Now the idea of Kcat brings up
another thing for us to think about
and enzymes are really remarkable. Okay?
We have seen that enzymes can speed up
reactions mind-boggling numbers of times.
And we have also introduced the concept here of
an enzyme having affinity for its substrate.
The idea of what a perfect
enzyme would mean,
starts to come into shape. We think
about "What would be a perfect enzyme"?
A perfect enzyme would be an enzyme
that would have as much velocity as possible
with as great an affinity for its substrate
as possible. Meaning that
to get them maximum velocity it wouldn't
take very much substrate;
because, the enzyme would be grabbing substrate
and converting it into product very readily.
So a perfect enzyme
would have a high velocity and a low Km.
Well we use Kcat as our measure of velocity
and Km is our measure of affinity for substrate.
High Kcat means high velocity,
low Km means high affinity.
The perfect enzyme will have
a large ratio of Kcat to Km.
So if we take those two numbers and we divide them
by each other, and we start by comparing enzymes,
we see enzymes have widely
varying ratios of Kcat/Km.
But we also see that there
is a sort of top echelon
beyond which enzymes really don't have a number that
increases very much. Now these numbers are very a little bit
from each other. But these are really the top echelon enzymes.
They don't have a Kcat/Km value
that's significantly different
These running orders of 10th to the 7th, in one case 10th to
the 9th, but most in the range of about 10th of the 8th.
We don't see enzymes are making to
the attempt to 15th for example.
Why is that? Well, what's happened with
these enzymes is they have reached
their maximum efficiency.
They can't get any more efficient.
There are two things that limit them.
One is they can't with shape
and sequence of amino acids,
make a better active site then what
they have made by evolution.
In that sense they literally are perfect.
Mutations that change those will always
make an enzyme that's less efficient.
There is a limit to what that efficiency can
be. The second thing is really interesting.
It is believed that the reason that we reach a
max with this in addition to what I have just mentioned
is that there is something else that is
limiting about the enzymatic reaction.
And the limiting thing for these enzymes
in a solution is 1 quantity.
And that's the rate with which
the substrate can diffuse in water.
Diffusion of course happens
with the mixing that we see.
In this diffusion that's bringing
substrate into the enzyme's active site.
And though that process of diffusion can itself occur at mind-
boggling rates, that's what allows enzymes to do what they do,
it, too, has a limit.
And so these enzymes are so efficient that they
are sitting, they're waiting on water to deliver substrate
to them. That's a remarkable thing.
Alright let's take and use now of some of these parameters
that we have been talking about with respect to kinetics
and understand enzymatic reactions.
I have shown several times now the plot of Vo versus S
and we saw that was a hyperbolic curve.
And you saw in that curve that at the very
top of that, we had something called Vmax.
And if I am eyeballing that curve
I have to ask myself "Well, have I
drawn Vmax at the right place?
Is it up a little bit? Is it down a little bit?" and I
have to make a judgement call with that.
I would like to have a more precise
way of saying "What is the Vmax?"
Well, one of the tricks or tools that we used
to do this, is to actually change the
analysis of the data a little bit.
Instead of plotting Vo versus the concentration of substrate,
that is the velocity versus the concentration of substrates,
I take the same data that I had for that Vo versus S plot.
And I invert it. I invert all the datas.
So I do what's called a double reciprocal plot
or a Lineweaver Burk Plot. They were
the people who came up with this.
And when I invert the data like that, what I
discover is that the hyperbolic plot becomes linear.
Now a linear plot is much more easy for us to interpret
to determine what these values are.
When I make such a double reciprocal plot,
I create a linear plot of the data and the linear plot
of the data I can draw a line through the points
and extrapolate through the axes, the y-axis and the x-axis.
When I do, I create an intercept on a y-axis
and the y-axis has the value of 1/Vmax.
I can very quickly, of course, invert
that value and I have got Vmax.
On the x-axis the intercept is -1/Km.
So if I take whatever that value the
intercept is and I take -1 over that
I would get Km. Very simple plot. So Lineweaver Burk Plots.
And there are other manipulations that people do a graphs.
Lineweaver Burk Plots help me to very readily
determine Vmax and Km from a set of data.