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¶þ¡¢¹¹ÐÍìØ(Configuration entropy)ºÍ¹¹ÏóìØ(Conformational entropy)
Configuration entropy is the entropy associated with the geometric configuration of individual components comprising a distributed physical system. Configuration entropy of a given configuration can be evaluated using an adaptation of the Boltzmann formula of statistical thermodynamics,
where kB is the Boltzmann constant and W probability of this configuration. Probability W is the ratio between the number of possible (spatial) arrangements of system components that can give the current configuration and the total number of possible arrangements yielding all possible configurations of the system. Note that number of configurations is different from the number of arrangements, for instance, because each given configuration (overall geometry pattern of the system) may allow permutations of system components without changing this pattern. Example: permutation of individual monomers in a macromolecule.
In application to macromolecules, configuration entropy is also known as conformational entropy.
It can be shown that the variation of configuration entropy of thermodynamic systems (e.g., ideal gas, and other systems with a vast number of internal degrees of freedom) on the course of thermodynamic processes is equivalent to the variation of the macroscopicentropy defined as dS = ¦ÄQ/T, ¦ÄQ amount of heat exchanged by the system with the surrounding media, and T system temperature. In application to thermodynamics systems, the Boltzmann equation shown in above is also known as microscopic definition of entropy.
Conformational entropy is the entropy associated with the physical arrangement of a polymer chain that assumes a compact or globular state in solution. The concept is most commonly applied to biological macromolecules such as proteins and RNA, but can also be used for polysaccharides and other polymeric organic compounds. To calculate the conformational entropy, the possible conformations assumed by the polymer may first be discretized into a finite number of states, usually characterized by unique combinations of certain structural parameters, each of which has been assigned an energy level. In proteins, backbone dihedral angles and side chain rotamers are commonly used as descriptors, and in RNA the base pairing pattern is used. These characteristics are used to define the degrees of freedom (in the statistical mechanics sense of a possible "microstate" . The conformational entropy associated with a particular conformation is then dependent on the probability associated with the occupancy of that state, as determined by the sum of the energies associated with the value of each parameter assumed in the state.
The entropy of heterogeneous random coil or denatured proteins is significantly higher than that of the folded native state tertiary structure. In particular, the conformational entropy of the amino acid side chains in a protein is thought to be a major contributor to the energetic stabilization of the denatured state and thus a barrier to protein folding. The conformational entropy of RNA and proteins can be estimated; for example, empirical methods to estimate the loss of conformational entropy in a particular side chain on incorporation into a folded protein can roughly predict the effects of particular point mutations in a protein. Side-chain conformational entropies can be defined as Boltzmann sampling over all possible rotameric states:
where R is the gas constant and pi is the probability of a residue being in rotamer i.
The limited conformational range of proline residues lowers the conformational entropy of the denatured state and thus increases the energy difference between the denatured and native states. A correlation has been observed between the thermostability of a protein and its proline residue content. |
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