Hogkin-Huxley Model 1&2 Flashcards
In long cellular processes e.g. dendrites, how does passive response change with distance from stimulus?
it decreases exponentially
what is the equation for the change in potential along dendrites?
define the terms of this equation
∆Vm = ∆Vmax * e^(-x/λ)
∆Vm- change in membrane potential
∆Vmax - the potential where input is injected (the highest potential)
x- the distance we measure from
λ- the length constant (the rate a which decay happens- calculated by working out the time to decrease to 37%)
What are the 3 components of resistance?
Rm, Ra and Rext
what is Ra?
how the dendrite resists down its axial length
what’s Rext?
the external resistivity of external medium (ECM)
What’s Rm?
the relationship between Rext and Ra
What happens if Rm is high?
there’s less current flowing out (less leaky), so the voltage will decay slower in space, hence travel further
define electrotonic conduction
the passive spread of voltage along a membrane
what property does lambda represent?
conductance
what 2 physiological conditions (linked to resistance) gives greatest conductance?
1) if Rm is high- there’s low ion channel density/high insulation (myelination) so the membrane is not very leaky- increases conductance
2) if Ra is low- the diameter of membrane process is high, thick dendrites so reduced resistance- better conductance
how is membrane potential calculated?
Vm= Vin - Vout
what is reversal potential
change in direction of net current as Vm swings around Es
what is driving force calculation?
Es- Vm
what is membrane current calculation?
Is-gs (Es-Vm)
what are the strengths of the RC-based leaky integrate and fire model
we have good biological understanding, it’s simple, has an exponential solution
what are the weaknesses of the RC-based leaky integrate and fire model?
does not properly model action potentials, real spikes have duration and after-hyperpolarisation (which LIF doesn’t take into consideration), different neurons have different spike shapes
put simply, where do spikes in a real neuron come from?
active currents
what does the conductance of active currents depend on?
Vm
write ohm’s law for active current
Iact= gact (Vm, t) (Er-Vm)
what does active current take into consideration which passive membrane models don’t?
membrane voltage (Vm)
what do active current explain which LIF model doesn’t?
variation in spiking- real neurons have ion channels which aren’t passive in their opening and closing- it is dependant on Vm
what passively prevents a runaway feedback loop of Na+ in AP generation?
passive K+ efflux, is prompted y depolarisation, as the Vm moves further away from Ek
(as well as actively gated ion channels)
Give an overview of gated-Na+ channels
these channels are controlled by gates
there are 2 gates- activating m-gates and inactivated h-gates.
m-gates are closed at rest and open almost immediately upon depolarisation, Na+ influx, after some delay (2-3m/s) h-gates start to close (this length of time changes how long spike is
both m and h gates need to be open for AP, part of why it is so transient
give an overview of K+ gated channels
K+ channels only have an activation gate - n-gate.
active K+ current is involved in the repolarisation of the membrane and after-hyperpolarisation
at rest, the n-gate is closed, with no active K+ efflux, under depolarisation n-gates remain initially closed for a short time, and after a delay (2-3m/s) they start opening allowing K+ efflux
the delay mmeans we can get a discrete AP spike
what did Hodgkin and Huxley posit opens/closes gates?
movement of charged particles in membrane
what do modern theories of gate opening/closing posit?
the gates undergo conformational change when charged particles bind
draw and explain the relationship between inactivation and activation rate and open/closed gates
closed (1-x) -alpha-> open (x)
open (x) -beta-> closed (1-x)
alpha= activation rate
beta= deactivation rate
x- proportion of active/open channels
x-1- proportion of inactive/closed channels
write an equation showing the relationship between alpha, beta and x at equilibrium
alpha (1-x) = Beta x
write the equation for calculating the change in X over time
∆X = alpha (1-x) ∆t- Bx ∆t
change in open gates= alpha (1-x) over time period - Bx over time period
how is this change in x over time written as a differential equation?
dx(t)/dt = alpha (1-x) - Bx
x as a function of time = rate of activation x number of closed doors - rate of inactivation x number of open doors
write the first order kinetics for K+ current (n-gate)
dn/dt= alpha n (v) (1-n) - Bn (V) n
write the conductance for K+ current
gk=gk max n^4
explain gk=gk max n^4
the conductance is equal to gk max to the power of 4- as there are 4 gates that make up the K+ channel- all 4 gates need to undergo conformational change for K+ conductance
write out the first order kinectics differential equations for Na+ current- m-gate and h-gate
dm/dt= alpha m(V)(1-m)-beta m (V)m
(m-gate)
dh/dt+ alpha h(v)(1-h)-beta h (V)h
h-gate
write out the conductance equation for Na+ current
gNa= gNa max m3 h
write the equation for capacitance current
Icap= Iion + Iinj
In addition to the 3 derivative equations previously written, what is the 4th Hodgkin-Huxley equation differential equation
Cm dv/dt= gNamaxm3h (ENa-V) + gkmaxn4 (Ek-V) + gL(EL-V)+ inj
What are the 4 variables taken into consideration by Hodgkin-Huxley Formalism?
1- voltage
2- m/h/n gating
3- membrane potential
4- alpha-beta ratio (open/closed gates)
