Integrating evolutionary trade-off models from microbiology with active foam physics simulations will enable prediction of spatial patterns in the spread of antibiotic-resistant bacterial colonies.

A coupled model — comprising (a) an evolutionary trade-off model of antibiotic resistance (cost-of-resistance vs. growth rate, following classic fitness-cost frameworks) and (b) an active-foam/active-matter physics simulation (treating bacterial colonies as a jammed, actively-driven foam of growing/dividing cells with mechanical interactions) — will predict the spatial pattern of resistant subpopulation spread (front velocity, sector angle distribution, spatial heterogeneity index, and clustering coefficient) within a bacterial colony expanding on a solid or semi-solid antibiotic gradient substrate, to within 15% relative error against experimental colony imaging data, and will outperform (lower prediction error) both (i) a pure reaction-diffusion (Fisher-KPP) model without mechanical foam physics and (ii) a pure foam-mechanics model without evolutionary trade-off terms, on held-out experimental replicates.

Minimum viable test (MVT):

1. Use published/available time-lapse colony expansion datasets (e.g., E. coli on antibiotic gradient agar, fluorescently labeled resistant vs. susceptible subpopulations) — target 3 independent published datasets or newly generated data from 20 replicate plates.
2. Build baseline Model A (Fisher-KPP reaction-diffusion with resistance as a genotype fraction field, no mechanics) and baseline Model B (active foam mechanics, homogeneous genotype, no trade-off) as null comparators.
3. Build integrated Model C: active foam/vertex-model mechanical layer (cell-cell forces, growth-induced pressure, jamming) coupled to a two-strain (or continuous trait) reaction-diffusion-selection layer parameterized by literature fitness-cost values (growth rate reduction 5–40% typical for resistance mutations) and local antibiotic concentration field.
4. Fit each model's free parameters on 60% of replicate colonies (training set); freeze parameters; predict spatial pattern metrics on remaining 40% (test set), blind to genotype-labeling ground truth during prediction generation.
5. Compare prediction error distributions (Model A vs B vs C) via paired statistical tests across test-set replicates.
6. Run sensitivity/ablation: remove trade-off term from Model C (set fitness cost = 0) and remove mechanical jamming term (set to well-mixed diffusion) to isolate which component drives predictive gains.

# Pseudocode outline

class FoamMechanicalLayer:
    # Vertex/particle-based model of growing, dividing cells
    def __init__(self, packing_fraction, division_rate, stiffness):
        ...
    def step(dt):
        compute_cell_cell_forces()
        update_positions_via_active_stress()
        handle_division_and_jamming()

class EvolutionaryTradeoffLayer:
    def __init__(self, fitness_cost, resistance_level, antibiotic_field):
        ...
    def local_growth_rate(cell, antibiotic_conc):
        base_rate = wildtype_growth_rate
        if cell.resistant:
            return base_rate * (1 - fitness_cost) * survival(antibiotic_conc, resistance_level)
        else:
            return base_rate * survival(antibiotic_conc, resistance=0)

class CoupledModel(FoamMechanicalLayer, EvolutionaryTradeoffLayer):
    def step(dt):
        antibiotic_field.diffuse(dt)
        for cell in cells:
            cell.growth_rate = local_growth_rate(cell, antibiotic_field.at(cell.pos))
            cell.mechanical_stress = compute_local_stress(cell)
            cell.growth_rate *= mechanical_inhibition(cell.mechanical_stress)  # jamming feedback
        FoamMechanicalLayer.step(dt)
        handle_stochastic_division_with_genotype_inheritance()

# Calibration
fit_parameters(CoupledModel, training_replicates, method="Bayesian MCMC or CMA-ES")
predictions = CoupledModel.simulate(test_conditions)
compare_spatial_statistics(predictions, experimental_test_data)