2. Biochemical reactions are aided by enzymes.
 Lysozyme is a good example of catalysis by a simple enzyme.
("Cartoon of lysozyme working") and
("Mechanism of lysozyme reaction")
 MichaelisMenten kinetics describes many enzymes which follow a simple reaction scheme of E + S <> ES > E + P, where E is enzyme, S is substrate, ES is the bound enzymesubstrate complex, and P is the product.(fig. 323, Lodish) (fig. 322a, Lodish) (fig. 322b, Lodish).
("Reaction rate vs. substrate concentration")

With this reaction scheme and three additional assumptions:
 1) The rate constant of the reaction, E + P > EP, is zero,
 2) S >> E, and
 3) steady state conditions,
the chemical reaction equations can be
solved to give the fundamental equation of MichaelisMenten kinetics:
V = V_{max} 
[S]
[S]+K_{m}



where V is the velocity of the reaction  the rate of product formation
in mMoles/litersecond. The constants V_{max} and K_{m} characterize the
particular reaction  For example the value of K_{m} depends upon the
values of the rate constants for the reaction. Note that V_{max} is the
maximum velocity  which is approached as substrate concentration
approaches infinity.

I've simulated a laboratory experiment with an enzyme catalyzed reaction where conditions 1) and 2) (above) are met but without the assumption of steady state kinetics. Notice that the particular starting concentrations and rate constants used in my example (typical of real reactions) results in very close to steadystate conditions for the enzymesubstrate complex. (The left panel shows substrate concentration in orange and product concentration in blue. The right panel shows enzyme concentration.)
The following is the same enzyme kinetics scheme modified to permit product to combine with enzyme to go backwards to form enzymesubstrate complex. Notice that we now have typical equilibrium kinetics, with exponential rise and fall of concentrations to nonzero equilibrium levels. However, real enzymes usually don't permit product to combine with the enzyme.
 Competitive inhibitors increase the apparent K_{M} while V_{max} is unchanged. Noncompetitive inhibitors decrease the apparent V_{max} while K_{M} is unchanged. Look at this
picture to see how the V vs. S plot changes when inhibitors are present.
 A
LineweaverBurke plot can help determine if an enzyme obeys MichaelisMenten kinetics. LineweaverBurke replotted MichaelisMenten data by plotting 1/V vs. 1/S instead of V vs. S. When data points are replotted on the 1/V vs. 1/S plot, they lie on a straight line IF the data obey MichaelisMenten kinetics. Your instructor will discuss how the following cases are related to the V vs. S plots. This first graph represents MichaelisMenten kinetics with increasing concentrations of a competitive inhibitor:
and the second plot with increasing concentrations of a noncompetitive inhibitor:
 (Obtain the algebraic expressions for the slope and intercept of an EadieHofstee plot. There will be a question about this on the first exam. Hint  either rearrange the MichaelisMenten equation to derive the answers yourself or search the web to find the answers.)
 Some enzymes are multisubunit. These "allosteric" enzymes have a sigmoid (Sshaped) relationship between reaction velocity and substrate concentration.
One of the relationships above is for an enzyme plus substrate alone, one is for an enzyme acting in presence of an inhibitor, and the remaining curve is for an enzyme acting in the presence of an activator. Do you know which is which? Do you see how a small change in enzyme structure and the resulting small change in the V vs. S relationship can cause a large change in reaction velocity?)
(Compare MichaelisMenten and allosteric kinetics to oxygen binding by myoglobin and hemoglobin. Myoglobin has a binding curve identical in shape to that for MichaelisMenten kinetics but hemoglobin has an sigmoid binding curve, like the V vs S relationship for allosteric enzymes.)
 Aspartate Transcarbamoylase (ATCase) is a multisubunit enzyme that catalyzes a reaction which leads to the synthesis of the pyrimidine ring of C, U, and T nucleotides. CTP, one of these products, is an inhibitor of this enzyme and ATP is an activator.