Cooperativity, protein folding thermodynamics

A. Cooper, Heat capacity of hydrogen-bonded networks an alternative vievt> of protein folding thermodynamics, in Biophys. Chem., 2000, 85, 25-39. 

Protein folding and unfolding is thus largely an "all or none"process that results horn a cooperative transition. For example, suppose that a protein is placed in conditions under which some part of the protein structure is thermodynamically unstable. As this part of the folded structure is disrupted, the interactions between it and the remainder of the protein will be lost. The loss of these interactions, in turn, will destabilize the remainder of the structure. Thus, conditions that lead to the disruption of any part of a protein structure are likely to unravel the protein completely. The structural properties of proteins provide a clear rationale for the cooperative transition. 

Thermodynamic stability is a global property of the enzyme structure, and contributions of individual amino acids toward the free energy of folding are additive and highly cooperative. Analysis of mutant proteins has defined the contributions of various amino acids toward the overall stability of the protein. Replacements which alter the formation of ion pairs, hydrogen bonds, van der Waals contacts, or hydrophobic interactions each tend to destabilize the folded protein by a qualitatively comparable amount (14). In one approach to this problem, site-specific substitution of amino acids has provided new approaches toward dissecting the kinetic mechanisms of protein folding (27). 

C. Origin of Cooperativity in Protein Folding and Two-State Thermodynamic Behavior in Protein Folding... 

Typically, the in vitro folding of a single domain globular protein resembles a first-order phase transition in the sense that the thermodynamic properties undergo an abrupt change, and the population of intermediates at equilibrium is very low. In other words, the process is cooperative and is well described by a two-state model [8]. The first attempts to explain protein folding cooperativity focused on the formation of secondary structure. Theoretical and experimental analysis of coil-helix transitions indeed proved that the process is cooperative [167]. However, the helix-coil transition is always continuous [168], and thus it cannot explain the two-state behavior of the protein folding transition. 

However, the uniqueness of the canonical approach can only be maintained as long as the investigated system fulfills the requirement of the thermodynamic limit, i.e., if finiteness, in particular surface effects, do not matter. Thus, the rapidly grown interest in the structural behavior of notoriously finite systems such as biomolecules confronted the thermodynamic analysis with the problem, to what extent a canonical analysis is still appropriate for the discussion of cooperative thermal behavior associated with structure formation processes such as protein folding or aggregation. Because of its simplicity, it is still popular to also apply the conventional canonical approach to such systems. However, the obvious violation of the thermodynamic limit condition leads to conceptual problems. Even the imagination of what temperature is, is strongly affected and requires a careful consideration. 

THERMODYNAMICS OF STRUCTURAL STABILITY AND COOPERATIVE FOLDING BEHAVIOR IN PROTEINS... 

Thermodynamics of Structural Stability and Cooperative Folding Behavior in Proteins... 

The folding of a protein into a compact structure is accompanied by a large decrease in conformational entropy (disorder) of the protein, which is thermodynamically unfavorable. The native, folded conformation is maintained by a large number of weak, noncovalent interactions that act cooperatively to offset the unfavorable reduction in entropy. These noncovalent interactions include hydrogen bonds, and electrostatic, hydrophobic, and van der Waals interactions. These interactions ensure that the folded protein is (often just marginally) more stable than the unfolded form. 

The structure-based thermodynamic method combines the derived binding free energy model with the formalism which computes probabilities of individual amino acids being folded in native-like conformations and thereby allows to determine structural stability of different protein regions [48-53]. In a single site thermodynamic mutation approach, the cooperativity of in-... 

Hilser, V. J. Freire, E. (1996b). Structure based calculation of the equilibrium folding pathway of proteins. Correlation with hydrogen exchange protection factors. J. Mol. Biol In Press. Hilser, V. J. Freire, E. (1996c). Structure-Based Statistical Thermodynamic Analysis of T4 Lysozyme Mutants Structural Mapping of Cooperative Interactions. Biophysical Chem.. ... 

The consequences of cooperative folding can be illustrated by considering the contents of a protein solution under conditions corresponding to the middle of the transition between the folded and unfolded forms. Under these conditions, the protein is half folded. Yet the solution will contain no half-folded molecules but, instead, will be a 50/50 mixture of fully folded and fully unfolded molecules (Figure 3.57). Structures that are partly intact and partly disrupted are not thermodynamically stable and exist only transiently. Cooperative folding ensures that partly folded structures that might interfere with processes within cells do not accumulate. 

Murphy, K.P. and Freire, E. (1992) Thermodynamics of structural stability and cooperative folding behavior in proteins. Advances in Protein Chemistry, 43, 313-361. 

Thermodynamics for the sequence with the native state shown in Fig. 4 with the contact interaction potentials By taken from Table III of Ref. 54 reveals that it folds cooperatively in an apparent two-state manner. This is also reflected in the thermal distribution of the overlap function values /i(x) at the folding transition temperature 7> (Fig. 4). A nearly bimodal distribution of h(y) with the peaks at X 0.2 (NBA) and x 0-6 (unfolded state) is observed. There is also nonneghgible contribution from the intermediate values of % representing partially folded structures. Experiments that probe in more detail the thermal unfolding of proteins are beginning to reveal the possible importance of these... 

---