The tertiary structure of protein, as well as the local secondary structure organization are fully determined by the angles of the peptidic bound. The backbone dihedral angles not only determine the global fold of the protein, but also the details of the local chain organization. Although a wealth of structural information is available in different databases and numerous structural biology softwares have been developed, rapid conformational characterization remains challenging.
We present here RamaDA, a program able to give a synthetic description of the conformation of a protein. The RamaDA program is based on a model where the Ramachadran plot is decomposed into seven conformational domains. Within the framework of this model, each amino-acid of a given protein is assigned to one of these domains.
From this assignment secondary structure elements can be detected with an accuracy equivalent to that of the DSSP program for helices and extended strands, and with the added capability of detecting PolyProline II secondary structures. Additionally, the determination of a z-score for each amino-acid of the protein emphasizes any irregularities in the element.
It is also possible to use this analysis to detect characteristic conformational patterns. In the case of EF-hands, calcium-binding helix-loop-helix domains, it is possible to design a strict consensus for the 9 amino-acids of the loop. 523 calcium binding protein files can be found into the entire PDB with this pattern and only 2.7% false positive hits are detected.
The program RamaDA gathers several tools in one and is then able to give a complete information on a protein structure, including loops and random coil regions. Through the example of EF-hands, a promising approach of structural biology is developed. RamaDA is freely available for download as well as online usage at http://ramada.u-strasbg.fr
We explored the Protein DataBank (PDB) to collect protein-ssDNA structures and create a multiconformational docking benchmark including both bound and unbound protein structures. Due to ssDNA high flexibility when not bound, no ssDNA unbound structure is included in the benchmark. For the 91 sequence-identity groups identified as bound-unbound structures of the same protein, we studied the conformational changes in the protein induced by the ssDNA binding. Moreover, based on several bound or unbound protein structures in some groups, we also assessed the intrinsic conformational variability in…
The importance of torsion vibration in the transmission of life information is indicated. The localization of quantum torsion state is proved. Following these analyses a formalism on the quantum theory of conformation-electron system is proposed. The conformational-electronic transition is calculated by non-adiabatic operator method. The protein folding is viewed from conformational quantum transition and the folding rate is calculated. The time-scale of microsecond to millisecond for the fundamental folding event (nucleation, collapse, etc) is deduced. The dependence of transition rate W on N…
Intrinsically disordered proteins (IDPs) and multidomain proteins with flexible linkers show a high level of structural heterogeneity and are best described by ensembles consisting of multiple conformations with associated thermodynamic weights. Determining conformational ensembles usually involves integration of biophysical experiments and computational models. In this review, we discuss current approaches to determining conformational ensembles of IDPs and multidomain proteins, including the choice of biophysical experiments, computational models used to sample protein conformations, models …
Although the importance of protein dynamics in protein function is generally recognized, the role of protein fluctuations in allosteric effects scarcely has been considered. To address this gap, the Kullback-Leibler divergence (Dx) between protein conformational distributions before and after ligand binding was proposed as a means of quantifying allosteric effects in proteins. Here, previous applications of Dx to methods for analysis and simulation of proteins are first reviewed, and their implications for understanding aspects of protein function and protein evolution are discussed. Next, equ…
Quantum mechanical calculations are performed on 116 conformers of the protein ubiquitin (Lange et al., Science 2008, 320, 1471-1475). The results indicate that the heat of formation (HOF), dipole moment, energy of the frontier orbitals HOMO and LUMO, and HOMO-LUMO gap fluctuate within their corresponding ranges. This study thus provides a link between the conformational dynamics of a protein and its electronic structure.
We use plasmon rulers to follow the conformational dynamics of a single protein for up to 24 h at a video rate. The plasmon ruler consists of two gold nanospheres connected by a single protein linker. In our experiment, we follow the dynamics of the molecular chaperone heat shock protein 90, which is known to show open and closed conformations. Our measurements confirm the previously known conformational dynamics with transition times in the second to minute time scale and reveals new dynamics on the time scale of minutes to hours. Plasmon rulers thus extend the observation bandwidth 3/4 order…
CLeFAPS, a fast and flexible pairwise structural alignment algorithm based on a rigid-body framework, namely CLePAPS, is proposed. Instead of allowing twists (or bends), the flexible in CLeFAPS means: (a) flexibilization of the algorithm's parameters through self-adapting with the input structures' size, (b) flexibilization of adding the aligned fragment pairs (AFPs) into an one-to-multi correspondence set instead of checking their position conflict, (c) flexible fragment may be found through an elongation procedure rooted in a vector-based score instead of a distance-based score. We perform a…
We study the conformational freedom of a protein made by two rigid domains connected by a flexible linker. The conformational freedom is represented as an unknown probability distribution on the space of allowed states. A new algorithm for the calculation of the Maximum Allowable Probability is proposed, which can be extended to any type of measurements. In this paper we use Pseudo Contact Shifts and Residual Dipolar Coupling. We reconstruct a single central tendency in the distribution and discuss in depth the results.
