Mathematical Modelling for Biology, Health, and Environment

An essential trait of cells is their ability to adapt to the environment. This requires cells to modulate their physiology in order to thrive as an individual or as a group of cells. At the heart of cellular adaptation is gene expression which controls what genetic information is converted into physiological output. Traditionally, gene expression is measured in bulk, averaged across entire cell populations. However, individual cells can behave very differently to each other even if they are genetically identical and exposed to the same environment; behaviour that remains obscured by the bulk activity. Individualism may present a selective advantage to the cell under certain environmental conditions, but not others. In this seminar I will present our recent findings on the molecular mechanisms that drive the decision to switch between individual and group behaviour of bacteria. 

Genomic instability allows cancer cells to rapidly vary the number of copies of each chromosome (karyotype) through chromosome missegregation events during mitosis, enabling genetic heterogeneity that leads to tumor metastasis and drug resistance. We construct a Markov chain that describes the evolution of the karyotypes of cancer cells. The Markov chain is based on a stochastic model of chromosome missegregation which incorporates the observed fact that individual chromosomes contain proliferative and anti-proliferative genes, leading to cells with varying fitness levels and allowing for Darwinian selection to occur. We analyze the Markov chain mathematically, and we use it to predict the long-term distribution of karyotypes of cancer cells. We then adapt it to study the behavior of tumors under targeted therapy and to model drug resistance.
This is joint work with Sam Bakhoum and Ashley Laughney

Please not this seminar talk will be on Tuesday 11:00, different from our standard seminar time.

Zoom link: https://qmul-ac-uk.zoom.us/j/81250086190

Elucidating the principles of bacterial motility and navigation is key to understand many important phenomena such as the spreading of infectious diseases. A prime challenge of swimming bacteria is to purposefully and efficiently navigate in their habitat, e.g. the soil, which constitutes a complex, structured environment.
In the first part of the talk, we will discuss Bayesian techniques for model inference from time discrete experimental tracking data in general. We showcase particularly methods to infer models with several layers of stochasticity, for example temporal noise and population heterogeneity. Furthermore, we demonstrate how challenges that arise when multidimensional dynamics is only partially observed, e.g. in the case of underdamped Langevin dynamics, colored noise or non-observed internal degrees of freedom, can be addressed.
In the second part, we will specifically address the navigation strategy of bacterial swimmers in heterogeneous environments, combing experiments with the soil bacterium Pseudomonas putida as a model organism and active particle modeling. The motility pattern of these bacteria in bulk and agar will be discussed with a particular focus on (anomalous) transport properties. Finally, we will argue that switching between multiple modes of motility that differ in their speed and chemotactic responsiveness provides the basis for robust and efficient chemotaxis.

Collective phenomena arise in a plethora of systems, ranging from seasonal animal migration, to the self-organization of chemical and mechanical man-made machines. Such systems are commonly studied through continuous models. In this talk, a discrete modeling approach based off cellular automata is showcased as an alternative, by presenting two biologically motivated models. The first model considers a hierarchically structured tumor cell population consisting of cancer stem cells and totally differentiated stem cells, and studies the effect of differential mobility and inhibitory processes between both populations on the tumor's invasive behavior. The second model considers a population of swarming individuals and studies how an anisotropic interaction neighborhood at the individual level, akin to a limited vision field, affects the formation of density patterns at the population level.

Motion of a particle suspended in a fluid flow is governed by hydrodynamic interactions. In Stokes flow regime where no fluid inertia is present, the motion of a passive particle is confined to streamlines of the background flow. However, for a small finite-size passive particle, the inertia of the fluid can lead to hydrodynamic forces that cause the particle to migrate across streamlines. For active particles interacting with flows, such as sperm cells swimming in fallopian tubes or microrobots programmed for targeted drug delivery applications, rich dynamical behaviors can arise even in Stokes flow regime where no fluid inertia is present. In this talk, I will present the rich nonlinear dynamics for particles suspended in 3D channel flows for two systems: (i) finite-size passive particles with fluid inertia, and (ii) point-like active particles without fluid inertia. For setup (i), one gets focusing of particles to specific stable locations in the duct cross section. Such particle focusing is exploited in biomedical technologies to separate particles by size in microfluidic channels. I will offer insights on how bifurcations in particle equilibria might be exploited to efficiently separate particles of different sizes in circular and spiral ducts. For setup (ii), I will present our investigation of a minimal model of a point-like active particle suspended in fluid flow through a straight channel with rectangular cross-sections. The system exhibits rich nonlinear and chaotic dynamics resulting in a diverse set of active particle trajectories with variations in system parameters and initial conditions.

TBA

The movement patterns of wild harbor seals have been extensively documented. However, the mechanisms driving these movements remain largely unknown. Our research aims to bridge this gap by systematically analyzing the sensory and orientation/navigation abilities of captive seals. Our research findings finally enable us to develop hypotheses that, using an interdisciplinary approach, can be tested by modelling the movement behavior of wild seals.

Cell division is the process of replicating existing cells to create new progeny. It underlies the persistence of all life on earth and is the mechanism that allows the repair of damaged tissue. However, unregulated cell division is the defining feature of cancer and so, for most organisms, careful regulation of cell division is critical. It is this regulatory process that we wish to understand both to inform regenerative medicine and cancer biology. To identify key regulators of cell division, we have used a protein tethering approach to identify the role of regulators for segregating genetic material during cell division. We found that protein kinases and phosphatases appear to be critical, these are proteins that add and remove phosphate residues from proteins to control how they function. These kinases and phosphatases are already known to be critical for cell division, so we used whole proteome approaches to identify their most critical targets. We also use machine learning methodology using data about phosphorylation events across the cell to predict the key regulation circuits that control cell division.

Biography: Peter completed a PhD at the University of Edinburgh with Noreen Murray studying viral restriction. He undertook post-doctoral training with David Porteous, also at the University of Edinburgh and Rodney Rothstein, at Columbia University, New York studying genetic recombination and kinetochore function. In 2011 he started his own laboratory at the National Institute of Medical Research in London, which later became the Francis Crick Institute, to study fundamental regulation of cell division. In 2018 the lab moved to East London to the School of Biological and Behavioural Sciences at Queen Mary University of London.

Population genetics is the discipline investigating genome diversity within and between populations. It aims to elucidate the historical adaptive and neural processes that characterised species' evolution. Therefore, this discipline has fundamental impact in biomedical sciences and conservation biology, among other fields. Recently, deep learning algorithms have provided a novel inferential framework in population genetics. Here, I will discuss how generative models have allowed the creation of realistic synthetic genetic data and the inference of complex models. I will then introduce ongoing work on using generative adversarial networks to infer the past demography of Anopheles gambiae mosquitoes, and how these findings may aid genomic monitoring of malaria in sub-Saharan Africa.