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108 lines
3.6 KiB
Typst
108 lines
3.6 KiB
Typst
#import "../preamble.typ": *
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#show: conf.with(num: 1)
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= Membrane Potential
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Outside the cells in the brain there is salt.
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Inside there is potassium.
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== Prerequisites for a Neuron to fire
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_Watch the embedded movie._
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There are different potentials build up in the membrane.
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+ The charge is in equillibrium. But there is a gradient of Pr and Cl
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+ Cloride will diffuse $==>$ on that side there are too many negative charges
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+ The negative charge pushes the potassium to this side
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+ Finally a potassium gradient stabilizes
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Why is the resulting potential negative?
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== Nernst and general Nernst eqation
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$
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V_(x) = (R T) / (z F) ln ([X]_(o) ) / ([X]_(i) ) \
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V_(x) = (R T) / (z F) ln (P_("K") [K]_(o) + P_("Cl") ["Cl"]_(o) + ... ) / (P_("K") [K]_(i) + P_("Cl") ["Cl"]_(i) + ... ) \
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$
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When the permeability for the potassium is low then the other ones play a bigger role.
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Potential is only there when permeability is existing.
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Q: What is similar to a low pass filter.
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In reality there are multiple conducters connected in parralel. Also the conductivity of the Na and K channles are changable.
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Q: What does a conductivity of $oo$ mean?
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= Hodgkin and Huxley
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Q: What have they done?
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A: They used squids to measure the axons, because they are $1"mm"$ thick
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Types of Neuronal Recording Methods
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- EEG (on top of the head)
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- ECoG (small hole in the head)
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- Extracellular (needles in the brain)
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- Intra cellular (needles in the cell of the brain)
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== Action Potential
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+ The cell gets excited
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+ Chainreaction of channel opening and gradient stabilisation
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- Sodium channels open
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- K chanels open
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- Na channels become refactory
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- ...
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+ Refactory period
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+ ...
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#highlight[TODO: continue the steps]
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Currents can add up to trigger an AP. THe refactory period is the time after an AP when Na channles are inactive. The firing rate is increaed with a highter input strenght.
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The lenght of the potiential depends on the type of cell. Then the refactory period is also longer. \
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The maximum firing rate is limited by the absolute refactory period.
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== The actual model
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$
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I_("inj") = I_(C) + sum I_(k) (t) , space C = Q/u , space I_(C) = C (dif u) / (dif t) = C (dif V) / (dif t) \
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I_(x) = I_(x) \
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C (dif V_m ) / (dif t) = - sum I_(k) + I_("inj") (t) \
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sum I_k = g_("Na") (V_m - V_("Na") )+ g_(K) (V_m - V_(K) )+ g_(L) (V_(m) - V_(L) )\
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C (dif V_m ) / (dif t) = - g_("Na") (V_m - V_("Na") )- g_(K) (V_m - V_(K) )- g_(L) (V_(m) - V_(L) ) + I_("inj") (t) \
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$
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Now the Equation becomes time dependent
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$
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C (dif V_m ) / (dif t) = - macron(g)_("Na") m^(3) h (V_m - V_("Na") )- macron(g)_(K) n (V_m - V_(K) )- macron(g)_(L) (V_(m) - V_(L) ) + I_("inj") (t). \
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dot(x)= - (1) / (tau_(x) u_(b)) A .
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$
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Capacitance is a biological constant.
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== Voltabe clamp method
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With this method it is possible to stimulate a cell and measure the floating current at the same time.
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There are substances to kill certain types of channels in the cell. If done so the graph of the potential changes.
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Also there is a method to measuer individual channels and their current they leave through.The AP is a positive feedback loop.
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The sodium channels cannot immeadiately open again. It takes about 1ms for them to open again. When measuring one always measurers multiple fibres (Suberposition).
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In the heart there are calcium channels.
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_Max firing frequency is about $1"kHz"$_
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== Propagation of AP
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There are multiple Methods of propagation the AP. One is to recreate the AP along the way (this takes time but is faster with higher diameter of the axon).
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The other method is the saltatory "jumpy" conduction. This is much faster and the AP jumps between the isolations.
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