Week 3 - I-V curves + Nerst Equation

membrane voltage

measured for the inside of the neuron relative to the outside of the neuron by convention, when the neuron is not firing it maintains a resting membrane potential of -65mV compared with extracellular space

I-V curve

graphical description of how ionic current changes as a function of membrane potential for fixed channel population under fixed ionic conditions, the current of any ion is determined by difference between membrane potential and equilibrium potential of that ion, so for K+ the driving force is realted to the difference between the equilibrium potential and membrane potential

what happens when conductance changes?

I-V curve slope changes too

Nerst equation

considered only 1 ion species at a time

determining resting membrane potential

K+ and Na+ currents have to be equal but opposite, if there is more K+ conductance/more K+ channels open the membrane potential is closer to K+ equilibrium potential but if there is more Na+ conductance/more Na+ channels open, the membrane potential is closer to Na+ equilibrium potential

constant field equation/goldman

this equation reminds us that membrane potential depends on relative conductances or permeabilities of the membrane to ions, and on the equilibrium potential of those ions

resting membrane potential

at rest Na+ and Cl- flow in and K+ flows out, active transport requires energy to maintain ionic gradients so 3 Na+ out and 2 K+ in, the transport system is electrogenic so it moves more + charge out of the cell than in contribution the membrane potential, moving so much + changer out makes the inside more -, this depends on equilibrium potentials, conductance and ATPases, Cl- distribution has little effect,

what happens if we inject positive charge into a cell and make the membrane potential more positive?

we’ll expect to see a change in a current not equilibrium potential so it will try to compensate, net movement of K+ out of the cell will occur to try to get back to equilibrium potential (depolarization effect)

what happens if we inject negative charge into a cell and make Vm more negative?

a net movement of K+ ions into the cell will occur to try to get back to equilibrium (hyperpolarization effect)

berstein’s theory on K+ equilibrium potential

believed that the membrane potential was essentially due to K+ equilibrium, tested this by varying the concentration of K+ in the bath and found predictable changes in the equilibrium potential, and that in turn regulated the membrane potential, he kept the intracellular concentration constant throughout but increased K+ extracellularly and found that it would increase membrane potential outside the cell proving that K+ is the main driver of resting membrane potential, Na+ does not play a role

las botanas A (slopes intersect)

shows that smaller slope means there are fewer open ion channels but still have the same ions cause same reversal potential for both slopes, allows separation of conductance and driving force, ionic solutions constant but change in conductance, shows curves pivoting around same reversal potential

las botanas B

the slope if the same for both IV curves but the curve of A’ shifted to the right so they have different reversal potentials but the conductance is the same so number of open channels is the same but different ionic solutions

las botanas C

shows that when membrane potential is equal to ion concentration equilibrium potential, the chemical gradient exactly balances the electrical gradient so there is no net ion movement, this does not mean zero conductance or that channels are closed we can still have current just no net flow

why action potentials matter?

a 5 mV shift in a single Na+ channel can cause paralysis, epilepsy or sudden death

Action potential

an explosive change in electrical activity, sudden change in the membrane potential, its functionally useless if there is no change in membrane potential, they are transported along the membrane of an excitable cell like the nerve or muscle cell, physical change/soliton nerve, ultra low proton emissions and electrical activity is what makes up an AP

AP stimuli

electrical change, chemical (taste, drugs, smell, neurotransmitters), mechanical (touch, pressure, sound), light (vision, photodetection) or temperature (hot and cold receptors)

current clamp

control the current injected into a neuron and measure the membrane potential, so for example inject positive current into the neuron and watch it fire action potentials

voltage clamp

control the neuron’s membrane potential so make it hold at a certain voltage and measure the currents that flow across its membrane, so like you can step the neuron to a depolarizes potential and measure voltage gated currents

hyperpolarization current clamp

inject in small negative current causes the membrane to move away from resting becoming more negative and moving away from resting potential, more negative inside cell than out, the more negative current put in the larger the hyperpolarization is

depolarization current clamp

if you inject in small positive current this causes the membrane to depolarize for the duration you are injecting the positive charge, this is linear so the more positive current you put in the larger the depolarization

what happens once you inject a large enough positive charge?

