Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

Accurate prediction of protein dihedral angles through conditional random field

Identifying local conformational changes induced by subtle differences on amino acid sequences is critical in exploring the functional variations of the proteins. In this study, we designed a computational scheme to predict the dihedral angle variations for different amino acid sequences by using conditional random field. This computational tool achieved an accuracy of 87% and 84% in 10-fold cross validation in a large data set for φ and Ψ, respectively. The prediction accuracies of φ and Ψ are positively correlated to each other for most of the 20 types of amino acids. Helical amino acids can achieve higher prediction accuracy in general, while amino acids in beet sheet have higher accuracy at specific angular regions. The prediction accuracy of φ is negatively correlated with amino acid flexibility represented by Vihinen Index. The prediction accuracy of φ can also be negatively correlated with angle distribution dispersion.     

Comparison of protein secondary structures based on backbone dihedral angles

In this article, we propose a relatively similar measure to compare protein secondary structures. We first transform a protein secondary structure into a special sequence representation (angle sequence) based on a partition of the backbone φ,ψ-space. Then, pairwise sequence distance is evaluated on the basis of a symbolic sequence complexity. To illustrate our approach, we construct the similarity tree of 24 proteins from PDB.     

GeoPCA: a new tool for multivariate analysis of dihedral angles based on principal component geodesics

The GeoPCA package is the first tool developed for multivariate analysis of dihedral angles based on principal component geodesics. Principal component geodesic analysis provides a natural generalization of principal component analysis for data distributed in non-Euclidean space, as in the case of angular data. GeoPCA presents projection of angular data on a sphere composed of the first two principal component geodesics, allowing clustering based on dihedral angles as opposed to Cartesian coordinates. It also provides a measure of the similarity between input structures based on only dihedral angles, in analogy to the root-mean-square deviation of atoms based on Cartesian coordinates. The principal component geodesic approach is shown herein to reproduce clusters of nucleotides observed in an η-θ plot. GeoPCA can be accessed via http://pca.limlab.ibms.sinica.edu.tw.     

Automated NMR determination of protein backbone dihedral angles from cross-correlated spin relaxation

The simultaneous interpretation of a suite of dipole-dipole and dipole-CSA cross-correlation rates involving the backbone nuclei ¹³C, ¹H,¹³CO, ¹⁵N and ¹H^N can be used to resolve the ambiguities associated with each individual cross-correlation rate. The method is based on the transformation of experimental cross-correlation rates via calculated values based on standard peptide plane geometry and solid-state ¹³CO CSA parameters into a dihedral angle probability surface. Triple resonance NMR experiments with improved sensitivity have been devised for the quantification of relaxation interference between ¹H(i)-¹³C(i)/¹⁵N(i)-¹H^N(i) and ¹H(i–1)-¹³C(i–1)/¹⁵N(i)-¹H^N(i) dipole-dipole mechanisms in ¹⁵N,¹³C-labeled proteins. The approach is illustrated with an application to ¹³C,¹⁵N-labeled ubiquitin.     

Prediction of backbone dihedral angles and protein secondary structure using support vector machines

Background  

The prediction of the secondary structure of a protein is a critical step in the prediction of its tertiary structure and, potentially, its function. Moreover, the backbone dihedral angles, highly correlated with secondary structures, provide crucial information about the local three-dimensional structure.     

A Bayesian-probability-based method for assigning protein backbone dihedral angles based on chemical shifts and local sequences

Chemical shifts contain substantial information about protein local conformations. We present a method to assign individual protein backbone dihedral angles into specific regions on the Ramachandran map based on the amino acid sequences and the chemical shifts of backbone atoms of tripeptide segments. The method uses a scoring function derived from the Bayesian probability for the central residue of a query tripeptide segment to have a particular conformation. The Ramachandran map is partitioned into representative regions at two levels of resolution. The lower resolution partitioning is equivalent to the conventional definitions of different secondary structure regions on the map. At the higher resolution level, the α and β regions are further divided into subregions. Predictions are attempted at both levels of resolution. We compared our method with TALOS using the original TALOS database, and obtained comparable results. Although TALOS may produce the best results with currently available databases which are much enlarged, the Bayesian-probability-based approach can provide a quantitative measure for the reliability of predictions.     

Lateral view flow system for studies of cell adhesion and deformation under flow conditions

Physical interactions between circulating cells and the vascular wall play a central role in inflammation, metastasis, atherosclerosis, and therapeutic cell delivery. Unfortunately, traditional in vitro flow assays cannot be used to visualize the details of cell-surface interactions in blood flow because of inappropriate geometry and the poor penetration of light in erythrocyte solutions. To overcome these obstacles, we have developed an agarose-cast cylindrical vessel system to examine the profiles of cells interacting with surfaces under flow conditions. This design allows observation and quantification of cell deformation as cells adhere to surfaces under dynamic flow conditions without modifying the microscope or optical path. Furthermore, our flow system is uniquely suited for monitoring the profiles of adherent leukocytes deforming in response to erythrocyte suspension flow. We have used this flow system to study the role of erythrocytes in leukocyte-substrate interactions. Our results show that the cell deformation index (the ratio of the cell length to cell height) is higher in erythrocyte solutions compared to erythrocyte-free saline. This novel lateral view flow system provides a powerful technique for visualizing and quantifying the morphological changes of cells in contact with substrates exposed to shear stress.     

