Forthcoming events in this series


Fri, 05 Feb 2016

14:00 - 15:00
L3

Qualitative behaviour of stochastic and deterministic models of biochemical reaction networks

Professor David Anderson
(Department of Mathematics Wisconsin University)
Abstract

If the abundances of the constituent molecules of a biochemical reaction system  are sufficiently high then their concentrations are typically modelled by a coupled set of ordinary differential equations (ODEs).  If, however, the abundances are low then the standard deterministic models do not provide a good representation of the behaviour of the system and stochastic models are used.  In this talk, I will first introduce both the stochastic and deterministic models.  I will then provide theorems that allow us to determine the qualitative behaviour of the underlying mathematical models from easily checked properties of the associated reaction network.  I will present results pertaining to so-called ``complex-balanced'' models and those satisfying ``absolute concentration robustness'' (ACR).  In particular, I will show how  ACR models, which are stable when modelled deterministically, necessarily undergo an extinction event in the stochastic setting.  I will then characterise the behaviour of these models prior to extinction.

Fri, 04 Dec 2015

14:00 - 15:00
L3

Transmural propagation of the action potential in mammalian hearts: marrying experimental and theoretical studies

Prof Godfrey Smith
(Institute of Cardiovascular & Medical Sciences University of Glasgow)
Abstract

Transmural propagation is a little studied feature of mammalian electrophysiology, this talk reviews our experimental work using different optical techniques to characterise this mode
of conduction under physiological and pathophysiological conditions.

Fri, 27 Nov 2015

14:00 - 15:00
L3

What can we reconstruct about neural organization from time series of electrophysiological recordings?

Dr David Holcman
(IBENS Ecole Normale Superieure)
Abstract

We will discuss how the analysis of a stochastic mean-field model for
synaptic activity can be used to reconstruct some parameters about
neuronal networks.  The method is based on a non-standard analysis of the
Fokker-Planck equation and the asymptotic computation of the spectrum for
the nonself-adjoint operator. Applications concern Up- and Down- states
and bursting activity in neuronal networks.

Fri, 20 Nov 2015

14:00 - 15:00
L3

oxDNA: A coarse-grained approach to model DNA

Prof Jonathan Doye
(Dept of Chemistry University of Oxford)
Abstract

Simulating the long time and length scales associated with DNA self-assembly
and DNA nanotechnology is not currently feasible with models at an atomic level
of detail. We, therefore, developed oxDNA a coarse-grained representation of
DNA that aims to capture the fundamental structural, thermodynamic and
mechanical properties of double-stranded and single-stranded DNA, which we have
subsequently applied to study a wide variety of DNA biophysical properties and
DNA nanotechnological systems.

Fri, 13 Nov 2015

14:00 - 15:00
L3

Mathematical modelling of breast cancer for personalised therapy

Miss Annalisa Occhipinti
(Computer Laboratory University of Cambridge)
Abstract

Ductal carcinoma is one of the most common cancers among women, and the main cause of death is the formation of metastases. The development of metastases is caused by cancer cells that migrate from the primary tumour site (the mammary duct) through the blood vessels and extravasating they initiate metastasis. In my talk, I present a multi-compartment mathematical model which mimics the dynamics of tumoural cells in the mammary duct, in the circulatory system and in the bone. Using a branching process approach, the model describes the relation between the survival times and the four markers mainly involved in metastatic breast cancer (EPCAM, CD47, CD44 and MET). In particular, the model takes into account the gene expression profile of circulating tumour cells to predict personalised survival probability. Gene expression data of metastatic breast cancer have been used to validate the model. The administration of drugs as bisphosphonates is also included in order to analyse the dynamic changes induced by the therapy.

Stochastic and deterministic processes are merged together to describe cancer progression and obtain personalised survival analysis based on the gene expression levels of each patient. The main aim of the talk is showing that Mathematics can have a strong impact in speeding cancer research, predicting survival probability and selecting the best cancer treatment. 

Fri, 06 Nov 2015

14:00 - 15:00
L3

Visual recognition of facial expression

Dr Simon Stringer
(Dept of Experimental Psychology University of Oxford)
Abstract

The first half of the lecture will begin by reviewing what is known about the
neural representation of faces in the primate visual system. How does the
visual system represent the spatial structure of faces, facial identity and
expression? We then discuss how depression is associated with negative
cognitive biases in the recognition of facial expression, whereby depressed
people interpret facial expressions more negatively. The second half of the
lecture presents computer simulations aimed at understanding how these facial
representations may develop through visual experience. We show how neural
representations of expression are linked to particular spatial relationships
between facial features. Building on this, we show how the synaptic connections
in the model may be rewired by visual training to eliminate the negative
cognitive biases seen in depression.

Fri, 30 Oct 2015

14:00 - 15:00
L3

Hybrid modelling of stochastic chemical kinetics

Dr Kostas Zygalakis
(School of Mathematics University of Southampton)
Abstract

It is well known that stochasticity can play a fundamental role in 
various biochemical processes, such as cell regulatory networks and 
enzyme cascades. Isothermal, well-mixed systems can be adequately 
modeled by Markov processes and, for such systems, methods such as 
Gillespie's algorithm are typically employed. While such schemes are 
easy to implement and are exact, the computational cost of simulating 
such systems can become prohibitive as the frequency of the reaction 
events increases. This has motivated numerous coarse grained schemes, 
where the ``fast'' reactions are approximated either using Langevin 
dynamics or deterministically.  While such approaches provide a good 
approximation for systems where all reactants are present in large 
concentrations,  the approximation breaks down when the fast chemical 
species exist in small concentrations,  giving rise to significant 
errors in the simulation.  This is particularly problematic when using 
such methods to compute statistics of extinction times for chemical 
species, as well as computing observables of cell cycle models.  In this 
talk, we present a hybrid scheme for simulating well-mixed stochastic 
kinetics, using Gillepsie--type dynamics to simulate the network in 
regions of low reactant concentration, and chemical langevin dynamics 
when the concentrations of all species is large.  These two regimes are 
coupled via an intermediate region in which a ``blended'' jump-diffusion 
model is introduced.  Examples of gene regulatory networks involving 
reactions occurring at multiple scales, as well as a cell-cycle model 
are simulated, using the exact and hybrid scheme, and compared, both in 
terms weak error, as well as computational cost.