Protein binding and function often involves conformational changes. Advanced NMR experiments indicate that these conformational changes can occur in the absence of ligand molecules (or with bound ligands), and that the ligands may 'select' protein conformations for binding (or unbinding). In this review, we argue that this conformational selection requires transition times for ligand binding and unbinding that are small compared to the dwell times of proteins in different conformations, which is plausible for small ligand molecules. Such a separation of timescales leads to a decoupling and tem…
Motivation: Protein sequence world is discrete as 20 amino acids (AA) while its structure world is continuous, though can be discretized into structural alphabets (SA). In order to reveal the relationship between sequence and structure, it is interesting to consider both AA and SA in a joint space. However, such space has too many parameters, so the reduction of AA is necessary to bring down the parameter numbers. Result: We've developed a simple but effective approach called entropic clustering based on selecting the best mutual information between a given reduction of AAs and SAs. The optimi…
Conformational changes upon protein-protein association are the key element of the binding mechanism. The study presents a systematic large-scale analysis of such conformational changes in the side chains. The results indicate that short and long side chains have different propensities for the conformational changes. Long side chains with three or more dihedral angles are often subject to large conformational transition. Shorter residues with one or two dihedral angles typically undergo local conformational changes not leading to a conformational transition. The relationship between the local …
Using the perturbation-response scanning (PRS) technique, we study a set of 23 proteins that display a variety of conformational motions upon ligand binding (e.g. shear, hinge, allosteric). In most cases, PRS determines residues that may be manipulated to achieve the resulting conformational change. PRS reveals that for some proteins, binding induced conformational change may be achieved through the perturbation of residues scattered throughout the protein, whereas in others, perturbation of specific residues confined to a highly specific region are necessary. Correlations between the experime…
The SARS-CoV-2 spike (S) protein facilitates viral infection, and has been the focus of many structure determination efforts. Its flexible loop regions are known to be involved in protein binding and may adopt multiple conformations. This paper identifies the S protein loops and studies their conformational variability based on the available Protein Data Bank (PDB) structures. While most loops had essentially one stable conformation, 17 of 44 loop regions were observed to be structurally variable with multiple substantively distinct conformations based on a cluster analysis. Loop modeling meth…
An approach that combines Self-Organizing maps, hierarchical clustering and network components is presented, aimed at comparing protein conformational ensembles obtained from multiple Molecular Dynamic simulations. As a first result the original ensembles can be summarized by using only the representative conformations of the clusters obtained. In addition the network components analysis allows to discover and interpret the dynamic behavior of the conformations won by each neuron. The results showed the ability of this approach to efficiently derive a functional interpretation of the protein d…
The Electron Microscopy Data Bank (EMDB) is a rapidly growing repository for the dissemination of structural data from single-particle reconstructions of supramolecular protein assemblies including motors, chaperones, cytoskeletal assemblies, and viral capsids. While the static structure of these assemblies provides essential insight into their biological function, their conformational dynamics and mechanics provide additional important information regarding the mechanism of their biological function. Here, we present an unsupervised computational framework to analyze and store for public acce…
A protein undergoes conformational dynamics with multiple time scales, which results in fluctuating enzyme activities. Recent studies in single molecule enzymology have observe this "age-old" dynamic disorder phenomenon directly. However, the single molecule technique has its limitation. To be able to observe this molecular effect with real biochemical functions {\it in situ}, we propose to couple the fluctuations in enzymatic activity to noise propagations in small protein interaction networks such as zeroth order ultra-sensitive phosphorylation-dephosphorylation cycle. We showed that enzyme …
A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible---heterogeneous as well as homogeneous---conformational distributions are taken into account without prejudgement, a single value of average transfer efficiency $\langle E\rangle$ between dyes at two chain ends is generally consistent with highly diverse, multiple values of…
Wayne State University（韦恩州立大学）；Univ. of Bari Aldo Moro（巴里大学阿尔多·莫罗分校）；National Research Council (CONICET)（国家研究委员会（CONICET））；Daruma Institute for Applied Intelligence（达摩应用智能研究所）
All-atom and coarse-grained molecular dynamics are two widely used computational tools to study the conformational states of proteins. Yet, these two simulation methods suffer from the fact that without access to supercomputing resources, the time and length scales at which these states become detectable are difficult to achieve. One alternative to such methods is based on encoding the atomistic trajectory of molecular dynamics as a shorthand version devoid of physical particles, and then learning to propagate the encoded trajectory through the use of artificial intelligence. Here we show that…
