Previous Section Table of Contents Next Section

Toy Model 2

Wire Diagram

Equations

\(\dot{X_1} = \alpha_1 \left[\frac{1 + \left(X_2/K_2\right)^{2} + \rho_1^{-1}\left(X_4/K_{4A}\right)^{2}}{1 + \left(X_2/K_2\right)^{2} + \left(X_4/K_{4A}\right)^{2}}\right] - \beta_1 X_1\) \(\dot{X_{A1}} = \alpha_{A1}X_1 - \beta_{A1} X_A - \beta_{A} X_{A1} X_{A2}\) \(\dot{X_{A2}} = \beta_{A1} X_A - \beta_{A2} X_{A2} - \beta_{A} X_{A1} X_{A2}\) \(\dot{X_2} = \beta_{A} X_{A1} X_{A2} - \beta_2 X_2\) \(\dot{X_3} = \alpha_3 \left[\frac{\rho_3^{-1} + \left(X_2/K_{2R}\right)^{2} + \rho_3^{-1}\left(X_4/K_4\right)^{2}}{1 + \left(X_2/K_{2R}\right)^{2} + \left(X_4/K_4\right)^{2}}\right] - \beta_1 X_1\) \(\dot{X_4} = \alpha_4X_3 - \beta_4 X_4\)

Architectural Constraints

\(\begin{equation}\\ \rho_1 > 1\\ \rho_3 > 1\\ \end{equation}\)

Resolve Co-Dominance

resolve_codominance=True

from dspace.display.UI.interactive_input import InteractiveInput

model_equations = ['X1. = a1*X5^-1 + a1*X2^2*K2^-2*X5^-1 + a1*rho1^-1*X4^2*K4A^-2*X5^-1 - b1*X1',
                   'XA1. = b1*X1 - bA1*XA1 - bA*XA1*XA2',
                   'XA2. = bA1*XA1 - bA2*XA2 - bA*XA1*XA2',
                   'X2. = bA*XA1*XA2 - b2*X2',
                   'X3. = a3*rho3^-1*X6^-1 + a3*X2^2*K2R^-2*X6^-1 + rho3^-1*a3*X4^2*K4^-2*X6^-1 - b3*X3',
                   'X4. = a4*X3 - b4*X4',
                   'X5 = 1 + X2^2*K2^-2 + X4^2*K4A^-2',
                   'X6 = 1 + X2^2*K2R^-2 + X4^2*K4^-2'
                   ]

architectural_constraints = ['rho1 > 1',
                             'rho3 > 1']

latex_symbols = {'X1':'X_1',
                 'X2':'X_2',
                 'X3':'X_3',
                 'X4':'X_4',
                 'XA1':'X_{A1}',
                 'XA2':'X_{A2}',
                 'X5':'X_5',
                 'X6':'X_6',
                 'a1':r'\alpha_{1}',
                 'a2':r'\alpha_{2}',
                 'a3':r'\alpha_{3}',
                 'a4':r'\alpha_{4}',
                 'aA1':r'\alpha_{A1}',
                 'b1':r'\beta_{1}',
                 'b2':r'\beta_{2}',
                 'b3':r'\beta_{3}',
                 'b4':r'\beta_{4}',
                 'bA':r'\beta_{A}',
                 'bA1':r'\beta_{A1}',
                 'bA2':r'\beta_{A2}',
                 'K2':'K_2',
                 'K2R':'K_{2R}',
                 'K4':'K_4',
                 'K4A':'K_{4A}',
                 'rho1':r'\rho_1',
                 'rho3':r'\rho_3',
                 }

toy_model_2=InteractiveInput(name="Toy Model 2",
                             equations=model_equations,
                             constraints=architectural_constraints,
                             symbols=latex_symbols,
                             resolve_codominance=True)

Previous Section Table of Contents Next Section

Jason G. Lomnitz
Savageau Lab
Department of Biomedical Engineering
University of California
Davis, CA 95616
jlomn@ucdavis.edu