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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.

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

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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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