Luciano A Abriata and Matteo Dal Peraro, Assessing the potential of atomistic molecular dynamics simulations to probe reversible protein-protein recognition and binding, Scientific Reports, 2015 pp. 1-12.
Protein-protein recognition and binding are governed by diffusion, noncovalent forces and conformational flexibility, entangled in a way that only molecular dynamics simulations can dissect at high resolution. Here we exploited ubiquitin’s noncovalent dimerization equilibrium to assess the potential of atomistic simulations to reproduce reversible protein-protein binding, by running submicrosecond simulations of systems with multiple copies of the protein at millimolar concentrations. The simulations essentially fail because they lead to aggregates, yet they reproduce some specificity in the binding interfaces as observed in known covalent and noncovalent ubiquitin dimers. Following similar observations in literature we hint at electrostatics and water descriptions as the main liable force field elements, and propose that their optimization should consider observables relevant to multi-protein systems and unfolded proteins. Within limitations, analysis of binding events suggests salient features of protein-protein recognition and binding, to be retested with improved force fields. Among them, that specific configurations of relative direction and orientation seem to trigger fast binding of two molecules, even over 50Å distances; that conformational selection can take place within surface-to-surface distances of 10 to 40Å i.e. well before actual intermolecular contact; and that establishment of contacts between molecules further locks their conformations and relative orientations.
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Karen N Allen et al., Monotopic Membrane Proteins Join the Fold, Trends In Biochemical Sciences, 44 (2019) 7-20.
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C B Anfinsen, Principles that govern the folding of protein chains., Science, 181 (1973) 223-230.
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A Bitran et al., Co-translational folding allows misfolding-prone proteins to circumvent deep kinetic traps, Biorxiv.Org, 2019.
Many large proteins suffer from slow or inefficient folding in vitro. Here, we provide evidence that this problem can be alleviated in vivo if proteins start folding co-translationally. Using an all-atom simulation-based algorithm, we compute the folding properties of various large protein domains as a function of nascent chain length, and find that for certain proteins, there exists a narrow window of lengths that confers both thermodynamic stability and fast folding kinetics. Beyond these lengths, folding is drastically slowed by non-native interactions …
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S Rackovsky, On the nature of the protein folding code., Proceedings Of The National Academy Of Sciences Of The United States Of America, 90 (1993) 644-648.
This paper investigates quantitatively the characteristics of the local folding code. The overlapping four-residue fragments which make up the amino acid sequences of 114 proteins are divided into classes on the basis of the physical properties of their constituent amino acids. The distribution of structural types associated with each class of sequence fragment is determined and compared with an ensemble of random structural distributions of the same size selected from the actual protein structures. A criterion is proposed, based on the relative entropies of the two types of distribution, and on a hypothesis as to the characteristics of fragments which code for local structure, that makes it possible to identify those four-residue sequence elements which encode specific time-averaged structure. It is determined that, by this criterion, only 60-70% of the four-residue fragments encode specific structures. It is suggested that the remaining sequence fragments intrinsically encode susceptibility to conformational alteration under the influence of long-range interactions and that this susceptibility is required for correct folding of the molecule. This feature introduces an inherent indeterminacy into the local folding code. The implications of this observation for the prediction of protein structure by various methods are briefly discussed.
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Joachim Schoeberl, Numerical Methods for Maxwell Equations , , 2009 pp. 1-12.
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F Claude Kempson, Brain and Mind, The Lancet, 1909 pp. 1-24.
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Cyrus Levinthal, Levinthal's Paradox, Mossbauer Spectroscopy In Biological Systems Proceedings Of A Meeting Held At Allerton House, Monticello, Illinois, 1969 pp. 22-24.
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T Saio et al., Structural Basis for Protein Antiaggregation Activity of the Trigger Factor Chaperone, Science, 344 (2014) 1250494-1250494.
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H Enatsu, Relativistic Hamiltonian Formalism in Quantum Field Theory and Micro-Noncausality, Prog. Theor. Phys., 1963.
An attempt is made to extend Heisenberg-Pauli's theory of quantized fields in a relativistically invariant way. The transformation theory of Dirac is used as a basis for that purpose. It is assumed that a mass variable is canonically conjugate to an invariant-time variable, being a common time to all fields. Considering that the field functions in the usual quantum field theory are those expressed in terms of a mass representation, we transform the field functions into those in an invariant-time representation. It is shown that in the new …
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A Brinker et al., Dual function of protein confinement in chaperonin-assisted protein folding, Cell, 2001.
Abstract The GroEL/GroES chaperonin system mediates the folding of a range of newly synthesized polypeptides in the bacterial cytosol. Using a rapid biotin-streptavidin-based inhibition of chaperonin function, we show that the cage formed by GroEL and its cofactor GroES can have a dual role in promoting folding. First, enclosure of nonnative protein in the GroEL: GroES complex is essential for folding to proceed unimpaired by aggregation. Second, folding inside the cage can be significantly faster than folding in free solution …
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F Huang et al., Distinguishing between cooperative and unimodal downhill protein folding, National Acad Sciences, 2007.
Conventional cooperative protein folding invokes discrete ensembles of native and denatured state structures in separate free-energy wells. Unimodal noncooperative (“downhill”) folding, however, proposes an ensemble of states occupying a single free- energy well for proteins folding at≥ 4× 10 4 s− 1 at 298 K. It is difficult to falsify unimodal mechanisms for such fast folding proteins by standard equilibrium experiments because both cooperative and unimodal mechanisms can present the same time-averaged structural …
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Heng Ma et al., Deep Generative Model Driven Protein Folding Simulation, Arxiv.Org, 2019.
Significant progress in computer hardware and software have enabled molecular dynamics (MD) simulations to model complex biological phenomena such as protein folding. However, enabling MD simulations to access biologically relevant timescales (e.g., beyond milliseconds) still remains challenging. These limitations include (1) quantifying which set of states have already been (sufficiently) sampled in an ensemble of MD runs, and (2) identifying novel states from which simulations can be initiated to sample rare events (e.g., sampling folding events). With the recent success of deep learning and artificial intelligence techniques in analyzing large datasets, we posit that these techniques can also be used to adaptively guide MD simulations to model such complex biological phenomena. Leveraging our recently developed unsupervised deep learning technique to cluster protein folding trajectories into partially folded intermediates, we build an iterative workflow that enables our generative model to be coupled with all-atom MD simulations to fold small protein systems on emerging high performance computing platforms. We demonstrate our approach in folding Fs-peptide and the $ββα$ (BBA) fold, FSD-EY. Our adaptive workflow enables us to achieve an overall root-mean squared deviation (RMSD) to the native state of 1.6$~Å$ and 4.4~$Å$ respectively for Fs-peptide and FSD-EY. We also highlight some emerging challenges in the context of designing scalable workflows when data intensive deep learning techniques are coupled to compute intensive MD simulations.
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John Horgan, Bayes's Theorem: What's the Big Deal? , , 2016 pp. 1-24.
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I N Berezovsky and Edward N Trifonov, Loop fold structure of proteins: resolution of Levinthal's paradox, Psychological Perspectives, 20 (2002) 5-6.
According to Levinthal a protein chain of ordinary size would require enormous time to sort its conformational states before the final fold is reached. Experimentally observed time of folding suggests an estimate of the chain length for which the time would be sufficient. This estimate by order of magnitude fits to experimentally observed universal closed loop elements of globular proteins—25–30 residues.
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K A Dill et al., The protein folding problem, Annualreviews.Org, 37 (2008) 289-316.
The “protein folding problem” consists of three closely related puzzles:(a) What is the folding code?(b) What is the folding mechanism?(c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein folding has …
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Stefan Auer et al., Importance of Metastable States in the Free Energy Landscapes of Polypeptide Chains, Arxiv.Org, 2007 17995375, cond-mat.soft (17) p. 178104.
We show that the interplay between excluded volume effects, hydrophobicity, and hydrogen bonding of a tube-like representation of a polypeptide chain gives rise to free energy landscapes that exhibit a small number of metastable minima corresponding to common structural motifs observed in proteins. The complexity of the landscape increases only moderately with the length of the chain. Analysis of the temperature dependence of these landscapes reveals that the stability of specific metastable states is maximal at a temperature close to the mid-point of folding. These mestastable states are therefore likely to be of particular significance in determining the generic tendency of proteins to aggregate into potentially pathogenic agents.
Published in: Physical Review Letters, 99 178104 (2007)
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Franc Avbelj and Ljudmila Fele, Prediction of the three‐dimensional structure of proteins using the electrostatic screening model and hierarchic condensation, Proteins: Structure, Function, And Bioinformatics, 31 (1998) 74-96.
