Kinetics

Three workflows fit time-resolved data in Gradiance. Each answers a different question — about an enzyme, a population, or a signal — but all three rely on initial-rate or curve-fit machinery you can switch between with one prompt.

Enzyme Kinetics (Michaelis-Menten)

The model

Initial reaction velocity v as a function of substrate concentration [S]:

v = (Vmax * [S]) / (Km + [S])

• Vmax — maximum velocity at saturating substrate
• Km — substrate concentration at half-Vmax. Lower means tighter binding.

Gradiance fits Michaelis-Menten directly with non-linear regression and reports both parameters with 95% CIs from the covariance matrix. Lineweaver-Burk and Eadie-Hofstee plots are produced for diagnostics, but the parameter estimates come from the non-linear fit, not from the linearized transforms (which bias toward the low-substrate points).

What you need

• Substrate concentrations spanning the expected Km — at minimum from 0.2× to 5× Km, ideally to 10×.
• Initial velocities, not endpoint signal. If you have time-course traces per well, see Kinetic ELISA below for getting initial slopes from them.
• Triplicate per substrate concentration is plenty.

Substrate inhibition

If your Vmax appears to peak and then decline at high [S], you likely have substrate inhibition. Tell the agent “fit with substrate inhibition” and it will use the Haldane equation (adds a Ki term). The classic Michaelis-Menten will fit to that data, but Vmax and Km will be biased.

Growth Curves

The models

Two models cover most bacterial and cell-line growth data:

• Logistic. S-shaped curve with a carrying capacity. Right when growth flattens at confluence or stationary phase.
• Gompertz. Asymmetric S-curve. Often a better fit for bacterial OD₆₀₀ data, where the deceleration into stationary phase is gradual.

What you get

• Doubling time — derived from the maximum specific growth rate.
• Lag phase — time before exponential growth begins.
• Maximum OD / density — the carrying capacity.

What you need

• A time column and a density column (OD₆₀₀, cell count, RFU, whatever your readout is).
• Media-only blanks plated alongside growth wells. The agent subtracts these to separate organism signal from media drift.
• Enough timepoints to capture lag, exponential, and stationary phases. Sparse sampling produces large CIs on doubling time.

Kinetic ELISA / Time-course initial slopes

What it does

For each well, fit the linear (or near-linear) early portion of the response curve and report the initial slope (v₀). Used when endpoint signal saturates and a real comparison needs the early-rate regime.

What you need

• One reading per well per timepoint, with timepoints in minutes (or seconds — units don't matter as long as they're consistent).
• Enough early timepoints to define a linear regime. The agent picks the linear window automatically; you can override (“use the first 5 minutes”).

What you get

• Initial slope per well, with a fit R² so you can see how linear the early phase actually was.
• When a time column varies signal across substrate concentrations (a kinetic ELISA-style design), this feeds directly into a Michaelis-Menten fit on the slopes.

Common QC for time-resolved fits

See Quality Control for the full list. Specific to kinetics:

• Vmax extrapolated. Your highest substrate concentration didn't reach saturation. Add a higher dose or accept the wider CI on Vmax.
• Lag-phase bleed-through. If the first few timepoints of a growth curve are still in lag, dropping them can dramatically tighten the fit. The agent will suggest this when residuals are systematically positive at early time.
• Non-linear initial rate. If the early portion of a kinetic ELISA already shows curvature, your “initial slope” is actually a chord — sample faster, or accept that the rate is concentration-dependent at all timepoints.

What the result looks like

Michaelis-Menten runs return Km and Vmax with 95% CIs and the diagnostic Lineweaver-Burk / Eadie-Hofstee plots. Growth runs return doubling time, lag, and carrying capacity. Kinetic ELISA runs return per-well initial slopes (and a downstream Michaelis-Menten if substrate-varied). Every run exports a figure, parameter table, and a Python script that reproduces the analysis. See Understanding your results for reading the result panel.