Biology subjects

Noble, R. J.

Publications and source records attributed to Noble, R. J..

8 recordsLinked to original sources

bioRxiv2026

Fluctuating DNA methylation sites encode colorectal tumour growth history

Determining the nature of human tumour growth is challenging given the impracticality of obtaining detailed data across time. A promising solution is to examine DNA regions whose methylation states fluctuate on clinically relevant timescales, permitting their use as high-resolution lineage tracers. However, existing methods developed for analysing the fluctuating methylation loci of normal tissue and lymphoid cancers are inapplicable to large solid tumours. Here we introduce a mechanistic computational model that tracks the evolution of heritable methylation marks as a tumour grows from a single gland to a mass of many cubic centimetres, and a coupled ABC-SMC inference workflow to estimate tumour growth parameters from multi-region bulk methylation arrays. We applied this framework to data from multiple regions of 10 resected colorectal tumours, including 3 adenomas and 7 carcinomas of diverse sizes and clinical stages. By exploring alternative models, we show that intratumour diversity, in terms of methylation errors, stems more from tumour growth via gland fission than from cell turnover within glands. Moreover, the extent of intratumour diversity varies widely between patients, mainly because of eight-fold variation in gland fission rates but also due to differences in methylation and demethylation rates. Inter-gland divergence patterns are consistent with neutral evolution of colorectal tumours and a cancer stem cell fraction of approximately 1%. As well as helping to resolve the nature of colorectal cancer growth and evolution, our results provide proof of principle for a method that may be adapted to infer the biological parameters of other types of solid tumour. Author summaryEstimating how fast, for how long, and in what way a tumour has been growing inside someones body is challenging. We sought a solution by looking at chemical marks on DNA that are imperfectly copied every time a cell divides. We built a computer model to track how the patterns of marks diverge among the cells of a colorectal tumour as it grows. By running many simulations and comparing the outcomes to data from 10 human tumours, we were able to reconstruct how each of them had grown. We found that growth rate varies widely and is not linked to the size of the tumour when it is removed. The rates at which the DNA marks change also vary but to a lesser degree. Our approach provides a new, inexpensive way to reconstruct tumour growth histories from tissue samples collected during routine surgery, without having to take multiple measurements over time. This approach could be applied to other human cancer types.

cancer biology↗

bioRxiv2023

Selective sweep probabilities in spatially expanding populations

Evolution during range expansions shapes biological systems from microbial communities and tumours up to invasive species. A fundamental question is whether, when a beneficial mutation arises during a range expansion, it will evade clonal interference and sweep through the population to fixation. However, most theoretical investigations of range expansions have been confined to regimes in which selective sweeps are effectively impossible, while studies of selective sweeps have either assumed constant population size or have ignored spatial structure. Here we use mathematical modelling and analysis to investigate selective sweep probabilities in the alternative yet biologically relevant scenario in which mutants can outcompete and displace a slowly spreading wildtype. Assuming constant radial expansion speed, we derive probability distributions for the arrival time and location of the first surviving mutant and hence find surprisingly simple approximate and exact expressions for selective sweep probabilities in one, two and three dimensions, which are independent of mutation rate. Namely, the selective sweep probability is approximately (1 - cwt/cm)d, where cwt and cm are the wildtype and mutant radial expansion speeds, and d the spatial dimension. Using agent-based simulations, we show that our analytical results accurately predict selective sweep frequencies in the two-dimensional spatial Moran process. We further compare our results with those obtained for alternative growth laws. Parameterizing our model for human tumours, we find that selective sweeps are predicted to be rare except during very early solid tumour growth, thus providing a general, pan-cancer explanation for findings from recent sequencing studies.

evolutionary biology↗

bioRxiv2023

Preventing evolutionary rescue in cancer

AO_SCPLOWBSTRACTC_SCPLOWFirst-line cancer treatment frequently fails due to initially rare therapeutic resistance. An important clinical question is then how to schedule subsequent treatments to maximize the probability of tumour eradication. Here, we provide a theoretical solution to this problem by using mathematical analysis and extensive stochastic simulations within the framework of evolutionary rescue theory to determine how best to exploit the vulnerability of small tumours to stochastic extinction. Whereas standard clinical practice is to wait for evidence of relapse, we confirm a recent hypothesis that the optimal time to switch to a second treatment is when the tumour is close to its minimum size before relapse, when it is likely undetectable. This optimum can lie slightly before or slightly after the nadir, depending on tumour parameters. Given that this exact time point may be difficult to determine in practice, we study windows of high extinction probability that lie around the optimal switching point, showing that switching after the relapse has begun is typically better than switching too early. We further reveal how treatment dose and tumour demographic and evolutionary parameters influence the predicted clinical outcome, and we determine how best to schedule drugs of unequal efficacy. Our work establishes a foundation for further experimental and clinical investigation of this evolutionarily-informed "extinction therapy" strategy.

