We still have a single substrate agent
S but now have two different enzyme agents,
P, one catalyzing the state change of the substrate from
1, the other doing the reverse.
Try running the system with 5000
S agents, all initially in state
0, with 50
Ks and 100
Ps. What is the steady state of
S in state
S(s~1?) ? How long does it take to get there?
Try varying the number of
P constant. For example, reduce
K to 10, increase it to 200 and then 1000. How does this affect the steady state? Do a few more cases and plot a rough dose-response curve.
In cases where there are very few
Ks, you might want to rescale the system by modifying the variable
rescale to 10 (say); this increases the size of the system 10-fold, while preserving the dynamics, thus minimizing stochastic fluctuations. This is a very useful general trick which can also be used to make a rough, but quick, simulation of a big system: to do this, change
rescale to (say) 0.1 which decreases the system 10-fold at the cost of increasing stochastic fluctuations.
What happens if, instead, the number of
Ss is similar to the number of
%agent: K(s) %agent: P(s) %agent: S(s~0~1) %var: 'fast' 10 %var: 'medium' 1 %var: 'slow' 0.1 %var: 'BND' 0.00001 %var: 'BRK' 0.1 %var: 'MOD' 0.1 K(s), S(s~0) -> K(s!0), S(s~0!0) @ 'BND'*'fast'/'rescale' K(s!0), S(s!0) -> K(s), S(s) @ 'BRK' K(s!1), S(s~0!1) -> K(s!1), S(s~1!1) @ 'MOD' P(s), S(s~1) -> P(s!0), S(s~1!0) @ 'BND'*'fast'/'rescale' P(s!0), S(s!0) -> P(s), S(s) @ 'BRK' P(s!1), S(s~1!1) -> P(s!1), S(s~0!1) @ 'MOD' %var: 'rescale' 1 %var: 'numk' 50 * 'rescale' %var: 'nump' 100 * 'rescale' %var: 'nums' 5000 * 'rescale' %init: 'numk' K(s) %init: 'nump' P(s) %init: 'nums' S(s~0) %var: 'numS1' S(s~1?) %obs: 'S1' 'numS1' / 'rescale'