Combinatorics of Contacts in Protein Contact Maps

Contacts play a fundamental role in the study of protein structure and folding problems. The contact map of a protein can be represented by arranging its amino acids on a horizontal line and drawing an arc between two residues if they form a contact. In this paper, we are mainly concerned with the combinatorial enumeration of the arcs in m-regular linear stack, an elementary structure of the protein contact map, which was introduced by Chen et al. (J Comput Biol 21(12):915–935, 2014). We modify the generating function for m-regular linear stacks by introducing a new variable y regarding to the number of arcs and obtain an equation satisfied by the generating function for m-regular linear stacks with n vertices and k arcs. Consequently, we also derive an equation satisfied by the generating function of the overall number of arcs in m-regular linear stacks with n vertices.     

Topology fingerprint approach to the inverse protein folding problem.

We describe the most general solution to date of the problem of matching globular protein sequences to the appropriate three-dimensional structures. The screening template, against which sequences are tested, is provided by a protein "structural fingerprint" library based on the contact map and the buried/exposed pattern of residues. Then, a lattice Monte Carlo algorithm validates or dismisses the stability of the proposed fold. Examples of known structural similarities between proteins having weakly or unrelated sequences such as the globins and phycocyanins, the eight-member alpha/beta fold of triose phosphate isomerase and even a close structural equivalence between azurin and immunoglobulins are found.     

Asymptotics of RNA shapes.

RNA shapes, introduced by Giegerich et al. (2004), provide a useful classification of the branching complexity for RNA secondary structures. In this paper, we derive an exact value for the asymptotic number of RNA shapes, by relying on an elegant relation between non-ambiguous, context-free grammars, and generating functions. Our results provide a theoretical upper bound on the length of RNA sequences amenable to probabilistic shape analysis (Steffen et al., 2006; Voss et al., 2006), under the assumption that any base can basepair with any other base. Since the relation between context-free grammars and asymptotic enumeration is simple, yet not well-known in bioinformatics, we give a self-contained presentation with illustrative examples. Additionally, we prove a surprising 1-to-1 correspondence between pi-shapes and Motzkin numbers.     

Topological classification and enumeration of RNA structures by genus

To an RNA pseudoknot structure is naturally associated a topological surface, which has its associated genus, and structures can thus be classified by the genus. Based on earlier work of Harer–Zagier, we compute the generating function $\mathbf{D}_{g,\sigma }(z)=\sum _{n}\mathbf{d}_{g,\sigma }(n)z^n$ for the number $\mathbf{d}_{g,\sigma }(n)$ of those structures of fixed genus $g$ and minimum stack size $\sigma $ with $n$ nucleotides so that no two consecutive nucleotides are basepaired and show that $\mathbf{D}_{g,\sigma }(z)$ is algebraic. In particular, we prove that $\mathbf{d}_{g,2}(n)\sim k_g\,n^{3(g-\frac{1}{2})} \gamma _2^n$ , where $\gamma _2\approx 1.9685$ . Thus, for stack size at least two, the genus only enters through the sub-exponential factor, and the slow growth rate compared to the number of RNA molecules implies the existence of neutral networks of distinct molecules with the same structure of any genus. Certain RNA structures called shapes are shown to be in natural one-to-one correspondence with the cells in the Penner–Strebel decomposition of Riemann’s moduli space of a surface of genus $g$ with one boundary component, thus providing a link between RNA enumerative problems and the geometry of Riemann’s moduli space.     

“It Ain’t Over ‘til it’s Over”: Rethinking the Darwinian Revolution

This paper attempts a critical examination of scholarly understanding of the historical event referred to as the Darwinian Revolution. In particular, it concentrates on some of the major scholarly works that have appeared since the publication in 1979 of Michael Ruses The Darwinian Revolution: Nature Red in Tooth and Claw. The paper closes by arguing that fruitful critical perspectives on what counts as this event can be gained by locating it in a range of historiographic and disciplinary contexts that include the emergence of the discipline of evolutionary biology (following the evolutionary synthesis), the 1959 Darwin centenary, and the maturation of the discipline of the history of science. Broader perspectives on something called the Darwinian Revolution are called for that include recognizing that it does not map a one-to-one correspondence with the history of evolution, broadly construed.     

