Modular DAG-RNN architectures for assembling coarse protein structures.

We develop and test machine learning methods for the prediction of coarse 3D protein structures, where a protein is represented by a set of rigid rods associated with its secondary structure elements (alpha-helices and beta-strands). First, we employ cascades of recursive neural networks derived from graphical models to predict the relative placements of segments. These are represented as discretized distance and angle maps, and the discretization levels are statistically inferred from a large and curated dataset. Coarse 3D folds of proteins are then assembled starting from topological information predicted in the first stage. Reconstruction is carried out by minimizing a cost function taking the form of a purely geometrical potential. We show that the proposed architecture outperforms simpler alternatives and can accurately predict binary and multiclass coarse maps. The reconstruction procedure proves to be fast and often leads to topologically correct coarse structures that could be exploited as a starting point for various protein modeling strategies. The fully integrated rod-shaped protein builder (predictor of contact maps + reconstruction algorithm) can be accessed at http://distill.ucd.ie/.     

hdANM: a new comprehensive dynamics model for protein hinges

Hinge motions are essential for many protein functions, and their dynamics are important to understand underlying biological mechanisms. The ways that these motions are represented by various computational methods differ significantly. By focusing on a specific class of motion, we have developed a new hinge-domain anisotropic network model (hdANM) that is based on the prior identification of flexible hinges and rigid domains in the protein structure and the subsequent generation of global hinge motions. This yields a set of motions in which the relative translations and rotations of the rigid domains are modulated and controlled by the deformation of the flexible hinges, leading to a more restricted, specific view of these motions. hdANM is the first model, to our knowledge, that combines information about protein hinges and domains to model the characteristic hinge motions of a protein. The motions predicted with this new elastic network model provide important conceptual advantages for understanding the underlying biological mechanisms. As a matter of fact, the generated hinge movements are found to resemble the expected mechanisms required for the biological functions of diverse proteins. Another advantage of this model is that the domain-level coarse graining makes it significantly more computationally efficient, enabling the generation of hinge motions within even the largest molecular assemblies, such as those from cryo-electron microscopy. hdANM is also comprehensive as it can perform in the same way as the well-known protein dynamics models (anisotropic network model, rotations-translations of blocks, and nonlinear rigid block normal mode analysis), depending on the definition of flexible and rigid parts in the protein structure and on whether the motions are extrapolated in a linear or nonlinear fashion. Furthermore, our results indicate that hdANM produces more realistic motions as compared to the anisotropic network model. hdANM is an open-source software, freely available, and hosted on a user-friendly website.     

Rigid domains in proteins: An algorithmic approach to their identification

A rigid domain, defined here as a tertiary structure common to two or more different protein conformations, can be identified numerically from atomic coordinates by finding sets of residues, one in each conformation, such that the distance between any two residues within the set belonging to one conformation is the same as the distance between the two structurally equivalent residues within the set belonging to any other conformation. The distance between two residues is taken to be the distance between their respective α carbon atoms. With the methods of this paper we have found in the deoxy and oxy conformations of the human hemoglobin α₁β₁ dimer a rigid domain closely related to that previously identified by Baldwin and Chothia (J. Mol. Biol. 129:175–220,1979). We provide two algorithms, both using the difference-distance matrix, with which to search for rigid domains directly from atomic coordinates. The first finds all rigid domains in a protein but has storage and processing demands that become prohibitively large with increasing protein size. The second, although not necessarily finding every rigid domain, is computationally tractable for proteins of any size. Because of its efficiency we are able to search protein conformations recursively for groups of non-intersecting domains. Different protein conformations, when aligned by superimposing their respective domain structures; can be examined for structural differences in regions complementing a rigid domain. © 1995 Wiley-Liss, Inc.     

