Concepts and schemes for the re-engineering of physical protein modules: generating nanodevices via targeted replacements with constrained amino acids

Physically building complex multi-molecular structures from naturally occurring biological macromolecules has aroused a great deal of interest. Here we focus on nanostructures composed of re-engineered, natural 'foldamer' building blocks. Our aim is to provide some of the underlying concepts and schemes for crafting structures utilizing such conformationally relatively stable molecular components. We describe how, via chemical biology strategies, it is further possible to chemically manipulate the foldamer building blocks toward specific shape-driven structures, which in turn could be used toward potential-designed functions. We outline the criteria in choosing candidate foldamers from the vast biological repertoire, and how to enhance their stability through selected targeted replacements by non-proteinogenic conformationally constrained amino acids. These approaches combine bioinformatics, high performance computations and mathematics with synthetic organic chemistry. The resulting artificially engineered self-organizing molecular scale structures take advantage of nature's nanobiology toolkit and at the same time improve on it, since their new targeted function differs from that optimized by evolution. The major challenge facing nanobiology is to be able to exercise fine control over the performance of these target-specific molecular machines.     

Modeling the Structure of RNA Molecules with Small-Angle X-Ray Scattering Data

We propose a novel fragment assembly method for low-resolution modeling of RNA and show how it may be used along with small-angle X-ray solution scattering (SAXS) data to model low-resolution structures of particles having as many as 12 independent secondary structure elements. We assessed this model-building procedure by using both artificial data on a previously proposed benchmark and publicly available data. With the artificial data, SAXS-guided models show better similarity to native structures than ROSETTA decoys. The publicly available data showed that SAXS-guided models can be used to reinterpret RNA structures previously deposited in the Protein Data Bank. Our approach allows for fast and efficient building of de novo models of RNA using approximate secondary structures that can be readily obtained from existing bioinformatic approaches. We also offer a rigorous assessment of the resolving power of SAXS in the case of small RNA structures, along with a small multimetric benchmark of the proposed method.     

Protecting buildings against feral pigeons

Feral pigeons (Columba livia, Gmelin 1789) cause different problems for building owners when using structures for daytime perching, sleeping, and breeding. Problems include fouling of building facades and pavements, transmission of allergens and pathogenic microorganisms, and infestations with ectoparasites emanating from breeding sites. Owners are primarily interested in keeping away unwanted pigeons from their property. Pest control companies offer different deterrent systems, of widely varying efficacy, for proofing buildings against feral pigeons. A better solution is avoiding attractive structures during building design or subsequent alterations of existing structures used by feral pigeons. With our study, we elaborate the relevant structural data to help to maintain a building free of pigeons. We performed experiments with free ranging feral pigeons in a feral pigeon loft in the City of Basel, Switzerland. The maximum outlet width a pigeon is not able to pass through is 4 cm; the respective outlet height is 5 cm and a pigeon-safe square opening is not larger than 6 × 6 cm. The maximum ledge width a pigeon is not able to sit on is 4 cm. The pigeon-safe angle of inclination for smooth construction materials (tinplate, glass, plastics) is 25°, for medium rough materials (wood, plane concrete) 35°, and for rough materials (sandstone, rough concrete) at least 50°. Additionally, we studied the behavioral strategies used by feral pigeons to surmount our experimental constructional restrictions, ledge width, and ledge inclinations. Our data provide the essential data to prevent feral pigeons from using building structures.     

Some fundamental aspects of building protein structures from fragment libraries

We have investigated some of the basic principles that influence generation of protein structures using a fragment-based, random insertion method. We tested buildup methods and fragment library quality for accuracy in constructing a set of known structures. The parameters most influential in the construction procedure are bond and torsion angles with minor inaccuracies in bond angles alone causing >6 A CalphaRMSD for a 150-residue protein. Idealization to a standard set of values corrects this problem, but changes the torsion angles and does not work for every structure. Alternatively, we found using Cartesian coordinates instead of torsion angles did not reduce performance and can potentially increase speed and accuracy. Under conditions simulating ab initio structure prediction, fragment library quality can be suboptimal and still produce near-native structures. Using various clustering criteria, we created a number of libraries and used them to predict a set of native structures based on nonnative fragments. Local CalphaRMSD fit of fragments, library size, and takeoff/landing angle criteria weakly influence the accuracy of the models. Based on a fragment's minimal perturbation upon insertion into a known structure, a seminative fragment library was created that produced more accurate structures with fragments that were less similar to native fragments than the other sets. These results suggest that fragments need only contain native-like subsections, which when correctly overlapped, can recreate a native-like model. For fragment-based, random insertion methods used in protein structure prediction and design, our findings help to define the parameters this method needs to generate near-native structures.     

