4/5/2001 1

Modeling of sub-cellular processes

• Muscle contraction is caused by release of calcium from intracellular compartments

• We study different triggers for this release

• The model includes diffusion of calcium and sodium ions and transport of these ions through cell membranes

• Co-work with Institute for Experimental Medical Research at Ullevål University Hospital

4/5/2001 2

Co-operation of membrane channels

4/5/2001 3

Matematical Formulation, sodium

A diffusion equation governs intracellular sodium (s). Membrane currents are incorporated as boundary conditions.

c

s

s

x

x

x

x

wcsI

wsI

wsI

n

sk

xskt

s

Γ,0

),,,(

),,(

),,(

,

NCX

NaK

Na

NCX

NaK

Na

2

4/5/2001 4

Matematical Formulation, calcium

The diffusion of calcium (c) is more complicated due to different types of intracellular buffers.

s

NCX

rel

Ca

NCX

rel

Ca

TRPN2

CMDN

,0

),,,(

),,(

),,(

),,())(1(

x

x

x

x

wcsI

wcI

wcI

n

ck

xwcIckt

ccI

c

c

4/5/2001 5

Calcium induced Calcium release