Accelerating and focusing protein-protein docking correlations using multi-dimensional rotational FFT generating functions

MOTIVATION: Predicting how proteins interact at the molecular level is a computationally intensive task. Many protein docking algorithms begin by using fast Fourier transform (FFT) correlation techniques to find putative rigid body docking orientations. Most such approaches use 3D Cartesian grids and are therefore limited to computing three dimensional (3D) translational correlations. However, translational FFTs can speed up the calculation in only three of the six rigid body degrees of freedom, and they cannot easily incorporate prior knowledge about a complex to focus and hence further accelerate the calculation. Furthemore, several groups have developed multi-term interaction potentials and others use multi-copy approaches to simulate protein flexibility, which both add to the computational cost of FFT-based docking algorithms. Hence there is a need to develop more powerful and more versatile FFT docking techniques. RESULTS: This article presents a closed-form 6D spherical polar Fourier correlation expression from which arbitrary multi-dimensional multi-property multi-resolution FFT correlations may be generated. The approach is demonstrated by calculating 1D, 3D and 5D rotational correlations of 3D shape and electrostatic expansions up to polynomial order L=30 on a 2 GB personal computer. As expected, 3D correlations are found to be considerably faster than 1D correlations but, surprisingly, 5D correlations are often slower than 3D correlations. Nonetheless, we show that 5D correlations will be advantageous when calculating multi-term knowledge-based interaction potentials. When docking the 84 complexes of the Protein Docking Benchmark, blind 3D shape plus electrostatic correlations take around 30 minutes on a contemporary personal computer and find acceptable solutions within the top 20 in 16 cases. Applying a simple angular constraint to focus the calculation around the receptor binding site produces acceptable solutions within the top 20 in 28 cases. Further constraining the search to the ligand binding site gives up to 48 solutions within the top 20, with calculation times of just a few minutes per complex. Hence the approach described provides a practical and fast tool for rigid body protein-protein docking, especially when prior knowledge about one or both binding sites is available.     

Calculation of the solution properties of flexible macromolecules: methods and applications

While the prediction of hydrodynamic properties of rigid particles is nowadays feasible using simple and efficient computer programs, the calculation of such properties and, in general, the dynamic behavior of flexible macromolecules has not reached a similar situation. Although the theories are available, usually the computational work is done using solutions specific for each problem. We intend to develop computer programs that would greatly facilitate the task of predicting solution behavior of flexible macromolecules. In this paper, we first present an overview of the two approaches that are most practical: the Monte Carlo rigid-body treatment, and the Brownian dynamics simulation technique. The Monte Carlo procedure is based on the calculation of properties for instantaneous conformations of the macromolecule that are regarded as if they were instantaneously rigid. We describe how a Monte Carlo program can be interfaced to the programs in the HYDRO suite for rigid particles, and provide an example of such calculation, for a hypothetical particle: a protein with two domains connected by a flexible linker. We also describe briefly the essentials of Brownian dynamics, and propose a general mechanical model that includes several kinds of intramolecular interactions, such as bending, internal rotation, excluded volume effects, etc. We provide an example of the application of this methodology to the dynamics of a semiflexible, wormlike DNA.     

Constrained geometric simulation of diffusive motion in proteins

We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins. The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein. Using random moves, the available conformational phase space of a 100 residue protein can be well explored in approximately 10-100 min of computer time using a single processor. All of the covalent, hydrophobic and hydrogen bond constraints are maintained, and van der Waals overlaps are avoided, throughout the simulation. We illustrate the results of a FRODA simulation on barnase, and show that good agreement is obtained with nuclear magnetic resonance experiments. We additionally show how FRODA can be used to find a pathway from one conformation to another. This directed dynamics is illustrated with the protein dihydrofolate reductase.     

