Cell-Free ATP Regeneration Kinetics (2D)

Reaction Status

● Active — synthesizing

Reactor Charge

Energy substrate S₀ 20 mM

Regeneration rate k_regen 0.050

Active ribosomes N 50

ATP affinity K_m 0.30 mM

Live Readouts

ATP / total pool

83%

Substrate left

20.0 mM

Protein yield

0.0 µM

Reaction time

0.0 min

How it works

Cell-free protein synthesis (CFPS) has no cell to regenerate its own ATP, so a secondary energy substrate S (e.g. phosphoenolpyruvate or creatine phosphate) rephosphorylates ADP back to ATP while ribosomes burn ATP to add amino acids to a growing chain:

dS/dt   = -k_regen · S · [ADP]
dATP/dt =  k_regen · S · [ADP]  -  N · v_max · ATP/(ATP+Km)
[ADP]   =  C_tot - ATP            (fixed adenylate pool)
dP/dt   =  N · v_max · ATP/(ATP+Km)

S₀ / k_regen — size and speed of the energy-regeneration system. A bigger, faster substrate pool keeps ATP high for longer.
N (ribosomes) — translation demand. More parallel ribosomes drain ATP faster per minute.
K_m — the ATP concentration at which translation runs at half its maximum rate (Michaelis-Menten saturation); a lower Km keeps protein production running even as ATP falls.
Once S is exhausted, regeneration stops, ATP collapses toward the ADP-dominated equilibrium, and translation — visible as the growing polypeptide chains on each ribosome — stalls. This substrate-exhaustion crash is exactly why real CFPS batch reactions plateau after 1–4 hours and why continuous-exchange (CECF) reactors that keep resupplying substrate reach far higher yields.

Note on this 2D port: the mass-action/Michaelis-Menten kinetics were checked term-by-term against the 3D original (dS/dt, dATP/dt, the fixed adenylate conservation ATP+ADP=C_tot, and dP/dt) and found internally consistent — no correction was needed. The strip chart below plots exactly these four state variables over time so the crash dynamics are visible directly, not just inferred from particle color.

ATP ADP Energy substrate Nascent protein

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