Journal: Algorithms for Molecular Biology : AMB

Article Title: Infrared: a declarative tree decomposition-powered framework for bioinformatics

doi: 10.1186/s13015-024-00258-2

Figure Lengend Snippet: The running example: graph coloring. A Example input graph. B One valid coloring with 4 colors, corresponding to an assignment of variables to colors (domain values) that satisfies all the inequality constraints along the edges. In our example extension, which minimizes the feature counting the different colors in each of its four cycles of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4$$\end{document} 4 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(v_2,v_3,v_5,v_6)$$\end{document} ( v 2 , v 3 , v 5 , v 6 ) , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(v_2,v_5,v_7,v_8)$$\end{document} ( v 2 , v 5 , v 7 , v 8 ) , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(v_5,v_6,v_7,v_8)$$\end{document} ( v 5 , v 6 , v 7 , v 8 ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_5,v_6,v_8,v_9$$\end{document} v 5 , v 6 , v 8 , v 9 , this coloring is not optimal (e.g. recolor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_3$$\end{document} v 3 )

Article Snippet: B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature.

Techniques:

Journal: Algorithms for Molecular Biology : AMB

Article Title: Infrared: a declarative tree decomposition-powered framework for bioinformatics

doi: 10.1186/s13015-024-00258-2

Figure Lengend Snippet: Dependency graph and tree decompositions of the running example (feature network \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {col}}$$\end{document} N col ). A The dependency graph contains one (binary) edge per dependency due to a constraint \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {\textsf{NotEquals}}}\in \mathcal {C} _{\text {col}}$$\end{document} NotEquals ∈ C col . The dependency hyperedges due to the three network functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {\textsf{Card}}}\in F_{\text {card}}$$\end{document} Card ∈ F card are colored. B Two possible tree decompositions of this dependency graph (and therefore \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {col}}$$\end{document} N col ). The difference set is underlined in each bag. Solving of the network could be based on either one, but with different run time, which is dominated by the largest bag (bold). Due to their largest bags of size 5 and 6, the two tree decompositions have respective width 4 and 5. The bags handling the 4-ary functions are highlighted, where colors correspond to the hyperedges of A. C Tree decomposition of the network without 4-ary functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {\textsf{Card}}}$$\end{document} Card . The functions don’t allow any tree decomposition with width 3; thus they make the problem more complex

Article Snippet: B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature.

Techniques:

Journal: Algorithms for Molecular Biology : AMB

Article Title: Infrared: a declarative tree decomposition-powered framework for bioinformatics

doi: 10.1186/s13015-024-00258-2

Figure Lengend Snippet: Illustration of the forward optimal evaluation and traceback algorithms (by the running example of graph coloring; Fig. ). We elaborate steps of the computation guided by the gentle tree decomposition corresponding to Fig. B (top). The indices of variables in the difference set are underlined. On the left, we sketch the computation of the messages \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{w\rightarrow u}$$\end{document} m w → u and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{u\rightarrow v}$$\end{document} m u → v : For every assignment of the separator set, the algorithm maximizes over assignments of the difference variable (it dismisses invalid assignments); in the computation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{u\rightarrow v}$$\end{document} m u → v , it used the already computed message \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{w\rightarrow u}$$\end{document} m w → u . On the right, we show the corresponding computations to assign values to the underlined variables during traceback: given an optimal assignment to the variables in v , we first infer that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_5=2$$\end{document} X 5 = is an optimal continuation, and finally \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_3=2$$\end{document} X 3 =

Article Snippet: B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature.

Techniques: Gentle

Journal: Algorithms for Molecular Biology : AMB

Article Title: Infrared: a declarative tree decomposition-powered framework for bioinformatics

doi: 10.1186/s13015-024-00258-2

Figure Lengend Snippet: RNA multitarget design. A Three target RNA secondary structures of length 100 as 2D plots (by VARNA ) and dot-bracket strings; taken from a multitarget design benchmark set . B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature. One can observe that (1) equal weights lead to different mean energies for the targets; (2) strong control of the G C weight is required to avoid extreme G C content for stable designs. To automate the calibration of weights (and target specific feature value combinations), we suggest multidimensional Boltzmann sampling in Section “Multidimensional Boltzmann sampling”

Article Snippet: B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature.

Techniques: Control, Sampling

Journal: Algorithms for Molecular Biology : AMB

Article Title: Infrared: a declarative tree decomposition-powered framework for bioinformatics

doi: 10.1186/s13015-024-00258-2

Figure Lengend Snippet: Modeling the sequence alignment of AAACUGG and ACGACGC. From left to right, we illustrate the alignment model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {ali}}$$\end{document} N ali ; a valid assignment; the corresponding alignment

Article Snippet: B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature.

Techniques: Sequencing

Journal: Algorithms for Molecular Biology : AMB

Article Title: Infrared: a declarative tree decomposition-powered framework for bioinformatics

doi: 10.1186/s13015-024-00258-2

Figure Lengend Snippet: Modeling sequence structure alignment. Example of a valid assignment and corresponding alignment with a pseudoknotted structure. The model contains one network function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {\textsf{BPMatch}}}$$\end{document} BPMatch per input base pair (arcs on top). These functions contribute \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document} τ for matches to canonical bases (dashed arcs)

Article Snippet: B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature.

Techniques: Sequencing

Journal: Algorithms for Molecular Biology : AMB

Article Title: Infrared: a declarative tree decomposition-powered framework for bioinformatics

doi: 10.1186/s13015-024-00258-2

Figure Lengend Snippet: Sketch of the 5-state Deterministic finite “Aho-Corasick” automaton accepting the three stop codons UGA, UUA, UUG. We do not draw back-transitions to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_0$$\end{document} q 0 , which occur implicitly for all not explicitly shown cases (i.e. A,C,G in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_0$$\end{document} q 0 ; C in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_1$$\end{document} q 1 , C,G in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_2$$\end{document} q 2 ; and C in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_3$$\end{document} q 3 ). To forbid , instead of accept, all of the three stop codons, we complement the language by making all states but \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_4$$\end{document} q 4 accepting

Article Snippet: B Histograms of the features G C content (left), and the Turner energies (kcal/mol) of the three targets (right) in 5000 sequences sampled from the multitarget design model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {N} _{\text {design}}$$\end{document} N design at weight -5 for every feature.

Techniques: