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

Abstract

Evolution is essential for shaping the biological functions. Darwin proposed the selection as the driving force for evolution upon mutations. While mutations are clear, the quantification of the selection force is still challenging. In this study, we identified and quantified both thermodynamic stability and kinetic accessibility as the selection forces for protein evolution. The protein evolution can be viewed and quantified as a trajectory moving along a super funneled energy landscape with a line attractor at the bottom. The resulting evolved sequences and structures show strong protein characteristics including the hydrophobic core, high designability and fast folding. The evolution principle uncovered here is validated on real proteins and shed light on the protein design.

Funneled energy landscape unifies principles of protein binding and evolution

“…The size of the local basin in the sequence space is determined by the binding-complex structure of the native state. The topography of the evolution energy landscape in the sequence space has a similar shape to the energy landscape of the evolution under folding requirement only (35). However, the evolved sequences encode different interaction patterns from those under the folding requirement only, which will be discussed in Hydrophobic Core for Folding and Coupling Network for Binding.…”

“…For independent folding and binding, the binding can be considered as rigid binding of two already-folded proteins. In this case, the expressions of Λ b and ∆G b only represent the binding requirement, and the folding requirement can be expressed with Λ f and ∆G f , as derived from a previous paper (35).…”

“…Different from our previous study, which concentrated on the evolution of individual domain folding (35), here, we…”

“…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.…”

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

“…Understanding of biomolecular dynamics is pivotal to reveal the function of biomolecules. Computer simulations of biomolecules, which made the biomolecular dynamics visible in silico, provide valuable insight for understanding how the dynamics of biomolecules drives biology processes (Cheatham and Kollman, 2000;Mirny and Shakhnovich, 2001;Norberg and Nilsson, 2002;Moraitakis et al, 2003;Levy et al, 2004;Zhou et al, 2004;Gao et al, 2005;Zuo et al, 2006Zuo et al, , 2009Li et al, 2008Li et al, , 2013Miyashita et al, 2009;Yang et al, 2014;Yan and Wang, 2019;Wu et al, 2020). In particular, molecular dynamics (MD) simulations can provide atomic-level details that are not always accessible in experiments and make this technique inevitable (Karplus and McCammon, 2002;Adcock and McCammon, 2006;Wang et al, 2009;Zuo et al, 2013).…”