3. Letting time run — what 'all at once' really means · Dr. Seok's Cancer-Cell Digital Twin, First Steps

Once you have rules you can let time run. It goes like this.

Read the state now
Compute the next value of every gene, each on its own
Only once all the computing is done, swap them in all together

Step 3 is the crux. If you overwrite values while you are still computing, the genes computed later end up reading values that have already changed. The result then depends on the order in which you happened to list the genes. Biology has no such order, so that is a bug in the model.

This scheme is called synchronous update. It is the most common and the easiest to compute. There is a price, and lesson 10 is where you pay it.

The left-hand version took one step in one tick; the right-hand version took two.

Python Runs in your browser

import bn

net = bn.mini()

# The common mistake — swapping values in while you are still computing
def step_wrong(state):
    s = dict(state)
    s["CD47"] = int(bool(s["DDX54"]))                       # <- CD47 has already changed here
    s["Cancer_Growth"] = int(bool(s["CD47"] and not s["p53"]))  # <- and this reads the changed value
    return tuple(s[g] for g in net.genes)

start = net.state(DDX54=1, p53=0, CD47=0, Cancer_Growth=0)
print("start   ", net.show(start))
print("correct ", net.show(net.step(start)))
print("wrong   ", net.show(step_wrong(dict(zip(net.genes, start)))))
print()
print("It is one step of difference, but differences like this pile up into a different fate.")

trace prints every time step as a table. It stops as soon as nothing changes any more.

Python Runs in your browser

import bn

net = bn.mini()

# A cell whose p53 still works
print("# p53 intact — the accelerator is down but the brake holds")
net.trace(net.state(DDX54=1, p53=1), n=6)

print()
print("# p53 mutated — the brake is broken")
net.trace(net.state(DDX54=1, p53=0), n=6)

It is this property that lets us start from any state at all. That is the key to the next lesson.

Python Runs in your browser

import bn

net = bn.mini()

# What if we start with the cancer signal already switched on?
print("# starting with Cancer_Growth set to 1 (but DDX54 switched off)")
net.trace(net.state(DDX54=0, p53=0, CD47=1, Cancer_Growth=1), n=6)

print()
print("The signal that was on switched itself off within two steps.")
print("The rules 'rewrite' the state — the initial value is a starting point, not a destination.")

🎮 Clock bench

Pick an initial state and press ▶ to let time run one tick at a time.

Same circuit, different starting point — see with your own eyes where each one goes.

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🤔 Check yourself

What must you always respect when computing new values under synchronous update?

🤔 Check yourself

In a synchronous model, what happens if you run the same initial state twice?

🤔 Check yourself

Why did Cancer_Growth drop to 0 even though we started it at 1?