Figure 1: Screen capture of the tutorial available at this link.
The ionic currents that are responsible for the changes in the membrane voltage are mentioned in the slide below from Dr. Peter Hunter's presentation available at this link.
Figure 2: Currents that
participate in depolarization and repolarization (Dr. Peter's Hunter slide available at the following link).
In summary, the series of events that are responsible for the action potential (depolarization) and the subsequent repolarization is as follows (relevant link) (Opie, L. H. 1998):
1. Sodium influx through the sodium channel: Sodium channels open very quickly and by allowing increased sodium (positive) ion flow inside the cell. They close immediately. The negative potential of the cell becomes very quickly less negative, then 0, then positive (depolarization) reaching a value of +47mV.
2. Calcium influx through the calcium channel: At about -20mV, calcium channels of L-type open very quickly and start closing slowly. Calcium (positive ions) flow inside the cell.
3. Potassium and chloride efflux carried by the Ito1 and Ito2 currents, respectively.
4. Potassium efflux through the slow delayed rectifier potassium channels, IKs.
5. Potassium (net) efflux through the rapid delayed rectifier K+ channels (IKr) and the inwardly rectifying K+ current, IK1.
This net outward, positive current (equal to loss of positive charge from the cell) causes the cell to repolarize.
The best known electrophysiology models are:
1. Hodgin-Huxley model: 3 currents (INa, IK, IL) and 3 gating variables (m,h,n).
2. DiFranscesco-Noble model of the Purkinje fiber cell: 12 currents (If, IK, IK1, It0, IbNa, IbCa, Ip, INaCa, INa, ICaf, ICas, Ipulse ) and 7 gating variables (y, x, r, m, h, d, f).
3. Beeler-Reuter ventricular cell model: 3 currents (INa, IS, Ix1, IK1) and 6 gating variables (m, h, j, d, f, x1).
4. Luo-Rudy mammalian ventricular cell model. The most recent version of the Luo-Rudy II model contains 14 currents (INa, ICa, ICaNa , ICaK , IK , INaCa , IK1 , IKp , Ip(Ca), INab ,ICab , INaK , InsNa , InsK ), 4 ﬂuxes (Irel , Iup , Ileak , Itr ), and 11 gating variables (m, h, j, d, f, fCa, X, X i , K1 , Kp , f NaK ).
5. Noble model of the guinea pig ventricular cell.
A comprehensive review on the Noble electrophysiology models is the following: Nickerson, D. P. and P. J. Hunter (2006). "The Noble cardiac ventricular electrophysiology models in CellML." Prog Biophys Mol Biol 90(1-3): 346-359.
Presentation of an electrophysiological model - Prediction of therapeutic approaches via electrophysiological modelling
Let us consider an electrophysiological model via an example of how electrophysiological modelling can provide therapeutic approaches with pharamaceutical compounds.
Some diseases are associated with specific well-defined profiles of differential expression of ion channels and transporters. For example, in congestive heart failure as mentioned in the study by Noble, D. and T.J. Colatsky (2000) Expert Opin Ther Targets. 2000 4(1):39-49 four major transporter proteins have altered levels of expression: the transient outward potassium current, Ito1, the inward rectifier potassium current, IK1 and the calcium pump in the sarcoplasmic reticulum (SERCA) or Iup are all downregulated, while the sodium-calcium exchanger is upregulated.
If we introduce these changes in electrophysiology cell models, we can reproduce the action potential prolongation and the early after depolarizations observed in cells from CHF patients. Also, if these pathologic cell models are incorporated in whole ventricle models, an arrhythmogenic behaviour is obtained (termed "Torsades de Pointes").
Specific drugs exist that can affect different aspects of the behavior of different channels. Is it possible to predict a combination of drugs that can correct the disease profile? Also can novel drugs be tested?
As mentioned in the article by Garny, A., D. Noble, et al. (2009) Philos Transact A Math Phys Eng Sci 367(1895): 1885-1905, in section 4d "Case study", it is estimated that approximately 40 per cent of all drugs have side effects on the rapid delayed rectiﬁer K current (IKr ; HERG channel), and therefore testing of this is a fundamental requirement for drug safety evaluation. IKr is one of the main contributors to repolarization, the process by which the voltage of the membrane of the cell is returned to control levels.
Let us consider the example of a specific compound, BRL32872, which had been for a long time a leader compound in the treatment of arrhythmias. For reference, it has been demonstrated that a successful strategy in order to treat a specific type of arrhythmias is the prolongation of the action potential. As the main factor that repolarizes the membrane and ends the action potential is the potassium rectifier current, it is reasonable to adopt approaches that partially block this current.
It has been determined that this compound has a dual action:
a. It mediates a 70% block of the IKr current: This effect alone would tend to increase the time for repolarization i.e. prolongate the action potential; but simultaneously it would result in incomplete repolarization and would lead to spontaneous reactivation of the IcaL. As a result the membrane voltage would oscillate around the 0 mV value.
b. It mediates a 20% block of the IcaL current. This allieviates the above mentioned effect of IcaL which constitutes the principal mediator of spontaneous membrane voltage oscillations.
