Protein Interaction Network Robustness

Network

Proteins (nodes) 55

Failure Mode

Random failure removes a uniformly random protein each step.

Live Readouts

Proteins remaining

55 / 55

Removed

Giant component

55 (100%)

Avg. degree ⟨k⟩

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How it works

Protein-protein interaction (PPI) networks are scale-free: their degree distribution follows a power law P(k) ∝ k^−γ, so most proteins have few interaction partners while a small number of hub proteins have very many. This network is grown with the Barabási–Albert preferential-attachment rule — each new protein wires to existing proteins with probability proportional to their current degree, the same "rich get richer" process thought to arise biologically from gene duplication and divergence.

P(attach to node i) = k_i / Σ_j k_j
P(k) ∝ k^(−γ),  γ ≈ 2–3 for most PPI networks

Whether the network stays connected as proteins are knocked out follows the Molloy–Reed / percolation criterion for a giant connected component:

κ = ⟨k²⟩ / ⟨k⟩ > 2  →  giant component survives

Because scale-free networks have a fat tail in ⟨k²⟩ driven by hubs, they are famously error-tolerant but attack-fragile (Albert, Jeong & Barabási, Nature 2000): removing random low-degree proteins barely changes ⟨k²⟩/⟨k⟩ and the network stays in one piece, but removing the highest-degree hubs first collapses κ below 2 after only a few knockouts, fragmenting the network — the network-biology signature of why hub proteins tend to be essential genes.

Random Failure — each step removes a uniformly random surviving protein (models random mutation/knockdown).
Targeted Attack — each step removes the surviving protein with the highest current degree (models selective hub inhibition).
Remove Next Protein / Auto-Attack — step through knockouts one at a time or watch the cascade automatically.
Node color scales with a protein's original degree (blue → low, orange/red → hub); nodes fade and shrink to zero as they're knocked out.

Giant component Fragmented / isolated

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