The Transition State

In the transition state, noncovalent bonds are in the process of being made and broken. At least one encounter complex can be found prior to the transition state, with additional intermediates occupying the energy landscape past the transition state. What is the molecular basis of the transition state for protein-protein interactions? The bound state of two proteins is characterized by local specific interactions (e.g., van der Waals, electrostatic) between widely desolvated binding sites, whereas the unbound state is characterized by complete solvation and higher translational and rotational freedom. During formation of the complex, the proteins have to pass through a free-energy maximum where translational-rotational entropy is reduced and the binding sites are partially desolvated, but short-range interactions and precise structural fitting have not yet been attained. This state is naturally the transition state. The transition state can be approached from the unbound state (association) and from the bound state (dissociation). Yet, by the principle of macro-molecular reversibility, the nature and structure of the transition state should be the same.

The free activation energies required for reaching the transition state from the free proteins, AGfn, and the complex AGfff (Fig. 1) are related to the rate constants of complex formation and complex dissociation, respectively. Thus, experimental information on the nature of the transition state is obtained from the rate constants of the interaction. Absolute values from bimolecular reactions are difficult to interpret; however, relative values of changes in the rate constants of association kon or dissociation koff upon mutation of individual amino acid residues allow for characterizing the features of the transition state. Mutation studies conducted on many protein interactions have clearly shown that rates of association are mostly affected by mutating charged residues [6]. Moreover, it is possible to introduce charge mutations at the periphery of the binding site that will affect only association, but not dissociation [7]. Mutations, which are neutral in respect to their charge, potently affect the dissociation rate constants. Masking electrostatic interactions between proteins by increasing the ionic strength has confirmed this observation; while the rate of dissociation is only marginally affected, the effect on the rate of association can be very large and is directly related to the electrostatic energy U of interaction between the two proteins according to Eq. (1):

ln kon =ln kon where Mkon is the basal rate of association in the absence of electrostatic forces, k is the inverse Debye length, and a is the minimal distance of approach [6,7].

Direct information on the properties of the transition state could be obtained by double mutant cycle analysis of changes in activation free energies AAGon, which are calculated from the association rate constants according to van't Hoff's isotherm:

AAGint(on) = AAGon( mut1,mut 2) AAGon( mut1) AAGon( mut2)

If the AAGfn invoked by two individual mutations on each protein are additive, the two residues do not interact during the transition state; however, if the change is less or more than additive, one may assume that these two residues interact at the transition state. Probing the structure of the transition state of barnase/barstar and thrombin/hirudin by this method has shown that only charged residues, which are in close proximity in the final complex, already interact in the transition state. No significant interaction was measured between uncharged residues at this stage [8,9]. A somewhat different approach to probe docking trajectories experimentally uses the analysis of O values (O=AAGfn/AAGD). A O value close to one indicates that a specific interaction is formed at the transition state, while a O value close to zero indicates that the interaction is formed after the transition state. In a study of the HyHEL-10 Fab complex, multiple replacements were made in two positions, with most of the replacements having O values close to zero. This was wt on interpreted as the transition state being early along the reaction trajectory, before short-range interactions (which have the largest contribution on AAGD) are formed [10]. The notion that short-range interactions affect koff, while longrange electrostatic interactions affect kon, was directly tested by introducing charged mutations at the vicinity, but outside the binding site of TEM1-BLIP. These mutations did increase specifically kon by 250-fold but did not affect koff (thus, the increase in kon equals the increase in KD and 0=1) [7]. These data suggest that long-range electrostatic interactions increase the rate of association by lowering the free energy of the transition state by the same magnitude as the equilibrium constant (see Fig. 1). While mutations of non-charged residues do not significantly affect the transition state for association, they can significantly alter koff and KD. These data imply that the transition state is stabilized by electrostatic interactions and its structure already resembles that of the final complex, but the proteins are not yet close and oriented enough for short-range interactions.

Association of a Protein Complex

While the major part of the activation free energy is required for desolvation of the binding interface as a prerequisite for the formation of specific short-range interactions, further intermediate states are postulated to occur on the pathway of complex formation (Fig. 1). Prior to the transition state, the two proteins diffuse in solution statistically until they enter a steering region, in which the progression along the association pathway is actively steered toward complex formation (Fig. 2). The forces important within this region are mainly electrostatic in nature, with nonspecific hydrophobic interactions contributing as well to steer association. Analysis of the contribution of electrostatic forces to the rate of association clearly indicates that their contribution steams from guiding the two proteins toward the transition state; from stabilizing the pre-transition-state encounter complex, in which the binding interface is still largely sol-vated; and from lowering the free energy of the transition state. Calculations of a three-dimensional energy landscape of these forces shows electrostatic steering by charged residues, which provides an energy funnel directed toward formation of the final complex [6]. At physiological salt concentrations this funnel extends to less then 20 A of interprotein distance and fades rapidly upon rotation (at 60° rotation from the bound conformation, all electrostatic steering is lost; see Fig. 2). It was shown that charged "hot spot" residues have the largest effect on the size and depth of these energy funnels. Potential "hot spot" residues can now be identified computationally, making it possible to engineer pairs of proteins with much higher rates of association and affinity.

A second mechanism that potentially steers association is a partial desolvation of inter-protein hydrophobic surfaces. This effect plays a significant role in all association processes, but becomes particularly dominant for complexes, in which one of the reactants is neutral or weakly charged. The interaction provides a slowly varying attractive force over a small but significant region of the molecular surface. In complexes with no strong charge complementarity, this region surrounds the binding site, and the orientation of the ligand in the encounter conformation with the lowest desolvation free energy is presented in a conformation similar to the formed complex. While the electrostatic contribution toward faster association can be easily verified from mutational studies and the effect of the ionic strength on kon, the contribution of desolvation effects can be assessed only from theoretical calculations [11]. The reason that mutation studies rarely identify noncharged residues, which significantly contribute to kon, may be attributed to the small contribution of individual side chains to desolvation-induced association, as this is more of a global effect of the protein.

Figure 2 Three-dimensional energy landscape of the association between wt TEM1-ß-lactamase with wt BLIP (A) and a much faster binding mutant (B). For demonstration, only the z-angle rotation is shown. The magnitude of the Debye-Hückel energy of interaction (AU) is plotted in three dimensions versus the distance and the relative rotation angle between the proteins. The arrows point at the 0° rotation angle, which is the X-ray crystallographic structure of the TEM1/BLIP complex. For details on the calculations employed, see Selzer and Schreiber [6].

Figure 2 Three-dimensional energy landscape of the association between wt TEM1-ß-lactamase with wt BLIP (A) and a much faster binding mutant (B). For demonstration, only the z-angle rotation is shown. The magnitude of the Debye-Hückel energy of interaction (AU) is plotted in three dimensions versus the distance and the relative rotation angle between the proteins. The arrows point at the 0° rotation angle, which is the X-ray crystallographic structure of the TEM1/BLIP complex. For details on the calculations employed, see Selzer and Schreiber [6].

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