A quantitative reference transcriptome for Nematostella vectensis early embryonic development : a pipeline for de novo assembly in emerging model systems

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in EvoDevo 4 (2013): 16, doi:10.1186/2041-9139-4-16.The de novo assembly of transcriptomes from short shotgun sequences raises challenges due to random and non-random sequencing biases and inherent transcript complexity. We sought to define a pipeline for de novo transcriptome assembly to aid researchers working with emerging model systems where well annotated genome assemblies are not available as a reference. To detail this experimental and computational method, we used early embryos of the sea anemone, Nematostella vectensis, an emerging model system for studies of animal body plan evolution. We performed RNA-seq on embryos up to 24 h of development using Illumina HiSeq technology and evaluated independent de novo assembly methods. The resulting reads were assembled using either the Trinity assembler on all quality controlled reads or both the Velvet and Oases assemblers on reads passing a stringent digital normalization filter. A control set of mRNA standards from the National Institute of Standards and Technology (NIST) was included in our experimental pipeline to invest our transcriptome with quantitative information on absolute transcript levels and to provide additional quality control. We generated >200 million paired-end reads from directional cDNA libraries representing well over 20 Gb of sequence. The Trinity assembler pipeline, including preliminary quality control steps, resulted in more than 86% of reads aligning with the reference transcriptome thus generated. Nevertheless, digital normalization combined with assembly by Velvet and Oases required far less computing power and decreased processing time while still mapping 82% of reads. We have made the raw sequencing reads and assembled transcriptome publically available. Nematostella vectensis was chosen for its strategic position in the tree of life for studies into the origins of the animal body plan, however, the challenge of reference-free transcriptome assembly is relevant to all systems for which well annotated gene models and independently verified genome assembly may not be available. To navigate this new territory, we have constructed a pipeline for library preparation and computational analysis for de novo transcriptome assembly. The gene models defined by this reference transcriptome define the set of genes transcribed in early Nematostella development and will provide a valuable dataset for further gene regulatory network investigations

Lattice and off-lattice side chain models of protein folding: Linear time structure prediction better than 86% of optimal

This paper considers the protein structure prediction problem for lattice and off-lattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven extremely useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of off-lattice models. The authors consider two side chain models: a lattice model that generalizes the HP model (Dill 85) to explicitly represent side chains on the cubic lattice, and a new off-lattice model, the HP Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. They describe algorithms for both of these models with mathematically guaranteed error bounds. In particular, the authors describe a linear time performance guaranteed approximation algorithm for the HP side chain model that constructs conformations whose energy is better than 865 of optimal in a face centered cubic lattice, and they demonstrate how this provides a 70% performance guarantee for the HP-TSSC model. This is the first algorithm in the literature for off-lattice protein structure prediction that has a rigorous performance guarantee. The analysis of the HP-TSSC model builds off of the work of Dancik and Hannenhalli who have developed a 16/30 approximation algorithm for the HP model on the hexagonal close packed lattice. Further, the analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Karplus et al. concerning the complexity of protein folding models that include side chains

The Pagenumber of Genus g Graph is 0(g)

In 1979, Berhart and Kainen conjectured that graphs of fixed genus g greater than or equal to 1 have unbounded pagenumber. This proves that genus g graphs can be embedded in 0(g) pages, thus disproving the conjecture. An Omega(square root of g) lower bound is also derived. The first algorithm in the literature for embedding an arbitrary graph in a book with a non-trivial upper bound on the number of pages is presented. First, the algorithm computes the genus g of a graph using the algorithm of Filotti, Miller, Reif (1979), which is polynomial-time for fixed genus. Second, it applies an optimal-time algorithm for obtaining an 0(g)-page book embedding. We give separate book embedding algorithms for the cases of graphs embedded in orientable and nonorientable surfaces. An important aspect of the construction is a new decomposition algorithm, of independent interest, for a graph embedded on a surface. Book embedding has application in several areas, two of which are directly related to the results obtained: fault-tolerant VLSI and complexity theory

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows however that the evolution of the statistical measures e.g Gibbs free energy, heat capacity, entropy is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.Comment: 21 Pages, no figure

Functional cis-regulatory genomics for systems biology

Gene expression is controlled by interactions between trans-regulatory factors and cis-regulatory DNA sequences, and these interactions constitute the essential functional linkages of gene regulatory networks (GRNs). Validation of GRN models requires experimental cis-regulatory tests of predicted linkages to authenticate their identities and proposed functions. However, cis-regulatory analysis is, at present, at a severe bottleneck in genomic system biology because of the demanding experimental methodologies currently in use for discovering cis-regulatory modules (CRMs), in the genome, and for measuring their activities. Here we demonstrate a high-throughput approach to both discovery and quantitative characterization of CRMs. The unique aspect is use of DNA sequence tags to “barcode” CRM expression constructs, which can then be mixed, injected together into sea urchin eggs, and subsequently deconvolved. This method has increased the rate of cis-regulatory analysis by >100-fold compared with conventional one-by-one reporter assays. The utility of the DNA-tag reporters was demonstrated by the rapid discovery of 81 active CRMs from 37 previously unexplored sea urchin genes. We then obtained simultaneous high-resolution temporal characterization of the regulatory activities of more than 80 CRMs. On average 2–3 CRMs were discovered per gene. Comparison of endogenous gene expression profiles with those of the CRMs recovered from each gene showed that, for most cases, at least one CRM is active in each phase of endogenous expression, suggesting that CRM recovery was comprehensive. This approach will qualitatively alter the practice of GRN construction as well as validation, and will impact many additional areas of regulatory system biology

Solving the 3D Ising Model with the Conformal Bootstrap

We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and OPE coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.Comment: 32 pages, 11 figures; v2: refs added, small changes in Section 5.3, Fig. 7 replaced; v3: ref added, fits redone in Section 5.

Stochastic approach to molecular interactions and computational theory of metabolic and genetic regulations

Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between transcription factors and the operators of genes and that between ligands and binding sites of allosteric enzymes are typical examples of such molecular interactions. In order to obtain the general mathematical framework of biological regulations, we formulate these interactions as finite Markov processes and establish a computational theory of regulatory activities of macromolecules based mainly on graphical analysis of their state transition diagrams. The contribution is summarized as follows: (1) Stochastic interpretation of Michaelis-Menten equation is given. (2) Notion of \textit{probability flow} is introduced in relation to detailed balance. (3) A stochastic analogy of \textit{Wegscheider condition} is given in relation to loops in the state transition diagram. (4) A simple graphical method of computing the regulatory activity in terms of ligands' concentrations is obtained for Wegscheider cases.Comment: 20 pages, 13 figure