Goldman’s Equation

Biol 313 Cell Neuro Goldman’s Equation - Calculates Vm, given the concentration of ions in and out and their relative permeabilities - The resting potential for sodium is 1/100th. Sodium will leak in during resting potential, resting potential will not equal equilibrium potential - At rest, membrane permeability to sodium is only .04 that of potassium so it helps the cell membrane the low sodium in along with the sodium-potassium pump’ - The driving force on sodium is a squid axon is Vm+ ENa+ which was 160-55w which is 115 mV - If you make membrane permeability of sodium, it has a strong drive to enter the cell - If the neuron is now more permeable to sodium than potassium, sodium will enter and enter enough that pushes the membrane potential (Vm) close to the equilibrium potential for sodium, membrane potential will become more positive - During an action potential Vm approaches Ena+ as the membrane becomes more permeable to the sodium more so than to potassium - If sodium channels close again V,m would decline, and approach rest, as potassium now has a high driving force pushing it out, and the sodium-potassium pump chugs along - - Action potentials are explosive events that are initiated when Vm reaches threshold Na channels are triggered to open by voltage. Voltage that is more positive than the resting potential usually is In a squid the peak of the action potentials Pm+ is 2o times that for potassium sp Pk+ + PNa+ = cl- (1:20:.45) - FOR SQUID AXON ION CONCENTRATION (1)20𝑚𝑀 + 20 (440𝑚𝑀) + .45 (51𝑚𝑀) 1(440𝑚𝑀) + 20 (50𝑚𝑀) + .45(560𝑚𝑀) 20𝑚𝑀 + 8800𝑚𝑀+ 22.95 58 · 𝑙𝑜𝑔 400𝑚𝑀 + 1000𝑚𝑀+ 25.2 𝑚𝑀 8842.95𝑚𝑀 58𝑚𝑉 · 𝑙𝑜𝑔 1652 𝑚𝑀 = 50𝑚𝑉𝑙𝑜𝑔5. 35 58 · 𝑙𝑜𝑔 = + 42mV Action potentials often lost only 1 more or less. If you view them on a larger scale they will look like this Sp structures call them spikes On a short time scale, they will look like this Once threshold Vm is closed Na+ channels open in the (+) feedback loop. Since the opening is targeted by (+)V1, what is a threshold? Hence, the Na= entering is balanced by Na+ leaving, one more Na+ enters equilibrium and is uprooted and the (+) feedback loop kicks in unstable equilibrium. Its perfectly possible (and actually The action potential is short-lived for two reasons : 1. Not channels clos eshortly after they open 2. There are voltage - gated potassium channels triggered to open by a positive Vm at the peak of the action potential Vm= +42 and the driving force on potassium at action potential peak df= 42-(-75) = + 117 - So when the voltage gated channel potassium channels open there's a large d.f on potassium for it’s exit. At the same time, sodium channels are closing with Pna+ going down while Pk+ goes up so Vm becomes more (-1) quietly - In fact may reach a point where sodium channels are virtually all closed and potassium are all open and Vm=Ek+. Thus is the after hyperpolarization. Extra material https://www.google.com/imgres?q=goldman%20equaTION&imgurl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FE14 hzilwOsc%2Fmaxresdefault.jpg&imgrefurl=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DE14hzilwO sc&docid=JEElVKE79LVVmM&tbnid=44g-hA8oRWKWRM&vet=12ahUKEwjYi9-Nzq6IAxXCMVkFHdbZA4o QM3oECH4QAA..i&w=1280&h=720&hcb=2&ved=2ahUKEwjYi9-Nzq6IAxXCMVkFHdbZA4oQM3oECH4QA A https://www.google.com/imgres?q=goldman%20equaTION&imgurl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FCH 0yRkuFSkA%2Fhq720.jpg%3Fsqp%3D-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD %26rs%3DAOn4CLAAcwYHj8KBcLH1Hi35ukA8fT5jtQ&imgrefurl=https%3A%2F%2Fm.youtube.com%2Fwatc h%3Fv%3DYOFXkZu-r8M&docid=aTRYl_BxBhbGxM&tbnid=C1uo1gQomDw-mM&vet=12ahUKEwjYi9-Nzq6 IAxXCMVkFHdbZA4oQM3oECHMQAA..i&w=686&h=386&hcb=2&ved=2ahUKEwjYi9-Nzq6IAxXCMVkFHd bZA4oQM3oECHMQAA https://www.google.com/url?sa=i&url=https%3A%2F%2Fm.youtube.com%2Fwatch%3Fv%3DYOFXkZu-r8M&ps ig=AOvVaw00Dn6_GDoToN6XPeH2GQMq&ust=1725722148952000&source=images&cd=vfe&opi=89978449& ved=0CBQQjRxqFwoTCPjvp4rQrogDFQAAAAAdAAAAABAK