Many symptoms of Parkinson’s disease are connected with abnormally high levels of synchrony in neural activity. A successful and established treatment for a drug-resistant form of the disease involves electrical stimulation of brain areas affected by the disease, which has been shown to desynchronize neural activity. Recently, a closed-loop deep brain stimulation has been developed, in which the provided stimulation depends on the amplitude or phase of oscillations that are monitored in patient’s brain. The aim of this work was to develop a mathematical model that can capture experimentally observed effects of closed-loop deep brain stimulation, and suggest how the stimulation should be delivered on the basis of the ongoing activity to best desynchronize the neurons. We studied a simple model, in which individual neurons were described as coupled oscillators. Analysis of the model reveals how the therapeutic effect of the stimulation should depend on the current level of synchrony in the network. Predictions of the model are compared with experimental data.

The derivation of so-called `effective descriptions' that explicitly incorporate microscale physics into a macroscopic model has garnered much attention, with popular applications in poroelasticity, and models of the subsurface in particular. More recently, such approaches have been applied to describe the physics of biological tissue. In such applications, a key feature is that the material is active, undergoing both elastic deformation and growth in response to local biophysical/chemical cues.

Here, two new macroscale descriptions of drug/nutrient-limited tissue growth are introduced, obtained by means of two-scale asymptotics. First, a multiphase viscous fluid model is employed to describe the dynamics of a growing tissue within a porous scaffold (of the kind employed in tissue engineering applications) at the microscale. Secondly, the coupling between growth and elastic deformation is considered, employing a morpho-elastic description of a growing poroelastic medium. Importantly, in this work, the restrictive assumptions typically made on the underlying model to permit a more straightforward multiscale analysis are relaxed, by considering finite growth and deformation at the pore scale.

In each case, a multiple scales analysis provides an effective macroscale description, which incorporates dependence on the microscale structure and dynamics provided by prototypical `unit cell-problems'. Importantly, due to the complexity that we accommodate, and in contrast to many other similar studies, these microscale unit cell problems are themselves parameterised by the macroscale dynamics.

In the first case, the resulting model comprises a Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. Stokes-type cell problems retain multiscale dependence, incorporating active cell motion [1]. Example numerical simulations indicate the influence of microstructure and cell dynamics on predicted macroscale tissue evolution. In the morpho-elastic model, the effective macroscale dynamics are described by a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection--reaction--diffusion equation [2].

[1] HOLDEN, COLLIS, BROOK and O'DEA. (2018). A multiphase multiscale model for nutrient limited tissue growth, ANZIAM (In press)

[2] COLLIS, BROWN, HUBBARD and O'DEA. (2017). Effective Equations Governing an Active Poroelastic Medium, Proceedings of the Royal Society A. 473, 20160755

Dr Nicola Beer heads up the Department of Stem Cell Engineering at the new Novo Nordisk Research Centre Oxford. Her team will use human stem cells to derive metabolically-relevant cells and tissues such as islets, hepatocytes, and adipocytes todiscover novel secreted factors and corresponding signalling pathways which modify cell function, health, and viability. Bycombining in vitro-differentiated human stem cell-derived models with CRISPR and other genomic targeting techniques, the teamassay cell function from changes in a single gene up to a genome-wide scale. Understanding the genes and pathways underlying cell function (and dysfunction) highlights potential targets for new Type 2 Diabetes therapeutics. Dr Beer will talk about the work ongoing in her team, as well as more broadly about the role of human stem cells in drug discovery and patient treatment.

Please note that this seminar will take place at the Physical and Theoretical Chemistry Laboratory within the
Department of Chemistry, room, PTCL lecture theatre.

The ability of cells to sense and respond to the mechanical properties of their environments is fundamental to cellular behaviour, with stiffness found to be a key control parameter. The physical mechanisms underpinning mechanosensing are, however, not well understood. I here consider the key physical cellular behaviours of active contractility of the internal cytoskeleton and cell growth, coupling these into mechanical models. These models suggest new distinct mechanisms of mechanotransduction in cells and tissues.

I will discuss a new theoretical approach to information and decisions in signalling systems and relate this to new experimental results about the NF-kappaB signalling system. NF-kappaB is an exemplar system that controls inflammation and in different contexts has varying effects on cell death and cell division. It is commonly claimed that it is information processing hub, taking in signals about the infection and stress status of the tissue environment and as a consequence of the oscillations, transmitting higher amounts of information to the hundreds of genes it controls. My aim is to develop a conceptual and mathematical framework to enable a rigorous quantifiable discussion of information in this context in order to follow Francis Crick's counsel that it is better in biology to follow the flow of information than those of matter or energy. In my approach the value of the information in the signalling system is defined by how well it can be used to make the "correct decisions" when those "decisions" are made by molecular networks. As part of this I will introduce a new mathematical method for the analysis and simulation of large stochastic non-linear oscillating systems. This allows an analytic analysis of the stochastic relationship between input and response and shows that for tightly-coupled systems like those based on current models for signalling systems, clocks, and the cell cycle this relationship is highly constrained and non-generic.

Multivariate cryptography is one of a handful of proposals for post-quantum cryptographic schemes, i.e. cryptographic schemes that are secure also against attacks carried on with a quantum computer. Their security relies on the assumption that solving a system of multivariate (quadratic) equations over a finite field is computationally hard. 

Groebner bases allow us to solve systems of polynomial equations. Therefore, one of the key questions in assessing the robustness of multivariate cryptosystems is estimating how long it takes to compute the Groebner basis of a given system of polynomial equations. 

After introducing multivariate cryptography and Groebner bases, I will present a rigorous method to estimate the complexity of computing a Groebner basis. This approach is based on techniques from commutative algebra and is joint work with Alessio Caminata (University of Barcelona).