In contrast, the enthalpy distribution function for the low-pH form of myoglobin does not show any special structure at any temperature.
For this form of myoglobin, the temperature evolution of the relative probabilities of the two populations can be obtained in detail from the master free energy function. For the high-pH form of myoglobin, the enthalpy distribution function that is obtained exhibits bimodal behavior at the temperature corresponding to the maximum in the heat capacity (Poland, 2001a), reflecting the presence of two populations of molecules (native and unfolded). Given the enthalpy distribution functions at several temperatures, one can then construct a master free energy function from which the probability distributions at all temperatures can be calculated. Named after Boltzmanns -theorem, Shannon defined the entropy (Greek capital letter eta) of a discrete random variable X. The enthalpy distribution function for a protein gives the fraction of protein molecules in solution having a given value of the enthalpy, which can be interpreted as the probability that a molecule picked at random has a given enthalpy value. In this method, the temperature dependence of the heat capacity is used to calculate moments of the protein enthalpy distribution function, which in turn, using the maximum-entropy method, are used to construct the actual distribution function. Using literature data for the low-pH form (Hallerbach and Hinz, 1999) and for the high-pH form (Makhatadze and Privalov, 1995), we applied a recently developed technique (Poland, 2001d) to calculate the free energy distributions for the two forms of the protein. At low pH (near 4.5), there are two weak maxima in the heat capacity at low and intermediate temperatures, respectively, whereas at high pH (near 10.7), there is one strong maximum at high temperature.
In the context of a brute force search (where every possibility is tested), a password entropy of 100 bits would require 2 100 attempts for all possibilities to be exhausted. The following thermodynamic properties will be calculated: density, dynamic viscosity, kinematic viscosity, specific enthalpy, specific entropy, specific isobar heat capacity cp, thermic conductivity, coefficient of thermal expansion, heat conductance, thermal diffusivity, Prandtl-number, coefficient of compressibility Z. The higher the entropy, the more difficult it will be for the password to be guessed.
The temperature dependence of the heat capacity of myoglobin depends dramatically on pH. The chapter discusses methods that can be used to evaluate changes in entropy in protein folding, binding, and oligomerization. The password generator also determines the password entropy, measured in bits.