Nanopore sequencing is a method to infer the sequence of nucleotides in DNA or RNA molecules from small variations in ionic current during transit through a nanoscale pore. We will give an introduction to nanopore sequencing and some of its applications and then explore simple models of the signal generation process. These can provide insight to guide optimisation of the system and inform the design of more flexible neural network models, capable of extracting the rich contextual information required for accurate sequence inference.

The Turing pattern is a key concept in the modern study of reaction-diffusion systems, with Turing patterns proposed a possible explanation for the spatial structure observed in myriad physical, chemical, and biological systems. Real-world systems are not always so clean as idealized Turing systems, and in this talk we will take up the case of more messy reaction-diffusion systems involving explicit space or time dependence in diffusion or reaction terms. Turing systems of this nature arise in several applications, such as when a Turing system is studied on a growing substrate, is subjected to a temperature gradient, or is immersed within a fluid flow. The analysis of these messy Turing systems is not as straightforward as in the idealized case, with the explicit space or time dependence greatly complicating or even preventing most standard routes of analysis. Motivated by patterning in phenomena involving explicit space or time dependence, and by the interesting mathematical challenges inherent in the study of such systems, in this talk we consider the following questions:

* Is it possible to obtain generalizations of the Turing instability conditions for non-autonomous, spatially heterogeneous reaction-diffusion systems?
* What can one say about predicting nascent patterns in these systems?
* What role does explicit space or time dependence play in selecting fully developed patterns in these systems?
* Is it possible to exploit this space or time dependence in order to manipulate the form of emergent patterns?

We will also highlight some of the applications opened up by the analysis of heterogeneous Turing systems.

The dynamics of a tissue in development or regeneration arises from the behaviour of its constituent cells and their interactions. We use mathematical models and inference from experimental data to to infer the likely cellular behaviours underlying changing tissue states. In this talk I will show examples of how we apply canonical birth-death process models to novel experimental data, how we are extending such models with volume exclusion and multistate dynamics, and how we attempt to more generally learn cell-cell interaction models directly from data in interpretable ways. The applications range from in vitro models of embryo development to in vivo blood regeneration that is disrupted with ageing.

Mathematical models of childhood diseases are often fitted using deterministic methods under the assumption of homogeneous contact rates within populations. Such models can provide good agreement with data in the absence of significant changes in population demography or transmission, such as in the case of pre-vaccine era measles. However, accurate modeling and forecasting after the start of mass vaccination has proved more challenging. This is true even in the case of measles which has a well understood natural history and a very effective vaccine. We demonstrate how the dynamics of homogeneous and age-structured models can be similar in the absence of vaccination, but diverge after vaccine roll-out. We also present some fundamental differences in deterministic and stochastic methods to fit models to data, and propose techniques to fit long term time series with imperfect covariate information. The methods we develop can be applied to many types of complex systems beyond those in disease ecology.
 

Approaches to personalized diagnosis and treatment in oncology are heavily reliant on computer models that use molecular and clinical features to
characterize an individual patient’s disease. Most of these models use genome and/or gene expression sequences to develop classifiers of a patient’s
tumor. However, in order to fully model the behavior and therapy response of a tumor, dynamic models are desirable that can act like a Digital Twin of
the cancer patient allowing prognostic and predictive simulations of disease progression, therapy responses and development of resistance. We are
constructing Digital Twins of cancer patients in order to perform dynamic and predictive simulations that improve patient stratification and
facilitate the design of individualized therapeutic strategies. Using a hybrid approach that combines artificial intelligence / machine learning
with dynamic mechanistic modelling we are developing a computational framework for generating Digital Twins. This framework can integrate
different types of data (multiomics, clinical, and existing knowledge) and produces personalized computational models of a patient’s tumor. The
computational models are validated and refined by experimental work and in retrospective patient studies. We present some of the results of the dynamic
Digital Twins simulations in neuroblastoma. They include (i) identification on non-MYCN amplified high risk patients; (ii) prediction of individual
patients’ responses to chemotherapy; and (iii) identification of new drug targets for personalized therapy. Digital Twin models allow the dynamic and
mechanistic simulation of disease progression and therapy response. They are useful for the stratification of patients and the design of personalized
therapies.

Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit a density-dependent dispersal rate.

Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion rate akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion. Moreover, we find that a second, independent density-dependent effect on phage dispersal spontaneously emerges as a result of the viral incubation period, during which phage is trapped inside the host unable to disperse. Our results indicate both that bacteriophage can be used as a controllable laboratory population to investigate the impact of density-dependent dispersal on evolution, and that the genetic diversity and adaptability of expanding viral populations could be much greater than is currently assumed.