Metabolic Pathway Analysis Dashboard

Executive Summary

This dashboard presents comprehensive analysis of metabolic pathways using the DMY shortest-path algorithm, including both single-objective optimization and multi-objective Pareto front analysis for metabolic engineering and systems biology.

Key Findings:

1. Single-objective: Optimal glycolytic pathway from glucose to pyruvate costs 12.7 units with net +2 ATP (0.16 ATP per cost unit)
2. Multi-objective: Five Pareto-optimal metabolic strategies discovered, trading ATP yield (12–23 molecules) against time (3.9–8.7 min), enzyme load, and metabolic load
3. Performance: DMY reaches ~4.8× speedup over Dijkstra at n=5,000 metabolites (k=⌈n^{1/3}⌉) in the shared benchmark set

Reproducibility: run the scripts with a fixed seed (OPTIM_SP_SEED=<int> or --seed=<int>) to regenerate the exact same synthetic metabolic networks and benchmarks. Default seed is 42 when left unspecified.

Part 1: Single-Objective Analysis

Figure 1: Metabolic Network Structure

Interpretation:

• Adjacency matrix showing reaction connectivity in central metabolism
• Dark cells indicate direct enzymatic conversions
• Glycolysis forms the main pathway backbone (Glucose → Pyruvate)
• Branch points at Pyruvate lead to fermentation (Lactate) or respiration (Acetyl-CoA)

Figure 2: Enzyme Cost Analysis

Key Insights:

Figure 3: ATP Yield by Pathway

Metabolic Economics:

• Glycolysis: Net +2 ATP (fast, universal)
• Fermentation: Net +2 ATP (anaerobic, produces lactate)
• Aerobic: Net +32 ATP (slow, requires oxygen)
• PPP+Glycolysis: Net +2 ATP (produces NADPH for biosynthesis)

Part 2: Multi-Objective Pareto Front Analysis

The Challenge

Real metabolic engineering involves optimizing multiple competing objectives:

• ATP Yield: Energy production efficiency
• Time: Speed of pathway completion
• Enzyme Load: Resource allocation cost
• Byproducts: Toxic metabolite accumulation

Figure 4: 2D Pareto Front Projections

Four critical trade-offs visualized:

1. ATP vs Time: Faster pathways produce less ATP
2. ATP vs Enzyme Load: High-yield pathways require more enzymes
3. Speed vs Cleanliness: Fast fermentation produces more byproducts
4. Efficiency vs Cleanliness: Clean pathways need more enzymes

Figure 5: 3D Pareto Front Visualization

3D Trade-off Space:

• X-axis (Time): Pathway completion time (~3.9–8.7 min)
• Y-axis (ATP): Net ATP production (≈12–23 molecules)
• Z-axis (Enzyme Load): Total enzyme requirement (≈11–17 units)

Special solutions highlighted:

• Blue Star (Balanced): Weighted solution (ATP≈23.0, Time≈5.8 min, Enzyme load≈12.5 units, Byproduct≈0.85×)
• Green Annotation: “Constraint load ≤0.3× infeasible” — the ε-constraint has no feasible solution for the seeded network
• Red Hexagon (Knee Point): Highest-efficiency trade-off (ATP≈13.2, Time≈8.7 min, Enzyme load≈16.5 units, Byproduct≈0.8×)

Pareto-Optimal Metabolic Pathways

Figure 6: Metabolic Strategy Comparison

Strategy Analysis:

• Balanced: 23 ATP in 5.8 min at moderate enzyme cost (default recommendation)
• Fastest: 14.8 ATP in 3.9 min using high enzyme load (short bursts)
• High-ATP Knee: 13.2 ATP in 8.7 min with load ≈0.80× (oxygen-rich)
• Constraint: Load ≤0.30× is infeasible in current network topology

Part 3: Algorithm Performance

Figure 7: Algorithm Performance Benchmark

Benchmark results use the shared seeded dataset from examples/comprehensive_demo/run_benchmarks.jl, with k = ⌈n^{1/3}⌉ applied throughout.

Key Insights:

• DMY (k = n^{1/3}) versus Dijkstra runtimes shown with error bars
• Crossover point: DMY overtakes Dijkstra once metabolic graphs exceed ~2,000 vertices
• Larger sparse metabolomes (5,000 vertices) enjoy ~4.8× speedups
• Smaller models remain Dijkstra-friendly due to DMY's preprocessing overhead
• Benchmark data from shared seeded dataset ensures consistency across examples

Key Takeaways

Single vs Multi-Objective

• Single: One "optimal" path (glycolysis for ATP)
• Multi: Five non-dominated strategies on the Pareto front
• Reality: Cells dynamically switch between strategies

Metabolic Flexibility

• Aerobic conditions: Choose high-ATP pathways
• Anaerobic stress: Switch to fermentation
• Biosynthesis needs: Activate pentose phosphate pathway
• Balanced growth: Use knee point strategy

Algorithm Performance

• Small networks (n<1000): Use Dijkstra
• Genome-scale (n>1000): DMY increasingly superior
• Sparse metabolomes: DMY's optimal domain

Reproducibility

Generate all figures:

julia --project=. examples/metabolic_pathway/generate_figures.jl

Run complete analysis:

julia --project=. examples/metabolic_pathway/metabolic_pathway.jl

Model Parameters:

• 17 metabolites in central carbon metabolism
• 19 enzymatic reactions with measured costs
• 4 objectives: ATP, time, enzyme load, byproducts
• Steady-state flux assumptions

References

1. Duan, R., Mao, J., & Yin, Q. (2025). "Breaking the Sorting Barrier for Directed SSSP". STOC 2025.
2. Multi-objective optimization: Ehrgott, M. (2005). "Multicriteria Optimization". Springer.
3. Metabolic data: KEGG, BioCyc, and BRENDA databases.
4. Berg, J.M., Tymoczko, J.L., & Stryer, L. Biochemistry (8th Edition).

Dashboard generated using DMYShortestPath.jl - Implementing breakthrough algorithms for metabolic network analysis with multi-objective optimization