StreAM-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_g$$\end{document}Tg: algorithms for analyzing coarse grained

BackgroundIn this work, we present a new coarse grained representation of RNA dynamics. It is based on adjacency matrices and their interactions patterns obtained from molecular dynamics simulations. RNA molecules are well-suited for this representation due to their composition which is mainly modular and assessable by the secondary structure alone. These interactions can be represented as adjacency matrices of k nucleotides. Based on those, we define transitions between states as changes in the adjacency matrices which form Markovian dynamics. The intense computational demand for deriving the transition probability matrices prompted us to develop StreAM-$$T_g$$Tg, a stream-based algorithm for generating such Markov models of k-vertex adjacency matrices representing the RNA.ResultsWe benchmark StreAM-$$T_g$$Tg (a) for random and RNA unit sphere dynamic graphs (b) for the robustness of our method against different parameters. Moreover, we address a riboswitch design problem by applying StreAM-$$T_g$$Tg on six long term molecular dynamics simulation of a synthetic tetracycline dependent riboswitch (500 ns) in combination with five different antibiotics.ConclusionsThe proposed algorithm performs well on large simulated as well as real world dynamic graphs. Additionally, StreAM-$$T_g$$Tg provides insights into nucleotide based RNA dynamics in comparison to conventional metrics like the root-mean square fluctuation. In the light of experimental data our results show important design opportunities for the riboswitch.

[1]  Wojciech Kasprzak,et al.  Bridging the gap in RNA structure prediction. , 2007, Current opinion in structural biology.

[2]  T. Schlick,et al.  Computational approaches to RNA structure prediction, analysis, and design. , 2011, Current opinion in structural biology.

[3]  Francisco C. Santos,et al.  Cooperation Prevails When Individuals Adjust Their Social Ties , 2006, PLoS Comput. Biol..

[4]  M. Parrinello,et al.  Polymorphic transitions in single crystals: A new molecular dynamics method , 1981 .

[5]  S. Nosé.  A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[6]  W. Delano.  The PyMOL Molecular Graphics System , 2002 .

[7]  Thorsten Strufe,et al.  StreAM- T_g : Algorithms for Analyzing Coarse Grained RNA Dynamics Based on Markov Models of Connectivity-Graphs , 2016, WABI.

[8]  Philipp Metzner,et al.  Estimating the sampling error: distribution of transition matrices and functions of transition matrices for given trajectory data. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Michael Müller,et al.  Thermodynamic characterization of an engineered tetracycline-binding riboswitch , 2006, Nucleic acids research.

[10]  K. Murphy,et al.  Computational approaches for RNA energy parameter estimation. , 2010, RNA.

[11]  Thorsten Strufe,et al.  StreaM - A Stream-Based Algorithm for Counting Motifs in Dynamic Graphs , 2015, AlCoB.

[12]  Jonathan Arnold,et al.  Secondary structural entropy in RNA switch (Riboswitch) identification , 2015, BMC Bioinformatics.

[13]  Alan S. Perelson,et al.  RNA Structural Motifs , 2011 .

[14]  A. Ferré-D’Amaré,et al.  Structural basis for specific, high-affinity tetracycline binding by an in vitro evolved aptamer and artificial riboswitch. , 2008, Chemistry & biology.

[15]  Giovanni Bussi,et al.  RNA folding pathways in stop motion , 2016, Nucleic acids research.

[16]  Tamar Schlick,et al.  Mathematical and Biological Scientists Assess the State-of-the-Art in RNA Science at an IMA Workshop RNA in Biology, Bioengineering and Biotechnology , 2010 .

[17]  D. Mathews,et al.  Accurate SHAPE-directed RNA structure determination , 2009, Proceedings of the National Academy of Sciences.

[18]  Magdalena A. Jonikas,et al.  Coarse-grained modeling of large RNA molecules with knowledge-based potentials and structural filters. , 2009, RNA.

[19]  C. Berens,et al.  A tetracycline-binding RNA aptamer. , 2001, Bioorganic & medicinal chemistry.

[20]  Joanna Trylska,et al.  Dependency Map of Proteins in the Small Ribosomal Subunit , 2006, PLoS Comput. Biol..

[21]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[22]  Thomas Simonson,et al.  Molecular mechanics models for tetracycline analogs , 2009, J. Comput. Chem..

[23]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[24]  Kay Hamacher,et al.  Visual analysis of patterns in multiple amino acid mutation graphs , 2014, 2014 IEEE Conference on Visual Analytics Science and Technology (VAST).

[25]  Marcus D. Hanwell,et al.  Avogadro: an advanced semantic chemical editor, visualization, and analysis platform , 2012, Journal of Cheminformatics.

[26]  F. Major,et al.  The MC-Fold and MC-Sym pipeline infers RNA structure from sequence data , 2008, Nature.

[27]  B. Alder,et al.  Studies in Molecular Dynamics. I. General Method , 1959 .

[28]  Frank Noé,et al.  Markov state models of biomolecular conformational dynamics. , 2014, Current opinion in structural biology.

[29]  Jay D Keasling,et al.  Model-Driven Engineering of RNA Devices to Quantitatively Program Gene Expression , 2011, Science.

[30]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[31]  T. Schlick,et al.  Exploring the repertoire of RNA secondary motifs using graph theory; implications for RNA design. , 2003, Nucleic acids research.

[32]  Mark Woodbridge,et al.  XperimentR: painless annotation of a biological experiment for the laboratory scientist , 2013, BMC Bioinformatics.

[33]  Thomas E Cheatham,et al.  Simulation and modeling of nucleic acid structure, dynamics and interactions. , 2004, Current opinion in structural biology.

[34]  Heinz-Jürgen Steinhoff,et al.  Ligand-induced conformational capture of a synthetic tetracycline riboswitch revealed by pulse EPR. , 2011, RNA.

[35]  Anna Walsh.  STUDIES IN MOLECULAR DYNAMICS , 1965 .

[36]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[37]  Eric Westhof,et al.  Frequency and isostericity of RNA base pairs , 2009, Nucleic acids research.

[38]  Barbara Fink,et al.  Molecular analysis of a synthetic tetracycline-binding riboswitch. , 2005, RNA.

[39]  Giovanni Bussi,et al.  Predicting the Kinetics of RNA Oligonucleotides Using Markov State Models. , 2016, Journal of chemical theory and computation.

[40]  Marc Vogel,et al.  Tetracycline determines the conformation of its aptamer at physiological magnesium concentrations. , 2014, Biophysical journal.

[41]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

[42]  Berk Hess,et al.  LINCS: A linear constraint solver for molecular simulations , 1997 .

[43]  Menglong Li,et al.  Unfolding mechanism of thrombin-binding aptamer revealed by molecular dynamics simulation and Markov State Model , 2016, Scientific Reports.

[44]  Frank Noé,et al.  EMMA: A Software Package for Markov Model Building and Analysis. , 2012, Journal of chemical theory and computation.

[45]  Peter C Anderson,et al.  Molecular simulations and Markov state modeling reveal the structural diversity and dynamics of a theophylline-binding RNA aptamer in its unbound state , 2017, PloS one.

[46]  Leonidas J. Guibas,et al.  Building Markov state models with solvent dynamics , 2013, BMC Bioinformatics.

[47]  S. Jager,et al.  Statistical Evaluation of HTS Assays for Enzymatic Hydrolysis of β-Keto Esters , 2015, PloS one.