StreAM- $$T_g$$ : Algorithms for Analyzing Coarse Grained RNA Dynamics Based on Markov Models of Connectivity-Graphs

StreAM-[Formula: see text]: algorithms for analyzing coarse grained RNA dynamics based on Markov models of connectivity-graphs

Background

In 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-\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, a stream-based algorithm for generating such Markov models of k-vertex adjacency matrices representing the RNA.

Results

We benchmark 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 (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-\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 on six long term molecular dynamics simulation of a synthetic tetracycline dependent riboswitch (500 ns) in combination with five different antibiotics.

Conclusions

The proposed algorithm performs well on large simulated as well as real world dynamic graphs. Additionally, 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 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.

Cleavage Product Accumulation Decreases the Activity of Cutinase during PET Hydrolysis

The Fusarium solani cutinase (FsC) is a promising candidate for the enzymatic degradation of the synthetic polyester polyethylene terephthalate (PET) but still suffers from a lack of activity. Using atomic MD simulations with different concentrations of cleavage product ethylene glycol (EG), we show influences of EG on the dynamic of FsC. We observed accumulation of EG in the active site region reducing the local flexibility of FsC. Furthermore, we used a coarse-grained mechanical model to investigate whether substrate binding in the active site causes an induced fit. We observed this supposed induced fit or "breath-like" movement during substrate binding indicating that the active site has to be flexible for substrate conversion. This guides rational design: mutants with an increased flexibility near the active site should be considered to compensate the solvent-mediated reduction in activity.