Finding rigid bodies in protein structures: Application to flexible fitting into cryoEM maps

We present RIBFIND, a method for detecting flexibility in protein structures via the clustering of secondary structural elements (SSEs) into rigid bodies. To test the usefulness of the method in refining atomic structures within cryoEM density we incorporated it into our flexible fitting protocol (Flex-EM). Our benchmark includes 13 pairs of protein structures in two conformations each, one of which is represented by a corresponding cryoEM map. Refining the structures in simulated and experimental maps at the 5–15 Å resolution range using rigid bodies identified by RIBFIND shows a significant improvement over using individual SSEs as rigid bodies. For the 15 Å resolution simulated maps, using RIBFIND-based rigid bodies improves the initial fits by 40.64% on average, as compared to 26.52% when using individual SSEs. Furthermore, for some test cases we show that at the sub-nanometer resolution range the fits can be further improved by applying a two-stage refinement protocol (using RIBFIND-based refinement followed by an SSE-based refinement). The method is stand-alone and could serve as a general interactive tool for guiding flexible fitting into EM maps.     

Method for identification of rigid domains and hinge residues in proteins based on exhaustive enumeration

Many proteins undergo large‐scale motions where relatively rigid domains move against each other. The identification of rigid domains, as well as the hinge residues important for their relative movements, is important for various applications including flexible docking simulations. In this work, we develop a method for protein rigid domain identification based on an exhaustive enumeration of maximal rigid domains, the rigid domains not fully contained within other domains. The computation is performed by mapping the problem to that of finding maximal cliques in a graph. A minimal set of rigid domains are then selected, which cover most of the protein with minimal overlap. In contrast to the results of existing methods that partition a protein into non‐overlapping domains using approximate algorithms, the rigid domains obtained from exact enumeration naturally contain overlapping regions, which correspond to the hinges of the inter‐domain bending motion. The performance of the algorithm is demonstrated on several proteins. Proteins 2015; 83:1054–1067. © 2015 Wiley Periodicals, Inc.     

Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory

The development of a two-step approach for multiscale modeling of macromolecular conformational changes is based on recent developments in rigidity and elastic network theory. In the first step, static properties of the macromolecule are determined by decomposing the molecule into rigid clusters by using the graph-theoretical approach FIRST and an all-atom representation of the protein. In this way, rigid clusters are not limited to consist of residues adjacent in sequence or secondary structure elements as in previous studies. Furthermore, flexible links between rigid clusters are identified and can be modeled as such subsequently. In the second step, dynamical properties of the molecule are revealed by the rotations-translations of blocks approach (RTB) using an elastic network model representation of the coarse-grained protein. In this step, only rigid body motions are allowed for rigid clusters, whereas links between them are treated as fully flexible. The approach was tested on a data set of 10 proteins that showed conformational changes on ligand binding. For efficiency, coarse-graining the protein results in a remarkable reduction of memory requirements and computational times by factors of 9 and 27 on average and up to 25 and 125, respectively. For accuracy, directions and magnitudes of motions predicted by our approach agree well with experimentally determined ones, despite embracing in extreme cases >50% of the protein into one rigid cluster. In fact, the results of our method are in general comparable with when no or a uniform coarse-graining is applied; and the results are superior if the movement is dominated by loop or fragment motions. This finding indicates that explicitly distinguishing between flexible and rigid regions is advantageous when using a simplified protein representation in the second step. Finally, motions of atoms in rigid clusters are also well predicted by our approach, which points to the need to consider mobile protein regions in addition to flexible ones when modeling correlated motions.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Multiscale simulations of heterogeneous model membranes

This review will focus on computer modeling aimed at providing insights into the existence, structure, size, and thermodynamic stability of localized domains in membranes of heterogeneous composition. Modeling the lateral organization within a membrane is problematic due to the relatively slow lateral diffusion rate for lipid molecules so that microsecond or longer time scales are needed to fully model the formation and stability of a raft in a membrane. Although atomistic simulations currently are not able to reach this scale, they can provide data on the intermolecular forces and correlations that are involved in lateral organization. These data can be used to define coarse grained models that are capable of predictions of lateral organization in membranes. In this paper, we review modeling efforts that use interaction data from MD simulations to construct coarse grained models for heterogeneous bilayers. In this review we will discuss MD simulations done with the aim of gaining the information needed to build accurate coarse-grained models. We will then review some of the coarse-graining work, emphasizing modeling that has resulted from or has a basis in atomistic simulations.     

