Reconstruction and stability of secondary structure elements in the context of protein structure prediction

A tile model of circuit topology for self-entangled biopolymers

Building on the theory of circuit topology for intra-chain contacts in entangled proteins, we introduce tiles as a way to rigorously model local entanglements which are held in place by molecular forces. We develop operations that combine tiles so that entangled chains can be represented by algebraic expressions. Then we use our model to show that the only knot types that such entangled chains can have are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and connected sums of these knots. This includes all proteins knots that have thus far been identified.

Characterizing the Structural and Functional Properties of Soybean Protein Extracted from Full-Fat Soybean Flakes after Low-Temperature Dry Extrusion

The soy protein isolates (SPI) extracted from different extruded full-fat soybean flakes (FFSF), and their conformational and functional properties were characterized. Overall, the free thiol (SH) content of SPI increased when the extrusion temperature was below 80 °C and decreased at higher temperatures. Soy glycinin (11S) showed higher stability than β-conglycinin (7S) during extrusion. Results also indicated that the increase in some hydrophobic groups was due to the movement of hydrophobic groups from the interior to the surface of the SPI molecules at extrusion temperatures from 60 to 80 °C. However, the aggregation of SPI molecules occurred at extrusion temperatures of 90 and 100 °C, with decreasing levels of hydrophobic groups. The extrusion temperature negatively affected the emulsifying activity index (EAI); on the other side, it positively affected the emulsifying stability index (ESI), compared to unextruded SPI.

Efficient Parameter Estimation of Generalizable Coarse-Grained Protein Force Fields Using Contrastive Divergence: A Maximum Likelihood Approach

Maximum Likelihood (ML) optimization schemes are widely used for parameter inference. They maximize the likelihood of some experimentally observed data, with respect to the model parameters iteratively, following the gradient of the logarithm of the likelihood. Here, we employ a ML inference scheme to infer a generalizable, physics-based coarse-grained protein model (which includes Go̅-like biasing terms to stabilize secondary structure elements in room-temperature simulations), using native conformations of a training set of proteins as the observed data. Contrastive divergence, a novel statistical machine learning technique, is used to efficiently approximate the direction of the gradient ascent, which enables the use of a large training set of proteins. Unlike previous work, the generalizability of the protein model allows the folding of peptides and a protein (protein G) which are not part of the training set. We compare the same force field with different van der Waals (vdW) potential forms: a hard cutoff model, and a Lennard-Jones (LJ) potential with vdW parameters inferred or adopted from the CHARMM or AMBER force fields. Simulations of peptides and protein G show that the LJ model with inferred parameters outperforms the hard cutoff potential, which is consistent with previous observations. Simulations using the LJ potential with inferred vdW parameters also outperforms the protein models with adopted vdW parameter values, demonstrating that model parameters generally cannot be used with force fields with different energy functions. The software is available at https://sites.google.com/site/crankite/.

Predicting protein β-sheet contacts using a maximum entropy-based correlated mutation measure

MOTIVATION

The problem of ab initio protein folding is one of the most difficult in modern computational biology. The prediction of residue contacts within a protein provides a more tractable immediate step. Recently introduced maximum entropy-based correlated mutation measures (CMMs), such as direct information, have been successful in predicting residue contacts. However, most correlated mutation studies focus on proteins that have large good-quality multiple sequence alignments (MSA) because the power of correlated mutation analysis falls as the size of the MSA decreases. However, even with small autogenerated MSAs, maximum entropy-based CMMs contain information. To make use of this information, in this article, we focus not on general residue contacts but contacts between residues in β-sheets. The strong constraints and prior knowledge associated with β-contacts are ideally suited for prediction using a method that incorporates an often noisy CMM.

RESULTS

Using contrastive divergence, a statistical machine learning technique, we have calculated a maximum entropy-based CMM. We have integrated this measure with a new probabilistic model for β-contact prediction, which is used to predict both residue- and strand-level contacts. Using our model on a standard non-redundant dataset, we significantly outperform a 2D recurrent neural network architecture, achieving a 5% improvement in true positives at the 5% false-positive rate at the residue level. At the strand level, our approach is competitive with the state-of-the-art single methods achieving precision of 61.0% and recall of 55.4%, while not requiring residue solvent accessibility as an input.

AVAILABILITY

http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software/

Exploring the energy landscapes of protein folding simulations with Bayesian computation

Nested sampling is a Bayesian sampling technique developed to explore probability distributions localized in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. The nested sampling algorithm also provides an efficient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post processing of the output. Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques, including parallel tempering. In this article, we describe a parallel implementation of the nested sampling algorithm and its application to the problem of protein folding in a Gō-like force field of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. We demonstrate the method by conducting folding simulations on a number of small proteins that are commonly used for testing protein-folding procedures. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high-level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force field used.

Deciphering the shape and deformation of secondary structures through local conformation analysis

Background

Protein deformation has been extensively analysed through global methods based on RMSD, torsion angles and Principal Components Analysis calculations. Here we use a local approach, able to distinguish among the different backbone conformations within loops, α-helices and β-strands, to address the question of secondary structures' shape variation within proteins and deformation at interface upon complexation.

Results

Using a structural alphabet, we translated the 3 D structures of large sets of protein-protein complexes into sequences of structural letters. The shape of the secondary structures can be assessed by the structural letters that modeled them in the structural sequences. The distribution analysis of the structural letters in the three protein compartments (surface, core and interface) reveals that secondary structures tend to adopt preferential conformations that differ among the compartments. The local description of secondary structures highlights that curved conformations are preferred on the surface while straight ones are preferred in the core. Interfaces display a mixture of local conformations either preferred in core or surface. The analysis of the structural letters transition occurring between protein-bound and unbound conformations shows that the deformation of secondary structure is tightly linked to the compartment preference of the local conformations.

Conclusion

The conformation of secondary structures can be further analysed and detailed thanks to a structural alphabet which allows a better description of protein surface, core and interface in terms of secondary structures' shape and deformation. Induced-fit modification tendencies described here should be valuable information to identify and characterize regions under strong structural constraints for functional reasons.