Defining transitions with the cooperative behaviors of the myosin heads
The transition in the T/T unit to the state Ca_on facilitates the binding between the myosin head and T/T unit. This is modeled by changing the transition rates between the no binding and the binding states according to the state of the T/T unit above the myosin head. Based on the idea give in [Rice et al., 2003], cooperativity is introduced by factor γn in the transition from N_XB to P_XB and factor γ-n in transitions from the binding states to N_XB. Here, n is an integer with the value 0, 1, or 2 depending on the states of neighboring myosin heads. We define n as the number of the neighboring myosin heads which binds or weakly binds with the actin filament. The dependence of the transitions to the neighboring myosin head states can be implemented by calling the function ng. The dependence of the transitions to the T/T unit states above can be implemented by calling the functions knp and kpn defined in Defining new parameters and functions of the Force Regulatory model.
[Rice et al., 2003] J. J. Rice, G. Stolovitzky and T. Tu and P. P. de Tombe. Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions. Biophys. J. 84, 897-909 (2003)
Constructing the transition paths
Go to the Myosin Head edit page by clicking on Myosin Head tab if you are not in the Myosin Head edit page. Add the transition paths from N_XB to P_XB, from P_XB to N_XB, from XB_PreR to N_XB and from XB_PostR to N_XB. For example, the path from N_XB to P_XB can be made by clicking on the green square button in the state box N_XB and dragging the orange arrow to the state box P_XB and releasing the mouse button.
Defining the transition rate from N_XB to P_XB
Click on the arrow from N_XB to P_XB. Click on the Define a rate button. Define the rate "r" in the Transition dialog.
Input the following codes in the Transition dialog. Here "get(MH, ng, -1)" and "get(MH, ng, 1)" return the values of ng on the right and left neighboring myosin heads, respectively. Zero is returned if there is no neighboring myosin head at the left or right. "get(TT, knp)" returns the value of knp on the T/T unit above the myosin head. "GAMMA" is the parameter given in the Your Custom Parameter form.
r = get(TT, knp) * GAMMA**(get(MH, ng, -1) + get(MH, ng, 1))
Click on the Close button.
Defining the transition rate from P_XB to N_XB
Click on the arrow from P_XB to N_XB. Click on the Define a rate button. Define the rate "r" in the Transition dialog.
Input the following codes in the Transition dialog. Here "get(MH, ng, -1)" and "get(MH, ng, 1)" return the values of ng on the right and left neighboring Myoin Heads, respectively. Zero is returned if there is no neighboring myosin head at the left or right. "get(TT, kpn)" returns the value of kpn on the T/T unit above the myosin head. "GAMMA" is the parameter given in the Your Custom Parameter form.
r = get(TT, kpn) * GAMMA**(-(get(MH, ng, -1) + get(MH, ng, 1)))
Click on the Close button.
Defining the transition rate from XB_PreR to N_XB
Click on the arrow from XB_PreR to N_XB. Click on the Define a rate button. Define the rate "r" in the Transition dialog.
Input the following codes in the Transition dialog.
r = get(TT, kpn) * GAMMA**(-(get(MH, ng, -1) + get(MH, ng, 1)))
Click on the Close button.
Defining the transition rate from XB_PostR to N_XB
Finally, you will define the transition from XB_PostR to N_XB that is accompanied with the myosin head dissociation from the actin filament and the ADP molecule release and the ATP molecule binding. Click on the arrow from XB_PostR to N_XB. Click on the Define a rate button. Click on the ADP release check box and the ATP binding check box to tell XB Modeler that this transition is accompanied with the ADP molecule release and ATP molecule binding. Define the rate "r" in the Transition dialog.
Input the following codes in the Transition dialog.
r = XB_STRONG * get(TT, kpn) * GAMMA**(-(get(MH, ng, -1) + get(MH, ng, 1)))
Click on the Close button.
Saving your model
After defining everything of your model, you will save the model. Click Save in the menu bar.
Enter a model name and note (optional) in the text boxes of the Save dialog, and click on the Save button.