cancer biology↗

bioRxiv2023

Better tree shape indices

The comparison and categorization of tree diagrams is fundamental to large parts of biology, linguistics, computer science, and other fields, yet the indices currently applied to describing tree shape have important flaws that complicate their interpretation and limit their scope. Here we introduce a new system of indices with no such shortcomings. Our indices account for node sizes and branch lengths and are robust to small changes in either attribute. Unlike currently popular phylogenetic diversity, phylogenetic entropy, and tree balance indices, our definitions assign interpretable values to all rooted trees and enable meaningful comparison of any pair of trees. Our self-consistent definitions further unite measures of diversity, richness, balance, symmetry, effective height, effective outdegree, and effective branch count in a coherent system, and we derive numerous simple relationships between these indices. The main practical advantages of our indices are in 1) quantifying diversity in non-ultrametric trees; 2) assessing the balance of trees that have non-uniform branch lengths or node sizes; 3) comparing the balance of trees with different leaf counts or outdegrees; 4) obtaining a coherent, generic, multidimensional quantification of tree shape that is robust to sampling error and inferential error. We illustrate these features by comparing the shapes of trees representing the evolution of HIV and of Uralic languages, and trees generated by computational models of tumour evolution. Given the ubiquity of tree structures, we identify a wide range of applications across diverse domains. tree indices, tree shape, tree balance, phylogenetic diversity, phylogenetic entropy, rooted trees

systems biology↗

bioRxiv2021

Robust, Universal Tree Balance Indices

Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet existing indices have important shortcomings, including that they are unsuited to the tree types commonly used to describe the evolution of tumours, microbial populations, and cell lines. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless index but account for node sizes, are defined for trees with any degree distribution, and enable more meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalised reciprocal of Sackins index. Hence we both unify and generalise the two most popular existing tree balance indices. Our indices are intrinsically normalised and can be computed in linear time. We conclude that these more widely applicable indices have potential to supersede those in current use.

evolutionary biology↗

bioRxiv2020

Paracrine behaviors arbitrate parasite-like interactions between tumor subclones

Explaining the emergence and maintenance of intratumor heterogeneity is an important question in cancer biology. Tumor cells can generate considerable subclonal diversity, which influences tumor growth rate, treatment resistance, and metastasis, yet we know remarkably little about how cells from different subclones interact. Here, we confronted two murine mammary cancer cell lines to determine both the nature and mechanisms of subclonal cellular interactions in vitro. Surprisingly, we found that, compared to monoculture, growth of the winner was enhanced by the presence of the loser cell line, whereas growth of the latter was reduced. Mathematical modeling and laboratory assays indicated that these interactions are mediated by the production of paracrine metabolites resulting in the winner subclone effectively farming the loser. Our findings add a new level of complexity to the mechanisms underlying subclonal growth dynamics.

cancer biology↗

bioRxiv2020

The logic of containing tumors

Challenging the paradigm of the maximum tolerated dose, recent studies have shown that a strategy aiming for containment, not elimination, can control tumor burden more effectively in vitro, in mouse models, and in the clinic. These outcomes are consistent with the hypothesis that emergence of resistance to cancer therapy may be prevented or delayed by exploiting competitive ecological interactions between drug-sensitive and resistant tumor cell subpopulations. However, although various mathematical and computational models have been proposed to explain the superiority of particular containment strategies, this evolutionary approach to cancer therapy lacks a rigorous theoretical foundation. Here we combine extensive mathematical analysis and numerical simulations to establish general conditions under which a containment strategy is expected to control tumor burden more effectively than applying the maximum tolerated dose. We show that when resistant cells are present, an idealized strategy of containing a tumor at a maximum tolerable size maximizes time to treatment failure (that is, the time at which tumor burden becomes intolerable). These results are very general and do not depend on any fitness cost of resistance. We further provide formulas for predicting the clinical benefits attributable to containment strategies in a wide range of scenarios, and we compare outcomes of theoretically optimal treatments with those of more practical protocols. Our results strengthen the rationale for clinical trials of evolutionarily-informed cancer therapy.

cancer biology↗

bioRxiv2019

When, why and how clonal diversity predicts future tumour growth

Intratumour heterogeneity holds promise as a prognostic biomarker in multiple cancer types. However, the relationship between this marker and its clinical impact is mediated by an evolutionary process that is not well understood. Here we employ a spatial computational model of tumour evolution to assess when, why and how intratumour heterogeneity can be used to forecast tumour growth rate, an important predictor of clinical progression. We identify three conditions that can lead to a positive correlation between clonal diversity and subsequent growth rate: diversity is measured early in tumour development; selective sweeps are rare; and/or tumours vary in the rate at which they acquire driver mutations. Opposite conditions typically lead to negative correlation. Our results further suggest that prognosis can be better predicted on the basis of both clonal diversity and genomic instability than either factor alone. Nevertheless, we find that, for predicting tumour growth, clonal diversity is likely to perform worse than conventional measures of tumour stage and grade. We thus offer explanations - grounded in evolutionary theory - for empirical findings in various cancers. Our work informs the search for new prognostic biomarkers and contributes to the development of predictive oncology.

cancer biology↗