The Limited Role of Nonnative Contacts in the Folding Pathways of a Lattice Protein

Models of protein energetics that neglect interactions between amino acids that are not adjacent in the native state, such as the Gō model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a crucial assumption that has never been critically evaluated in a broad context: Detailed mechanisms of protein folding are not biased by nonnative contacts, typically argued to be a consequence of sequence design and/or topology. Here we present, using computer simulations of a well-studied lattice heteropolymer model, the first systematic test of this oft-assumed correspondence over the statistically significant range of hundreds of thousands of amino acid sequences that fold to the same native structure. Contrary to previous conjectures, we find a multiplicity of folding mechanisms, suggesting that Gō-like models cannot be justified by considerations of topology alone. Instead, we find that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies: The order in which native contacts accumulate is profoundly insensitive to omission of nonnative interactions, provided that native contact heterogeneity is retained. This robustness holds over a surprisingly wide range of folding rates for our designed sequences. Mirroring predictions based on the principle of minimum frustration, fast-folding sequences match their Gō-like counterparts in both topological mechanism and transit times. Less optimized sequences dwell much longer in the unfolded state and/or off-pathway intermediates than do Gō-like models. For dynamics that bridge unfolded and unfolded states, however, even slow folders exhibit topological mechanisms and transit times nearly identical with those of their Gō-like counterparts. Our results do not imply a direct correspondence between folding trajectories of Gō-like models and those of real proteins, but they do help to clarify key topological and energetic assumptions that are commonly used to justify such caricatures.     

Lattice Models for Protein Organization throughout Thylakoid Membrane Stacks

Proteins in photosynthetic membranes can organize into patterned arrays that span the membrane’s lateral size. Attractions between proteins in different layers of a membrane stack can play a key role in this ordering, as was suggested by microscopy and fluorescence spectroscopy and demonstrated by computer simulations of a coarse-grained model. The architecture of thylakoid membranes, however, also provides opportunities for interlayer interactions that instead disfavor the high protein densities of ordered arrangements. Here, we explore the interplay between these opposing driving forces and, in particular, the phase transitions that emerge in the periodic geometry of stacked thylakoid membrane disks. We propose a lattice model that roughly accounts for proteins’ attraction within a layer and across the stromal gap, steric repulsion across the lumenal gap, and regulation of protein density by exchange with the stroma lamellae. Mean-field analysis and computer simulation reveal rich phase behavior for this simple model, featuring a broken-symmetry striped phase that is disrupted at both high and low extremes of chemical potential. The resulting sensitivity of microscopic protein arrangement to the thylakoid’s mesoscale vertical structure raises intriguing possibilities for regulation of photosynthetic function.     

蛋白质的折叠

重点介绍了蛋白质折叠的热力学控制学说和动力学控制学说,简单介绍了几种蛋白质折叠模型并分析了多肽链在体内进行快速折叠的原因。     

A Simple Lattice Model That Captures Protein Folding,Aggregation and Amyloid Formation

The ability of many proteins to convert from their functional soluble state to amyloid fibrils can be attributed to inter-molecular beta strand formation. Such amyloid formation is associated with neurodegenerative disorders like Alzheimer''s and Parkinson''s. Molecular modelling can play a key role in providing insight into the factors that make proteins prone to fibril formation. However, fully atomistic models are computationally too expensive to capture the length and time scales associated with fibril formation. As the ability to form fibrils is the rule rather than the exception, much insight can be gained from the study of coarse-grained models that capture the key generic features associated with amyloid formation. Here we present a simple lattice model that can capture both protein folding and beta strand formation. Unlike standard lattice models, this model explicitly incorporates the formation of hydrogen bonds and the directionality of side chains. The simplicity of our model makes it computationally feasible to investigate the interplay between folding, amorphous aggregation and fibril formation, and maintains the capability of classic lattice models to simulate protein folding with high specificity. In our model, the folded proteins contain structures that resemble naturally occurring beta-sheets, with alternating polar and hydrophobic amino acids. Moreover, fibrils with intermolecular cross-beta strand conformations can be formed spontaneously out of multiple short hydrophobic peptide sequences. Both the formation of hydrogen bonds in folded structures and in fibrils is strongly dependent on the amino acid sequence, indicating that hydrogen-bonding interactions alone are not strong enough to initiate the formation of beta sheets. This result agrees with experimental observations that beta sheet and amyloid formation is strongly sequence dependent, with hydrophobic sequences being more prone to form such structures. Our model should open the way to a systematic study of the interplay between the factors that lead to amyloid formation.     