We describe a method for predicting the three‐dimensional (3‐D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main‐chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high‐resolution x‐ ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte …
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Franc Avbelj and L Fele, Role of main-chain electrostatics, hydrophobic effect and side-chain conformational entropy in determining the secondary structure of proteins, Studies In History And Philosophy Of Science Part B, 279 (1998) 665-684.
The physiochemical bases of amino acid preferences for α-helical, β-strand, and other main- chain conformational states in proteins is controversial. Hydrophobic effect, side-chain conformational entropy, steric factors, and main-chain electrostatic interactions have all been advanced as the dominant physical factors which determine these preferences. Many attempts to resolve the controversy have focused on small model systems. The disadvantage of such systems is that the amino acids in small molecules are largerly …
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T Babej et al., Coarse-grained lattice protein folding on a quantum annealer, Arxiv.Org, 2018.
Lattice models have been used extensively over the past thirty years to examine the principles of protein folding and design. These models can be used to determine the conformation of the lowest energy fold out of a large number of possible conformations. However, due to the size of the conformational space, new algorithms are required for folding longer proteins sequences. Preliminary work was performed by Babbush et al. [3] to fold a small peptide on a planar lattice using a quantum annealing device. We extend this work by providing improved Ising-type Hamiltonian encodings for the problem of finding the lowest energy conformation of a lattice protein. We demonstrate a decrease in quantum circuit complexity from quadratic to quasilinear in certain cases. Additionally, we generalize to three spatial dimensions in order to obtain results with higher correlation to the actual atomistic 3D structure of the protein and outline our heuristic approach for splitting large problem instances into smaller subproblems that can be directly solved with the current D-Wave 2000Q architecture. To the best of our knowledge, this work sets a new record for lattice protein folding on a quantum annealer by folding Chignolin (10 residues) on a planar lattice and Trp-Cage (8 residues) on a cubic lattice.
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Marco Baiesi et al., Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding, Arxiv.Org, 2018 1809.02173v3, q-bio.BM (1) p. 39.
Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence of specific patterns adopted by protein sequences and structures to deal with backbone self-entanglement. A large scale analysis of the Protein Data Bank shows that loops significantly intertwined with another chain portion are typically closed by weakly bound amino acids. Why is this energetic frustration maintained? A possible picture is that entangled loops are formed only toward the end of the folding process to avoid kinetic traps. Consistently, these loops are more frequently found to be wrapped around a portion of the chain on their N-terminal side, the one translated earlier at the ribosome. Finally, these motifs are less abundant in natural native states than in simulated protein-like structures, yet they appear in 32% of proteins, which in some cases display an amazingly complex intertwining.
Published in: Scientific Reports (2019) 9:8426
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David Baker, What has de novo protein design taught us about protein folding and biophysics?, Protein Science, 28 (2019) 678-683.
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David Balchin et al., In vivo aspects of protein folding and quality control., Science, 2016 27365453, 353 (6294) p. aac4354.
Most proteins must fold into unique three-dimensional structures to perform their biological functions. In the crowded cellular environment, newly synthesized proteins are at risk of misfolding and forming toxic aggregate species. To ensure efficient folding, different classes of molecular chaperones receive the nascent protein chain emerging from the ribosome and guide it along a productive folding pathway. Because proteins are structurally dynamic, constant surveillance of the proteome by an integrated network of chaperones and protein degradation machineries is required to maintain protein homeostasis (proteostasis). The capacity of this proteostasis network declines during aging, facilitating neurodegeneration and other chronic diseases associated with protein aggregation. Understanding the proteostasis network holds the promise of identifying targets for pharmacological intervention in these pathologies.
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Keith Baverstock, Crick’s sequence hypothesis - a review, Communicative & Integrative Biology, 12 (2019) 59-64.
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D Beck, Methods for molecular dynamics simulations of protein folding/unfolding in solution, Methods, 34 (2004) 112-120.
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Arieh Ben-Naim, Levinthal’s Paradox Revisited, and Dismissed, Open Journal Of Biophysics, 02 (2012) 23-32.
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Arieh Ben-Naim, Response to comments on my article: Levinthal’s question revisited and answered. Ben-Naim, A. (2012), Journal of Biomolecular Structure and Dynamics, 30, 113–124, Journal Of Biomolecular Structure And Dynamics, 31 (2013) 1028-1033.
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Arieh Ben-Naim, Solvent-induced forces in protein folding reflections on the protein folding problem, Current Opinion In Colloid & Interface Science, 18 (2013) 502-509.
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Igor N Berezovsky et al., Basic units of protein structure, folding, and function, Progress In Biophysics And Molecular Biology, 128 (2017) 85-99.
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Fernando Bergasa-Caceres et al., Nature's Shortcut to Protein Folding., The Journal Of Physical Chemistry B, 123 (2019) 4463-4476.
This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut to efficient folding. Nature's Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature's establishment of this scaffold of nonlocal contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature's Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature's Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.
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Fernando Bergasa-Caceres et al., Nature’s Shortcut to Protein Folding, The Journal Of Physical Chemistry B, 123 (2019) 4463-4476.
This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut
to efficient folding. Nature’s Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions
of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature’s establishment of this scaffold of nonlocal
contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To
support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature’s Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature’s Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.
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Valentino Bianco et al., In Silico Evidence That Protein Unfolding is a Precursor of Protein Aggregation., Chemphyschem : A European Journal Of Chemical Physics And Physical Chemistry, 21 (2020) 377-384.
We present a computational study on the folding and aggregation of proteins in an aqueous environment, as a function of its concentration. We show how the increase of the concentration of individual protein species can induce a partial unfolding of the native conformation without the occurrence of aggregates. A further increment of the protein concentration results in the complete loss of the folded structures and induces the formation of protein aggregates. We discuss the effect of the protein interface on the water fluctuations in the protein hydration shell and their relevance in the protein-protein interaction.
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Daniel Bonetti et al., Estimation of Distribution Algorithm for Protein Structure Prediction, Arxiv.Org, 2019 1901.01059v1, q-bio.BM.
Proteins are essential for maintaining life. For example, knowing the structure of a protein, cell regulatory mechanisms of organisms can be modeled, supporting the development of disease treatments or the understanding of relationships between protein structures and food attributes. However, discovering the structure of a protein can be a difficult and expensive task, since it is hard to explore the large search to predict even a small protein. Template-based methods (coarse-grained, homology, threading etc) depend on Prior Knowledge (PK) of proteins determined using other methods as X-Ray Crystallography or Nuclear Magnetic Resonance. On the other hand, template-free methods (full-atom and ab initio) rely on atoms physical-chemical properties to predict protein structures. In comparison with other approaches, the Estimation of Distribution Algorithms (EDAs) can require significant less PK, suggesting that it could be adequate for proteins of low-level of PK. Finding an EDA able to handle both prediction quality and computational time is a difficult task, since they are strong inversely correlated. We developed an EDA specific for the ab initio Protein Structure Prediction (PSP) problem using full-atom representation. We developed one univariate and two bivariate probabilistic models in order to design a proper EDA for PSP. The bivariate models make relationships between dihedral angles ϕ and ψ within an amino acid. Furthermore, we compared the proposed EDA with other approaches from the literature. We noticed that even a relatively simple algorithm such as Random Walk can find the correct solution, but it would require a large amount of prior knowledge (biased prediction). On the other hand, our EDA was able to correctly predict with no prior knowledge at all, characterizing such a prediction as pure ab initio.
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Esther Braselmann et al., Folding the proteome, Trends In Biochemical Sciences, 38 (2013) 337-344.
Protein folding is an essential prerequisite for protein function and hence cell function. Kinetic and thermody- namic studies of small proteins that refold reversibly were essential for developing our current understanding of the fundamentals of protein folding mechanisms. However, we still lack sufficient understanding to accu- rately predict protein structures from sequences, or the effects of disease-causing mutations. To date, model proteins selected for folding studies represent only a small fraction of the complexity of the proteome and are unlikely to exhibit the breadth of folding mechanisms used in vivo. We are in urgent need of new methods – both theoretical and experimental – that can quantify the folding behavior of a truly broad set of proteins under in vivo conditions. Such a shift in focus will provide a more comprehensive framework from which to understand the connections between protein folding, the molecular basis of disease, and cell function and evolution.
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R A Broglia et al., HIV-1 protease folding and the design of drugs which do not create resistance, Current Opinion In Structural Biology, 18 (2008) 60-66.
Human immunodeficiency virus type 1 (HIV-1) protease (PR) plays an essential role in the life cycle of the virus. Consequently, its inhibition can control acquired immunodeficiency syndrome (AIDS). Any pharmacological treatment targeting the active site of the protease is known to generate escape mutants. On the other hand, if a drug targets a site crucial for the correct folding of the protease, mutations affecting this region would denaturate the protein and thus will not be expressed. We review the progress in our understanding of the folding of the protease, which has been instrumental in the design of a (non-conventional) folding inhibitor. The transferability of these results to other proteins testify to the universality of the folding–inhibition scenario for the design of leads of drugs which are unlikely to generate resistance.
