The shapes of backbones of chain molecules: Three-dimensional characterization by spherical shape maps

In this work we present a new method to characterize the shape of flexible chain molecules. The procedure associates a sphere and a spherical shape map with each given molecular backbone. Each point on the sphere is classified according to the crossing pattern obtained when the backbone is looked at along a direction defined by the center of the sphere and the chosen point. The approach is simple to implement. It consists of the following steps: (a) enclosing the backbone by a sphere, whose center is the geometrical center of the backbone; (b) projecting the backbone onto a plane tangent to the sphere at the given point; and (c) characterizing the resulting planar curve by a vector specifying the number and handedness type of the crossings. When the procedure is repeated for all points on the spherical surface, the latter is divided into regions that are equivalence classes of points, corresponding to directions from where the backbone has the same overcrossing pattern. The computation of these equivalence classes is performed automatically by the computer, by determining the boundary of the regions characterized by different crossing vectors. The characterization provided is thus direction independent since it takes into account all possible directions from where a backbone can be analyzed. The procedure is illustrated for a number of supersecondary protein structures and small proteins. We find that a characterization of substructures can be obtained in terms of the arrangement of the equivalence region for the viewing directions from where the backbone shows no crossings. For instance, an α-helix is represented by a spherical map with a small “band” region of no crossings perpendicular to the helical axis. Other supersecondary structural features are described in a similar fashion. A number of refinements of the method, based on the distances between crossings, are also given for the case of irregular backbones. © 1992 John Wiley & Sons, Inc.     

The characterization of pc-polylines representing protein backbones

The backbone of a protein is typically represented as either a C _α-polyline, a three-dimensional (3D) polyline that passes through the C _α atoms, or a tuple of ϕ,ψ pairs while its fold is usually assigned using the 3D topological arrangement of the secondary structure elements (SSEs). It is tricky to obtain the SSE composition for a protein from the C _α-polyline representation while its 3D SSE arrangement is not apparent in the two-dimensional (2D) ϕ,ψ representation. In this article, we first represent the backbone of a protein as a pc-polyline that passes through the centers of its peptide planes. We then analyze the pc-polylines for six different sets of proteins with high quality crystal structures. The results show that SSE composition becomes recognizable in pc-polyline presentation and consequently the geometrical property of the pc-polyline of a protein could be used to assign its secondary structure. Furthermore, our analysis finds that for each of the six sets the total length of a pc-polyline increases linearly with the number of the peptide planes. Interestingly a comparison of the six regression lines shows that they have almost identical slopes but different intercepts. Most interestingly there exist decent linear correlations between the intercepts of the six lines and either the average helix contents or the average sheet contents and between the intercepts and the average backbone hydrogen bonding energetics. Finally, we discuss the implications of the identified correlations for structure classification and protein folding, and the potential applications of pc-polyline representation to structure prediction and protein design.     

An Automatic Search for Similar Spatial Arrangements of α-Helices and β-Strands in Globular Proteins

Abstract

A fast search algorithm to reveal similar polypeptide backbone structural motifs in proteins is proposed. It is based on the vector representation of a polypeptide chain fold in which the elements of regular secondary structures are approximated by linear segments (Abagyan and Maiorov, J. Biomol. Struct. Dyn. 5, 1267–1279 (1988)). The algorithm permits insertions and deletions in the polypeptide chain fragments to be compared. The fast search algorithm implemented in FASEAR program is used for collecting βαβ supersecondary structure units in a number of α/β proteins of Brookhaven Data Bank. Variation of geometrical parameters specifying backbone chain fold is estimated. It appears that the conformation of the majority of the fragments, although almost all of them are right-handed, is quite different from that of standard βαβ units. Apart from searching for specific type of secondary structure motif, the algorithm allows automatically to identify new recurrent folding patterns in proteins. It may be of particular interest for the development of tertiary template approach for prediction of protein three-dimensional structure as well for constructing artificial polypeptides with goal-oriented conformation.     

