Stochastic modelling and inference for evolution in ageing and infectious diseases

Counting processes are an important class of stochastic processes with numerous interdisciplinary applications, including to evolving biological systems. Counting processes can be the basis for forward generative models, which can help develop a mechanistic understanding of a phenomenon, or for inferential methods. In this thesis we develop a bottom-up microscopic model of a phenomenon in mitochondrial biology and ageing. Mitochondria are organelles that possess their own DNA, involved in crucial physiological functions. A typical eukaryotic cell hosts a population of mitochondrial DNA molecules, where mutations can expand and cause dysfunctions. With age, skeletal muscle suffers a reduction in strength and functionality; in mammals, this has been connected to the clonal expansion of mitochondrial deletion mutations. The mechanism driving this phenomenon remains poorly understood despite intense research. We develop a stochastic population dynamics model corresponding to a novel evolutionary mechanism, termed stochastic survival of the densest, and we show that it can account for the expansion of mitochondrial mutations in skeletal muscle through a literature-parameterised model. We predict that a species can invade a system in a wave-like fashion, without having an explicit replicative advantage and even if preferentially eliminated. We establish that this mechanism is driven by the combined effect of stochasticity, differences in carrying capacity (or density) and spatial structure. Part of the work for this thesis coincided with the COVID-19 pandemic. We look at another application of counting processes, modelling data collected within the SIREN study, part of the national response to the pandemic. We estimate parameters of counting processes modelling SARS‑CoV‑2 infection events, that correspond to the reduction in rate of infection associated with COVID-19 vaccination (vaccine effectiveness), with a previous infection, or both (hybrid protection). We highlight short-term vaccine effectiveness that subsequently wanes, and confirm the immune escape of the Omicron variant.Open Acces

Antibody correlates of protection against Delta infection after vaccination: A nested case-control within the UK-based SIREN study

Objectives: To investigate serological correlates of protection against SARS-CoV-2 B.1.617.2 (Delta) infection after two vaccinations.// Methods: We performed a case-control study, where cases were Delta infections after the second vaccine dose and controls were vaccinated, never infected participants, matched by age, gender and region. Sera were tested for anti-SARS-CoV-2 Spike antibody levels (anti-S) and neutralising antibody titres (nAbT), using live virus microneutralisation against Ancestral, Delta and Omicron (BA.1, B.1.1.529). We modelled the decay of anti-S and nAbT for both groups, inferring levels at matched calendar times since the second vaccination. We assessed differences in inferred antibody titres between groups and used conditional logistic regression to explore the relationship between titres and odds of infection.// Results: In total, 130 sequence-confirmed Delta cases and 318 controls were included. Anti-S and Ancestral nAbT decayed similarly between groups, but faster in cases for Delta nAbT (p = 0.02) and Omicron nAbT (p = 0.002). At seven days before infection, controls had higher anti-S levels (p 40 were associated with reduced odds of Delta infection (89%, [69–96%]; p 100 (p = 0.009) and >400 (p = 0.007).// Conclusions: We have identified correlates of protection against SARS-CoV-2 Delta, with potential implications for vaccine deployment, development, and public health response

Antibody correlates of protection from SARS-CoV-2 reinfection prior to vaccination : a nested case-control within the SIREN study

Funding: This study was supported by the U.K. Health Security Agency, the U.K. Department of Health and Social Care (with contributions from the governments in Northern Ireland, Wales, and Scotland), the National Institute for Health Research, and grant from the UK Medical Research Council (grant number MR/W02067X/1). This work was supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (CC2087, CC1283), the UK Medical Research Council (CC2087, CC1283), and the Wellcome Trust (CC2087, CC1283).Objectives To investigate serological differences between SARS-CoV-2 reinfection cases and contemporary controls, to identify antibody correlates of protection against reinfection. Methods We performed a case-control study, comparing reinfection cases with singly infected individuals pre-vaccination, matched by gender, age, region and timing of first infection. Serum samples were tested for anti-SARS-CoV-2 spike (anti-S), anti-SARS-CoV-2 nucleocapsid (anti-N), live virus microneutralisation (LV-N) and pseudovirus microneutralisation (PV-N). Results were analysed using fixed effect linear regression and fitted into conditional logistic regression models. Results We identified 23 cases and 92 controls. First infections occurred before November 2020; reinfections occurred before February 2021, pre-vaccination. Anti-S levels, LV-N and PV-N titres were significantly lower among cases; no difference was found for anti-N levels. Increasing anti-S levels were associated with reduced risk of reinfection (OR 0·63, CI 0·47-0·85), but no association for anti-N levels (OR 0·88, CI 0·73-1·05). Titres >40 were correlated with protection against reinfection for LV-N Wuhan (OR 0·02, CI 0·001–0·31) and LV-N Alpha (OR 0·07, CI 0·009–0·62). For PV-N, titres >100 were associated with protection against Wuhan (OR 0·14, CI 0·03–0·64) and Alpha (0·06, CI 0·008–0·40). Conclusions Before vaccination, protection against SARS-CoV-2 reinfection was directly correlated with anti-S levels, PV-N and LV-N titres, but not with anti-N levels. Detectable LV-N titres were sufficient for protection, whilst PV-N titres >100 were required for a protective effect. Trial registration number ISRCTN11041050Publisher PDFPeer reviewe

Coarsening and percolation in a disordered ferromagnet

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Utility of Equivariant Message Passing in Cortical Mesh Segmentation

The automated segmentation of cortical areas has been a long-standing challenge in medical image analysis. The complex geometry of the cortex is commonly represented as a polygon mesh, whose segmentation can be addressed by graph-based learning methods. When cortical meshes are misaligned across subjects, current methods produce significantly worse segmentation results, limiting their ability to handle multi-domain data. In this paper, we investigate the utility of E(n)-equivariant graph neural networks (EGNNs), comparing their performance against plain graph neural networks (GNNs). Our evaluation shows that GNNs outperform EGNNs on aligned meshes, due to their ability to leverage the presence of a global coordinate system. On misaligned meshes, the performance of plain GNNs drop considerably, while E(n)-equivariant message passing maintains the same segmentation results. The best results can also be obtained by using plain GNNs on realigned data (co-registered meshes in a global coordinate system).Comment: 13 pages, 3 figures, accepted for MIUA 202

Coarsening and percolation in a disordered ferromagnet

By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder (either random bonds or random fields) we show that a critical percolation structure forms at an early stage. This structure is then rendered more and more compact by the ensuing coarsening process. Our results are compared to the nondisordered case, where a similar phenomenon is observed, and they are interpreted within a dynamical scaling framework

Coarsening and percolation in the Ising Model with quenched disorder

Through large-scale numerical simulations, we study the phase ordering kinetics of the 2d Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities-the winding angle and the pair-connectedness-we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model