Modeling large RNAs and ribonucleoprotein particles using molecular mechanics techniques.

There is a growing body of low-resolution structural data that can be utilized to devise structural models for large RNAs and ribonucleoproteins. These models are routinely built manually. We introduce an automated refinement protocol to utilize such data for building low-resolution three-dimensional models using the tools of molecular mechanics. In addition to specifying the positions of each nucleotide, the protocol provides quantitative estimates of the uncertainties in those positions, i.e., the resolution of the model. In typical applications, the resolution of the models is about 10-20 A. Our method uses reduced representations and allows us to refine three-dimensional structures of systems as big as the 16S and 23S ribosomal RNAs, which are about one to two orders of magnitude larger than nucleic acids that can be examined by traditional all-atom modeling methods. Nonatomic resolution structural data--secondary structure, chemical cross-links, chemical and enzymatic footprinting patterns, protein positions, solvent accessibility, and so on--are combined with known motifs in RNA structure to predict low-resolution models of large RNAs. These structural constraints are imposed on the RNA chain using molecular mechanics-type potential functions with parameters based on the quality of experimental data. Surface potential functions are used to incorporate shape and positional data from electron microscopy image reconstruction experiments into our models. The structures are optimized using techniques of energy refinement to get RNA folding patterns. In addition to providing a consensus model, the method finds the range of models consistent with the data, which allows quantitative evaluation of the resolution of the model. The method also identifies conflicts in the experimental data. Although our protocol is aimed at much larger RNAs, we illustrate these techniques using the tRNA structure as an example and test-bed.     

The Quaternary Arrangement of HslU and HslV in a Cocrystal: A Response to Wang, Yale

Protease HslV and ATPase HslU form an ATP-dependent protease in bacteria. We have previously determined the structure of the components of this protease. In the case of HslU, the structure was derived from HslU-HslV cocrystals, combining phase information from MAD and the previously determined HslV model. Whereas the structures of the components were confirmed in detail by later structures, the quaternary arrangement of HslV and HslU was not reproduced in later crystal forms. In a recent communication to this journal, Wang attempted a reinterpretation of our original data to account for this difference. In response, we demonstrate that difference Pattersons, difference Fouriers, molecular replacement calculations, R factors, and omit maps all support our original analysis and prove that the suggested reinterpretation is false by these criteria. In particular, we show that our crystals are essentially untwinned and that only the originally reported quaternary arrangement of HslV and HslU particles is consistent with the experimental data. We finally demonstrate that Wang's newly introduced R(tpart) method to predict translational corrections for a subset of the unit cell contents is systematically flawed.     

Empirical‐likelihood‐based criteria for model selection on marginal analysis of longitudinal data with dropout missingness

Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating equation (WGEE) approach is widely adopted for marginal analysis. Model selection on marginal mean regression is a crucial aspect of data analysis, and identifying an appropriate correlation structure for model fitting may also be of interest and importance. However, the existing information criteria for model selection in WGEE have limitations, such as separate criteria for the selection of marginal mean and correlation structures, unsatisfactory selection performance in small‐sample setups, and so forth. In particular, there are few studies to develop joint information criteria for selection of both marginal mean and correlation structures. In this work, by embedding empirical likelihood into the WGEE framework, we propose two innovative information criteria named a joint empirical Akaike information criterion and a joint empirical Bayesian information criterion, which can simultaneously select the variables for marginal mean regression and also correlation structure. Through extensive simulation studies, these empirical‐likelihood‐based criteria exhibit robustness, flexibility, and outperformance compared to the other criteria including the weighted quasi‐likelihood under the independence model criterion, the missing longitudinal information criterion, and the joint longitudinal information criterion. In addition, we provide a theoretical justification of our proposed criteria, and present two real data examples in practice for further illustration.     

