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