Developmental Kinetics

This applet shows the active concentrations of various compounds during the first 8 hours of development. You can choose which variables to plot on the graph by checking the box next to their name in the plot column. (Note: the the activity level is plotted on the graph, not the absolute concentration.) The rate-constant coefficients k1 through k14 can be altered by typing in the appropriate box. You can choose whether to keep the enzyme level constant during the experiment, or have it gradually increase over the course of time, which simulates production of more CAR1, etc. as the cell develops.

Brief description of the model:

The network is shown on the right. The governing equations for the seven variables are given by

[ACA]' = k1[CAR1]-k2[ACA][PKA]
[PKA]' = k3[cAMPi]-k4[PKA]
[ERK2]' = k5[CAR1]-k6[PKA][ERK2]
[RegA]' = k7-k8[ERK2][RegA]
[cAMPi]' = k9[ACA]-k10[RegA][cAMPi]
[cAMPe]' = k11[ACA]-k12[cAMPe]
[CAR1]' = k13[cAMPe]-k14[CAR1]

Where ' stands for differentiation with respect to time and where
  • k1 affects activation of ACA (adenylyl cyclase)
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  • k2 affects inactivation of ACA
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  • k3 affects activation of PKA (protein kinase)
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  • k4 affects inactivation of PKA
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  • k5 affects activation of ERK2 (protein kinase)
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  • k6 affects inactivation of ERK2
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  • k7 affects activation of RegA (internal phosphodiesterase)
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  • k8 affects inactivation of RegA
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  • k9 is the proportion of cAMP not secreted
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  • k10 affects the breakdown of internal cAMP
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  • k11 is the proportion of cAMP secreted
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  • k12 is the activity of PdsA (extracellular phosphodiesterase)
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  • k13 affects activation of CAR1 (cAMP receptor)
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  • k14 affects inactivation of CAR1
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    The equations are integrated using the explicit Euler's method with a time step of dt=0.01 min.

    This applet simulates a modified version of a model for spontaneous oscillations during the aggregation stage of Dictyostelium (Laub, M.T., and Loomis, W. F. (1998) A molecular network that produces spontaneous oscillations in excitable cells of Dictyostelium. Mol. Biol. Cell 9, 3521-3532.)
    This page and applet were built by Samuel Payne.