Peptide Plane Research Articles

A Numerical Integrator for Kinetostatic Folding of Protein Molecules Modeled as Robots with Hyper Degrees of Freedom

The kinetostatic compliance method (KCM) models protein molecules as nanomechanisms consisting of numerous rigid peptide plane linkages. These linkages articulate with respect to each other through changes in the molecule dihedral angles, resulting in a kinematic mechanism with hyper degrees of freedom. Within the KCM framework, nonlinear interatomic forces drive protein folding by guiding the molecule’s dihedral angle vector towards its lowest energy state in a kinetostatic manner. This paper proposes a numerical integrator that is well suited to KCM-based protein folding and overcomes the limitations of traditional explicit Euler methods with fixed step size. Our proposed integration scheme is based on pseudo-transient continuation with an adaptive step size updating rule that can efficiently compute protein folding pathways, namely, the transient three-dimensional configurations of protein molecules during folding. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed integrator.

A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal 13C′ CSA-13C′-13Cα DD CCR rate ΓzC′/C′Cα and present a novel 3D version of the transverse ΓxyC′/C′Cα CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ΓxyN/NH and ΓzN/NH CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.

Predicting protein flexibility with AlphaFold.

AlphaFold2 has revolutionized protein structure prediction from amino-acid sequence. In addition to protein structures, high-resolution dynamics information about various protein regions is important for understanding protein function. Although AlphaFold2 has neither been designed nor trained to predict protein dynamics, it is shown here how the information returned by AlphaFold2 can be used to predict dynamic protein regions at the individual residue level. The approach, which is termed cdsAF2, uses the 3D protein structure returned by AlphaFold2 to predict backbone NMR NH S2 order parameters using a local contact model that takes into account the contacts made by each peptide plane along the backbone with its environment. By combining for each residue AlphaFold2's pLDDT confidence score for the structure prediction accuracy with the predicted S2 value using the local contact model, an estimator is obtained that semi-quantitatively captures many of the dynamics features observed in experimental backbone NMR NH S2 order parameter profiles. The method is demonstrated for a set nine proteins of different sizes and variable amounts of dynamics and disorder.

Description of peptide bond planarity from high-resolution neutron crystallography.

Neutron crystallography is a highly effective method for visualizing hydrogen atoms in proteins. In our recent study, we successfully determined the high-resolution (1.2 Å) neutron structure of high-potential iron-sulfur protein, refining the coordinates of some amide protons without any geometric restraints. Interestingly, we observed that amide protons are deviated from the peptide plane due to electrostatic interactions. Moreover, the difference in the position of the amide proton of Cys75 between reduced and oxidized states is possibly attributed to the electron storage capacity of the iron-sulfur cluster. Additionally, we have discussed about the rigidity of the iron-sulfur cluster based on the results of the hydrogen-deuterium exchange. Our research underscores the significance of neutron crystallography in protein structure elucidation, enriching our understanding of protein functions at an atomic resolution.

Revisiting the concept of peptide bond planarity in an iron-sulfur protein by neutron structure analysis.

The planarity of the peptide bond is important for the stability and structure formation of proteins. However, substantial distortion of peptide bonds has been reported in several high-resolution structures and computational analyses. To investigate the peptide bond planarity, including hydrogen atoms, we report a 1.2-Å resolution neutron structure of the oxidized form of high-potential iron-sulfur protein. This high-resolution neutron structure shows that the nucleus positions of the amide protons deviate from the peptide plane and shift toward the acceptors. The planarity of the H─N─C═O plane depends strongly on the pyramidalization of the nitrogen atom. Moreover, the orientation of the amide proton of Cys75 is different in the reduced and oxidized states, possibly because of the electron storage capacity of the iron-sulfur cluster.

Microsecond Backbone Motions Modulate the Oligomerization of the DNAJB6 Chaperone.

DNAJB6 is a prime example of an anti-aggregation chaperone that functions as an oligomer. DNAJB6 oligomers are dynamic and subunit exchange is critical for inhibiting client protein aggregation. The T193A mutation in the C-terminal domain (CTD) of DNAJB6 reduces both chaperone self-oligomerization and anti-aggregation of client proteins, and has recently been linked to Parkinson's disease. Here, we show by NMR, including relaxation-based methods, that the T193A mutation has minimal effects on the structure of the β-stranded CTD but increases the population and rate of formation of a partially folded state. The results can be rationalized in terms of β-strand peptide plane flips that occur on a timescale of ≈100 μs and lead to global changes in the overall pleat/flatness of the CTD, thereby altering its ability to oligomerize. These findings help forge a link between chaperone dynamics, oligomerization and anti-aggregation activity which may possibly lead to new therapeutic avenues tuned to target specific substrates.

