From cell death to embryo arrest: mathematical models of human preimplantation embryo development

Abstract

Human preimplantation embryos exhibit high levels of apoptotic cells and high rates of developmental arrest during the first week in vitro. The relation between the two is unclear and difficult to determine by conventional experimental approaches, partly because of limited numbers of embryos. We apply a mixture of experiment and mathematical modeling to show that observed levels of cell death can be reconciled with the high levels of embryo arrest seen in the human only if the developmental competence of embryos is already established at the zygote stage, and environmental factors merely modulate this. This suggests that research on improving in vitro fertilization success rates should move from its current concentration on optimizing culture media to focus more on the generation of a healthy zygote and on understanding the mechanisms that cause chromosomal and other abnormalities during early cleavage stages.

Figure 1

Light and confocal micrographs showing cellular and nuclear morphology in human preimplantation embryos. Nuclei are labeled with 4′, 6-diamidino-2-phenylindole (blue). (A) Fragmenting day 2 human embryo, with fragments arrowed. (B) Nuclei from a day 6 blastocyst showing TUNEL-labeled (pink) fragmented nuclei () and healthy interphase nucleus (▸). (C) Day 2 4-cell embryo. (D) Day 4 8-cell embryo with TUNEL-labeled polar body (). (E) Day 4 embryo with 13 cells and 15 nuclei, including 2 fragmenting () and one in mitosis (m). Note TUNEL-labeled polar body. (F) Day 4 morula with 18 nuclei, including 2 in mitosis (m); 1 fragmented nucleus that is TUNEL-labeled () and 1 fragmented nucleus with no TUNEL labeling (▸). (G) Day 4 morula with 24 nuclei, including 7 condensed, TUNEL-labeled nuclei (). (H) Day 6 blastocyst with 87 nuclei, 12 of which are TUNEL-labeled and mostly localized to the region of the inner cell mass.

Figure 2

(A) Proportion of fragmented nuclei against number of intact nuclei for 203 day 6 blastocysts (10). Fragmenting and healthy nuclei were labeled with polynucleotide-specific fluorochromes and counted by using fluorescence microscopy (e.g., ref. 10). (B) Proportion of 994 embryos that have arrested by a given developmental stage. Accumulated retrospective control data from culture studies observing embryo development in vitro to day 6.

Figure 3

(A; main figure) Schematic representation of branching process model of cell division and cell death in an embryo, and approximate correspondence between generations, developmental stages and chronological time, with day of oocyte retrieval being day 0. The equivalence between generations 0 to 4 and the 1- to 16- cell stages is straightforward, but that for subsequent generations is more imprecise. Confocal analysis of preimplantation human embryos indicates that compaction does not occur before the 16- to 32-cell stages (i.e., generations 4 and 5) (14). Newly expanded blastocysts of good morphology on day 5 were found to have, on average, 58 cells (8), which means that they were at about generation 6. Day 6 and 7 blastocysts had a mean of 84 and 126 cells, respectively. Thus we can assign generations 4 and 5 to the morula stage, and 6 to 8 to the blastocyst stage. To relate the model to the data in Fig. 2A, we make the simplest possible choice that each fragmented nucleus in Fig. 2A is equivalent to one cell dying during the last generation simulated by the model. This assumption was tested and found to be reasonable by extending the model to allow for different rates of dead cell clearance (see supplemental Appendix, www.pnas.org). (B Inset) Choice of actions and associated probabilities at each branch.

Figure 4

Cell death in normally developing embryos of good morphology: average percentage of nuclei in each embryo that is fragmented or TUNEL labeled; values are mean ± SEM.

Figure 5

Embryo loss levels predicted by preliminary model. (A) Embryo loss rate at each generation for a choice of other parameters: ○ α = 0.145, n_s = 2 (Fit I, Table 1); ● α = 0.139, n_s = 0 (Fit IV, Table 1); .⋄ α = 0.485, n_s = 2; ♦ α = 0.3, n_s = 0. (B) Embryo loss rate at the 8th generation as a function of α, assuming cell death starts respectively at generation 0 and 2. In all cases, δ = 0.11, except for Fit IV, where δ = 0.076. The dependence of the embryo loss level on δ is much weaker than that on α or n_s and hence is not shown.