The 3D version of this simulator follows one Hfr x F- mating pair as a single bead chain feeding through one pilus. This 2D counterpart instead simulates the real quantity the original Wollman-Jacob experiment actually measured: the population-level recombinant frequency curve for each marker, built from thousands of independent mating pairs rather than animated as one pair's geometry.
Each simulated pair i gets two independent random numbers drawn once per experiment: a pilus-contact onset time Si (mating pairs don't all form simultaneously — real cultures mix over several minutes) and a spontaneous bridge-lifetime Di (the mechanically fragile mating bridge shears apart at a random time, exactly the fragility the original blender-based interruption technique exploited). Both are drawn from exponential distributions:
S_i ~ Exponential(mean = pairing-onset spread)
D_i ~ Exponential(mean = τ, mean bridge lifetime)
marker j (map-minute t_j) crosses in pair i iff
D_i ≥ t_j (bridge survives long enough)
AND S_i + t_j ≤ elapsed time (transfer has reached t_j by now)
Recombinant frequency(t_j, T) = fraction of all N pairs satisfying both, at global clock T
Because Si and Di are independent, the frequency curve has a clean closed form once T is large: it rises as a sigmoid (from the spread of onset times) toward a plateau equal to exp(-t_j / τ) — the probability a pair's bridge survives at least until marker j's entry time. This reproduces the real, historically puzzling observation that markers further from the origin plateau at a lower maximum frequency, even after arbitrarily long mating: it isn't that transfer stops, it's that more and more bridges have already spontaneously broken by the time a distant marker's turn comes. The single-pair 3D model has no way to show this population effect at all — every pair there is bound to reach 100% of whichever markers it reaches.
- Transfer rate / Temperature — identical Q10 ≈ 2 rate law to the 3D model; sets how fast the shared clock advances, in simulated map-minutes per real second.
- Mean bridge lifetime τ — the new, genuinely 2D-only parameter: average time a mating bridge survives before spontaneously shearing. Locked once conjugation starts, like a real strain/stirring-rate choice.
- Pairing-onset spread — how desynchronized real pilus-contact formation is across the population; zero spread would make every curve a step function at its marker's entry time.
- Interrupt Mating — freezes the shared clock, letting you read off the exact recombinant-frequency snapshot at a chosen interruption time, the same measurement the historical experiment made by shearing every pair apart at once.