arXiv subjects

Michael D. Nicholson

Publications and source records attributed to Michael D. Nicholson.

4 recordsLinked to original sources

arXiv2024

Quantifying "just-right" APC inactivation for colorectal cancer initiation

Dysregulation of the tumour suppressor gene Adenomatous Polyposis Coli (APC) is a canonical step in colorectal cancer development. Curiously, most colorectal tumours carry biallelic mutations that result in only partial loss of APC function, suggesting that a "just-right" level of APC inactivation, and hence Wnt signalling, provides the optimal conditions for tumorigenesis. Mutational processes act variably across the APC gene, which could contribute to the bias against complete APC inactivation. Thus the selective consequences of partial APC loss are unclear. Here we propose a mathematical model to quantify the tumorigenic effect of biallelic APC genotypes, controlling for somatic mutational processes. Analysing sequence data from >2500 colorectal cancers, we find that APC genotypes resulting in partial protein function confer about 50 times higher probability of progressing to cancer compared to complete APC inactivation. The optimal inactivation level varies with anatomical location and additional mutations of Wnt pathway regulators. We use this context dependency to assess the regulatory effect of secondary Wnt drivers in combination with APC in vivo, and provide evidence that mutant AMER1 combines with APC genotypes that lead to relatively low Wnt. The fitness landscape of APC inactivation is consistent across microsatellite unstable and POLE-deficient colorectal cancers and tumours in patients with Familial Adenomatous Polyposis, suggesting a general "just-right" optimum, and pointing to Wnt hyperactivation as a potential cancer vulnerability.

q-bio.QM↗

arXiv2023

Sequential mutations in exponentially growing populations

Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will it take for these cells to appear. For exponentially growing populations, these questions have been tackled only in special cases so far. Here, within a multitype branching process framework, we consider a general mutational path where mutations may be advantageous, neutral or deleterious. In the biologically relevant limiting regimes of large times and small mutation rates, we derive probability distributions for the number, and arrival time, of cells with n mutations. Surprisingly, the two quantities respectively follow Mittag-Leffler and logistic distributions regardless of $n$ or the mutations' selective effects. Our results provide a rapid method to assess how altering the fundamental division, death, and mutation rates impacts the arrival time, and number, of mutant cells. We highlight consequences for mutation rate inference in fluctuation assays.

q-bio.PE↗

arXiv2019

Competing evolutionary paths in growing populations with applications to multidrug resistance

Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur, and via which sequence of steps is it most likely to emerge? For growing populations, these questions can be formulated in a general framework of branching processes spreading through a graph from a root to a target vertex. Cells have a particular fitness value on each vertex and can transition along edges at specific rates. Vertices represents cell states, say \mic{genotypes }or physical locations, while possible transitions are acquiring a mutation or cell migration. We focus on the setting where cells at the root vertex have the highest fitness and transition rates are small. Simple formulas are derived for the time to reach the target vertex and for the probability that it is reached along a given path in the graph. We demonstrate our results on \mic{several scenarios relevant to the emergence of drug resistance}, including: the orderings of resistance-conferring mutations in bacteria and the impact of imperfect drug penetration in cancer.

q-bio.PE↗

arXiv2016

Universal asymptotic clone size distribution for general population growth

Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria-Delbrück or Lea-Coulson model, is often assumed but seldom realistic. In this article we generalise this model to different types of wild-type population growth, with mutants evolving as a birth-death branching process. Our focus is on the size distribution of clones - that is the number of progeny of a founder mutant - which can be mapped to the total number of mutants. Exact expressions are derived for exponential, power-law and logistic population growth. Additionally for a large class of population growth we prove that the long time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law. Considering metastases in cancer as the mutant clones, upon analysing a data-set of their size distribution, we indeed find that a power-law tail is more likely than an exponential one.

q-bio.PE↗