Quantifying the topography of the intrinsic energy landscape of flexible biomolecular recognition

Biomolecular functions are determined by their interactions with other molecules. Biomolecular recognition is often flexible and associated with large conformational changes involving both binding and folding. However, the global and physical understanding for the process is still challenging. Here, we quantified the intrinsic energy landscapes of flexible biomolecular recognition in terms of binding–folding dynamics for 15 homodimers by exploring the underlying density of states, using a structure-based model both with and without considering energetic roughness. By quantifying three individual effective intrinsic energy landscapes (one for interfacial binding, two for monomeric folding), the association mechanisms for flexible recognition of 15 homodimers can be classified into two-state cooperative “coupled binding–folding” and three-state noncooperative “folding prior to binding” scenarios. We found that the association mechanism of flexible biomolecular recognition relies on the interplay between the underlying effective intrinsic binding and folding energy landscapes. By quantifying the whole global intrinsic binding–folding energy landscapes, we found strong correlations between the landscape topography measure Λ (dimensionless ratio of energy gap versus roughness modulated by the configurational entropy) and the ratio of the thermodynamic stable temperature versus trapping temperature, as well as between Λ and binding kinetics. Therefore, the global energy landscape topography determines the binding–folding thermodynamics and kinetics, crucial for the feasibility and efficiency of realizing biomolecular function. We also found “U-shape” temperature-dependent kinetic behavior and a dynamical cross-over temperature for dividing exponential and nonexponential kinetics for two-state homodimers. Our study provides a unique way to bridge the gap between theory and experiments.Biomolecules realize their functions through interacting with other molecules. Fully understanding the manner in which a protein participates in the process of biomolecular recognition is the basis for studying cellular activity. The first proposal of the binding mechanism was given by Fischer, called “lock-and-key,” to explain the rigid biomolecular docking (1). However, more and more experimental evidence has been accumulating in favor of the idea that protein binding often associates conformational changes. In this regard, considering the local configurational plasticity in protein–protein interactions, two scenarios have been proposed. One is named “induced fit” (2) and the other is called “conformational selection” (3). Furthermore, increasing recent evidence demonstrates that some isolated proteins are found to be disordered at physiological conditions. These proteins, known as “intrinsically disordered proteins” (IDPs), have refreshed our understanding of protein folding and function (4–6). The unstructured characteristic provides binding of IDPs with the advantage of multiple targeted partners, high association rates, high specificity, and moderate affinity (7, 8). For IDPs, the global conformational changes are always associated in their binding, known as “binding induced folding.” By investigating the synchronization of binding and folding, the association mechanism of IDPs can be classified into cooperative “coupled binding–folding” as well as noncooperative “binding prior to folding” and “folding prior to binding” (Fig. 1). As a result, it is now recognized that not only the well-defined 3D structure but also the conformational flexibility are critical pieces of information to determine the function of protein.Open in a separate windowFig. 1.The schematic diagram of three typical association mechanisms for IDPs. The diagonal line represents the cooperative process with binding and folding strongly coupled. The noncooperative processes are represented by the two lines along the rectangular edge, corresponding to binding prior to folding (up) and folding prior to binding (down), respectively.The energy landscape theory has been proposed to help understand the dynamics of protein folding (9–12). The shape of the folding energy landscape of naturally evolved proteins appears to be minimally frustrated and funneled so that the Levinthal’s paradox (13) can be solved with folding going through multiple routes toward the native structure rather than one single specific pathway (14–16). The folding landscape is widely studied in experiments and simulations (17–21) and has deepened our understanding of protein folding. As folding can be regarded as self-binding, the flexible recognition with large global conformational changes can be regarded as a process of binding coupled with folding—i.e., binding–folding. Therefore, binding and folding are analogous to each other except for the chain connectivity. It is expected that Levinthal’s paradox also exists in flexible protein binding. Therefore, it is feasible to extend the folding energy landscape concept to the binding dynamics to solve the conformational search problem in flexible binding and investigate the function of protein (22–27). The funneled binding landscape indicates that naturally evolved binding also follows the principle of minimal frustration, resulting in a reasonable physiological time for realizing the function of protein with vital activity.However, protein binding involving at least two chains is certainly different from protein folding in some respects. The global binding–folding energy landscape is expected to be a combination or interactions of an interfacial binding energy landscape and two monomeric folding energy landscapes (28). The flexible binding–folding energy landscape, as a result of the delicate combination or balance of folding and binding, controls the way a protein realizes its function during the protein–protein associations. For the noncooperative folding prior to binding scenario, the monomeric folding energy landscapes are expected to be more funneled than the interfacial binding energy landscapes, and vice versa for the binding prior to folding scenario. The cooperative coupled binding–folding scenario is an intermediary between the two noncooperative scenarios. Notice that the global binding–folding energy landscapes do not require that the three individual binding and folding energy landscapes are necessarily all funneled. For IDPs, they do not fold to a specific 3D structure, and therefore, their individual folding energy landscapes will be highly rugged. However, IDPs realize their functions by folding to ordered structures upon binding to their targets (29, 30). In other words, coupled with binding, the individual folding energy landscapes with functional rearrangements have been changed with strong bias toward the native binding structure during the associations. In conclusion, the binding–folding energy landscapes are the underlying key factors governing the protein–protein interactions and control the realization of protein’s function.In our work, we focused on the flexible biomolecular recognition in terms of binding–folding dynamics of 15 homodimers, which are formed by two identical monomers each (SI Appendix, Fig. S7). We quantified the whole global intrinsic landscape and the three individual intrinsic energy landscapes (one for interfacial binding, two for monomeric folding) from underlying density of states (DOS) extracted from the binding–folding dynamics using a structure-based model both with and without considering energetic roughness. We showed that the topography of each individual effective landscape and the whole global landscape of flexible recognition in terms of binding–folding can be quantified by a dimensionless ratio Λ of the energy gap between native state and average of nonnative states versus roughness modulated by the entropy. We found that the association mechanism of flexible recognition strongly relies on the interplay between the topographies of the underlying effective intrinsic binding and folding energy landscapes. This interplay changes with different strengths of nonnative interactions. We also showed that the whole global landscape topography measure is strongly correlated with the thermodynamics characterized by the binding transition temperature versus the glassy trapping temperature and the kinetics characterized by the binding time. By investigating the kinetics of Troponin C site, which is a two-state homodimer, we demonstrated that the temperature-dependent kinetic behavior is under the control of the topography of energy landscapes. The results are consistent with the previous analytical theories and experiments (31–33). Therefore, our work gives strong evidence that the topography of the intrinsic energy landscape is the key to understanding the binding–folding mechanism in terms of both thermodynamics and kinetics. Since the thermodynamics and kinetics of binding–folding dynamics can be explicitly measured by experiments (31, 34–36), and the underlying physical observable quantities are found to be strongly dependent on the theoretical energy landscape topography, our simulation findings can be regarded as the quantitative connections between the experiments and theory. This provides a unique way to bridge the theory and experimental measurements of flexible biomolecular recognition.