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A slope greater than one thus indicates positively cooperative binding between the receptor and the ligand, while a slope less than one indicates negatively cooperative binding. Transformations of equations into linear forms such as this were very useful before the widespread use of computers, as they allowed researchers to determine parameters ...
The first description of cooperative binding to a multi-site protein was developed by A.V. Hill. [4] Drawing on observations of oxygen binding to hemoglobin and the idea that cooperativity arose from the aggregation of hemoglobin molecules, each one binding one oxygen molecule, Hill suggested a phenomenological equation that has since been named after him:
Given two different points (x 1, y 1) and (x 2, y 2), there is exactly one line that passes through them. There are several ways to write a linear equation of this line. If x 1 ≠ x 2, the slope of the line is . Thus, a point-slope form is [3]
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...
Ecologists have proposed a wide range of factors determining the slope and elevation of the species–area relationship. [2] These factors include the relative balance between immigration and extinction, [ 3 ] rate and magnitude of disturbance on small vs. large areas, [ 3 ] predator-prey dynamics, [ 4 ] and clustering of individuals of the ...
Specifically, a straight line on a log–log plot containing points (x 0, F 0) and (x 1, F 1) will have the function: = (/) (/), Of course, the inverse is true too: any function of the form = will have a straight line as its log–log graph representation, where the slope of the line is m.
Progress curve for an enzyme reaction. The slope in the initial rate period is the initial rate of reaction v. The Michaelis–Menten equation describes how this slope varies with the concentration of substrate. Enzyme assays are laboratory procedures that measure the rate of enzyme reactions. Since enzymes are not consumed by the reactions ...
From this plot, − Δ r H / R is the slope, and Δ r S / R is the intercept of the linear fit. By measuring the equilibrium constant , K eq , at different temperatures, the Van 't Hoff plot can be used to assess a reaction when temperature changes.