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A Hybrid Experimental/Modeling Approach to Studying Pituitary Cell
Dynamics
Richard Bertram
Department of Mathematicsand
Programs in Neuroscience and Molecular Biophysics Florida State University, Tallahassee, FL.
Biodynamics 2013
Funding: National Science Foundation DMS1220063
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Joël Tabak Patrick Fletcher
Maurizio Tomaiuolo(Univ. Pennsylvania)
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Five types of anterior pituitary endocrine cells
1. Lactotrophs: secrete prolactin
2. Somatotrophs: secrete growth hormone
3. Gonadotrophs: secrete luteinizing hormone andfollicle stimulating hormone
4. Corticotrophs: secrete ACTH
5. Thyrotrophs: secrete thyroid stimulating hormone
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Goal
Use mathematical modeling and analysis to help understand the electrical activity of the different types of endocrine pituitary cells
Van Goor et al., J. Neurosci., 2001:5902, 2001
Spiking, littlesecretion Bursting,
much moresecretion
What makes pituitary cells burst and secrete?
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Equations
voltage
IK activation
cytosolic calcium
IBK activation
Ionic current have an Ohmic form, e.g.,
Conductance and time constants are all parameters.There are more parameters in the equilibrium functions.
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Pituitary cells are very heterogeneousThe mix of ionic currents within a single cell type is highly variable, as shown with the GH4C1 cell line…
Cell 1
Cell 2
Cell 3
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Why does heterogeneity matter?
One spiking model cell
Another spiking model cell
A third spikingmodel cell
Tomaiuolo et al., Biophys. J., 103:2021, 2012
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What we’d like to do…
Parameterize the model to an individual cell,while still patched onto that cell. Then differentcells will have different parameter vectors.
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0 0.5 1 1.5-70
-60
-50
-40
-30
-20
-10
Time (sec)
V (mV)
period
activesilent
amplitude
min
peaks
Set parameters to fit features of the voltage trace,rather than the voltage trace itself
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Also fit voltage clamp data
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100
0
100
200
300
400
500
600
I(pA
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-150
-100
-50
0
50
100
V(m
V)
time(sec)
Maximize where
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Optimization using a genetic algorithm
p1
p2
p1
p2
p1
p2
repeat
selection
replication with mutation
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Cost < $ 1000
We need rapid calibration, so use a Programmable Graphics Processing Unit (GPU)
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Feature planes can be rapidly computed
100x100 grid10,000 simulations
Simulation time=70 sec eachTotal computation time=20 sec
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0 2 4 6 8 10
-60
-50
-40
-30
-20
-10
time (s)
V (m
V)
Example: Calibrate, predict, and test
The model (red) is fit to a bursting Gh4 cell (black)
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gBK
BK
Peaks per Event
0 1 2 3 4 5
2
4
6
8
10
1
2
3
4
5
Feature plane for BK conductance and time constant
Best fit to bursting data Block BK current
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0 2 4 6 8 10-70
-60
-50
-40
-30
-20
-10
0
10
time (s)
V (m
V)
BK current blocked in cell with paxillin
Actual cell (black) and model (red) convert from bursting to spiking
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gBK
BK
Peaks per Event
0 1 2 3 4 5
2
4
6
8
10
1
2
3
4
5
Feature plane for BK conductance and time constant
Best fit to bursting data Double BK time constant
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The Dynamic Clamp: a tool for adding a model current to a real cell
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0 2 4 6 8 10-70
-60
-50
-40
-30
-20
-10
0
10
time (s)
V (m
V)
BK current added via D-clamp, with τBK=10 ms
Adding BK current with slow activation converts bursting to spiking
Black=cell
Red=model
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gBK
BK
Peaks per Event
0 1 2 3 4 5
2
4
6
8
10
1
2
3
4
5
Feature plane for BK conductance and time constant
Best fit to bursting data Increase BK conductance
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0 2 4 6 8 10
-60
-50
-40
-30
-20
-10
time (s)
V (m
V)
BK conductance added to a bursting cell
Bursting persists, with more spikes per burst
Black=cell
Red=model
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Prediction: Reducing K(dr) conductance increases the burstiness
Diameter: active phase durationColor: number of spikes per active phase
Teka et al., J. Math. Neurosci., 1:12, 2011
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Prediction tested using D-clamp
Control cell
Subtract some K(dr) current
Subtract more K(dr)current
Summary
Bertram et al., in press
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The “traditional” approach