The ability to absorb mutations while retaining structure and function, or mutational robustness, is a remarkable property of natural proteins. In this Letter, we use a computational model of organismic evolution [Zeldovich et al, PLOS Comp Biol 3(7):e139 (2007)], which explicitly couples protein physics and population dynamics, to study mutational robustness of evolved model proteins. We find that dominant protein structures which evolved in the simulations are highly designable ones, in accord with some of the earlier observations. Next, we compare evolved sequences with the ones designed to fold into the same dominant structures and having the same thermodynamic stability, and find that evolved sequences are more robust against point mutations, being less likely to be destabilized upon them. These results point to sequence evolution as an important method of protein engineering if mutational robustness of the artificially developed proteins is desired. On the biological side, mutational robustness of proteins appears to be a natural consequence of the mutation-selection evolutionary process.
Several physical mechanisms have been proposed to explain allostery in proteins. They differ by the number of internal states that they assume a protein to occupy, leaving open the question of what controls the emergence of these distinct physical forms of allostery. Here, we analyze a simplified model of protein allostery under a range of physical and evolutionary constraints. We find that two archetypal mechanisms can emerge through evolution: a single-state mechanism where ligand binding induces a displacement along a soft normal mode or a multi-state mechanism where ligand binding induces …
The cosmological model of eternal inflation and the transition from chance to biological evolution in the history of life: The possibility of chance emergence of the replication and translation systems, and the protein superfolds
During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous proteins, to propose stochastic models of experimental protein evolution. These models predict quantitatively important features of experimentally evolved sequence libraries, like fitness distributions and position-specific mutational spectra. They also allow us to efficiently simulate sequence libraries for a vast array of combinations of experimental parameters…
The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein structures are considered to be aperiodic, and may have evolved this way for functional purposes, especially in instances that require a combination of softness and rigidity within the same molecule. By analyzing the solved protein structures, we show that orientational symmetry is broken in the aperiodic arrangement of the secondary structural elements (SSE…
Evolution of the genetic code. Why are there strong and weak letter doublets? The first gene, the first protein. Early (ancient) biosynthesis of protein
Proteins are regularly described with some general indices (mass fractal dimension, surface fractal dimension, entropy, enthalpy, free energies, hydrophobicity, denaturation temperature etc..), which are inherently statistical in nature. These general indices emerge from innumerable (innately context-dependent and time-dependent) interactions between various atoms of a protein. Many a studies have been performed on the nature of these inter-atomic interactions and the change of profile of atomic fluctuations that they cause. However, we still do not know, under a given context, for a given dur…
Emergence of new protein structures has proved difficult to trace in nature and engineer in the laboratory. However, one aspect of structure evolution has proved immensely helpful for determining the three-dimensional structure of proteins from their sequences: in the vast majority of cases, proteins that share more than 30% sequence identity have similar structures. Below this mark is the "twilight zone" where proteins may have identical or very different structures. These observations form the foundational intuition behind structure homology modeling. Despite their importance, however, they …
The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly-coupled amino acid network whose interactions and motions are captured by the mechan…
RNA protein interactions control the fate of cellular RNAs and play an important role in gene regulation. An interdependency between such interactions allows for the implementation of logic functions in gene regulation. We investigate the interplay between RNA binding partners in the context of the statistical physics of RNA secondary structure, and define a linear correlation function between the two partners as a measurement of the interdependency of their binding events. We demonstrate the emergence of a long-range power-law behavior of this linear correlation function. This suggests RNA se…
We report that protein confinement within nanoscopic vesicular compartments corresponds to a liquid-liquid phase transition with the protein/water within vesicle lumen interacting very differently than in bulk. We show this effect leads to considerable structural changes on the proteins with evidence suggesting non-alpha helical conformations. Most importantly both aspects lead to a significant improvement on protein stability against thermal denaturation up to 95degC at neutral pH, with little or no evidence of unfolding or reduced enzymatic activity. The latter parameter does indeed exhibit …
