Erythroblasts

An ordinary differential equations model of bone marrow erythropoiesis was developed in the past (see [6] (link)–[9] , [21] (link)). We briefly sketch this model for self-consistancy. The model consists of concatenated cell compartments describing the dynamics of the following bone marrow cell stages of erythropoiesis: haematopoietic stem cells (S), burst forming units - erythroid (BE), colony forming units - erythroid (CE), proliferating erythroblasts (PEB), maturing erythroblasts (MEB), reticulocytes (RET) and mature erythrocytes (ERY). Differentiation of cells is modelled by fluxes from one compartment to the next stage. Proliferation is modelled by amplification in the corresponding compartment (see [21] (link)). Compartment sizes are modelled by balance equations of the form where is the amplification, the transit time, is the influx from the previous compartment, and the content of the compartment. The stem cell compartment has a different structure: Here, the percentage of self-renewing cell divisions and the percentage of proliferating cells is regulated by the bone marrow cell compartments (details see section A.2 in file S1). The stem cell compartment is identical to those used in other lineage models of our group [5] (link), [11] (link), [12] (link).
Maturation is modelled by a set of concatenated first order transitions of the form where is the content of the -th subcompartment of , is the influx from the previous compartment and is the delay parameter with delay time . In [11] (link) it has been shown that this results in Gamma-distributed delay times with expectation and variance . Later, this principle is not only applied to model maturation but also to delay chemotherapy action and (delayed) absorption of EPO injections.
The differential equations system is regulated by several feedback loops. Loop 1 and 2 are feedbacks regarding the stem cell self-renewal and proliferation [9] , [22] . Loop 3 is mediated by the cytokine EPO which increases amplification ( ) or shortens maturation time ( ) in all bone marrow compartments except for the stem cells [7] . Endogenous EPO production is regulated by oxygen saturation. For a brief explanation of the model of endogenous EPO regulation see the file S1.
Quantities that depend on EPO concentration are typically regulated by so called Z-functions. The Z-function is a monotone function with minimum and maximum . It reads as follows
where is the steady state value, is the sensitivity of under stimulation and is the EPO concentration relative to steady-state (See also [9] , p. 69.)
A further model assumption is that in steady state most erythrocytes die dependent on age (i.e. similar to a first-in-first-out kinetic), but under stimulation, erythrocyte degradation occurs more randomly (i.e. exponential decay) [21] (link). Finally, iron metabolism is not explicitly modelled and it is assumed that iron supply is not a limiting factor. A complete set of model equations and parameters can be found in the file S1.
This model of bone marrow erythropoiesis was established on the basis of several experimental results for example on irradiation, bleeding, hypoxia and hypertransfusion in mice [9] . But so far, neither applications of EPO nor chemotherapy were considered. Due to its successes in explaining the above mentioned scenarios, we adopt the assumptions and equations of this cell kinetic model. They serve as a backbone of our comprehensive model in the sense that all other parts, i.e. pharmacokinetics and -dynamics of EPO and chemotherapy injections, are attached to this structure.

Each cohort performed independent epigenome-wide association studies (EWASs) according to a pre-specified analytic plan. For each CpG site, placental methylation was reported as the average β-value, ranging from 0 (unmethylated) to 1 (fully methylated). Two sex-stratified models were fit using the R package limma [44 (link)]: 1) an unadjusted model with placental methylation β-values as the dependent variable and gestational age (continuous) as the independent variable; and 2) an adjusted model that included estimated proportions of trophoblasts, syncytiotrophoblast, stromal, Hofbauer, endothelial, and nucleated red blood cells as model covariates [45 (link)]. By comparing the coefficients for gestational age from the two models within each sex strata, we can make an indirect assessment about the extent to which increasing gestational age may be altering the cellular composition of the placenta [46 (link)]. Large differences between the unadjusted and cell-type adjusted coefficients are proposed to represent CpG methylation signals that are not independently correlated with the amount of time spent in utero but rather are primarily driven by differences in cell-type proportions.
Proportions of the placental cell types were estimated using a reference-based deconvolution method via the R package planet [45 (link)]. The planet algorithm was developed by characterizing the methylomes of placentas collected from terminated and healthy term pregnancies and therefore requires that users specify whether their samples were collected during the first or third trimester. For our analyses, we applied this approach as designed for all third trimester samples (≥28 weeks gestation); for any second trimester samples (<28 weeks gestation), we interpolated cell-type proportions by simply averaging across first and third trimester estimates per the planet authors’ recommendations (V. Yuan and W. Robinson, personal communication, 17 February 2021). Heatmaps of the estimated placental cell-type proportions were produced by each cohort using R package pheatmap [47 ], with hierarchical clustering performed using Ward’s method and annotations for infant sex and gestational age [48 ].

Potential covariates were selected based on previous literature. Maternal covariates included age at intake, education level, categorized into low and medium education versus higher education, parity, as nulliparous versus multiparous, smoking during pregnancy, divided into no smoking and quitting when pregnancy was known versus sustained smoking, and neighbourhood deprivation index, based on the Dutch deprivation index and categorized in tertiles [33 ]. This index is calculated based on residents’ characteristics, such as education, income, and job market position. Child sex was also included as a covariate. Maternal information was obtained via questionnaires sent out in each pregnancy trimester. Information on child sex and birth weight was obtained from midwife and hospital records. Cord blood cell-type proportions were obtained from the ‘Salas’ reference panel for the estimation of cell-type proportion in the ‘FlowSorted.CordBlood.Combined.450 K’ Bioconductor package [34 (link)]. This reference set includes the following cell types: CD8+ T cells, CD4+ T cells, natural killer cells, B cells, monocytes, granulocytes, nucleated red blood cells. Covariate missing values (up to a maximum of 8% for maternal smoking) were imputed using the Markov chain Monte Carlo method, and pooled analysis was conducted from five imputed datasets [35 (link)].