Hogkin-Huxley Model 1&2

Question 1

In long cellular processes e.g. dendrites, how does passive response change with distance from stimulus?

Answer 1

it decreases exponentially

Question 2

what is the equation for the change in potential along dendrites?
define the terms of this equation

Answer 2

∆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%)

Question 3

What are the 3 components of resistance?

Answer 3

Rm, Ra and Rext

Question 4

what is Ra?

Answer 4

how the dendrite resists down its axial length

Question 5

what’s Rext?

Answer 5

the external resistivity of external medium (ECM)

Question 6

What’s Rm?

Answer 6

the relationship between Rext and Ra

Question 7

What happens if Rm is high?

Answer 7

there’s less current flowing out (less leaky), so the voltage will decay slower in space, hence travel further

Question 8

define electrotonic conduction

Answer 8

the passive spread of voltage along a membrane

Question 9

what property does lambda represent?

Answer 9

conductance

Question 10

what 2 physiological conditions (linked to resistance) gives greatest conductance?

Answer 10

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

Question 11

how is membrane potential calculated?

Answer 11

Vm= Vin - Vout

Question 12

what is reversal potential

Answer 12

change in direction of net current as Vm swings around Es

Question 13

what is driving force calculation?

Answer 13

Es- Vm

Question 14

what is membrane current calculation?

Answer 14

Is-gs (Es-Vm)

Question 15

what are the strengths of the RC-based leaky integrate and fire model

Answer 15

we have good biological understanding, it’s simple, has an exponential solution

Question 16

what are the weaknesses of the RC-based leaky integrate and fire model?

Answer 16

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

Question 17

put simply, where do spikes in a real neuron come from?

Answer 17

active currents

Question 18

what does the conductance of active currents depend on?

Answer 18

Vm

Question 19

write ohm’s law for active current

Answer 19

Iact= gact (Vm, t) (Er-Vm)

Question 20

what does active current take into consideration which passive membrane models don’t?

Answer 20

membrane voltage (Vm)

Question 21

what do active current explain which LIF model doesn’t?

Answer 21

variation in spiking- real neurons have ion channels which aren’t passive in their opening and closing- it is dependant on Vm

Question 22

what passively prevents a runaway feedback loop of Na+ in AP generation?

Answer 22

passive K+ efflux, is prompted y depolarisation, as the Vm moves further away from Ek
(as well as actively gated ion channels)

Question 23

Give an overview of gated-Na+ channels

Answer 23

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

Question 24

give an overview of K+ gated channels

Answer 24

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

Question 25

what did Hodgkin and Huxley posit opens/closes gates?

Answer 25

movement of charged particles in membrane

Question 26

what do modern theories of gate opening/closing posit?

Answer 26

the gates undergo conformational change when charged particles bind

Question 27

draw and explain the relationship between inactivation and activation rate and open/closed gates

Answer 27

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

Question 28

write an equation showing the relationship between alpha, beta and x at equilibrium

Answer 28

alpha (1-x) = Beta x

Question 29

write the equation for calculating the change in X over time

Answer 29

∆X = alpha (1-x) ∆t- Bx ∆t change in open gates= alpha (1-x) over time period - Bx over time period

Question 30

how is this change in x over time written as a differential equation?

Answer 30

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

Question 31

write the first order kinetics for K+ current (n-gate)

Answer 31

dn/dt= alpha n (v) (1-n) - Bn (V) n

Question 32

write the conductance for K+ current

Answer 32

gk=gk max n^4

Question 33

explain gk=gk max n^4

Answer 33

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

Question 34

write out the first order kinectics differential equations for Na+ current- m-gate and h-gate

Answer 34

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

Question 35

write out the conductance equation for Na+ current

Answer 35

gNa= gNa max m3 h

Question 36

write the equation for capacitance current

Answer 36

Icap= Iion + Iinj

Question 37

In addition to the 3 derivative equations previously written, what is the 4th Hodgkin-Huxley equation differential equation

Answer 37

Cm dv/dt= gNamaxm3h (ENa-V) + gkmaxn4 (Ek-V) + gL(EL-V)+ inj

Question 38

What are the 4 variables taken into consideration by Hodgkin-Huxley Formalism?

Answer 38

1- voltage 2- m/h/n gating 3- membrane potential 4- alpha-beta ratio (open/closed gates)