Protein secondary structure assignment using pc-polyline and convolutional neural network.

The assignment of protein secondary structure elements (SSEs) underpins structural analysis and prediction. The backbone of a protein could be adequately represented using a pc-polyline that passes through the centers of its peptide planes. One salient feature of pc-polyline representation is that the secondary structure of a protein becomes recognizable in a matrix whose elements are the pairwise distances between two peptide plane centers. Thus, a pc-polyline could in turn be used to assign SSEs. Using convolutional neural network (CNN) here we confirm that a pc-polyline indeed contains enough information for it to be used for the accurate assignments of the six SSE types: α-helix, β-sheet, β-bulge, 310 -helix, turn and loop. The applications to three large data sets show that the assignments by our CNN-based p2psse program agree very well with those by dssp, stride and quite well with those by five other programs. The analyses of their SSE assignments raise some general questions about the characterizations of protein secondary structure. In particular the analyses illustrate the difficulty with giving a quantitative and consistent definition for each of the six SSE types especially for 310 -helix, β-bulge, turn or loop in terms of either backbone H-bond patterns, or backbone dihedral angles, or Cα -polyline or pc-polyline. The difficulty suggests that the SSE space though being dominated by the regions for the six SSE types is to a certain degree continuous. The program is available at https://github.com/wlincong/p2pSSE.

Protein secondary structure motifs: A kinematic construction.

The kinematic geometry of protein backbone structures, constrained by either single or multiple hydrogen bonds (H-bonds), possibly in a periodic array, is discussed. These structures include regular secondary structure elements α-helices and β-sheets but also include other short H-bond stabilized irregular structural elements like β-turns. The work here shows that the variations observed in such structures have simple geometrical correlations consistent with constrained motion kinematics. A new classification of the ideal helices is given, in terms of the parameter α, the angle at a Cα atom to its two neighboring Cα 's along the helix, and shown how it can be generalized to include nonideal helices. Specifically, we derive an analytical expression of the backbone dihedrals, (ϕ, ψ), in terms of the parameter α subject to the constraint that the peptide planes are parallel to the helical axis. Helices constructed in this way exhibit near-vertical alignment of the C = O and N - H units and are the canonical objects of this study. These expressions are easily modifiable to include perturbations of parameters relevant to nonplanar peptide units and noncanonical angles. The addition of a second parameter, ε0 , inclination of successive peptide planes along a helix with respect to the helical axis leads to a generalization of the previous expression and provides an efficient parametrization of such structures in terms of coordinates consistent with H-bond parameters. An analogs parametrization of β-turns, using inverse kinematic methods, is also given. Besides offering a unifying viewpoint, our results may find useful applications to protein and peptide design.

Peptide bond planarity constrains hydrogen bond geometry and influences secondary structure conformations.

An extensive database study of hydrogen bonds in different protein environments showed systematic variations in donor-acceptor-acceptor antecedent angle (Ĥ) and donor-acceptor distance. Protein environments were characterized by depth (distance of amino acids from bulk solvent), secondary structure, and whether the donor/acceptor belongs to the main chain (MC) or side chain (SC) of amino acids. The MC-MC hydrogen bonds (whether in secondary structures or not) have Ĥ angles tightly restricted to a value of around 155°, which was distinctly different from other Ĥ angles. Quantum chemical calculations attribute this characteristic MC-MC Ĥ angle to the nature of the electron density distribution around the planar peptide bond. Additional classical simulations suggest a causal link between MC-MC Ĥ angle and the conformation of secondary structures in proteins. We also showed that donor-acceptor distances are environment dependent, which has implications on protein stability. Our results redefine hydrogen bond geometries in proteins and suggest useful refinements to existing molecular mechanics force fields.

