Dose Response Curve

Dose Response Curve


The dose–response relationship, or exposure–response relationship, describes the change in effect on an organism caused by differing levels of exposure (or doses) to a stressor (usually a chemical) after a certain exposure time, or to a food. This may apply to individuals (e.g., the dose makes the poison: a small amount has no significant effect, a large amount is fatal), or to populations (e.g.: how many people or organisms are affected at different levels of exposure).

Studying dose response, and developing dose–response models, is central to determining "safe", "hazardous" and (where relevant) beneficial levels and dosages for drugs, pollutants, foods, and other substances to which humans or other organisms are exposed. These conclusions are often the basis for public policy.

The U.S. Environmental Protection Agency has developed extensive guidance and reports on dose-response modeling and assessment, as well as software. The U.S. Food and Drug Administration also has guidance to elucidate dose-response relationships during drug development.

A dose–response curve is a simple X–Y graph relating the magnitude of a stressor (e.g. concentration of a pollutant, amount of a drug, temperature, intensity of radiation) to the response of the receptor (e.g. organism or population under study). The response may be a physiological or biochemical response, or even death (mortality), and thus can be counts (or proportion, e.g., mortality rate), ordered descriptive categories (e.g., severity of a lesion), or continuous measurements (e.g., blood pressure).[4] A number of effects (or endpoints) can be studied, often at different organizational levels (e.g., population, whole animal, tissue, cell).

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Labii has developed a widget Dose Response Curve to perform dose-response relationship analysis. We have simply the whole process into 3 steps.

Step 1: Prepare Layout

96-well plate layout is supported.

You can prepare the layout in 3 ways:

  1. Click Edit Plate

  2. Update layout value

    1. Type in the layout into the layout wells

    2. Copy the layout from your excel/word and paste them into the layout wells

    3. Drag and drop and select a table format files you already have, the widget will import the data from your file.

  3. Click Save

  4. Click the edit icon to update the dilute factors, default to 1. Use this field to document how the samples been diluted.

When preparing the layout, here are a few rules to follow:

  1. Use the first cell as the concentration unit. For example ug/ml.

  2. Use CONC to mark a serious of standard concentration in either the first column or first row.

  3. Use BLANK to mark a well as blank. The BLANK value will be used to subtract the background signal.

  4. Use POSITIVE to mark a well as positive (upper) control.

  5. The same name is treated as duplicates.

  6. Leave a well blank to exclude the data point in the analysis.

Step 2: Prepare ELISA Data

The process to prepare the value is very similar to prepare the layout. Simply copy the response data into the 96 wells and it is ready to go.

Leave a well empty to exclude the well in analysis.

Step 3: Analyze

Once the data is ready, to perform the dose response curve is as simple as a click. Click the Analysis button and the analysis will start right away. All results will be included in the analysis section once finished. The analysis only takes a few seconds.

Here are the details about the analysis:

1. Generate the average response of blanks.

Labii will use the layout you created at step 1 to find all blank wells. The average value will be calculated and displayed back to you.

2. Generate the average response of positive controls.

Similar to the blanks, the positive wells, and their average value will be generated.

The positive control is optional. If provided, they can be used to transform the response value to the percentage (%) in final data analysis.

3. Subtract background absorbance and apply data transformation.

The response data will first subtract the background value (average_blank), and apply data transformation if provided.

Labii support the following data transformation methods, you can click the "edit" icon to change it:

  • x

  • log(x)

  • log10(x)

  • 10^x

  • (x/POSITIVE)*100

The transformed data will be displayed and can be downloaded.

4. Fit the standard curve with 4PL.

Four-parameter logistic (4PL) curve is a regression model often used to analyze bioassays such as ELISA. They follow a sigmoidal, or "s", shaped curve. This type of curve is particularly useful for characterizing bioassays because bioassays are often only linear across a specific range of concentration magnitudes. Beyond this linear range, the responses quickly plateau and approach the minimum and maximum.

Four parameter logistic curve refers to the following four parameters:

  • Minimum: the point of smallest response; can be baseline response, control or response when treatment concentration is zero.

  • Maximum: the point of greatest response

  • Inflection point: the dose at which the curvature of the response line changes; where the rate of change switches signs; often referred to as the IC50 or EC50

  • Hill slope: the slope of the curve at the inflection point

Levenberg–Marquardt algorithm is used to fit the curve. The initial value for each parameter can be modified for each sample by clicking the "edit" icon. This is useful in cases with multiple minima, the algorithm converges to the global minimum only if the initial guess is already somewhat close to the final solution.

5. Plot the dose response curve.

Each of the data point, as well as the estimate plot will be generated. Labii also generated the standard error for each data points if duplicates exist.

The X-Axis can be scaled for better display, you can do so via clicking "edit" icon:

  • x

  • log(x)

  • log10(x)

  • 10^x

6. Calculate EC50(IC50), Hill slope, Minimal and Maximum response.

The final calculated value will be display for further use.


For advanced settings, you have the option to:

  • Transform the response value

  • Set the scale of X-Axis

  • Add the initial settings parameters for one or more sample.


Please note the Levenberg–Marquardt algorithm is designed to find the curve for the best fit. However, as mentioned above, some data that contains multiple minima might end up the algorithm not finding the best fit. See the picture below:

Update or try a different initial guess might be helpful to find the best fitting.

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