目标和干扰子之间的拓扑性质差异可以削弱拥挤效应

"拥挤效应"被认为是外周视觉物体辨认过程中的一个重要瓶颈.它是指当目标被干扰子包围,在外周视野呈现时,观察者辨认目标的能力被大大削弱,尤其是当目标和干扰子之间存在某种相似性时.许多研究分别试图在不同层次上提出解释这一现象的机制.本文通过三个实验,使用了不同的视觉刺激图形的辨认任务(例如,三角形和箭头的朝向判断、数字和字母的辨认以及S形图形的朝向辨认),测量了目标和干扰子之间中心距离的阈值,结果一致地发现,当目标和干扰子之间存在拓扑性质差异(洞的个数差异)时,拥挤效应会显著降低,并且排除了目标和干扰子之间的主观相似性、形状和面积差异等可能的因素.从知觉组织的角度验证了当目标和干扰子之间存在拓扑性质差异时,拥挤效应会显著降低,这是首次发现的一个影响拥挤效应的新的维度.本文结果不仅为拥挤效应的机制提供了一个新的解释,也为大范围首先拓扑知觉在知觉物体形成中的作用提供了支持性证据.     

Nonadditivity in conformational entropy upon molecular rigidification reveals a universal mechanism affecting folding cooperativity

Previously, we employed a Maxwell counting distance constraint model (McDCM) to describe α-helix formation in polypeptides. Unlike classical helix-coil transition theories, the folding mechanism derives from nonadditivity in conformational entropy caused by rigidification of molecular structure as intramolecular cross-linking interactions form along the backbone. For example, when a hydrogen bond forms within a flexible region, both energy and conformational entropy decrease. However, no conformational entropy is lost when the region is already rigid because atomic motions are not constrained further. Unlike classical zipper models, the same mechanism also describes a coil-to-β-hairpin transition. Special topological features of the helix and hairpin structures allow the McDCM to be solved exactly. Taking full advantage of the fact that Maxwell constraint counting is a mean field approximation applied to the distribution of cross-linking interactions, we present an exact transfer matrix method that does not require any special topological feature. Upon application of the model to proteins, cooperativity within the folding transition is yet again appropriately described. Notwithstanding other contributing factors such as the hydrophobic effect, this simple model identifies a universal mechanism for cooperativity within polypeptide and protein-folding transitions, and it elucidates scaling laws describing hydrogen-bond patterns observed in secondary structure. In particular, the native state should have roughly twice as many constraints as there are degrees of freedom in the coil state to ensure high fidelity in two-state folding cooperativity, which is empirically observed.     

The high-resolution NMR structure of the early folding intermediate of the Thermus thermophilus ribonuclease H

Elucidation of the high-resolution structures of folding intermediates is a necessary but difficult step toward the ultimate understanding of the mechanism of protein folding. Here, using hydrogen-exchange-directed protein engineering, we populated the folding intermediate of the Thermus thermophilus ribonuclease H, which forms before the rate-limiting transition state, by removing the unfolded regions of the intermediate, including an α-helix and two β-strands (51 folded residues). Using multidimensional NMR, we solved the structure of this intermediate mimic to an atomic resolution (backbone rmsd, 0.51 Å). It has a native-like backbone topology and shows some local deviations from the native structure, revealing that the structure of the folded region of an early folding intermediate can be as well defined as the native structure. The topological parameters calculated from the structures of the intermediate mimic and the native state predict that the intermediate should fold on a millisecond time scale or less and form much faster than the native state. Other factors that may lead to the slow folding of the native state and the accumulation of the intermediate before the rate-limiting transition state are also discussed.     

A framework for describing topological frustration in models of protein folding

In a natively folded protein of moderate or larger size, the protein backbone may weave through itself in complex ways, raising questions about what sequence of events might have to occur in order for the protein to reach its native configuration from the unfolded state. A mathematical framework is presented here for describing the notion of a topological folding barrier, which occurs when a protein chain must pass through a hole or opening, formed by other regions of the protein structure. Different folding pathways encounter different numbers of such barriers and therefore different degrees of frustration. A dynamic programming algorithm finds the optimal theoretical folding path and minimal degree of frustration for a protein based on its natively folded configuration. Calculations over a database of protein structures provide insights into questions such as whether the path of minimal frustration might tend to favor folding from one or from many sites of folding nucleation, or whether proteins favor folding around the N terminus, thereby providing support for the hypothesis that proteins fold co-translationally. The computational methods are applied to a multi-disulfide bonded protein, with computational findings that are consistent with the experimentally observed folding pathway. Attention is drawn to certain complex protein folds for which the computational method suggests there may be a preferred site of nucleation or where folding is likely to proceed through a relatively well-defined pathway or intermediate. The computational analyses lead to testable models for protein folding.     

