Complete Question
The complete question is shown on the first uploaded image
Answer:
[S]<<KM | [S]=KM | [S]>>KM | Not true
____________ | Half of the active | Reaction rate is | Increasing
is about | sites are filled of | independent of |
will
equal to
. | | [S] | lower KM
_____________________________________________|____________
[ES] is much | | Almost all active
lower than | | sites are filled
| |
Explanation:
Generally the combined enzyme
is mathematically represented as
![[ES] = \frac{[E_{total}][S]}{K_M + [S]}----(1)](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%5BS%5D%7D%7BK_M%20%2B%20%5BS%5D%7D----%281%29)
for Michaelis-Menten equation
Where
is the substrate concentration and
is the Michaelis constant
Considering the statement ![[S] < < K_M](https://tex.z-dn.net/?f=%5BS%5D%20%3C%20%3C%20K_M)
Looking at the equation
is denominator so it can be ignored(it is far too small compared to
) hence the above equation becomes
![[ES] = \frac{[E_{total}][S]}{K_M}](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%5BS%5D%7D%7BK_M%7D)
Since
is less than
it means that ![\frac{[S]}{K_M} < < 1](https://tex.z-dn.net/?f=%5Cfrac%7B%5BS%5D%7D%7BK_M%7D%20%20%3C%20%3C%201)
so it means that ![[ES] < < [E_{total}]](https://tex.z-dn.net/?f=%5BES%5D%20%3C%20%3C%20%5BE_%7Btotal%7D%5D)
What this means is that the number of combined enzymes
i.e the number of occupied site is very small compared to the the total sites
i.e the total enzymes concentration which means that the free sites [
i.e the concentration of free enzymes is almost equal to ![[E_{total}]](https://tex.z-dn.net/?f=%5BE_%7Btotal%7D%5D)
Considering the second statement
![[S] = K_M](https://tex.z-dn.net/?f=%5BS%5D%20%3D%20K_M)
So this means that equation one would now become
![[ES] = \frac{[E_{total}][S]}{2[S]} = \frac{[E_{total}]}{2}](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%5BS%5D%7D%7B2%5BS%5D%7D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%7D%7B2%7D)
So this means that half of the active sites that is the total enzyme concentration are filled with S
Considering the Third Statement
![[S] >>K_M](https://tex.z-dn.net/?f=%5BS%5D%20%3E%3EK_M)
In this case the
in the denominator of equation 1 would be neglected and the equation becomes
![[ES] = \frac{[E_{total}] [S]}{[S]} = [E_{total}]](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%20%5BS%5D%7D%7B%5BS%5D%7D%20%3D%20%5BE_%7Btotal%7D%5D)
This means that almost all the sites are occupied with substrate
The rate of this reaction is mathematically defined as
Where v is the rate of the reaction(also know as the velocity of the reaction at a given time t) and
is he maximum velocity of the reaction
In this case also the
at the denominator would be neglected as a result of the statement hence the equation becomes
![v = \frac{V_{max}[S]}{[S]} = V_{max}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7BV_%7Bmax%7D%5BS%5D%7D%7B%5BS%5D%7D%20%3D%20V_%7Bmax%7D)
So it means that the reaction does not depend on the concentration of substrate [S]
For the final statement(Not True ) it would match with condition that states that increasing
will lower ![K_M](https://tex.z-dn.net/?f=K_M)
This is because
does not depend on enzyme concentration it is a property of a enzyme