Question #fe76a

2 Answers
Apr 6, 2015

The slope represents #K_"m"/V_("max")#.

The starting curve for your double reciprocal plot is actually the Michaelis-Menten Plot, which looks like this

http://chemwiki.ucdavis.edu/Biological_Chemistry/Catalysts/Enzymatic_Kinetics/Michaelis-Menten_Kinetics_1

The above plot shows the rate of an enzyme-catalyzed reaction, #V#, as a function of the substrate concentration, #[S]#.

The equation plotted looks like this

#V = (V_("max") * [S])/(K_m + [S])#, where

#V_("max")# - the maximum rate of the reaction;
#K_m# - the substrate concentration when the rate is equal to #V_("max")/2#.

Now, you need to get from #V# and #[S]# to #1/V# and #1/([S])#, so just use the multiplicative inverse of the above equation to get

#1/V = (K_m + [S])/(V_("max") * [S])#

#1/V = K_m/(V_("max") * [S]) + cancel([S])/(cancel([S]) * V_("max"))#

#1/V = K_m/(V_("max") * [S]) + 1/V_("max")#

Now, to get to slope, think of the #y = mx + b" "# equation for a line

#underbrace(1/V)_("y") = underbrace(K_m/V_("max"))_(color(red)(m)) * underbrace(1/([S]))_text(x) + underbrace(1/(V_max))_(b)#

This plot is called the Lineweaver-Burk plot and it looks like this

http://themedicalbiochemistrypage.org/enzyme-kinetics.php

Apr 6, 2015

The slope is equal to #K_"m""/"V_"max"#.

A double reciprocal plot is used for analyzing enzyme kinetics.

It is a useful method for analyzing the Michaelis-Menten equation:

#V = (V_"max"[S])/(K_"m" + [S])#

where #V# is the reaction velocity, #V_"max"# is the maximum reaction velocity, #[S]# is the substrate concentration, and #K_"m"# is the Michaelis-Menten constant.

Taking the reciprocal gives

#1/V = (K_"m" + [S])/(V_"max"[S]) = K_"m"/V_"max" 1/([S]) + 1/V_"max"#

The equation is of the form #y = mx + b#

where #y = 1/V#, #m = K_"m"/V_"max"#, #x = 1/([S])#, and #b = 1/V_"max"#.

A plot of #y# vs #x# or #1/V# vs #1/([S])# is called a double reciprocal plot or a Lineweaver-Burk plot.

themedicalbiochemistrypage.org

The #x#-intercept is #-1/K_"m"#.

The #y#-intercept #b = 1/V_"max"#.

And the slope #m = K_"m"/V_"max"#.