Current protocols for delivering radiotherapy are based primarily on tumour stage and nodal and metastases status, even though it is well known that tumours and their microenvironments are highly heterogeneous. It is well established that the local oxygen tension plays an important role in radiation-induced cell death, with hypoxic tumour regions responding poorly to irradiation. Therefore, to improve radiation response, it is important to understand more fully the spatiotemporal distribution of oxygen within a growing tumour before and during fractionated radiation. To this end, we have extended a spatially resolved mathematical model of tumour growth, first proposed by Greenspan (Stud Appl Math 51:317-340, 1972), to investigate the effects of oxygen heterogeneity on radiation-induced cell death. In more detail, cell death due to radiation at each location in the tumour, as determined by the well-known linear-quadratic model, is assumed also to depend on the local oxygen concentration. The oxygen concentration is governed by a reaction-diffusion equation that is coupled to an integro-differential equation that determines the size of the assumed spherically symmetric tumour. We combine numerical and analytical techniques to investigate radiation response of tumours with different intratumoral oxygen distribution profiles. Model simulations reveal a rapid transient increase in hypoxia upon regrowth of the tumour spheroid post-irradiation. We investigate the response to different radiation fractionation schedules and identify a tumour-specific relationship between inter-fraction time and dose per fraction to achieve cure. The rich dynamics exhibited by the model suggest that spatial heterogeneity may be important for predicting tumour response to radiotherapy for clinical applications.

The majority of homeobox genes are highly conserved across animals, but the eutherian-specific ETCHbox genes, embryonically expressed and highly divergent duplicates of CRX, are a notable exception. Here we compare the ETCHbox genes of 34 mammalian species, uncovering dynamic patterns of gene loss and tandem duplication, including the presence of a large tandem array of LEUTX loci in the genome of the European rabbit (Oryctolagus cuniculus). Despite extensive gene gain and loss, all sampled species possess at least two ETCHbox genes, suggesting their collective role is indispensable. We find evidence for positive selection and show that TPRX1 and TPRX2 have been the subject of repeated gene conversion across the Boreoeutheria, homogenising their sequences and preventing divergence, especially in the homeobox region. Together, these results are consistent with a model where mammalian ETCHbox genes are dynamic in evolution due to functional overlap, yet have collective indispensable roles.

In vivo tumours are highly heterogeneous entities which often comprise intratumoural regions of hypoxia and widespread necrosis. In this paper, we develop a new three phase model of nutrient-limited, avascular tumour growth to investigate how dead material within the tumour may influence the tumour’s growth dynamics. We model the tumour as a mixture of tumour cells, dead cellular material and extracellular fluid. The model equations are derived using mass and momentum balances for each phase along with appropriate constitutive equations. The tumour cells are viewed as a viscous fluid pressure, while the extracellular fluid phase is viewed as inviscid. The physical properties of the dead material are intermediate between those of the tumour cells and extracellular fluid, and are characterised by three key parameters. Through numerical simulation of the model equations, we reproduce spatial structures and dynamics typical of those associated with the growth of avascular tumour spheroids. We also characterise novel, non-monotonic behaviours which are driven by the internal dynamics of the dead material within the tumour. Investigations of the parameter sub-space describing the properties of the dead material reveal that the way in which non-viable tumour cells are modelled may significantly influence the qualitative tumour growth dynamics.

In vivo tumours are highly heterogeneous, often comprising regions of hypoxia and necrosis. Radiotherapy significantly alters the intratumoural composition. Moreover, radiation-induced cell death may occur via a number of different mechanisms that act over different timescales. Dead material may therefore occupy a significant portion of the tumour volume for some time after irradiation and may affect the subsequent tumour dynamics. We present a three phase tumour growth model that accounts for the effects of radiotherapy and use it to investigate how dead material within the tumour may affect the spatio-temporal tumour response dynamics. We use numerical simulation of the model equations to characterise qualitatively different tumour volume dynamics in response to fractionated radiotherapy. We demonstrate examples, and associated parameter values, for which the properties of the dead material significantly alter the observed tumour volume dynamics throughout treatment. These simulations suggest that for some cases it may not be possible to accurately predict radiotherapy response from pre-treatment, gross tumour volume measurements without consideration of the dead material within the tumour.

Eutherian Totipotent Cell Homeobox (ETCHbox) genes are mammalian-specific PRD-class homeobox genes with conserved expression in the preimplantation embryo but fast-evolving and highly divergent sequences. Here we exploit an ectopic expression approach to examine the role of bovine ETCHbox genes and show that ARGFX and LEUTX homeodomain proteins upregulate genes normally expressed in the blastocyst; the identities of the regulated genes suggest that, in vivo, the ETCHbox genes play a role in coordinating the physical formation of the blastocyst structure. Both genes also downregulate genes expressed earlier during development and genes associated with an undifferentiated cell state, possibly via the JAK/STAT pathway. We find evidence that bovine ARGFX and LEUTX have overlapping functions, in contrast to their antagonistic roles in humans. Finally, we characterise a mutant bovine ARGFX allele which eliminates the homeodomain and show that homozygous mutants are viable. These data support the hypothesis of functional overlap between ETCHbox genes within a species, roles for ETCHbox genes in blastocyst formation and the change of their functions over evolutionary time.