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| In [[biochemistry]], an '''Eadie–Hofstee diagram''' (also '''Woolf–Eadie–Augustinsson–Hofstee''' or '''Eadie–Augustinsson plot''') is a graphical representation of [[enzyme kinetics]] in which [[reaction rate]] is plotted as a [[Function (mathematics)|function]] of the ratio between rate and [[substrate (biochemistry)|substrate]] [[concentration]]:
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| :<math>v = -K_m { v \over [S] } + V_\max</math> | | Look at my webpage: clash of clans hack android ([http://circuspartypanama.com sneak a peek at this web-site.]) |
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| where ''v'' represents reaction rate, ''K<sub>m</sub>'' is the [[Michaelis–Menten constant]], [''S''] is the substrate concentration, and ''V''<sub>max</sub> is the maximum reaction rate.
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| It can be derived from the Michaelis–Menten equation as follows:
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| :<math>v = {{V_\max{} [S]} \over {K_m + [S]}}</math>
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| invert and multiply with <math>V_\max</math>:
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| :<math> {V_\max \over v} = {{V_\max{}(K_m+[S])}\over{V_\max{}[S]}} = {{K_m+[S]}\over{[S]}}</math>
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| Rearrange:
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| :<math> V_\max = {{{vK_m} \over {[S]}} + {{v[S]} \over {[S]}}} = {{vK_m}\over {[S]}} + v</math>
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| Isolate v:
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| :<math>v = -K_m{v \over {[S]}} + V_\max</math>
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| A plot of v against ''v''/[S] will hence yield ''V''<sub>max</sub> as the y-intercept, ''V''<sub>max</sub>/K<sub>m</sub> as the x-intercept, and ''K<sub>m</sub>'' as the negative slope. Like other techniques that linearize the [[Michaelis–Menten equation]], the Eadie-Hofstee plot was used historically for rapid identification of important kinetic terms like ''K<sub>m</sub>'' and ''V''<sub>max</sub>, but has been superseded by [[nonlinear regression]] methods that are significantly more accurate and no longer computationally inaccessible. It is also more robust against error-prone data than the [[Lineweaver–Burk plot]], particularly because it gives equal weight to data points in any range of substrate concentration or reaction rate. (The Lineweaver–Burk plot unevenly weights such points.) Both plots remain useful as a means to present data graphically.
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| One drawback from the Eadie–Hofstee approach is that neither [[ordinate]] nor [[abscissa]] represent [[independent variable]]s: both are dependent on reaction rate. Thus any experimental error will be present in both axes. Also, experimental error or [[Propagation of uncertainty|uncertainty will propagate]] unevenly and become larger over the [[abscissa]] thereby giving more weight to smaller values of ''v''/[S]. Therefore, the typical measure of goodness of fit for [[linear regression]], the correlation coefficient ''R'', is not applicable.
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| ==See also==
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| * [[Michaelis–Menten equation]]
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| * [[Lineweaver–Burk plot]]
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| * [[Hanes–Woolf plot]]
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| ==References==
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| * {{cite journal | last = Eadie | first = GS | year = 1942 | title = The Inhibition of Cholinesterase by Physostigmine and Prostigmine | journal = Journal of Biological Chemistry | volume = 146 | pages = 85–93}}
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| * {{cite journal | last = Hofstee | first = BHJ | year = 1959 | title = Non-Inverted Versus Inverted Plots in Enzyme Kinetics | journal = Nature | pmid = 14402470 | volume = 184 | pages = 1296–1298 | doi = 10.1038/1841296b0 | issue=4695}}
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| * {{cite journal | last = Dowd | first = JE | coauthors = and Riggs, DS | year = 1965 | title = A Comparison of Estimates of Michaelis–Menten Kinetic Constants from Various Linear Transformations | journal = Journal of Biological Chemistry | volume = 240 | pages = 863–869 | pmid = 14275146}}
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| * {{cite journal | last = Atkins | first = GL | coauthors = and Nimmo, IA | year = 1975 | title = A comparison of seven methods for fitting the Michaelis–Menten equation | journal = Biochemical Journal | volume = 149 | issue = 3 | pages = 775–777 | pmid = 1201002 | pmc = 1165686}}
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| {{DEFAULTSORT:Eadie-Hofstee diagram}}
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| [[Category:Diagrams]]
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| [[Category:Enzyme kinetics]]
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