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R A Broglia et al., HIV-1 protease folding and the design of drugs which do not create resistance, Current Opinion In Structural Biology, 18 (2008) 60-66.
Human immunodeficiency virus type 1 (HIV-1) protease (PR) plays an essential role in the life cycle of the virus. Consequently, its inhibition can control acquired immunodeficiency syndrome (AIDS). Any pharmacological treatment targeting the active site of the protease is known to generate escape mutants. On the other hand, if a drug targets a site crucial for the correct folding of the protease, mutations affecting this region would denaturate the protein and thus will not be expressed. We review the progress in our understanding of the folding of the protease, which has been instrumental in the design of a (non-conventional) folding inhibitor. The transferability of these results to other proteins testify to the universality of the folding–inhibition scenario for the design of leads of drugs which are unlikely to generate resistance.
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R A Broglia et al., Simple models of protein folding and of non-conventional drug design, Iopscience.Iop.Org, .
While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information in order to predict the three-dimensional, biologically active, native conformation of a protein whose sequence is known. Using insights obtained from simple model simulations of the folding of proteins, in particular the fact that this phenomenon is essentially controlled by conserved (native) contacts among (few) strongly interacting ('hot'), as a rule hydrophobic, amino acids, which …
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Ron O Dror, Computational biology: Structure and organization of biomolecules and cells, , 2017.
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Debayan Chakraborty et al., A multifunnel energy landscape encodes the competing α-helix and β-hairpin conformations for a designed peptide, Physical Chemistry Chemical Physics, 22 (2020) 1359-1370.
Depending on the amino acid sequence, as well as the local environment, some peptides have the capability to fold into multiple secondary structures. Conformational switching between such structures is a key element of protein folding and aggregation. Specifically, understanding the molecular mechanism underlying the transition from an a-helix to a b-hairpin is critical because it is thought to be a harbinger of amyloid assembly. In this study, we explore the energy landscape for an 18-residue peptide (DP5), designed by Araki and Tamura to exhibit equal propensities for the a-helical and b-hairpin forms. We find that the degeneracy is encoded in the multifunnel nature of the underlying free energy landscape. In agreement with experiment, we also observe that mutation of tyrosine at position 12 to serine shifts the equilibrium in favor of the a-helix conformation, by altering the landscape topography. The transition from the a-helix to the b-hairpin is a complex stepwise process, and occurs via collapsed coil-like intermediates. Our findings suggest that even a single mutation can tune the emergent features of the landscape, providing an efficient route to protein design. Interestingly, the transition pathways for the conformational switch seem to be minimally perturbed upon mutation, suggesting that there could be universal microscopic features that are conserved among different switch-competent protein sequences.
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Samuel S Cho et al., P versus Q: structural reaction coordinates capture protein folding on smooth landscapes., Proceedings Of The National Academy Of Sciences Of The United States Of America, 103 (2006) 586-591.
Minding your p's and q's has become as important to protein-folding theorists as it is for those being instructed in the rules of etiquette. To assess the quality of structural reaction coordinates in predicting the transition-state ensemble (TSE) of protein folding, we benchmarked the accuracy of four structural reaction coordinates against the kinetic measure P(fold), whose value of 0.50 defines the stochastic separatrix for a two-state folding mechanism. For two proteins that fold by a simple two-state mechanism, c-src SH3 and CI-2, the Phi-values of the TSEs predicted by native topology-based reaction coordinates (including Q, the fraction of native contacts) are almost identical to those of the TSE based on P(fold), with correlation coefficients of >0.90. For proteins with complex folding mechanisms that have especially broad, asymmetrical free energy barriers such as the designed 3-ankyrin repeating protein (3ANK) or proteins with distinct intermediates such as cyanovirin-N (CV-N), we show that the ensemble of structures with P(fold) = 0.50 generally does not include the chemically relevant transition states. This weakness of P(fold) limits its usefulness in protein folding studies. For such systems, elucidating the essential features of folding mechanisms requires using multiple reaction coordinates, although the number is still rather small. At the same time, for simple folding mechanisms, there is no indication of superiority for P(fold) over structurally chosen and thermodynamically relevant reaction coordinates that correctly measure the degree of nativeness.
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Hoi Sung Chung and William A Eaton, ScienceDirect Protein folding transition path times from single molecule FRET, Current Opinion In Structural Biology, 48 (2018) 30-39.
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Matteo Colombo and Cory Wright, First principles in the life sciences: the free-energy principle, organicism, and mechanism, Synthese, 46 (2018) 1-26.
The free-energy principle states that all systems that resist a tendency to physical disintegration must minimize their free energy. Originally proposed to account for perception, learning, and action, the free-energy principle has been applied to the evolution, development, morphology, and function of the brain, and has been called a postulate, an unfalsifiable principle, a natural law, and an imperative. While it might afford a theoretical foundation for understanding the relationship between environment, life, and mind, its epistemic status and scope are unclear. Also unclear is how the free-energy principle relates to prominent theoretical approaches to life science phenomena, such as organicism and mechanicism. This paper clarifies both issues, and identifies limits and prospects for the free-energy principle as a first principle in the life sciences.
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Ulf H Danielsson et al., A Gauge Field Theory of Chirally Folded Homopolymers with Applications to Folded Proteins, Arxiv.Org, 2009 0902.2920v2, cond-mat.stat-mech (2) p. 021910.
We combine the principle of gauge invariance with extrinsic string geometry to develop a lattice model that can be employed to theoretically describe properties of chiral, unbranched homopolymers. We find that in its low temperature phase the model is in the same universality class with proteins that are deposited in the Protein Data Bank, in the sense of the compactness index. We apply the model to analyze various statistical aspects of folded proteins. Curiously we find that it can produce results that are a very good good match to the data in the Protein Data Bank.
Published in: Phys.Rev.E82:021910,2010
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Jens Danielsson et al., Thermodynamics of protein destabilization in live cells, Proceedings Of The National Academy Of Sciences Of The United States Of America, 112 (2015) 12402-12407.
Although protein folding and stability have been well explored under simplified conditions in vitro, it is yet unclear how these basic self-organization events are modulated by the crowded interior of live cells. To find out, we use here in-cell NMR to follow at atomic resolution the thermal unfolding of a β-barrel protein in- side mammalian and bacterial cells. Challenging the view from in vitro crowding effects, we find that the cells destabilize the pro- tein at 37 °C but with a conspicuous twist: While the melting tem- perature goes down the cold unfolding moves into the physiological regime, coupled to an augmented heat-capacity change. The effect seems induced by transient, sequence-specific, interactions with the cellular components, acting preferentially on the unfolded ensemble. This points to a model where the in vivo influence on protein behavior is case specific, determined by the individual protein’s interplay with the functionally optimized “interaction landscape” of the cellular interior.
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Suman Das et al., Comparative Roles of Charge, pi, and Hydrophobic Interactions in Sequence-Dependent Phase Separation of Intrinsically Disordered Proteins, , 2020.
Biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins and nucleic acids can serve important biological functions; yet current understanding of the effects of amino acid sequences on LLPS is limited. Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular LLPS, we used the N-terminal intrinsically disordered region (IDR) of the DEAD-box helicase Ddx4 as a test case to conduct extensive multiple-chain simulations to assess the roles of electrostatic, hydrophobic, cation-$π$, and aromatic interactions in sequence-specific phase behaviors. Three different residue-residue interaction schemes sharing the same electrostatic potential were evaluated. We found that neither a common scheme based on amino acid hydrophobicity nor one augmented with arginine/lysine-aromatic cation-$π$ interactions can consistently account for the available experimental LLPS data on the wildtype, a charge-scrambled mutant, a phenylalanine-to-alanine (FtoA) mutant and an arginine-to-lysine (RtoK) mutant of the Ddx4 IDR. In contrast, an interaction scheme based on contact statistics among folded globular protein structures reproduces the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. This finding underscores the important role of $π$-related interactions in LLPS and that their effects are embodied to a degree in classical statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on protein concentration in the aqueous medium. Analytical theory suggests that this dependence entails enhanced inter-protein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.
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Ken A Dill et al., The protein folding problem: when will it be solved?, Current Opinion In Structural Biology, 17 (2007) 342-346.
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K A Dill et al., Physical limits of cells and proteomes, National Acad Sciences, 2011.