NMR “Crystallography” of Membrane Proteins Aligned in Native-Like Bilayers

Oriented-sample (OS) solid-state NMR can be used to determine structures of membrane proteins without crystallization and use of cryogenic temperatures. Here, the orientationally dependent dipolar couplings and chemical shifts provide direct input for structure calculations. However, so far only the 1H-15N dipolar couplings and 15N chemical shifts have been routinely assessed in 15N labeled protein samples. While highly efficient for determining the tilt angles of short α-helical peptides, these two measurements alone are likely insufficient for determining protein structures of arbitrary topology. Therefore, determination of tertiary structures of membrane proteins by OS NMR requires measurements of additional angular restraints. Here we have developed a new experimental triple-resonance NMR technique, which was applied to uniformly doubly (15N, 13C) labeled Pf1 coat protein reconstituted in magnetically aligned DMPC/DHPC bicelles. The previously inaccessible 1Hα-13Cα dipolar couplings, which represent powerful chiral angular restraints, have been measured for the resolved NMR resonances of the transmembrane domain of Pf1. Inclusion of the third restraint makes it possible to determine the torsion angles Φ and Ψ between the adjacent peptide planes without assuming α-helical structure a priori. Using our recently developed structure calculation algorithm [1], simultaneous fitting of three restraints per peptide plane has resulted in families of structures which have subsequently been filtered using various Rosetta scoring functions including the energetics within the membrane environment, hydrogen bonding, and potential steric clashes. Such structural validation protocol has led to a consensus α-helical transmembrane structure for Pf1 coat protein, albeit obtained in a de novo fashion, thus greatly enhancing utility of OS NMR as a “crystallography” in near-native membrane environments. [1]. Lapin, J. and Nevzorov A.A., Validation of protein backbone structures calculated from NMR angular restraints using Rosetta, J. Biomol. NMR, 2019; 73(5):229-244.

NMR “Crystallography” for Uniformly (13C, 15N)‐Labeled Oriented Membrane Proteins

AbstractIn oriented‐sample (OS) solid‐state NMR of membrane proteins, the angular‐dependent dipolar couplings and chemical shifts provide a direct input for structure calculations. However, so far only 1H–15N dipolar couplings and 15N chemical shifts have been routinely assessed in oriented 15N‐labeled samples. The main obstacle for extending this technique to membrane proteins of arbitrary topology has remained in the lack of additional experimental restraints. We have developed a new experimental triple‐resonance NMR technique, which was applied to uniformly doubly (15N, 13C)‐labeled Pf1 coat protein in magnetically aligned DMPC/DHPC bicelles. The previously inaccessible 1Hα–13Cα dipolar couplings have been measured, which make it possible to determine the torsion angles between the peptide planes without assuming α‐helical structure a priori. The fitting of three angular restraints per peptide plane and filtering by Rosetta scoring functions has yielded a consensus α‐helical transmembrane structure for Pf1 protein.

NMR “Crystallography” for Uniformly (13C, 15N)‐Labeled Oriented Membrane Proteins

In oriented-sample (OS) solid-state NMR of membrane proteins, the angular-dependent dipolar couplings and chemical shifts provide a direct input for structure calculations. However, so far only 1 H-15 N dipolar couplings and 15 N chemical shifts have been routinely assessed in oriented 15 N-labeled samples. The main obstacle for extending this technique to membrane proteins of arbitrary topology has remained in the lack of additional experimental restraints. We have developed a new experimental triple-resonance NMR technique, which was applied to uniformly doubly (15 N, 13 C)-labeled Pf1 coat protein in magnetically aligned DMPC/DHPC bicelles. The previously inaccessible 1 Hα -13 Cα dipolar couplings have been measured, which make it possible to determine the torsion angles between the peptide planes without assuming α-helical structure a priori. The fitting of three angular restraints per peptide plane and filtering by Rosetta scoring functions has yielded a consensus α-helical transmembrane structure for Pf1 protein.

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.

Can the geometry of all-atom protein trajectories be reconstructed from the knowledge of Cα time evolution? A study of peptide plane O and side chain Cβ atoms.

