Funneled energy landscape unifies principles of protein binding and evolution

Most proteins have evolved to spontaneously fold into native structure and specifically bind with their partners for the purpose of fulfilling biological functions. According to Darwin, protein sequences evolve through random mutations, and only the fittest survives. The understanding of how the evolutionary selection sculpts the interaction patterns for both biomolecular folding and binding is still challenging. In this study, we incorporated the constraint of functional binding into the selection fitness based on the principle of minimal frustration for the underlying biomolecular interactions. Thermodynamic stability and kinetic accessibility were derived and quantified from a global funneled energy landscape that satisfies the requirements of both the folding into the stable structure and binding with the specific partner. The evolution proceeds via a bowl-like evolution energy landscape in the sequence space with a closed-ring attractor at the bottom. The sequence space is increasingly reduced until this ring attractor is reached. The molecular-interaction patterns responsible for folding and binding are identified from the evolved sequences, respectively. The residual positions participating in the interactions responsible for folding are highly conserved and maintain the hydrophobic core under additional evolutionary constraints of functional binding. The positions responsible for binding constitute a distributed network via coupling conservations that determine the specificity of binding with the partner. This work unifies the principles of protein binding and evolution under minimal frustration and sheds light on the evolutionary design of proteins for functions.

Proteins in nature have a high degree of thermodynamic and kinetic specificities different from random heteropolymers of amino acids (1–3). Except for intrinsically disordered proteins, naturally occurring proteins are believed to evolve to spontaneously fold into stable native structure and specifically bind with partners for fulfilling the biological functions (4–6). Directed evolution, which mimics natural evolution via rounds of mutagenesis and selections in the laboratory, has also successfully obtained desired protein functions (7–11). According to Darwin, protein sequences evolve through random mutations for the fitness (12). The evolutionary constraint to fold into a particular, stable three-dimensional structure has been considered as the fitness to greatly restrict the sequence space of protein evolution (13–18). However, the biological functions of the proteins are often performed through binding with their partners. The evolutionary selection ultimately operates on the functions other than the structures.A protein’s biological function, such as binding/recognition, conformation dynamics, and activity, can be described by its thermodynamics and kinetics, which are determined by the underlying interactions between the residues. The principle of minimal frustration has been fruitful in illustrating how the global pattern of interactions determines thermodynamic stability and kinetic accessibility of protein folding and binding (3, 19–25). The principle requires that energetic conflicts are minimized in folded native states, so that a sequence can spontaneously fold. Because of the functional necessity, naturally occurring sequences are actually in the tradeoff for coding the capacity to simultaneously satisfy stable folding and functional binding. From the view of localized frustration (23–27), naturally occurring proteins maintain a conserved network of minimally frustrated interactions at the hydrophobic core. In contrast, highly frustrated interactions tend to be clustered on the surface, often near binding sites that become less frustrated upon binding. A natural question is how the evolution sculpts the interaction patterns that conflict with the overall folding of minimal frustration but are specific for protein binding.Extensive statistical analysis of the evolutionary information has shown that native structures of protein folding and binding can be reliably predicted from the global pattern of interactions between amino acids extracted from homologous native sequences (NSs) (28–34). This indicates that thermodynamic and kinetic specificities of protein folding and binding are encoded as the evolutionary footprints on the NSs. In this sense, thermodynamic and kinetic specificities should be not only the evolutionary outcomes but also the selection pressures on protein evolution. The proposed selection fitness quantified by the folding requirement of the thermodynamic stability and the kinetic accessibility has successfully evolved sequences and structures of small domains with strong protein characteristics, including the hydrophobic core, high designability, and fast folding (35). The principle of minimal frustration as a rule to quantify the selection fitness has provided the physical mechanism and mathematical formations for the theoretical and computational studies of protein-folding evolution.Different from our previous study, which concentrated on the evolution of individual domain folding (35), here, we incorporated the constraint of functional binding into the selection fitness under the principle of minimal frustration. Thermodynamic stability and kinetic accessibility were derived and quantified from the global funneled energy landscape, which satisfies the requirements of both folding into the stable structure and binding with the specific partner. The evolution under the selection fitness of optimizing both folding and binding requirements is realized through a bowl-like energy landscape with a closed-ring attractor at the bottom. The sequence space is increasingly reduced until this ring attractor is reached. The interaction patterns respectively responsible for the folding and binding are extracted from the evolved sequences. The residual positions participating in the interactions responsible for folding are highly conserved and maintain the hydrophobic core under additional evolutionary constraints of functional binding. The positions responsible for binding constitute a distributed network via coupling conservations of the residual positions. This distributed network with coupling conservations determines the specificity of the binding with the partner, and the interactions involving the positions of the network can be influenced and adjusted depending on the binding partner. This work unifies the principles of protein binding and evolution and provides an evolution strategy to generate evolved sequences similar to naturally occurring sequences.