What are the physical limits to cell behavior? Often, the physical limitations can be dominated by the proteome, the cell’s comple- ment of proteins. We combine known protein sizes, stabilities, and rates of folding and diffusion, with the known protein-length distributions PðNÞ of proteomes (Escherichia coli, yeast, and worm), to formulate distributions and scaling relationships in order to address questions of cell physics. Why do mesophilic cells die around 50°C? How can the maximal growth-rate temperature (around 37 °C) occur so close to the cell-death temperature? The model shows that the cell’s death temperature coincides with a denaturation catastrophe of its proteome. The reason cells can function so well just a few degrees below their death temperature is because proteome denaturation is so cooperative. Why are cells so dense-packed with protein molecules (about 20% by volume)? Cells are packed at a density that maximizes biochemical reaction rates. At lower densities, proteins collide too rarely. At higher den- sities, proteins diffuse too slowly through the crowded cell. What limits cell sizes and growth rates? Cell growth is limited by rates of protein synthesis, by the folding rates of its slowest proteins, and—for large cells—by the rates of its protein diffusion. Useful insights into cell physics may be obtainable from scaling laws that encapsulate information from protein knowledge bases.
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Simon Ebbinghaus et al., Protein folding stability and dynamics imaged in a living cell, Nature Publishing Group, 7 (2010) 319-323.
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Ron O Dror, Energy functions and their relationship to molecular conformation, , 2017.
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Jeremy England et al., Rattling the cage: computational models of chaperonin-mediated protein folding, Current Opinion In Structural Biology, 18 (2008) 163-169.
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Yi Fang and Junmei Jing, Geometry, thermodynamics, and protein, Journal Of Theoretical Biology, 262 (2010) 383-390.
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Yi Fang, Gibbs Free Energy Formula for Protein Folding, Thermodynamics - Fundamentals And Its Application In Science, Chapter 3, 1-36.
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Yi Fang, Protein Folding: The Gibbs Free Energy, Arxiv.Org, 2012 related:OgzB2M4OhQAJ, q-bio.BM.
The fundamental law for protein folding is the Thermodynamic Principle: the amino acid sequence of a protein determines its native structure and the native structure has the minimum Gibbs free energy. If all chemical problems can be answered by quantum mechanics, there should be a quantum mechanics derivation of Gibbs free energy formula G(X) for every possible conformation X of the protein. We apply quantum statistics to derive such a formula. For simplicity, only monomeric self folding globular proteins are covered. We point out some immediate applications of the formula. We show that the formula explains the observed phenomena very well. It gives a unified explanation to both folding and denaturation; it explains why hydrophobic effect is the driving force of protein folding and clarifies the role played by hydrogen bonding; it explains the successes and deficients of various surface area models. The formula also gives a clear kinetic force of the folding: Fi(X) = - \nablaxi G(X). This also gives a natural way to perform the ab initio prediction of protein structure, minimizing G(X) by Newton's fastest desciending method.
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Yi Fang, Ben-Naim’s “Pitfall”: Don Quixote’s Windmill, Open Journal Of Biophysics, 03 (2013) 13-21.
Ben-Naim in three articles dismissed and “answered” the Levinthal’s paradox. He announces there are pitfalls caused by the “misinterpretation” of thermodynamic hypothesis. He claims no existence of Gibbs free energy formula where the variable is a protein’s conformation X . His Gibbs energy functional is G(T, P, N, P(R)), where the variable is probability distributions P (R) of the conformations. His “minimum distribution Peq” is wrong. By carefully establishing thermodynamic systems, we demonstrate how to apply quantum statistics to derive Gibbs free energy formula G(X). The formula of the folding force is given.
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Alexey N Fedorov and Thomas O Baldwin, Cotranslational Protein Folding, Journal Of Biological Chemistry, 272 (1997) 32715-32718.
Alexey N. Fedorov, Thomas O. Baldwin
(web, pdf)
Alexei V Finkelstein et al., There and back again: Two views on the protein folding puzzle, Physics Of Life Reviews, 21 (2017) 56-71.
(web, pdf)
Eva Pebay-Peyroula and Christophe Chipot François Dehez, Binding of ADP in the Mitochondrial ADP/ATP Carrier Is Driven by an Electrostatic Funnel, Journal Of The American Chemical Society, 2008 pp. 1-9.
The ADP/ATP carrier (AAC) is a membrane protein of paramount importance for the energy- fueling function of the mitochondria, transporting ADP from the intermembrane space to the matrix and ATP in the opposite direction. On the basis of the high-resolution, 2.2-Å structure of the bovine carrier, a total of 0.53 μs of classical molecular dynamics simulations were conducted in a realistic membrane environment to decipher the early events of ADP3- translocation across the inner membrane of the mitochondria. Examination of apo-AAC underscores the impermeable nature of the carrier, impeding passive transport of permeants toward the matrix. The electrostatic funnel illuminated from three-dimensional mapping of the electrostatic potential forms a privileged passageway anticipated to drive the diphosphate nucleotide rapidly toward the bottom of the internal cavity. This conjecture is verified in the light of repeated, independent numerical experiments, whereby the permeant is dropped near the mouth of the mitochondrial carrier. Systematic association of ADP3- to the crevice of the AAC, an early event in its transport across the inner membrane, is accompanied by the formation of an intricate network of noncovalent bonds. Simulations relying on the use of an adaptive biasing force reveal for the first time that the proposed binding site corresponds to a minimum of the free energy landscape delineating the translocation of ADP3- in the carrier. The present work paves the way to the design of novel nucleotides and new experiments aimed at unveiling key structural features in the chronology of ADP/ATP transport across the mitochondrial membrane.
(pdf)
Monika Fuxreiter, ScienceDirect Fold or not to fold upon binding — does it really matter?, Current Opinion In Structural Biology, 54 (2018) 19-25.
(web, pdf)
Małgorzata Gadzała et al., The aqueous environment as an active participant in the protein folding process, Journal Of Molecular Graphics And Modelling, 87 (2019) 227-239.
(web, pdf)
Meng Gao et al., Water dynamics clue to key residues in protein folding, Biochemical And Biophysical Research Communications, 392 (2010) 95-99.
(web, pdf)
Anne Gershenson and Lila M Gierasch, Protein folding in the cell: challenges and progress, Current Opinion In Structural Biology, 21 (2011) 32-41.
(web, pdf)
Anne Gershenson et al., Successes and challenges in simulating the folding of large proteins, Journal Of Biological Chemistry, 295 (2020) 15-33.
Computational simulations of protein folding can be used to interpret experimental folding results, to design new folding experiments and to test the effects of mutations and small molecules on folding. However, while major experimental and computational progress has been made in understanding how small proteins fold, research on larger, multi-domain proteins, which comprise the majority of proteins, is less advanced. Specifically, large proteins often fold via long-lived partially folded intermediates, whose structures, potentially toxic oligomerization and interactions with cellular chaperones remain poorly understood. Molecular dynamics (MD) based folding simulations that rely on knowledge of the native structure can provide critical, detailed information on folding free energy landscapes, intermediates and pathways. Further, increases in computational power and methodological advances have made folding
simulations of large proteins practical and valuable. Here, using serpins that inhibit proteases as an example, we review native-centric methods for simulating the folding of large proteins. These synergistic approaches range from Gō and related structure-based models (SBMs) that can predict the effects of the native structure on folding to all- atom-based methods that include side chain chemistry and can predict how disease-associated mutations may impact folding. The application of these computational approaches to serpins and other large proteins highlights the successes and limitations of current computational methods and underscores how computational results can be used to inform experiments. These powerful simulation approaches in combination with experiments can provide unique insights into how large proteins fold and misfold expanding our ability to predict and manipulate protein folding.
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Stefano Gianni and Per Jemth, Protein folding: Vexing debates on a fundamental problem, Biophysical Chemistry, 212 (2016) 17-21.
(web, pdf)
Marco Giulini and Raffaello Potestio, A deep learning approach to the structural analysis of proteins, Arxiv.Org, 2019 1901.00915v1, cond-mat.soft.
Deep Learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in which DL-based approaches can be profitably employed. To express the full potential of these techniques, though, it is a prerequisite to express the information contained in the molecule's atomic positions and distances in a set of input quantities that the network can process. Many of the molecular descriptors devised insofar are effective and manageable for relatively small structures, but become complex and cumbersome for larger ones. Furthermore, most of them are defined locally, a feature that could represent a limit for those applications where global properties are of interest. Here, we build a deep learning architecture capable of predicting non-trivial and intrinsically global quantities, that is, the eigenvalues of a protein's lowest-energy fluctuation modes. This application represents a first, relatively simple test bed for the development of a neural network approach to the quantitative analysis of protein structures, and demonstrates unexpected use in the identification of mechanically relevant regions of the molecule.
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Johan A Grahnen et al., Biophysical and structural considerations for protein sequence evolution., Bmc Evolutionary Biology, 11 (2011) 361-18.
