MARKOV INa

	Linking a genetic defect to its cellular phenotype
	Na+ channel mutation that causes both Brugada and Long-QT phenotypes

Linking a genetic phenotype to its cellular phenotype

Clancy, C. E. and Y. Rudy (1999). "Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia." Nature 400(6744): 566-9.

Advances in genetics and molecular biology have provided an extensive body of information on the structure and function of the elementary building blocks of living systems. Genetic defects in membrane ion channels can disrupt the delicate balance of dynamic interactions between the ion channels and the cellular environment, leading to altered cell function. As ion-channel defects are typically studied in isolated expression systems, away from the cellular environment where they function physiologically, a connection between molecular findings and the physiology and pathophysiology of the cell is rarely established. Here we describe a single-channel-based Markovian modelling approach that bridges this gap. We achieve this by determining the cellular arrhythmogenic consequences of a mutation in the cardiac sodium channel that can lead to a clinical arrhythmogenic disorder (the long-QT syndrome) and sudden cardiac death.

Formulation of the wild-type and mutant I Na channels are provided below .

WILD-TYPE CHANNEL	MUTANT CHANNEL
Maximum WT membrane conductance (G Na )= 18.5 WT Rate Constants C3  ==>  C2 a 11 = 3.802/(0.1027*exp(-v/17.0)+0.20*exp(-v/150));  C2  ==>  C1 a 12 = ( 3.802/(0.1027*exp(-v/15.0)+0.23*exp(-v/150)));  C1  ==>  O a 13 = 3.802/(0.1027*exp(-v/12.0)+0.250*exp(-v/150));  C2  ==> C3 b 11 = 0.1917*exp(-v/20.3);  C1  ==>  C2 b 12 = 0.20*exp(-(v-5)/20.3);  O  ==>  C1 b 13 =0.22*exp(-(v-10)/20.3);  O  ==>  IF a 2 = (9.178*exp(v/29.68)); IF  ==>  O b 2 = ((a 13 *a 2 *a 3 )/(b 13 *b 3 )); IF  ==>  C1 a 3 = (3.7933e-10*exp(-v/5.2));  C1  ==>  IF b 3 = ( 0.0084+0.00002*v);  IF  ==>  IS a 4 = a2/100; IS  ==>  IF b 4 = a 3 ;	Maximum D KPQ membrane conductance (G Na )= 15.5 D KPQ Rate Constants xC3  ==>  xC2 a 11 = 1.25*( 3.802/(0.1027*exp(-v/17.0)+0.20*exp(-v/150)));  xC2  ==>  xC1 a 12 = 1.25*( 3.802/(0.1027*exp(-v/15.0)+0.23*exp(-v/150)));  xC1  ==>  xO a 13 = 1.25*(3.802/(0.1027*exp(-v/12.0)+0.250*exp(-v/150))); xC2  ==>  xC3 b 11 = 0.1917*exp(-v/20.3); xC1  ==>  xC2 b 12 = 0.20*exp(-(v-5)/20.3);  xO  ==>  xC1 b 13 = 0.22*exp(-(v-10)/20.3); UO  ==>  IF a 2 = (9.178*exp(v/100)); IF  ==>  UO b 2 = ((a 13 *a 2 *a 3 )/(b 13 *b 3 )); IF  ==>  UC1 a 3 = 20*(3.7933e-10*exp(-v/5.2));  UC1  ==>  IF b 3 = 2*(0.0084+0.00002*v); IF  ==>  IS a 4 = a 2 /100;  IS  ==>  IF b 4 = a 3 ;   mu 1 = 2e-6;  background to burst transition rate   mu 2 = 1e-4;  burst to background transition rate x represents U (upper, background mode) or L (lower, burst mode), as transition rates in the background or burst modes are the same.

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Na⁺ channel mutation that causes both Brugada and Long-QT phenotypes

Clancy, C. E. and Y. Rudy (2002). "Na(+) channel mutation that causes both Brugada and long-QT syndrome phenotypes: a simulation study of mechanism." Circulation 105(10): 1208-13.