Many proteins carry out their biological functions by forming the characteristic tertiary structures. Therefore, the search of the stable states of proteins by molecular simulations is important to understand their functions and stabilities. However, getting the stable state by conformational search is difficult, because the energy landscape of the system is characterized by many local minima separated by high energy barriers. In order to overcome this difficulty, various sampling and optimization methods for conformations of proteins have been proposed. In this study, we propose a new conform…
The conformations available to polypeptides are determined by the interatomic forces acting on the peptide units, whereby backbone torsion angles are restricted as described by the Ramachandran plot. Although typical proteins are composed predominantly from α-helices and β-sheets, they nevertheless adopt diverse tertiary structure, each folded as dictated by its unique amino-acid sequence. Despite such uniqueness, however, the functioning of many proteins involves changes between quite different conformations. The study of large-scale conformational changes, particularly in large systems, is f…
We combined the genetic crossover, which is one of the operations of genetic algorithm, and replica-exchange method in parallel molecular dynamics simulations. The genetic crossover and replica-exchange method can search the global conformational space by exchanging the corresponding parts between a pair of conformations of a protein. In this study, we applied this method to an $α$-helical protein, Trp-cage mini protein, which has 20 amino-acid residues. The conformations obtained from the simulations are in good agreement with the experimental results.
In this conceptual paper we propose to explore the analogy between ontic/epistemic description of quantum phenomena and interrelation between dynamics of conformational and functional states of proteins. Another new idea is to apply theory of automata to model the latter dynamics. In our model protein's behavior is modeled with the aid of two dynamical systems, ontic and epistemic, which describe evolution of conformational and functional states of proteins, respectively. The epistemic automaton is constructed from the ontic automaton on the basis of functional (observational) equivalence rela…
Protein conformational transitions, which are essential for function, may be driven either by entropy or enthalpy when molecular systems comprising solute and solvent molecules are the focus. Revealing thermodynamic origin of a given molecular process is an important but difficult task, and general principles governing protein conformational distributions remain elusive. Here we demonstrate that when protein molecules are taken as thermodynamic systems and solvents being treated as the environment, conformational entropy is an excellent proxy for free energy and is sufficient to explain protei…
Protein binding often involves conformational changes. Important questions are whether a conformational change occurs prior to a binding event ('conformational selection') or after a binding event ('induced fit'), and how conformational transition rates can be obtained from experiments. In this article, we present general results for the chemical relaxation rates of conformational-selection and induced-fit binding processes that hold for all concentrations of proteins and ligands and, thus, go beyond the standard pseudo-first-order approximation of large ligand concentration. These results all…
Motivation: Proteins are known to undergo conformational changes in the course of their functions. The changes in conformation are often attributable to a small fraction of residues within the protein. Therefore identification of these variable regions is important for an understanding of protein function. Results: We propose a novel method for identification of local conformational changes in proteins. In our method, backbone conformations are encoded into a sequence of letters from a 16-letter alphabet (called D2 codes) to perform structural comparison. Since we do not use clustering analysi…
The binding of a ligand molecule to a protein is often accompanied by conformational changes of the protein. A central question is whether the ligand induces the conformational change (induced-fit), or rather selects and stabilizes a complementary conformation from a pre-existing equilibrium of ground and excited states of the protein (selected-fit). We consider here the binding kinetics in a simple four-state model of ligand-protein binding. In this model, the protein has two conformations, which can both bind the ligand. The first conformation is the ground state of the protein when the liga…
The current capacity of computers makes it possible to perform simulations of small systems with portable, explicit-solvent potentials achieving high degree of accuracy. However, simplified models must be employed to exploit the behaviour of large systems or to perform systematic scans of smaller systems. While powerful algorithms are available to facilitate the sampling of the conformational space, successful applications of such models are hindered by the availability of simple enough potentials able to satisfactorily reproduce known properties of the system. We develop an interatomic potent…
