Heat capacity of the native state

Fig. 3. Denaturational increment of the partial specific heat capacity of pancreatic ribo-nuclease A (RNase), hen egg-white lysozyme (Lys), and sperm whale myoglobin (Mb). The dashed lines represent the parts of these functions that were obtained by a linear extrapolation of th partial heat capacity of the native state. The dot-and-dash lines show the behavior when the values measured at 50°C are assumed to be temperature independent.

The partial molar heat capacity can be considered to be composed of intrinsic and hydration contributions. The intrinsic component contains contributions from covalent and non-covalent interactions. It has been shown that about 85% of the total heat capacity of the native state of a protein in solution is due to the covalent structure [72]. Changes in the heat capacity upon unfolding are therefore primarily interpreted as due to changes in the hydration. A physical picture of energy fluctuations means changing the conformation between ordered and less ordered structures. This can be achieved by hindered internal rotations, low frequency... 

Because the absolute value of the heat capacity of the native state is always larger than the heat capacity of the unfolded state, and because they have different temperature dependencies, the heat capacity change upon unfolding is positive and temperature dependent itself ... 

From the thermodynamic data obtained by DSC at T1/2 an extrapolation of the thermodynamic quantities to other temperatures can be performed. For a valid extrapolation, however, the accuracy of Cj,n(7 ) and CpjiiJ ) is critical. Usually the thermodynamic parameters at temperatures below Ti/2 are of interest. The heat capacity of the native state can be determined directly by DSC from the experimental protein heat capacity in this temperature range. The heat capacity of the denatured state, however, has... 

The average properties of the transition state may be estimated from a variety of criteria. The Tanford j8t value, measured from the relative sensitivities of the folding kinetics and equilibrium constants to [GdmCl] (Chapter 18, section Bl, equation 18.9), is 0.6, indicating that about 60% of the surface area of the protein is buried in the transition state for folding, relative to that buried in the native structure. The change in heat capacity of the transition state relative to that... 

The transition of a protein or a single cooperative domain from the native to the denatured state is always accompanied by a significant increase of its partial heat capacity (see, for reviews, Sturtevant, 1977 Privalov, 1979). The denaturationaJ increment of heat capacity A JCP = C° Cp amounts to 25-50% of the partial heat capacity of the native protein and does not depend noticeably on the environmental conditions under which denaturation proceeds (Fig. 1) or on the method of denaturation. However, it is different foi different proteins and seems to correlate with the number of contacts between nonpolar groups in native proteins (Table I). On the other hand, the partial specific heat capacities of denatured states of different proteins appear to be rather similar (Tiktopulo et... 

Upon unfolding, an increase (ACp)n in the specific heat capacity of the protein, amounting to 5-25 UK 1 mol 1 at 25°C, is measured. The differences in (ACp) between proteins are due to differences in the specific heat capacities of their native states the specific heat capacities of the unfolded states are similar and do not depend appreciably on the solvent conditions or the denaturing agent. 

For a two-state unfolding reaction N U, the baseline is a weighted sum of two curves representing the heat capacities of the native and unfolded species, with the weights determined by the relative populations of the native and unfolded states, Pn and Pu, respectively ... 

TABLE 8.7. Thermodynamics characteristics of the proteins (partiai moiar heat capacity of the native, Cp(kJK moi ), and unfoided state, (kJK moi ), and the heat capacity, A Cp kJmoi ), enthaipy, A H kJmoi ), entropy, A S(J moi ), and Gibbs energy changes upon unfoiding, A G(kJ moi )). ... 

The simplest way to derive thermodynamic parameters from UV melting data is to apply a van t Hoff analysis of the data by assuming a two-state model (i.e. native and denatured states) and that the difference in heat capacities of the native and denatured states, ACp°, is zero (13-16) (more complex models are described in Section 5). At each temperature the absorbance can be used to calculate the fraction of strands in the native and denatured states, thereby allowing the calculation of an equilibrium constant (10). Thus, the absorbance versus temperature profile is used to determine the temperature dependence of... 

If A Cp is zero there is no cold denaturation, because only one temperature exists at which A G vanishes. For a reliable extrapolation of protein stability over a long temperature interval it is therefore of utmost importance to know accurately the heat capacities of the native and denatured state of the protein in the same temperature region. 

From equation 36 it is evident that a direct integration of a Cp(T)-curve yields the relative partition function Q [37,41,42]. Before numeric integration of the experimental Cp(T)-curve the heat capacity of the reference species has to be subtracted. For practical reasons this usually works best, if either the heat capacity of the native or that of the denatured state is used as reference heat capacity. For a reliable deconvolution of the experimental heat capacity curve it is essential that either or Cp > can be extrapolated accurately into the transition region. Depending on whether the native or the denatured state is taken as reference state equation 34 shows that the following relations hold 1 Wn 1 No... 

In all globular proteins studied, a significant increase in the heat capacity of the denatured protein relative to the native state has been observed in the vicinity of the denaturation transition. (This quantity is represented in... 

