Virus Entry: Receptor Binding & Membrane Fusion (2D)

Receptor Binding

Spike affinity ratio r = [L]/Kd 1.00

Hill coefficient n (cooperativity) 2.0

Entry Pathway

Route into the cell

Acidification rate k 0.90 s⁻¹

Live Readout

Step: Approaching

P(bind), Hill eq.

0.00%

Empirical rate

— (0 trials)

Attempts (fail/bound)

0 / 0

Endosome pH

7.40

Elapsed

0.0 s

Genome release

—

How it works

Each contact between the spike protein and a host-cell receptor is resolved by the Hill–Langmuir occupancy equation, the same saturation-binding model used for hemoglobin–O₂ and drug–receptor kinetics:

P(bind) = r^n / (1 + r^n)
r = [L] / Kd   (spike-affinity slider)
n = Hill coefficient (cooperativity)

Every probe rolls a uniform random number against this probability — over many attempts the empirical rate readout converges on the analytic curve plotted in the dose-response pane, which is exactly what a real binding assay does. If bound, either the spike undergoes a conformational change that fuses the viral and cell membranes directly, or the virus is engulfed into an endosome whose pH falls by real acidification kinetics as V-ATPase pumps protons in:

pH(t) = pH_end + (pH_start − pH_end)·e^(−k·t)

Fusion triggers once pH(t) crosses the ≈5.5 threshold real class-I fusion proteins (e.g. influenza hemagglutinin) require — the acidification-rate slider (k) controls how quickly that happens, and the pH-vs-time pane plots the live curve against the trigger line.

Matched receptor Spike protein Endosome / genome