The Mitochondrial Intermembrane Space Oxireductase Mia40 Funnels the Oxidative Folding Pathway of the Cytochrome c Oxidase Assembly Protein Cox19

Mia40-catalyzed disulfide formation drives the import of many proteins into the mitochondria. Here we characterize the oxidative folding of Cox19, a twin CX₉C Mia40 substrate. Cox19 oxidation is extremely slow, explaining the persistence of import-competent reduced species in the cytosol. Mia40 accelerates Cox19 folding through the specific recognition of the third Cys in the second helical CX₉C motif and the subsequent oxidation of the inner disulfide bond. This renders a native-like intermediate that oxidizes in a slow uncatalyzed reaction into native Cox19. The same intermediate dominates the pathway in the absence of Mia40, and chemical induction of an α-helical structure by trifluoroethanol suffices to accelerate productive folding and mimic the Mia40 folding template mechanism. The Mia40 role is to funnel a rough folding landscape, skipping the accumulation of kinetic traps, providing a rationale for the promiscuity of Mia40.     

Chaperonin-mediated Protein Folding

We have been studying chaperonins these past twenty years through an initial discovery of an action in protein folding, analysis of structure, and elucidation of mechanism. Some of the highlights of these studies were presented recently upon sharing the honor of the 2013 Herbert Tabor Award with my early collaborator, Ulrich Hartl, at the annual meeting of the American Society for Biochemistry and Molecular Biology in Boston. Here, some of the major findings are recounted, particularly recognizing my collaborators, describing how I met them and how our great times together propelled our thinking and experiments.     

On the Characterization and Software Implementation of General Protein Lattice Models

Abstract models of proteins have been widely used as a practical means to computationally investigate general properties of the system. In lattice models any sterically feasible conformation is represented as a self-avoiding walk on a lattice, and residue types are limited in number. So far, only two- or three-dimensional lattices have been used. The inspection of the neighborhood of alpha carbons in the core of real proteins reveals that also lattices with higher coordination numbers, possibly in higher dimensional spaces, can be adopted. In this paper, a new general parametric lattice model for simplified protein conformations is proposed and investigated. It is shown how the supporting software can be consistently designed to let algorithms that operate on protein structures be implemented in a lattice-agnostic way. The necessary theoretical foundations are developed and organically presented, pinpointing the role of the concept of main directions in lattice-agnostic model handling. Subsequently, the model features across dimensions and lattice types are explored in tests performed on benchmark protein sequences, using a Python implementation. Simulations give insights on the use of square and triangular lattices in a range of dimensions. The trend of potential minimum for sequences of different lengths, varying the lattice dimension, is uncovered. Moreover, an extensive quantitative characterization of the usage of the so-called “move types” is reported for the first time. The proposed general framework for the development of lattice models is simple yet complete, and an object-oriented architecture can be proficiently employed for the supporting software, by designing ad-hoc classes. The proposed framework represents a new general viewpoint that potentially subsumes a number of solutions previously studied. The adoption of the described model pushes to look at protein structure issues from a more general and essential perspective, making computational investigations over simplified models more straightforward as well.     

First-Principles Protein Folding Simulations

Abstract

It is widely believed that the prediction of the three-dimensional structures of proteins from the first principles is impossible. This view is based on the fact that the number of possible structures for each protein is astronomically large. The question is then why a protein folds into its native structure with the proper biological functions in the time scale of milliseconds to minutes, and this is called Levinthal's paradox. In this article I will discuss our strategy for attacking the protein folding problem. Our approach consists of two elements: the inclusion of accurate solvent effects and the development of powerful simulation algorithms that can avoid getting trapped in states of energy local minima. For the former, we discuss several models varying in nature from crude (distance-dependent dielectric function) to rigorous (reference interaction site model). For the latter, we show the effectiveness of Monte Carlo simulated annealing and generalized-ensemble algorithms.     

Ultrafast Protein Folding in Membrane-Mimetic Environments

Proteins fold on timescales from hours to microseconds. In addition to protein size, sequence, and topology, the environment represents an equally important factor in determining folding speed. This is particularly relevant for proteins that require a lipid membrane or a membrane mimic to fold. However, only little is known about how properties of such a hydrophilic/hydrophobic interface modulate the folding landscape of membrane-interacting proteins. Here, we studied the influence of different membrane-mimetic micellar environments on the folding and unfolding kinetics of the helical-bundle protein Mistic. Devising a single-molecule fluorescence spectroscopy approach, we extracted folding and unfolding rates under equilibrium conditions and dissected the contributions from different detergent moieties to the free-energy landscape. While both polar and nonpolar moieties contribute to stability, they exert differential effects on the free-energy barrier: Hydrophobic burial stabilizes the folded state but not the transition state in reference to a purely aqueous environment; by contrast, zwitterionic headgroup moieties stabilize the folded state and, additionally, lower the free-energy barrier to accelerate the folding of Mistic to achieve ultrafast folding times down to 35 μs.     

Stoichiometry versus Hydrophobicity in Protein Folding

Abstract

In a channel-forming bundle of five alpha-helices of poly-L-alanine, the replacement of all the alanyl side-chains lining the inner wall by serines is shown, by energy optimization, to produce only small modifications of the packing. The stability of the bundle is larger than that of the pure alanyl package, owing to hydrogen bonding between serine hydroxyls and carbonyl oxygens. The energy profile for sodium as well as the water-channel interactions are favored by the presence of the OH groups and by the lability of the seryl side chains. The possible general significance of the results is suggested.     

