Rising demand-2

 We continue exploring ways to raise CA output (v Rising demand and Rising demand-1). CA-1 was exposed to a rising demand from  20 to 70 relative units.

delivery[1, 1, k, 2] {k, 20, 70}
If[ p[1,prev] > p[1,now], augment[1, 0, 0]]

The image depicts two CA exposed respectively to demands = 20 and 70.

The left graph depicts tolerance accumulation of the isolated stem process (CA-0). At low demand CA-1 accumulated less tolerance than CA-0 (right graph). As demand rose, CA-1 accumulated more and more tolerance and became vigorous.

Despite its  weak physique” already  at a demand of 20, CA-1 delivered twice as much as CA-0. The graph depicts CA-1 output as a multiple of CA-0 output.   Health is expressed in relation  with the isolated CA-0 whose health = 0.

Even a small demand deteriorates CA-1 health, since CA-1 diverts some of its  resources to the output,   accumulates less tolerance, and its health is low (fragile). As demand rises CA-1 adapts better and better. 

Demand in an ongoing CA

The foregoing analysis depicts CA-1 behavior under the control the two functions: delivery and augment. Next we investigate their effect on an evolving CA . CA-1 starts as an isolated process. At time = 20 the demand starts rising.  When demand rises, CA-1 augments its state, raises k which then raises delivery.  Above k = 70, k remains constant.

delivery[1, 1, k, 2] ;
If[ p[1,prev] > p[1,now], augment[1, 0, 0]; Min[++k, 70]]

The next image depicts CA-1 cell count. CA-1 starts as an isolated process. At time = 20 it enters a transient phase during which it reacts to the rising  demand. When demand reaches 70 CA-1 settles at an attractor and starts oscillating.

 The left graph is a 20 days running average of CA-1[output] – CA-0[output]. On the right is the total proliferon output, CA-1[output] + CA-0[output].

The last image depicts CA-1 tolerance accumulation relative to CA-0. CA-1[tolerance] – CA -0[tolerance].

The experiment illustrates again that interaction with the environment, like demand, rescues the CA from isolation. It starts differentiating and when it attains its solution (attractor) it delivers as much as it can. It delivers and its tolerance declines. Then it pauses to regain its breath, delivers again and so on.

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

augment: [j, j-1, While[p[j-1] > set point]
Argument[1]: Augmented CA. 
Argument[2]: Augmenting CA.
Argument[3]: Delivery condition.
p[j,  now]:  daily production.
p[j,  prev]:  yesterday’s  production.