Modeling of sarcomere and muscle

Modeling of myosin arm

Property of myosin arm spring

In XB Modeler, we assume that myosin arm behaves like a linear spring for positive stretches while a nonlinear behavior is introduced for negative stretches based on the slacks of myosin arm [Kaya et al., 2010] as depicted in the stretch (x)-force (Farm) curve (black) below. The strain energy W_arm is given by integrating the force Farm from x=0. In XB Modeler, the sum of all forces generated by the myosin arms gives the contractile force of muscle. You can adjust the spring constant kxb of the myosin arm by clicking Edit Parameter in the menu bar of your model editor page and then clicking the Spring tab.

myosin arm strain energy

[Kaya et al., 2010] M. Kaya and H. Higuchi. Non-linear elasticity and an 8 nm working stroke of single myosin molecules in myofilaments. Science 329, 686-689 (2010)

Determination of initial arm stretch

XB Modeler determines the initial arm stretch xinit at the transition form a no binding state to a bind state from the Boltzmann distribution given by the strain energy Warm. XB Modeler holds the inverse function of Rand(x) and applys it to a given random number between 0 and 1 to determine xinit, when a transition from a no binding state to a binding state takes place.

Initail arm strech from the Boltzmann factor