Myoglobin as a test case in the construction of space-filling models of proteins using dihedral angles

A method for construction of space-filling models of proteins of improved accuracy was developed from the dihedral angle technique proposed by Hauschka and Segal (P. V. Hauschka and D. M. Segal, Biopolymers, 4 , 1051, 1966). Tools were designed to facilitate the marking of accurate reference lines on component atoms and a simple method for cementing the fixed angles was devised. The torsion angle method was extended to include all side chains. The improved technique was used to assemble a model of sperm whale metmyoglobin from the x-ray data.     

Quantification of plantar soft tissue changes due to aging in various metatarsophalangeal joint angles with realistic tissue deformation

The nonlinearity of plantar soft tissue is seldom examined because of the small extent of deformation induced during indentation for measurement purposes. Furthermore, in most indentation experiments, the metatarsophalangeal joint (MTPJ) angle is not well controlled, although it has been proven to have a significant stiffening effect on sub-metatarsal head (MTH) pads. Hence, the study aims to quantify changes in the mechanical properties of plantar soft tissue due to aging under an experimental condition which is similar to walking. This is done by subjecting the tissue to an appropriate level of deformation at various MTPJ angles. A custom-made in vivo tissue indenter was used to measure directly the force-indentation response of the plantar tissue of two healthy groups: “Young” (n=25, mean age 22) and “Elderly” (n=25, mean age 67) subjects. Tests were performed on the 2nd sub-MTH pad at angles of 0°, 20°, 40° MTPJ dorsiflexion, as well as at the hallux and heel pad at 0° MTPJ angle. At all three plantar sites tested, elderly subjects showed significantly higher tissue stiffness than the young (p<0.05). However, the stiffening effect of MTPJ angle was not notably influenced by aging. In this work, tissue stiffness is quantified in stiffness constant (K) based on the proposed indentation technique. It is hypothesized that the increase in stiffness with age observed is probably due to compositional change in the plantar soft tissue.     

Local interactions as a structure determinant for protein molecules: II

Van der Waals interactions between sidechains are indicated to be important in determining the native state of the proteins of known structure by the following observations:

• 1.1.|the average radial distribution of polarity increases continuously from the center of the molecule to its periphery.
• 2.2.|nonpolar sidechains tend to occur in clusters.
• 3.3.|the frequencies of long-range nearest-neighbor pairs are markedly non-random; each type of sidechain seeks nearest-neighbors of similar polarity. To investigate how these interactions affect the overall structure of the protein molecule, three simpified models are treated: a sheath-core model composed of independent residues, a modification accounting approximately for the connected nature of the chain, and a model consisting of three concentric spherical phases.

     

Triceps surae muscle-tendon unit length changes as a function of ankle joint angles and contraction levels: the effect of foot arch deformation

The purpose of this study was to clarify how foot deformation affects the relationship between triceps surae muscle-tendon unit (MTU) length and ankle joint angle. For six women and six men a series of sagittal magnetic resonance (MR) images of the right foot were taken, and changes in MTU length (the displacement of the calcaneal tuberosity), foot arch angle, and ankle joint angle were measured. In the passive session, each subject's ankle joint was secured at 10° dorsiflexed position, neutral position (NP), and 10° and 20° plantar flexed positions while MR images were acquired. In the active session, each subject was requested to perform submaximal isometric plantar flexions (30%, 60%, and 80% of voluntary maximum) at NP. The changes in MTU length in each trial were estimated by two different formulae reported previously. The changes of the measured MTU length as a function of ankle joint angles observed in all trials of the active session were significantly (p<0.05) larger than corresponding values in the passive session and by the estimation formulae. In the passive session, MTU length changes were significantly smaller than the estimated values when the ankle was plantar flexed. The foot arch angle increased as the contraction level increased from rest (117 ± 4°) to 80% (125 ± 3°), and decreased as the ankle was positioned further into plantar flexion in the passive session (115 ± 3°). These results indicate that foot deformation profoundly affects the triceps surae MTU length-ankle joint angle relationship during plantar flexion.     

The elixir phase of chain molecules

A phase of matter is a familiar notion for inanimate physical matter. The nature of a phase of matter transcends the microscopic material properties. For example, materials in the liquid phase have certain common properties independent of the chemistry of the constituents: liquids take the shape of the container; they flow; and they can be poured—alcohol, oil, and water as well as a Lennard-Jones computer model exhibit similar behavior when poised in the liquid phase. Here, we identify a hitherto unstudied “phase” of matter, the elixir phase, in a simple model of a polymeric chain whose backbone has the correct local cylindrical symmetry induced by the tangent to the chain. The elixir phase appears on breaking the cylindrical symmetry by adding side spheres along the negative normal direction, as in proteins. This phase, nestled between other phases, has multiple ground states made up of building blocks of helices and almost planar sheets akin to protein native folds. We discuss the similarities of this “phase” of a finite size system to the liquid crystal and spin glass phases. Our findings are relevant for understanding proteins; the creation of novel bioinspired nanomachines; and also may have implications for life elsewhere in the cosmos.     

Worm-like chain model extensions for highly stretched tropocollagen molecules

Tropocollagen plays a very important role in the load bearing functionality of soft tissues. In the context of multi-scale modeling the response of tropocollagen molecules to stretch should be very carefully predicted in order to describe the mechanical behavior of soft tissues. To this end, the worm-like chain (WLC) model is often applied, although it is restricted to the entropic force regime which is essential at moderate deformations. To describe molecular forces under larger stretches several extensions of the WLC have been proposed for deoxyribonucleic acid (DNA). This contribution aims to investigate the applicability of these models in the context of tropocollagen and discusses the feasibility of their application. Finally, the models are validated in comparison to experimental data available in the literature.