6. Hemoglobin Variants There are almost 500 naturally occurring variants of hemoglobin. Most are the result of a single amino acid substitution in a globin polypep-tide chain. Some variants produce clinical illness, though not all variants have deleterious effects. A brief sample is presented below.

HbS (sickle-cell Hb): substitutes a Val for a Glu on the surface Hb Cowtown: eliminates an ion pair involved in T-state stabilization

Hb Memphis: substitutes one uncharged polar residue for another of similar size on the surface Hb Bibba: substitutes a Pro for a Leu involved in an a helix Hb Milwaukee: substitutes a Glu for a Val Hb Providence: substitutes an Asn for a Lys that normally projects into the central cavity of the tetramer Hb Philly: substitutes a Phe for a Tyr, disrupting hydrogen bonding at the a1ft1 interface

Explain your choices for each of the following:

(a) The Hb variant least likely to cause pathological symptoms.

(b) The variant(s) most likely to show pI values different from that of HbA when run on an isoelectric focusing gel.

(c) The variant(s) most likely to show a decrease in BPG binding and an increase in the overall affinity of the hemoglobin for oxygen.

7. Reversible (but Tight) Binding to an Antibody An antibody binds to an antigen with a Kd of 5 X 10~8 m. At what concentration of antigen will 6 be (a) 0.2, (b) 0.5, (c) 0.6, (d) 0.8?

8. Using Antibodies to Probe Structure-Function Relationships in Proteins A monoclonal antibody binds to G-actin but not to F-actin. What does this tell you about the epitope recognized by the antibody?

T9. The Immune System and Vaccines A host organism needs time, often days, to mount an immune response against a new antigen, but memory cells permit a rapid response to pathogens previously encountered. A vaccine to protect against a particular viral infection often consists of weakened or killed virus or isolated proteins from a viral protein coat. When injected into a human patient, the vaccine generally does not cause an infection and illness, but it effectively "teaches" the immune system what the viral particles look like, stimulating the production of memory cells. On subsequent infection, these cells can bind to the virus and trigger a rapid immune response. Some pathogens, including HIV, have developed mechanisms to evade the immune system, making it difficult or impossible to develop effective vaccines against them. What strategy could a pathogen use to evade the immune system? Assume that antibodies and/or T-cell receptors are available to bind to any structure that might appear on the surface of a pathogen and that, once bound, the pathogen is destroyed.

10. How We Become a "Stiff" When a higher vertebrate dies, its muscles stiffen as they are deprived of ATP, a state called rigor mortis. Explain the molecular basis of the rigor state.

11. Sarcomeres from Another Point of View The symmetry of thick and thin filaments in a sarcomere is such that six thin filaments ordinarily surround each thick filament in a hexagonal array. Draw a cross section (transverse cut) of a myofibril at the following points: (a) at the M line; (b) through the I band; (c) through the dense region of the A band; (d) through the less dense region of the A band, adjacent to the M line (see Fig. 5-31b, c).

Biochemistry on the Internet

12. Lysozyme and Antibodies To fully appreciate how proteins function in a cell, it is helpful to have a three-dimensional view of how proteins interact with other cellular components. Fortunately, this is possible using on-line protein databases and the three-dimensional molecular viewing utilities Chime and Protein Explorer. If you have not yet installed the Chime plug-in on your computer, go to www.mdlchime.com/chime and follow the instructions for your operating system and browser. Once chime is installed, go to the Protein Data Bank (www.rcsb.org/pdb).

In this exercise you will examine the interactions between the enzyme lysozyme (Chapter 4) and the Fab portion of the anti-lysozyme antibody. Use the PDB identifier 1FDL to explore the structure of the IgG1 Fab fragment-lysozyme complex (antibody-antigen complex). View the structure using Protein Explorer, and also use the information in the PDBsum summary of the structure to answer the following questions.

(a) Which chains in the three-dimensional model correspond to the antibody fragment and which correspond to the antigen, lysozyme?

(b) What secondary structure predominates in this Fab fragment?

(c) How many amino acid residues are in the heavy and light chains of the Fab fragment? In lysozyme? Estimate the percentage of the lysozyme that interacts with the antigen-binding site of the antibody fragment.

(d) Identify the specific amino acid residues in lysozyme and in the variable regions of the Fab heavy and light chains that appear to be situated at the antigen-antibody interface. Are the residues contiguous in the primary sequence of the polypeptide chains?

13. Exploring Reversible Interactions of Proteins and Ligands with Living Graphs ^ Use the living graphs for Equations 5-8, 5-11, 5-14, and 5-16 to work through the following exercises.

(a) Reversible binding of a ligand to a simple protein, without cooperativity. For Equation 5-8, set up a plot of 6 versus [L] (vertical and horizontal axes, respectively). Examine the plots generated when Kd is set at 5 ¡m, 10 ¡m, 20 ¡m, and 100 ¡m. Higher affinity of the protein for the ligand means more binding at lower ligand concentrations. Suppose that four different proteins exhibit these four different Kd values for ligand L. Which protein would have the highest affinity for L?

Examine the plot generated when Kd = 10 ¡m. How much does 6 increase when [L] increases from 0.2 ¡m to 0.4 ¡m? How much does 6 increase when [L] increases from 40 ¡m to 80 ¡m?

You can do the same exercise for Equation 5-11. Convert [L] to pO2 and Kd to P50. Examine the curves generated when P50 is set at 0.5 kPa, 1 kPa, 2 kPa, and 10 kPa. For the curve generated when P50 = 1 kPa, how much does 6 change when the pO2 increases from 0.02 kPa to 0.04 kPa? From 4 kPa to 8 kPa?

(b) Cooperative binding of a ligand to a multisubunit protein. Using Equation 5-14, generate a binding curve for a protein and ligand with Kd = 10 ¡m and n = 3. Note the altered definition of Kd in Equation 5-16. On the same plot, add a curve for a protein with Kd = 20 ¡m and n = 3. Now see how both curves change when you change to n = 4. Generate Hill plots (Eqn 5-16) for each of these cases. For Kd = 10 ¡m and n = 3, what is 6 when [L] = 20 ¡m?

(c) Explore these equations further by varying all the parameters used above.

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