Kinetics

Choose the method that matches your measurements: Michaelis-Menten for initial velocity versus substrate concentration, logistic or exponential models for growth, or an initial-slope calculation for a kinetic trace. Each selected dataset retains its fitted quantities and method settings.

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 the fitted Vmax under this model. It is not generally a direct binding-affinity measurement.

Gradiance fits Michaelis-Menten directly with non-linear regression and reports Km, Vmax, R², RMSE, and AIC. When the fitted covariance supports them, it also reports local 95% Student-t intervals for Km and Vmax. The supported result contains the direct nonlinear curve; it does not produce Lineweaver-Burk or Eadie-Hofstee plots.

What you need

• Substrate concentrations including at least two distinct positive values. Use enough range to assess whether the response approaches saturation; no fixed range guarantees an identifiable fit.
• Initial velocities measured in a suitable early time window. Kinetic ELISA can estimate a slope from each trace; using those slopes in a separate substrate-response fit requires matching units and an appropriate experimental design.
• At least three total observations, with explicit substrate and rate units. Preserve replicate identifiers and confirm whether observations are fitted individually or averaged by substrate concentration.

Substrate inhibition

A response that peaks and then declines at high [S] is not described by the supported Michaelis-Menten method. Substrate-inhibition models and Ki estimation are outside the supported launch contract; the system should refuse that request rather than substitute a basic fit.

Growth curves

Supply time and response for one growth series and choose a model. Logistic fitting estimates lower and upper plateaus, a growth-rate parameter, and midpoint time. Exponential fitting estimates the starting response and rate over the selected growth phase. Neither model silently replaces the other.

• Logistic: use a time range covering the transition and plateau.
• Exponential: select the phase where exponential growth is scientifically plausible.

At least four distinct timepoints are required. Record time and response units and any media-blank correction. The result includes the fitted curve, parameters, R², RMSE, and doubling time when the estimated rate is positive. Logistic lag time is a model-derived tangent estimate. Sparse sampling or missing plateaus can leave these quantities poorly determined; no parameter confidence intervals are asserted by this method.

Kinetic ELISA / time-course initial slopes

Analyze one well or trace per selected dataset. Supply time and signal with at least four distinct timepoints. The calculator sorts time, starts with the first 30% of observations (at least four), and expands the window while checking linear-fit R². The starting fraction and R² threshold are configurable method options, with defaults of 0.3 and 0.98.

The result records the initial slope, intercept, number of fitted points, and R² alongside the observations and selected linear fit. Review the chosen window for lag, saturation, and substrate depletion. A low-R² or nonpositive slope receives a warning. This data-dependent window rule does not establish a protocol-valid initial-rate interval; use the experimental context to select and review the supplied trace.

The slope has signal-per-time units. It becomes an input to a separate Michaelis-Menten analysis only when traces represent comparable initial rates at known substrate concentrations. That second calculation does not automatically propagate the first-stage slope uncertainty.

Checks recorded for supported Michaelis-Menten fits

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

• Possible missing saturation. The calculator warns when the highest substrate concentration is below three times the fitted Km. Vmax and Km may be poorly constrained.
• Low R². Michaelis-Menten warns below 0.90. This is a review prompt, not a universal experimental-quality threshold.
• Interval unavailable. Too few residual degrees of freedom or near-singular covariance can prevent interval estimation. The warning does not identify the experimental cause.

What the result looks like

A successful supported Michaelis-Menten run returns one nonlinear curve, Km, Vmax, fit statistics, and any estimable parameter intervals. Growth returns its selected model and curve; kinetic ELISA returns the initial-slope fit. Free accounts include 20 free runs per calendar month (UTC) and can export PNG and basic CSV results. Entitled accounts may also export a Python saved-fit replay, which does not rerun preprocessing or refit the original data. See Understanding your results for reading the result panel.