2. Rules make the cell — three words: AND, OR, NOT · Dr. Seok's Cancer-Cell Digital Twin, First Steps

Switches on their own do nothing. The cell only moves once the switches press on each other. Writing down the rules of that pressing is what this lesson is about.

Figures in biology papers only ever show two kinds of arrow.

Figure	Meaning	Logic
A → B	A switches B on (activation)	`B* = A`
A ⊣ B	A switches B off (inhibition)	`B* = not A`

The star (*) marks the value at the next time step. B* = A reads "if A is on now, then B is on at the next instant".

When several arrows come in, you have to decide between AND and OR. And you cannot tell which from the figure — the person building the model decides.

This is a truth table. Three lines and the entire grammar of Boolean modelling is done.

Python Runs in your browser

# The three logical operations — in Python they are spelled and, or, not
print("A  B  | A and B   A or B   not A")
print("-" * 40)
for A in [0, 1]:
    for B in [0, 1]:
        print(f"{A}  {B}  |    {int(A and B)}         {int(A or B)}        {int(not A)}")

Read the Cancer_Growth rule out loud — "if CD47 is on and at the same time p53 is off".

Python Runs in your browser

import bn

net = bn.mini()

print("regulation in this circuit")
print("-" * 46)
for u, v, sign in net.edges:
    arrow = "-> on   " if sign > 0 else "-| off  "
    print(f"  {u:<14} {arrow} {v}")

print()
print("written as logic")
print("-" * 46)
print("  CD47*          = DDX54")
print("  Cancer_Growth* = CD47 and not p53")
print("  DDX54*         = DDX54          (held as background, keeps its value)")
print("  p53*           = p53            (held as background, keeps its value)")

Trace the figure with your finger. How many places could you cut it?

Python Runs in your browser

import bn
import matplotlib.pyplot as plt

net = bn.mini()
net.draw()                      # green arrow = switches on, red T-bar = switches off
plt.tight_layout()

print("There is only one road to cancer: DDX54 -> CD47 -> Cancer_Growth")
print("and p53 is standing in the way of that last step.")

🎮 Rule bench

Swap AND for OR and see for yourself what changes.

Change the operator and both the truth table and the 'conditions for cancer' change with it.

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🤔 Check yourself

For C* = A and not B, which (A, B) switches C on?

🤔 Check yourself

How do you decide whether the same arrow diagram becomes AND or OR?

🤔 Check yourself

In B* = not A, what does the star mean?