Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling.

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses. In this work, we present a compartment model of tumour volume and tumour composition, which, despite relative simplicity, is capable of producing a wide range of patient responses. We then develop novel statistical methodology and leverage a cohort of existing clinical data to produce a predictive model of both tumour volume progression and the associated level of uncertainty that evolves throughout a patient's course of treatment. To capture inter-patient variability, all model parameters are patient specific, with a bootstrap particle filter-like Bayesian approach developed to model a set of training data as prior knowledge. We validate our approach against a subset of unseen data, and demonstrate both the predictive ability of our trained model and its limitations.

Rapid Evolution of the Embryonically Expressed Homeobox Gene LEUTX within Primates.

LEUTX is a homeodomain transcription factor expressed in the very early embryo with a function around embryonic genome activation. The LEUTX gene is found only in eutherian mammals including humans but, unlike the majority of homeobox genes, the encoded amino acid sequence is very different between divergent mammalian species. However, whether dynamic evolution has also occurred between closely related mammalian species remains unclear. In this work, we perform a comparative genomics study of LEUTX within the primates, revealing dramatic evolutionary sequence change between closely related species. Positive selection has acted on sites in the LEUTX protein, including six sites within the homeodomain; this suggests that selection has driven changes in the set of downstream targets. Transfection into cell culture followed by transcriptomic analysis reveals small functional differences between human and marmoset LEUTX, suggesting rapid sequence evolution has fine-tuned the role of this homeodomain protein within the primates.

PRD-Class Homeobox Genes in Bovine Early Embryos: Function, Evolution, and Overlapping Roles.

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 characterize 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.

An in silico Model of T Cell Infiltration Dynamics Based on an Advanced in vitro System to Enhance Preclinical Decision Making in Cancer Immunotherapy.

Cancer immunotherapy often involves the use of engineered molecules to selectively bind and activate T cells located within tumour tissue. Fundamental to the success of such treatments is the presence or recruitment of T cells localised within the tumour microenvironment. Advanced organ-on-a-chip systems provide an in vitro setting in which to investigate how novel molecules influence the spatiotemporal dynamics of T cell infiltration into tissue, both in the context of anti-tumour efficacy and off-tumour toxicity. While highly promising, the complexity of these systems is such that mathematical modelling plays a crucial role in the quantitative evaluation of experimental results and maximising the mechanistic insight derived. We develop a mechanistic, mathematical model of a novel microphysiological in vitro platform that recapitulates T cell infiltration into epithelial tissue, which may be normal or transformed. The mathematical model describes the spatiotemporal dynamics of infiltrating T cells in response to chemotactic cytokine signalling. We integrate the model with dynamic imaging data to optimise key model parameters. The mathematical model demonstrates a good fit to the observed experimental data and accurately describes the distribution of infiltrating T cells. This model is designed to complement the in vitro system; with the potential to elucidate complex biological mechanisms, including the mode of action of novel therapies and the drivers of safety events, and, ultimately, improve the efficacy-safety profile of T cell-targeted cancer immunotherapies.

Dynamic Molecular Evolution of Mammalian Homeobox Genes: Duplication, Loss, Divergence and Gene Conversion Sculpt PRD Class Repertoires.

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.

The importance of dead material within a tumour on the dynamics in response to radiotherapy.

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.

The Evolution of Tumour Composition During Fractionated Radiotherapy: Implications for Outcome.

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.