Evolution and similarity evaluation of protein structures in contact map space

Prediction of fold from amino acid sequence of a protein has been an active area of research in the past few years, but the limited accuracy of existing techniques emphasizes the need to develop newer approaches to tackle this task. In this study, we use contact map prediction as an intermediate step in fold prediction from sequence. Contact map is a reduced graph-theoretic representation of proteins that models the local and global inter-residue contacts in the structure. We start with a population of random contact maps for the protein sequence and "evolve" the population to a "high-feasibility" configuration using a genetic algorithm. A neural network is employed to assess the feasibility of contact maps based on their 4 physically relevant properties. We also introduce 5 parameters, based on algebraic graph theory and physical considerations, that can be used to judge the structural similarity between proteins through contact maps. To predict the fold of a given amino acid sequence, we predict a contact map that will sufficiently approximate the structure of the corresponding protein. Then we assess the similarity of this contact map with the representative contact map of each fold; the fold that corresponds to the closest match is our predicted fold for the input sequence. We have found that our feasibility measure is able to differentiate between feasible and infeasible contact maps. Further, this novel approach is able to predict the folds from sequences significantly better than a random predictor.     

A new Motzkin class for joint RNA secondary structures

In general RNA prediction problem includes genetic mapping, physical mapping and structure prediction. The ultimate goal of structure prediction is to obtain the three dimensional structure of bimolecules through computation. The key concept for solving the above mentioned problem is the appropriate representation of the biological structures. Even though, the problems that concern representations of certain biological structures like secondary structures either are characterized as NP-complete or with high complexity, few approximation algorithms and techniques had been constructed, mainly with polynomial complexity, concerning the prediction of RNA secondary structures. In this paper, a new class of Motzkin paths is introduced, the so-called semi-elevated inverse Motzkin peakless paths for the representation of two interacting RNA molecules. The basic combinatorial interpretations on single RNA secondary structures are extended via these new Motzkin paths on two RNA molecules and can be applied to the prediction methods of joint structures formed by interacting RNAs.     

Simple and Direct Assembly of Kymographs from Movies Using KYMOMAKER

In tracking analysis, the movement of cargos by motor proteins in axons is often represented by a time‐space plot termed a ‘kymograph’. Manual creation of kymographs is time‐consuming and complicated for cell biologists. Therefore, we developed KYMOMAKER, a simple system that automatically creates a kymograph from a movie without generating multiple time‐dissected movie stacks. In addition, KYMOMAKER can automatically extract faint vesicle traces, and can thereby effectively analyze cargos expressed at low levels in axons. A filter can be applied to remove traces of non‐physiological movements and to extract meaningful traces of anterograde or retrograde cargo transport. For example, only cargos that move at a speed of >0.4 µm/second for a distance of >1 µm can be included. Another function of KYMOMAKER is to create a color kymograph in which the color of the trace varies according to the position of the fluorescent particle in the axis perpendicular to the long axis of the axon. Such positional information is completely lost in conventional kymographs. KYMOMAKER is an open access program that can be easily used to analyze vesicle transport in axons by cell biologists who do not have specific knowledge of bioimage informatics .      

An effective sequence-alignment-free superpositioning of pairwise or multiple structures with missing data

Background

Superpositioning is an important problem in structural biology. Determining an optimal superposition requires a one-to-one correspondence between the atoms of two proteins structures. However, in practice, some atoms are missing from their original structures. Current superposition implementations address the missing data crudely by ignoring such atoms from their structures.

Results

In this paper, we propose an effective method for superpositioning pairwise and multiple structures without sequence alignment. It is a two-stage procedure including data reduction and data registration.

