Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial*
framework**
Consortium leader
PETER PAZMANY CATHOLIC UNIVERSITY
Consortium members
SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER
The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***
**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben
***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.
PETER PAZMANY CATHOLIC UNIVERSITY
SEMMELWEIS UNIVERSITY
Peter Pazmany Catholic University Faculty of Information Technology
MODELLING NEURONS AND NETWORKS
Lecture 5
GENESIS exercises, part 1
www.itk.ppke.hu
(Idegsejtek és neuronhálózatok modellezése)
(Első GENESIS gyakorlat)
Szabolcs Káli
Overview
In this lesson you will learn first about the GENESIS simulation
environment and the scripting language used by GENESIS. Then we will explore current and voltage clamp experiments in a squid axon model with Hodgkin-Huxley type ion channels.
Lesson topics:
• The GENESIS simulation environment
• Voltage clamp experiments: Characterizing the Na and K conductance.
• Current clamp experiments: Action potential properties, threshold currents, hyperpolarizing pulses.
GEneral NEural SImulation System
• has been developed since 1985
• object-oriented modular design
• two-level user interface:
— script language interpreter
— graphical interface (XODUS)
• a parallelized implementation also exists The GENESIS simulation environment
GENESIS example
//genesis script for a simple compartment simulation //(Tutorial #1)
// create a parent element create neutral /cell
// create an instance of the compartment object create compartment /cell/soma
// set some internal fields
setfield /cell/soma Rm 10 Cm 2 Em 25 inject 5 // create and display a graph inside a form create xform /data
create xgraph /data/voltage xshow /data
// set up a message (PLOT Vm) to the graph
addmsg /cell/soma /data/voltage PLOT Vm *volts *red
addmsg /cell/soma /data/voltage PLOT inject *current *blue // make some buttons to execute simulation commands
create xbutton /data/RESET -script reset create xbutton /data/RUN -script "step 100"
create xbutton /data/QUIT -script quit
check // perform a consistency check for each element reset // initialize each element before starting the simulation
Output of the example script
The output of the example script after running it.
Before you begin...
In a terminal window, type
cp /usr/local/src/genesis-2.3/genesis/.simrc ~
(substitute your GENESIS installation directory everywhere)
export PATH=$PATH:/usr/local/src/genesis-2.3/genesis
Start the tutorial:
cd /usr/local/src/genesis-2.3/genesis/Scripts/squid genesis Squid
Hodgkin-Huxley model simulations
Attention: you need to hit <ENTER> within the dialog field (or click the button next to it) after changing a value!
Voltage clamp experiments:
1. Switch to voltage clamp mode in the control window. Understand the meaning of buttons and graphs.
2. Run a series of voltage clamp experiments (by changing the clamp voltage between -40 and +140 mV) with Na channels blocked to characterize the K conductance. (Use overlay; time 20; holding time 2. Click reset after
running a simulation.)
3. Plot the maximal current and the maximal conductance as a function of holding potential. What is the reversal potential for the K current?
4. Similarly characterize the Na conductance and current
Hodgkin-Huxley model simulations 2
Current clamp experiments:
5. Switch to current clamp mode. Observe action potentials with the default parameters.
6. Determine the threshold current for a single action potential.
7. Is it possible to generate a half-height action potential?
8. Can you find a current that generates 2/3/... action potentials?
9. What is the minimal current that elicits repetitive action potentials?
10.How does the firing rate depend on the injected current?
11.When action potentials are evoked by short current pulses, what is the relationship between pulse length and threshold current?
12.Using two pulses, determine the absolute and relative refractory periods of the model.
13.What happens after a large hyperpolarizing current pulse? Why? (look at the State Plots as well)
Bonus exercises
• Try changing the extracellular Na and K ion concentrations in the HH model. How do they affect the properties of the action potential?
• Explore signal propagation in a passive cable using the "Cable"
tutorial (/usr/local/src/genesis-2.3/genesis/Scripts/cable).
Or
• Explore the generation of pacemaker activity in simple networks using the "CPG" tutorial (/usr/local/src/genesis-2.3/genesis/Scripts/CPG).
