9. Two valleys — why a cancer cell never comes back on its own · Dr. Seok's Cancer-Cell Digital Twin, First Steps

What the positive feedback loop from the last lesson — DDX54 → MDM2 ⊣ p53 ⊣ DDX54 — actually does is the subject of this one.

That loop creates two forces that push each other away. If DDX54 wins, p53 is held down; with p53 held down, DDX54 gets stronger still. And the same in reverse. So there is no middle ground — one of the two wins outright.

This is called bistability. It is why the cell ends up with two valleys, 'normal' and 'cancer'.

And out of it comes the central fact of cancer therapy — the cancer attractor cannot get out by itself. That is what the words 'fixed point' mean. Something has to push from outside.

There are only two attractors — one normal oscillation, one cancer fixed point.

Python Runs in your browser

import bn

net = bn.twin()
land = net.landscape()
land.summary()

Three digits decide the fate. The other five can be anything at all.

Python Runs in your browser

import bn

net = bn.twin()
land = net.landscape()

# Find what the states in the cancer basin have in common
cancer = land.states_with("cancer")
print(f"{len(cancer)} of {land.total} initial states flow into cancer\n")

print(f"how often each gene was 1 across those {len(cancer)} states")
print("-" * 52)
for i, g in enumerate(net.genes):
    on = sum(s[i] for s in cancer)
    tag = "  <- all the same! this digit decides the fate" if on in (0, len(cancer)) else ""
    print(f"  {g:<15} {on:>2}/{len(cancer)}{tag}")

Where the ridge can be cleared is already visible here. The rest of the course is how to find it systematically.

Python Runs in your browser

import bn

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

# Nudge the cancer cell 'just once' - flip one gene and let go
print("Flip one gene at the cancer fixed point and let go - then what?")
print("-" * 60)
for i, g in enumerate(net.genes):
    poked = list(cancer)
    poked[i] = 1 - poked[i]
    fate = net.label(net.attractor(tuple(poked)))
    mark = "  <- escaped!" if fate != "cancer" else ""
    print(f"  {g:<15} {cancer[i]} -> {poked[i]}   final: {fate}{mark}")

print()
print("Three of the eight digits (DDX54, p53, MDM2) clear the ridge on a single flip.")
print("For the other five the rules restore the original value straight away.")
print()
print("The trouble is that 'flip it once and take your hand off' is very hard in a real cell.")
print("So real therapy holds the value down instead - the subject of lesson 11.")

🎮 Valley bench

Shows the size of the two valleys and the push needed to cross between them.

Drag the marble and drop it. Which valley does it roll into?

Loading…

🤔 Check yourself

What does it mean therapeutically that the cancer attractor is a fixed point?

🤔 Check yourself

Why did flipping CD47 once at the cancer fixed point send it straight back to cancer?

Answer CD47* = DDX54 and not p53, and DDX54 is still on. A transient perturbation changes only the initial state; the rules are unchanged, so it snaps back. Note that DDX54, p53 and MDM2 were the exceptions — those three sit on the loop.

🤔 Check yourself

What creates bistability?