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Single ion channels
 Neher & Sakmann 1970s, Nobel 1991
 Patch clamp
 Seal pipette against membrane to measure currents (~2pA)
 Distinctive properties
 Discrete levels of conduction
 rapid transitions
 seemingly random
 Nothing like the macroscopic behavior from HodgkinHuxley model
 Model
 Integral membrane protein
 Selectivity filter to sort out ions
 Aqueous pore
 gate that opens/closes to let ion through
 How selective?
 Li can seemingly substitute for Na
 Can quantify selectivity
 Set
 Then replace extracellular Na with same amount of Li
 If channels substitute Li perfectly for Na, no current will flow
 Find the amount of extracellular Li that makes the current zero

 Measuring relative permeability of channel to various ions
 Many different ions can flow through the sodium and potassium channels, some better than sodium and potassium!
 Linear approximation for permeation
 I = γ(V_{m} − V_{n})
 I is the open channel current, γ the open channel conductance, V_{n} is the reversal potential.
 If screening of ion is perfect, then V_{n} is the Nernst potential
 Otherwise V_{n} is weighted sum of ions that can permeate
 Model for gate
 : random variable of state of gate (open/closed), either 0 or 1
 average of
 : random variable of conductance 0 or γ
 Based on ,
 : random variable of single channel current, 0 or I
 Assume cells have N channels that are identical but statistically independent
 If N is large, total conductance is about the mean = Ng
 (specific conductance)
 Same with current:
 Model for state of channel
 First order reversible reaction for probability gate is open
