Summary

This PR removes the Catalyst.jl dependency from JumpProblemLibrary by converting all @reaction_network definitions to direct jump rate functions and state change vectors while maintaining mathematical equivalence.

Changes Made

JumpProblemLibrary

• ✅ Removed Catalyst dependency from Project.toml and imports
• ✅ Updated JumpProblemNetwork structure to store direct jump functions and state changes
• ✅ Converted all @reaction_network definitions to direct implementations

Converted Jump Problems:

1. DNA repressor model: 6 reactions with negative feedback regulation
2. Birth-death process: Simple production/degradation kinetics
3. Nonlinear reactions: Including 3rd order kinetics with proper binomial coefficients
4. Oscillatory system: 12 reactions with hill function regulation
5. Multistate model: Complex 18-reaction network with 9 species
6. Twenty gene network: Programmatically constructed gene regulation network
7. DNA dimer repressor: Gene repression via protein dimerization
8. Diffusion network: Parameterized 1D lattice diffusion

Mathematical Equivalence

All conversions preserve the mathematical meaning of the original Catalyst networks:

Mass Action Kinetics

• Elementary reactions: A + B → C becomes k * A * B
• Higher order reactions: 2A → B becomes k * A * (A-1) / 2 (proper binomial coefficients)
• Third order reactions: 3C → 3A becomes k * C * (C-1) * (C-2) / 6

Example Conversion

Original Catalyst:

dna_rs = @reaction_network begin
    k1, DNA --> mRNA + DNA
    k2, mRNA --> mRNA + P  
    k3, mRNA --> 0
    k4, P --> 0
    k5, DNA + P --> DNAR
    k6, DNAR --> DNA + P
end

Converted Direct Implementation:

function dna_repressor_jumps(u, p, t)
    DNA, mRNA, P, DNAR = u
    k1, k2, k3, k4, k5, k6 = p
    [
        k1 * DNA,           # k1: DNA --> mRNA + DNA
        k2 * mRNA,          # k2: mRNA --> mRNA + P  
        k3 * mRNA,          # k3: mRNA --> 0
        k4 * P,             # k4: P --> 0
        k5 * DNA * P,       # k5: DNA + P --> DNAR
        k6 * DNAR           # k6: DNAR --> DNA + P
    ]
end

dna_nu = [
    [0, 1, 0, 0],    # k1: mRNA production
    [0, 0, 1, 0],    # k2: protein production  
    [0, -1, 0, 0],   # k3: mRNA degradation
    [0, 0, -1, 0],   # k4: protein degradation
    [-1, 0, -1, 1],  # k5: repressor binding
    [1, 0, 1, -1]    # k6: repressor unbinding
]

Technical Implementation

• Jump rate functions: Compute propensities based on current state
• State change vectors (nu matrices): Define how each reaction affects species counts
• Combinatorial factors: Proper handling for higher order reactions
• Hill function helper: For complex regulatory dynamics
• Updated JumpProblemNetwork: Stores jump functions and state changes in prob_data

Complex Networks Converted

Multistate Model (18 reactions, 9 species)

Complex biochemical signaling network with multiple binding states and phosphorylation.

Twenty Gene Network (80 species)

Programmatically constructed gene regulation network with:

• 20 genes (G), 20 mRNAs (M), 20 proteins (P), 20 induced genes (G_ind)
• Different expression rates for odd vs even genes
• Cross-regulation between gene pairs

Oscillatory System with Hill Functions

12 reactions including hill function regulation for biological oscillations.

Testing

• ✅ All Jump problems verified - reaction rates compute correctly
• ✅ Hill function implementations confirmed mathematically equivalent
• ✅ Comprehensive test suite covering all converted problems
• ✅ Jump rate calculations validated for correctness
• ✅ State change matrices verified for proper species accounting

Benefits

• 🚀 Reduced dependencies: Eliminates Catalyst dependency
• ⚡ Better performance: Direct functions avoid symbolic overhead
• 🔧 Simplified maintenance: No dependency on symbolic ecosystem
• 📦 Smaller footprint: Reduced package loading times
• 🔒 Increased stability: Fewer moving parts in dependency chain

Backwards Compatibility

• All existing problem names and interfaces preserved
• JumpProblemNetwork structure maintains same API
• Compatible with all jump simulation algorithms in JumpProcesses.jl
• Jump process construction patterns remain unchanged

🤖 Generated with Claude Code