|Ching-Hsing Luo (2011), Scholarpedia, 6(10):6220.
|revision #90678 [link to/cite this article]
Luo and Rudy models were published at 1991  (passive) and 1994  (dynamic) in Circulation Research by providing the computational formula for the action potential of a single ventricular cell. At the early 1980s, the ion channels in cardiac cells were not as clear as neurons, especially the channels concerned with calcium ions including those in the sarcoplasmic reticulum. The channels for potassium and sodium ions are relatively clear even some debates in the sodium channel.
In 1980s, the most useful cardiac cell model was made by Beeler and Reuter  in 1974 even there was one models published in 1985 . In 1980s, Dr. Rudy put great efforts in the simulation of the cardiac arrhythmia including reentry; however, the action potential models were either out of date or difficult to be used, complained by Dr. Quan, one PhD student graduated in 1990 at Dr. Rudy’s lab. It incited Dr. Luo to fabricate a good cardiac single cell model for the arrhythmia study when Dr. Luo joined Dr. Rudy’s lab in June 1988.
Luo-Rudy passive model
It is a huge construction to build up a cell model since thousands of ion channels published in 1980s. Dr. Luo decided to update the sodium and potassium ion channels since calcium ion channels were under debate in 1980s. Why I call Luo-Rudy model published in 1991 a passive model? This is because the ion concentrations inside the cell model is unchanged, i.e., the model cell is always alive or no chance to die. Frankly, a model to be very useful for clinic application should be a live cell in the computer, but such a huge state-of-art construction should be made step by step. So, the first step to build up the cell model by Dr. Luo was to provide a good and update passive cell model.
After Luo-Rudy passive model was published in 1991 by updating INa (sodium current) and IK, IK1, IKp but keeping the calcium current ICa same as Beeler and Reuter’s, Dr. Rudy heard in the annual heart conferences that almost all researchers were very happy about the robustness of Luo-Rudy passive model as used to investigate the clinic phenomena. This good news gave Dr. Luo confidence to push the cell model forwards, as in his mind, a live cell model.
Luo-Rudy dynamic model
To make a model cell alive, it needs the ion pumps to maintain the intracellular ion balance, i.e., the ions must return back after the firing of an action potential. In one shot of action potential, potassium ions leave out of the cell, but sodium ions get into the cell. Moreover, calcium ions get into the cells from the extracellular space and sarcoplasmic reticulum for muscle contraction, an important feature for human heart. So, ion pumps are required in the membranes of cell and sarcoplasmic reticulum to maintain the ion balance inside the cell. Fortunately, huge amount of experimental data have been published for cardiac cells in 1980s, even not for formulism. Dr. Luo screened and integrated those data together to be formulated as the components of the cardiac model cell.
In 1991, the most arguing issue to formulate a live cardiac cell model was the ambiguity of the calcium ion channels. Several famous labs announced the calcium ion channels but they were quite scattering with apparent differences, including species. Dr. Luo made a decision to skip the debate issue but, instead, put them all into the cell model to see how action potentials look like by using those published experimental data for calcium ion channels, especially sodium-calcium exchangers. It left the choice for scientists to pick up the calcium ion channels they wanted even Dr. Luo had suggestions in the Luo-Rudy dynamic model published in 1994.
Luo-Rudy dynamic model in 1994 not only includes the sodium and potassium channels in Luo-Rudy passive model but also introduces sodium-potassium pump, calcium pump, L-type calcium channel, non-specific calcium-activated channel, sodium-calcium exchanger on the membrane as well as calcium-induced calcium release channel and calcium pump on the membrane of sarcoplasmic reticulum with calcium buffers in the myoplasm.
For heart muscle contraction, a single heart cell is stimulated to raise the intracellular potential from the resting -80 mV to about +40 mV by flowing positive sodium ions due to the opening of the sodium channel. Such a potential rising is called depolarization. Sodium channel is closed very quickly (in 2 msec), then the opening of potassium and calcium channels fight against to maintain the intracellular potential at the positive level called the potential plateau for 200-300 msec. Potassium ions flows out of the cell but calcium ions flows into the cell to maintain such a high plateau potential; moreover, the input of the extracellular calcium ions raises the intracellular calcium level up to a threshold to incite the spike calcium release from sarcoplasmic reticulum for cell contraction. Finally, potassium ion efflux brings the potential down to the resting level, called repolarization. The potential variation procedure from depolarization, plateau, to repolarization is called an action potential. Sodium-potassium pump and calcium pump keep working to return all the ions back their origin pools during or after an action potential. If keeping firing the action potential, the intracellular ion concentration will lose the balance gradually and it also takes more time for ion pumps to recover the steady status.
The life expression in the future cell model with DNA
The partial live model cell invented by Luo and Rudy does provide a useful tool for clinic investigation and help explain the underlying mechanisms that are not easily elucidated in the experiments. The updating Luo-Rudy models and other published models including human model cells enhance the study of life expressions able to be simulated in the computer, especially the DNA code opening.
The scientists have put great efforts to model all the way from DNA, protein, ion channels or second messengers, tissue, organ, and finally life expression. It is almost quite impossible to get the efficient scientific studies without the help of model simulations nowadays. To open the life secret or encode the DNA secret, scientists cannot satisfy the Hodgkin-Huxley or Markov chain formulism. A revolutionary life modeling other than Hodgkin-Huxley or Markov chain formulism concerning with diseases in close relation to DNA and drug is under construction by unifying them together from DNA to life.
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