Toward energy-aware model

Here you will modify your model according to the discussion in Energy aware transition control to make an energy aware model.

Copying your model

Go to the Cell Models page in your dashboard and click on the Copy button on the row of the previous 3 state model to construct a new model by modifying it.

Then a copy of the model appears on the top row. Click the Edit button.

Modifying your custom parameter

Then Cell modeling page appears. Click Edit Parameters from the menu bar, and click on the Your Custom Parameter tab. Comment out or delete the setup sentences of the parameters “hf” and “hb” and set the new parameter as “h0 = 200”. Add the definitions of the chemical energies "U_PreR" and "U_PostR" for the states XB_PreR and XB_PostR, respectively. Here “E_ATP” is the ATP molecule hydrolysis energy that is given in the Common parameters form of Edit Parameters. Then click on the Close button.

Defining the forward head rotation transition rate

Click on the arrow from XB_PreR to XB_PostR, and then click on the Define a rate button. Comment out or delete the sentence of the previous setup of the transition rate “r = hf”, and add the following two sentences.

W_arm = spring_energy(arm_stretch() + X_STROKE) 
r = h0 * exp( - ( U_PostR + W_arm  -  U_PreR) / KB_T )

Here the function “arm_stretch()” returns the myosin arm stretch at the current state XB_PreR. By adding the stroke distance "X_STROKE", the arm stretch after the transition to the state XB_PostR is obtained. The function “spring_energy” returns the strain energy of the myosin arm for a given argument. Thus “W_arm” is the strain energy after the transition. The parameter “KB_T” is the heat energy given by XB Modeler. This value is equal to the product of Boltzmann constant (K_B) and Absolute temperature(T) indicated in the Common parameters form of the Edit Parameters menu. After finishing the text input, click on the Close button on the transition dialog. See Energy aware transition control to understand the reason for this setting.

Defining the backward head rotation transition rate

Click on the arrow from XB_PostR to XB_PreR, and then click on the Define a rate button.

Comment out or delete the sentence of the previous setup of the transition rate “r = hb”, and add the following two sentences.

W_arm = spring_energy(arm_stretch() + X_STROKE) 
r = h0 * exp( - W_arm / KB_T )

Here the function “arm_stretch()” returns the myosin arm stretch at the current state XB_PostR. By adding the stroke distance "X_STROKE", the arm stretch after the transition to the state XB_PreR is obtained. The function “spring_energy” returns the strain energy of the myosin arm for a given argument. Thus “W_arm” is the strain energy after the transition. After finishing the text input, click on the Close button og the transition dialog.

Plotting the results

You have finished the definition of your new model. Save the new model, run the Force Velocity Relationship test and plot the results as described in Save your model and Run a simulation. With the energy aware model, the ATP consumption rate varies with the shortening velocity. The maximum efficiency decreases to 40%.

Results of Force Velocity Relationship test with the energy aware model

Towards Force Control Regulation

You have constructed the basic mechanism of force generation. However, you have not yet implemented force control regulation in the model. In muscles, the contractile force is controlled by change of calcium ion concentration. Now you will include force regulatory unit as described in Defining T/T Unit states and modifying the Myosin Head model.