Conclusions

Numerical experiments demonstrated that our method is effective and efficient. The code package of protein structure superposition method for addressing the cases with missing data is implemented by MATLAB, and it is freely available from: http://sourceforge.net/projects/pssm123/files/?source=navbar

     

Testing Pairwise Association between Spatially Autocorrelated Variables: A New Approach Using Surrogate Lattice Data

Background

Independence between observations is a standard prerequisite of traditional statistical tests of association. This condition is, however, violated when autocorrelation is present within the data. In the case of variables that are regularly sampled in space (i.e. lattice data or images), such as those provided by remote-sensing or geographical databases, this problem is particularly acute. Because analytic derivation of the null probability distribution of the test statistic (e.g. Pearson''s r) is not always possible when autocorrelation is present, we propose instead the use of a Monte Carlo simulation with surrogate data.

Methodology/Principal Findings

The null hypothesis that two observed mapped variables are the result of independent pattern generating processes is tested here by generating sets of random image data while preserving the autocorrelation function of the original images. Surrogates are generated by matching the dual-tree complex wavelet spectra (and hence the autocorrelation functions) of white noise images with the spectra of the original images. The generated images can then be used to build the probability distribution function of any statistic of association under the null hypothesis. We demonstrate the validity of a statistical test of association based on these surrogates with both actual and synthetic data and compare it with a corrected parametric test and three existing methods that generate surrogates (randomization, random rotations and shifts, and iterative amplitude adjusted Fourier transform). Type I error control was excellent, even with strong and long-range autocorrelation, which is not the case for alternative methods.

Conclusions/Significance

The wavelet-based surrogates are particularly appropriate in cases where autocorrelation appears at all scales or is direction-dependent (anisotropy). We explore the potential of the method for association tests involving a lattice of binary data and discuss its potential for validation of species distribution models. An implementation of the method in Java for the generation of wavelet-based surrogates is available online as supporting material.     

Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics-inspired method

Background

Many proteins tune their biological function by transitioning between different functional states, effectively acting as dynamic molecular machines. Detailed structural characterization of transition trajectories is central to understanding the relationship between protein dynamics and function. Computational approaches that build on the Molecular Dynamics framework are in principle able to model transition trajectories at great detail but also at considerable computational cost. Methods that delay consideration of dynamics and focus instead on elucidating energetically-credible conformational paths connecting two functionally-relevant structures provide a complementary approach. Effective sampling-based path planning methods originating in robotics have been recently proposed to produce conformational paths. These methods largely model short peptides or address large proteins by simplifying conformational space.

Methods

We propose a robotics-inspired method that connects two given structures of a protein by sampling conformational paths. The method focuses on small- to medium-size proteins, efficiently modeling structural deformations through the use of the molecular fragment replacement technique. In particular, the method grows a tree in conformational space rooted at the start structure, steering the tree to a goal region defined around the goal structure. We investigate various bias schemes over a progress coordinate for balance between coverage of conformational space and progress towards the goal. A geometric projection layer promotes path diversity. A reactive temperature scheme allows sampling of rare paths that cross energy barriers.

Results and conclusions

Experiments are conducted on small- to medium-size proteins of length up to 214 amino acids and with multiple known functionally-relevant states, some of which are more than 13Å apart of each-other. Analysis reveals that the method effectively obtains conformational paths connecting structural states that are significantly different. A detailed analysis on the depth and breadth of the tree suggests that a soft global bias over the progress coordinate enhances sampling and results in higher path diversity. The explicit geometric projection layer that biases the exploration away from over-sampled regions further increases coverage, often improving proximity to the goal by forcing the exploration to find new paths. The reactive temperature scheme is shown effective in increasing path diversity, particularly in difficult structural transitions with known high-energy barriers.

