Thermodynamics of Protein Protein Interactions

Specific protein-protein interactions provide a major part of the basic organization of living cells. The structure of a protein complex embeds the information about the relative mutual organization of two proteins in a frozen state; however, it does not intuitively provide information on the affinity between two proteins or the time-dependent process of complex assembly and dissociation. For a mechanistic understanding of biological processes and for engineering proteins that fulfill specific therapeutic tasks, we require physicochemical observables that describe the pathway of protein-protein interactions in detail. The binding affinity between proteins,

given by the equilibrium concentrations of the proteins [A] and [B] and the complex [AB], is directly related to the free energy of interaction AG° = -RTln Ka. Thus, complex formation only takes place if AG° < 0. The free energy of the complex formation can readily be analyzed by measuring Ka (Fig. 1); for example, the energetic contributions AAGd of individual residues can be determined by measuring changes in the Ka upon mutation. According to the Gibbs-Helmholtz relation AG° = AH°-TAS°, both the enthalpy AH° and the entropy AS° of the complex formation contribute to AG°. AH° reflects the strength of the interactions between two proteins (e.g., van der Waals, hydrogen bonds, salt bridges) relative to those existing with the solvent molecules, which are excluded from the binding interface. AS° , on the other hand, mainly reflects two contributions: changes in solvation entropy and changes in conformational entropy. Upon binding, the water released from the binding sites leads to a gain in solvent entropy. This gain is particularly important for hydrophobic patches on the protein surface (hydrophobic effect). At the same time, the proteins

Handbook of Cell Signaling, Volume 1

Figure 1 Free energy profile describing the pathway for the formation of a protein-protein complex (AB) from the free proteins A and B via the encounter complex AB*, the transition state AB^, and the intermediate AB**. Comparison of the profiles for the wt proteins (—) with a mutant affecting long-range electrostatic interactions ( ) and a mutant affecting short-range interactions (------), respectively. The free energies, AG, are indicated for both the complex formation AG° and the transition state, as well as the changes in free energy of the encounter complex.

reaction coordinate

Figure 1 Free energy profile describing the pathway for the formation of a protein-protein complex (AB) from the free proteins A and B via the encounter complex AB*, the transition state AB^, and the intermediate AB**. Comparison of the profiles for the wt proteins (—) with a mutant affecting long-range electrostatic interactions ( ) and a mutant affecting short-range interactions (------), respectively. The free energies, AG, are indicated for both the complex formation AG° and the transition state, as well as the changes in free energy of the encounter complex.

and individual residues within the proteins lose conformational freedom, resulting in a negative change in conformational entropy. The loss of conformational freedom was estimated to be on the order of 15 kcal/mol at 25° C, but values between 0 and 30 kcal/mol have been cited as well [1]. What do we know about the contributions toward entropy and enthalpy on the molecular level? Dehydration of nonpolar residues during association is always entropically favorable, while that of polar residues is unfavorable. The enthalpies are nevertheless negative, as they represent the energy of interaction of atoms at the interface relative to their interactions with water. As several partially canceling factors contribute toward the entropy and enthalpy of interaction, it is not surprising that for most mutant complexes the difference in free energy of binding is much smaller than the accompanying changes in AH° and AS°. This has been emphasized by theoretical studies showing that, on forming a cavity in water to accommodate a solvent molecule, the change in the enthalpy of water (solvation) is exactly balanced by the entropy of the cavity; thus, changes in AH° and AS° cancel out each other in AG° [2]. Enthalpy-entropy compensations, then, seem to be a characteristic of weak noncovalent interactions, including protein-protein interactions.

Interaction Kinetics

While analysis of the Ka can provide an extensive thermodynamic picture of the complex, it does not allow any conclusion about the pathway that leads to the formation of the complex from the individual proteins. This is entirely determined by the shape of the full free energy landscape given by all possible states between the free proteins and the complex, most of which are not accessible experimentally. On this free energy landscape, the reaction itself most likely follows the pathway requiring the least free energy. This pathway is called the reaction coordinate and can be studied experimentally through the rates of association and of dissociation. Analysis of these kinetic parameters for several structurally and physicochemically well-defined protein-protein interactions allowed for establishing basic concepts of how proteins form complexes. In the following, we will give an overview about how kinetics can be used for analyzing the interaction pathway through the free energy landscape and how this can be understood on the molecular level.

In a general term, association of a protein complex (AB) from the unbound components (A + B) can be best described using a four state model:

In this scheme, A and B are two proteins in solution, forming the complex AB. The reaction diagram of this interaction (Fig. 1) resembles that of protein folding, with the transition state being the most unstable species along the reaction pathway, which occurs at the highest peak of a reaction coordinate diagram. Two pre-complex states are formed along the reaction pathway. The encounter complex is positioned before the transition state for association (AB*) and the intermediate complex (AB**), which is between the transition state and the final complex. In physical terms, the encounter complex tends to dissociate readily (with k-1 >> k2), while the intermediate is already committed to form the final complex (thus, k3>> k_2). It has to be emphasized that experimentally one often observes only the transition between A + B to AB and that the equilibrium dissociation constant (KD) equals koff/kon. Yet, under certain experimental conditions, the pre-complexes are observable. A good example for such a case is the interaction between Ras and the Ras-binding domain of c-Raf1. Here, a two-step association process was suggested, with an initial rapid equilibrium step followed by an isomerization reaction occurring at the rate of several hundreds per second [3].

The intermediate (AB**) is formed after the rate-limiting step for association, (k3 >> k-2); therefore, it does not affect the overall rate of association. The intermediate can be envisioned as a partially formed complex that has to reorganize to form the final complex. This reorganization step can be fast, such as for the interaction between cystatin A and papain (230 s-1), or slow, such as for the interaction between lysozyme and HyHEL-10 and HyHEL-26 (~10-3 s-1) [4,5]. A major problem in investigating this intermediate is to find a probe that can monitor independently the formation of the intermediate versus the formation of the final complex.

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