# LIGAND Connections: A Platform Significantly Expanded

## From Framework to Full Research Platform

When LIGAND Connections began, it was a theoretical framework — a set of mathematical relationships linking the Fano plane PG(2, F₂) to protein fold classification and ligand binding geometry. The L0 through L7 layer hierarchy existed as equations on paper. The Fano incidence ratios (17→7 for L1, 28→17 for L6) described critical angles. The harmonic spectrum φ/πⁿ quantized biological function classes. The Cartan decompositions gave algebraic structure. But translating that framework into something a working researcher could actually use — designing ligands, running predictions, exporting synthesis protocols, tracking experiments — required building an entire computational research environment around it.

That environment now exists. LIGAND Connections is a full-stack platform where the mathematics is no longer decorative: it drives every computation, every prediction, every export. A researcher can sit down, identify a protein target by its CATH superfamily, map it to the correct Fano point, compute the critical binding angle, predict the thermodynamic affinity, generate a complete SPPS synthesis protocol, and export everything in ten different formats — all within the same application, in a single session.

The expansion has been substantial across every axis.

**The Design Wizard** replaced what was previously a manual, multi-step process requiring separate calculations and cross-referencing between documents. It now guides users through seven structured steps — from goal definition to experiment creation — with auto-filling geometry from known reference presets (L1: 17/7, L6: 28/17, L7: 28/17) and real-time computation of binding free energies and CDR arm extensions. At the end of the wizard, the platform automatically creates the ligand record, the target record (if new), and a private experiment entry. What used to take an hour of setup takes minutes.

**The Alpha-Flex Engine** represents the most technically ambitious addition. Derived from the BIOOS V48 computational script, this engine maps peptide sequences onto golden-ratio Fano manifolds using Numba-accelerated numerical computation. It produces per-residue metrics across multiple signal dimensions: sigma profiles, determinant landscapes, Fano lane distributions, hydrophobicity mapping, and full manifold trajectories in both real and imaginary components. The genetic algorithm optimizer can evolve novel peptide sequences by fitness criteria, and the G-code compiler translates sequences into geometric instruction sets for downstream pipeline integration. This is no longer a theoretical framework — it is a working computational tool that takes an amino acid sequence as input and returns a complete manifold characterization as output.

**Genome-to-Proteome search** expanded from a simple translation tool into a four-tab research hub. The BLAST-style alignment tool scores unknown protein sequences against the L1/L6/L7 library using a weighted composite of motif matching (40%), fold signature detection (30%), amino acid composition analysis (20%), and local Smith-Waterman alignment (10%). Live NCBI database integration means researchers can search for any protein in the public databases, fetch the full sequence, and immediately run it through the alignment pipeline — without leaving the application. The reverse translation and codon table tools complete the nucleotide-to-protein workflow.

**The export pipeline** now produces ten formats organized into data exports (CSV, JSON, Excel) and scientific exports (YAML configuration, SPPS synthesis protocols, PDF reports, LaTeX formula documents, FASTA sequences). The YAML export captures the complete Fano-derived geometry, spectral processing parameters, and all reference ligand data. The SPPS export generates full Fmoc/tBu solid-phase peptide synthesis protocols — including the L7 pentadic 5-channel recipes with r17^α, equivs_a, and RT_a formulas — with reagent lists, conditions, and expected yields. A researcher can hand the SPPS PDF to a synthesis lab and they have everything they need.

**Private experiments** introduced per-user data ownership. Reference experiments (the published L1, L6, and L7 results) remain visible to everyone as benchmarks. But any experiment a user creates — whether through the Wizard or the Experiments page — is scoped to their session and invisible to other users. This enables multiple researchers to use the same platform instance without data collision.

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## The Infrastructure Beneath

The technical infrastructure was rebuilt to support this expansion. The backend, originally a monolithic server file, was decomposed into eleven modular API routers (auth, payments, alphaflex, blast, calc, chat, data, export, genome, layers, seed), each handling a distinct domain. MongoDB stores all persistent data with proper ObjectId handling and projection-based serialization. Every mathematical computation was verified against a 105-check automated test suite that validates critical angle calculations, binding affinity derivations, harmonic spectrum values, Cartan matrix properties, and Fano combinatorial identities. All 105 checks pass.

Authentication moved from anonymous browser IDs to Emergent-managed Google Social Login with cookie-based sessions, giving users persistent identity across devices. A full Stripe subscription layer implements tiered access (Free, Researcher, Operator, Validator, Admin) with real-time usage tracking — the free tier measures cumulative active time to the second and gates features after 2 hours or 3 exports. The webhook flow handles subscription lifecycle events (creation, update, cancellation) with live Stripe keys.

The frontend received a complete visual overhaul. The previous functional-but-generic interface was replaced with a purpose-built "Tactical Genomics" design system: Barlow Condensed for headings, JetBrains Mono for data, Manrope for body text, all set against a #050505 dark canvas with #0A0A0A card surfaces and razor-thin white/4% borders. Framer Motion handles page transitions and staggered entrance animations. The sidebar uses a motion-animated active indicator that slides between navigation items. Glass morphism, radial glows, grid-pattern backgrounds, and monospaced data displays create a visual language that reads as "research instrument" rather than "web application." Every interactive element carries a data-testid for automated validation.

The AI Research Assistant, powered by OpenAI GPT-4o-mini through the Emergent LLM Key, is trained on the complete LIGAND Connections framework. It handles questions spanning Fano geometry, Lie algebra theory, Cartan matrices, protein fold classification, binding thermodynamics, and practical design guidance. Session-based conversation history persists, and quick-start prompts help new users engage immediately.

What began as a mathematical framework document is now a fully operational research platform — designed, computed, tracked, exported, and billed — with every feature traceable back to the algebraic geometry that started it all.

*LIGAND Connections v3.0 — March 2026*