BACKGROUND:Protein sequence evolution is constrained by the biophysics of folding and function, causing interdependence between interacting sites in the sequence. However, current site-independent models of sequence evolutions do not take this into account. Recent attempts to integrate the influence of structure and biophysics into phylogenetic models via statistical/informational approaches have not resulted in expected improvements in model performance. This suggests that further innovations are needed for progress in this field.
RESULTS:Here we develop a coarse-grained physics-based model of protein folding and binding function, and compare it to a popular informational model. We find that both models violate the assumption of the native sequence being close to a thermodynamic optimum, causing directional selection away from the native state. Sampling and simulation show that the physics-based model is more specific for fold-defining interactions that vary less among residue type. The informational model diffuses further in sequence space with fewer barriers and tends to provide less support for an invariant sites model, although amino acid substitutions are generally conservative. Both approaches produce sequences with natural features like dN/dS < 1 and gamma-distributed rates across sites.
CONCLUSIONS:Simple coarse-grained models of protein folding can describe some natural features of evolving proteins but are currently not accurate enough to use in evolutionary inference. This is partly due to improper packing of the hydrophobic core. We suggest possible improvements on the representation of structure, folding energy, and binding function, as regards both native and non-native conformations, and describe a large number of possible applications for such a model.
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Torin Greenwood and Christine E Heitsch, Deconvolving RNA Base Pairing Signals, Arxiv.Org, 2018 1801.03055v1, math.CO.
The structure of an RNA sequence encodes information about its biological function. A sequence is typically predicted to fold to a single minimum free energy conformation. But, an increasing number of RNA molecules are now known to fold into multiple stable structures. Discrete optimization methods are commonly used to predict foldings, and adding experimental data as auxiliary information improves prediction accuracy when there is a single dominant conformation. In this paper, we analyze the outputs of existing structural prediction models when they receive auxiliary data derived from a mixture of structures. Under a binary model of auxiliary data, we find that current structural prediction methods typically favor distributions with one dominant structure, and hence cannot guarantee accurate reconstruction of multimodal distributions. Additionally, we analyze empirical distributions of auxiliary data used in current prediction models. We show that even when the structures in a distribution are known in advance, it is difficult to determine the weightings of the structures using auxiliary data.
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Amit J Gupta et al., Active Cage Mechanism of Chaperonin-Assisted Protein Folding Demonstrated at Single-Molecule Level, Journal Of Molecular Biology, 426 (2014) 2739-2754.
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A Brenda Guzovsky et al., Localization of Energetic Frustration in Proteins, , 2018.
We present a detailed heuristic method to quantify the degree of local energetic frustration manifested by protein molecules. Current applications are realized in computational experiments where a protein structure is visualized highlighting the energetic conflicts or the concordance of the local interactions in that structure. Minimally frustrated linkages highlight the stable folding core of the molecule. Sites of high local frustration, in contrast, often indicate functionally relevant regions such as binding, active or allosteric sites.
(web, pdf)
Ulf Hensen et al., Exploring Protein Dynamics Space: The Dynasome as the Missing Link between Protein Structure and Function, Plos One, 7 (2012) e33931-16.
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Karan S Hingorani and Lila M Gierasch, Comparing protein folding in vitro and in vivo: foldability meets the fitness challenge, Current Opinion In Structural Biology, 24 (2014) 81-90.
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B Honig, Protein folding: from the levinthal paradox to structure prediction, Studies In History And Philosophy Of Science Part B, 293 (1999) 283-293.
This article is a personal perspective on the developments in the field of protein folding over approximately the last 40 years. In addition to its historical aspects, the article presents a view of the principles of protein folding with particular emphasis on the relationship of these principles to the problem of protein structure prediction. It is argued that despite much that is new, the essential elements of our current understanding of protein folding were anticipated by researchers many years ago. These elements include the recognition of the central …
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Naoto Hori et al., Ion Condensation onto Ribozyme is Site-Specific and Fold-Dependent, Arxiv.Org, 2019.
The highly charged RNA molecules, with each phosphate carrying a single negative charge, cannot fold into well-defined architectures with tertiary interactions, in the absence of ions. For ribozymes, divalent cations are known to be more efficient than monovalent ions in driving them to a compact state although Mg$^{2+}$ ions are needed for catalytic activities. Therefore, how ions interact with RNA is relevant in understanding RNA folding. It is often thought that most of the ions are territorially and non-specifically bound to the RNA, as predicted by the counterion condensation (CIC) theory. Here, we show using simulations of ${\it Azoarcus}$ ribozyme, based on an accurate coarse-grained Three Site Interaction (TIS) model, with explicit divalent and monovalent cations, that ion condensation is highly specific and depends on the nucleotide position. The regions with high coordination between the phosphate groups and the divalent cations are discernible even at very low Mg$^{2+}$ concentrations when the ribozyme does not form tertiary interactions. Surprisingly, these regions also contain the secondary structural elements that nucleate subsequently in the self-assembly of RNA, implying that ion condensation is determined by the architecture of the folded state. These results are in sharp contrast to interactions of ions (monovalent and divalent) with rigid charged rods in which ion condensation is uniform and position independent. The differences are explained in terms of the dramatic non-monotonic shape fluctuations in the ribozyme as it folds with increasing Mg$^{2+}$ or Ca$^{2+}$ concentration.
(web, pdf)
L S Itzhaki and P G Wolynes, The quest to understand protein folding, Current Opinion In Structural Biology, 18 (2008) 1-3.
(web, pdf)
Sophie E Jackson and Alan R Fersht, Folding of chymotrypsin inhibitor 2. 1. Evidence for a two-state transition, Biochemistry, 30 (1991) 10428-10435.
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S E Jackson, How do small single-domain proteins fold?, Folding & Design, 3 (1998) R81-91.
Many small, monomeric proteins fold with simple two-state kinetics and show wide variation in folding rates, from microseconds to seconds. Thus, stable intermediates are not a prerequisite for the fast, efficient folding of proteins and may in fact be kinetic traps and slow the folding process. Using recent studies, can we begin to search for trends which may lead to a better understanding of the protein folding process?
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William M Jacobs and Eugene I Shakhnovich, Accurate Protein-Folding Transition-Path Statistics from a Simple Free-Energy Landscape., The Journal Of Physical Chemistry B, 122 (2018) 11126-11136.
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths-the rare trajectories that transit between the folded and unfolded ensembles-using only thermodynamic information, such as a low-dimensional equilibrium free-energy landscape. However, commonly used one-dimensional landscapes typically fall short of this aim, because an empirical coordinate-dependent diffusion coefficient has to be fit to transition-path trajectory data in order to reproduce the transition-path dynamics. We show that an alternative, first-principles free-energy landscape predicts transition-path statistics that agree well with simulations and single-molecule experiments without requiring dynamical data as an input. This "topological configuration" model assumes that distinct, native-like substructures assemble on a time scale that is slower than native-contact formation but faster than the folding of the entire protein. Using only equilibrium simulation data to determine the free energies of these coarse-grained intermediate states, we predict a broad distribution of transition-path transit times that agrees well with the transition-path durations observed in simulations. We further show that both the distribution of finite-time displacements on a one-dimensional order parameter and the ensemble of transition-path trajectories generated by the model are consistent with the simulated transition paths. These results indicate that a landscape based on transient folding intermediates, which are often hidden by one-dimensional projections, can form the basis of a predictive model of protein-folding transition-path dynamics.
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Christian M Kaiser and Kaixian Liu, Folding up and Moving onâNascent Protein Folding on the Ribosome, Journal Of Molecular Biology, 430 (2018) 4580-4591.
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Raisa Kantaev et al., Manipulating the Folding Landscape of a Multidomain Protein, The Journal Of Physical Chemistry B, 122 (2018) 11030-11038.
Folding of proteins to their functional
conformation is paramount to life. Though 75% of the
proteome consists of multidomain proteins, our knowledge of
folding has been based primarily on studies conducted on
single-domain and fast-folding proteins. Nonetheless, the
complexity of folding landscapes exhibited by multidomain
proteins has received increased scrutiny in recent years. We
study the three-domain protein adenylate kinase from E. coli
(AK), which has been shown to fold through a series of
pathways involving several intermediate states. We use a
protein design method to manipulate the folding landscape of
AK, and single-molecule FRET spectroscopy to study the effects on the folding process. Mutations introduced in the NMP binding (NMPbind) domain of the protein are found to have unexpected effects on the folding landscape. Thus, while stabilizing mutations in the core of the NMPbind domain retain the main folding pathways of wild-type AK, a destabilizing mutation at the interface between the NMPbind and the CORE domains causes a significant repartition of the flux between the folding pathways. Our results demonstrate the outstanding plasticity of the folding landscape of AK and reveal how specific mutations in the primary structure are translated into changes in folding dynamics. The combination of methodologies introduced in this work should prove useful for deepening our understanding of the folding process of multidomain proteins.
