|
|
| (472 intermediate revisions by more than 100 users not shown) |
| Line 1: |
Line 1: |
| {{about|the biological application of the Nernst equation|the general equation|Nernst equation}}
| | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
|
| |
|
| In a [[biological membrane]], the '''reversal potential''' (also known as the '''Nernst potential''') of an [[ion]] is the [[membrane potential]] at which there is no net (overall) flow of that particular ion from one side of the membrane to the other. In the case of [[post-synaptic]] [[neuron]]s, the reversal potential is the membrane potential at which a given [[neurotransmitter]] causes no net current flow of ions through that neurotransmitter [[Receptor (biochemistry)|receptor's]] [[ion channel]].<ref name="Purves" >{{cite book | author = Dale Purves, et al. | title = Neuroscience, 4th Edition | publisher = Sinauer Associates | pages = 109–11 | year = 2008 | isbn = 978-0-87893-697-7}}</ref>
| | If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]] |
| | * Only registered users will be able to execute this rendering mode. |
| | * Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere. |
|
| |
|
| In a single-ion system, ''reversal potential'' is synonymous with '''equilibrium potential'''; their numerical values are identical. The two terms refer to different aspects of the difference in membrane potential. ''Equilibrium'' refers to the fact that the net ion flux at a particular voltage is zero. That is, the outward and inward rates of ion movement are the same; the ion flux is in equilibrium. ''Reversal'' refers to the fact that a change of membrane potential on either side of the equilibrium potential reverses the overall direction of ion flux.<ref name="Purves" />
| | Registered users will be able to choose between the following three rendering modes: |
|
| |
|
| The reversal potential is often called the "Nernst potential", as it can be calculated from the [[Nernst equation]]. Ion channels conduct most of the flow of simple ions in and out of [[cell (biology)|cells]]. When a channel type that is selective to one species of ion dominates within the membrane of a cell (because other ion channels are closed, for example) then the voltage inside the cell will equilibrate (i.e. become equal) to the reversal potential for that ion (assuming the outside of the cell is at 0 volts). For example, the [[resting potential]] of most cells is close to the [[potassium|K]]<sup>+</sup> (potassium ion) reversal potential. This is because at resting potential, potassium conductance dominates. During a typical [[action potential]], the small resting ion conductance mediated by potassium channels is overwhelmed by the opening of a large number of [[sodium|Na]]<sup>+</sup> (sodium ion) channels, which brings the membrane potential close to the reversal potential of sodium.
| | '''MathML''' |
| | :<math forcemathmode="mathml">E=mc^2</math> |
|
| |
|
| The relationship between the terms "reversal potential" and "equilibrium potential" only holds true for single-ion systems. In multi-ion systems, there are areas of the cell membrane where the summed currents of the multiple ions will equal zero. While this is a reversal potential in the sense that membrane potential reverses direction, it is not an equilibrium potential because not all (and in some cases, none) of the ions are in equilibrium and thus have net fluxes across the membrane. When a cell has significant permeabilities to more than one ion, the cell potential can be calculated from the [[Goldman-Hodgkin-Katz equation]] rather than the Nernst equation.
| | <!--'''PNG''' (currently default in production) |
| | :<math forcemathmode="png">E=mc^2</math> |
|
| |
|
| ==Mathematical models==
| | '''source''' |
| The term ''driving force'' is related to equilibrium potential, and is likewise useful in understanding the current in biological membranes. Driving force refers to the difference between the actual membrane potential and an ion's equilibrium potential. It is defined by the following equation:
| | :<math forcemathmode="source">E=mc^2</math> --> |
|
| |
|
| :<math>{I_{ion}} = {g_{ion}} ({V_m}-{E_{ion}})\,</math> where <math>{V_m}-{E_{ion}}</math> is the Driving Force. | | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
|
| |
|
| In words, this equation says that: the ionic current (I<sub>ion</sub>) is equal to that ion's conductance (g<sub>ion</sub>) multiplied by the driving force, which is represented by the difference between the membrane potential and the ion's equilibrium potential (i.e. V<sub>m</sub>-E<sub>ion</sub>). Note that the ionic current will be zero if the membrane is impermeable (g<sub>ion</sub> = 0) to the ion in question, regardless of the size of the driving force.
