4D DNA Blueprint #5 — Decoding the stiffness signal: from letters to physics

[ Where we are ]

In #4 we read GC content as a rough proxy for firmness and turned a sequence into shells. “Rough proxy” should bother you — and it bothered this work for several versions, because exactly how much GC stiffens a region was a number chosen by hand. A hand-chosen number is a place where you could be fooling yourself. This episode removes it. We derive the stiffness weight from physics, and then confirm the answer three independent ways — the third against real measurements. A knob becomes a measurement.

5.1 The problem: a knob you picked

The stiffness signal combines a few ingredients of composition into one number that says how firm a region’s interface is. The dominant ingredient is GC content. The honest trouble: for several versions, the weight on GC — how strongly each bit of GC counts toward firmness — was simply set by hand to a value that gave sensible-looking shells. That is precisely the move #3’s constitution warns against. So the question for this episode is blunt: can that weight be derived instead of chosen?

5.2 The physics: how bases stack

Yes — and the physics has been known for decades. A DNA double helix is held together not only by the rungs of the ladder but by how neighbouring base pairs stack against each other, like coins in a roll. Each kind of neighbour-pair contributes a measurable amount of stability, tabulated in what are called nearest-neighbour energies (the standard SantaLucia 1998 values). Add them up along a sequence and you get its duplex stability - how hard the helix is to pull apart — in real energy units (kcal/mol).

Here is the key fact: GC-containing steps are more stable than AT-containing ones. So a GC-rich region is genuinely, physically stiffer — harder to open — and by a known amount. That is not a chosen weight; it is a thermodynamic measurement.

5.3 Leg one: the weight, derived

Now compute, for a real region, how its physics-based stability changes as its GC goes up. On a test locus (a mouse skeletal gene), each added unit of GC raises stability by about +1.10 kcal/mol, and the relationship is almost perfectly straight (the fit explains about 99% of the variation). In other words, the direction and size of GC’s effect on firmness fall straight out of the stacking energies. The hand-picked weight is replaced by a derived one. Leg one is the derivation itself.

5.4 Leg two: it generalizes

A number derived on one gene could be a fluke of that gene. So apply the same derivation across many regions: fifty-one loci drawn from six species spanning very different animals. The GC-stiffness relationship holds every time, explaining more than 96% of the variation at each locus. The weight is not a quirk of one sequence; it is a general property of how DNA stacks. Leg two is breadth.

5.5 Leg three: it matches reality

Derivation and generalization are still about the sequence and its physics. The strongest test is against something measured in living cells. There are genome-wide measurements of how tightly DNA is packaged onto its spools (nucleosome occupancy). If our reading of GC as firmness is right, GC should come out as a strong positive predictor of that measured packaging — and it does. In a held-out regression over more than twenty-three thousand windows, the GC effect is strongly positive (a coefficient of about +4.06, with an overwhelming statistical strength, t around 27). The sequence reading and the measurement agree. Leg three is reality.

Three legs — physics, breadth, and measurement — all point the same way. The center of the stiffness signal is no longer a choice.

5.6 Try it yourself

1. Take the GC track you built in #4.
2. If you can, replace “fraction GC” with a stability estimate using published nearest-neighbour energies: slide the same window, sum the step energies, and plot that instead.
3. Compare the two tracks. You will see they rise and fall together — because GC is what drives the stability — but the energy track is now in real units and rests on physics, not on a weight you guessed.

That swap, from a chosen weight to a derived one, is the whole lesson: wherever a reading leans on a number, ask whether the number can come from physics instead of preference.

— WHERE THIS STOPS — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — “Decoded” means something precise and limited: the hand-tuning of the GC weight is closed, and its sign and size are confirmed three ways, including against measurement. It does not mean every downstream number in the model is independently measured. Some pieces of the machinery ahead (the switch behaviour, the size integrator) are still principled models, not wet-lab measurements — and we will label them honestly as such when we reach them. One knob is now physics; the rest of the reading still has to earn each of its numbers. — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

— CHECK IT IN THE PAPER — — — — — — — — — — — — — — — — — — — — — — — — — — — — — - This episode is the teaching version of the whitepaper’s decoding of the GC weight from nearest-neighbour thermodynamics and its three-legged confirmation (derivation, cross-species generalization, and a held-out regression against measured nucleosome occupancy). The relevant modules are gamma_decode, generalize, and w_at_decode. Full paper, proofs & reproducibility bundle (always-latest, now v8): https://doi.org/10.5281/zenodo.20471407 — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

Next up — #6: Shape is not strength. A droplet can be perfectly round and still shatter the instant you touch it. Roundness is not rigidity — so where does rigidity come from? We meet the shell, and a single law that runs from a molecular droplet to an eggshell.

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — Part of the 4D DNA Blueprint series. Full paper, proofs & reproducibility bundle (always-latest): https://doi.org/10.5281/zenodo.20471407 Project: https://jamming-physics.org/ 4D DNA Blueprint — what the sequence fixes, and what it does not. © 2026 Young Jae Lee — CC BY 4.0