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Susan Khor, Formation of native shortcut networks and two-state protein folding, Arxiv.Org, 2019 1902.06333v2, q-bio.MN.
A dynamic network-centric approach to study two-state folding from native structure called network dynamics (ND) is introduced. ND applies two fundamental principles of protein folding: hydrophobicity and loop-entropy, on a protein's native residue network (PRN0) to generate its native shortcut network (SCN0). ND generates barrier heights that correlate significantly (-0.7) with folding rate, and positions the transition-state (TS) for 52 proteins within 0.1 <= Q < 0.5 of its reaction coordinate, which monitors SCN0 completion. ND trajectories through SCN0 space are reasonable; they support our previous work on identifying initial fold steps. Both relative contact order (RCO) and network clustering coefficient C, computed on ND generated SCN0s, correlate significantly with all three folding kinetic variables: folding rate, TS placement and native-state (NS) stability. Some of these correlations are stronger or become significant when computed on partial than on complete SCN0s. In particular, contrary to previous findings, RCO can correlate significantly with NS stability. This revelation is made possible by ND, which provides a computationally light way to explore partially folded proteins via incomplete SCN0s. ND analysis affirms the presence of NS topology in its TS SCN0s, and finds C to be a better measure of protein topology than RCO, to shed light on the hypothesized relationship between NS structure and folding rate. Within the ND-TS region, C_SCN0 correlates significantly with folding rate, while SCN0_RCO does not. However, strong TS NS structural correlations, in terms of both SCN0_RCO and C_SCN0, is also producible by a randomized version of ND.
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Judith Klein-Seetharaman et al., Long-range interactions within a nonnative protein., Science, 295 (2002) 1719-1722.
Protein folding and unfolding are coupled to a range of biological phenomena, from the regulation of cellular activity to the onset of neurodegenerative diseases. Defining the nature of the conformations sampled in nonnative proteins is crucial for understanding the origins of such phenomena. We have used a combination of nuclear magnetic resonance (NMR) spectroscopy and site-directed mutagenesis to study unfolded states of the protein lysozyme. Extensive clusters of hydrophobic structure exist within the wild-type protein even under strongly denaturing conditions. These clusters involve distinct regions of the sequence but are all disrupted by a single point mutation that replaced residue Trp62 with Gly located at the interface of the two major structural domains in the native state. Thus, nativelike structure in the denatured protein is stabilized by the involvement of Trp62 in nonnative and long-range interactions.
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Anton A Komar, Unraveling co-translational protein folding: Concepts and methods, Methods, 137 (2018) 71-81.
(web, pdf)
Georg Krainer et al., Ultrafast Protein Folding in Membrane- Mimetic Environments, Journal Of Molecular Biology, 430 (2018) 554-564.
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Sergei V Krivov, Protein Folding Free Energy Landscape along the Committor - the Optimal Folding Coordinate, Journal Of Chemical Theory And Computation, 14 (2018) 3418-3427.
(web, pdf)
Jan Kubelka et al., The protein folding ‘speed limit’, Current Opinion In Structural Biology, 14 (2004) 76-88.
(web, pdf)
JA Vila, Metamorphic Proteins in light of Anfinsen's Dogma, The Journal Of Physical Chemistry Letters, 2020 pp. 4998-4999.
It is a common belief that metamorphic proteins challenge Anfinsen's thermodynamic hypothesis (or dogma). Here we argue against this view aims to show that metamorphic proteins not just fulfill Anfinsen's dogma but also exhibit marginal stability comparable to that seen on macromolecules and macromolecular complexes. This work contributes to our general understanding of protein classification and may spur significant progress in our effort to analyze protein evolvability.
(web, pdf)
C Levinthal Levinthal, How to Fold Graciously , Mössbauer Spectroscopy In Biological Systems, .
(web, pdf)
Yanjun Li et al., FoldingZero: Protein Folding from Scratch in Hydrophobic-Polar Model, Arxiv.Org, 2018 1812.00967v1, cs.LG.
De novo protein structure prediction from amino acid sequence is one of the most challenging problems in computational biology. As one of the extensively explored mathematical models for protein folding, Hydrophobic-Polar (HP) model enables thorough investigation of protein structure formation and evolution. Although HP model discretizes the conformational space and simplifies the folding energy function, it has been proven to be an NP-complete problem. In this paper, we propose a novel protein folding framework FoldingZero, self-folding a de novo protein 2D HP structure from scratch based on deep reinforcement learning. FoldingZero features the coupled approach of a two-head (policy and value heads) deep convolutional neural network (HPNet) and a regularized Upper Confidence Bounds for Trees (R-UCT). It is trained solely by a reinforcement learning algorithm, which improves HPNet and R-UCT iteratively through iterative policy optimization. Without any supervision and domain knowledge, FoldingZero not only achieves comparable results, but also learns the latent folding knowledge to stabilize the structure. Without exponential computation, FoldingZero shows promising potential to be adopted for real-world protein properties prediction.
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Shneior Lifson and A Roig, On the Theory of Helix—Coil Transition in Polypeptides, The Journal Of Chemical Physics, 34 (1961) 1963-1974.
The evaluation of the configurational partition function of a polypeptide molecule, with the internal rotation angles as variables, leads to an improved treatment of the phenomenon of helix‐coil transition in polypeptide molecules. The conditional probabilities of occurrence of helical and coiled states of the peptide units are obtained in the form of a 3×3 matrix. The order of this matrix is the lowest possible for the model employed, and is derived by a logical procedure which serves to eliminate redundancies in the enumeration of states. The eigenvalues of this matrix yield the various molecular averages as functions of the degree of polymerization, temperature, and molecular constants. Explicit formulas are given for the degree of intramolecular hydrogen bonding, average number of helical sequences, and the distribution of their lengths, as well as the number average and the weight average of these lengths.The evaluation of the configurational partition function of a polypeptide molecule, with the internal rotation angles as variables, leads to an improved treatment of the phenomenon of helix‐coil transition in polypeptide molecules. The conditional probabilities of occurrence of helical and coiled states of the peptide units are obtained in the form of a 3×3 matrix. The order of this matrix is the lowest possible for the model employed, and is derived by a logical procedure which serves to eliminate redundancies in the enumeration of states. The eigenvalues of this matrix yield the various molecular averages as functions of the degree of polymerization, temperature, and molecular constants. Explicit formulas are given for the degree of intramolecular hydrogen bonding, average number of helical sequences, and the distribution of their lengths, as well as the number average and the weight average of these lengths.
(web, pdf)
Kresten Lindorff-Larsen et al., How Fast-Folding Proteins Fold, Science, 334 (2011) 517-520.
An outstanding challenge in the field of molecular biology has been to understand the process by which proteins fold into their characteristic three-dimensional structures. Here, we report the results of atomic-level molecular dynamics simulations, over periods ranging between 100 ms and 1 ms, that reveal a set of common principles underlying the folding of 12 structurally diverse proteins. In simulations conducted with a single physics-based energy function, the proteins, representing all three major structural classes, spontaneously and repeatedly fold to their experimentally determined native structures. Early in the folding process, the protein backbone adopts a nativelike topology while certain secondary structure elements and a small number of nonlocal contacts form. In most cases, folding follows a single dominant route in which elements of the native structure appear in an order highly correlated with their propensity to form in the unfolded state.
(web, pdf)
Feng Liu and Martin Gruebele, Downhill dynamics and the molecular rate of protein folding, Chemical Physics Letters, 461 (2008) 1-8.
(web, pdf)
Jiaojiao Liu et al., Can all-atom protein dynamics be reconstructed from the knowledge of C-alpha time evolution?, Arxiv.Org, 2019 1901.06864v1, q-bio.BM.
We inquire to what extent protein peptide plane and side chain dynamics can be reconstructed from knowledge of C-alpha dynamics. Due to lack of experimental data we analyze all atom molecular dynamics trajectories from Anton supercomputer, and for clarity we limit our attention to the peptide plane O atoms and side chain C-beta atoms. We try and reconstruct their dynamics using four different approaches. Three of these are the publicly available reconstruction programs Pulchra, Remo Scwrl4. The fourth, Statistical Method, builds entirely on statistical analysis of Protein Data Bank (PDB) structures. All four methods place the O and C-beta atoms accurately along the Anton trajectories. However, the Statistical Method performs best. The results suggest that under physiological conditions, the all atom dynamics is slaved to that of C-alpha atoms. The results can help improve all atom force fields, and advance reconstruction and refinement methods for reduced protein structures. The results provide impetus for development of effective coarse grained force fields in terms of reduced coordinates.
(web, pdf)
Francesco Mallamace et al., Energy landscape in protein folding and unfolding, Proceedings Of The National Academy Of Sciences Of The United States Of America, 113 (2016) 3159-3163.
(web, pdf)
Leandro Martínez, Introducing the Levinthal’s Protein Folding Paradox and Its Solution, Journal Of Chemical Education, 91 (2014) 1918-1923.