This is joint work with A. Duncan (Imperial) and R. Erban (Oxford)

Fri, 16 Oct 2015

14:00 - 15:00
L3

What’s lumen got to do with it? Mechanics and transport in lung morphogenesis

Dr Sharon Lubkin
(Dept of Maths UCSU)
Abstract

Mammalian lung morphology is well optimized for efficient bulk transport of gases, yet most lung morphogenesis occurs prenatally, when the lung is filled with liquid - and at birth it is immediately ready to function when filled with gas. Lung morphogenesis is regulated by numerous mechanical inputs including fluid secretion, fetal breathing movements, and peristalsis. We generally understand which of these broad mechanisms apply, and whether they increase or decrease overall size and/or branching. However, we do not generally have a clear understanding of the intermediate mechanisms actuating the morphogenetic control. We have studied this aspect of lung morphogenesis from several angles using mathematical/mechanical/transport models tailored to specific questions. How does lumen pressure interact with different locations and tissues in the lung? Is static pressure equivalent to dynamic pressure? Of the many plausible cellular mechanisms of mechanosensing in the prenatal lung, which are compatible with the actual mechanical situation? We will present our models and results which suggest that some hypothesized intermediate mechanisms are not as plausible as they at first seem.

 

Fri, 19 Jun 2015

14:00 - 15:00
L5

Biological Simulation – from simple cells to multiscale frameworks

Dr Dawn Walker
(Dept of Bioengineering University of Sheffield)
Abstract

As the fundamental unit of life, the biological cell is a natural focus for computational simulations of growing cell population and tissues. However, models developed at the cellular scale can also be integrated into more complex multiscale models in order to examine complex biological and physical process that scan scales from the molecule to the organ.

This seminar will present a selection of the cellular scale agent-based modelling that has taken place at the University of Sheffield (where one software agent represents one biological cell) and how such models can be used to examine collective behaviour in cellular systems. Finally some of the issues in extending to multiscale models and the theoretical and computational methodologies being developed in Sheffield and by the wider community in this area will be presented.

Fri, 05 Jun 2015

14:00 - 15:00
L5

Comparing networks using subgraph counts

Prof Charlotte Deane
(Dept of Statistics University of Oxford)
Abstract

Data in many areas of science and sociology is now routinely represented in the form of networks. A fundamental task often required is to compare two datasets (networks) to assess the level of similarity between them. In the context of biological sciences, networks often represent either direct or indirect molecular interactions and an active research area is to assess the level of conservation of interaction patterns across species.

Currently biological network comparison software largely relies on the concept of alignment where close matches between the nodes of two or more networks are sought. These node matches are based on sequence similarity and/or interaction patterns. However, because of the incomplete and error-prone datasets currently available, such methods have had limited success. Moreover, the results of network alignment are in general not amenable for distance-based evolutionary analysis of sets of networks. In this talk I will describe Netdis, a topology-based distance measure between networks, which offers the possibility of network phylogeny reconstruction.

Fri, 22 May 2015

14:00 - 15:00
L3

Clinically-driven computational cardiac modelling of arrhythmias & electrotherapy: the good, the bad and the basic

Dr Martin Bishop
(King’s College London)
Abstract

Sudden cardiac arrhythmic death remains a major health challenge in Western Society. Recent advances in computational methods and technologies have made clinically-based cardiac modelling a reality. An important current focus is the use of modelling to understand the nature of arrhythmias in the setting of different forms of structural heart disease. However, many challenges remain regarding the best use of these models to inform clinical decision making and guide therapies. In this talk, I will introduce a diverse sample of applications of modelling in this context, ranging from basic science studies which aim to leverage a fundamental mechanistic understanding of different aspects of pathological cardiac function, to direct clinical-application projects which aim to use modelling to immediately inform a clinical therapy. I will also discuss the challenges involved in clinically-driven modelling, and how to both engage, and manage, the expectations of clinicians at the same time, particularly with respect to the potential uses of 'patient-specific' modelling.

Fri, 15 May 2015

14:00 - 15:00
L3

Towards consistent and effective modeling in the stochastic reaction-diffusion framework

Prof Stefan Engblom
(Uppsala University)
Abstract

I this talk I will try to give an overview of recent progress in
spatial stochastic modeling within the reaction-diffusion
framework. While much of the initial motivation for this work came
from problems in cell biology, I will also highlight some examples
from epidemics and neuroscience.

As a motivating introduction, some newly discovered properties of
optimal controls in stochastic enzymatic reaction networks will be
presented. I will next detail how diffusive and subdiffusive reactive
processes in realistic geometries at the cellular scale may be modeled
mesoscopically. Along the way, some different means by which these
models may be analyzed with respect to consistency and convergence
will also be discussed. These analytical techniques hint at how
effective (i.e. parallel) numerical implementations can be
designed. Large-scale simulations will serve as illustrations.