The size of an enzyme is typically not indicative of the rate of the reaction that it catalyzes. All other parameters are taken into account when considering reaction velocity.

Allosteric enzymes have multiple active sites, which affect each other. More often than not, allosteric enzymes will have sigmoidal plots when reaction velocity is plotted against enzyme concentration, and thereby display cooperativity. Cooperativity means that when one active site is bound by substrate, the other sites become easier to bind for substrate. Hemoglobin is a notable example of a protein that exhibits this type of enzyme kinetics.

Both myoglobin (Mb) and hemoglobin (Hb) use heme groups to bind to oxygen. However, Hb contains four heme groups, whereas Mb contains only one. Single-ligand binding appears as a hyperbolic curve in ligand binding graphs, whereas sigmoidal curves indicate cooperative binding. As one ligand (oxygen) binds to hemoglobin, this makes it easier and more favorable for the second oxygen to bind, and so on for the third and finally the fourth oxygen; each oxygen binding allows the one following it to bind more easily. This behavior is responsible for creating the sigmoidal curve - the slope of the curve increases with pressure, indicating better binding capability, up to the point where the Hb starts to become totally saturated with oxygen molecules.

A catalyst works to speed up a reaction by lowering the Ea (activation energy), which is related to chemical kinetics. A catalyst has nothing to do with thermodynamics, and can neither change the of a reaction, nor make a non-spontaneous one occur.

Additionally, by definition a catalyst is not consumed in a reaction, and it is regenerated after the reaction occurs. This allows for the possibility of a catalyst having an enormous impact on the rate of a reaction, as it is can once again exert its effects after being regenerated.

Enzymes are substrate specific molecules that lower the activation energy and increase the reaction rate of product formation. Enzymes do not change the equilibrium of product formation; this characteristic stays the same under the influence of enzymes.

Apoenzymes are holoenzymes without a coenzyme. There are no prosthetic enzymes, only prosthetic groups. Phosphorylases generally remove phosphate groups from substrates, and kinases generally add phosphate groups to substrates.

Covalent modification - e.g phosphorylating a molecule to activate it.

Proteolytic cleavage - e.g zymogen becoming activated when cleaved.

Association with other polypeptides - e.g enzyme may have both catalytic and regulatory subunits - regulatory controls activity of the catalytic.

Allosteric regulation - e.g allosteric site on an enzyme that can become bound by a molecule, altering the protein's function.

From the answer choices, we see that there are a variety of constants that we're presented with. However, it is the Michaelis constant that signifies the amount of substrate at which an enzymatic reaction will be at half of its maximum value. The other constants, though related in some way to enzymatic reactions, do not answer the question.

The rate constant signifies the reaction rate at any given point in time, while the equilibrium constant is a thermodynamic value that tells us the spontaneity of the reaction.

A first order reaction is one in which the amount of product is dependent on only one reactant. For instance:

The above reaction is first order because the amount of product produced depends solely on the concentration of A. Therefore, a first order reaction is one in which the reaction is directly proportional to the reactant concentration.

Note: bimolecular reaction and second order reaction are synonymous.

is the maximal velocity of an enzyme-catalyzed reaction. This occurs when all active sites of enzymes are occupied with substrate, and new openings will be filled immediately from the excess substrate. The enzyme is saturated with excessive substrate, so the reaction velocity no longer depends on substrate concentration.