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

Joël Tabak Patrick Fletcher

Maurizio Tomaiuolo(Univ. Pennsylvania)

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

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?

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.

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

Why does heterogeneity matter?

One spiking model cell

Another spiking model cell

A third spikingmodel cell

Tomaiuolo et al., Biophys. J., 103:2021, 2012

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.

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

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

Optimization using a genetic algorithm

p1

p2

p1

p2

p1

p2

repeat

selection

replication with mutation

Cost < $ 1000

We need rapid calibration, so use a Programmable Graphics Processing Unit (GPU)

Feature planes can be rapidly computed

100x100 grid10,000 simulations

Simulation time=70 sec eachTotal computation time=20 sec

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)

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

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

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

The Dynamic Clamp: a tool for adding a model current to a real cell

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

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

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

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

Prediction tested using D-clamp

Control cell

Subtract some K(dr) current

Subtract more K(dr)current

Summary

Bertram et al., in press

The “traditional” approach

Our new approach

Thank you