Protein design as a challenge for peptide chemists

All efforts to turn the ultimate goal in protein de novo design into reality–the construction of new macromolecules with predetermined three-dimensional structure and well-defined functionality–failed because the mechanism of folding has still to be unravelled. In the present review, various attempts to apply synthetic tools for inducing native-like structural features in peptides in order to bypass the folding problem are described. Besides well-established methods for the nucleation and stabilization of secondary structures, e.g. α-helices, β-sheets and β-turns, topological templates as ‘built-in’ folding devices have more recently become the key elements for the induction of protein-like folding units (template-assembled synthetic proteins, TASP). Progress in the synthetic strategy and structural characterization of this new type of macromolecules opens the way for the design of functional TASP molecules.     

Protein folding and the organization of the protein topology universe

The mechanism by which proteins fold to their native states has been the focus of intense research in recent years. The rate-limiting event in the folding reaction is the formation of a conformation in a set known as the transition-state ensemble. The structural features present within such ensembles have now been analysed for a series of proteins using data from a combination of biochemical and biophysical experiments together with computer-simulation methods. These studies show that the topology of the transition state is determined by a set of interactions involving a small number of key residues and, in addition, that the topology of the transition state is closer to that of the native state than to that of any other fold in the protein universe. Here, we review the evidence for these conclusions and suggest a molecular mechanism that rationalizes these findings by presenting a view of protein folds that is based on the topological features of the polypeptide backbone, rather than the conventional view that depends on the arrangement of different types of secondary-structure elements. By linking the folding process to the organization of the protein structure universe, we propose an explanation for the overwhelming importance of topology in the transition states for protein folding.     

Investigation of a physical basis for conformational similarity in proteins

Amino acid residues in a globular protein fold against one another into a compact structure. We have sought common physical factors within similarly folded backbone structures in such proteins which might influence the folding and which could be used in predicting the backbone structure. The physical factors examined are the 10 orthogonal ones identified by Kideraet al. (1985a). Comparison of the smoothed physical factor profiles between sequences, which have similar backbone structures, shows that there is good agreement among the profiles of helical stretches, but not for other backbone structures that have been examined. This is ascribed to the fact that helical structures involve local interactions, which then require similar physical profiles to form, but that other structures are not so strongly locally determined in the native structure.On leave from University of the Witwatersrand, Wits 2050, South Africa.     

Altered Backbone and Side-Chain Interactions Result in Route Heterogeneity during the Folding of Interleukin-1β (IL-1β)

Deletion of the β-bulge trigger-loop results in both a switch in the preferred folding route, from the functional loop packing folding route to barrel closure, as well as conversion of the agonist activity of IL-1β into antagonist activity. Conversely, circular permutations of IL-1β conserve the functional folding route as well as the agonist activity. These two extremes in the folding-functional interplay beg the question of whether mutations in IL-1β would result in changes in the populations of heterogeneous folding routes and the signaling activity. A series of topologically equivalent water-mediated β-strand bridging interactions within the pseudosymmetric β-trefoil fold of IL-1β highlight the backbone water interactions that stabilize the secondary and tertiary structure of the protein. Additionally, conserved aromatic residues lining the central cavity appear to be essential for both stability and folding. Here, we probe these protein backbone-water molecule and side chain-side chain interactions and the role they play in the folding mechanism of this geometrically stressed molecule. We used folding simulations with structure-based models, as well as a series of folding kinetic experiments to examine the effects of the F42W core mutation on the folding landscape of IL-1β. This mutation alters water-mediated backbone interactions essential for maintaining the trefoil fold. Our results clearly indicate that this perturbation in the primary structure alters a structural water interaction and consequently modulates the population of folding routes accessed during folding and signaling activity.