The sum of the two effects is the net prolongation of the action potential.
We can actually "test" this drug ourselves, understand its mode of action and grasp the strategy that can be implemented to treat a condition by using different compounds, each having different properties. We will folow the example of the study by Garny, A., D. Noble, et al. (2009) Philos Transact A Math Phys Eng Sci367(1895): 1885-1905 for the BRL32872 compound, which is mentioned in section 4d and we will reproduce figure 8a following the instructions below (kindly provided by Dr. Alan Garny).
For this purpose, we will obtain an electrophysiology model from the repository and we
will initially simulate it in normal conditions. Then, in order to treat the arrhythmias, we will try to apply interventions that will increase the duration of the action potential,
similarly to the mode of action of the therapeutic compound. We will first block the potassium rectifier current by 70% and we will examine the result. Then, we will block the calcium L-type
channel by 20% and we will evaluate the final result.
We will work with the Noble 2K electrophysiology model in the CellML standard. The model is represented in the image below (from the CellML site).
Figure 3: Schematic representation of the Noble 2K guinea pig ventricular model (from the CellML site)
We will simulate the model with the instructions that follow that were kindly provided by Dr. Alan Garny
(Note: The instructions were slightly modified by the author of the site and comments were added as well).
Figure 4: Simulation result for normal conditions. The upper pannel represents parameter V (membrane voltage), the middle panel parameter i_Ca_L (L-type calcium current) and the bottom panel parameter i_Kr (rapid delayer rectifier potassium current).
Figure 5: Blocking the rapid delayed rectifier potassium current by 80% by entering the above values (80% of the initial values).
Figure 6: Simulation result for 80% blockade of the i_Kr (rapid delayer rectifier potassium current). The upper pannel represents parameter V (membrane voltage), the middle panel parameter i_Ca_L (L-type calcium current) and the bottom panel parameter i_Kr (rapid delayer rectifier potassium current).
Figure 7: Blocking the L-type calcium current by 20% by entering the above value (20% of the initial value which was 1).
Figure 8: Simulation result for 80% blockade of the i_Kr (rapid delayer rectifier potassium current) and 20% block of the IcaL current. The upper pannel represents parameter V (membrane voltage), the middle panel parameter i_Ca_L (L-type calcium current) and the bottom panel parameter i_Kr (rapid delayer rectifier potassium current).
Basic Research and Systems Biology meet Applied Science and the Pharmaceutical Industry
Part of an article from "The Economist" available at this link is pasted below.
"In contrast to the two years it takes to assess the effects of a new compound using conventional research methods, Dr.Young's approach takes an average of just two weeks. "
"The pharmaceutical industry stands to gain much from this approach. Around 40% of the compounds that drug
companies test cause arrhythmia, a disturbance to the normal heart rate. Drugs such as the anti-inflammatory medicine Vioxx and the diabetes treatment Avandia have been linked with an increased risk
of heart disease. The result is that billions have been wiped off their makers' share prices.
Not surprisingly, the pharmaceutical industry has sought out Denis Noble of Oxford University, the creator of the beating-heart model, to help. Dr Noble is now part of a consortium involving four drug firms—Roche, Novartis, GlaxoSmithKline and AstraZeneca—that is trying to unravel how new drugs may affect the heart. Virtual drugs are introduced into the model and researchers monitor the changes they cause just as if the medicines were being applied to a real heart. The production of some proteins increases while others are throttled back; these changes affect the flow of blood and electrical activity. The drugs can then be tweaked in order to boost the beneficial effects and reduce the harmful ones.
Systems biology thus speeds up the drug-testing process. Malcolm Young is the head of a firm called e-Therapeutics, which is based in Newcastle upon Tyne. Using databases of tens of thousands of interactions between the components of a cell, his company claims to have developed the world's fastest drug-profiling system. In contrast to the two years it takes to assess the effects of a new compound using conventional research methods, Dr Young's approach takes an average of just two weeks. Moreover, the company has been looking at drugs known to have damaging side effects and has found that its method would have predicted them".
Hunter, P. J., E. J. Crampin, et al. (2008). "Bioinformatics, multiscale modeling and the IUPS Physiome Project." Brief Bioinform 9(4): 333-343
Nickerson, D. P. and P. J. Hunter (2006). "The Noble cardiac ventricular electrophysiology models in CellML." Prog Biophys Mol Biol 90(1-3): 346-359.
Noble, D. and T.J. Colatsky (2000) “A return to rational drug discovery: computer-based models of cells, organs and systems in drug target identification” Expert Opin Ther Targets. 2000 4(1):39-49
Garny, A., D. Noble, et al. (2009). "CELLULAR OPEN RESOURCE (COR): current status and future directions." Philos Transact A Math Phys Eng Sci 367(1895): 1885-1905.
Opie, L. H. (1998),The Heart, Physiology, from Cell to Circulation (Lippincott-Raven Publishers)