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Abstracts 2023/24

Abstracts Term 3

3rd June. Michael Plank. Mathematical modelling to support New Zealand’s Covid-19 response.

In this talk, I will describe some of the ways in which mathematical modelling contributed to the Covid-19 pandemic response in New Zealand. New Zealand adopted an elimination strategy at the beginning of the pandemic and used a combination of public health measures and border restrictions to keep incidence of Covid-19 low until high vaccination rates were achieved. The low or zero prevalence for first 18 months of the pandemic called for a different set of modelling tools compared to high-prevalence settings. It also generated some unique data that can give valuable insights into epidemiological characteristics and dynamics. As well as describing some of the modelling approaches used, I will reflect on the value modelling can add to decision making and some of the challenges and opportunities in working with stakeholders in government and public health.

Abstracts Term 2

22nd January. Helen Bryne. Applications of Topological Data Analysis in Biology.

The past twenty-five years have seen an unparalleled increase in the diversity, quantity and quality of data that can be extracted from biological systems. For example, it is now possible to generate exquisitely detailed 3D renderings of tumour vascular networks which show how their architecture changes over time and in response to treatment. Developing methods that can quantify and compare such complex biological datasets is an active area of research. In this talk, I will show how topological data analysis, a mathematical field that studies the “shape” of data, can be used to analyse different such high-dimensional data. I will focus on three case studies which illustrate how topological data analysis can be used: to quantify dynamics changes in vascular networks; to investigate how the structure of the extracellular matrix affects immune cell infiltration in lung cancer; and to analyse flow cytometry data in order to predict risk of relapse in paediatric leukaemia.

29th January 2024. Karen Page. Positional information theory.

We study the positional information conferred by the morphogens Sonic Hedgehog and BMP in neural tube patterning. We use the mathematics of information theory to quantify the information that cells use to decide their fate. We study the encoding, recoding and decoding that take place as the morphogen gradient is formed, triggers a nuclear response and determines cell fates using a gene regulatory network.

5th February. Paolo Ribeca. On embeddings, distances, phylogenies, and All That.

An increasing number of applications in the life sciences and public health require large collections of genomic sequences to be stored, classified, searched, retrieved and interpreted. That bears obvious parallels with use cases typical of the Internet and its content, which are often the starting point for techniques based on machine learning and AI. Here we explore this connection in some detail, showing how several ideas originally proposed in the field of big data have been successfully transferred to bioinformatics – while others, surprisingly, have not. In particular, we focus on the concept of embedding biological sequences into “latent” spaces, showcasing a few of its promising applications and its intriguing connection with seemingly unrelated concepts in bioinformatics and genomics.

12th February 2024. Guillaume Charras (UCL). Control of morphogenesis by the actin cortex in single cells and multicellular aggregates.

The actin cortex is a thin meshwork of actin filaments, myosin motors and actin-binding proteins that lies below the membrane. Mechanical changes in the cortex play an essential role in morphogenesis of cells and tissues. I will present work examining the role of the cortex in cell division and the shape of multicellular aggregates.

As they enter mitosis, cells undergo profound shape changes that are controlled by gradients in mechanical tension arising in the submembranous actin cortex. These changes are controlled by RhoGTPases, key regulators of the cytoskeleton and contractility. In turn, RhoGTPase activity is regulated by RhoGEFs that activate them and RhoGAPs that inactivate them. Despite their central role in cell morphogenesis, we know little about how RhoGEFs control the changes in cell mechanics that drive shape change. I will present work examining the link between signalling and cell mechanics using AFM, imaging, and optogenetics.

During embryonic morphogenesis, tissue shape arises from interactions between cells. In tissues, the spatial patterning of cellular surface stresses generated by myosins interplays with intercellular adhesions to yield complex shapes. I will present recent work examining how tension in the cell cortex and across intercellular contacts shapes small aggregates of cells, such as the early C Elegans embryo.

19th February 2024

26th February 2024. Meaghan Kall.

4th March 2024. Nir Gov (Weizmann Institute, Israel). Guided by curvature: A theoretical model of cellular shape dynamics and motility, coupling curvature and activity.

