A mathematical model for eph/ephrin-directed segregation of intermingled cells.

Eph receptors, the largest family of receptor tyrosine kinases, control cell-cell adhesion/de-adhesion, cell morphology and cell positioning through interaction with cell surface ephrin ligands. Bi-directional signalling from the Eph and ephrin complexes on interacting cells have a significant role in controlling normal tissue development and oncogenic tissue patterning. Eph-mediated tissue patterning is based on the fine-tuned balance of adhesion and de-adhesion reactions between distinct Eph- and ephrin-expressing cell populations, and adhesion within like populations (expressing either Eph or ephrin). Here we develop a stochastic, Lagrangian model that is based on Eph/ephrin biology: incorporating independent Brownian motion to describe cell movement and a deterministic term (the drift term) to represent repulsive and adhesive interactions between neighbouring cells. Comparison between the experimental and computer simulated Eph/ephrin cell patterning events shows that the model recapitulates the dynamics of cell-cell segregation and cell cluster formation. Moreover, by modulating the term for Eph/ephrin-mediated repulsion, the model can be tuned to match the actual behaviour of cells with different levels of Eph expression or activity. Together the results of our experiments and modelling suggest that the complexity of Eph/ephrin signalling mechanisms that control cell-cell interactions can be described well by a mathematical model with a single term balancing adhesion and de-adhesion between interacting cells. This model allows reliable prediction of Eph/ephrin-dependent control of cell patterning behaviour.

The generation of live offspring from vitrified oocytes.

Oocyte cryopreservation is extremely beneficial for assisted reproductive technologies, the treatment of infertility and biotechnology and offers a viable alternative to embryo freezing and ovarian grafting approaches for the generation of embryonic stem cells and live offspring. It also offers the potential to store oocytes to rescue endangered species by somatic cell nuclear transfer and for the generation of embryonic stem cells to study development in these species. We vitrified mouse oocytes using a range of concentrations of trehalose (0 to 0.3 M) and demonstrated that 0.1 and 0.3 M trehalose had similar developmental rates, which were significantly different to the 0.2 M cohort (P<0.05). As mitochondria are important for fertilisation outcome, we observed that the clustering and distribution of mitochondria of the 0.2 M cohort were more affected by vitifrication than the other groups. Nevertheless, all 3 cohorts were able to develop to blastocyst, following in vitro fertilisation, although developmental rates were better for the 0.1 and 0.3 M cohorts than the 0.2 M cohort (P<0.05). Whilst blastocysts gave rise to embryonic stem-like cells, it was apparent from immunocytochemistry and RT-PCR that these cells did not demonstrate true pluripotency and exhibited abnormal karyotypes. However, they gave rise to teratomas following injection into SCID mice and differentiated into cells of each of the germinal layers following in vitro differentiation. The transfer of 2-cell embryos from the 0.1 and 0.3 M cohorts resulted in the birth of live offspring that had normal karyotypes (9/10). When 2-cell embryos from vitrified oocytes underwent vitrification, and were thawed and transferred, live offspring were obtained that exhibited normal karyotypes, with the exception of one offspring who was larger and died at 7 months. We conclude that these studies highlight the importance of the endometrial environment for the maintenance of genetic stability and thus the propagation of specific genetic traits.