Past Mathematical Biology and Ecology Seminar

4 December 2015
14:00
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.

  • Mathematical Biology and Ecology Seminar
27 November 2015
14:00
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.

  • Mathematical Biology and Ecology Seminar
20 November 2015
14:00
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.

  • Mathematical Biology and Ecology Seminar
13 November 2015
14:00
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. 

  • Mathematical Biology and Ecology Seminar
6 November 2015
14:00
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.

  • Mathematical Biology and Ecology Seminar
30 October 2015
14:00
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)

  • Mathematical Biology and Ecology Seminar
16 October 2015
14:00
Dr Sharon Lubkin
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.

 

  • Mathematical Biology and Ecology Seminar
19 June 2015
14:00
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.

  • Mathematical Biology and Ecology Seminar

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