Modelling ion channels

Question 1

describe what kinetic models aim to explore

Answer 1

how ion channel opens and closes
what states the channel occupies
binding and gating steps
translate structure into function
(dont model structure)

Question 2

describe the flaws with the simplest possible kinetic model

Answer 2

single closed state and open state model
A+R (rev kf and kr) AR
agonist binding causes a direct transition
- we know this is flawed as there are conformational state transitions (too instentatneous)
the concepts of desensitization and partial agonists suggest that all binding cant directly cause a response. (must be a state in between)

Question 3

describe the Del castillo katz model

Answer 3

is the simplest realistic model
binding and gating are seperate steps
A + R (rev kf and kr) AR (rev gf and gr) AR active
there are two equllibrium conditions Ka (first rxn) and E (denoting efficacy, second rxn)
-two occupied states two closed states one open state.

Question 4

describe the limits of population data

Answer 4

binding affinity/ apparent affinity (kd) measured in experiments actually measures occupancy of receptors in multiple states. (in ligand binding experiments when flushed through filter and bound receptor agonists are measured, both active AR and AR are being measured so KD is not equal to KA but
equal to KA/1+E )

this is not equal to intrinsic affinity Ka (the equilibrium constant in dck first reaction which actually measures affinity.) this is because efficacy will also have an effect on Kd.

modelling is therefore needed as intrinsic affinity and efficacy cannot be measured.

Question 5

describe how KA and E can be obtained from kinetic modelling

Answer 5

rate for each state is measured.
(routes producing that state-routes out)

for castillo katz these rates are (3 confirmations):

dpR/dt= (Kr x pAR) - (Kf x A x pR)

dpAR/dt = (Kf x A x pR) + (Gr x pARactive) - (Kr x pAR) - (Gf x pAR)

dpARactive/dt= (gf x pAR) - (gr x pARactive)

pAR= proportion of total receptor at AR state (PAR= AR/R total)
pR=R/R total
proportion is used instead of concentration

lamda: exponential rate constant
W: fraction of total receptor population that occupies states (different for each state and changes over time)

lamda2-lamda1 (k1+k-1+a+b) + (a x k1 x A + b x k-1 x a + a x k-1)= 0 solves for lamda values
(second bracket is factors for production of each state)

therefore: proportion of receptors at set time=
Pr (infinity) + W1 x e^-lamda1 x t + W2 x e^lamda 2 x t

Question 6

what are some benefits of kinetic modelling

Answer 6

links experimental results to an approximation of reality (can only quantify thermodynamically stable states where drugs are bound for long time)

aids understanding of MOA

allows testing for specific claims ex: mutation caused a shift in Kd
and allows for impossible experiments ex: what would happen if efficacy decreased 10-fold

allows prediction of pharmacological effects before spending time and money at lab