Protein Interaction Network Robustness — 2D Percolation

Network

Proteins (nodes) 55

Failure Mode

Random failure removes a uniformly random protein each step.

Live Readouts

Proteins remaining

55 / 55

Removed fraction f

Giant component S

100%

κ = ⟨k²⟩/⟨k⟩

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Predicted f_c (random)

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Observed collapse f

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How it works

This is a genuine 2D counterpart: the network is laid out with a real 2D force-directed physics engine (Coulomb-like node repulsion F ∝ 1/d plus Hookean spring attraction along surviving edges, both computed directly in the plane — not a projection of a 3D scene), and a second live chart tracks the percolation curve S(f): the giant-component fraction as a function of the fraction f of proteins removed.

repulsion: F = k_r / d²           (per pair, alive nodes only)
spring:    F = k_s · (d − L₀)      (per surviving edge)
integrate: v += (F/m)·dt;  v *= damping;  x += v·dt

The chart also draws the analytic Molloy–Reed / Cohen et al. (2000) prediction for the critical removal fraction at which a configuration-model random network's giant component vanishes under uniform random node removal:

κ = ⟨k²⟩ / ⟨k⟩   (computed from the intact network's degree sequence)
f_c = 1 − 1/(κ − 1)

Because targeted hub removal deletes far more edges per node than random removal, its empirical collapse point falls well below this random-removal prediction — the same "robust yet fragile" asymmetry the 3D companion sim shows, here made quantitative with a live number instead of only a visual read.

Random Failure — each step removes a uniformly random surviving protein.
Targeted Attack — each step removes the surviving protein with the highest current degree.
κ is recomputed once per network build from the intact degree sequence (Molloy–Reed theory is defined on the original topology, not the damaged one).
The dashed vertical line on the chart marks the predicted f_c; the small diamond marks where the simulated giant component actually first drops below 10% of surviving nodes.

Giant component Fragmented / isolated

Protein Interaction Network Robustness — 2D Percolation View