Non linear switch

This experiment describes the interaction between two CAs. Their mutual impact = { 1, 0 }. CA-1 affects CA-2 and is not affected  by it. In the first two frames only CA-2 was planted and the space of CA-1 is empty. CA-2 lives 88 days and then dies. In the second frame couple, both zygotes were planted.  CA-2 died immediately while  CA-1 lived.  In the third frame couple, CA-1 zygote  was planted 6 days after CA-2 zygote . In the last frame couple CA-1 zygote was planted 61 days after that of CA-2.

The relationship between the delay of  CA-1 seeding and CA-2 cell production is depicted in the first graph. CA-1 drives the system. From t > 11 and on, whenever CA-1 is on,  after a short while CA-2 will be off. Cell production is roughly proportional to delay and remains constant when t >=88. At t=6  CA-1 stimulates CA-2 growth and cell production.


Imagine that after planting a zygote the CA grows to its maximal size an then dies this is defined as turnover. In the first frame couple a CA-2 zygote matured in 88 days and then died. During this period it produced 54 cells.  In the third frame couple,  CA-2 matured in 97 days and produced 69 cells   In the last frame couple CA-2 matured in 62 days and produced 52 cells. The time it takes a zygote to fully mature is called turnover time. In this context CA-1 controls turnover time and cell production.


How to set the system so as to get the highest cell yield in the shortest time? We have to maximize the fraction f = (cell production)/ (turnover time). At delay = 6,  CA-2 matures in 97 days. During this period it produces 69 cells. f = 69/97 = 0.71  At delay = 61,  f =  52/61 = 0.86.  The lower graph indicates that f reaches its maximum at delay = 31.

Further reading:
When to harvest a CA?

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