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A Phantom Bursting Mechanism
for Episodic Bursting
Richard Bertram, Joseph Rhoads,
Wendy Cimbora
ANUP UMRANIKAR
Introduction
 Bursting = Periods of electrical spiking followed by
periods of rest
 Bursting is observed in cells such as
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R15 neuron of aplysia
Thalamic neurons
Pyramidal neurons
Trigeminal neurons
Pancreatic beta-cells
Pituitary gonadotrophs
Episodic (or Compound) Bursting
 Complex form of bursting observed in beta-cells of
islets of Langerhans in pancreas and GnRH of
pituitary gland
 Episodes of several bursts followed by long silent
phases or ‘deserts’
 Paper discusses episodic bursting using a minimal
model
 Depending on location in parameter space, model
produces fast, slow and episodic bursting
Mathematical Model
 Two slow variables interact with the fast subsystem
 Planar fast subsystem given by
 Expressions for ionic current are given by
Parameter Values
 In paper, all simulations and bifurcations were
calculated using XPPAUT software package; CVODE
numerical method used to solve differential
equations
 I’ve used MATLAB for simulations; used ode15s to
solve differential equations
Fast Bursting
Fast Bursting – My Results
Fast Bursting – Bifurcation Diagram
 Fast/slow analysis of fast bursting (s2 = 0.49). The solid
portion of the z-curve represents branches of stable steady
states. Dashed curves represent unstable steady states. The
two branches of filled circles represent the maximum and
minimum values of periodic solutions. The green dot-dashed
curve is the s1 nullcline. HB=supercritical Hopf bifurcation,
HM=homoclinic bifurcation, LK=lower knee, UK=upper knee.
Slow Bursting
Slow Bursting – My Results
Episodic Bursting
Episodic Bursting – My Results
Conclusion
 Model described in minimal, with two fast and two slow
variables
 Slow variables represent activation variables of
hyperpolarizing K+ currents. However, similar behavior
could be achieved by defining slow variables in other
ways, such as inactivation variables of depolarizing
currents or as a combination of activation and
deactivation
 Behaviors not restricted to specific details of this model
 Also, more complex neurons or endocrine cell models
can be achieved using this minimal model, as long as
model possesses at least two slow variables with
disparate time scales
References
 Bertram, R., Rhoads, J., Cimbora, W., 2008. A
phantom bursting mechanism for episodic bursting.
Bull. Math. Biol. 70, 1979-1993
 Bertram, R., Previte, J., Sherman, A., Kinard, T.A.,
Satin, L.S., 2000. The phantom burster model for
pancreatic β-cells. Biophys. J. 79, 2880–2892