Topological aspects of the conformational transformations in polypeptides and proteins

The topological aspects of the conformational transformations in a polypeptide chain are investigated in relation to the problem of selecting the minimum-energy pathways in protein folding.     

A simple topological representation of protein structure: implications for new, fast, and robust structural classification

A topological representation of proteins is developed that makes use of two metrics: the Euclidean metric for identifying natural nearest neighboring residues via the Delaunay tessellation in Cartesian space and the distance between residues in sequence space. Using this representation, we introduce a quantitative and computationally inexpensive method for the comparison of protein structural topology. The method ultimately results in a numerical score quantifying the distance between proteins in a heuristically defined topological space. The properties of this scoring scheme are investigated and correlated with the standard Calpha distance root-mean-square deviation measure of protein similarity calculated by rigid body structural alignment. The topological comparison method is shown to have a characteristic dependence on protein conformational differences and secondary structure. This distinctive behavior is also observed in the comparison of proteins within families of structural relatives. The ability of the comparison method to successfully classify proteins into classes, superfamilies, folds, and families that are consistent with standard classification methods, both automated and human-driven, is demonstrated. Furthermore, it is shown that the scoring method allows for a fine-grained classification on the family, protein, and species level that agrees very well with currently established phylogenetic hierarchies. This fine classification is achieved without requiring visual inspection of proteins, sequence analysis, or the use of structural superimposition methods. Implications of the method for a fast, automated, topological hierarchical classification of proteins are discussed.     

Topological analysis of the fusion process between cellular and subcellular compartments

The study presents an application of the theory of homeomorphic transformations of topological manifolds and the operation of the connected sum of manifolds for topological analysis of membrane transformations during the fusion process between cellular and subcellular compartments. The biological cell and the subcellular structures in the form of vesicles are modelled by an arrangement of two concentric spheres corresponding to the inner and outer layer of the membrane bounding the vesicles. The analysis shows eight succeeding topological stages of membrane transformations during the fusion process and these stages are characterized. It is concluded that there is a vectorial translocation of lipid molecules from the outer layers of the membranes before the fusion process to the internal layer of the membrane bounding the vesicle after the fusion process and there is no lipid translocation in the reverse direction.     

Mechanical analyses of morphological and topological transformation of liposomes

Liposomes are micro-compartments made of lipid bilayer membranes possessing the characteristics quite similar to those of biological membranes. To form artificial cell-like structures, we made liposomes that contained subunit proteins of cytoskeletons: tubulin or actin. Spherical liposomes were transformed into bipolar or cell-like shapes by mechanical forces generated by the polymerization of encapsulated subunits of microtubules. On the other hand, disk- or dumbbell-shaped liposomes were developed by the polymerization of encapsulated actin. Dynamic processes of morphological transformations of liposomes were visualized by high intensity dark-field light microscopy. Topological changes, such as fusion and division of membrane vesicles, play an essential role in cellular activities. To investigate the mechanism of these processes, we visualized the liposomes undergoing topological transformation in real time. A variety of novel topological transformations were found, including the opening-up of liposomes and the direct expulsion of inner vesicles.     

Protein folding and wring resonances

The polypeptide chain of a protein is shown to obey topological constraints which enable long range excitations in the form of wring modes of the protein backbone. Wring modes of proteins of specific lengths can therefore resonate with molecular modes present in the cell. It is suggested that protein folding takes place when the amplitude of a wring excitation becomes so large that it is energetically favorable to bend the protein backbone. The condition under which such structural transformations can occur is found, and it is shown that both cold and hot denaturation (the unfolding of proteins) are natural consequences of the suggested wring mode model. Native (folded) proteins are found to possess an intrinsic standing wring mode.     

Topological model of the division process of cellular and subcellular compartments

The application of the theory of homeomorphic transformations of topological manifolds and the operation of the connected sum of manifolds for a formation of a topological model of membrane transformations during the division process of cellular and subcellular compartments, has been shown. The biological cell and the subcellular structures in the form of vesicles are modelled by an arrangement of two concentric spheres corresponding to the inner and outer layer of the membrane bounding the vesicle. The analysis shows eight succeeding topological stages of membrane transformations during the division process and these stages are characterised. It is concluded that there is a vectorial translocation of lipid molecules from the inner layer of the membrane bounding the vesicle before the division process to the outer layer of the membranes after the division process and there is no lipid translocation from the outer layer to the inner layers during the division process.     

Dissociative mechanism for irreversible thermal denaturation of oligomeric proteins

Protein stability is a fundamental characteristic essential for understanding conformational transformations of the proteins in the cell. When using protein preparations in biotechnology and biomedicine, the problem of protein stability is of great importance. The kinetics of denaturation of oligomeric proteins may have characteristic properties determined by the quaternary structure. The kinetic schemes of denaturation can include the multiple stages of conformational transitions in the protein oligomer and stages of reversible dissociation of the oligomer. In this case, the shape of the kinetic curve of denaturation or the shape of the melting curve registered by differential scanning calorimetry can vary with varying the protein concentration. The experimental data illustrating dissociative mechanism for irreversible thermal denaturation of oligomeric proteins have been summarized in the present review. The use of test systems based on thermal aggregation of oligomeric proteins for screening of agents possessing anti-aggregation activity is discussed.     