this generates an action potential, but after that even if you inject more positive charge you still get the same action potential then then it hyperpolarizes and goes back to resting, response is no longer linear due to influx of Na+

threshold

critical value of membrane potential at which an action potential is generated, this is when Na+ exceeds K+ efflux causing positive feedback to set in and an action potential to be initiated

action potentials general properties

when stimulus reaches past threshold it causes a depolarization due to voltage gated na+ channel, this causes Na+ gate to close and K+ gate to open causing repolarization due to large increase in K+ permeability and loss of + charge on inner surface of the membrane membrane potential then returns to K+ equilibrium potential

ionic basis of AP

the channels are all voltage gated so all IV curves are rectified, depolarization increases membrane conductance to Na+ initially and to K+ after delay, the effect of Na+ conductance is regenerative so positive feedback (more depolarization = more Na+ influx), the negative feedback is k+ channel dependent, depolarization increases number of K+ open channels, efflux of K+, repolarization and return of K+ conductance to resting levels

properties of AP

its triggered by depolarization, it has to excess threshold value to trigger AP (55mv), its all or none, it propagates without decreasing in magnitude so its the same size at all times, its followed by refractory period

which ions are on the move in an AP?

there are two main phases being the early inward current driven by voltage gated Na+ and the late outward current driven by voltage gated K+ for as long as the voltage clamp at threshold is going on

capacitative current

property of the cell membrane to store electrical charge current

AP amplitude

depends on Na+ driving force, so lowering the Na+ reduces Na+ equilibrium potential, it also causes a slower upstroke and lower peak, however there is no change in action potential duration

ion substitution experiments (hodgkin and huxley)

they wanted to figure out which ions were responsible for which phases of current so prove that Na+ was responsible for early inward and K+ for early outward, they replaced Na+ with choline cause its also a large monovalent molecule but its impermeant through voltage gated Na+ channels and found they were only left with the late outward current, then they used TTX which blocks Na+ channels and saw the same thing then TEA which blocks K+ channels and saw they only had the early inward current

TTX

blocks Na+ current so you only get the late outward K+ current

TEA

blocks K+ current so you only get early inward Na+ current

dependence of early/late currents on potential

the early current is Na+ and the late one is K+, Na+ current reverses at +52mV (reversal potential) and at 65mV it flips to outward, the late K+ current increases with increased depolarization, initial step to -85mV produces a small inward current but no voltage gated channels are opened

inactivation

this causes a decline in Na+ current, known as the absolute refractory period, the range is measured by parameter h which varies between 0 being complete inactivation and 1 being no inactivation at all

depolarizing vs hyperpolarizing

the fractional change in Na+ current as a function of membrane potential during prepulse stimulation, when we hyperpolarize, early inward current is larger due to more Na_ channels opening, when we depolarize early inward current is smaller due to less Na+ channels opening

absolute refractory period

the time following an AP where a stimulus can’t elicit a second AP due to inactivation of Na+ channels, the falling phase of the AP, channels are closing so can’t open again, this is due to Na+ channel inactivation so you cant generate action potentials during this period

relative refractory period

the time following an absolute refractory period when the threshold for initiation of a second action potential is increases, Na+ channels recover from inactivation and K+ channels close, this is due to K+ channel activity, possible to generate action potentials but requires more stimulation for the previous AP

voltage gated channel structure

there are 4 transmembrane domains, there are 6 subunits in each domain and the S4 is common across all of the domains, it as an amino and carboxyl terminal end

S4 helix

it has + charge residues (lysine or arginine) at every 3rd position in the transmembrane domain, it is highly conserved, depolarization displaces the + charges outward causing the helix to move out increasing probability of a channel opening, it acts as a sensor, at rest the internal negativity keeps it at the cytoplasmic end, depolarization allows it to move outward leading to conformational change allowing gate to open

TTX, STX, u-CTX

blocks Na+ voltage gated channels, sensitive for S5 - S6

overall structure

S1-S4 makes up the alpha subunit, then there is a selectivity filter and S5-S6

selectivity filter

P loops between S5 and S6, its what allows Na+ to flow in, the alpha subunit is the main one but sometimes accessory units like beta aid in localization + cell targeting but don’t for voltage, the DEKA motif refers to the amino acid found in the selectivity filter of each domain

activation gate

opens rapidly with depolarization, controls rising phase of AP, its voltage dependent, formed by intracellular ends of the S6 segments in each of the 4 domains and its opening is controlled by S4 voltage sensor segments, S4 movement is mechanically coupled to the S5-S6 linker and S6 helices acting as the door/actual activation gate

inactivation gate

found between the DII-DIV cytoplasmic loop, IFM (isoleucine, phenylalanine, methionine) AA sequence forms core of the fast inactivation gate of Na+ channels, it has a ball and cain mechanisms so after channel opens IFM motif swings in and blocks open pore from the inside, produces fast inactivation, inactivation ball blocks open channel

recovery from inactivation

requires repolarization back to resting membrane potential, sets max firing rate of APs, ensures unidirectional propagation down length of the axon

binding of local anesthetics

binding to S6 region blocks Na+ binding so no more Na+

ball and chain model of inactivation

an intracellular blocking particle is tethered to the cytoplasmic end of the channel by flexible link, during inactivation ball blocks channel, lipid soluble toxins can eliminate activation when applied to neurons so holds S6 region open

Dravet syndrome

severe developmental epileptic encephalopathy, onset in 1st year, prolonged febrile seizures, progressive epilepsy and developmental delay due to SCN1A loss of function mutation causes lack of voltage gated Na+ channels, too much glutamate causing seizures/epilepsy, dont get enough inhibition due to impaired Nav1.1 in interneurons

onset and early clinical presentation (dravet syndrome)

5-8 months of age, prev normal development, initial seizures are febrile, prolonged hemiclonic or generalized tonic-clonic seizures often triggered by fever, infection or vaccination, early flag is status epilepticus in infancy with normal early EEG/MRI

prevalence, prognosis and cure (dravet syndrome)

1 in 15 to 40k live birhts, 70-85% have de novo SCN1A mutations, prognosis is lifelong epilepsy, developmental delay and gait abnormalities (issues walking, sitting and talking), high risk of sudden unexpected death in epilepsy

diagnosis (dravet syndrome)

clinical suspicion in infant with febrile seizures, EEG often normal early, abnormal later, MRI usually normal early, definitive diagnosis SCN1A genetic testing so see if they have the mutation

treatment principles (dravet syndrome)

avoid Na+ channel blockers and goal is to reduce seizures and prevent status epilepticus

Nav channelopathies

voltage gated Na+ channels control threshold, spike timing and refractory period, small kinetic changes produce large physiological effect, gain of function consists of persistent Na+ current and hyperexcitability while loss of function consists of reduced spike initiation and conduction failure

SCN1A network disinhibition (dravet syndrome)

the channel is expressed in GABAergic interneurons like the cortex and HPC, typical mutations include truncations, frameshifts and nonsense, missense in S4, S5-S6 (IFM motif) and DIII to DIV (inactivation gate), core effect is loss of function in inhibitory interneurons so reduced GABA firing therefore increased network hyperexcitability, key idea is failure of inhibition not overactive excitation

structural hotspots of pathogenic mutations

S4 segments (shifted voltage sensitivity, S5-S6 pore (reduced conductance, DIII-DIV linker (IFM, failure of fast inactivation), S6 hinges (failure of gate closure)