Protein-protein association:
from biophysical understanding to protein design

 protein-protein association


 Description of the experimental system

The complex formed between TEM1--lactamase and its protein inhibitor BLIP is a suitable protein-protein interaction system for the study of the basic biophysical principles governing the processes of association, dissociation and complex stability. The structure of the unbound proteins, as well as of the complex were solved to high resolution. Both are single domain proteins, binding each other at a nM affinity, with the association reaction being diffusion limited at µM protein concentrations which were used for measurements (Albeck & Schreiber 1999). The proteins are stable, easy to manipulate, and could be expressed to high yields in E.coli (Albeck & Schreiber 1999).

Fig. 1. Relating kon to electrostatic energy of interaction between two proteins (U). (A) plotting lnkon versus the Debye-Huckel parameter . (B) Bronsted analysis of the change in lnkon versus (at I=0) (Selzer & Schreiber 1999). (C) calculated versus experimentally determined rates of association using PARE for calculations (Selzer et al. 2000).

 Relating kon to the magnitude of electrostatic forces

In the following chapter I will describe the relationship between the kinetics of association and the electrostatic energy of interaction between a pair of proteins and how this relation is used for calculating association rate constants. In 1996 Schreiber and Fersht have shown that the rate constant for association varies with the charge and the concentration of salt according to the Debye-Huckel theory for electrolite solutions (Schreiber & Fersht 1996). Zhou and co-workers suggested that the average Boltzmann factor of attractive electrostatic forces in the region where association occurs is directly related to the increase in the rate of association for ligand-protein and protein-protein interactions. In a further development (Selzer & Schreiber 1999), we have shown that kon of a protein complex can be calculated from the Debye-Huckel theory (Selzer & Schreiber 1999) according to eq. 2:

equation

where kon and are the rates of association in the presence and absence of electrostatic forces respectively, U is the electrosatic energy of interaction, K  is the inverse Debye length and a is the minimal distance of approach (see Fig. 1 and (Selzer & Schreiber 1999)). Hence, kon is the sum of two components: (i) the basal rate of association in the absence of electrostatic forces (), (ii) the contribution of the electrostatic energy of interaction between the proteins. Equation 2 suggests that a plot of kon versus (which is proportional to the ionic strength (I)) is linear, with the slope being equal to . The intercept of the line at = 0 corresponds to the basal rate (ln) and the intercept at = 1 corresponds to lnkon at the absence of salt. Fig. 1a shows that this linear relation holds for the association of TEM1-BLIP, interferon-receptor and barnase-barstar (Schreiber & Fersht 1996; Piehler & Schreiber 1999a; Selzer & Schreiber 1999; Selzer et al. 2000). Similar plots drawn for different mutants of these protein complexes yield distinct slopes. A Bronsted plot of the fitted values of (at I=0) for different mutant complexes of barnase and barstar, plotted versus their respective lnkon is shown in Fig. 1b. The Bronsted value of ~1 determined in this case indicates that the rate of association is directly related to the change in electrostatic energy of interaction between the two proteins (Selzer & Schreiber 1999).

 Calculating kon values

As indicated above, the electrostatic energy of interaction between two proteins (U) is linearly related to the rate of association. Therefore, one can expect that calculating the value of U as the difference in the total electrostatic energy of the complex minus that of the two unbound proteins may also relate to kon. Initially these calculations were performed using DelPhi (at a range of dielectric constants, charge files, and encounter complex structures - for details see (Selzer & Schreiber 1999)). These calculations did indicate that only Coulombic interactions have to be considered, and that a homogeneous dielectric constant of 80 can do. However, the use of a homogeneous dielectric constant causes an overestimation of the contribution of remote residues. This problem was fixed by incorporating a non-linear term in the electrostatic energy calculations (). The algorithm was written as a computer program (PARE - Predicting Association Rate Enhancement) (Selzer et al. 2000; Selzer & Schreiber 2001). The ability of PARE to predict values of kon was evaluated for the interactions between barnase and barstar, hirudin and thrombin and AChE with fasciculin (including all available mutants). An excellent linear relation is seen between the calculated and experimentally measured values of kon for all three systems (Fig. 1c - correlation coefficient of 0.98 for the 32 mutations analyzed (Selzer et al. 2000)). Thus, it seems that PARE is generally applicable.

 Designing faster and tighter binding protein complexes

The real challenge of any theoretical calculation is in its predictive power for design purposes. Here we set upon increasing the rate of association of a protein complex while keeping the rate of dissociation unchanged (resulting in an increased binding affinity). The design strategy was to optimize the electrostatic attraction between TEM1 and BLIP (whose association is diffusion controlled, but without much electrostatic guidance (Albeck & Schreiber 1999)) using PARE for the calculations. Potential sites for mutation were probed only outside the binding interface in order to avoid changes in the short-range interactions stabilizing the complex.

This work came to answer three questions: (i) to test the ability of PARE to predict the increase in kon,(ii) to evaluate whether the electrostatic contributions of residues located outside the binding site follow the same basic principles as found for interfacial residues and (iii) to measure how increased long-range electrostatic attraction affect koff. Fig. 2a shows a surface representation of BLIP, with the residues probed for faster association colored. The calculations suggest a broad range of expected changes in kon upon mutation. By far the largest change was calculated for the mutation D163K (over 20 fold). Fig. 2b is a plot of the experimental versus calculated values of kon for 11 single and multiple mutant BLIP proteins, which were expressed and their binding kinetics analyzed. The fastest BLIP mutant enhanced binding by 250 fold, with the theoretically calculated data fitting exactly the experimentally measured values (Selzer et al. 2000). While association increased dramatically, the dissociation rate constant was unchanged, contributing to a net increase of 250 fold in the binding affinity (Fig. 2c) (Selzer et al. 2000). The design strategy presented here is applicable for increasing rates of association and affinities of protein complexes in general.

