Specificity and affinity quantification of flexible recognition from underlying energy landscape topography

Abstract

Flexibility in biomolecular recognition is essential and critical for many cellular activities. Flexible recognition often leads to moderate affinity but high specificity, in contradiction with the conventional wisdom that high affinity and high specificity are coupled. Furthermore, quantitative understanding of the role of flexibility in biomolecular recognition is still challenging. Here, we meet the challenge by quantifying the intrinsic biomolecular recognition energy landscapes with and without flexibility through the underlying density of states. We quantified the thermodynamic intrinsic specificity by the topography of the intrinsic binding energy landscape and the kinetic specificity by association rate. We found that the thermodynamic and kinetic specificity are strongly correlated. Furthermore, we found that flexibility decreases binding affinity on one hand, but increases binding specificity on the other hand, and the decreasing or increasing proportion of affinity and specificity are strongly correlated with the degree of flexibility. This shows more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Our work provides a theoretical foundation and quantitative explanation of the previous qualitative studies on the relationship among flexibility, affinity and specificity. In addition, we found that the folding energy landscapes are more funneled with binding, indicating that binding helps folding during the recognition. Finally, we demonstrated that the whole binding-folding energy landscapes can be integrated by the rigid binding and isolated folding energy landscapes under weak flexibility. Our results provide a novel way to quantify the affinity and specificity in flexible biomolecular recognition.

Figure 1. The binding affinity (stability) for rigid (independent) and flexible (effective) binding shown in (A) heat capacity curves and (B) free energy landscapes for Lambda Cro repressor (PDB: 1cop) and Lambda repressor (PDB: 1lmb).

The solid and corresponding dotted lines represent rigid and flexible binding respectively. Free energy landscapes are plotted at the rigid binding transition temperatures, which are calculated from the peaks of heat capacity curves for binding, respectively. Free energy is in reduced unit. is the fraction of native interfacial binding contacts. "Ind" and "Eff" are the abbreviations for "Independent" and "Effective" binding, respectively.

Figure 2. The energy, entropy and free energy of rigid and flexible binding for Lambda Cro repressor.

The profiles are plotted at (A) rigid binding temperature (), and (B) corresponding rigid and flexible binding transition temperature (). Energy, entropy and free energy are in reduced unit.

Figure 3. The relationship of the topography of energy landscapes between rigid and flexible binding.

The quantities of topography of energy landscapes are shown in (A) energy gap , (B) energy roughness , (C) entropy and (D) energy landscape topography measure .

Figure 4. The differences of thermodynamics and kinetics between rigid and flexible binding.

(A) The free energy landscapes of rigid and flexible binding are plotted at the corresponding binding temperature . (B) The differences of kinetics, represented by the ratio of binding time between rigid and flexible binding, are plotted along the differences of intrinsic specificity between rigid and flexible binding.

Figure 5. The differences between rigid and flexible binding energy landscapes changes with interfacial flexibility.

(A) The differences between rigid and flexible binding energy landscapes are described by the , where and are the quantities of the rigid and flexible binding. The quantities are , and , corresponding to the binding transition temperature, glassy trapping temperature and binding energy landscape topography measure, respectively. (B) The differences of kinetics, represented by the ratio of association time between rigid and flexible binding, are plotted as a function of . describes the degree of interfacial flexibility.

Figure 6. The folding stability for folding with and without interfacial binding shown in (A) heat capacity curves and (B) free energy landscapes for Lambda Cro repressor (red) and Lambda repressor (blue).

The solid and corresponding dotted lines represent isolated (independent) and dimeric (effective) folding respectively. Free energy landscapes are plotted at the isolated folding transition temperatures, which are calculated from the peaks of heat capacity curves for folding, respectively. Free energy is in reduced unit.

Figure 7. The evolution of the differences between the combined and whole global binding-folding energy landscapes as a function of .

The difference between the combined and whole global binding-folding energy landscapes is described by the , where and are the energy landscape topography measures of the combined and whole global binding-folding. "Comb" and "Glob" are the abbreviations for "combined" and "whole global" binding-folding, respectively.