Plasmid Instability: Mean-Field & Drift (2D)

Fermentation Controls

Segregation loss rate p 1.0%

Metabolic burden 20%

Selection pressure (antibiotic) 40%

Effective population N 300

Simulation speed 1.0×

Culture State

Producers 100%Cheaters 0%

Generation

0.0

Relative titer

100%

Plasmid-bearing F

100.0%

Stable eq. F*

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How it works

This is a mean-field / diffusion model of the same fermentation, not a per-cell simulation. F(t), the plasmid-bearing fraction, follows a Wright–Fisher-style stochastic differential equation:

drift(F) = (s − b)·F·(1−F) − p·(1−b)·F
dF = drift(F)·dt + sqrt(F(1−F)/N)·dW

s = selection pressure, b = metabolic burden,
p = segregation loss rate, N = effective
population size (sets drift-noise strength),
dW = Gaussian white noise increment.

The deterministic part is a replicator equation: selection pushes F up, burden and segregation pull it down. Turn off drift noise and the trajectory is the exact ODE solution (RK4); turn it on and finite-population sampling noise can tip a marginal culture either way — smaller N drifts more, exactly as a small seed flask is riskier than a large production tank.

Colony grid — a top-down 2D "microplate" of cells that redistributes itself to track F(t) each tick.
Phase portrait — plots drift(F) against F; the curve's zero-crossings are the equilibria. Drag on it to set F directly and see which basin it falls into.
History strip — scrolling trace of F over the last ~150 generations.

Real-world relevance: the stable equilibrium F* = 1 − p(1−b)/(s−b) (when s>b) is the titer a production run settles at under continuous antibiotic selection; when burden exceeds selection there is no positive equilibrium and F decays to zero — the culture collapses no matter how it started.

Plasmid-bearing (producer) Plasmid-free (cheater)

drag to set F

Plasmid Segregational Instability — Mean-Field & Drift (2D)