Stoichiometry and Topology in Protein Folding

Abstract

Crystals of the small ribosomal subunit from Thermus thermophilus diffract to 3Å and exhibit reasonable isomorphism and moderate resistance to irradiation. A 5Å MIR map of this particle shows a similar shape to the part assigned to this particle within the cryo-EM reconstructions of the whole ribosome and contains regions interpretable either as RNA chains or as protein motifs. To assist phasing at higher resolution we introduced recombinant methods aimed at extensive selenation for MAD phasing. We are focusing on several ribosomal proteins that can be quantitatively detached by chemical means. These proteins can be modified and subsequently reconstituted into depleted ribosomal cores. They also can be used for binding heavy atoms, by incorporating chemically reactive binding sites, such as -SH groups, into them. In parallel we are co-crystallizing the ribosomal particles with tailor made ligands, such as antibiotics or cDNA to which heavy-atoms have been attached or diffuse the latter compounds into already formed crystals.     

蛋白质折叠和分子伴侣

一个有活性的蛋白质分子不但有特定的氨基酸序列,还处于特定的由氨基酸序列决定的三维空间结构。三维结构的完整性受到干扰,生物活性也会发生变化：有时即使只是轻微的破坏,都可能导致其生物活性全部丧失。所以蛋白质的生物功能是与其三维空间结构密切联系在一起的。     

Toward Correct Protein Folding Potentials

Empirical protein folding potentialfunctions should have a global minimum nearthe native conformationof globular proteins that fold stably, andthey should give the correct free energy offolding. We demonstrate that otherwise verysuccessful potentials fail to have even alocal minimumanywhere near the native conformation, anda seemingly well validated method ofestimatingthe thermodynamic stability of the nativestate is extremely sensitive to smallperturbations inatomic coordinates. These are bothindicative of fitting a great deal ofirrelevant detail. Here weshow how to devise a robust potentialfunction that succeeds very well at bothtasks, at least for alimited set of proteins, and this involvesdeveloping a novel representation of thedenatured state.Predicted free energies of unfolding for 25mutants of barnase are in close agreementwith theexperimental values, while for 17 mutantsthere are substantial discrepancies.     

Back to Units of Protein Folding

Abstract

In response to the criticism by A. Finkelstein (J. Biomol. Struct. Dyn. 20, 311–314, 2002) of our Communication (J. Biomol. Struct. Dyn. 20, 5–6, 2002) several issues are dealt with. Importance of the notion of elementary folding unit, its size and structure, and the necessity of further characterization of the units for the elucidation of the protein folding in vivo are discussed. The criticism (J. Biomol. Struct. Dyn. 20, 311–314, 2002) on the hierarchical protein folding is also briefly addressed.     

50+ Years of Protein Folding

The ability of proteins to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference–10-11 orders of magnitude–is the same as between the lifespan of a mosquito and the age of the Universe. This review (based on the literature and some personal recollections) describes a winding road to understanding spontaneous folding of protein structure. The main attention is given to the free-energy landscape of conformations of a protein chain–especially to the barrier separating its unfolded (U) and the natively folded (N) states–and to physical the-ories of rates of crossing this barrier in both directions: from U to N, and from N to U. It is shown that theories of both these processes come to essentially the same result and outline the observed range of folding and unfolding rates for single-domain globular proteins. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control, and explain the observed maximal size of “foldable” protein domains.     

蛋白质在大肠杆菌间周质中的折叠

随着分子伴侣的发现和外源基因表达技术的发展 ,大肠杆菌间周质蛋白质的折叠成为研究热点。间周质 (ｐｅｒｉｐｌａｓｍ)是革兰氏阴性菌内膜与外膜之间的区域 ,对外界环境变化的适当能力很脆弱 ,例如ｐＨ、温度、渗透压[1] 。重组技术表达的重要蛋白质大多含有二硫键 ,二硫键的形成在真核生物是在内质网中完成的 ,而大肠杆菌是在间周质中进行的。催化大肠杆菌间周质蛋白质折叠会遇到两个限速步骤 ,被两类酶催化 :二硫键氧化还原酶 (Ｄｓｂ)和肽酰 脯氨酰顺反异构酶 (ｐｅｐｔｉｄｙｌ ｐｒｏｌｙｌｃｉｓ ｔｒａｎｓｉｓｏ ｍｅｒａｓｅ ,…     

Experimental and Theoretical Protein Folding

Abstract

Resonance Raman spectra with Q-band excitation are reported for microperoxidase-11, the cytochrome c analog. Spectra were acquired in the mid-frequency range for the oxidized, and reduced forms of the undecapeptide, as well as for the imidazole and carbonyl complexes. Oxidation and spin state marker bands of the undecapeptides are consistent with a six-coordinate, low spin iron in both oxidation states. Porphyrin core size correlations yield a porphyrin-centre to pyrrole-nitrogen distance of 2.00 Å for MP11, suggestive of a six-coordinate species in a distorted heme environment. Molecular dynamics results show that the non-planarity of the heme of the parent cytochrome is conserved in the microperoxidase and its carbonmonoxy analog.