Donut-shaped fingerprint in homologous polypeptide relationships—A topological feature related to pathogenic structural changes in conformational disease

Features of homologous relationship of proteins can provide us a general picture of protein universe, assist protein design and analysis, and further our comprehension of the evolution of organisms. Here we carried out a study of the evolution of protein molecules by investigating homologous relationships among residue segments. The motive was to identify detailed topological features of homologous relationships for short residue segments in the whole protein universe. Based on the data of a large number of non-redundant proteins, the universe of non-membrane polypeptide was analyzed by considering both residue mutations and structural conservation. By connecting homologous segments with edges, we obtained a homologous relationship network of the whole universe of short residue segments, which we named the graph of polypeptide relationships (GPR). Since the network is extremely complicated for topological transitions, to obtain an in-depth understanding, only subgraphs composed of vital nodes of the GPR were analyzed. Such analysis of vital subgraphs of the GPR revealed a donut-shaped fingerprint. Utilization of this topological feature revealed the switch sites (where the beginning of exposure of previously hidden “hot spots” of fibril-forming happens, in consequence a further opportunity for protein aggregation is provided; 188-202) of the conformational conversion of the normal α-helix-rich prion protein PrP^C to the β-sheet-rich PrP^Sc that is thought to be responsible for a group of fatal neurodegenerative diseases, transmissible spongiform encephalopathies. Efforts in analyzing other proteins related to various conformational diseases are also introduced.     

Reversible topological organization within a polytopic membrane protein is governed by a change in membrane phospholipid composition

Once inserted, transmembrane segments of polytopic membrane proteins are generally considered stably oriented due to the large free energy barrier to topological reorientation of adjacent extramembrane domains. However, the topology and function of the polytopic membrane protein lactose permease of Escherichia coli are dependent on the membrane phospholipid composition, revealing topological dynamics of transmembrane domains after stable membrane insertion (Bogdanov, M., Heacock, P. N., and Dowhan, W. (2002) EMBO J. 21, 2107-2116). In this study, we show that the high affinity phenylalanine permease PheP shares many similarities with lactose permease. PheP assembled in a mutant of E. coli lacking phosphatidylethanolamine (PE) exhibited significantly reduced active transport function and a complete inversion in topological orientation of the N terminus and adjoining transmembrane hairpin loop compared with PheP in a PE-containing strain. Introduction of PE following the assembly of PheP triggered a reorientation of the N terminus and adjacent hairpin to their native orientation associated with regain of wild-type transport function. The reversible orientation of these secondary transport proteins in response to a change in phospholipid composition might be a result of inherent conformational flexibility necessary for transport function or during protein assembly.     

Novel approach for alpha-helical topology prediction in globular proteins: generation of interhelical restraints

The protein folding problem represents one of the most challenging problems in computational biology. Distance constraints and topology predictions can be highly useful for the folding problem in reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel optimization framework for predicting topological contacts and generating interhelical distance restraints between hydrophobic residues in alpha-helical globular proteins. It should be emphasized that since the model does not make assumptions about the form of the helices, it is applicable to all alpha-helical proteins, including helices with kinks and irregular helices. This model aims at enhancing the ASTRO-FOLD protein folding approach of Klepeis and Floudas (Journal of Computational Chemistry 2003;24:191-208), which finds the structure of global minimum conformational energy via a constrained nonlinear optimization problem. The proposed topology prediction model was evaluated on 26 alpha-helical proteins ranging from 2 to 8 helices and 35 to 159 residues, and the best identified average interhelical distances corresponding to the predicted contacts fell below 11 A in all 26 of these systems. Given the positive results of applying the model to several protein systems, the importance of interhelical hydrophobic-to-hydrophobic contacts in determining the folding of alpha-helical globular proteins is highlighted.     

Enzymatic computing

The conformational dynamics of enzymes is a computational resource that fuses milieu signals in a nonlinear fashion. Response surface methodology can be used to elicit computational functionality from enzyme dynamics. We constructed a tabletop prototype to implement enzymatic signal processing in a device context and employed it in conjunction with malate dehydrogenase to perform the linearly inseparable exclusive-or operation. This shows that proteins can execute signal processing operations that are more complex than those performed by individual threshold elements. We view the experiments reported, though restricted to the two-variable case, as a stepping stone to computational networks that utilize the precise reproducibility of proteins, and the concomitant reproducibility of their nonlinear dynamics, to implement complex pattern transformations.     

