przez Fatima Sharif 3 lat temu
278
mod 3
przez Fatima Sharif 3 lat temu
278
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idenitfy critical points, cross at x axis is css
d/dx {f(xss)} = 0 (y axis)
determine stability by lookin at a fllow directions
preturb off its xss: n = x -x*
dn/dt= d/dt (x-x*)= f(x) - f(x*)
= f(x) = f(x* + n)
= 0 + nf' (x*) + 0
< 0 stable
speeding toward
> 0 unstable
speeding away
derivative of f(x*) is not 0 bc this is f''
via expansion taylor dn/dy = f(x*) + nf'(x*) + O(n²)
very small perturbation so third term is negligible
dn/dt = f(x) - 0
Depolarizing or depolarizing voltage
Change I app very fast
to create steps (pulses)
instantanous
dv/dt = 0 0 = Iapp - I mem (C +) I mem = Iapp
What happend to C ?????
(Depolarizaing) Pulses
steps to higher voltages)
2 - Compare
3- Correct
4 - Inject
5 - Monitor
axons dont have other than Na + an k+ channels
capaticence = ability to store and separate charge = lipid bilayer because they are impermeatble
kirchoffs current law =I res + I cap - I app = 0
current balance equation
C(dV/dt) = Iapp - Imem
Imem = Σion
Ileak + Ina + Ikv Hogdkin-Huxley
Ileak +Ica (Bistable)
Ileak Passive cell
Iion= gk(Vm-Ek)
exponential relaxtation
dv/dt= [(Iapp +gkEk)/C] - (gk/C) V phase diagram
Vss = (Iapp/gk)+ Ek
J/K
or from equation
when f(0) ; 0 = Iapp - gk(Vss - Ek)
-Iapp, left shift
+Iapp, right shift
When Iapp = 0 , resting potential
slope = gk/C
exponential time contant = C/gk
Iapp
+ / OUTWARD
+ ions in --> out
Na + or Ca2+ leaving
- ion out --> in
ex GABA cl- outward currnets
Cl- entering
- / INWARD
hyperpolarizing
applied current
depolarizing
- in --> out
Cl- moving out the cell
doesn't happen?
+ ions out --> in
Na+ or Ca++ entering
Ires
Vm = Ek + Vres =φin - φ* + φ* - φout
Vm = Ek+ Ires / gk
Ik = gk(Vm-Ek) chord conductance equation form
current over resistor (ion channel)
when Ik is - , Vm is less than Equilibrium
when Ik is + , Vm is greater than Equilibrium
K+ driving out of cell
Ek = φin -φ*
special case of ghk current equation
GK -- current ---> voltage ---> nernst
Vres
φ* - φout
Ires/ gk
IresR
R=1/gk
I cap
for every one charge that enters, one leaves from other side through nothing actually really passes
Icap = dQ/dt = C (dVm/dt)
Q = CVm
C = capacitance
constant field theory
ions move single file through the membrane
ions in membrane behave like ions in a solution
obey nerst-planck equation
voltage changes linearly through membrane
electric field is constant
Vm = φin - φout
as +ions that are higher [outside] are allowed in move in, will do so nonlinearly because gradually will want to move in less because electromotive force that is opposing the still existing concentration graduient
Goldman hodkin katz (ghk) voltage equatoion
note that cl has flip i/o so that we don't need to use z
+1 * +1 = -1 ^ 2
1*2 = -1^2
α = PNa/PK
how close Vm will be to nerst depending on [K+]
K+ dominates resting potential
only revelent when [K+] is low
a<<<1 and so [Na]i<<<[K]i therfore
assume Pcl<<< PK (we did same for Ca++)
nernst EQUILIBRIUM potential
finding when electromotive force and concentration graduant force are equal opposing
E force - C force = 0
RT(ln[Kin]/[Kout])/zF
no net current
V= φin - φout = Ek
GHK current density equation
predicts non lineariity bc mutiple variables inviolved
ions move because diffsion and drift (C and electromotove)
[S]out
[S]i
Ps
zF
zV/Vθ
vθ = RT/F
opposite for K+ and flip out and in anions
inwardly rectifying K+ potassium current
shifts
toward depolarization with equal but opposite Iapplied is smaller than toward hypoerpolarizatneasier to flow inward
for Na+
ratio defines amount of retification
reversal potential = nernst potential where current reverses
outward (convex), small g, + current
as V--> -inf, denom --> inf // I Na --> 0
as V --> inf, denom --> 1 /// I Na prop to [Na+]i
inward reticification (concave), g large, current flows easy when inward (-, <0)
