Biochemical motifs (4)
Basic GTPase signaling modules
and feedback
B.N. Kholodenko. Cell-signalling dynamics in time and space.
Nature Reviews Molecular Cell Biology, 7(3):165–176, 2006
Phosphorylation cycle
Kinase
Inactive
M
phosphatase
Mp
Active
Phosphorylation cycle
Kinase
Inactive
M
phosphatase
Mp
Active
Each reaction is Michaelian Kinase
M
phosphatase
Mp
But we will allow the amt of kinase
and phosphatase to vary too… Kinase
M
phosphatase
Mp
So we will express these
rates in terms of total
amounts of Kinase and
Phosphatase
Full Expressions Kinase
M
Mp
Without feedback: Fast equilibration
Mp
Time (seconds)
System has a single biologically relevant steady state
Feedback
We now consider a variety of feedback
from the active protein Mp to the other
parts of the system.
We will see that this feedback will have
implications on the dynamics.
Positive feedback to kinase
Kinase
M
phosphatase
Mp
Kinase rate increases as Mp increases
Kinase
M
phosphatase
Mp
Positive
feedback
term
Model equations
Bistable “switch”
Mp
High steady state
Low SS
Ekin
Negative feedback to kinase
production rate
Kinase
M
phosphatase
Mp
Now kinase is a variable
Kinase
Kinase equation:
Kinase
I >1 for negative feedback
Full Model
Stable cycles can be found
Ekin
Mp
Ekin
Mp
Ekin
Mp
Bifurcation diagram
Zoom view: Hopf Bifurcation