11. Perturbation — the one line that pins a gene down · Dr. Seok's Cancer-Cell Digital Twin, First Steps

Virtual genetic manipulation is startlingly simple. You just let that one gene skip its rule when updating.

new[g] = perturb[g] if g in perturb else rule[g](state)
#         ^ the pinned value   ^ the original rule

That single line expresses both experiments.

Name	Code	At the bench
Knockout (KO)	`{"DDX54": 0}`	siRNA/shRNA knockdown, CRISPR deletion
Overexpression (OE)	`{"p53": 1}`	Plasmid delivery, inducible expression systems

There is one important difference. The 'single flip' of lesson 9 changed only the initial state. A perturbation changes the rules themselves. It is like keeping the drug on board.

Check that the first column stays pinned at ○ throughout. Below it, the dominoes fall.

Python Runs in your browser

import bn

net = bn.twin()
cancer = net.state(DDX54=1, MDM2=1, CD47=1, PDL1=1, Proliferation=1)

print("# untreated - immovable at the cancer fixed point")
net.trace(cancer, n=4)

print()
print("# DDX54 knockout - pin DDX54 to 0")
net.trace(cancer, n=8, perturb={"DDX54": 0})

The results already diverge. Note that the immune targets on their own (PDL1, CD47) do not work.

Python Runs in your browser

import bn

net = bn.twin()
cancer = net.state(DDX54=1, MDM2=1, CD47=1, PDL1=1, Proliferation=1)

print("apply various treatments to one cancer cell and read off the final fate")
print("-" * 62)
for name, p in [
    ("untreated",                    None),
    ("DDX54 knockout",               {"DDX54": 0}),
    ("p53 overexpression",           {"p53": 1}),
    ("MDM2 knockout",                {"MDM2": 0}),
    ("PDL1 knockout (anti-PD1)",     {"PDL1": 0}),
    ("CD47 knockout (anti-CD47)",    {"CD47": 0}),
    ("p53 knockout",                 {"p53": 0}),
]:
    a = net.attractor(cancer, p)
    kind = "fixed point" if len(a) == 1 else f"period {len(a)}"
    print("  " + bn.pad(name, 30) + "-> " + bn.pad(net.label(a), 12) + f"({kind})")

This is a choice you must make, and write down in your documentation, when you build a model.

Python Runs in your browser

import bn

net = bn.twin()

# A perturbation changes the initial state too - so you 'start out already on the drug'
cancer = net.state(DDX54=1, MDM2=1, CD47=1, PDL1=1, Proliferation=1)
p = {"DDX54": 0}

path = net.run(cancer, 6, perturb=p)
i = net.genes.index("DDX54")
print("values at the DDX54 position:", [s[i] for s in path])
print("It is already 0 at t=0 - because it skips the rule and is pinned.")
print()
print("Had we left the initial state alone and only changed the rules, t=0 would be 1,")
print("and there really are cases where that one time step changes the outcome.")

🎮 Perturbation bench

Pick KO / untreated / OE for each gene. The trajectory is recomputed immediately.

You can apply several at once — that is combination therapy.

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🤔 Check yourself

How do you express a gene knockout in a Boolean model?

🤔 Check yourself

What is the decisive difference between the 'single flip' of lesson 9 and the perturbation of lesson 11?

🤔 Check yourself

Why apply the perturbed value to the initial state as well?