PLEASE HELP FAST-enzyme had a Vmax of 1200 mM product/min and a Km of 200 mM?

Question

The famous scientist Willy Nohwit had a great fondness for Yu-Gi-Oh cards (one of those monster card games), but decided to see if he could make some money making a similar set of cards, using enzymes instead of monsters. Each card would have the name of an enzyme, along with it’s Vmax and Km (instead of a monsters attack and defense).

His favorite card was an enzyme with the made-up name of Mega-zyme.
This enzyme had a Vmax of 1200 mM product/min and a Km of 200 mM

a) What would be the rate of this enzyme when the substrate concentration is 200 mM? Why?

b) In the presence of an opposing inhibitor card, the Megazyme has a Vmax of only 800 mM, while its Km remains at 200mM. What kind of inhibition is this? Why?

c) In the absence of any inhibitor, could any concentration of substrate ever generate a rate of 2000 mM product/min in this enzyme? Why?

Answer 1

(a) using the michelis menten equation:

V= (Vmax * [S]) / (Km + [S])

and substiuting your values of Km, Vmax and [S] as 1200, 200 and 200 respectively we get a rate (V) of 600mM per sec

(b) There's two types of inhibitor: competitive and non-competitive. Competitive bind to an enzyme's active site, competing with the substrate and raising the Km of the enzyme.

Non competitive inhibitors bind allosterically (some where else besides the active site), altering the shape of the active site so that the substrate binds with less affinity to the enzyme; they lower the Vmax of an enzyme.

Your inhibitor in (b) is, therefore, a non-competitive inhibitor.

(c) No. The maximum rate of this enzyme is, as said, 1200mM per sec. This maximum rate is a reflection on 2 things:
1. how fast the substrate diffuses into the active site and how fast the product diffuses out of the active site.

2. The rate at which chemical bonds can be re-arranged.

Answer 2

Vmax is the maximum output of the enzyme in terms of product per unit time
Km is the mechaelis menten constant, it's the dissociation constant of the enzyme-substrate complex. Essentially it means how tightly the enzyme binds the substrate; lower numbers means tighter binding. Km and Vmax define how efficient and fast an enzyme is.

From wikipedia.

Reaction rate/velocity V

The speed V means the number of reactions per second that are catalyzed by an enzyme. With increasing substrate concentration [S], the enzyme is asymptotically approaching its maximum speed Vmax, but never actually reaching it. Because of that, no [S] for Vmax can be given. Instead, the characteristic value for the enzyme is defined by the substrate concentration at its half-maximum speed (Vmax/2). This KM value is also called Michaelis-Menten constant.

[edit] Michaelis constant 'KM'

Since Vmax cannot be reached at any substrate concentration (because of its asymptotic behaviour, V keeps growing at any [S], albeit ever more slowly), enzymes are usually characterized by the substrate concentration at which the rate of reaction is half its maximum. This substrate concentration is called the Michaelis-Menten constant (KM) a.k.a. Michaelis constant. This represents (for enzyme reactions exhibiting simple Michaelis-Menten kinetics) the dissociation constant (affinity for substrate) of the enzyme-substrate (ES) complex. Low values indicate that the ES complex is held together very tightly and rarely dissociates without the substrate first reacting to form product.

It is worth noting that KM can only be used to describe an enzyme's affinity for substrate when product formation is rate-limiting, i.e., when k2 << k-1 and KM becomes k-1/k1. Often, k2 >> k-1, or k2 and k-1 are comparable.[4]

The kinetics of Megazyme mean its a very fast enzyme, and only losely binds the substrate.

Here are some more hints.

a) V (velocity) = Vmax*([S]/Km+[S])

b) Answer above is right.

Inhibition; there are two broad types; reversible and irreversible. Irreversible inhibition very tightly binds (ie covalently) to the enzyme at the binding site, while reversible binds the active site losely. The former 'takes out' the enzyme, while the later just inhibits the substrate from binding to the enzyme. Reversible inhibition is either competitive, means the inhibitor binds near the active site, or noncompetitive, where the inhibitor does not bind the active site. In competitive inhibition is reversed by increased substrate concentration, whereas that's not the case with noncompetitive inhibition.

c) the answer is self-evident, given the knowledge of the Vmax.