| | ==Demos== |
|
| |
|
| A related equation (which is derived from the more general equation above) determines the magnitude of an [[end plate current]] (EPC), at a given membrane potential, in the [[neuromuscular junction]]:
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
|
| |
|
| :<math>EPC = {g_{ACh}} ({V_m}-{E_{rev}})\,</math>
| |
|
| |
|
| where EPC is the end plate current, g<sub>ACh</sub> is the ionic conductance activated by [[acetylcholine]], V<sub>m</sub> is the membrane potential, and E<sub>rev</sub> is the reversal potential. When the membrane potential is equal to the reversal potential, V<sub>m</sub>-E<sub>rev</sub> is equal to 0 and there is no driving force on the ions involved.<ref name="Purves" />
| | * accessibility: |
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
|
| |
|
| ==Use in research== | | ==Test pages == |
| When V<sub>m</sub> is at the reversal potential (V<sub>m</sub>-E<sub>rev</sub> is equal to 0), the identity of the ions that flow during an EPC can be deduced by comparing the reversal potential of the EPC to the equilibrium potential for various ions. For instance several excitatory [[ionotropic]] ligand-gated [[neurotransmitter]] [[Receptor (biochemistry)|receptors]] including [[glutamate receptor]]s ([[AMPA]], [[NMDA]], and [[kainate]]), [[nicotinic]] [[acetylcholine]] (nACh), and [[serotonin]] (5-HT<sub>3</sub>) receptors are nonselective cation channels that pass Na<sup>+</sup> and K<sup>+</sup> in nearly equal proportions, giving an equilibrium potential close to 0 mV. The inhibitory ionotropic ligand-gated neurotransmitter receptors that carry Cl<sup>–</sup>, such as [[GABA]]<sub>A</sub> and [[glycine]] receptors, have equilibrium potentials close to the resting potential (approximately –70 mV) in neurons.<ref name="Purves" />
| |
|
| |
|
| This line of reasoning led to the development of experiments (by Akira Takeuchi and Noriko Takeuchi in 1960) that proved that acetylcholine-activated ion channels are approximately equally permeable to Na<sup>+</sup> and K<sup>+</sup> ions. The experiment was performed by lowering the external Na<sup>+</sup> concentration, which lowers (more negative) the Na<sup>+</sup> equilibrium potential and produces a negative shift in reversal potential. Conversely, increasing the external K<sup>+</sup> concentration raises (more positive) the K<sup>+</sup> equilibrium potential and produces a positive shift in reversal potential.<ref name="Purves" />
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| | *[[Displaystyle]] |
| | *[[MathAxisAlignment]] |
| | *[[Styling]] |
| | *[[Linebreaking]] |
| | *[[Unique Ids]] |
| | *[[Help:Formula]] |
|
| |
|
| ==See also==
| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| *[[Electrochemical potential]]
| | *[[Url2Image|Url2Image (private Wikis only)]] |
| *[[Cell potential]] | | ==Bug reporting== |
| *[[Goldman equation]] | | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
| | |
| ==References== | |
| {{reflist}}
| |
| | |
| ==External links==
| |
| * [http://www.nernstgoldman.physiology.arizona.edu/ Nernst/Goldman Equation Simulator]
| |
| * [http://www.physiologyweb.com/calculators/nernst_potential_calculator.html Nernst Equation Calculator]
| |
| * [http://www.physiologyweb.com/calculators/ghk_equation_calculator.html Goldman-Hodgkin-Katz Equation Calculator]
| |
| * [http://www.physiologyweb.com/calculators/electrochemical_driving_force_calculator.html Electrochemical Driving Force Calculator]
| |
| | |
| [[Category:Membrane biology]]
| |
This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.
If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]
- Only registered users will be able to execute this rendering mode.
- Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.
Registered users will be able to choose between the following three rendering modes:
MathML
Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.
Demos
Here are some demos:
- accessibility:
- Safari + VoiceOver: video only, File:Voiceover-mathml-example-1.wav, File:Voiceover-mathml-example-2.wav, File:Voiceover-mathml-example-3.wav, File:Voiceover-mathml-example-4.wav, File:Voiceover-mathml-example-5.wav, File:Voiceover-mathml-example-6.wav, File:Voiceover-mathml-example-7.wav
- Internet Explorer + MathPlayer (audio)
- Internet Explorer + MathPlayer (synchronized highlighting)
- Internet Explorer + MathPlayer (braille)
- NVDA+MathPlayer: File:Nvda-mathml-example-1.wav, File:Nvda-mathml-example-2.wav, File:Nvda-mathml-example-3.wav, File:Nvda-mathml-example-4.wav, File:Nvda-mathml-example-5.wav, File:Nvda-mathml-example-6.wav, File:Nvda-mathml-example-7.wav.
- Orca: There is ongoing work, but no support at all at the moment File:Orca-mathml-example-1.wav, File:Orca-mathml-example-2.wav, File:Orca-mathml-example-3.wav, File:Orca-mathml-example-4.wav, File:Orca-mathml-example-5.wav, File:Orca-mathml-example-6.wav, File:Orca-mathml-example-7.wav.
- From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.
Test pages
To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:
Bug reporting
If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .
