Superfunneled Energy Landscape of Protein Evolution Unifies the Principles of Protein Evolution, Folding, and Design

Evolution shapes interaction patterns for epistasis and specific protein binding in a two-component signaling system

The elegant design of protein sequence/structure/function relationships arises from the interaction patterns between amino acid positions. A central question is how evolutionary forces shape the interaction patterns that encode long-range epistasis and binding specificity. Here, we combined family-wide evolutionary analysis of natural homologous sequences and structure-oriented evolution simulation for two-component signaling (TCS) system. The magnitude-frequency relationship of coupling conservation between positions manifests a power-law-like distribution and the positions with highly coupling conservation are sparse but distributed intensely on the binding surfaces and hydrophobic core. The structure-specific interaction pattern involves further optimization of local frustrations at or near the binding surface to adapt the binding partner. The construction of family-wide conserved interaction patterns and structure-specific ones demonstrates that binding specificity is modulated by both direct intermolecular interactions and long-range epistasis across the binding complex. Evolution sculpts the interaction patterns via sequence variations at both family-wide and structure-specific levels for TCS system.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

EspcTM: Kinetic Transition Network Based on Trajectory Mapping in Effective Energy Rescaling Space

The transition network provides a key to reveal the thermodynamic and kinetic properties of biomolecular systems. In this paper, we introduce a new method, named effective energy rescaling space trajectory mapping (EspcTM), to detect metastable states and construct transition networks based on the simulation trajectories of the complex biomolecular system. It mapped simulation trajectories into an orthogonal function space, whose bases were rescaled by effective energy, and clustered the interrelation between these trajectories to locate metastable states. By using the EspcTM method, we identified the metastable states and elucidated interstate transition kinetics of a Brownian particle and a dodecapeptide. It was found that the scaling parameters of effective energy also provided a clue to the dominating factors in dynamics. We believe that the EspcTM method is a useful tool for the studies of dynamics of the complex system and may provide new insight into the understanding of thermodynamics and kinetics of biomolecular systems.

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.

Frustration and inhomogeneous environments in relaxation of open chains with Ising-type interactions

Frustration can contribute to very slow relaxation times in large open chains, as in spin glasses and in biopolymers. However, frustration may not be sufficient to produce broken ergodicity in finite systems. Here we employ a system-plus-reservoir approach to investigate how strongly inhomogeneous environments and frustration compete in the relaxation of finite open chains. We find a sufficient condition for our inhomogeneous environments to break ergodicity. We use the microscopic model to derive a Markovian quantum master equation for a generic chain with ultrastrong intrachain couplings. We show that this microscopic model avoids a spurious broken ergodicity we find in the phenomenological model. We work out an explicit example of broken ergodicity due to the inhomogeneous environment of an unfrustrated spin chain as far as simulating a recent experiment on protein denaturation (where environment inhomogeneity is especially relevant). We finally show that an inhomogeneous environment can mitigate the effects of frustration-induced degeneracies.