     

Characterization and application of porous gold nanoparticles as 2‐photon luminescence imaging agents: 20‐fold brighter than gold nanorods

Two‐photon nonlinear microscopy with the aid of plasmonic contrast agents is an attractive bioimaging technique capable of generating high‐resolution images in 3 dimensions and facilitating targeted imaging with deep tissue penetration. In this work, physically synthesized gold nanoparticles containing multiple nanopores are used as 2‐photon contrast agents and are reported to emit a 20‐fold brighter 2‐photon luminescence as compared to typical contrast agents, that is, gold nanorods. A successful application of our porous gold nanoparticles is experimentally demonstrated by in vitro nonlinear optical imaging of adipocytes at subcellular level.      

The formation and development of cellulose-synthesizing linear terminal complexes (TCs) in the plasma membrane of the marine red algaErythrocladia subintegra Rosenv.

Summary The formation and development of linear terminal complexes (TCs), the putative cellulose synthesizing units of the red algaErythrocladia subintegra Rosenv., were investigated by a freeze etching technique using both rotary and unidirectional shadowing. The ribbon-like cellulose fibrils ofE. subintegra are 27.6 ± 0.8 nm wide and only 1–1.5 nm thick. They are synthesized by TCs which are composed of repeating transverse rows formed of four particles, the TC subunits. About 50.4 ± 1.7 subunits constitute a TC. They are apparently more strongly interconnected in transverse than in longitudinal directions. Some TC subunits can be resolved as doublets by Fourier analysis. Large globular particles (globules) seem to function as precursor units in the assembly and maturation of the TCs. They are composed of a central hole (the core) with small subunits forming a peripheral ridge and seem to represent zymogenic precursors. TC assembly is initiated after two or three gobules come into close contact with each other, swell and unfold to a nucleation unit resembling the first 2–3 transverse rows of a TC. Longitudinal elongation of the TC occurs by the unfolding of globules attached to both ends of the TC nucleation unit until the TC is completed. The typical intramembranous particles observed inErythrocladia (unidirectional shadowing) are 9.15 ± 0.13 nm in diameter, whereas those of a TC have an average diameter of 8.77 ± 0.11 nm. During cell wall synthesis membranes of vesicles originating from the Golgi apparatus and which seem to fuse with the plasma membrane contain large globules, 15–22 nm in diameter, as well as tetrads with a particle diameter of about 8 nm. The latter are assumed to be involved in the synthesis of the amorphous extracellular matrix cell wall polysaccharides. The following working model for cellulose fibril assembly inE. subintegra is suggested: (1) the ribbon-like cellulose fibril is synthesized by a single linear TC; (2) the number of glucan chains per microfibril correlates with the number of TC subunits; (3) a single subunit synthesizes 3 glucan chains which appear to stack along the 0.6 nm lattice plane; (4) lateral aggregation of the 3-mer stacks leads to the crystalline microfibril.Dedicated to Prof. Dr. Dr. h.c. Eberhard Schnepf on the occasion of his retirement     

High-density SNP linkage map construction and QTL mapping for flavonoid-related traits in a tea plant (<Emphasis Type="Italic">Camellia sinensis</Emphasis>) using 2b-RAD sequencing

Background

Flavonoids are important components that confer upon tea plants a unique flavour and health functions. However, the traditional breeding method for selecting a cultivar with a high or unique flavonoid content is time consuming and labour intensive. High-density genetic map construction associated with quantitative trait locus (QTL) mapping provides an effective way to facilitate trait improvement in plant breeding. In this study, an F1 population (LJ43×BHZ) was genotyped using 2b-restriction site-associated DNA (2b-RAD) sequencing to obtain massive single nucleotide polymorphism (SNP) markers to construct a high-density genetic map for a tea plant. Furthermore, QTLs related to flavonoids were identified using our new genetic map.