An adhesive-cohesive model for protein compressibility has been proposed by Dadarlat and Post [57]. This model assumes that the compressibility is a competition between adhesive protein-water interactions and cohesive protein-protein interactions. Computer simulations suggest that the intrinsic compressibility largely accounts for the experimental compressibilities indicating that the contribution of hydration water is small. The model also accounts for the correlation between the compressibility of the native state and the change in heat capacity upon unfolding for nine single chain proteins. 

Dadarlat and Post [57] have found an interesting correlation between the heat capacity changes of unfolding and the compressibility of the native state of proteins. This can be rationalized from a similar dependence of these quantities on the distribution of the atom types, polar/charged versus nonpolar. 

Finally, DSC permits the determination of the absolute values of heat capacity in the native and the unfolded states. These values are related to the amino acid residues exposed to water in each state and therefore contain structural information on these states. This provides the basis for an analysis of the thermodynamics of unfolding in terms of structure [43,44], some aspects of which will be sketched below. 

Figure 2.13. Dependence of partial molar heat capacity of a protein on the temperature (thermogram). The denatured protein always has a higher heat capacity than the native one. The high heat capacity at the peak stems from the increasing fluctuation in the system. In contrast to the native state, many more conformations are possible and the protein switches back and forth between different...

Fig. 6. Thermodynamic stability of TmDHFR in 2.9 M GdmCl. (O) AG2.9 m GdmCl calculated according to Backmann et al. (with KHm = -466 kJ/mol, T = 333AT, ACp = 22.4 kJ/(mol K) and F, = 5 X 10 M for the enthalpy of melting, the melting temperature, the change in heat capacity between the native and unfolded states, and the monomer concentration, respectively. (A) Denaturant concentration of half-denaturation ( ) melting point in 2.9 M GdmCl.

The reciprocal value of the relative partition function is related to either the fraction of the native or denatured state. Figure 7 shows the numerical integration procedure for the heat capacity curve of the two-state unfolding transition of ROP wt protein [53,54]. This is a homo-dimeric small protein that unfolds according to the mechanism N2 2D. The straight line indicates the extrapolation of the native state heat capacity Cp,N(T). According to eq. 36 the enthalpy has been calculated relative to the native state by integration of the heat capacity difference Cp T) — Cp t (T)... 

Cp n T) is the heat capacity function of the native state, ACp T) = Cp j) T)-Cp n(T) is the difference between the extrapolated heat capacity functions of the denatured and native states at temperature T, and the term ACpOiD describes the sigmoidal baseline under the transition peak. The term [A°/f°(T)] aDQ N characterises the heat absorption peak. The product Q n d = ctN(l Q n) is responsible for the appearance of the characteristic shape of the heat capacity peak. Typical curves are given in Figures 1 and 4. 

An effective fit strategy starts with the extrapolation of the heat capacities of the pure native and denatured states... 

Texturization is not measured directly but is inferred from the degree of denaturation or decrease of solubility of proteins. The quantities are determined by the difference in rates of moisture uptake between the native protein and the texturized protein (Kilara, 1984), or by a dyebinding assay (Bradford, 1976). Protein denaturation may be measured by determining changes in heat capacity, but it is more practical to measure the amount of insoluble fractions and differences in solubility after physical treatment (Kilara, 1984). The different rates of water absorption are presumed to relate to the degree of texturization as texturized proteins absorb water at different rates. The insolubility test for denaturation is therefore sometimes used as substitute for direct measurement of texturization. Protein solubility is affected by surface hydrophobicity, which is directly related to the extent of protein-protein interactions, an intrinsic property of the denatured state of the proteins (Damodaran, 1989 Vojdani, 1996). 

We cannot answer the question posed by Anfin-sen s hypothesis. Does the native state have a minimum value of the Gibbs energy Nevertheless, it is observed that proteins usually behave as if folded, unfolded forms are in a true thermodynamic equilibrium, and that this equilibrium is attained rapidly. The difference AG between a folded and a denatured protein is only 21-63 kj mol-1, which shows that folded proteins are only marginally more stable than are unfolded polypeptide chains.645 The value of AG of unfolding as a function of temperature T is given by Eq. 29-13, where AH(T) and ACp are the changes in enthalpy and heat capacity upon unfolding.645 646... 

Fig. 4. Schematic representation of the partition function [Eq. (1)] for protein folding/unfolding. Each state, from the native state (i = 0) to the unfolded state (i = n) and all intermediates (i = 1 to n - 1), is assigned a AG relative to the native state from which the statistical weights are obtained. The partition function, Q, is simply the sum of the statistical weights of all the states. Other important parameters, including the population of each state [Eq. (2)], the excess enthalpy [Eq. (3)], and the excess heat capacity [Eq. (4)], are determined from the partition function as described in the text.

The main consequence of a heat capacity difference between native and denatured states of a protein is that the thermodynamic functions that determine the transition between these states are all temperature-depen-dent. Indeed, since... 

Fio. 6. The Gibbs energy difference of the native and denatured states of myoglobin and ribonuclease A calculated per mole of amino acid residues under the same conditions as indicated in Fig. 4. The dot-and-dash lines represent functions obtained in the assumption that the denaturation heat capacity increment is temperature independent. 

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