Residue coordination in proteins conforms to the closest packing of spheres

Saturation Mutagenesis of the Transmembrane Region of HokC in Escherichia coli Reveals Its High Tolerance to Mutations

Cells adapt to different stress conditions, such as the antibiotics presence. This adaptation sometimes is achieved by changing relevant protein positions, of which the mutability is limited by structural constrains. Understanding the basis of these constrains represent an important challenge for both basic science and potential biotechnological applications. To study these constraints, we performed a systematic saturation mutagenesis of the transmembrane region of HokC, a toxin used by Escherichia coli to control its own population, and observed that 92% of single-point mutations are tolerated and that all the non-tolerated mutations have compensatory mutations that reverse their effect. We provide experimental evidence that HokC accumulates multiple compensatory mutations that are found as correlated mutations in the HokC family multiple sequence alignment. In agreement with these observations, transmembrane proteins show higher probability to present correlated mutations and are less densely packed locally than globular proteins; previous mutagenesis results on transmembrane proteins further support our observations on the high tolerability to mutations of transmembrane regions of proteins. Thus, our experimental results reveal the HokC transmembrane region high tolerance to loss-of-function mutations that is associated with low sequence conservation and high rate of correlated mutations in the HokC family sequences alignment, which are features shared with other transmembrane proteins.

Thermodynamics of hydrophobic-polar model proteins on the face-centered cubic lattice

The HP model, a coarse-grained protein representation with only hydrophobic (H) and polar (P) amino acids, has already been extensively studied on the simple cubic (SC) lattice. However, this geometry severely restricts possible bond angles, and a simple improvement is to instead use the face-centered cubic (fcc) lattice. In this paper, the density of states and ground state energies are calculated for several benchmark HP sequences on the fcc lattice using the replica-exchange Wang-Landau algorithm and a powerful set of Monte Carlo trial moves. Results from the fcc lattice proteins are directly compared with those obtained from a previous lattice protein folding study with a similar methodology on the SC lattice. A thermodynamic analysis shows comparable folding behavior between the two lattice geometries, but with a greater rate of hydrophobic-core formation persisting into lower temperatures on the fcc lattice.

A novel measure to analyze protein structures: Aspect ratio in protein alpha shapes

Proteins' three-dimensional (3D) structures are analyzed traditionally using geometric descriptors such as torsional angles and inter-atomic distances. In this study a measure that is borrowed from computational geometry, aspect ratio of each tetrahedron in alpha shapes of proteins, is utilized. This geometric descriptor differentiates alpha and beta structural classes of proteins when combined with principal components analysis. The method converts the structures of individual proteins, 3D coordinates of the atoms, to points on a plane. It has a high degree of accuracy in differentiating R and T structures of hemoglobin. Therefore, it is anticipated that the geometric measure can be used successfully in a method that is extended to solve classification problems in machine learning.

Emergent protein folding modeled with evolved neural cellular automata using the 3D HP model

We used cellular automata (CA) for the modeling of the temporal folding of proteins. Unlike the focus of the vast research already done on the direct prediction of the final folded conformations, we will model the temporal and dynamic folding process. To reduce the complexity of the interactions and the nature of the amino acid elements, lattice models like HP were used, a model that categorizes the amino acids regarding their hydrophobicity. Taking into account the restrictions of the lattice model, the CA model defines how the amino acids interact through time to obtain a folded conformation. We extended the classical CA models using artificial neural networks for their implementation (neural CA), and we used evolutionary computing to automatically obtain the models by means of Differential Evolution. As the iterative folding also provides the final folded conformation, we can compare the results with those from direct prediction methods of the final protein conformation. Finally, as the neural CA that provides the iterative folding process can be evolved using several protein sequences and used as operators in the folding of another protein with different length, this represents an advantage over the NP-hard complexity of the original problem of the direct prediction.

Orientational distributions of contact clusters in proteins closely resemble those of an icosahedron

The orientational geometry of residue packing in proteins was studied in the past by superimposing clusters of neighboring residues with several simple lattices (Bagci et al., Proteins 2003;53:56-67; Raghunathan et al., Protein Sci 1997;6:2072-2083). In this work, instead of a lattice we use the regular polyhedron, the icosahedron, as the model to describe the orientational distribution of contacts in clusters derived from a high-resolution protein dataset (522 protein structures with high resolution < 1.5 A). We find that the order parameter (orientation function) measuring the angular overlap of directions in coordination clusters with directions of the icosahedron is 0.91, which is a significant improvement in comparison with the value 0.82 for the order parameter with the face-centered cubic (fcc) lattice. Close packing tendencies and patterns of residue packing in proteins are considered in detail and a theoretical description of these packing regularities is proposed.

