Unformatted text preview: The Nernst Equation Eq. 1a Eion = (RT/zF) * ln([Ion]out/[Ion]in) for example ENa = RT/zF *ln([Na]out/[Na]in) Eq. 1b Eion =(0.198Τ/Ζ) × (log [Ion]out/[Ion]in) where T is in degrees kelvin Eq 1b Eion = (57.5/z) log10([Ion]out/[Ion]in) at 17oC The equation for the magnitude of the chemical force (in afus) driving an ion through the CM Eq. 2a |Fchemical| = RT/F *|ln([Ion]out/[Ion]in)| Eq. 2b |Fchemical| = 57.5* |log10([Ion]out/[Ion]in)| at 17oC (note that there is no z in Eq. 2a & 2b) You might have noticed that equation 1a and 2a are remarkably similar. In fact you can combine the two and derive the magnitude of the chemical force as a function of the equilibrium potential (Eion). You do this by rearranging equation 1 and solving for RT/F *ln([Iout]/[Iin]) Eq. 2c |Fchemical| = RT/F *|ln([Ion]out/[Ion]in| = |z * Eion| The equation for the magnitude of the electrical force driving an ion through the CM is Eq. 3 |Felectrical| = |z*V| The equation for the net force driving an ion through the CM is Eq. 4a Fnet = Fchemical + Felectrical
This is vector notation remembering to take into account the direction of the forces (arrows in lecture) You can substitute Eq. 2c and 3 for Fchemical and Felectrical to get Eq. 4b Fnet = zV - z Eion = z(V- Eion)
We subtracted because we are really looking for the difference between the electrical and chemical force. When V = Eion, the ion is in equilibrium and there should be no net force acting on it. The GHK Equation only accounting for the three most common ions (note other ions may be used if the cell is permeable to them)
Eq. 5a ER = p [Cl ]i + p k [ K ]o + p Na [ Na ]o RT * ln cl F p cl [Cl ]o + p k [ K ]i + p Na [ Na ]i Eq. 5b E R = 57.5* log p cl [Cl ]i + p k [ K ]o + p Na [ Na ]o at17 o p cl [Cl ]o + p k [ K ]i + p Na [ Na ]i The steady state voltage at the injection point Eq. 6 ΔVss = IinRm Where Iin is the injected current, Rm is the input (often the total) resistance of the cell. Where rm is the membrane resistance of a unit length (e.g., Ω-cm) and cm is the membrane capacitance per unit length (e.g., F/cm). The time constant Eq. 7 τ= rmcm The time constant equation Eq. 8 ΔV(t) = ΔVss [1-e-(t/ τ)] The space (length) constant Eq. 9 λ = (rm/ri)1/2 Where rm is the membrane resistance for the length of neuron we are looking at (e.g., Ω-cm), and ri is the internal
resistance for the length of neuron we are looking at (e.g., Ω/cm) The space constant equation Eq. 10 ΔV(x) = ΔVss e-(x/λ) The unified equation Eq. 11 ΔV = ΔVss [1-e-(t/ τ)]*[e-(x/λ)] These can be found on extra practice on homework (“Study Questions”) The time it takes a cell to go through a given voltage change given the cell is stimulated (hyperpolarized or depolarized) Eq. 12 You can generate this by modifying Extra Practice Problem 4 from homework 2 The voltage change after a cell has been stimulated and then turned off (one time, without being turned back on). This equation ONLY works when toff (the time off) is greater than 0. Eq. 13 This was solved in Extra Practice Problem 2 from homework 2 The time a cell will cross a certain voltage after being stimulated and then TURNED OFF. This equation ONLY works when toff (the time off) is greater than 0 Eq. 14 This was solved in Extra Practice Problem 9 from homework 2 ...
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- Fall '08
- Neurobiology, Ion, Eq., Walther Nernst, goldman equation