484
10 The Statistical Basis of Bioenergetics
environment are selected out in evolution, unless all the produced forms have a
biological purpose. The final configuration has important flex joints, surface-charge
distributions, binding loci, and crevasses and pockets with specific weak adhesion
surfaces, all as needed for the proper functioning of the protein. 53
Protein Conformational Transitions
As proteins are formed in natural environments, they first tend to form segments
of coils and sheets, which then fold into final configurations. Zimm and Bragg 54
first showed how one can establish, by comparing theoretical models to experiment,
answers to how protein tertiary structure forms from its secondary structure. Their
work and the efforts that followed showed that proteins with residue lengths up
to about 100 (1) can fold without the need for templates or auxiliary mechanisms,
although the required time needed can be drastically different with templates and/or
catalysts; (2) will make the folding transition with a high degree of ‘cooperation’,
in that the process acts positively on itself, speeding the condensation of the whole
protein chain once it starts; (3) pass rapidly through any intermediates; (4) may be
reversible by environmental changes; and (5) lead to a final configuration that has
a certain uniqueness, suggesting it has a minimum energy, at least among various
accessible and nearby conformational states.
As a simple sample model, consider a protein chain consisting of N identical
smallest segments that can either be twisted into a helical segment (h) or be left
in an open configuration (o). (In a real protein, the smallest segment will have five
amino acids, with the first forming a hydrogen bond with the fifth, making part of a
helix.) A given chain can be characterized by the locations of the helical segments
relative to the open stretches, such as ‘oohohhhooo’. The hydrogen bonding will
make the ‘h’ regions lower in binding energy than the ‘o’ regions. We will let G =
H − T TS be the Gibbs free energy released by the transition of one ‘o’ to one
‘h’ region. The energy released in the form of heat will be H and the entropy
gained will be S. For our case, as helical segments are being formed, H will
be negative since the formation of hydrogen bonding releases energy, and S will
be negative since the formation of a helical segment makes the protein chain more
ordered. Thus, there will be a ‘melting’ temperature given by
T m = | //S|
53 There are now many elaborate statistical and kinetic theories to describe protein chain folding.
One goal is to have a computer program predict the final folding, given an initial amino acid
sequence. Another is to have a program that will design a set of possible sequences for a given
function. For an overview, see Ken Dill et al., The Protein-Folding Problem, 50 Years On, Science
338, 6110, 1042–1046 (23 Nov 2012).
54 B.H. Zimm, J.K. Bragg, Theory of the Phase Transition between Helix and Random Coils in
Polypetide Chains, J Chem Phys 31, 526–531 (1959).
10 The Statistical Basis of Bioenergetics
environment are selected out in evolution, unless all the produced forms have a
biological purpose. The final configuration has important flex joints, surface-charge
distributions, binding loci, and crevasses and pockets with specific weak adhesion
surfaces, all as needed for the proper functioning of the protein. 53
Protein Conformational Transitions
As proteins are formed in natural environments, they first tend to form segments
of coils and sheets, which then fold into final configurations. Zimm and Bragg 54
first showed how one can establish, by comparing theoretical models to experiment,
answers to how protein tertiary structure forms from its secondary structure. Their
work and the efforts that followed showed that proteins with residue lengths up
to about 100 (1) can fold without the need for templates or auxiliary mechanisms,
although the required time needed can be drastically different with templates and/or
catalysts; (2) will make the folding transition with a high degree of ‘cooperation’,
in that the process acts positively on itself, speeding the condensation of the whole
protein chain once it starts; (3) pass rapidly through any intermediates; (4) may be
reversible by environmental changes; and (5) lead to a final configuration that has
a certain uniqueness, suggesting it has a minimum energy, at least among various
accessible and nearby conformational states.
As a simple sample model, consider a protein chain consisting of N identical
smallest segments that can either be twisted into a helical segment (h) or be left
in an open configuration (o). (In a real protein, the smallest segment will have five
amino acids, with the first forming a hydrogen bond with the fifth, making part of a
helix.) A given chain can be characterized by the locations of the helical segments
relative to the open stretches, such as ‘oohohhhooo’. The hydrogen bonding will
make the ‘h’ regions lower in binding energy than the ‘o’ regions. We will let G =
H − T TS be the Gibbs free energy released by the transition of one ‘o’ to one
‘h’ region. The energy released in the form of heat will be H and the entropy
gained will be S. For our case, as helical segments are being formed, H will
be negative since the formation of hydrogen bonding releases energy, and S will
be negative since the formation of a helical segment makes the protein chain more
ordered. Thus, there will be a ‘melting’ temperature given by
T m = | //S|
53 There are now many elaborate statistical and kinetic theories to describe protein chain folding.
One goal is to have a computer program predict the final folding, given an initial amino acid
sequence. Another is to have a program that will design a set of possible sequences for a given
function. For an overview, see Ken Dill et al., The Protein-Folding Problem, 50 Years On, Science
338, 6110, 1042–1046 (23 Nov 2012).
54 B.H. Zimm, J.K. Bragg, Theory of the Phase Transition between Helix and Random Coils in
Polypetide Chains, J Chem Phys 31, 526–531 (1959).