How cells can control their shapes, and utilize these shape changes functionally, for example during migration, is an ongoing challenge in biology. We theoretically explore a mechanism whereby the membrane is deformed by curved membrane proteins that recruit cytoskeleton-based forces, such as the recruitment of actin polymerization to the membrane. Combining these two membrane deforming mechanisms, opens up the possibility for a variety of feedbacks. For example, convex proteins (protruding outwards) enhance their aggregation when recruiting protrusive forces (due to actin polymerization), and this coupling can induce strong pattern formation that spontaneously breaks the uniform state. The study of how membranes deform and evolve when driven by this curvature-activity coupling for unrestricted (large) deformations, has only just began. We have found that this system can explain the lamellipodia-driven spreading of adhering cells, and that it contains the minimal ingredients to exhibit spontaneous motility. Surprisingly, this minimal model can explain a variety of observed cellular dynamics, such as phagocytosis and how migrating cells move over curved surfaces. The simplicity of the model, with a small number of components, enables us to gain deep understanding and understand the physics driving biological phenomena.


Abstracts Term 1 2023

23rd October. Igor Nesteruk. Inverse problems of COVID-19 pandemic dynamic and endemic characteristics of SARS-CoV-2 infection

Solutions of some inverse problems of COVID-19 pandemic dynamic are presented. The model of exponential growth, classical and generalized SIR models, their exact solutions and parameter identification procedures were successfully applied to simulate and predict different waves of the COVID-19 pandemic. Hidden periods of the epidemic, detection of new waves, data incompleteness, necessity of High Performance Computing, and development of a user-friendly interface are discussed. Some results about visible and real sizes of the pandemic waves are presented. To simulate the influence of vaccination and testing levels, incomes, seasonal factors, density and urbanization of population, simple comparative and statistical analysis’s with linear and non-linear correlations were used. The peculiarities of the pandemic in rich and poor countries are presented.

High numbers of circulating variants and re-infections together with pessimistic predictions for the Omicron wave duration force studies about the endemic stage of the disease. The modified SIR model showed the presence of equilibrium. The global numbers of new daily cases (estimated with the use of 2022 datasets) can range between 300 thousand and one million, daily deaths – between one and 3.3 thousand. The 2023 datasets showed that t average values of daily deaths per million still vary between 0.12 and 0.41. It means that annual global number of COVID-19 related deaths is still approximately twice higher than the seasonal influenza mortality. Increase of case fatality risks (CFR) in 2023 show that infection is still dangerous despite of increasing the vaccination level. Very low CFR figures in South Korea and very high ones in the UK need further investigations.

30th October. Emily Nixon. Mathematical modelling of infectious diseases within a One Health framework

Infectious diseases, particularly zoonotic pathogens, continue to pose global threats to both human and animal populations. An effective strategy for understanding and better managing zoonotic threats could be to use mathematical modelling that takes a One Health approach, recognizing the interdependence of human, animal, and environmental health. However, traditionally, these components have not been studied simultaneously and there are challenges with integrating data and models across these different spheres. In this talk I will give an example of a research project that I have been involved in that has taken a One Health approach to investigate the impact of a vaccine for zoonotic pathogen, Lassa Fever virus. I will discuss the lessons learnt from this project relating to the challenges of mathematical modelling within a One Health framework and the potential future directions for this field.

6th November. Annabelle Ballesta. Quantitative Systems Pharmacology to Personalize Temozolomide-based Drug Combinations against Brain Tumors.

Objectives: Large inter-patient heterogeneity in anticancer drug response highlights the critical need for personalized cancer management which has favored the generation of multi-type individual patient data. However, quantitative systems pharmacology (QSP) approaches handling the complexity of multiple preclinical and clinical data types for designing patient-specific treatments are critically lacking. Multiple regulatory pathways may be altered initially or activated upon drug exposure in cancer cells, which advocates for the design of combination therapies simultaneously inhibiting multiple targets. Such considerations are backed up by success stories of associating cytotoxic drugs with targeted therapies. The approach was developed here for Glioblastoma (GBM), the most frequent and aggressive primary brain tumors in adults, which is associated to a median overall survival <18 months despite intensive treatments combining maximal safe neurosurgery, radiotherapy and temozolomide (TMZ)-based chemotherapy. The objective was to develop a QSP pipeline to potentiate TMZ treatment by priming cancer cells with targeted molecules affecting key intracellular functions.

