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Bard Ermentrout
Mind the gap: gap junctions, synchrony and death
Recent experimental studies have shown that electrical coupling (gap junctions) between oscillating neurons encourages synchronization. In this talk, I examine two consequences of this.
In an inhibitory oscillating network based on a model for the slug procerebral lobe, the inhibition discourages synchrony. However, in addition to synaptic inhibition, there are also local gap junctions. I show that this combination can lead to the emergence of traveling waves in the lobe without the need for a frequency gradient. In the second part of the talk, I consider the effects of gap junctions on persistent activity produced by recurrent excitatory neurons. Using a conductance-based model, I show how this coupling destroys persistent activity and then use a reduced model which can be studied via a Fokker-Planck equation. Here I show that the mechanism by which persistent activity is lost depends on the level of noise in the network.
Bob Guy
Modeling Fibrin Gel Formation: Continuous to Discrete
Hemostasis is the normal physiological response to blood
vessel injury and is essential to maintaining the integrity of the
vascular system. It consists of two interacting processes: platelet
aggregation and coagulation. The first involves cell-cell adhesion
resulting in a platelet aggregate, and the second involves an enzyme
network that leads to the formation of a fibrin gel. Though both
processes contribute to the formation of blood clots, those formed at
high shear rates are composed primarily of platelets and clots formed
at low shear rates are composed predominantly of fibrin gel. In order
to understand this phenomenon, a simple mathematical model of
chemically-induced monomer production, polymerization, and gelation
under shear flow is presented. The model is used to explore how the
shear rate and other parameters control the formation of fibrin gel.
The results show that the thrombin inhibition rate, the gel
permeability, and the shear rate are key parameters in regulating the
height of the clot. Experiments show that the gel permeability
depends on the chemical environment in which it was made. However,
the reasons for these structural differences are unclear. Discrete,
Monte Carlo simulations of fibrin polymerization are used to explore
what factors determine the microstructure of the gel.
Eric Marland
Discretely Distributing Carbon
Concern about global climate change has heightened interest in the global cycling of carbon. With an evolving political environment of commitments to limit emissions of greenhouse gas emissions and of markets for trading in emissions permits, there is further need to accurately evaluate carbon stocks and flows.
One component of the global carbon cycle that has been particularly contentious is the carbon that is physically held in harvested wood products. I will talk briefly about the approaches that have been used, or are currently being used, to deal with the carbon stored in wood products, describe the mathematical implications of these approaches, and propose an alternative approach. The alternative approach provides a more flexible and realistic description of the amount of carbon in wood products and can be applied with limited demands on both the amount of data available and on the computational skills of the accountant.
Alex Mogilner
Actin-myosin treadmill: how scaling and perturbation theory helps to understand cell motility
In simple-shaped cells crawling on surfaces, actin polymers at the leading edge are organized in a dendritic network with precisely graded density and push the cell front forward. Meanwhile, myosin concentrates at the rear, contracts and pulls the cell body forward. Tremendously comlex molecularly, this system is relatively simple mechanically. I will show how transport and kinetics equations can be solved analytically using scaling, non-dimensionalization and perturbation theory, and discuss biological implications.
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