We inquire to what extent can the geometry of protein peptide plane and side chain atoms be reconstructed from the knowledge of Cα time evolution. Due to the lack of experimental data, we analyze all atom molecular dynamics trajectories from the Anton supercomputer, and for clarity, we limit our attention to the peptide plane O atoms and side chain Cβ atoms. We reconstruct their positions using four different approaches. Three of these are the publicly available reconstruction programs Pulchra, Remo, and Scwrl4. The fourth, Statistical Method, builds entirely on the statistical analysis of Protein Data Bank structures. All four methods place the O and Cβ atoms accurately along the Anton trajectories; the Statistical Method gives results that are closest to the Anton data. The results suggest that when a protein moves under physiological conditions, its all atom structures can be reconstructed with high accuracy from the knowledge of the Cα atom positions. This can help to better understand and improve all atom force fields, and advance reconstruction and refinement methods for reduced protein structures. The results provide impetus for the development of effective coarse grained force fields in terms of reduced coordinates.

Validation of protein backbone structures calculated from NMR angular restraints using Rosetta.

Multidimensional solid-state NMR spectra of oriented membrane proteins can be used to infer the backbone torsion angles and hence the overall protein fold by measuring dipolar couplings and chemical shift anisotropies, which depend on the orientation of each peptide plane with respect to the external magnetic field. However, multiple peptide plane orientations can be consistent with a given set of angular restraints. This ambiguity is further exacerbated by experimental uncertainty in obtaining and interpretingsuch restraints. The previously developed algorithms for structure calculations using angular restraints typically involve a sequential walkthrough along the backbone to find the torsion angles between the consecutive peptide plane orientations that are consistent with the experimental data. This method is sensitive to experimental uncertainty in interpreting the peak positions of as low as ± 10Hz, often yielding high structural RMSDs for the calculated structures. Here we present a significantly improved version of the algorithm which includes the fitting of several peptide planes at once in order to prevent propagation of error along the backbone. In addition, a protocol has been devised for filtering the structural solutions using Rosetta scoring functions in order to find the structures that both fit the spectrum and satisfy bioinformatics restraints. The robustness of the new algorithm has been tested using synthetic angular restraints generated from the known structures for two proteins: a soluble protein 2gb1 (56 residues), chosen for its diverse secondary structure elements, i.e. an alpha-helix and two beta-sheets, and a membrane protein 4a2n, from which the first two transmembrane helices (having a total of 64 residues) have been used. Extensive simulations have been performed by varying the number of fitted planes, experimental error, and the number of NMR dimensions. It has been found that simultaneously fitting two peptide planes always shifted the distribution of the calculated structures toward lower structural RMSD values as compared to fitting a single torsion-angle pair. For each protein, irrespective of the simulation parameters, Rosetta was able to distinguish the most plausible structures, often having structural RMSDs lower than 2Å with respect to the original structure. This study establishes a framework for de-novo protein structure prediction using a combination of solid-state NMR angular restraints and bioinformatics.

Study of correlations between protein peptide plane dynamics and side chain dynamics.

Protein dynamics is pivotal to biological processes. However, experiments are very demanding and difficult to perform, and all-atom molecular dynamics simulations can still not provide all the answers. This motivates us to analyze protein dynamics in terms of different reduced coordinate representations. We then need to resolve how to reconstruct the full all-atom dynamics from its coarse grained approximation. Accordingly we scrutinize all-atom molecular dynamics trajectories in terms of crystallographic Protein Data Bank (PDB) structures, and inquire to what extent is it possible to predict the dynamics of side chain Cβ atoms in terms of the static properties of backbone Cα and O atoms. Here we find that simulated Cβ dynamics at near physiological conditions can be reconstructed with very high precision, using the knowledge of the crystallographic backbone Cα and O positions. The precision we can reach with our PDB-based Statistical Method reconstruction exceeds that of popular all-atom reconstruction methods such as Remo and Pulchra, and is fully comparable with the precision of the highly elaborate Scwrl4 all-atom reconstruction method that we have enhanced with the knowledge of the backbone Cα and O atom positions. We then conclude that in a dynamical protein that moves around at physiological conditions, the relative positions of its Cβ atoms with respect to the backbone Cα and O atoms, deviate very little from their relative positions in static crystallographic PDB structures. This proposes that the dynamics of a biologically active protein could remain subject to very similar, stringent stereochemical constraints that dictate the structure of a folded crystallographic protein. Thus, our results provide a strong impetus to the development of coarse grained techniques that are based on reduced coordinate representations.

