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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:
This last form of the Hill equation is advantageous because a plot of versus [] yields a linear plot, which is called a Hill plot. [ 7 ] [ 8 ] Because the slope of a Hill plot is equal to the Hill coefficient for the biochemical interaction, the slope is denoted by n H {\displaystyle n_{H}} .
The graph of this function is a line with slope and y-intercept. The functions whose graph is a line are generally called linear functions in the context of calculus . However, in linear algebra , a linear function is a function that maps a sum to the sum of the images of the summands.
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 ...
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 ...
Once the inhibitor is bound to the enzyme, the slope will be affected, as the K m either increases or decreases from the original K m of the reaction. [4] [5] [6] Most competitive inhibitors function by binding reversibly to the active site of the enzyme. [1] As a result, many sources state that this is the defining feature of competitive ...
[16] [17] [18] This 'expected' slope, as it is known, is essential for detecting allometry because scaling variables are comparisons to other things. Saying that mass scales with a slope of 5 in relation to length doesn't have much meaning unless knowing the isometric slope is 3, meaning in this case, the mass is increasing extremely fast.
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.