Due to the complexity of proteins, challenges remain in the accurate
modeling of protein interactions and their use in protein design and fold-
ing. As these algorithms become increasingly accurate, protein folding should
become predictive, with the potential of designing enzymes that are cap-
able of reactions that are not catalyzed by naturally occurring proteins.
Problems
13.1 Write the classical expression for kinetic energy for a molecule with two nuclei and two
electrons, assuming that the nuclei are stationary.
13.2 Write the classical expression for potential energy for a molecule with (a) two nuclei, A
and B, and two electrons, and (b) two nuclei, A and B, and three electrons.
13.3 Write Schrödinger’s equation for a H 2 molecule. Assume that the nuclei do not interact.
13.4 Write Schrödinger’s equation for a He 2 +molecule.
13.5 Electrons must be considered as identical particles: how does this influence the wavefunc-
tions describing molecules?
13.6 Why does the interaction between two atoms have an attractive 1/r^6 dependence at large
distances?
13.7 In a Hückel model, what effect does an increase in coupling have on the energetics?
13.8 Qualitatively, how are σand πmolecular orbitals related to atomic orbitals?
13.9 How is a peptide bond formed?
13.10 In a solvent such as benzene the dielectric constant is 4 compared to 78.5 for water. In
which system would an electrostatic interaction between two charges be more pronounced?
13.11 Since the interactions, such as hydrogen bonds, found in proteins, are weak compared to
covalent bonds, what stabilizes the folding of a protein?
13.12Why are the (φ,ψ) coordinates of proteins found in only certain regions of a Ramachandran
plot?
13.13 Since hydrogen bonds to water are not possible in the membrane, how can hydrogen
bonds be formed in the cell membrane for membrane proteins?
CHAPTER 13 CHEMICAL BONDS AND PROTEIN INTERACTIONS 289
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