Complex physiological interactions determine the functional consequences of gene abnormalities and make mechanistic interpretation of phenotypes extremely difficult. A recent example is a single mutation in the C terminus of the cardiac Na(+) channel, 1795insD. The mutation causes two distinct clinical syndromes, long QT (LQT) and Brugada, leading to life-threatening cardiac arrhythmias. Coexistence of these syndromes is seemingly paradoxical; LQT is associated with enhanced Na(+) channel function, and Brugada with reduced function. Using a computational approach, we demonstrate that the 1795insD mutation exerts variable effects depending on the myocardial substrate.

Formulation of the wild-type and mutant I Na channels are provided below .

WILD-TYPE CHANNEL	MUTANT CHANNEL
WT Channel Rate Constants C3 ==> C2 a11 = 3.802/(0.1027*exp(-v/17.0)+0.20*exp(-v/150)); C2 ==> C1 a12 = 3.802/(0.1027*exp(-v/15.0)+0.23*exp(-v/150)); C1 ==> O a13 = 3.802/(0.1027*exp(-v/12.0)+0.25*exp(-v/150)); IC3 ==> IC2 a11 = 3.802/(0.1027*exp(-v/17.0)+0.20*exp(-v/150)); IC2 ==> IF a12 = 3.802/(0.1027*exp(-v/15.0)+0.23*exp(-v/150)); C2 ==> C3 b11 = 0.1917*exp(-v/20.3); C1 ==> C2 b12 = 0.20*exp(-(v-5)/20.3); O ==> C1 b13 = 0.22*exp(-(v-10)/20.3); IC2 ==> IC3 b11 = 0.1917*exp(-v/20.3); IF ==> IC2 b12 = 0.20*exp(-(v-5)/20.3); O ==> IF a2 = (9.178*exp(v/29.68)); IF ==> O b2 = (a13*a2*a3)/( b13*b3); IF ==> C1 a3 = (3.7933*10 -7 )*exp(-v/7.7); IC2 ==> C2 a3 = (3.7933*10 -7 )*exp(-v/7.7); IC3 ==> C3 a3 = (3.7933*10 -7 )*exp(-v/7.7); C1 ==> IF b3 = (0.0084+0.00002*v); C2 ==> IC2 b3 = (0.0084+0.00002*v); C3 ==> IC3 b3 = (0.0084+0.00002*v); IF ==> IM1 a4 = a2/100; IM1 ==> IF b4 = a3; IM1 ==> IM2 a5 = a2/(9.5*10 4 ); IM2 ==> IM1 b5 = a3/50;	1795insD Mutant Channel Rate Constants xC3  ==>  xC2 a11 = 3.802/(0.1027*exp(-v/17.0)+0.20*exp(-v/150)); xC2  ==>  xC1 a12 = 3.802/(0.1027*exp(-v/15.0)+0.23*exp(-v/150)); xC1  ==>  xO a13 = 3.802/(0.1027*exp(-v/12.0)+0.25*exp(-v/150)); UIC2  ==>  UIF a12 = 3.802/(0.1027*exp(-v/15.0)+0.23*exp(-v/150)); UIF  ==>  UIC2 b12 = 0.20*exp(-(v-5)/20.3); xC2  ==>  xC3 b11 = 0.1917*exp(-v/20.3); xC1  ==>  xC2 b12 = 0.20*exp(-(v-5)/20.3); xO  ==>  xC1 b13 = 0.22*exp(-(v-10)/20.3); UO  ==>  UIF a2 = (9.178*exp(v/29.68)); UIF  ==>  UO b2 = (a13*a2*a3)/( b13*b3); UIF  ==>  UC1 a3 = ((3.7933*10 -7 )*exp(-v/7.7))/2.5; UIC2  ==>  UC2 a3 = ((3.7933*10 -7 )*exp(-v/7.7))/2.5; UIC3  ==>  UC3 a3 = ((3.7933*10 -7 )*exp(-v/7.7))/2.5; UC1  ==>  UIF b3 = (0.0084+0.00002*v); UC2  ==>  UIC2 b3 = (0.0084+0.00002*v); UC3  ==>  UIC3 b3 = (0.0084+0.00002*v); UIF  ==>  UIM a4 = a2/100; UIM  ==>  UIF b4 = a3; UIM  ==>  UIM2 a5 = a2/(3.5*10 4 ); UIM2  ==>  UIM b5 = a3/20; Transition rates between modes are: background to burst   (U => L) = 1*10 -7 ms -1 burst to background   (L => U) = 9.5*10 -4 ms -1 x represents U or L since transition rates within Background or Burst modes are the same.

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

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