Electrophysiological cell biology and modeling of the heart Ulrike Henrion Ulrika Englund Nina...
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Transcript of Electrophysiological cell biology and modeling of the heart Ulrike Henrion Ulrika Englund Nina...
Electrophysiological cell biology and modeling of the heart
Ulrike Henrion
Ulrika Englund
Nina Ottosson
Jakob Renhorn
Fredrik Elinder
Johan Brask
Sara Börjesson
Ion channels generate electrical impulses
Calculations of ion channel kinetics and action potentials
4n 3n 3n 1n
C1 C2 C3 C4 O5
1n 2n 3n 4n
K channel
4am 3am 2 am 1am C1 « C2 « C3 « C4 « O5 1bm 2bm 3bm 4bm
4am 3am 2 am 1am I 1 « I 2 « I 3 « I 4 « I 5
1bm 2bm 3bm 4bm
βhαh βhαh βhαh βhαh βhαh
Na channel
Leak channel OEquivalent circuit
The physical interpretation of transitions(Eyring rate theory or transition-state theory)
kCO C O kOC kCO = keq exp(zF(V-Veq)/(RT)) kOC = keq exp(-z(1-)F(V-Veq)/(RT)) RT/F 25 mV keq, rate constant when kCO = kOC z, valency of the transition (=the number of charges traversing the entire membrane voltage) , symmetry factor (the fraction of the total drop of voltage across the membrane that the gate traverses before reaching the activation energy peak) V, the absolute membrane voltage Veq, the membrane voltage when kCO = kOC F, Faraday's constant; R, gas constant; T, absolute temperature
dO/dt = kCO * C – kOC * O O = O + dO/dt
kCOkOC
Action potential algorithmSeminar 21 January 2011, FE
0) Decide Vstart Normally -70 mV
1) Calculate rate constants αm = 360 ( 48 + V ) / (1 - exp((-48 - V) / 3)) βm = 400 (-57 - V ) / (1 - exp(( 57 + V) / 20))
2) Calculate initial conditions
m∞ = m / (m + m)
3) Calculate new gating parameter, use a short time step dt m = m + (αm(1-m) - βmm)dt
4) Calculate conductances
GNa = m2h GNa,max where GNa,max = 2.5 μS
5) Calculate ion currents INa = GNa (V-VNa) where VNa = 50 mV
6) Calculate change in membrane potential
IC = IS - (INa + IK + Ileak) dV/dt = IC / CM where CM = 2 pF
7) Calculate new membrane potential
V = V + dV/dt
8) GOTO Calculate rate constants
Calculation of action potentials in 1952
General goals
• Describe ion channel kinetics with physically sound and molecularly meaningful equations
• Use the ion channel kinetics to calculate electrical behaviour of different types of cells
• Explore non-linearity from modification of ion channel molecules to changes in excitability of cells, tissues, networks and organs (brain and heart)
Four voltage sensors acting in parallel make a sigmoidal opening
4n 3n 3n 1n
C1 C2 C3 C4 O5
1n 2n 3n 4n
A multi-state model for Na channel gating
Keynes & Elinder, 1998, 1999
Electrical activity in the heart is generated by voltage-gated ion channels
HCN Na CaL
Kto Ks Kr
0.0 0.5 1.0 1.5
-80
-60
-40
-20
0
20
40
60
Time (s)
Vo
ltag
e (m
V)
outside
inside
A two-state HCN channel model can generate unstable rhythmicity
C Oα
β
α = k exp(-(V+45)/25)β = k exp(+(V+45)/25)
0 1 2 3 4 5
-80
-60
-40
-20
0
20
Time (s)
Vo
ltag
e (m
V)
k = 5/s k = 500/s
A Four-state model for HCN gating
Männikkö et al., 2002, NatureMännikkö et al., 2005, J Gen PhysiolElinder et al., 2006, J PhysiolBruning-Wright et al., 2007, J Gen Physiol
CI OI
CII OII
CI
OII
OI
CII
The four-state model prevents cardiac arrhythmia
CI
OII
OI
CII
C O
0 1 2 3 4 5
-80
-60
-40
-20
0
20
Time (s)
Vo
ltag
e (m
V)
0 1 2 3 4 5
-80
-60
-40
-20
0
20
Time (s)
Vo
ltag
e (m
V)
k = 5/s k = 500/s
The lipoelectric mechanism in the treatment of epilepsy
Börjesson et al., 2008 & 2010, Biophys J
++++ +
+++
Arachidonic acid
++++ +
+++
Arachidonic acid-me
++++ +
+++
Arachidonyl amine
+
Modification of the voltage sensor movement affects excitability
0 10 20 30
-100
-50
0
50
Time (ms)
Vo
lta
ge
(mV
)
0 10 20 30
-100
-50
0
50
Time (ms)
V = 5 mV
Börjesson et al., 2010, BJ
-4 -2 0 2 4
1
2
3 Equivalentnumber ofK channels(relative)
VK (mV)
Excitability of hippocampus CA1 neuron
Tigerholm et al., in preparation