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Computational Neuroscience 1 > Hogkin-Huxley Model 1&2 > Flashcards

Hogkin-Huxley Model 1&2 Flashcards

1
Q

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

A

it decreases exponentially

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2
Q

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

A

∆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%)

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3
Q

What are the 3 components of resistance?

A

Rm, Ra and Rext

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4
Q

what is Ra?

A

how the dendrite resists down its axial length

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5
Q

what’s Rext?

A

the external resistivity of external medium (ECM)

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6
Q

What’s Rm?

A

the relationship between Rext and Ra

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7
Q

What happens if Rm is high?

A

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

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8
Q

define electrotonic conduction

A

the passive spread of voltage along a membrane

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9
Q

what property does lambda represent?

A

conductance

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10
Q

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

A

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

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11
Q

how is membrane potential calculated?

A

Vm= Vin - Vout

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12
Q

what is reversal potential

A

change in direction of net current as Vm swings around Es

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13
Q

what is driving force calculation?

A

Es- Vm

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14
Q

what is membrane current calculation?

A

Is-gs (Es-Vm)

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15
Q

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

A

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

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16
Q

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

A

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

17
Q

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

A

active currents

18
Q

what does the conductance of active currents depend on?

A

Vm

19
Q

write ohm’s law for active current

A

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

20
Q

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

A

membrane voltage (Vm)

21
Q

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

A

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

22
Q

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

A

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

23
Q

Give an overview of gated-Na+ channels

A

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

24
Q

give an overview of K+ gated channels

A

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

25
Q

what did Hodgkin and Huxley posit opens/closes gates?

A

movement of charged particles in membrane

26
Q

what do modern theories of gate opening/closing posit?

A

the gates undergo conformational change when charged particles bind

27
Q

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

A

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

28
Q

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

A

alpha (1-x) = Beta x

29
Q

write the equation for calculating the change in X over time

A

∆X = alpha (1-x) ∆t- Bx ∆t

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

30
Q

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

A

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

31
Q

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

A

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

32
Q

write the conductance for K+ current

A

gk=gk max n^4

33
Q

explain gk=gk max n^4

A

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

34
Q

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

A

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

35
Q

write out the conductance equation for Na+ current

A

gNa= gNa max m3 h

36
Q

write the equation for capacitance current

A

Icap= Iion + Iinj

37
Q

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

A

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

38
Q

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

A

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

Computational Neuroscience 1 (5 decks)

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