Daniel at al., 1998 three state model.

 

The state transition rates of the chemical reactions for the simplified three state cycle, proposed by Daniel at al., 1998, are formulated via forward and reverse strain dependent rates. For convenience the actomyosin states are denoted by both numeric and generic state labels: 1 = M.ADP.Pi, 2=A.M.ADP.Pi, 3=A.M.ADP.

The states of three-state cross-bridge cycle are defined as: state 1, detached crossbridge, M.ADP.Pi; state 2, myosin weakly bound to actin, A.M.ADP.Pi, and state 3, myosin strongly bound to actin after Pi release, A.M.ADP. The set of biochemical states including ADP release, subsequent ATP binding followed by hydrolysis are lumped into the transition from state 3 to state 1. The transition between the states is defined by six state transition rates,      .

These transition rates are consistent with Kramers' theory and completely specify the strain dependence of transition rates between these states.

1. Myosin binding step, M.ADP.Pi    A.M.ADP.Pi, is achieved by thermal fluctuations of the detached myosin molecule, and the strain-dependent binding rate varies with displacement between associated actin site and myosin rest location,    ,

where      is crossbridge stiffness,      is absolute temperature and        is Boltzmann’s constant.

2. The transition rate A·M·ADP·Pi     A·M·ADP includes Pi release (if [Pi]>0) and power stroke. Following the approach of Pate and Cook 1989, the state rate can be reduced to (Daniel at al., 1998):

3. The strain dependent rate of merged step including ADP release, ATP binding to myosin, detachment form actin and hydrolysis (i.e., A.M.ADP     A.M        A.M.ATP       M.ATP       M.ATDP.Pi)  is defined as:

,

,

The reverse rates           and            are calculated from equilibrium thermodynamics,

 

.

Because ATP binding is much faster than the reverse rate        , it is therefore reasonable to take         to be small and constant.