Methods: A mathematical model of TMZ cellular pharmacokinetics-pharmacodynamics (PK-PD) based on ordinary differential equations (ODEs) was designed. It describes key regulatory networks that count among the most deregulated pathways in GBM according to TCGA [6]. TMZ PK-PD model was connected to a minimal cell population model that represented cell viability during drug exposure. Model calibration consisted in a modified least square approach ensuring data best-fit under biologically-sound constraints. The minimization task was performed by the Covariance Matrix Evolutionary Strategy (CMAES) algorithm.

Results: Parameters of TMZ PK-PD model were estimated in sequential steps involving the use of longitudinal and dose-dependent datasets (295 datapoints in total). Most of the datasets were performed in two LN229 glioblastoma human cell lines: the parental TMZ sensitive (MGMT-) and the MGMT-overexpressing TMZ resistant (MGMT+) cells [7-11]. The model was able to faithfully reproduce these multi-type datasets coming from several independent studies. Next, the calibrated model was used as a powerful tool to investigate new therapeutic targets. As a start, we investigated drug combinations involving TMZ and only one targeted inhibitor. The only strategy leading to a drastic increase of TMZ efficacy in both parental and resistant cell lines consisted in the complete (>90%) inhibition of the BER pathway, prior to TMZ exposure. Such high level of inhibition being challenging to achieve in the clinics, we further explored the combination of TMZ and two inhibitors. This numerical study revealed three possible parameters to be jointly targeted: MGMT protein level, BER activity, and HR activity. The optimal strategy, defined as the one requiring the smallest percentages of inhibition for both targets, was the combined administration of BER and HR inhibitors, prior to TMZ exposure. This therapeutic strategy was investigated experimentally in both LN229 cell lines and led to a drastic increase in TMZ efficacy.

Conclusions: A model of TMZ PK-PD model was carefully calibrated to data and allowed to identify a non-intuitive TMZ-based drug combination leading to a drastic increase of cell death in initially resistant cells. This QSP model is being personalized using multi-omics datasets available in GBM patient-derived cell lines towards the design of patient-specific therapeutic strategies.

13th November. Chris Overton. Time Delays in Infectious Disease Data: Theory and Practice.

During infectious disease outbreaks, time delay distributions (which describe the distribution of times between epidemiological events) have a large influence on the observed dynamics. Common time delays include the incubation period, generation time, detection delay, and hospital length of stay. Quantifying these is vital for understanding the pathogen and designing appropriate interventions.

With such an important role played by delay distributions, a lot of scientific literature has focused on their estimation, often using flawed or biased approaches. Epidemic dynamics introduce biases to the study of time delay distributions, including right-truncation and dynamical biases. Not only do these biases make robust estimation of the delay distributions challenging, but they also introduce further complications into other data streams, such as biasing the observed severity of cases or introducing backfilling delays.

In this talk, I introduce many of the theoretical challenges relating to time delay distributions, demonstrate that these are mathematical in nature, and illustrate the effect of these challenges in practice. I derive and present some of the new methods developed to overcome these challenges during the COVID-19 and Mpox outbreaks.

20th November 2023. Alex Browning. Identifying cell-to-cell variability using mathematical and statistical modelling.

Cell-to-cell variability is often a primary source of variability in experimental data. Yet, it is common for mathematical analysis of biological systems to neglect biological variability by assuming that model parameters remain fixed between measurements. In this two-part talk, I present new mathematical and statistical tools to identify cell-to-cell variability from experimental data, based on mathematical models with random parameters. First, I identify variability in the internalisation of material by cells using approximate Bayesian computation and noisy flow cytometry measurements from several million cells. Second, I develop a computationally efficient method for inference and identifiability analysis of random parameter models based on an approximate moment-matched solution constructed through a multivariate Taylor expansion. Overall, I show how analysis of random parameter models can provide more precise parameter estimates and more accurate predictions with minimal additional computational cost compared to traditional modelling approaches.