A growing number of experimental evidence shows that it is general for a ligand binding protein to have a potential for allosteric regulation and for further evolution. In addition, such proteins generically change their conformation upon binding. O. Rivoire has recently proposed an evolutionary scenario that explains these properties as a generic byproduct of selection for exquisite discrimination between very similar ligands. The initial claim was supported by two classes of basic examples: continuous protein models with small numbers of degrees of freedom, on which the development of a conf…
The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable. However, the evolution of the conformational states of proteins mostly shows non-Markovian behavior, recognizable by non-monoexponential state dwell time histograms. The application of a Hidden Markov Model technique to a cyclic system demonstrating semi-Markovian dynamics is presented in this paper and the required extension of the model design is discussed. As …
We explore how inherent flexibility of a protein molecule influences the mechanism controlling the kinetics of allosteric transitions using a variational model inspired from work in protein folding. The striking differences in the predicted transition mechanism for the opening of the two domains of calmodulin (CaM) emphasizes that inherent flexibility is key to understanding the complex conformational changes that occur in proteins. In particular, the C-terminal domain of CaM (cCaM) which is inherently less flexible than its N-terminal domain (nCaM) reveals "cracking" or local partial unfoldin…
Statistical thermodynamics basis of energy and residue position fluctuations is explained for native proteins. The protein and its surroundings are treated as a canonical system with emphasis on the effects of energy exchange between the two. Fluctuations of the energy are related to fluctuations of residue positions, which in turn are related to the connectivity matrix of the protein, thus establishing a connection between energy fluctuation pathways and protein architecture. The model gives the locations of hotspots for ligand binding, and identifies the pathways of energy conduction within …
This chapter describes the application of constrained geometric simulations for prediction of antibody structural dynamics. We utilize constrained geometric simulations method FRODAN, which is a low computational complexity alternative to Molecular Dynamics (MD) simulations that can rapidly explore flexible motions in protein structures. FRODAN is highly suited for conformational dynamics analysis of large proteins, complexes, intrinsically disordered proteins and dynamics that occurs on longer biologically relevant time scales which are normally inaccessible to classical MD simulations. This …
The function of membrane-embedded proteins such as ion channels depends crucially on their conformation. We demonstrate how conformational changes in asymmetric membrane proteins may be inferred from measurements of their diffusion. Such proteins cause local deformations in the membrane, which induce an extra hydrodynamic drag on the protein. Using membrane tension to control the magnitude of the deformations and hence the drag, measurements of diffusivity can be used to infer--- via an elastic model of the protein--- how conformation is changed by tension. Motivated by recent experimental res…
Expanding Protein Structure Prediction into Conformational State Space
National Library of Medicine, National Institutes of Health（美国国家医学图书馆，美国国立卫生研究院）；University of Pennsylvania（宾夕法尼亚大学）；University of Maryland（马里兰大学）；University of Toronto, Mississauga（多伦多大学密西沙加分校）；University of Toronto（多伦多大学）；Stockholm University（斯德哥尔摩大学）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Millennium Institute for Integrative Biology (iBio)（整合生物学千年研究所（iBio））
The protein folding is regarded as a quantum transition between torsion states on polypeptide chain. The deduction of the folding rate formula in our previous studies is reviewed. The rate formula is generalized to the case of frequency variation in folding. Then the following problems about the application of the rate theory are discussed: 1) The unified theory on the two-state and multi-state protein folding is given based on the concept of quantum transition. 2) The relationship of folding and unfolding rates vs denaturant concentration is studied. 3) The temperature dependence of folding r…
Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers of mass in proteins and a statistical analysis of conformation changes in the side-chains upon binding. Normal mode analysis and an elastic network model were applied to a set of protein complexes to calculate the residue fluctuations and develop the residue classification. Comparison with a classification based on normalized B-factors suggests that the B-fac…
The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We demonstrate here the isomorphism between the protein sequences and designable structures for two and three dimensional lattice proteins of very long aminoacid chains using exact enumerations and intuitive considerations.We emphasize that the topological arrangement of the aminoacid residues alone is adequate to deduce the designable and non-designable sequences witho…
Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP alpha-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent smFRET experiments. We find that alpha-synuclein is disordered with conformational statistics that are intermediate between random walk and collapsed globule behavior. An advantage of cali…