as V --> -inf, num --> denom // I Na prop to [Na+]0
as V --> inf, num --> 0 // I na+ therefore --> 0
Na+ and ca2+ channels
4 * 6tmd (1p), basically 4 of ^ connected
K+ channels
closed at rest
6tmd, 1p, 4x
***** 4rth tmd has + reasons that allow voltage dep gating
TRP
KCNQ
Kca ca2+activated
Kv voltage dep
Open at rest therefore determine most of resting
4 tmd 1p, 2x
k2p channels
2tmd 1p, 4x
KcsA
picture is half
showing xx // xx
Kir inward-reticfying
extenstive
x^2
when x*2
factor by 4
membrane capacitance
membrane resistance Rm = Rm/ SA
4πr^2
intensive
capacitance
memebrane reistivity Rm = 10000 Ωc^2
conductance is nonnegative NOT CURRENT
n gates
4 gates
so the moventnt of any one 4 gates has ability to move close gate since 4 particles must be in a particular configuration
IK+ activation and decativation
I na inactivation
inactivation - activating stimulus maintained but conductance went away
when you try to evoke Na current again there is a refractory period u can evoke same activation. time constant has to do with recovery timee fold of its final value
Na+ inactivated but K+ activated
voltage dependant rate constant
gating variable (m)
(bc channels have voltage dependant gates)
which also is why they inactivate after same evokedvoltage too
order of magitigude (10x) faster, react to changes
dm/dt = α(1-m) - βm
= α-m(α+β)
dx/dt = a + bx
antiderivative
τ = 1/ b
xss = a/b
dc/dt = j - kc
Cdv/dt = I app - gk ( V - Ek)
How close is M to its steady state value? How fast is scaled by time constast (big-slow vv)
Tau
M ss
(1-m) ⇌ m
m[0,1]
β : open --> closed
α: closed --> open
deactivation- falls back to 0 state bc evoked stimulus is removed
Na+ activation
separation and subtraction of ionic currents
LAST THREE MINUTES OF 9.1????????????
embracing currents can be isolated via ion subsists ion and digital subtraction
transient (happens when inactivate)
capacitive transient
I ion - Activation of K+ current when voltage back -10 --> -70, low driving force because ion channels decativate
only flows at instant voltage changes
I T
restorative e
regernative regernative
mathematically stable unrealistic because system cant maintain like a pen standing upright
restoraive restorative
equal and opposite so cancel out
3 points at which intersect
state stapcs vs parameter (Iapp)= bifurfaction diagram
hyteresis
shifting Iapp can chahnge stabilities
membrane bistability
stable at 2 different Vs and a transient current can switch you between the two
currents on either eside of the 2 steady states are resorative (positive conductance) an perturbation would restore to Ek. membrane would fall back down unless you reach threshold
3 times interescts x axis, current is 0
perisistent
delayed-reticifier
I potassium - DR = conductance m^n (Driving force)
opposite shape for hyperpolarization
activation by hyperpolarization
Ih or Isag
inward recitfying potassium current Kir
always open until threshold or
actiavtion by depolarization
I CaV depolarization activated Ca2+ current
V dep current
basically same as conductance equation with the factor of driving force
V dep conductance
I Kv
once reaches m inf all conduxctance is available (all channels open)
physiological range
Subtopic
slope g / E is equilib / current is dep on driving force (E--> eq disparity / once cross x, start leaving cell vs entering / there's a curve when whntering is highly pref
move up and squash
THRESHOLD is AP THRESHOLD
ALL OR NONE
point of highest slope
determines whether channels are open or closed (max vs min conductance
conductance as a function of voltage
peaks at Na becomes given a voltage and also where I will eventually steady given voltage
K+ , delayed outward current
Na+, early inward current
changing Na concent only saw change in the early inward curent
the 2 blips at +70 and +90 mv are evoke at volatges above nerst potential
