Markovian Model of IKr

In certain applications, we need to express the ionic current in terms of a Markovian state-specific model of the ion channel kinetics.  Important examples include simulations of genetic mutations in the ion channel proteins.  Such simulations require explicit representation of ion channel states (closed, open, inactivated) which are not represented in the Hodkin-Huxley fomalisim of the original LRd model.
 
 

Reference:  Cellular consequences of HERG mutations in the
Long QT Syndrome: Precursors to sudden cardiac death.
by Colleen E. Clancy and Yoram Rudy   Cardivas Res 2001;50:301-313


Formulation of the wild-type and mutant IKr channels are provided below.
 
IKr formulation
IKr  = GKr * P(O) * (Vm-EK)
P(O) = open probability of IKr
GKr = 0.0135 * ([K+]o)0.59
EK = (R*T/F) * ln([K+]o/[K+]i)

Wild-type rate constants
C1 ==> O or C1 ==> I 
aa =  65.5*e-3  * exp (0.05547153*(v-36))
C2 ==> C1 
ain=  2.172
C3 ==> C2 
a =  55.5 *e-3 * exp (0.05547153*(v-12))
C2 ==> C3
b =   2.357*e-3 * exp (-0.036588*(v)) 
C1 ==> C2
bin =  1.077
O ==> C1
bb =  2.9357*e-3 * exp (-0.02158*(v)) 
I ==> O
ai =  0.439 * exp (-0.02352*(v+25)) * 4.5/[K+]o
O ==> I 
bi =  0.656 * exp (0.000942*(v)) * (4.5/ [K+]o)0.3
I ==> C1 
mu =  (ai * bb * aa)/(aa *bi)


T474I rates
C1 ==> O 
aa =  65.5*e-3 * exp (0.05547153*(v+25)) 
C3 ==> C2 
a =  55.5*e-3 * exp (0.05547153*(v+6))

R56Q rates
C2 ==> C3 
b =  2.357*e-3 * exp (-0.036588*(v)) * 10.5 
O ==> C1
bb =  2.9357*e-3 * exp (-0.02158*(v))* 6.3

N629D rates
O ==> I 
bi = 0.0
N629D loss of selectivity
Na:K permeability (PNa/PK) = 0.65
EK = (R*T/F) * ln([K+]o + PNa/PK * [Na+]o / [K+]i  + PNa/PK * [Na+]i )

Syntax note:     e-n is 10-n     exp (n) is en
 
 

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