Linear Sigmoidal Curve
Linear Sigmoidal Curve - Related Videos
01:28
Elasticity of a Linear Demand Curve
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2024
A linear demand curve, which plots the relationship between price and quantity demanded, is a straight line, but the elasticity along this line is not constant. This means that the responsiveness of consumers to price changes varies at different points on the line. Vertical Intercept: Quantity demanded is zero; elasticity theoretically approaches infinity due to division by zero, making it not directly calculable. Elastic Demand Zone: Between the vertical intercept and the midpoint, demand is...
01:20
Calibration Curves: Linear Least Squares
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2024
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably. For data that follow a straight line, the standard method for fitting is the linear...
07:43
Calibration Curves
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2023
Source: Laboratory of Dr. B. Jill Venton - University of Virginia Calibration curves are used to understand the instrumental response to an analyte and predict the concentration in an unknown sample. Generally, a set of standard samples are made at various concentrations with a range than includes the unknown of interest and the instrumental response at each concentration is recorded. For more accuracy and to understand the error, the response at each concentration can be repeated so an error...
06:35
Linearization of the Bradford Protein Assay
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Cited by 292 •
2010
The accuracy and sensitivity of protein determination by the rapid and convenient Bradford assay is compromised by intrinsic nonlinearity. We show a simple linearization procedure that greatly increases the accuracy, improves the sensitivity of the assay about 10-fold, and significantly reduces interference by detergents.
02:44
Heating and Cooling Curves
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2020
When a substance—isolated from its environment—is subjected to heat changes, corresponding changes in temperature and phase of the substance is observed; this is graphically represented by heating and cooling curves. For instance, the addition of heat raises the temperature of a solid; the amount of heat absorbed depends on the heat capacity of the solid (q = mcsolidΔT). According to thermochemistry, the relation between the amount of heat absorbed or released by a substance, q, and its...
FAQs
The slope, midpoint, and lower and upper limits are the main interpretive parameters. Slope describes how sharply response changes, the midpoint locates the central transition, and the limits identify the response boundaries approached at low and high input values. Together, these parameters allow investigators to compare curve shape, position, and usable measurement behavior across clinical experiments.
Near the inflection point, small changes in input correspond to the most rapid changes in measured response. The curve is approximately linear in this central region, making it especially useful for relating changes in concentration, analyte level, or stimulus intensity to changes in outcome. Outside that region, the changing curvature must be considered when interpreting response differences.
The asymptotes matter because they indicate where additional input produces progressively less change in response. Measurements near either boundary may therefore provide less useful separation between input levels than measurements in the central portion. Recognizing these limits helps investigators identify the range in which a clinical assay or pharmacological comparison can meaningfully distinguish responses.
Curve fitting begins with paired measurements of the varying input and clinical response, followed by estimation of the model parameters that best describe their relationship. Investigators then examine the fitted slope, midpoint, and limits, with attention to the central approximately linear region. This workflow converts response data into a model that can support calibration, dose-response analysis, or biomarker interpretation.
In assay calibration, the fitted relationship connects analyte level with the measured clinical signal and identifies the portion where that relationship is approximately linear. The model’s midpoint, slope, and response limits help characterize calibration behavior. This supports selection of a useful operating range and interpretation of measurements without treating every part of the curve as equally responsive.
With dose-response data, the model helps quantify how clinical response changes as drug concentration varies. Researchers can use the fitted relationship to compare treatments, examine differences in sensitivity, and locate the input range in which response changes are most informative. The curve therefore provides a structured way to interpret pharmacological measurements beyond isolated response values.