10.8 The Partition Function for Ensembles
483
twist in each amino acid, with steric restrictions creating large forbidden zones in
the landscape. 52
The existence of a unique natural protein fold does NOT mean that the protein
‘finds’ the valley with the lowest energy in an optimization function, since the
sequence of folding locks in subfolds before the final fold forms. An example
of such subfolds are the alpha helicies and the beta sheets. Other more complex
subfolds are common to many proteins. In any case, the final configuration must
have some stability under small changes in temperature and chemical environment,
and so the energy landscape must have a relatively strong local minimum at the
natural fold. In addition, evolution would favor proteins which fold into useful
structures even when a subclass of mutations cause variations. Evolution might
even make selection of a certain variability in amino-acid sequencing not to protect
against mutation, but to permit mutations to produce variability.
Understanding a protein tertiary structure helps us determine its biochemical
action, its stability, the variability and pathology when DNA mutation of its code
is present, its ancestry in the evolution of proteins, how variations in the amino
acids transform its purpose, and how imitators, inhibitors, and enhancers can be
constructed for pharmacological applications. Protein folding we recognize as a
central topic in describing life on Earth.
As an introduction to the topic of protein folding, we examine if biological
protein folding into natural forms occur spontaneously in the cell protoplasm, or
if the process requires ancillary structures? An answer comes from a statistical
analysis of the folding probabilities as a function of temperature in comparison with
experiment.
As indicated, proteins smaller than about 100 amino acids ‘spontaneously’ fold
and unfold according to the temperature. They do so in times on the order of
microseconds. This rapidity indicates that the protein folds by a sequence of quick
subfolds, creating local substructures first. However, the process is well represented
by a two-state system, folded or unfolded, rather than a sequence of quasi-stable
intermediates. In addition, the proportion of unfolded chains as a function of
temperature has a sharp sigmoid shape, indicating that there are cooperative effects,
i.e. once the folded protein starts to unfold, the unfolded segments increase the
chance that the remaining folded chain will unfold. This effect can be explained
by the increase in thermal motion of the released chain segments and their new
exposure to water and other ions in the environment.
For natural protein structures, the particular identity of local sequence of amino
acids is not as important as the conformation after global folding. Biological
polypeptide chains have a unique fold. Nature has already picked an amino acid
sequence that will fold into a single stable form. Sequences that fold into several
distinctly different structures with about the same binding energy in the natural
52 For an early study of the angle restrictions, see G.N. Ramachandran, C. Ramakrishnan,
V. Sasisekharan, Sterochemistry of the polypeptide chain configurations, J Mol Bio 7, 95–99
(1963).
483
twist in each amino acid, with steric restrictions creating large forbidden zones in
the landscape. 52
The existence of a unique natural protein fold does NOT mean that the protein
‘finds’ the valley with the lowest energy in an optimization function, since the
sequence of folding locks in subfolds before the final fold forms. An example
of such subfolds are the alpha helicies and the beta sheets. Other more complex
subfolds are common to many proteins. In any case, the final configuration must
have some stability under small changes in temperature and chemical environment,
and so the energy landscape must have a relatively strong local minimum at the
natural fold. In addition, evolution would favor proteins which fold into useful
structures even when a subclass of mutations cause variations. Evolution might
even make selection of a certain variability in amino-acid sequencing not to protect
against mutation, but to permit mutations to produce variability.
Understanding a protein tertiary structure helps us determine its biochemical
action, its stability, the variability and pathology when DNA mutation of its code
is present, its ancestry in the evolution of proteins, how variations in the amino
acids transform its purpose, and how imitators, inhibitors, and enhancers can be
constructed for pharmacological applications. Protein folding we recognize as a
central topic in describing life on Earth.
As an introduction to the topic of protein folding, we examine if biological
protein folding into natural forms occur spontaneously in the cell protoplasm, or
if the process requires ancillary structures? An answer comes from a statistical
analysis of the folding probabilities as a function of temperature in comparison with
experiment.
As indicated, proteins smaller than about 100 amino acids ‘spontaneously’ fold
and unfold according to the temperature. They do so in times on the order of
microseconds. This rapidity indicates that the protein folds by a sequence of quick
subfolds, creating local substructures first. However, the process is well represented
by a two-state system, folded or unfolded, rather than a sequence of quasi-stable
intermediates. In addition, the proportion of unfolded chains as a function of
temperature has a sharp sigmoid shape, indicating that there are cooperative effects,
i.e. once the folded protein starts to unfold, the unfolded segments increase the
chance that the remaining folded chain will unfold. This effect can be explained
by the increase in thermal motion of the released chain segments and their new
exposure to water and other ions in the environment.
For natural protein structures, the particular identity of local sequence of amino
acids is not as important as the conformation after global folding. Biological
polypeptide chains have a unique fold. Nature has already picked an amino acid
sequence that will fold into a single stable form. Sequences that fold into several
distinctly different structures with about the same binding energy in the natural
52 For an early study of the angle restrictions, see G.N. Ramachandran, C. Ramakrishnan,
V. Sasisekharan, Sterochemistry of the polypeptide chain configurations, J Mol Bio 7, 95–99
(1963).