Monte Carlo Fixation Analysis for GPCR-Class Signalling under the Drift Barrier

Python implementation of the drift-barrier fixation analysis reported in Appendix B of the manuscript “The Cost Is Not the Constraint: A Drift-Barrier Analysis of GPCR-Class Signalling in Unicellular Systems.” The code computes the standing bioenergetic cost of a complete GPCR-class signalling unit (2700 residues) and of a bacterial two-component sensor (500 residues), expresses both as fractions of the cellular lifetime energy budget, and evaluates the drift-barrier fixation condition s = ηb − c > 1/(2Nₑ) by Monte Carlo sampling (N = 200,000 draws, seed = 42). Outputs include: deterministic burden fractions (0.22% and 0.04% of budget) and relative burden ρ = 5.40; the copy number required for a prohibitive burden (4.63 × 10⁵ per cell); admissible parameter volumes under a common sampling scheme (55.7% and 74.0%); verification of Corollary R2.1, that setting η = 0 yields s < 0 in all draws regardless of benefit magnitude; sensitivity sweeps over cellular energy budget and receptor copy number across an order of magnitude in each direction; and two figures — a phase map in the (η, b) plane and the fixable fraction as a function of effective population size. Prior distributions are stipulated rather than estimated and are documented in the script header. Fraction-of-parameter-space figures are informative as comparisons between architectures under a common scheme, not as probabilities. All results are deterministic given the fixed seed.