Directed Evolution of a Synthetic Gene Circuit — 2D Model

Target & Selection

Target expression P_target 60 au

Mutation strength σ 0.06

Selection pressure (survivors) 20%

Population State

Generation

Best error

—

Best P_ss

— au

Population mean err

—

Best Circuit's Parts

Promoter strength k_tx—

RBS strength k_tl—

Degradation rate k_deg—

How it works

Each candidate is a synthetic gene circuit built from three standardized (BioBrick-style) parts: a promoter of transcription strength k_tx ∈ [0,1], a ribosome-binding site of translation strength k_tl ∈ [0,1], and a terminator/mRNA context that sets an effective protein degradation-and-dilution rate k_deg ∈ [0.1, 2.0] h⁻¹. Protein level P(t) follows the standard gene-expression ODE:

dP/dt = 100 · k_tx · k_tl  −  k_deg · P
Steady state:  P_ss = 100 · k_tx · k_tl / k_deg

This 2D view plots every candidate on the k_tx–k_tl plane. Because P_ss depends only on the ratio k_tx·k_tl / k_deg, one target level traces out a whole family of curves — one per k_deg slice, k_tl = P_target·k_deg / (100·k_tx) — shown as dashed lines. A point's radius encodes its own k_deg (bigger = faster degradation, needs a stronger promoter/RBS pair to hit the same target), so the population visibly spreads across several curves rather than collapsing to one spot.

The population (40 candidate circuits) evolves by a real genetic algorithm — this is directed evolution / adaptive laboratory evolution, used in real biofoundries when rational part selection alone can't hit a target:

Fitness = −(P_ss − P_target)², so circuits closer to the target score higher.
Selection keeps only the top fraction (survivor %) of the population each generation, unchanged (elitism).
Mutation perturbs each surviving parent's three parameters with Gaussian noise of width σ, clipped to valid part ranges, to refill the population.
Step Generation advances one round; Auto-Evolve runs continuously so you can watch the cluster of points converge and flatten onto the nearest iso-expression curve instead of collapsing to one point.

Marker color encodes fitness (teal = near target, red = far); the best circuit each generation is drawn larger with a glowing ring. Drag to pan, scroll to zoom.

Generation 0

Near target (high fitness) Far from target Marker size = k_deg

drag to pan · scroll to zoom