Protein family classification using sparse markov transducers.

We present a method for classifying proteins into families based on short subsequences of amino acids using a new probabilistic model called sparse Markov transducers (SMT). We classify a protein by estimating probability distributions over subsequences of amino acids from the protein. Sparse Markov transducers, similar to probabilistic suffix trees, estimate a probability distribution conditioned on an input sequence. SMTs generalize probabilistic suffix trees by allowing for wild-cards in the conditioning sequences. Since substitutions of amino acids are common in protein families, incorporating wild-cards into the model significantly improves classification performance. We present two models for building protein family classifiers using SMTs. As protein databases become larger, data driven learning algorithms for probabilistic models such as SMTs will require vast amounts of memory. We therefore describe and use efficient data structures to improve the memory usage of SMTs. We evaluate SMTs by building protein family classifiers using the Pfam and SCOP databases and compare our results to previously published results and state-of-the-art protein homology detection methods. SMTs outperform previous probabilistic suffix tree methods and under certain conditions perform comparably to state-of-the-art protein homology methods.     

Membrane transport through α-heltical bundles. IV. Preliminary model building investigation of helix-helix interactions

Previously we made order of magnitude estimates that suggested the possibility of forming proton wires between facing α-helices joined by knobs-into-holes packing (Dunker, Marvin, Zaleske & Jones, 1976; Dunker & Marvin, 1978). Such structures may be a feature of membrane proteins. Since our original work, another type of packing, called ridges-into-grooves, has been identified as a way of meshing adjoining α-helices. Using precision (CPK) molecular models, we have investigated the possibility of forming proton wires: (1) in order to improve on our previous order of magnitude estimates, and (2) in order to evaluate the different kinds of packing interfaces for their ability to support stereochemically feasible proton wires.We found knobs-into-holes and ridges-into=grooves packing to support exactly the same proton wires. The positions of the side chains are determined more by the geometry of the hydrogen-bonding network rather than by the type of packing originally used to locate the appropriate residues. Thus, we suggest that a new name is needed for such packing, which we propose to call “H-bond packing”.In our earlier investigations we arbitrarily restricted our attention to proton wires parallel to the packing interface. By lifting this restriction, we found it possible to construct many additional types of wires. The model building exercises suggested that both parallel-to-the-interface and non-parallel-to-the-interface wires are feasible, except that the non-parallel wires are restricted in length depending on the angle with the interface, whereas the parallel wires apparently can be continued indefinitely. The various types of wires share local hydrogen bonding patterns and so could easily connect together.In our model building of several representative wires, we investigated the limitations with regard to type of and combinations of side chains. We also determined possible variations in the origins of such side chains on the helical backbones.These preliminary model building studies provide the basis for determining possible hydrogen bonding between the helical segments of membrane proteins. From these data we are formulating preliminary proposals for the helix-helix interactions of the bacteriorhodopsin molecule, which are to be presented in future paper.     

Designing a nanotube using naturally occurring protein building blocks

Here our goal is to carry out nanotube design using naturally occurring protein building blocks. Inspection of the protein structural database reveals the richness of the conformations of proteins, their parts, and their chemistry. Given target functional protein nanotube geometry, our strategy involves scanning a library of candidate building blocks, combinatorially assembling them into the shape and testing its stability. Since self-assembly takes place on time scales not affordable for computations, here we propose a strategy for the very first step in protein nanotube design: we map the candidate building blocks onto a planar sheet and wrap the sheet around a cylinder with the target dimensions. We provide examples of three nanotubes, two peptide and one protein, in atomistic model detail for which there are experimental data. The nanotube models can be used to verify a nanostructure observed by low-resolution experiments, and to study the mechanism of tube formation.     

