which occurs when ATP and the sum of adenine nucleotides transiently decay [84]. Understanding cytosolic Pi as a dynamic variable and implementation of import from the vacuole turned out to be central in understanding the glycolytic imbalance [57]. Although the availability of Pi was essential for lower glycolysis progression via GAPDH [57], adenine nucleotides exert allosteric regulation on the important controlling enzyme PFK [85].

5. New Intracellular Metabolomic and Fluxomic Data Boost Understanding of Glycolytic Response

Scale-down approaches have been developed to understand long-standing problems in industrial bioreactors. Although this has granted valuable knowledge, essential intracellular properties such as in vivo fluxes and kinetics have been captured with only limited resolution, constraining model development. In fact, this has become one of the main challenges in the development of high quality predictive kinetic models, since often multiple variables, such as transcriptomics, metabolomics and fluxomic data, interact to result in the final response[1] .
Early works aimed to understand glycolytic oscillations did so with small datasets, reducing their range of implementation. On most occasions only extracellular data such as growth and nutrient exchange rates was available [48] or a few metabolites at most [47], until in vivo quantification of metabolite concentrations and fluxes became a common practice, where most cofactors, glycolytic intermediates and rates were simultaneously observable[58]. Later, a standardized dynamic glucose perturbation experimental setup with CEN-PK yeast strains was adopted (see Table 2). This consisted of chemostat growth at dilution rate of 0.1 h−1, followed by an external glucose perturbation, where extracellular concentration increased to 1 g L−1. These stimulus response experiments were used to infer more physiological patterns [82]and the use of Nuclear Magnetic Resonance (NMR) and Mass Spectroscopy (MS) techniques made a wide range of intracellular metabolites measurable. From only a few glycolytic concentrations, datasets gradually grew to include most metabolites in glycolysis, the trehalose cycle, the TCA cycle, and the PPP. Adenine nucleotides and NAD:NADH ratio have also been made a standard and other nucleotides and amino acids which are affected by carbon uptake dynamics are quantified in the most recent publications.
Table 2. Glucose perturbation experiments in S. cerevisiae with intracellular metabolome quantification: Stirred tank reactors (STR) operated in chemostat. Shake flasks (SF) in batch conformation. Metabolite pools: glycolysis (GLYCO), tricarboxylic acid cycle (TCA), pentose phosphate pathway (PPP), trehalose cycle (TRE), nucleotides (NUC), Amino acids (AAs). Even though intracellularly localized, variables measured were whole cell, and exceptions are pointed. From the literature pool of articles obtained in the systematic reviewing process, the works displayed measured experimentally intracellular variables such as metabolite concentrations or fluxes. Literature is ordered by glucose input regime.
   Rizzi et al. [86]  Theobald et al. [82]  Vaseghi et al. [59]  Visser et al.[33]
Glucose input regime Glucose-limited to glucose pulse (0.25 g L−1) Glucose-limited to glucose pulse (1 g L−1) Glucose-limited to glucose pulse (1 g L−1) Glucose-limited to glucose pulse (1 g L−1)
Experimental setup 30 °C, pH5, aerobic, D = 0.1 h−1, STR, direct sampling 30 °C, pH5, aerobic, D = 0.1 h−1, STR, direct sampling 30 °C, pH5, aerobic, D = 0.1 h−1, STR, direct sampling 30 °C, pH5, aerobic, D = 0.05 h−1, STR, BioScope sampling
