Metabolic Steady State: Enzyme-Kinetics Convergence (2D)

This is the 2D companion to the 3D flux-balance-analysis polytope simulator, and it deliberately answers a different question with a different, independently-computed model. The 3D scene treats the network's steady state as a static linear program: enforce mass balance as a hard constraint and jump straight to whichever vertex of the feasible polytope maximizes a chosen objective. This simulator instead asks how a real network actually arrives at (or fails to reach) that steady state, by integrating explicit Michaelis-Menten enzyme kinetics forward in time with a fourth-order Runge-Kutta solver: an intermediate metabolite pool B is filled by a constant uptake rate and drained by two competing saturable enzymes, and its concentration relaxes dynamically toward the point where total drain equals total uptake. Adjust each branch's maximum rate and the byproduct enzyme's substrate affinity to watch the flux split shift in real time, or push uptake past the branches' combined capacity to see the pool accumulate indefinitely instead of settling — a genuine dynamical-systems view of the same phenomenon the 3D polytope only shows in its final, static form.