The emergence of biochemical activities in a protein seem to commence with the onset of atomic mean-square displacements along the protein lattice. The ensuing protein dynamical transition has been discussed extensively in the literature, and often with conflicting conclusions. Here we clarify the phenomenon by establishing a deep connection between the dynamical transition and the pseudogap state where high-temperature superconductivity comes to its end. For this we first show how to endow proteins with an order parameter akin the quasiparticle wave function in superconductors. We then presen…
Concordia University（康考迪亚大学）；Rutgers University – Camden（罗格斯大学卡姆登分校）
Predicting the structure of a protein from its sequence is a cornerstone task of molecular biology. Established methods in the field, such as homology modeling and fragment assembly, appeared to have reached their limit. However, this year saw the emergence of promising new approaches: end-to-end protein structure and dynamics models, as well as reinforcement learning applied to protein folding. For these approaches to be investigated on a larger scale, an efficient implementation of their key computational primitives is required. In this paper we present a library of differentiable mappings f…
Tsinghua University（清华大学）；Beijing Academy of Artificial Intelligence（北京智源人工智能研究院）；Tencent Quantum Lab（腾讯量子实验室）
Protein is linked to almost every life process. Therefore, analyzing the biological structure and property of protein sequences is critical to the exploration of life, as well as disease detection and drug discovery. Traditional protein analysis methods tend to be labor-intensive and time-consuming. The emergence of deep learning models makes modeling data patterns in large quantities of data possible. Interdisciplinary researchers have begun to leverage deep learning methods to model large biological datasets, e.g. using long short-term memory and convolutional neural network for protein sequ…
In the protein sequence space, natural proteins form clusters of families which are characterized by their unique native folds whereas the great majority of random polypeptides are neither clustered nor foldable to unique structures. Since a given polypeptide can be either foldable or unfoldable, a kind of "folding transition" is expected at the boundary of a protein family in the sequence space. By Monte Carlo simulations of a statistical mechanical model of protein sequence alignment that coherently incorporates both short-range and long-range interactions as well as variable-length insertio…
Upon studying the B-Factors of all the atoms of all non-redundant proteins belonging to 76 most commonly found structural domains of all four major structural classes, it was found that the residue mobility has decreased during the course of evolution. Though increased residue-flexibility was preferred in the early stages of protein structure evolution, less flexibility is preferred in the medieval and recent stages. GLU is found to be the most flexible residue while VAL recorded to have the least flexibility. General trends in decrement of B-Factors conformed to the general trend in the order…
ProLLM: Protein Chain-of-Thoughts Enhanced LLM for Protein-Protein Interaction Prediction
Rutgers University（罗格斯大学）；University of Liverpool（利物浦大学）；Peking University（北京大学）；Massachusetts Institute of Technology（麻省理工学院）；New Jersey Institute of Technology（新泽西理工学院）
Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. Due to their symmetry, these proteins constitute excellent model systems to investigate how evolution relates to structure, folding and function. Here, we propose a scheme to map evolutionary information at the sequence level to a coarse-grained model for repeat-protein folding and use it to investigate the folding of thousands of repeat-proteins. We model the energetics by a combination of an inverse Potts model scheme with an explicit mechanistic model of duplications and delet…
Towards coevolution-aware ancestral sequence reconstruction
Sorbonne Université（索邦大学）；CNRS, Computational, Quantitative and Synthetic Biology（法国国家科学研究中心，计算、定量与合成生物学）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；DISAT, Politecnico di Torino（都灵理工大学地球与环境科学系）；Institut Universitaire de France (IUF)（法国高等研究院）
The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations result from mechanical perturbations in cells. These different topologies have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations to show that sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulated overextension on four different sequences of DNA ((AA)12, (AT)12, (GG)12 and (GC)12) with supercoiling densities w…
Stockholm University（斯德哥尔摩大学）；University of Gothenburg（哥德堡大学）；Heidelberg University（海德堡大学）；KTH（皇家理工学院）；Karolinska Intitutet（卡罗林斯卡学院）；University of California, Berkeley（加州大学伯克利分校）；Goethe University Frankfurt & Frankfurt Institute for Advanced Studies（法兰克福歌德大学与法兰克福高等研究院）；Chalmers University of Technology（查尔姆斯理工大学）；Uppsala University（乌普萨拉大学）；University of Tübingen（蒂宾根大学）；Lund University（隆德大学）
