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5th Annual Student
Workshop: Abstracts
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Calcium Dynamics
The concentration of free intracellular calcium is used by almost every
cell type to control a wide variety of cellular processes, including
movement, secretion, differentiation and gene expression. However, it's
not a simple control process; in many cases the calcium concentration
oscillates, and it is the frequency of the oscillation that appears to
carry the signal.
In this first talk I'll give an overview of calcium dynamics, from both
a physiological and mathematical point of view. I'll discuss how to
model the various calcium pumps, channels and transporters, with
detailed discussion of intracellular calcium channels such as the
inositol trisphosphate and ryanodine receptors.
We'll use both simple ODE models as well as more complicated PDE
models, and, time permitting, discuss such things as calcium
microdomains, homogenisation, and stochastic models.
These calcium models form the basis of many other models in cell
physiology, and will appear in various guises in my other talks in this
series.
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Saliva Secretion
If you don't secrete saliva properly you get something called,
surprise, surprise, 'dry mouth'. It doesn't sound too nasty, but
actually it is. You can't eat or talk properly, just for a start.
Saliva secretion is controlled by ion channels at the apical and basal
ends of parotid acinar cells, which are a type of secretory epithelial
cell. Much like other transporting epithelia, such as Na-transporting
epithelia in the gut or kidney, these cells transport water by
transporting Cl- ions through the cell and letting water follow by
osmosis. However, the cells also have to control their cell volume at
the same time, which is not necessarily easy to do.
I'll discuss a relatively simple model of water transport by parotid
acinar cells, with brief digressions on other interesting models of
water transport (such as uphill transport), and I'll show how the
overall process is controlled by calcium. As usual, I'll present a lot
of data, including stochastic single-channel data, and try to show how
the models can answer important questions.
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Airway Smooth Muscle
Airway smooth muscle has the honour of being the only known tissue
whose only function is pathological; contraction of airway smooth
muscle causes asthma, and, as far as we know, it doesn't do anything
else. Therefore, a lot of people put a lot of effort into understanding
how the contraction of airway smooth muscle is controlled.
In this talk I'll discuss older models of skeletal muscle contraction
(the Huxley model) and show how these models have been adapted to model
smooth muscle, and why (the Hai-Murphy model). I'll then show how these
models can be used to study airway smooth muscle and what we can learn
about the mechanics of airway contraction. I'll present a lot of data
from various laboratories and discuss how we can use our models to try
and understand what is happening in airway smooth muscle cells and in
strips of smooth muscle.
Mathematically, we'll be using conservation equations coupled with ODEs
and (possibly) PDEs. Calcium, of course, plays an important role and
we'll show how muscle models interact with the calcium models discussed
in Talk 1.
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GnRH Neurons
This talk will be the first of two talks on neurons. GnRH neurons are
in the hypothalamus, and control the release of gonadotropin from
gonadotrophs in the pituitary. However, release of GnRH is controlled
by an intricate combination of membrane ion channels, bursting
electrical potential, intracellular calcium release, and feedback from
the periphery.
I'll discuss models of bursting electrical activity in other
neurosecretory cells and show how GnRH cells are different in some
ways, similar in others. I'll discuss the differences between
measurements in cell lines, such as GT1 cells, and measurements in
vivo.
Finally, I'll present a preliminary model of a GnRH neuron that shows
how the careful control of various membrane currents leads to
electrical bursting.
Although there is a lot known about electrical bursting in other
neurosecretory cells, such as pancreatic beta cells, or pituitary
gonadotrophs, GnRH neurons are much less well understood. So this talk
will show how results from a range of other cell types can be used to
inform and direct studies in GnRH neurons.
Mathematically, the important tools are those of nonlinear dynamics and
bifurcation theory and an important part of the talk will be to show
how bursting electrical activity can be analysed using these tools.
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Vertebrate
Photoreceptors
My final talk is the second one on neurons; in it I shall look at
models of a very particular kind of neuron, the vertebrate
photoreceptor. This cell type typifies the property of adaptation
(which is seen in many other physiological contexts); indeed, the
mechanisms by which light adaptation occurs as a result of
intracellular biochemistry is a fascinating example of how complicated
nonlinear behaviour can result from relatively simple biochemical
networks.
Vertebrate photoreceptors have the wonderful property that they respond
principally to changes in light intensity, not to the intensity of the
background light; this property is so important that it appears at many
levels of the visual system, beginning at the level of the
intracellular biochemical kinetics.
I shall present some relatively simple models of vertebrate
photoreceptors, discussing the various ion channels and reactions that
mediate light adaptation. I shall consider such questions as
reproducible single-photon responses, the differences between rods and
cones, and consider briefly the responses of the retina as a whole. If
time permits I'll also discuss lateral inhibition and the
Hartline-Ratliff equations, which strictly speaking, are more to do
with the invertebrate retina, but no matter.
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