CPSP-tools--exact and complete algorithms for high-throughput 3D lattice protein studies

Background

The principles of protein folding and evolution pose problems of very high inherent complexity. Often these problems are tackled using simplified protein models, e.g. lattice proteins. The CPSP-tools package provides programs to solve exactly and completely the problems typical of studies using 3D lattice protein models. Among the tasks addressed are the prediction of (all) globally optimal and/or suboptimal structures as well as sequence design and neutral network exploration.

Results

In contrast to stochastic approaches, which are not capable of answering many fundamental questions, our methods are based on fast, non-heuristic techniques. The resulting tools are designed for high-throughput studies of 3D-lattice proteins utilising the Hydrophobic-Polar (HP) model. The source bundle is freely available [1].

Conclusion

The CPSP-tools package is the first set of exact and complete methods for extensive, high-throughput studies of non-restricted 3D-lattice protein models. In particular, our package deals with cubic and face centered cubic (FCC) lattices.

An adaptive bin framework search method for a beta-sheet protein homopolymer model

BACKGROUND

The problem of protein structure prediction consists of predicting the functional or native structure of a protein given its linear sequence of amino acids. This problem has played a prominent role in the fields of biomolecular physics and algorithm design for over 50 years. Additionally, its importance increases continually as a result of an exponential growth over time in the number of known protein sequences in contrast to a linear increase in the number of determined structures. Our work focuses on the problem of searching an exponentially large space of possible conformations as efficiently as possible, with the goal of finding a global optimum with respect to a given energy function. This problem plays an important role in the analysis of systems with complex search landscapes, and particularly in the context of ab initio protein structure prediction.

RESULTS

In this work, we introduce a novel approach for solving this conformation search problem based on the use of a bin framework for adaptively storing and retrieving promising locally optimal solutions. Our approach provides a rich and general framework within which a broad range of adaptive or reactive search strategies can be realized. Here, we introduce adaptive mechanisms for choosing which conformations should be stored, based on the set of conformations already stored in memory, and for biasing choices when retrieving conformations from memory in order to overcome search stagnation.

CONCLUSION

We show that our bin framework combined with a widely used optimization method, Monte Carlo search, achieves significantly better performance than state-of-the-art generalized ensemble methods for a well-known protein-like homopolymer model on the face-centered cubic lattice.

In silico protein fragmentation reveals the importance of critical nuclei on domain reassembly

Protein complementation assays (PCAs) based on split protein fragments have become powerful tools that facilitate the study and engineering of intracellular protein-protein interactions. These assays are based on the observation that a given protein can be split into two inactive fragments and these fragments can reassemble into the original properly folded and functional structure. However, one experimentally observed limitation of PCA systems is that the folding of a protein from its fragments is dramatically slower relative to that of the unsplit parent protein. This is due in part to a poor understanding of how PCA design parameters such as split site position in the primary sequence and size of the resulting fragments contribute to the efficiency of protein reassembly. We used a minimalist on-lattice model to analyze how the dynamics of the reassembly process for two model proteins was affected by the location of the split site. Our results demonstrate that the balanced distribution of the "folding nucleus," a subset of residues that are critical to the formation of the transition state leading to productive folding, between protein fragments is key to their reassembly.

Coarse-grained representation of beta-helical protein building blocks

A general strategy to develop coarse-grained models of beta-helical protein fragments is presented. The procedure has been applied to a building block formed by a two-turn repeat motif from E. coli galactoside acetyltransferase, which is able to provide a very stable self-assembled tubular nanoconstruct upon stacking of its replicas. For this purpose, first, we have developed a computational scheme to sample very efficiently the configurational space of the building block. This method, which is inspired by a strategy recently designed to study amorphous polymers and by an advanced Monte Carlo algorithm, provides a large ensemble of uncorrelated configurations at a very reasonable computational cost. The atomistic configurations provided by this method have been used to obtain a coarse-grained model that describes the amino acids with fewer particles than those required for full atomistic detail, i.e., two, three, or four depending on the chemical nature of the amino acid. Coarse-grained potentials have been developed considering the following types of interactions: (i) electrostatic and van der Waals interactions between residues i and i + n with n >/= 2; (ii) interactions between residues i and i + 1; and (c) intra-residue interactions. The reliability of the proposed model has been tested by comparing the atomistic and coarse-grained energies calculated for a large number of independent configurations of the beta-helical building block.

Folding kinetics of a lattice protein via a forward flux sampling approach

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.

How well can we understand large-scale protein motions using normal modes of elastic network models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.

Coarse-graining: A procedure to generate equilibrated and relaxed models of amorphous polymers

We present a coarse-graining procedure to construct models of amorphous polymers. The method, which was applied to polyethylene, is based on a generation-relaxation strategy previously developed to provide independent atomistic microstructures. The coarse-graining was performed by assigning positions to mesoscopic particles denoted blobs, which represent groups of atoms, through distance, angle and dihedral distribution functions. The interaction energy between pairs of blobs was evaluated through a soft potential, whose parameters were derived from atomistic models. Three levels of coarse-graining that differ in the number of atoms included in the blob have been considered. The structural and energy-related properties calculated using the coarse-grained models developed in this study are in good agreement with those obtained using atomistic simulations.

