Gibbs free energy of unfolding

Q In a typical AFM experiment to mechanically unfold a single globular protein, the cantilever arm moved by 25 nra with an average force of 150 pN as the polypeptide chain unravelled. How much mechanical work was done in the process How does this compare to the Gibbs free energy of unfolding ... 

An equilibrium between adsorbed, native protein and adsorbed, unfolded protein. Attainment of this substate of equilibrium is largely driven by the Gibbs free energy of unfolding. 

For that reason and for other reasons explained in detail in Section VA, the proportionality constant a, which relates the Gibbs free energy of unfolding at the interface to that in the bulk, was set equal to zero. The affinity constant, K, defined by Eq. (30) is shown in Tables 5,7,9,11, 13, 15, and 17, with the parameter a being equal to 0.0 in all studied cases. Statistically, the goodness of fit of the model equation can be quantified by the value of the mean square of errors (MSE) in addition to the graphical representation of the regressed data. 

TABLE 4 Gibbs Free Energy of Unfolding, Protein, Solid, and Water Surface Energies, and the Work of Adhesion for Proteins Used in Figs. 4 and 5... 

Fortunately, the number of states that ever become populated is relatively small, even under conditions that maximize the population of intermediates. It is apparent that the folding/unfolding partition function can be simplified so that it includes only those states that are relevant to the folding process. The approach that we have undertaken involves the use of the native conformation as a template to generate partially folded conformations, and to evaluate the Gibbs free energy of those conformations according to the rules described in Section III. 

The stability of all dimers was assessed by temperature-induced unfolding experiments monitored by circular dichroism spectroscopy in the absence of guanidinium hydrochloride. It was therefore possible to derive the standard free energy of unfolding from data fitting using the Gibbs-Helmholtz equation (15.1) adapted to a two state monomer-dimer equilibrium. 

AGtf(r), Af/ftCD, and AS T) being the variations of Gibbs free energy, of enthalpy, and of entropy, respectively, upon unfolding. 

Section 6.1 considered the noncovalent binding energies that stabilize a protein strnctnre. However, the folding of a protein depends ultimately on the difference in Gibbs free energy (AG) between the folded (F) and unfolded (U) states at some temperature T ... 

We are interested in knowing the Gibbs free energy difference at zero force, AG, rather than the free energy difference AF between the folded state at n and the unfolded extended state at nax- We can express Eqs. (40) and (41) in terms of G (rather than F) and define the corrected work flj (F) along a path,... 

The thermodynamic parameters in Table II can be used to calculate the thermodynamic quantities necessary to define the partition function. Essentially, the strategy to calculate the folding/unfolding partition function from structural data involves the identification and enumeration of states and the assignment of Gibbs free energies to those states. Once this task is accomplished, the evaluation of the partition function is straightforward, as illustrated in Fig. 4. 

It must be noted that stability and cooperativity are different concepts. Stability is dictated by the Gibbs free energy difference between the folded and unfolded states and is usually reflected in the transition temperature or the resistance of the native state to the effects of denaturing agents, whereas cooperativity is reflected in the population of intermediate states. 

Fig. 9. Calculated overall free energy of stabilization (AGtota ) for yeast phos-phoglycerate kinase at pH 6.5 and 0.7 M GuHCl. This curve displays two zeros, corresponding to the temperatures of cold and heat denaturation. Also shown in the curve are the cooperative Gibbs free energies (AG ) associated with the uncompensated exposure of apolar surfaces on unfolding of each of the domains. For both domains, AG is positive for the heat denaturation and close to zero for the cold denaturation. This behavior results in a cooperative heat denaturation and a non-cooperative cold denaturation. [Reprinted from Freire el al. (1991).]...

In the following, we elucidate what thermodynamic properties are required for calculating the stability diagram of a protein. The Gibbs free energy difference between the unfolded and native state is defined as ... 

Fig. 31. Denaturation pressure ( p ), volume change of pressure-induced unfolding (A T°), and standard Gibbs free energy change (AG ), extrapolated to 1 bar, for the pressure-induced tmfolding of SNase at different molar concentrations (c) of cosolvents.

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