Duration 500 s 180 s 180 s 80 s
Strain CBS 7336 (ATCC 32167) CBS 7336 (ATCC 32167) CBS 7336 (ATCC 32167) CEN.PK113-7D
Measurement technique Enzymatic assay Enzymatic assay: metabolites, NAD(H) HPLC: adenine nucleotides Enzymatic assay: metabolites, NAD(H) Enzymatic assay: ATP, NADX and G6P MS: glycolytic intermediates
Intracellular variables measured GLYCO: G6P. GLYCO: G6P, F6P, FBP, GAP, 3PG, PEP, PYR. NUC: NAD(H), AXP (whole cell and cytoplasmic). Pi. GLYCO: G6P, F6P. PPP: 6PG. NUC: NADP(H). GLYCO: G6P, F6P, G1P, FBP, 2GP+3PG, PEP, PYR. NUC: ATP, NADX.
Glucose input regime Glucose-limited to glucose pulse (1 g L−1) Glucose-limited to glucose pulse (1 g L−1) Glucose-limited to glucose pulse (1 g L−1) Trehalose-limited to glucose pulse (20 g L−1)
Experimental setup 30 °C, pH5, aerobic, D = 0.05 h−1, STR, BioScope sampling 30 °C, pH5, aerobic, D = 0.05 h−1, STR, BioScope sampling 30 °C, pH5, aerobic, D = 0.05 h−1, STR, direct sampling 30 °C, pH4.8, aerobic, SF, direct sampling.
Duration 180 s 180 s 300 s 30 min
Strain CEN.PK113-7D CEN.PK113-7D CEN.PK113-7D BY4741
Measurement technique MS Enzymatic analysis: NAD(H) MS MS MS
Intracellular variables measured GLYCO: G6P, F6P, FBP, 2/3PG, PEP, PYR. TCA: ISOCIT, FUM, MAL, AKG, SUC. PPP: 6PG. TRE: G1P, T6P, TRE. NUC: AXP, NADH:NAD ratio. GLYCO: G6P, F6P, F1,6P2, F2,6P2, 2/3PG, PEP. TCA: ISOCIT, AKG, SUC, FUM, MAL. PPP: 6PG. TRE: G1P, T6P. NUC: AXP, NADH:NAD ratio. GLYCO: G6P, F6P, F1,6P2, F2,6P2, 2/3PG, PEP. TCA: ISOCIT, AKG, SUC, FUM, MAL. PPP: 6PG. TRE: G1P, T6P. NUC: AXP, NADH:NAD ratio. AAs. GLYCO: G6P, F6P, FBP, G3P, 2/3PG, PEP. TCA: AKG, MAL. PPP: 6PG, R5P, R1P. TRE: T6P, G1P. NUC: ATP, ADP, AMP, IMP, INO, HYP, GTP, GDP, GMP.
  Van Heerden et al. [55] Suarez-Mendez et al. , Suarez-Mendez et al. [71] Canelas et al. [2] Kumar et al. [87]
Glucose input regime Glucose-limited to glucose pulse (20 g L−1) Glucose-limited to feast–famine cycles (0.08 g L−1 max.) Glucose-limited. Dilution rates from 0.025 to 0.375 h−1 Glucose-limited. Dilution rates from 0.050 to 0.342 h−1
Experimental setup 30 °C, pH5, aerobic, D = 0.1 h−1, STR, BioScope sampling 30 °C, pH5, aerobic, D = 0.1 h−1, STR, direct sampling 30 °C, pH5, aerobic, STR, direct sampling 30 °C, pH5, aerobic, STR, direct sampling
Duration 340 s 400 s N/A (ss) N/A (ss)
Strain CEN.PK113-7D CEN.PK113-7D CEN.PK113-7D,mtlD1 CEN.PK113-7D
Measurement technique MS Reaction rates calculated by piecewise affine approximation (13C data) MS Reaction rates calculated by piecewise affine approximation (13C data) MS Reaction rates calculated with a stoichiometric model MS
Intracellular variables measured GLYCO: G6P, F6P, FBP. TRE: G1P, UDPG, T6P, TRE. PPP: 6PG. NUC: AXP, cAMP, UXP, GXP. Fluxes within glycolysis and trehalose cycle. GLYCO: G6P, F6P, FBP, G3P, GLYC, DHAP, GAP, 2PG, 3PG, PEP, PYR. TCA: CIT, FUM, ISOCIT, MAL, AKG, SUC. PPP: 6PG, E4P, R5P, RBUP5, S7P, X5P. TRE: G1P, UDPG, T6P, TRE. NUC: AXP. Fluxes within glycolysis and trehalose cycle. GLYCO: G6P, F6P, FBP, F26BP, G3P, DHAP, GAP, 2PG, 3PG, PEP, PYR. TCA: CIT, FUM, ISOCIT, MAL, OAA, SUC. PPP: 6PG, E4P, R5P, RBUP5, S7P, X5P. TRE: G1P, T6P, TRE. NUC: AXP, UXP, cAMP, NAD:NADH ratio. AAs. Fluxes within glycolysis. GLYCO: G6P, F6P, FBP, G3P, DHAP, 2/3PG, PEP, PYR. TCA: CIT, FUM, OAA, ISOCIT, MAL, AKG, SUC. PPP: 6PG, R5P, RBUP5, S7P. TRE: G1P, UDPG. NUC: AXP, GXP, IXP, TXP, UXP, dAXP, dGXP, dUXP. AAs.

This entry is adapted from the peer-reviewed paper 10.3390/metabo12010074

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