Mathematical Biology and Medicine

Modelos matemáticos para entender el funcionamiento del sistema inmunológico

Forthcoming seminars:

Maths-Bio-Medicine seminars are intended to be of interest to a wide audience. MSc and PhD students are strongly encouraged to participate.
  • Dr Chris Abbosh (University College London)
    15th March at 12:00 in MALL 1, in the School of Mathematics.
    Coffee and tea will be available 11:30-11:50 in the Maths Common Room (level 9, School of Mathematics).
    Minimal residual disease and non-invasive tracking of tumour heterogeneity in non-small cell lung cancer using liquid biopsy
    The Cancer Research UK funded study TRACERx (TRAcking Cancer Evolution through therapy (Rx)) aims to recruit patients undergoing surgery for early-stage non-small-cell lung cancer (NSCLC). Patients donate blood pre- and post- operatively alongside multi-region sampled primary tumour tissue. Up to 40 percent of patients undergoing surgery for NSCLC experience relapse of their disease. At this point patients are approached for relapse tissue sampling. TRACERx therefore provides a strong platform for evaluating circulating tumor DNA (ctDNA) in early-stage NSCLC and a minimal residual disease (MRD) setting.
    In this presentation I will discuss data arising from a phylogenetic, patient-specific approach to ctDNA evaluation in the first 100 patients analysed as part of TRACERx and highlight clinicopathological factors associated with ctDNA detection in early-stage NSCLC suggesting the existence of distinct tumour phenotypic characteristics that predict the presence of ctDNA at measurable quantities in plasma. Additionally, I will discuss tumor volume limit of detection analyses and highlight potential implications of our findings within the context of early cancer detection. Finally, I will examine data arising from the ctDNA profiling of post-operative plasma samples taken in the adjuvant setting. This data demonstrates that ctDNA detection is specific for NSCLC relapse and that ctDNA detection precedes clinical diagnosis of NSCLC relapse, additionally I will provide examples of using phylogenetic ctDNA profiling to characterize the subclonal nature of relapsing NSCLC. To complete this presentation I will focus on steps being taken to translate these technology to clinic in industry led trials.


Forthcoming programs, conferences and workshops

Jobs News

Mathematical Immunology and Quantitative Immunotherapy, MedImmune

Develop novel computer models describing the dynamics of immune cells, especially T-cells, their interactions with tumour cells and the influence of pharmacotherapies targeting tumour-immune cell interactions. Participate in QuanTII activities, including attending network-wide training events, group meetings, seminars, workshops and training courses, and taking part in collaborations, research visits and secondments.

Within-host mathematical models of Yersinia pestis infection

Martín López-García, Grant Lythe, Carmen Molina-París
A within-host, mechanistic, stochastic model of the infection process of Yersinia pestis within humans will be developed. This module will predict the probability of infection and the time to symptoms for an individual exposed to a given dose of Yersinia pestis. Published data from animal models (primarily primate) will be leveraged, together with available human clinical case data. A within-host mechanistic model of the effect of a range of treatments (e.g., different varieties of antibiotic) will be developed, allowing different dosing strategies to be tested.

Models of adaptive immune responses following exposure to Ebola virus

Martín López-García, Grant Lythe, Carmen Molina-París
This project is based on the hypothesis that a specific adaptive immune response in lethal Ebola Virus (EBOV) infection can be protective upon transfer to naive EBOV infected recipients. That is, that the timing and characteristics of the specific adaptive immune response initiated in an EBOV infected individual are predictors of survival or death. The aim of the project, in collaboration with Public Health England (PHE), is to develop mathematical models of adaptive immune responses following exposure to Ebola virus disease. The mathematical models, together with clinical data, provided by Professor Miles Carroll (PHE), of innate and adaptive immune responses to EBOV, as well as with Bayesian methods, will allow us to characterise and quantify the temporal dynamics of host adaptive cells during an infection, and in doing so, identify the differences in host adaptive immune responses that lead to survival or death.

Current and recent visitors

  • Joe Gillard and Tom Laws
  • Mario Castro works on mathematical models of systems where fluctuations are relevant (cellular and receptor immunology) and on pattern formation in spatially extended systems (from tumor cell modeling to cauliflower morphogenesis or nano-structuring). The figure shows comparisons of different mathematical models with real experiments.
  • Madhulika Mishra (IISc Bangalore)
  • Narmada Sambaturu (IISc Bangalore)
  • Sathya Baarathi (IISc Bangalore)
  • Shamik Majumdar (IISc Bangalore)

Applications for research leading to a PhD are welcome. Please apply here, naming a potential project and supervisor. Sample projects are as follows:
  • Analysis of high-throughput genomic data applied to diseases such as cancer
    Arief Gusnanto, Charles Taylor, Jeanine Houwing-Duistermaat
    Statistical modelling of copy number alteration in cancer: using statistical methodology to discover patterns within the genomic copy number alteration profiles in cancer patients and how the pattern can be utilised for improved prediction of cancer survival and patients' clinical characteristics.
    Genetic association in complex diseases and cancer: a collaboration with research groups in the School of Medicine to perform fine mapping around a previously identified location to identify genetic variants that are associated with cancer.
  • Mathematical immunology
    Grant Lythe and Carmen Molina-París
    Development of stochastic mathematical and computational models of the immune system in health and disease, of intra-cellular signalling to understand cell fate, and development of diffusive motion models of cell-cell interactions and receptor-ligand interactions.
  • Modelling biodiversity and ecosystems
    Sandro Azaele
    In this project you will be developing mathematical and computational tools for modeling spatial and temporal patterns in ecosystems, understanding their principal drivers across different scales, at population and community level. This will also help developing methodologies for upscaling biodiversity information from fine-scale sampling.
  • Modelling evolution on molecular and macroscopic scales
    Mauro Mobilia
    Inspired by recent results in biology, and also in behavioural sciences, we will combine notions of non-linear dynamics and evolutionary game together with the theory of stochastic processes and numerical simulations to investigate how noise and mobility influences the formation of coherent patterns.
  • Modelling of biomolecules
    Oliver Harlen and Daniel Read, in collaboration with the Astbury Centre
    Simulating the motions of large biomolecules such molecular motors and also soft colloidal particles, entities that are large enough to be beyond the scope of atomistic simulations (that model the motion of individual atoms), but small enough to be affected by thermal fluctuations (Brownian motion).

Recent programs, conferences and workshops