Results

A total of 13,446 polymorphic SNP markers were developed using 2b-RAD sequencing, and 4,463 of these markers were available for constructing the genetic linkage map. A 1,678.52-cM high-density map at an average interval of 0.40 cM with 4,217 markers, including 427 frameset simple sequence repeats (SSRs) and 3,800 novel SNPs, mapped into 15 linkage groups was successfully constructed. After QTL analysis, a total of 27 QTLs related to flavonoids or caffeine content (CAF) were mapped to 8 different linkage groups, LG01, LG03, LG06, LG08, LG10, LG11, LG12, and LG13, with an LOD from 3.14 to 39.54, constituting 7.5% to 42.8% of the phenotypic variation.

Conclusions

To our knowledge, the highest density genetic map ever reported was constructed since the largest mapping population of tea plants was adopted in present study. Moreover, novel QTLs related to flavonoids and CAF were identified based on the new high-density genetic map. In addition, two markers were located in candidate genes that may be involved in flavonoid metabolism. The present study provides valuable information for gene discovery, marker-assisted selection breeding and map-based cloning for functional genes that are related to flavonoid content in tea plants.

     

A protein map and its application

Graphical representation of gene sequences provides a simple way of viewing, sorting, and comparing various gene structures. Here we first report a two-dimensional graphical representation for protein sequences. With this method, we constructed the moment vectors for protein sequences, and mathematically proved that the correspondence between moment vectors and protein sequences is one-to-one. Therefore, each protein sequence can be represented as a point in a map, which we call protein map, and cluster analysis can be used for comparison between the points. Sixty-six proteins from five protein families were analyzed using this method. Our data showed that for proteins in the same family, their corresponding points in the map are close to each other. We also illustrate the efficiency of this approach by performing an extensive cluster analysis of the protein kinase C family. These results indicate that this protein map could be used to mathematically specify the similarity of two proteins and predict properties of an unknown protein based on its amino acid sequence.     

Allele Interaction – Single Locus Genetics Meets Regulatory Biology

Background

Since the dawn of genetics, additive and dominant gene action in diploids have been defined by comparison of heterozygote and homozygote phenotypes. However, these definitions provide little insight into the underlying intralocus allelic functional dependency and thus cannot serve directly as a mediator between genetics theory and regulatory biology, a link that is sorely needed.

Methodology/Principal Findings

We provide such a link by distinguishing between positive, negative and zero allele interaction at the genotype level. First, these distinctions disclose that a biallelic locus can display 18 qualitatively different allele interaction sign motifs (triplets of +, – and 0). Second, we show that for a single locus, Mendelian dominance is not related to heterozygote allele interaction alone, but is actually a function of the degrees of allele interaction in all the three genotypes. Third, we demonstrate how the allele interaction in each genotype is directly quantifiable in gene regulatory models, and that there is a unique, one-to-one correspondence between the sign of autoregulatory feedback loops and the sign of the allele interactions.

Conclusion/Significance

The concept of allele interaction refines single locus genetics substantially, and it provides a direct link between classical models of gene action and gene regulatory biology. Together with available empirical data, our results indicate that allele interaction can be exploited experimentally to identify and explain intricate intra- and inter-locus feedback relationships in eukaryotes.     

Stacks in canonical RNA pseudoknot structures

In this paper we study the distribution of stacks/loops in k-non-crossing, τ-canonical RNA pseudoknot structures (〈k,τ〉-structures). Here, an RNA structure is called k-non-crossing if it has no more than k-1 mutually crossing arcs and τ-canonical if each arc is contained in a stack of length at least τ. Based on the ordinary generating function of 〈k,τ〉-structures [G. Ma, C.M. Reidys, Canonical RNA pseudoknot structures, J. Comput. Biol. 15 (10) (2008) 1257] we derive the bivariate generating function , where T_k,τ(n,t) is the number of 〈k,τ〉-structures having exactly t stacks and study its singularities. We show that for a specific parametrization of the variable u, T_k,τ(x,u) exhibits a unique, dominant singularity. The particular shift of this singularity parametrized by u implies a central limit theorem for the distribution of stack-numbers. Our results are of importance for understanding the ‘language’ of minimum-free energy RNA pseudoknot structures, generated by computer folding algorithms.