National Center for Computational Sciences（国家计算科学中心）；Oak Ridge National Laboratory（橡树岭国家实验室）
Automated identification of protein conformational states from simulation of an ensemble of structures is a hard problem because it requires teaching a computer to recognize shapes. We adapt the naive Bayes classifier from the machine learning community for use on atom-to-atom pairwise contacts. The result is an unsupervised learning algorithm that samples a `distribution' over potential classification schemes. We apply the classifier to a series of test structures and one real protein, showing that it identifies the conformational transition with > 95% accuracy in most cases. A nontrivial fea…
Neurotensin receptor 1 (NTSR1) is a G protein-coupled receptor that is important for signaling in the brain and the gut. Its agonist ligand neurotensin (NTS), a 13-amino-acid peptide, binds with nanomolar affinity from the extracellular side to NTSR1 and induces conformational changes that trigger intracellular signaling processes. Our goal is to monitor the conformational dynamics of single fluorescently labeled NTSR1. For this, we fused the fluorescent protein mNeonGreen to the C terminus of NTSR1, purified the receptor fusion protein from E. coli membranes, and reconstituted NTSR1 into lipo…
Proteins are the "work horses" in biological systems. In almost all functions specific proteins are involved. They control molecular transport processes, stabilize the cell structure, enzymatically catalyze chemical reactions; others act as molecular motors in the complex machinery of molecular synthetization processes. Due to their significance, misfolds and malfunctions of proteins typically entail disastrous diseases, such as Alzheimer's disease and bovine spongiform encephalopathy (BSE). Therefore, the understanding of the trinity of amino acid composition, geometric structure, and biologi…
The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system. Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we …
ENSEMBITS: an alphabet of protein conformational ensembles
Department of Computer Science, Vanderbilt University（范德比尔特大学计算机科学系）；Center for AI in Protein Dynamics, Vanderbilt University（蛋白质动力学中的人工智能中心，范德比尔特大学）；Department of Molecular Physiology and Biophysics, Vanderbilt University（分子生理学与生物物理学系，范德比尔特大学）
One of the key limitations of Molecular Dynamics simulations is the computational intractability of sampling protein conformational landscapes associated with either large system size or long timescales. To overcome this bottleneck, we present the REinforcement learning based Adaptive samPling (REAP) algorithm that aims to efficiently sample conformational space by learning the relative importance of each reaction coordinate as it samples the landscape. To achieve this, the algorithm uses concepts from the field of reinforcement learning, a subset of machine learning, which rewards sampling al…
The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors - myosin V and kinesin KIF1A - and performed numerical investigations of their conformational relaxation properties within the coarse-gra…
ConforNets: Latents-Based Conformational Control in OpenFold3
Department of Systems Biology, Columbia University, NY, USA（系统生物学系，哥伦比亚大学，纽约，美国）；Department of Computer Science, Columbia University, NY, USA（计算机科学系，哥伦比亚大学，纽约，美国）；Department of Computer Science, Princeton University, Princeton, NJ, USA（计算机科学系，普林斯顿大学，普林斯顿，新泽西州，美国）
The aim of this work was to find a minimal set of structurally stable pentapeptides, which allows forming a polypeptide chain of a required 3D structure. To search for factors that ensure structural stability of the pentapeptide, we generated peptide sequences with no more than three functional groups, based on the alanine pentapeptide AAAAA. We analyzed 44,860 structures of peptides by the molecular dynamics method and found that 1,225 pentapeptides over 80% of the simulation time were in a stable conformation. Clustering of these conformations revealed 54 topological types of conformationall…
Conformational fluctuations are believed to play an important role in the process by which transcription factor proteins locate and bind their target site on the genome of a bacterium. Using a simple model, we show that the binding time can be minimized, under selective pressure, by adjusting the spectrum of conformational states so that the fraction of time spent in more mobile conformations is matched with the target recognition rate. The associated optimal binding time is then within an order of magnitude of the limiting binding time imposed by thermodynamics, corresponding to an idealized …
Most known proteins in nature consist of multiple domains. Interactions between domains may lead to unexpected folding and misfolding phenomena. This study of human γD-crystallin, a two-domain protein in the eye lens, revealed one such surprise: conformational catalysis of misfolding via intermolecular domain interface ''stealing''. An intermolecular interface between the more stable domains outcompetes the native intramolecular domain interface. Loss of the native interface in turn promotes misfolding and subsequent aggregation, especially in cataract-related γD-crystallin variants. This phen…
Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity $D_I$. We find that the radius of gyration $R_g$ of the proteins exhibits $1/f$ fluctuations, that are synchronous with the fluctuations of $D_I$. Our analysis demonstrates the validity of the local Stokes-Einstein type relation $D_I\propto1/(R_g + R_0)$, where $R_0\sim0.3$ nm is assumed to be a hydration layer around the protein. From the analy…