Development of novel statistical potentials for protein fold recognition

The need to perform large-scale studies of protein fold recognition, structure prediction and protein-protein interactions has led to novel developments of residue-level minimal models of proteins. A minimum requirement for useful protein force-fields is that they be successful in the recognition of native conformations. The balance between the level of detail in describing the specific interactions within proteins and the accuracy obtained using minimal protein models is the focus of many current protein studies. Recent results suggest that the introduction of explicit orientation dependence in a coarse-grained, residue-level model improves the ability of inter-residue potentials to recognize the native state. New statistical and optimization computational algorithms can be used to obtain accurate residue-dependent potentials for use in protein fold recognition and, more importantly, structure prediction.

Lattice models of peptide aggregation: Evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.

Continuous anisotropic representation of coarse-grained potentials for proteins by spherical harmonics synthesis

A new method is presented for extracting statistical potentials dependent on the relative side chain and backbone orientations in proteins. Coarse-grained, anisotropic potentials are constructed for short-, medium-, and long-range interactions using the Boltzmann method and a database of non-homologous protein structures. The new orientation-dependent potentials are analyzed using a spherical harmonics decomposition method with real eigenfunctions. This method permits a more realistic, continuous angular representation of the coarse-grained potentials. Results of tests for discriminating the native protein conformations from large sets of decoy proteins, show that the new continuous distance- and orientation-dependent potentials present significantly improved performance. Novel graphical representations are developed and used to depict the orientational dependence of the interaction potentials. These new continuous anisotropic statistical potentials could be instrumental in developing new computational methods for structure prediction, threading and coarse-grained simulations.

Functional motions can be extracted from on-lattice construction of protein structures

The three-dimensional structure of a 1509-residue protein-hemagglutinin is reconstructed on a simple cubic lattice by retaining all lattice sites that fall within close proximity of the X-ray coordinates. Coarse-grained normal modes analysis is performed using these lattice sites as the nodes of an elastic network. The collective deformations of the protein can still be extracted from such a structure that just mimics the overall shape of the protein but not its mass distribution. These results emphasize that the overall shape rather than the details of the protein fold determines the dynamical domains in proteins. Thus, low-resolution protein structures, even those constructed on a regularly spaced lattice, can provide insights about the functionally important global dynamics around the native state.

The origin and extent of coarse-grained regularities in protein internal packing

Despite the suitability of various lattice geometries for coarse-grained modeling of proteins, the actual packing geometry of residues in folded structures has remained largely unexplored. A strong tendency to assume a regular packing geometry is shown here by optimally reorienting and superimposing clusters of neighboring residues from databank structures examined on a coarse-grained (single-site-per-residue) scale. The orientation function (or order parameter) of the examined coordination clusters with respect to fcc lattice directions is found to be 0.82. The observed geometry, which may be termed an incomplete distorted face-centered cubic (fcc) packing, is apparently favored by the drive to maximize packing density, in a fashion analogous to the way identical spheres pack densely and follow fcc geometry. About 2/3 of all residues obey this packing geometry, while the remainder occupy other context-dependent positions. The preferred coordination directions show relatively small variations over the various amino acid types, consistent with uniform residue viewpoint. Both the extremes of solvent-exposed and completely buried residue neighborhoods approximate the same generic packing, the only difference being in the numbers (and not the orientations) of coordination sites that are occupied (or left void for solvent occupancy). We observe the prevalence of a rather uniform (tight) residue packing density throughout the structure, including even the residues packed near solvent-exposed regions. The observed orientation distribution reveals an underlying, intrinsic orientation lattice for proteins.

Nonatomic solvent-driven Voronoi tessellation of proteins: an open tool to analyze protein folds

A three-dimensional Voronoi tessellation of folded proteins is used to analyze geometrical and topological properties of a set of proteins. To each amino acid is associated a central point surrounded by a Voronoi cell. Voronoi cells describe the packing of the amino acids. Special attention is given to reproduction of the protein surface. Once the Voronoi cells are built, a lot of tools from geometrical analysis can be applied to investigate the protein structure; volume of cells, number of faces per cell, and number of sides per face are the usual signatures of the protein structure. A distinct difference between faces related to primary, secondary, and tertiary structures has been observed. Faces threaded by the main-chain have on average more than six edges, whereas those related to helical packing of the amino acid chain have less than five edges. The faces on the protein surface have on average five edges within 1% error. The average number of faces on the protein surface for a given type of amino acid brings a new point of view in the characterization of the exposition to the solvent and the classification of amino acid as hydrophilic or hydrophobic. It may be a convenient tool for model validation.