Most of fluxes kinetics are as previously described [29 ,30 (link),33 (link)] (S2 Table ). All kinetic equations in this work are based on mechanistic formulations known as biologically relevant, rather than using empirical equations. Reactions rate are composed of multiplicative Michaelis-Menten kinetics accounting for each substrates involved. In the case of energetic nucleotides, ratios are used (AMP/ATP, ATP/ADP, NADH/NAD, NADP/NADPH, ADP/ATP, NAD/NADH, NADPH/NADP). This approach was successful in another work on the modeling of the metabolism of skeletal muscle cells [36 (link)] as well as in our previous work on a similar modelling approach applied to another CHO cell line [29 , 30 (link), 33 (link)]. The regulation of glycolysis is as previously described [33 (link)], with feedback inhibition phenomena of hexokinase (VHK), phosphoglucose isomerase (VPGI) and reverse lactate dehydrogenase (VrLDH), by glucose-6-phosphate, phosphoenolpyruvate and pyruvate, respectively. The AMP-to-ATP ratio activates phosphofructokinase (VPFK), lactate dehydrogenase (VLDH) and VHK, while fructose-6-phosphate activates pyruvate kinase (VPK). The reactions involving an inhibition mechanism were described according to the mathematical formulation of a non-competitive inhibition (Eq 1 ). However, the reaction mechanism used to describe activation phenomena is that for non-essential activation as proposed in [37 ] (Eq 2 ).
In the present work, VPFK is inhibited by intracellular citrate and extracellular lactate [38 (link),39 (link)], and VPK is inhibited by alanine [40 (link),41 ]. The reverse reaction of alanine aminotransferase (VrAlaTA) is also inhibited by glutamine to account for the switch from alanine production to alanine consumption when glutamine level is low, as observed in our experimental data. Reverse reactions are also modeled for glutamine synthetase (VGlnT), glutamate dehydrogenase (VGLDH), lactate dehydrogenase (VLDH), glutamate transport (VGluT) and adenylate kinase (VAK), but not for VASTA because there was no evidence from our measurements of a net production of extracellular aspartate, but only a net consumption.
The cell specific growth rate is modeled as a multiplicative Michaelis-Menten mechanism accounting for major precursors of cell building blocks, an approach that has been previously successfully applied to plant [27 (link)] and mammalian cells [29 ,30 (link),31 (link)]. All extracellular amino acids included in the model were considered, as well as the intracellular levels of glucose-6-phosphate, citrate and ribulose-5-phosphate, which act as the respective precursors for glycogen, proteins and lipids, and nucleotides such as DNA and RNA. For each of those species, a different affinity constant was determined, to represent the situation when one species, for instance glutamine, is nearly depleted without significantly affecting the growth rate. A specific set of affinity constants was also used to describe the mAb production rate. Finally, inhibitory effects of lactate and ammonia on the growth rate were added to account for their accumulation in the culture media. A non-competitive inhibition mechanism was applied [42 (link)], with a distinct affinity constant for lactate regarding the growth (Equation 33 inS2 Table ) and VPFK (Equation 3 in S2 Table ) reactions.
In the present work, VPFK is inhibited by intracellular citrate and extracellular lactate [38 (link),39 (link)], and VPK is inhibited by alanine [40 (link),41 ]. The reverse reaction of alanine aminotransferase (VrAlaTA) is also inhibited by glutamine to account for the switch from alanine production to alanine consumption when glutamine level is low, as observed in our experimental data. Reverse reactions are also modeled for glutamine synthetase (VGlnT), glutamate dehydrogenase (VGLDH), lactate dehydrogenase (VLDH), glutamate transport (VGluT) and adenylate kinase (VAK), but not for VASTA because there was no evidence from our measurements of a net production of extracellular aspartate, but only a net consumption.
The cell specific growth rate is modeled as a multiplicative Michaelis-Menten mechanism accounting for major precursors of cell building blocks, an approach that has been previously successfully applied to plant [27 (link)] and mammalian cells [29 ,30 (link),31 (link)]. All extracellular amino acids included in the model were considered, as well as the intracellular levels of glucose-6-phosphate, citrate and ribulose-5-phosphate, which act as the respective precursors for glycogen, proteins and lipids, and nucleotides such as DNA and RNA. For each of those species, a different affinity constant was determined, to represent the situation when one species, for instance glutamine, is nearly depleted without significantly affecting the growth rate. A specific set of affinity constants was also used to describe the mAb production rate. Finally, inhibitory effects of lactate and ammonia on the growth rate were added to account for their accumulation in the culture media. A non-competitive inhibition mechanism was applied [42 (link)], with a distinct affinity constant for lactate regarding the growth (Equation 33 in
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