Receptor theory and singlechannels

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Receptor theory and single-channels
MSc (Neuroinformatics//Neuroscience) D J A
Wyllie Centre for Integrative Physiology Email
dwyllie1_at_staffmail.ed.ac.uk
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del Castillo - Katz (1957)
Del Castillo Katz attempted to quantify the
action of partial agonist at the NMJ They
postulated a specific mechanism
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Definitions
Definitions used in the model R - resting state
of the receptor AR - occupied but shut state
AR - open state KA, the equilibrium
constant and is defined as k-1/k1 EA, the
equilibrium constant for the isomerization
reaction defined as b/a, where b is the opening
rate constant, and a is the closing rate constant.
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Equilibrium Occupancy of AR
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More equations!
It is important to realise that the EC50 is
dependent both on K and E
This looks like the Hill-Langmuir equation but
remember Keff is an equilibrium constant that
depends on both AFFINITY and EFFICACY
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The extended del Castillo-Katz mechanism for the
nicotinic receptor
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Mean Lifetimes
The mean lifetime of a state is equal to the
reciprocal of the sum of all the rate constants
that describe routes for leaving that state
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Types of Activity
k-2 gtgt b
k-2 ? b
k-2 ltlt gating
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Bursts of openings are seen with ACh nicotinic
receptors
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Equating observed parameters with rate constants
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Different agonists give different durations of
bursts
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Single-channel kinetics
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Markov Processes
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Gaussians and Exponentials
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The 2 state model
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Another definition of a pdf probability density
function
f(t) aexp(-at)
Distribution of open times
f(t) bexp(-bt)
Distribution of closed times
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Example of an open time pdf
t 3.2 ms
f(t)aexp(-at) therefore f(t)
312.5exp(-312.5t)
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del CastilloKatz model (1957)
Definitions used in the model R - resting
state of the receptor mean lifetime 1/(A ?
k1) AR - occupied but shut state mean lifetime
1/(k-1 b) AR - open state mean lifetime
1/a KA, the equilibrium constant and is defined
as k-1/k1 EA, the equilibrium constant for the
isomerization reaction defined as b/a, (b is the
opening rate constant and a is the closing rate
constant. What sort of single-channel activity
does this model predict?
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Single-channel openings are not fixed in duration
and occur randomly and in bursts
For the simulation the follow parameters were
used k-1 500 s-1, k1 107 M-1s-1 a 100
s-1, b 500 s-1 and A 1 mM
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Distributions of open and shut times
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Burst properties generated from the simulation
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Single-channel amplitudes are normally distributed
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but distributions of dwell times are generally
quite complicated