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Rat liver folate metabolism can provide an independent functioning of associated metabolic pathways

Folate metabolism in mammalian cells is essential for multiple vital processes, including purine and pyrimidine synthesis, histidine catabolism, methionine recycling, and utilization of formic acid. It remains unknown, however, whether these processes affect each other via folate metabolism or can function independently based on cellular needs. We addressed this question using a quantitative mathematical model of folate metabolism in rat liver cytoplasm. Variation in the rates of metabolic processes associated with folate metabolism (i.e., purine and pyrimidine synthesis, histidine catabolism, and influxes of formate and methionine) in the model revealed that folate metabolism is organized in a striking manner that enables activation or inhibition of each individual process independently of the metabolic fluxes in others. In mechanistic terms, this independence is based on the high activities of a group of enzymes involved in folate metabolism, which efficiently maintain close-to-equilibrium ratios between substrates and products of enzymatic reactions.


AT (AICAR Transformylase, EC 2.1.2.3). AT catalyzes irreversible reaction of formyl group
transfer from 10-THF to AICAR via a random sequential bi-bi mechanism 1 providing the second of the two folate-requiring reactions in purine de novo biosynthesis. The reaction rate in the model is described by the corresponding equation: to THF using NADPH as a cofactor. The reaction mechanism is random sequential bi-bi 2 . Under physiological conditions the enzyme is saturated with NADPH (Supplementary texts S1, S4).
Thus, the reaction rate can be described by Michaelis-Menten equation with one substrate: FTHFD (Formyltetrahydrofolate dehydrogenase, EC 1.5.1.6). FTHFD catalyzes irreversible reaction of NADP -dependent oxidation of 10-THF to THF and CO 2 3,4 . Under intracellular conditions the enzyme is supposed to be saturated with NADP, since the corresponding Michaelis constant value is substantially lower than the intracellular NADP concentration (Supplementary texts S1, S4). Also, the enzyme is strongly inhibited by THF [5][6][7] . In the model the FTHFD reaction rate is described by the equation taken from 7 :

FTHFS (Formyltetrahydrofolate synthetase, EC 6.3.4.3). FTHFS catalyzes the reversible
ATP-dependent synthesis of 10-formyltetrahydrofolate from formate and tetrahydrofolate. While a ping-pong mechanism was proposed for the reaction based on the enzyme crystal structure analysis 8 there are no strong evidences supporting this mechanism. The reaction rate in the model is described by equation for random-order sequential bi-bi mechanism 9,10 with assumption that enzyme is saturated with ATP and ADP (Supplementary texts S1, S4). Transferase reaction follows the random sequential bi-bi mechanism 11 . The overall reaction is considered to be irreversible 12,13  conversion between THF and serine and CH2-THF and glycine. Reaction mechanism is random sequential bi-bi 23 . The enzyme is inhibited by 5-THF and CH3-THF 24 . The inhibition constant value for 5-THF monoglutamate is equal to 130 µM 24 . Even after a 10 fold decrease that can be expected for polyglutamate this value remains high compared to 5-THF concentration in cells (     5 and for K eq2 = 21 7 and using equations S3.7-S3.9 one can get the value for K eq3 = K eq1 /K eq2 = 0.76.

Supplementary text S4. Enzyme kinetic parameters.
In the model we tried to used enzyme kinetic parameters obtained for rodent liver, if available, making preference for rat liver. All enzyme activities used in the model were obtained for rat liver and presented as mmol per hour per kg of wet liver, that is a very close estimation for mmol per hour per liter. In case if enzyme activity in the literature was normalized to protein we recalculated the activity as per kg using protein concentration of 200 g per kg of wet liver 1 .
If enzyme activity or catalytic constant in the literature was measured at temperature other than    The kinetics of folate pool can be described by the following equation: where F is folate pool (sum of concentrations of polyglutamate forms of folates), V FPGS is the rate of folylpolyglutamate synthase, V degr is the rate of non-enzymatic folate pool degradation.
The rate for non-enzymatic folate degradation can be described as follows: where k degr is reaction rate constant for the non-enzymatic folate pool degradation. The estimation for the rate constant k degr of folate pool degradation at physiological conditions can be obtained from experiments with prolonged feeding of rats with folate-free diet. 6 That gives us an estimation for the characteristic time of folate pool turnover that is equal to 1/k degr = 333 h. This time is several orders of magnitude bigger than characteristic times of folate metabolites and folate dependent processes ( Table 2, 5). Thus for all metabolic processes associated with folate metabolism in our model we can consider folate pool as a constant model parameter.