Hub Persistence Across Domains: Biology, Engineering, and the Brain
Three domains — protein networks, CPU design, and the human brain connectome — all confirm the Functional Proximity Law. Here is what the numbers say.
Three Domains, One Pattern
The Functional Proximity Law was tested across 23 independent domains. Here are three that illustrate the pattern most clearly.
1. Human Brain Connectome (n=16 regions)
- The brain connectome was modelled as two layers:
- structural — white matter tract connectivity (DTI)
- functional — fMRI co-activation patterns
Result: r = +0.703 (p = 0.004).
The same brain regions — prefrontal cortex, posterior cingulate, precuneus — are hubs in both structure and function. This is not coincidental: these regions evolved as integrators, and their physical connectivity reflects their functional role.
The law predicts this: structural and functional connectivity are functionally similar (both describe information routing in the brain at runtime).
2. p53 DNA Damage Response (n=15 proteins, 4 layers)
- The p53 network was modelled across four interaction layers:
- phosphorylation, ubiquitination, acetylation, transcription_binding
Result: r(phosphorylation ↔ ubiquitination) = +0.928 (p = 0.012).
p53, MDM2, and ATM are top hubs across all four layers. These proteins sit at the centre of every post-translational modification cascade because they are the master regulators — no matter which type of modification you look at, the same nodes are central.
3. CPU Block Design (n=10 components, 3 layers)
As described in the explainer post: r(signal ↔ power) = +0.62, r(signal ↔ scan) = −0.65.
The execute and decode blocks are persistent hubs across signal and power layers. The scan chain inverts this — by design.
The Pattern
| Domain | Similar-layer r | Dissimilar-layer r | |---|---|---| | Brain connectome | +0.703 | — | | p53 network (4-layer) | +0.928 | +0.732 | | CPU block design | +0.622 | −0.649 | | Linux kernel (v6.x) | +0.703 | −0.145 |
In every case: similar layers correlate positively, dissimilar layers correlate less or negatively.
What This Means for Network Science
Hub persistence is not random. It is determined by the functional relationship between layers. This gives us a principled way to predict, before running any analysis, which layers should share their hub identity — and which should diverge.
This is testable, falsifiable, and domain-agnostic. That is what makes it a law rather than an observation.