Reversal of peptide backbone direction may result in the mirroring of protein structure

In linear polypeptides, inversion of amino acid chirality (all- to all- ) achieves a mirroring of side chain positions and interactions in conformational space. A similar mirroring of side chain positions is independently achieved by a reversal of the direction of the peptide backbone (retro modification). Thus, while an all- chain could be expected to adopt a perfect ‘mirror image’ of the three-dimensional structure of its parent all- protein, the retro-all- chain could be expected to adopt a topological equivalent of such a mirror image, through the symmetry transformations of side chain interactions. These notions, supported by sequence analyses, modelling studies, and evidence relating to the activity of ‘retro-inverso’ peptides, are extended towards the proposal, that the backbone reversed chain of a large globular protein might recognize the chiral opposite of the parent protein's substrate(s).     

Protein structural alignment for detection of maximally conserved regions

An algorithm for comparison of homologous protein structures and for study of conformational changes in proteins, has been developed. The method is based on identification of pieces of the two molecules that have similar shapes, as determined by the local conformation of the polypeptide chain. Pieces that superpose within a specified tolerance are assembled into domains based on similar transformations for superposition. The result is sets of pieces that represent conserved structural elements and conserved spatial relationships between structural elements within the proteins being compared. A similarity criterion based on maximum distance rather than on root mean square deviation reduces bias by outliers. The utility of the method is demonstrated by using examples from the protein kinase family.     

Fusion and scission of membranes: Ubiquitous topological transformations in cells

The 2016 Nobel Prizes were awarded to Yoshinori Ohsumi for autophagy and to David Thouless, Duncan Haldane and Michael Kosterlitz for topological transitions. Both of these phenomena are intrinsically related when it comes to membranes. Here, we give a brief account on topological transformations of lipid membranes, commonly known as membrane fusion and membrane scission, and introduce the underlying topological invariant, the genus. The genus of a shape is a useful concept to distinguish unambiguously the processes of membrane fusion/scission and offers a simple method to describe complex, cellular membrane structures, such as fenestrated cristae. We distinguish and highlight the connection between topological transformations of lipid membranes and the recent awards, and point out the extraordinarily large number of topological changes during autophagy.      

Organization of the Sindbis virus nucleocapsid as revealed by bifunctional cross-linking agents

Purified Sindbis virus nucleocapsids were reacted with a variety of bifunctional protein-specific cross-linking agents. The products were analyzed in concentration-gradient polyacrylamide gels and amounts of various products determined. These studies indicated that available lysine residues within adjacent capsid proteins in purified intact nucleocapsids are separated by 6 A. The capsid proteins in intact nucleocapsids are cross-linked in a pattern predicted for discrete monomeric entities, rather than in dimeric or trimeric aggregates. Purified, soluble capsid protein exists in a conformation that differs from the arrangement of protein within nucleocapsids. These conformational differences suggest that topological changes may occur in the capsid protein during virus maturation. Cross-linked nucleocapsids that were treated with RNases resulted in the generation of RNA-free protein shells that retained hexagonal morphology, indicating that, together, the RNA and protein form the outer surface of the nucleocapsid. These data are used to produce a model of the Sindbis virus nucleocapsid in which the proteins are arranged quasi-equivalently in a T = 4 icosahedral shell.     

Topoisomer gel retardation: detection of anti-Z-DNA antibodies bound to Z-DNA within supercoiled DNA minicircles.

Small DNA fragments of approximately 350 bp in length, either with or without d(CG)n tracts, are ligated into underwound DNA minicircles to generate topoisomeric rings with different topological linking numbers, Lk. These minicircles, differing by an Lk of one, can be separated by acrylamide gel electrophoresis. Furthermore, electrophoresis can be used to reveal DNA double helix conformational changes that are induced by supercoiling, such as left-handed Z-DNA. When anti-Z-DNA antibodies are added to such minicircles, their binding leads to a selective retardation of the electrophoretic migration of the Z-DNA containing circles. This effect is not seen with relaxed minicircles and those with insufficient torsional stress to induce a conformational transition. Thus the technique of 'topoisomer gel retardation' presents a very sensitive assay for the identification of proteins that selectively bind to DNA conformations stabilized by negative DNA supercoiling.     

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.     

Calculation of rigid-body conformational changes using restraint-driven Cartesian transformations

We present an approach for calculating conformational changes in membrane proteins using limited distance information. The method, named restraint-driven Cartesian transformations, involves 1) the use of relative distance changes; 2) the systematic sampling of rigid body movements in Cartesian space; 3) a penalty evaluation; and 4) model refinement using energy minimization. As a test case, we have analyzed the structural basis of activation gating in the Streptomyces lividans potassium channel (KcsA). A total of 10 pairs of distance restraints derived from site-directed spin labeling and electron paramagnetic resonance (SDSL-EPR) spectra were used to calculate the open conformation of the second transmembrane domains of KcsA (TM2). The SDSL-EPR based structure reveals a gating mechanism consistent with a scissoring-type motion of the TM2 segments that includes a pivot point near middle of the helix. The present approach considerably reduces the amount of time and effort required to establish the overall nature of conformational changes in membrane proteins. It is expected that this approach can be implemented into restrained molecular dynamics protocol to calculate the structure and conformational changes in a variety of membrane protein systems.     

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

Results

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

Conclusions

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.