Solutions for Voltage clamp experiments: K channel
Exercise 2. Plots with clamp voltages -40mV, 10mV, 60mV,110mV,140mV
Solutions for Voltage clamp experiments: K reversal potential
3. Traces with -30, -20, -10, 0, 10, 10 mV clamp voltages. Because channel current changes from positive to negative between -10mV and -20mV (channel current graph) the reversal potential of the K channel is approximately -15mV.
Analytic method for determining the exact value of the reversal potential
(Nernst equation)
In this case:
T = 300K , Kout squid = 10mM , Kin squid = 301mM , Vresting = 0 mV
Substituting the variables, we get the reversal potential:
VK squid = -13mV
Solutions II.: Na channel properties
Na reversal potential
5. Traces with 100,110,120mV clamp voltages. Because channel current changes from positive to negative between 110mV and 120mV (channel current graph) the reversal potential of the Na channel is approximately 115mV.
Analytic method for determining the exact value of the reversal potential:
(Nernst equation)
In this case:
T = 300K , Naout squid = 460mM , Nain squid = 71mM , Vresting = 0 mV
The reversal potential is:
VNa squid = 118.2mV
Solutions for current clamp experiments
6. Determining the minimum injection current to elicit action potentials. Injection currents are 0.016, 0.017, 0.018 μA. AP threshold is approximately 0.018 μA.
Solutions for current clamp experiments:
Multiple APs
8. It is possible to find a current that generates 2 APs. To make sure that the cell will not fire again, the simulation time and pulse width are set to 200 ms.
There are cases when the model generates more than 2 APs (and not unlimited) if the injection current is raised further by a small amount.
Solutions for current clamp experiments:
Multiple APs
9. About 0.05 μA injected current is the minimum to elicit repetitive APs.
Solutions for current clamp experiments:
Multiple APs
10. The dependence of the firing rate on the injected current: With 0.1 nA injection the cell fires about every 15 milliseconds.
Solutions for current clamp experiments:
Multiple APs
10. The dependence of the firing rate on the injected current: overlay of the 0.1 nA and 0.2 nA plots.
Solutions for current clamp experiments:
Multiple APs
10. The dependence of the firing rate on the injected current. Firing frequency measured at 0.05, 0.1, 0.15, 0.2, 0.3, 0.4nA injected current.
Solutions for current clamp experiments:
Multiple APs
11. With a 0.5 millisecond pulse, the threshold current is approximately 0.105 μA
Solutions for current clamp experiments:
Multiple APs
11. With a 1 millisecond pulse, the threshold current is approximately 0.055 μA
Solutions for current clamp experiments:
Multiple APs
11. With a 2 millisecond pulse, the threshold current is approximately 0.031 μA.
Solutions for current clamp experiments:
Multiple APs
11. Minimum injected current that elicits an action potential as a function of pulse length (the threshold for constant injection is 0.018nA)
Solutions for current clamp experiments: Refractory periods
12. The absolute refractory period is approximately 8ms. First 1ms,0.1uA pulse is given at 2ms; second 1ms,0.4uA pulse is given 8ms later. Applying the second pulse 1ms later evokes action potential.
Solutions for current clamp experiments: Refractory periods
12. The relative refractory period is approximately 16ms. First a 1 ms, 0.06 μA pulse is given at 2 ms; then a 1 ms, 0.06 μA pulse is given 16 ms later. Applying the second
Solutions for current clamp experiments: Hyperpolarizing current
13. After a long hyperpolarizing current (-0.05 μA, 25 ms) an action potential is evoked.
State plot: K channel activation vs. membrane potential. Lower plot legend: black trace: Na activation; red trace: Na inactivation, blue trace : K activation.
Summary
In this lesson we learned about:
• The GENESIS simulation environment. We learned about the scripting language used by the program, how it describes neurons and how to build GUI elements to control the simulation.
• We performed some voltage-clamp experiments to gain a better understanding of voltage-gated conductances in the neuronal membrane.
• Next we did current-clamp experiments to analyze the behavior of ion channels under various circumstances and how they work together to produce action potentials.
• Then we explained the mechanics of different cell behaviors: The minimal current to elicit spikes, repetitive spiking, absolute and
relative refractory periods and the effects of hyperpolarizing currents.