Efficient electrostatic solvation model for protein-fragment docking

A method is presented for the fast evaluation of the binding energy of a protein-small molecule complex with electrostatic solvation. It makes use of a fast preprocessing step based on the assumption that the main contribution to electrostatic desolvation upon ligand binding originates from the displacement of the first shell of water molecules. For a rigid protein, the precomputation of the energy contributions on a set of grids allows the estimation of the energy in solution of about 300 protein-fragment binding modes per second on a personal computer. The docking procedure is applied to five rigid binding sites whose size ranges from 17 residues to a whole protein of 107 amino acids. Using a library of 70 mainly rigid molecules, known micromolar inhibitors or close analogs are docked and prioritized correctly. The docking based rank-ordering of the library requires about 5 h and is proposed as a complementary approach to structure-activity relationships by nuclear magnetic resonance. Proteins 2001;42:256-268.     

Improving ranking of models for protein complexes with side chain modeling and atomic potentials

An atomically detailed potential for docking pairs of proteins is derived using mathematical programming. A refinement algorithm that builds atomically detailed models of the complex and combines coarse grained and atomic scoring is introduced. The refinement step consists of remodeling the interface side chains of the top scoring decoys from rigid docking followed by a short energy minimization. The refined models are then re‐ranked using a combination of coarse grained and atomic potentials. The docking algorithm including the refinement and re‐ranking, is compared favorably to other leading docking packages like ZDOCK, Cluspro, and PATCHDOCK, on the ZLAB 3.0 Benchmark and a test set of 30 novel complexes. A detailed analysis shows that coarse grained potentials perform better than atomic potentials for realistic unbound docking (where the exact structures of the individual bound proteins are unknown), probably because atomic potentials are more sensitive to local errors. Nevertheless, the atomic potential captures a different signal from the residue potential and as a result a combination of the two scores provides a significantly better prediction than each of the approaches alone. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

On the optimality of coarse behavior rules

Animal behavior can be characterized by the degree of responsiveness it has to variations in the environment. Some behavior rules lead to fine-tuned responses that carefully adjust to environmental cues, while other rules fail to discriminate as carefully, and lead to more inflexible responses. In this paper we seek to explain such inflexible behavior. We show that coarse behavior, behavior which appears to be rule-bound and inflexible, and which fails to adapt to predictable changes in the environment, is an optimal response to a particular type of uncertainty we call extended uncertainty. We show that the very variability and unpredictability that arises from extended uncertainty will lead to more rigid and possibly more predictable behavior. We relate coarse behavior to the failures to meet optimality conditions in animal behavior, most notably in foraging behavior, and also address the implications of extended uncertainty and coarse behavior rules for some results in experimental versus naturalistic approaches to ethology.     

Actin: From Cell Biology to Atomic Detail

Over the past 2 decades our knowledge about actin filaments has evolved from a rigid “pearls on a string” model to that of a complex, highly dynamic protein polymer which can now be analyzed at atomic detail. To achieve this, exploring actin's oligomerization, polymerization, polymorphism, and dynamic behavior has been crucial to understanding in detail how this abundant and ubiquitous protein can fulfill its various functions within living cells. In this review, a correlative view of a number of distinct aspects of actin is presented, and the functional implications of recent structural, biochemical, and mechanical data are critically evaluated. Rational analysis of these various experimental data is achieved using an integrated structural approach which combines intermediate-resolution electron microscopy-based 3-D reconstructions of entire actin filaments with atomic resolution X-ray data of monomeric and polymeric actin.     

Local rigidity of a protein molecule

Distribution of soft and rigid substructures within a protein molecule has been implicated in several occasions and most recently from the imaging and indentation experiments using an atomic force microscope. In this paper, previously reported result of mechanical extension experiments on the recombinant bovine carbonic anhydrase II, Q253C, is re-analyzed to estimate the distribution of Young's modulus, Y, in this protein. The force vs. extension curve of the enzymatically active, type I conformer gave an estimate of Y increasing from 40 to 220 MPa as the polypeptide chain was extended from 10 to 75 nm indicating the presence of a rigid core structure. The enzymatically inactive type II, in contrast, gave an almost constant modulus of 55+/-15 MPa in the same extension range in agreement with the previous proposal that it lacked a core structure.     