Fig. 2. Designing faster binding protein complexes. (A) calculated rate increase, red is for a mutation predicted to increase the rate more than 10 fold, yellow over 50% increase and blue less than 50 % increase. The interface is colored Green. (B) predicted versus experimentally determined rate constants. (C) kon, koff and binding affinity of the experimentally measured mutant complexes. Rates of association and dissociation were measured in a stopped flow, and BIAcore respectively.

 Mechanism of protein-protein association

The association of a pair of proteins, A and B, can be described as a two step reaction:

where A:B is the encounter complex and AB is the final complex. According to this scheme two proteins will diffuse randomly in solution until they reach an area, designated as the "steering region" where mutual electrostatic attraction leads them to the formation of an encounter complex which evolves into the final complex (see Fig. 3b).

Following is a summary of experimental data and theoretical simulations which can serve as a basis for understanding the reaction mechanism for association:

  1. Only charged residues alter kon (see Fig. 1 in (Selzer & Schreiber 2001)).
  2. 2. A Bronsted analysis relating the change in kon to the change in electrostatic energy of interaction shows a linear relation between the two with a slope of ~1 (Fig. 2a and (Selzer & Schreiber 1999)).
  3. Probing the structure of the activated complex using double mutant cycles has shown that only charged residues which are in close contact in the final complex, interact in the activated complex, while neutral residues do not interact at this stage (Schreiber & Fersht 1996). Masking electrostatic forces by salt causes the loss of some, but not all pairwise interactions at the activated complex, suggesting that the steering region at high salt is more limited, albeit maintains its specificity (Frisch et al. 2001).
  4. The change in entropy upon forming the activated complex is close to zero, while the enthalpy changes with the free energy for the mutants analyzed (Frisch et al. 2001).
  5. Increasing long range electrostatic attraction through mutagenesis increases specifically kon, but does not affect koff (Selzer et al. 2000), with the increase being proportional to the increase in Debye-Huckel energy of interaction of the final complex relative to the unbound proteins.
  6. Simulating the Debye-Huckel energy of interaction during association gives rise to an energy funnel, with the final complex being at the minima (Fig. 3a). For faster associating protein complexes the energy funnel deepens and its volume increases. Mutations with the largest impact on association (hot spots for association) have the largest effect on the size and depth of the energy funnel (Selzer & Schreiber 2001).


Fig. 3. (A) 3D energy landscape of the association pathway of wt TEM1 with wt BLIP and the (+6) mutant which binds TEM1 250 fold faster. The magnitude of the Debye Huckel energy of interaction () is plotted in 3D versus the distance and the relative rotation angle between the proteins. (B) Free energy profile for protein-protein association. A+B represent the free proteins, A:B is the encounter complex, and AB is the final complex. Line 2 represents the case where electrostatic attraction between the proteins is increased relative to lane 1.

From these experimental evidence we suggest the following reaction mechanism for protein complex association: Two unbound proteins diffuse randomly in solution until they reach an area, designated as the "steering region" (see Fig. 3a and b).

The size of the steering region is proportional to the magnitude of mutual electrostatic forces. The energy diagram in the steering region resembles a funnel, leading the protein towards the formation of the encounter complex (Selzer & Schreiber 2001; Schreiber 2002). The nature of the encounter complex has been a matter of considerable research. It is described as a low free energy attractor, i.e., a precursor state before docking which is an ensemble of configurations whose average resembles the final complex. The formation of the final complex requires overcoming the transition state where desolvation and structural rearrangement occurs. Double-mutant cycle data showed that the activated complex is stabilized by specific long range electrostatic interactions, but not by short range interactions which stabilize the complex (H-bonds, Van der Waals) (Schreiber & Fersht 1996; Frisch et al. 2001).

Furthermore, the activated complex seems to be at least partially solvated (Frisch et al. 2001). Surprisingly, koff was found to be independent on the magnitude of long-range electrostatic forces (Selzer et al. 2000; Selzer & Schreiber 2001). This suggests that the rate determining transition state along the dissociation pathway is from [AB] to [A:B] (Selzer & Schreiber 2001), and koff = k-2. Thus pairs of proteins forming an encounter complex will tend to dissociate more readily than to evolve into the final complex. Using the same assumptions the association rate constant will be given by: . With k2 being independent of the magnitude of long-range electrostatic forces, the ratio of k1/k-1 reflects the net change in the association rate constant upon changing electrostatic forces (for detailed analysis see (Selzer & Schreiber 2001)). This analysis is based on experimental observations for the association of barnase-barstar (Schreiber & Fersht 1993a; Schreiber et al. 1994; Schreiber & Fersht 1995; Schreiber & Fersht 1996; Schreiber et al. 1997) and TEM1-BLIP (Albeck & Schreiber 1999; Selzer et al. 2000) at protein concentration where diffusion is limiting the rate of the reaction, and might differ for other protein systems.