Computational Validation

Proof of Concept

Topological Superiority

Aim 1 validates ring topology through dimensionless ODE modeling and Lyapunov stability analysis.
The six-variable Monod consumer-resource system proves asymptotic stability at the interior fixed point, with cascade extinction behavior demonstrating topological biocontainment.

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Section 1

Abstract

Lake Budi, a brackish coastal system in Lafkenche territory (southern Chile), faces terminal eutrophication and fecal contamination driven by benthic anoxia and internal phosphorus cycling. Conventional remediation fails because it does not restructure the underlying microbial ecology.

Central Hypothesis: We propose encoding biocontainment into population topology—a biocontainment architecture that is topological rather than genetic. The project is named Füzi Poiesis: Füzi (salt water in Mapudungun), combined with poiesis (autopoietic self-generating capacity, Maturana 1980).

Design: A three-strain synthetic consortium coupled through circular auxotrophic dependency. Strain A (ΔleuB) produces microcin J25. Strain B (ΔtrpB) expresses heterologous SQR + persulfide dioxygenase. Strain C (ΔhisD) contains a dual-input AND-gate circuit (P_lux + OmpR-controlled promoter) driving alkaline phosphatase.

Central Finding: In two-strain pairs, escape mutants persist parasitically on intact partners. In three-strain rings, escape from one partner leaves mutants unable to access metabolites from a third strain, forcing system-level collapse. This converts local stability (pair) into closed-loop failure (ring).

        Deliverables:
        Three fully annotated genetic designs in Benchling (pFP-A, pFP-B, pFP-C)
AND-gate Boolean logic validation via Hill-equation transfer functions
Dimensionless six-variable ODE system with Lyapunov stability (Re(λ_max) ≈ −0.215)
Cascade extinction simulation showing ring vs. pair topologies

      

Section 2

Project Aims

Aim 1: Computational Validation ✓ COMPLETED

Design and computationally validate three-strain consortium. Specify annotated plasmids in Benchling. Demonstrate Lyapunov stability (Re(λ_max) ≈ −0.215) and cascade extinction under single-member loss. Scope: computational only, no laboratory synthesis.

Aim 2: Biological Validation (FUTURE)

Validate in Halomonas elongata under Lake Budi conditions (5–15 g/L NaCl). Recalibrate ODE parameters. Construct consortium and validate stability + remediation in microcosms. Success criteria: escape mutant frequency <10⁻⁵, ≥80% phosphorus removal.

Aim 3: Deployment (VISIONARY)

Validated consortium in pumice-biochar matrix in Lake Budi littoral zone. Contingent on Aim 2 success, EIA, and Lafkenche community free, prior, informed consent.

Section 4

DNA Constructs & Strain Architecture

All three strains are coupled through circular auxotrophic dependency, creating a closed metabolic ring where each strain depends on metabolites from the next. This topology provides qualitatively superior biocontainment compared to two-strain pairs.

Strain A (pFP-A, 4626 bp)

Function: Anti-coliform — Microcin J25 production
Promoter: BBa_J23119 (constitutive)
Gene: mcjABCD operon (Solbiati et al. 1999)
Activity: Lasso peptide selective for Enterobacteriaceae (21 aa)
Auxotrophy: ΔleuB (requires leucine from Strain B)
Vector: pBR322 derivative, ori, AmpR

Strain B (pFP-B, 3677 bp)

Function: Anti-H₂S — Sulfide oxidation pathway
Promoter: BBa_J23119 (constitutive)
Genes: Bicistronic sqr-pdo cassette
SQR source: Rhodobacter capsulatus DSM-155
PDO source: Cupriavidus pinatubonensis JMP134
Activity: 267 nmol·mg⁻¹·min⁻¹ at pH 8.0
Auxotrophy: ΔtrpB (requires tryptophan from Strain C)

Strain C (pFP-C_FINAL, 5148 bp)

Function: Anti-eutrophication AND-gate
LuxR Cassette: BBa_J23119 → RBS (5,000 a.u.) → luxR (BBa_C0062)
AND-gate: P_lux (BBa_R0062) × BBa_R0082 (OmpR-controlled)
Output: RBS (10,000 a.u.) → phoA_opt (codon-optimized GC 51%)
Logic: AHL AND osmolarity rise → phoA expression
Auxotrophy: ΔhisD (requires histidine from Strain A)

Architectural Rationale

pFP-C Integration: luxR is constitutively expressed on the same plasmid, eliminating hidden burden assumptions and ensuring LuxR availability for AHL sensing from Strain A.

