Bke2 Biochemistry Exercises

Suggested answers to Group Excercise: Enzyme structure and function

a) Which of the amino acids Asp, Glu, Lys, Ser, or Tyr is most likely to be involved in binding pyruvate to the enzyme pyruvate dehydrogenase? Why?
b) Which of the amino acids Asp, Glu, His, Lys, or Arg is most ideally suited to participate in acid-base catalysis near neutral pH? Why?

Answer:
a) Lysine. Pyruvate is negatively charged, and lysine has a positively charged side chain (none of the other choices do). Charge-charge interactions are common in substrate-enzyme interactions.
b) Histidine, because it has a pKa near 7 (pKa = 6 to 7 in most cases). The two protonatable groups of the imidaloze ring can function as hydrogen bond donors and acceptors over a wide range of pH.
Describe each of the four major "modes" of enzymatic catalysis. What is the estimated rate acceleration from each of these modes?

Answer:
The overall rate accelerations achieved by enzymes are typically 10⁸ - 10¹². Chemical modes of catalysis provide rate enhancements of about 10 - 100. Effects due to binding and orientation of the reactants provides the rest.

Chemical modes of catalysis utilize reactive residues in the active site to enhance the rate of the reaction. Amino acid residues used for chemical catalysis have polar, ionizable, side chains that take active part in the reaction mechanism and that undergo chemical changes during the reaction. Because ionizable groups take part in catalysis, the reaction rate of an enzyme is pH-dependent. The way in which pH affects the rate can suggest which types of residue take part in catalysis. The two major types of chemical catalysis are acid-base catalysis, and covalent catalysis.
Acid-base catalysis: The acceleration of a reaction is achieved by catalytic transfer of a proton. This is the most common type of chemical catalysis, both in organic chemistry and in enzymatic reactions. Because the side chain of histidine has a pKa of about 6 to 7 in most proteins, it is an ideal group for proton transfer at neutral pH. Histidine is therefore frequently found in the active site of enzymes utilizing acid-base catalysis. (The estimated rate acceleration from acid-base catalysis is about 10 - 100 times.)
Covalent catalysis: In covalent catalysis, a substrate or part of it is bound covalently to the form a reactive intermediate, from which a portion of the substrate is transferred to a second substrate. (Estimated rate acceleration 10 - 100 times.)

Binding modes of catalysis account for the major part of the rate acceleration provided by enzymes.
The proximity effect: By binding multiple substrates an enzyme brings them close together, effectively increasing their concentration. The proximity effect is also at work in single-substrate reactions in which the substrate is bound close to catalytic residues in the active site. (Estimated rate acceleration 10⁴ - 10⁵ times.)
Transition state stabilisation: In order for an enzyme to lower the activation energy of a reaction it must reduce the energy difference between the substrate and the transition state. This means it must bind more strongly to the transition state than to the substrate. By tight binding of the transition state in the active site of an enzyme, the transition state is stabilized, thereby lowering its energy. That makes it easier to get "over the hill"to product. Active sites achieve tight binding of transition states by having a shape that more closely matches the transition state than the substrate(s) or product(s), and by providing charged ligands to bind oppositely charged groups present only in the transition state (or similarly, by providing a more apolar binding site for a transition state with a decreased localized charge). (The estimated rate acceleration from transition state stabilisation is > 10⁴ - 10⁵ times.)
Some enzymes catalyze reactions at rates close to, or even faster than, that expected for free diffusion (10⁸ to 10⁹ M^-1s^-1) of the substrate to the enzyme. Explain how this is possible.

Answer:
The binding of a substrate to an enzyme is usually fast, and so the actual catalytic steps will not be "waiting around" for that to happen. However, if the catalytic parts of the reaction are very fast, as for electron transfers, some proton transfer reactions, and many simple associations, the binding step may be the slowest, that is, the "rate-determining" step. In these cases, the overall rate of the reaction may approach the upper limit for catalysis. The rate of catalysis may be even faster if there is electrostatic attraction between the reactants that speeds up the rate of diffusion. Some enzymes use "electrostatic funneling" to attract charged substrates and guide them into the active site.
Explain why very tight binding of a substrate to an enzyme is not desirable for enzyme catalysis, whereas tight binding of the transition state is.

Answer:
The key point here is that it is the DIFFERENCE in energy between the ES complex and the transition state (the activation energy for the forward reaction) that counts. Tight binding of a substrate corresponds to an ES complex that is very stable (low energy). That makes it harder to get from there "up" to the transition state, so the activation energy is effectively increased. And that slows down the reaction. Tight binding of the transition state, on the other hand, makes IT more stable (lower energy) and so it is easier to get there starting from the ES complex. So, the activation energy is effectively decreased and that increases the rate of the reaction (see Figure 6.9 in Horton, both 2nd and 3rd edition).
Explain why an enzyme increases the rate of a reaction in both the forward and reverse directions.

Answer:
Both the forward and the reverse reactions follow the same mechanism (but in opposite directions of course). The rate of the forward reaction depends on the activation energy from ES to the transition state (that is, the difference in the energy between them). The rate of the reverse reaction depends on the activation energy from as viewed from EP's side of the hill. If you lower the hill, it is easier to get over it from that side, too.
The proteases chymotrypsin, trypsin and elastase belong to the same family of enzymes. Their amino acid sequences are very similar, and so are their structures. Their active sites have the same catalytic amino acids, but there are differences in their pockets that determine which peptides they will cleave.

a) Describe the common features of the active sites in these enzymes. What are the important catalytic residues, and what type of catalysis do they perform?
b) What kind of kinetic mechanism (sequential ordered, sequential random, ping-pong) is employed by these enzymes?
c) How do the three enzymes achieve their different substrate specificities?

Answer:
a) These three proteins are all 'serine proteases'. At the active site are three residues - a serine, a histidine, and an aspartic acid, which are required for catalysis (known as the 'catalytic triad'). Histidine acts as an acid-base catalyst in several steps of the reaction mechanism. In the initial step it removes a proton from serine to make serine a more powerful nucleophile and prepare it for covalent catalysis. The aspartate orients the histidine, and takes part in transition state stabilisation. For details, refer to Horton, Figure 6.27 in 2nd ed. or Figure 6.25 in 3rd ed.
b)The kinetic mechanism of serine proteases is of the ping-pong type. The substrate (a protein) binds, the first catalytic step occurs and one product is released (C-terminal half of the protein), a second catalytic event occurs, and the second product (N-terminal half of the protein) is released (see Horton, Figure 5.8 in 2nd ed. or Figure 5.7 in 3rd ed).
c) Each serine protease is more able to act on certain peptide substrates rather than others, due to the shape of its own particular active site. For example, chymotrypsin has a large non-polar pocket near the active site which favours the binding of a peptide with a large non-polar side chain. In trypsin, an aspartate in that side-chain binding pocket makes it easier to bind to (and so cut) a peptide with a positively charged side chain (i.e. lysine or arginine).

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