(web, pdf)
Alexey V Melkikh and Dirk K F Meijer, On a generalized Levinthal's paradox: The role of long- and short range interactions in complex bio-molecular reactions, including protein and DNA folding, Progress In Biophysics And Molecular Biology, 132 (2018) 57-79.
(web, pdf)
Yinglong Miao et al., Accelerated molecular dynamics simulations of protein folding, Journal Of Computational Chemistry, 36 (2015) 1536-1549.
(web, pdf)
M Michel et al., PconsFold: improved contact predictions improve protein models, Prog. Theor. Phys., 2014.
… To whom correspondence should be addressed. Search for other works by this author on: Oxford Academic. PubMed. Google Scholar. Arne Elofsson. Bioinformatics, Volume 30, Issue 17, 1 September 2014, Pages i482–i488, https://doi.org/ 10.1093 / bioinformatics / btu458 …
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Soumya Mishra et al., Inaccurate secondary structure predictions often indicate protein fold switching, Protein Science, 2019 pp. pro.3664-7.
(web, pdf)
Ron O Dror, Molecular dynamics simulation, , 2017.
(pdf)
H B Movahed, Simulation of Protein Folding, Pdfs.Semanticscholar.Org, .
Understanding the mechanism of protein folding is often referred as the second half of genetics. By solving this problem, there will be a revolution in drug industry (folding of peptide is an important issue in biotechnology) as well as finding cures for the diseases …
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Rishi Mukhopadhyay et al., Protein Fold Family Recognition From Unassigned Residual Dipolar Coupling Data, Arxiv.Org, 2019 1911.00383v1, q-bio.BM.
Despite many advances in computational modeling of protein structures, these methods have not been widely utilized by experimental structural biologists. Two major obstacles are preventing the transition from a purely-experimental to a purely-computational mode of protein structure determination. The first problem is that most computational methods need a large library of computed structures that span a large variety of protein fold families, while structural genomics initiatives have slowed in their ability to provide novel protein folds in recent years. The second problem is an unwillingness to trust computational models that have no experimental backing. In this paper we test a potential solution to these problems that we have called Probability Density Profile Analysis (PDPA) that utilizes unassigned residual dipolar coupling data that are relatively cheap to acquire from NMR experiments.
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Sean Mullane, Protein folding in the modern era: a pedestrian’s guide, , 2020 pp. 1-20.
(pdf)
Federico Norbiato et al., Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures, Arxiv.Org, 2019 1911.08590v1, cond-mat.soft.
Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.
(web, pdf)
Yuan-Ping Pang, How fast fast-folding proteins fold in silico, Biochemical And Biophysical Research Communications, 492 (2017) 135-139.
(web, pdf)
Pape, Peptide Lecture, , 2006 pp. 1-50.
(pdf)
Chiwook Park et al., Energetics-based Protein Profiling on a Proteomic Scale: Identification of Proteins Resistant to Proteolysis, Journal Of Molecular Biology, 368 (2007) 1426-1437.
Native states of proteins are flexible, populating more than just the unique native conformation. The energetics and dynamics resulting from this conformational ensemble are inherently linked to protein function and regulation. Proteolytic susceptibility is one feature determined by this conformational energy landscape. As an attempt to investigate energetics of proteins on a proteomic scale, we challenged the Escherichia coli proteome with extensive proteolysis and determined which proteins, if any, have optimized their energy landscape for resistance to proteolysis. To our surprise, multiple soluble proteins survived the challenge. Maltose binding protein, a survivor from thermolysin digestion, was characterized by in vitro biophysical studies to identify the physical origin of proteolytic resistance. This experimental characterization shows that kinetic stability is responsible for the unusual resistance in maltose binding protein. The biochemical functions of the identified survivors suggest that many of these proteins may have evolved extreme proteolytic resistance because of their critical roles under stressed conditions. Our results suggest that under functional selection proteins can evolve extreme proteolysis resistance by modulating their conformational energy landscapes without the need to invent new folds, and that proteins can be profiled on a proteomic scale according to their energetic properties by using proteolysis as a structural probe.
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S Piana and Kresten Lindorff-Larsen, Atomic-level description of ubiquitin folding, National Acad Sciences, 2013.
Equilibrium molecular dynamics simulations, in which proteins spontaneously and repeatedly fold and unfold, have recently been used to help elucidate the mechanistic principles that underlie the folding of fast-folding proteins. The extent to which the conclu- sions drawn from the analysis of such proteins, which fold on the microsecond timescale, apply to the millisecond or slower folding of naturally occurring proteins is, however, unclear. As a first at- tempt to address this outstanding issue, we examine here the folding of ubiquitin, a 76-residue-long protein found in all eukar- yotes that is known experimentally to fold on a millisecond time- scale. Ubiquitin folding has been the subject of many experimental studies, but its slow folding rate has made it difficult to observe and characterize the folding process through all-atom molecular dynam- ics simulations. Here we determine the mechanism, thermodynam- ics, and kinetics of ubiquitin folding through equilibrium atomistic simulations. The picture emerging from the simulations is in agree- ment with a view of ubiquitin folding suggested from previous experiments. Our findings related to the folding of ubiquitin are also consistent, for the most part, with the folding principles derived from the simulation of fast-folding proteins, suggesting that these principles may be applicable to a wider range of proteins.
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Ron O Dror, Project ideas, , 2017.
(pdf)
Ron O Dror, Protein structure, , 2017.
(pdf)
Leonid Mimy and Alvin Kho, Protein structure forces, and folding, , 2005.
(pdf)
Ron O Dror, Protein structure prediction, , 2017.
(pdf)
David G Rattray and Leonard J Foster, ScienceDirect Dynamics of protein complex components, Current Opinion In Chemical Biology, 48 (2018) 81-85.
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J D Rimer et al., Crystal Growth Inhibitors for the Prevention of L-Cystine Kidney Stones Through Molecular Design, Science, 330 (2010) 337-341.
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Bruno Rizzuti and Valerie Daggett, Using simulations to provide the framework for experimental protein folding studies, Archives Of Biochemistry And Biophysics, 531 (2013) 128-135.
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Marina V Rodnina and Wolfgang Wintermeyer, Protein Elongation, Co-translational Folding and Targeting, Journal Of Molecular Biology, 428 (2016) 2165-2185.
The elongation phase of protein synthesis defines the overall speed and fidelity of protein synthesis and affects protein folding and targeting. The mechanisms of reactions taking place during translation elongation remain important questions in understanding ribosome function. The ribosome—guided by signals in the mRNA—can recode the genetic information, resulting in alternative protein products. Co-translational protein folding and interaction of ribosomes and emerging polypeptides with associated protein biogenesis factors determine the quality and localization of proteins. In this review, we summarize recent findings on mechanisms of translation elongation in bacteria, including decoding and recoding, peptide bond formation, tRNA–mRNA translocation, co-translational protein folding, interaction with protein biogenesis factors and targeting of ribosomes synthesizing membrane proteins to the plasma membrane. The data provide insights into how the ribosome shapes composition and quality of the cellular proteome.
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Mary A Rohrdanz et al., Discovering Mountain Passes via Torchlight: Methods for the Definition of Reaction Coordinates and Pathways in Complex Macromolecular Reactions, Annual Review Of Physical Chemistry, 64 (2013) 295-316.
The long-timescale dynamics of macromolecular systems can be oftentimes viewed as a reaction connecting metastable states of the system. In the past decade, various approaches have been developed to discover the collective motions associated with this dynamics. The corresponding collective vari- ables are used in many applications, e.g., to understand the reaction mecha- nism, to quantify the system’s free energy landscape, to enhance the sampling of the reaction path, and to determine the reaction rate. In this review we focus on a number of key developments in this field, providing an overview of several methods along with their relative regimes of applicability.
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Alexander Schug and José N Onuchic, From protein folding to protein function and biomolecular binding by energy landscape theory, Current Opinion In Pharmacology, 10 (2010) 709-714.
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Siddhartha Sen and H Paul Voorheis, Protein folding: Understanding the role of water and the low Reynolds number environment as the peptide chain emerges from the ribosome and folds, Journal Of Theoretical Biology, 363 (2014) 169-187.
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Eugene Serebryany et al., Conformational catalysis of cataract-associated aggregation by interacting intermediates in a human eye lens crystallin, Arxiv.Org, 2019 1904.03653v1, q-bio.BM.
Most known proteins in nature consist of multiple domains. Interactions between domains may lead to unexpected folding and misfolding phenomena. This study of human {}D-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 {}D-crystallin variants. This phenomenon is likely a contributing factor in the development of cataract disease, the leading worldwide cause of blindness. However, interface stealing likely occurs in many proteins composed of two or more interacting domains.
