Calculator
Formula used
This tool assumes first-order decay of mRNA abundance over time.
- C(t) = C0 e-k t
- t1/2 = \ln(2)/k
- \tau = 1/k (mean lifetime)
- Multi-point fit uses \ln C(t) = b - k t with linear regression.
Tip: background subtraction can model constant detection bias, but too much subtraction can distort early points.
How to use this calculator
- Select an estimation method that matches your data.
- Choose the time unit used in your measurements.
- Optional: enter a background level to subtract.
- For regression, paste your time-course points line by line.
- Press Compute Half-Life to view results above.
- Use the export buttons to download CSV or PDF.
Professional notes on mRNA half-life estimation
1) Why half-life is a useful kinetic summary
Half-life condenses an exponential decay curve into one interpretable number. Values can span minutes to many hours depending on organism and cell state. A practical planning range is 0.2–10 hours, corresponding to k ≈ 0.058–0.0012 min-1 when time is in minutes.
2) The first-order model behind the calculator
The default model assumes first-order loss, where the degradation rate is proportional to current abundance: C(t)=C0·e-kt. This is often reasonable after transcription is halted or after a pulse-labeling window. Deviations may occur with processing delays, feedback, or multiple pathways.
3) Sampling design and data density
For reliable estimation, collect enough points to be linear on a log scale. Three points are the minimum for regression, but 5–8 points typically stabilize k. Spacing times near 0.5×, 1×, 2×, and 3× the expected half-life provides strong leverage for the fit. Include replicates when possible to quantify technical variation.
4) Normalization, background, and detection limits
Levels can be raw counts, normalized expression, or relative fractions. Keep units consistent across time points. Background subtraction can correct a constant offset, but excessive subtraction can produce non-positive values. The clamp option prevents log failures and highlights when values approach the detection floor.
5) Two-point versus multi-point regression
Two-point estimates are fast but sensitive because k depends on a single ratio. Multi-point regression uses all points and reports fit quality. Regression often reduces uncertainty and provides residuals that identify problematic time points or batch effects.
6) Interpreting k, mean lifetime, and half-life
The decay constant k is the fundamental parameter; half-life is ln(2)/k, and mean lifetime is 1/k. If k is 0.023 min-1, half-life is about 30 minutes and mean lifetime about 43 minutes. Converting units only changes scale, not biology.
7) Using R² and residuals for quality control
In log-linear fitting, a high R² indicates that ln(C) is well explained by time, but it does not guarantee correctness. Inspect residuals: systematic patterns suggest non-exponential behavior, while isolated spikes suggest outliers. If R² is low, add points or revisit normalization.
8) Reporting results and exporting for documentation
For traceable reporting, record method, time unit, k, half-life, and background correction. When a confidence interval is available, include it alongside R² and the time points. The CSV export supports plotting and archiving, while the PDF provides a compact summary for sharing.
FAQs
1) What inputs should I use for “level”?
Use any positive quantity proportional to abundance: normalized expression, molecule counts, or relative fraction. Consistency across time points matters more than absolute units.
2) Why does the regression use ln(level)?
Exponential decay becomes linear on a log scale: ln(C)=b−kt. Linear regression then estimates the slope, which maps directly to k.
3) When should I choose the two-point method?
Use it when you only have two reliable measurements or need a quick sanity check. For publication-quality estimates, multi-point regression is typically more robust.
4) What does “background subtraction” represent?
It removes a constant offset from all levels, such as baseline signal or systematic noise. If subtraction makes values non-positive, reduce the background or enable clamping.
5) How should I interpret R² in this context?
R² summarizes how well time explains ln(C). Values near 1 indicate a strong log-linear trend, but you should still review residuals for patterns or outliers.
6) Why are confidence intervals sometimes blank?
Intervals require a slope standard error, which needs at least three degrees of freedom. With too few points or nearly identical times, uncertainty estimates may be unavailable.
7) Can this model handle non-exponential decay?
This calculator assumes first-order decay. If your data show multi-phase behavior, consider fitting separate regimes or using a bi-exponential or mechanistic model in a dedicated analysis workflow.