Osmolarity as Phosphate Proxy: BBa_R0082 (OmpR-controlled) acts as osmolarity sensor, coupling phoA activation to ecological signal of algal biomass accumulation. Aim 2 validates correlation in Lake Budi.

Section 5

Results & Quantitative Validation

The dimensionless six-ODE Monod system integrates population dynamics (n_A, n_B, n_C) with resource pools (s_A, s_B, s_C). Parameters: μ_max ≈ 0.7 h⁻¹, Y ≈ 0.45, δ ≈ 0.143 (Shou et al. 2007).

n* = 0.629

Interior Fixed Point

Re(λ_max) = −0.215

Dominant Eigenvalue

τ ≈ 50

Cascade Extinction Time

6.9 h

Escape Isolate Half-Life

Figure 4: AND-gate transfer functions and Boolean truth table

Figure 4: Sub-Aim 1.2 — AND-gate: Transfer Functions and Response Surface
Left: X₁ (AHL signal, intact consortium) Hill function, Kd = 10.0 nM, n=2. Center: X₂ (SRP sensor, excess phosphorus) Basal eutrophication threshold at 0.5 mg/L (Quesille 2022). Right: AND-gate truth table. phoA expression only reaches 95% (ON state, green bar) when both signals present (1,1). All other input states: OFF (<5%, orange bars). Implementation: OmpR/BBa_R0082 osmolarity proxy as contingency.

$Figure 5: Computational proof of concept$

Figure 5: Computational Proof of Concept — Topological Biocontainment of Three-Strain Hypercycle
Panel I (Monoculture): Strain A alone exhibits exponential decay (dn/dτ = −δ·n) at rate −δ ≈ −0.143. Isolated obligate mutant reaches extinction threshold in ~60 h real time.
Panel II (Closed Pair Mutualism): Two-strain obligate pair A+B converges to interior fixed point n* = 0.629 (≈6.3 × 10⁸ cells/mL). Locally Lyapunov-stable. Perturbation response: asymmetric.
Panel III (Three-Strain Hypercycle): Three-strain ring converges to identical fixed point n* = 0.629, s* = 0.628, max Re(λ) = −0.215. Indistinguishable from pair in equilibrium. τ half-stabilization ≈ 40 dimensionless units.
Panel IV (Cascade Extinction): Ring response (red, dashed): removal of Strain A at τ=50 triggers cascade collapse of n_B, n_C within τ≈50 units (~300 h). Pair response (orange): Strain B persists at 40% of pair equilibrium due to residual s_A pools. Topological distinction: ring fails closed; pair fails open.

Figure 6: Structural biocontainment and eigenvalue stability

Figure 6: Structural Biocontainment — Escape Dynamics and Lyapunov Stability
Left Panel: Exponential decay kinetics of escaped isolate without amino acid supplier. Loss rate: dn/dτ = −δ·n with τ½ ≈ 6.9 h (vertical dashed line). Functional extinction <24 h. Shaded region shows viable cell window. Beyond τ½, isolate density drops below 10³ cells/mL—below proliferation threshold.
Right Panel: Jacobian eigenvalue spectrum at interior fixed point (τ = 60, post-convergence). Green square (3-strains, 6×6): All Re(λ) < 0, Lyapunov-stable. Dominant eigenvalue Re(λ_max) ≈ −0.215. Blue square (2-strains, 4×4): Also stable semiplane. Topological advantage manifest under perturbation (Panel IV), not equilibrium dynamics.

Key Findings

Panel I (Monoculture): Obligate mutant cannot self-sustain; exponential decay confirms auxotrophic dependency architecture.

Panel II (Pair): Two-strain mutualism achieves stable coexistence at interior fixed point.

Panel III (Ring): Three-strain system mathematically identical to pair in equilibrium.

Panel IV (Cascade Extinction): Ring topology enforces system-level collapse on single-member loss; pair permits parasitic persistence.

        Central Proof of Concept:

        Topological biocontainment converts parasitic survival risk into cascade extinction.

        Ring architecture fails closed; obligate pair fails open.

        This qualitative distinction emerges from population topology alone.