Learning MHC I--peptide binding

MOTIVATION AND RESULTS: Motivated by the ability of a simple threading approach to predict MHC I--peptide binding, we developed a new and improved structure-based model for which parameters can be estimated from additional sources of data about MHC-peptide binding. In addition to the known 3D structures of a small number of MHC-peptide complexes that were used in the original threading approach, we included three other sources of information on peptide-MHC binding: (1) MHC class I sequences; (2) known binding energies for a large number of MHC-peptide complexes; and (3) an even larger binary dataset that contains information about strong binders (epitopes) and non-binders (peptides that have a low affinity for a particular MHC molecule). Our model significantly outperforms the standard threading approach in binding energy prediction. In our approach, which we call adaptive double threading, the parameters of the threading model are learnable, and both MHC and peptide sequences can be threaded onto structures of other alleles. These two properties make our model appropriate for predicting binding for alleles for which very little data (if any) is available beyond just their sequence, including prediction for alleles for which 3D structures are not available. The ability of our model to generalize beyond the MHC types for which training data is available also separates our approach from epitope prediction methods which treat MHC alleles as symbolic types, rather than biological sequences. We used the trained binding energy predictor to study viral infections in 246 HIV patients from the West Australian cohort, and over 1000 sequences in HIV clade B from Los Alamos National Laboratory database, capturing the course of HIV evolution over the last 20 years. Finally, we illustrate short-, medium-, and long-term adaptation of HIV to the human immune system. AVAILABILITY: http://www.research.microsoft.com/~jojic/hlaBinding.html.     

Using surface envelopes for discrimination of molecular models

Shape information about macromolecules is increasingly available but is difficult to use in modeling efforts. We demonstrate that shape information alone can often distinguish structural models of biological macromolecules. By using a data structure called a surface envelope (SE) to represent the shape of the molecule, we propose a method that generates a fitness score for the shape of a particular molecular model. This score correlates well with root mean squared deviation (RMSD) of the model to the known test structures and can be used to filter models in decoy sets. The scoring method requires both alignment of the model to the SE in three-dimensional space and assessment of the degree to which atoms in the model fill the SE. Alignment combines a hybrid algorithm using principal components and a previously published iterated closest point algorithm. We test our method against models generated from random atom perturbation from crystal structures, published decoy sets used in structure prediction, and models created from the trajectories of atoms in molecular modeling runs. We also test our alignment algorithm against experimental electron microscopic data from rice dwarf virus. The alignment performance is reliable, and we show a high correlation between model RMSD and score function. This correlation is stronger for molecular models with greater oblong character (as measured by the ratio of largest to smallest principal component).     

Analysis of the free energy in a stochastic RNA secondary structure model

There are two custom ways for predicting RNA secondary structures: minimizing the free energy of a conformation according to a thermodynamic model and maximizing the probability of a folding according to a stochastic model. In most cases, stochastic grammars are used for the latter alternative applying the maximum likelihood principle for determining a grammar's probabilities. In this paper, building on such a stochastic model, we will analyze the expected minimum free energy of an RNA molecule according to Turner's energy rules. Even if the parameters of our grammar are chosen with respect to structural properties of native molecules only (and therefore, independent of molecules' free energy), we prove formulae for the expected minimum free energy and the corresponding variance as functions of the molecule's size which perfectly fit the native behavior of free energies. This gives proof for a high quality of our stochastic model making it a handy tool for further investigations. In fact, the stochastic model for RNA secondary structures presented in this work has, for example, been used as the basis of a new algorithm for the (nonuniform) generation of random RNA secondary structures.     

A cell-based framework for modeling cardiac mechanics

Cardiomyocytes are the functional building blocks of the heart—yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell–cell and cell–matrix interactions.

     

Models of the structure and voltage-gating mechanism of the shaker K+ channel

In the preceding, accompanying article, we present models of the structure and voltage-dependent gating mechanism of the KvAP bacterial K+ channel that are based on three types of evidence: crystal structures of portions of the KvAP protein, theoretical modeling criteria for membrane proteins, and biophysical studies of the properties of native and mutated voltage-gated channels. Most of the latter experiments were performed on the Shaker K+ channel. Some of these data are difficult to relate directly to models of the KvAP channel's structure due to differences in the Shaker and KvAP sequences. We have dealt with this problem by developing new models of the structure and gating mechanism of the transmembrane and extracellular portions of the Shaker channel. These models are consistent with almost all of the biophysical data. In contrast, much of the experimental data are incompatible with the "paddle" model of gating that was proposed when the KvAP crystal structures were first published. The general folding pattern and gating mechanisms of our current models are similar to some of our earlier models of the Shaker channel.     

Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models.