# Lineweaver-Burk plot or double reciprocal plot: Enzyme Kinetics

Hi, this is Dr. Vijay. Today I am going to explain Lineweaver-Burk
or double reciprocal plot, from this we can easily calculate Km and Vmax. Before going to Lineweaver-Burk plot, we can
see here, which we studied in the previous video, we got here hyperbolic curve and the
equation is, the Michaelis-Menten equation is, from this hyperbolic curve, the initial
velocity is equal to maximum velocity multiplied by concentration of the substrate divided
by Km value plus concentration of the substrate. So, this equation, Michaelis-Menten equation
derived from this hyperbolic curve. You can see here from this plot, in order
to calculate Km value, we should know the maximum velocity. From the maximum velocity or Vmax, we are
going to take half the maximum velocity and then we can calculate Km value. So, from this graph practically not always
possible to achieve the maximum velocity. If you want to achieve maximum velocity, we
should have a large amount of substrates. So, it’s may be sometimes it’s not practical
to calculate Km from the maximum velocity because to achieve maximum velocity, we should
have a lot of substrates and curve itself is a hyperbolic curve Suppose we make this
equation, Michaelis-Menten equation to a linear form of graph or the linear form of equation,
then it is easy to extend that line in order to calculate either Km or Vmax. That is a Lineweaver-Burk plot or double reciprocal
plot. So, this Lineweaver-Burk plot is done by taking
this Michaelis-Menten equation. So, it is nothing but they are taking reciprocal
of this Michaelis-Menten equation. So, by taking reciprocal of this equation
we can plot what is called Lineweaver-Burk plot or double reciprocal plot. First, I’m going to explain how to derive
the equation, that is Lineweaver-Burk equation, it is nothing but reciprocal of Michaelis-Menten
equation. So, let me write first Michaelis-Menten equation,
the initial velocity or velocity is equal to maximum velocity Vmax, multiplied by the
concentration of substrate, divided by Km plus the concentration of substrate. This is Michaelis Menten equation. So, we will do reciprocal of this equation. That is one by velocity or initial velocity
is equal to, we are going to taking reciprocal of this equation, so this Km plus substrate
will come to the numerator, Vmax multiplied by concentration of substrate. If you simplify the equation, Km divided by
Vmax, times substrate concentration plus the concentration of substrate divided by Vmax,
multiplied by concentration of substrate. So, we can cancel this concentration of substrate
here. So, one by velocity is equal to Km by Vmax,
so this substrate concentration we can write one by concentration of the substrate plus
one by Vmax. So, by looking at this equation, suppose we
plot the velocity and the one by substrate concentration, we will get a linear equation. So, I’m going to show this graph, that is
double reciprocal plot. So, this equation is derived from by taking
the reciprocal of Michaelis Menten Equation. From this equation, we can easily calculate
Vmax, the reaction need not achieve the maximum velocity. If you plot one by substrate concentration
and one by velocity. Now here I am going to take, so in the X-axis
on right hand side, I’m going to take one by substrate concentration and in the Y-axis,
I’m going to take the velocity. Now I will plot a graph, suppose if you go
on increasing the one by substrate concentration and velocity also increases, so the graph
looks like this, we got a linear from of graph if you increase one by substrate concentration
the velocity also increases we got a graph here. Now if you extend this graph, so we need not
wait for the maximum velocity because this graph is a linear from. Now we will extend this graph, it will bisect
Y-axis and further if you extend is graph it will bisect the X-axis also and we got
now 2 intersection points. So, now after extending this line, this line
intercept Y-axis at a point and also it intercepts X-axis at a point. The line of intersection at the X-axis is
nothing but minus one by Km and the line which intercepts Y-axis that point is going to be
our one by Vmax. So, what we have done? we plotted the one
by substrate concentration on X-axis versus one by initial velocity on Y-axis. So, we got a graph that is linear form till
here, from here to here and we extend this line backwards, so that this line intercepts
Y-axis that intersection point is now our one be maximum velocity and still if you extend,
go on extend, it will intercept X-axis and that point going to be our minus one by Km
value. So, by using this Lineweaver-Burk plot, we
can calculate Km and Vmax very easily, that is 2 intercept points and another important
significance of this Lineweaver-Burk plot is we can study mechanism of action of enzyme
inhibitors. So, I’m going to explain in the future videos,
the enzyme inhibition by using this Lineweaver-Burk plot, that is why I made this video. So, you need to understand the Lineweaver-Burk
plot or double reciprocal plot is a just simply a reciprocal of Michaelis Menten equation,
where it is a hyperbolic plot, here in this it is a linear equation. So, by using this linear equation, we can
easily calculate Km and Vmax. We need not wait for the maximum velocity
to achieve because in order to achieve maximum velocity we require a lot of substrate concentration
and by using the equation we can easily calculate Km and Vmax and also, we can study the action
of enzyme inhibitors. So, this is about Lineweaver-Burk plot or
double reciprocal plot. Thanks for watching.