One-carbon metabolism during the menstrual cycle and pregnancy

Many enzymes in one-carbon metabolism (OCM) are up- or down-regulated by the sex hormones which vary diurnally and throughout the menstrual cycle. During pregnancy, estradiol and progesterone levels increase tremendously to modulate physiological changes in the reproductive system. In this work, we extend and improve an existing mathematical model of hepatic OCM to understand the dynamic metabolic changes that happen during the menstrual cycle and pregnancy due to estradiol variation. In particular, we add the polyamine drain on S-adenosyl methionine and the direct effects of estradiol on the enzymes cystathionine β-synthase (CBS), thymidylate synthase (TS), and dihydrofolate reductase (DHFR). We show that the homocysteine concentration varies inversely with estradiol concentration, discuss the fluctuations in 14 other one-carbon metabolites and velocities throughout the menstrual cycle, and draw comparisons with the literature. We then use the model to study the effects of vitamin B12, vitamin B6, and folate deficiencies and explain why homocysteine is not a good biomarker for vitamin deficiencies. Additionally, we compute homocysteine throughout pregnancy, and compare the results with experimental data. Our mathematical model explains how numerous homeostatic mechanisms in OCM function and provides new insights into how homocysteine and its deleterious effects are influenced by estradiol. The mathematical model can be used by others for further in silico experiments on changes in one-carbon metabolism during the menstrual cycle and pregnancy.

In specifying the differential equations, we use lower case letters and simple abbreviations for the variables (substrates); these abbreviations are indicated in Table 1, below. Velocities are always indicated by V X where the subscript X gives the acronym of the enzyme that catalyzes that particular velocity. Each velocity depends on the current values of substrates. The 18 differential equations are simply mass balance equations that say that the rate of change of the concentration of a substrate is the sum of the velocities of the reactions that make the substrate minus the sum of the reactions that use the substrate. Justifications for most of the model equations can be found in the 2018 paper [1], and all new additions are explained in the Methods. The full differential equations follow: Some of the reactions depend on the concentrations of other substrates that are not variable (in the model) and are assumed to be constant. These are give in Table B. The details of the biochemistry and the biology are in the functional forms that show how each of the velocities depends on the current values of the variables that influence it. Many reactions have Michaelis-Menten kinetics in one of the following standard forms: for unidirectional, one substrate, unidirectional, two substrates, and bidirectional, two substrates, two products, respectively. For these reactions, Table C lists the K m and V max values. In general, we take K m values from the literature. V max values are extremely variable because they depend on enzyme expressions levels that vary in time and therefore experimental measurements in vivo are difficult and unreliable. We usually adjust the V max values so as to obtain the typical substrate concentration values that we find in the literature. Parameters have sometimes been chosen by comparing model outputs in various circumstances to qualitative and quantitative experimental data. The effects of estradiol on V PEMT , V CBS , V TS , and V DHFR and the new form of V CBS are discussed in detail in the Methods. All other reactions with nonstandard kinetics follow, and have been justified in [1].
where V max = 144 for males and V max = 117 for females because a higher percentage of body mass is muscle in males.
parameter value reference K m 49 [32] K i 16 [32] GNMT. The velocity of the GNMT reaction is given by .
where V max = (525)(gnmt + (.5)(gnmtf )) for males and V max = (1225)(gnmt + (.5)(gnmtf )) for females. gnmt represents the concentration of free enzyme and gnmtf represents the concentration of enzyme with one molecule of 5mTHF bound to it. These details are not indicted in Figure 1 but can be found, with justifications, in [33].
parameter value reference K m 100 [32] K i 35 [32] MAT-I. The velocity of the MAT-I reaction is given by MAT-III. The velocity of the MAT-III reaction is given by NE. The kinetics of the non-enzymatic reversible reaction between thf and ch2 are taken to be mass action, with rate constants are k 1 = 0.15, and k 2 = 12. hcho represents formaldehyde, which is a constant in the program.
Other transmethylation fluxes. We treat all other fluxes in the transmethylation pathway as "other" and give this pathway "average" kinetic parameters.