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V Sharma et al., Protein folding as an evolutionary process, Physica A, 388 (2009) 851-862.
Protein folding is often depicted as a motion along descending paths on a free energy landscape that results in a concurrent decrease in the conformational entropy of the polypeptide chain. However, to provide a description that is consistent with other natural processes, protein folding is formulated from the principle of increasing entropy. It then becomes evident that protein folding is an evolutionary process among many others. During the course of folding protein structural hierarchy builds up in succession by diminishing energy density gradients in the quest for a stationary state determined by surrounding density-in-energy. Evolution toward more probable states, eventually attaining the stationary state, naturally selects steeply ascending paths on the entropy landscape that correspond to steeply descending paths on the free energy landscape. The dissipative motion of the non-Euclidian manifold is non-deterministic by its nature which clarifies why it is so difficult to predict protein folding
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Adam K Sieradzan et al., Shielding effect in protein folding, Journal Of Molecular Graphics And Modelling, 79 (2018) 118-132.
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D Thirumalai et al., Protein folding: from theory to practice, Current Opinion In Structural Biology, 23 (2013) 22-29.
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Michael Thommen et al., Co-translational protein folding: progress and methods, Current Opinion In Structural Biology, 42 (2017) 83-89.
Proteins are synthesized as linear polymers and have to fold into their native structure to fulfil various functions in the cell. Folding can start co-translationally when the emerging peptide is still attached to the ribosome and is guided by the environment of the polypeptide exit tunnel and the kinetics of translation. Major questions are: When does co-translational folding begin? What is the role of the ribosome in guiding the nascent peptide towards its native structure? How does translation elongation kinetics modulate protein folding? Here we suggest how novel structural and biophysical approaches can help to probe the interplay between the ribosome and the emerging peptide and present future challenges in understanding co-translational folding.
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Ha H Truong and Susan Marqusee, Probing Protein Folding Landscape by Using Combined Force Spectroscopy and Molecular Dynamics Simulations, Biophysj, 2018 vol. 114 (Supplement 1) p. 412a.
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Franco O Tzul et al., Evidence for the principle of minimal frustration in the evolution of protein folding landscapes, Proceedings Of The National Academy Of Sciences Of The United States Of America, 114 (2017) E1627-E1632.
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Jorge Vila, Metamorphic Proteins in light of Anfinsen’s Dogma, , 2020 pp. 1-4.
It is a common belief that metamorphic proteins challenge Anfinsen’s thermodynamic hypothesis (or dogma). Here we argue against this view aims to show that metamorphic proteins not just fulfill the Anfinsen's dogma but also exhibit marginal stability comparable to that seen on macromolecules and macromolecular complexes. This work contributes to our general understanding of protein classification and may spur significant progress in our effort to analyze protein evolvability.
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C Wagner and T Kiefhaber, Intermediates can accelerate protein folding, Proceedings Of The National Academy Of Sciences Of The United States Of America, 96 (1999) 6716-6721.
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Ian M Walsh et al., Synonymous codon substitutions perturb cotranslational protein folding in vivo and impair cell fitness., Proceedings Of The National Academy Of Sciences Of The United States Of America, 117 (2020) 3528-3534.
In the cell, proteins are synthesized from N to C terminus and begin to fold during translation. Cotranslational folding mechanisms are therefore linked to elongation rate, which varies as a function of synonymous codon usage. However, synonymous codon substitutions can affect many distinct cellular processes, which has complicated attempts to deconvolve the extent to which synonymous codon usage can promote or frustrate proper protein folding in vivo. Although previous studies have shown that some synonymous changes can lead to different final structures, other substitutions will likely be more subtle, perturbing predominantly the protein folding pathway without radically altering the final structure. Here we show that synonymous codon substitutions encoding a single essential enzyme lead to dramatically slower cell growth. These mutations do not prevent active enzyme formation; instead, they predominantly alter the protein folding mechanism, leading to enhanced degradation in vivo. These results support a model in which synonymous codon substitutions can impair cell fitness by significantly perturbing cotranslational protein folding mechanisms, despite the chaperoning provided by the cellular protein homeostasis network.
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Arieh Warshel and Ram Prasad Bora, Perspective: Defining and quantifying the role of dynamics in enzyme catalysis, The Journal Of Chemical Physics, 144 (2016) 180901-18.
Enzymes control chemical reactions that are key to life processes, and allow them to take place on the time scale needed for synchronization between the relevant reaction cycles. In addition to general interest in their biological roles, these proteins present a fundamental scientific puzzle, since the origin of their tremendous catalytic power is still unclear. While many different hypotheses have been put forward to rationalize this, one of the proposals that has become particularly popular in recent years is the idea that dynamical effects contribute to catalysis. Here, we present a critical review of the dynamical idea, considering all reasonable definitions of what does and does not qualify as a dynamical effect. We demonstrate that no dynamical effect (according to these definitions) has ever been experimentally shown to contribute to catalysis. Furthermore, the existence of non-negligible dynamical contributions to catalysis is not supported by consistent theoretical studies. Our review is aimed, in part, at readers with a background in chemical physics and biophysics, and illustrates that despite a substantial body of experimental effort, there has not yet been any study that consistently established a connection between an enzyme’s conformational dynamics and a significant increase in the catalytic contribution of the chemical step. We also make the point that the dynamical proposal is not a semantic issue but a well-defined scientific hypothesis with well-defined conclusions
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Paul C Whitford and José N Onuchic, ScienceDirect What protein folding teaches us about biological function and molecular machines, Current Opinion In Structural Biology, 30 (2015) 57-62.
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Anna Jean Wirth and Martin Gruebele, Quinary protein structure and the consequences of crowding in living cells: Leaving the test-tube behind, Bioessays, 35 (2013) 984-993.
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Anna Jean Wirth et al., Temporal Variation of a Protein Folding Energy Landscape in the Cell, Journal Of The American Chemical Society, 135 (2013) 19215-19221.
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Yan Xu et al., Stabilizing Effect of Inherent Knots on Proteins Revealed by Molecular Dynamics Simulations, Biophysj, 115 (2018) 1681-1689.
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Hugo Yebenes et al., Chaperonins: two rings for folding, Trends In Biochemical Sciences, 36 (2011) 424-432.
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Qinyi Zhao, On the indirect relationship between protein dynamics and enzyme activity, Progress In Biophysics And Molecular Biology, 125 (2017) 52-60.
The behaviors of simple thermal systems have been well studied in physical chemistry and the principles obtained from such studies have been applied to complex thermal systems, such as proteins and en- zymes. But the simple application of such principles is questionable and may lead to mistakes under some circumstances. In enzymology, the transition state theory of chemical reactions has been accepted as a fundamental theory, but the role of protein dynamics in enzyme catalysis is controversial in the context of transition state theory. By studying behaviors of complex thermal systems, we have revised the Arrhenius equation and transition state theory and our model is validated in enzymology. Formally speaking, the revised Arrhenius equation is apparently similar to a conventional Arrhenius equation, but the physical meanings of its parameters differ from that of traditional forms in principle. Within this model, the role of protein dynamics in enzyme catalysis is well defined and quantified.
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Victor Zhao et al., Effect of protein structure on evolution of cotranslational folding, Arxiv.Org, 2020 2004.03326v1, q-bio.BM.
Cotranslational folding is expected to occur when the folding speed of the nascent chain is faster than the translation speed of the ribosome, but it is difficult to predict which proteins cotranslationally fold. Here, we simulate evolution of model proteins to investigate how native structure influences evolution of cotranslational folding. We developed a model that connects protein folding during and after translation to cellular fitness. Model proteins evolved improved folding speed and stability, with proteins adopting one of two strategies for folding quickly. Low contact order proteins evolve to fold cotranslationally. Such proteins adopt native conformations early on during the translation process, with each subsequently translated residue establishing additional native contacts. On the other hand, high contact order proteins tend not to be stable in their native conformations until the full chain is nearly extruded. We also simulated evolution of slowly translating codons, finding that slowing translation at certain positions enhances cotranslational folding. Finally, we investigated real protein structures using a previously published dataset that identified evolutionarily conserved rare codons in E. coli genes and associated such codons with cotranslational folding intermediates. We found that protein substructures preceding conserved rare codons tend to have lower contact orders, in line with our finding that lower contact order proteins are more likely to fold cotranslationally. Our work shows how evolutionary selection pressure can cause proteins with local contact topologies to evolve cotranslational folding.
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Ron O Dror, lecture 4-5 MD 1 2017 - with notes.key, , 2017.
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S Prigge, Prigge, , 2010 pp. 1-11.
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Arjan van der Vaart, Coupled binding–bending–folding: The complex conformational dynamics of protein-DNA binding studied by atomistic molecular dynamics simulations, Bba - General Subjects, 1850 (2015) 1091-1098.
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