Tolerance accumulator

We explore the properties of   the tolerance accumulator  which was introduced in the previous experiment . The proliferon consists of a stem CA-0, CA-1 and CA-2.  CA-2 gets resources from CA-1 and accumulates them. In the previous experiment demand oscillated. Here demand rises to a maximum = 40 and then  declines to zero not to rise again.

delivery[2, 1, k, 2] ;
delivery[2, 2, k, 2] ;
If[ p[1,prev] > p[1,now], set rule[250]]; Min[++k, 40], else [set rule[600]]

Before the experiment started CA-0 planted two zygotes which grew into mature isolated CA. When the experiment begins demand starts rising. CA-1 and CA-2  switch  between rules 600 and 250. as described before. CA-2 and CA-3 are accumulators.

Both CA depend on the triggering of the demand. When it rises they thrive and when it vanishes they die. The relationship between CA-1 and CA-2 is somewhat intricate. CA-1 delivers its daily production to CA-2. If it would not deliver it CA-2 would look like CA-1. Production delivery by CA-1 is more than a transfer of resources. It stimulates CA-2 to produce more and raise its output.

We might try to prolong CA-2  survival by delivering to it an additional daily ration   produced by CA-4 (not depicted):  delivery[2,4, k, 2] ; CA-2 would accumulate more tolerance and produce more, yet could not improve its survival.

CA-3 is an accumulator which does not depend on demand.  It  produces tolerance and accumulates it (middle curve). delivery[3, 3, 40, 2].   In addition it may accumulate tolerance delivered to it by CA-1 (upper curve). [3, 1, 40, 2]

Mutual interaction

Compare this experiment with a two compartment model. Y1 contains resources and delivers them to Y2 which delivers them to the environment. Their relationship is described by two differential equations.

Y2 is a passive container which receives and delivers. The left arrow stands for a constant rate of delivery from Y1 to Y2. In the above experiment each compartment is a process (CA).  The arrow indicates more than just a constant transfer rate of resources. It actually triggers Y2.

delivery: [j, j-1, While[p[j-1] > set point], 2]
Argument[1]: Activated CA.
Argument[2]: Activating CA.
Argument[3]: Delivery condition.
Argument[4]: Delivery amount.
p[j]:  daily production