Myoglobin ligand gate mechanism analysis by a novel 3D visualization technique

A protein is commonly visualized as a discrete piecewise linear curve, conventionally characterized in terms of the extrinsically determined Ramachandran angles. However, in addition to the extrinsic geometry, the protein has also two independent intrinsic geometric structures, determined by the peptide planes and the side chains respectively. Here we develop a novel 3D visualization method that instead of the extrinsic geometry utilizes the intrinsic geometry of side chains. We base our approach on a series of orthonormal coordinate frames along the protein side chains in combination with a mapping of the atoms positions onto a unit sphere, for visualization purposes. We develop our methodology in terms of an example, by analyzing the acidity dependence of the presumed myoglobin ligand gate. In the literature, the ligand gate is often asserted to be highly localized at the distal histidine, its functioning being regulated by environmental changes. Thus, we investigate whether any $${\mathrm{pH}}$$ dependence can be detected in the orientation of the distal and proximal histidine residues, using existing crystallographic data. We observe no $${\mathrm{pH}}$$ dependence, in support of the alternative proposals that the ligand gate is more complex and might even be located elsewhere. Our methodology should help the planning of future myoglobin structure experiments, to identify the ligand gate position and its mechanism. More generally, our methodology is designed to visually depict the spatial orientation of side chain covalent bonds in a protein. As such, it can be eventually advanced into a general visual 3D tool for protein structure analysis for purposes of prediction, validation and refinement. It can serve as a complement to widely used visualization suites such as VMD, Jmol, PyMOL and others.

Transition of Metastable Cross-α Crystals into Cross-β Fibrils by β-Turn Flipping.

The ensemble of native, folded state was once considered to represent the global energy minimum of a given protein sequence. More recently, the discovery of the cross-β amyloid state revealed that deeper energy minima exist, often associated with pathogenic, fibrillar deposits, when the concentration of proteins reaches a critical value. Fortunately, a sizable energy barrier impedes the conversion from native to pathogenic states. However, little is known about the structure of the related transition state. In addition, there are indications of polymorphism in the amyloidogenic process. Here, we report the first evidence of the conversion of metastable cross-α-helical crystals to thermodynamically stable cross-β-sheet-like fibrils by a de novo designed heptapeptide. Furthermore, for the first time, we demonstrate at atomic resolution that the flip of a peptide plane from a type I to a type II' turn facilitates transformation to cross-β structure and assembly of a dry steric zipper. This study establishes the potential of a peptide turn, a common protein secondary structure, to serve as a principal gatekeeper between a native metastable folded state and the amyloid state.

Intrinsic protein geometry with application to non-proline cis peptide planes

The shape of a protein can be modeled by the \(\hbox {C}^{\alpha }\) atoms of its backbone, the mathematical description employing the notion of extrinsic geometry of a discrete piecewise linear chain. We advance differential geometry of a natively framed discrete chain to argue the existence of two additional, independent and intrinsic geometric structures, provided by the peptide planes and side chains, respectively. We develop our general methodology within a case study: analysis of the intrinsic geometry of atoms that are located around a non-proline cis peptide plane. We show that the native peptide plane framing allows for revealing of atomic positions anomalies. That way, we identify a number of entries that display such anomalies around their non-proline cis peptide planes within the ultrahigh-resolution structures in PDB. We propose that our approach can be extended into a visual analysis and refinement tool that is applicable even when resolution is limited or data is incomplete, for example when there are atoms missing in an experimental construct.

Arginine side chain stacking with peptide plane stabilizes the protein helix conformation in a cooperative way.

A combined experimental and computational study is performed for arginine side chain stacking with the protein α-helix. Theremostability measurements of Aristaless homeodomain, a helical protein, suggest that mutating the arginine residue R106, R137 or R141, which has the guanidino side chain stacking with the peptide plane, to alanine, destabilizes the protein. The R-PP stacking has an energy of ∼0.2-0.4 kcal/mol. This stacking interaction mainly comes from dispersion and electrostatics, based on MP2 calculations with the energy decomposition analysis. The calculations also suggest that the stacking stabilizes 2 backbone-backbone h-bonds (i→i-4 and i-3→i-7) in a cooperative way. Desolvation and electrostatic polarization are responsible for cooperativity with the i→i-4 and i-3→i-7 h-bonds, respectively. This cooperativity is supported by a protein α-helices h-bond survey in the pdb databank where stacking shortens the corresponding h-bond distances.