Sodium as nutrient and toxicant

Background and Scope

Because of the crucial role coarse roots (>2 mm diameter) play in plant functions and terrestrial ecosystems, detecting and quantifying the size, architecture, and biomass of coarse roots are important. Traditional excavation methods are labor intensive and destructive, with limited quantification and repeatability of measurements over time. As a nondestructive geophysical tool for delineating buried features in shallow subsurface, ground penetrating radar (GPR) has been applied for coarse root detection since 1999. This article reviews the state-of-knowledge of coarse root detection and quantification using GPR, and discusses its potentials, constraints, possible solutions, and future outlooks. Some useful suggestions are provided that can guide future studies in this field.

Conclusions

The feasibility and accuracy of coarse root investigation by GPR have been tested in various site conditions (mostly in controlled conditions or within plantations) and for different plant species (mostly tree root systems). Thus far, single coarse root identification and coarse root system mapping have been conducted using GPR, including roots under pavements in urban environment. Coarse root diameter and biomass have been estimated from indexes extracted from root GPR radargrams. Coarse root development can be observed by repeated GPR scanning over time. Successful GPR-based coarse root investigation is site specific, and only under suitable conditions can reliable measurements be accomplished. The best quality of root detection by GPR is achieved in well-drained and electrically-resistive soils (such as sands) under dry conditions. Numerous factors such as local soil conditions, root electromagnetic properties, and GPR antenna frequency can impact the reliability and accuracy of GPR detection and quantification of coarse roots. As GPR design, data processing software, field data collection protocols, and root parameters estimation methods are continuously improved, this noninvasive technique could offer greater potential to study coarse roots.     

A novel unstructured scaffold based on 4EBP1 enables the functional display of a wide range of bioactive peptides

Target validation using protein aptamers enables the characterization of a specific function of a target protein in an environment that resembles native conditions as closely as possible. A major obstacle to the use of this technology has been the generation of bioactive aptamers, which is dependent on the choice of scaffold. Constraining binding peptides within a particular scaffold does not necessarily result in binding aptamers, as suboptimal presentation of peptides can occur. It is therefore understandable that different peptides might require different scaffolds for optimal presentation. In this article, we describe a novel scaffold protein that bypasses the conventional requirement for scaffolds to have known rigid structures and yet successfully presents several peptides that need to adopt a wide range of conformations for binding to their target protein. Using an unstructured protein, 4EBP1, as scaffold, we successfully construct binding aptamers to three different target proteins: Mdm2, proliferating cell nuclear antigen, and cyclin A. The Mdm2-binding aptamer constructed using 4EBP1 as scaffold demonstrates better stability and bioactivity compared to that constructed using thioredoxin as scaffold. This new scaffold protein, which makes it relatively easy to create bioactive aptamers based on known interaction sequences, will greatly facilitate the aptamer approach to target validation.     

A large scale test of computational protein design: folding and stability of nine completely redesigned globular proteins

A previously developed computer program for protein design, RosettaDesign, was used to predict low free energy sequences for nine naturally occurring protein backbones. RosettaDesign had no knowledge of the naturally occurring sequences and on average 65% of the residues in the designed sequences differ from wild-type. Synthetic genes for ten completely redesigned proteins were generated, and the proteins were expressed, purified, and then characterized using circular dichroism, chemical and temperature denaturation and NMR experiments. Although high-resolution structures have not yet been determined, eight of these proteins appear to be folded and their circular dichroism spectra are similar to those of their wild-type counterparts. Six of the proteins have stabilities equal to or up to 7kcal/mol greater than their wild-type counterparts, and four of the proteins have NMR spectra consistent with a well-packed, rigid structure. These encouraging results indicate that the computational protein design methods can, with significant reliability, identify amino acid sequences compatible with a target protein backbone.