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NMR Spectroscopy in Chemical Reaction Network Modelling} @@ -101,79 +101,81 @@ \label{pullback} \end{figure} \begin{figure} - \begin{tikzcd} - \bullet && \bullet & \bullet &&&& \bullet && \bullet & \bullet && \\ - \\ - \bullet && \bullet & \bullet &&&& \bullet && \bullet \\ - \bullet && \bullet &&&&& \bullet &&& \bullet \\ - &&&&&&&&&&& \bullet & \bullet \\ - &&&&&&&&&&& \bullet \\ - &&&&&& \bullet \\ - \bullet && \bullet & \bullet &&&& \textcolor{white}{\bullet} && \bullet & \bullet \\ - \\ - \bullet && \bullet & \bullet &&&& \bullet && \bullet & \bullet \\ - \bullet && \bullet & \bullet && \bullet && \bullet && \bullet \\ - &&&& \bullet & \bullet \\ - &&& \bullet & \bullet - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-1, to=1-3] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-1, to=3-1] - \arrow[no head, from=1-3, to=1-4] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-3, to=3-3] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-4, to=3-4] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=1-8, to=1-10] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=1-8, to=3-8] - \arrow[no head, from=1-10, to=1-11] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=1-10, to=3-10] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-11, to=4-11] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=3-1, to=3-3] - \arrow[no head, from=3-3, to=3-4] - \arrow[no head, from=3-3, to=4-3] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=3-8, to=3-10] - \arrow[no head, from=3-10, to=4-11] - \arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-6pt}, dashed, from=3-10, to=5-12] - \arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-12pt}, dashed, from=3-10, to=5-13] - \arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=12pt}, dashed, from=3-10, to=6-12] - \arrow[no head, from=4-1, to=3-1] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=4-1, to=4-3] - \arrow[no head, from=4-8, to=3-8] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=4-8, to=4-11] - \arrow[no head, from=5-12, to=5-13] - \arrow[no head, from=5-12, to=6-12] - \arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-6pt}, dashed, from=7-7, to=8-10] - \arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=6pt}, dashed, from=7-7, to=10-8] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-1, to=8-3] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-1, to=10-1] - \arrow[no head, from=8-3, to=8-4] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-3, to=10-3] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-4, to=10-4] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-8, to=8-10] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-8, to=10-8] - \arrow[no head, from=8-10, to=8-11] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-10, to=10-10] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-11, to=10-11] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=10-1, to=10-3] - \arrow[no head, from=10-3, to=10-4] - \arrow[no head, from=10-3, to=11-3] - \arrow[no head, from=10-3, to=11-4] - \arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-6pt}, dashed, from=10-3, to=12-5] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=10-4, to=11-6] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=10-8, to=10-10] - \arrow[no head, from=10-10, to=10-11] - \arrow[no head, from=10-10, to=11-10] - \arrow[no head, from=11-1, to=10-1] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=11-1, to=11-3] - \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=11-3, to=13-4] - \arrow[color={rgb,255:red,92;green,214;blue,92}, curve={height=-6pt}, dashed, from=11-4, to=12-6] - \arrow[color={rgb,255:red,92;green,92;blue,214}, curve={height=6pt}, dashed, from=11-4, to=13-5] - \arrow[no head, from=11-8, to=10-8] - \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=11-8, to=11-10] - \arrow[no head, from=12-5, to=11-6] - \arrow[no head, from=12-5, to=12-6] - \arrow[no head, from=12-5, to=13-5] - \arrow[no head, from=13-4, to=12-5] - \end{tikzcd} - \caption{Beispiel für ein tatsächliches Pushout-Pullback Konstrukt (oben links), ein zu kleines Pushout (oben rechts), ein zu großes Pushout (unten links) und ein zu kleines Pullback (unten rechts). } - \label{pushpullex} + + \begin{tikzcd} + \bullet && \bullet & \bullet &&&& \bullet && \bullet & \bullet && \\ + \\ + \bullet && \bullet & \bullet &&&& \bullet && \bullet \\ + \bullet && \bullet &&&&& \bullet &&& \bullet \\ + &&&&&&&&&&& \bullet & \bullet \\ + &&&&&&&&&&& \bullet \\ + &&&&&& \bullet \\ + \bullet && \bullet & \bullet &&&& \textcolor{white}{\bullet} && \bullet & \bullet \\ + \\ + \bullet && \bullet & \bullet &&&& \bullet && \bullet & \bullet \\ + \bullet && \bullet & \bullet && \bullet && \bullet && \bullet \\ + &&&& \bullet & \bullet \\ + &&& \bullet & \bullet + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-1, to=1-3] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-1, to=3-1] + \arrow[no head, from=1-3, to=1-4] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-3, to=3-3] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-4, to=3-4] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=1-8, to=1-10] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=1-8, to=3-8] + \arrow[no head, from=1-10, to=1-11] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=1-10, to=3-10] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=1-11, to=4-11] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=3-1, to=3-3] + \arrow[no head, from=3-3, to=3-4] + \arrow[no head, from=3-3, to=4-3] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=3-8, to=3-10] + \arrow[no head, from=3-10, to=4-11] + %\arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-6pt}, dashed, from=3-10, to=5-12] + %\arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-12pt}, dashed, from=3-10, to=5-13] + %\arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=12pt}, dashed, from=3-10, to=6-12] + \arrow[no head, from=4-1, to=3-1] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=4-1, to=4-3] + \arrow[no head, from=4-8, to=3-8] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=4-8, to=4-11] + \arrow[no head, from=5-12, to=5-13] + \arrow[no head, from=5-12, to=6-12] + %\arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-6pt}, dashed, from=7-7, to=8-10] + %\arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=6pt}, dashed, from=7-7, to=10-8] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-1, to=8-3] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-1, to=10-1] + \arrow[no head, from=8-3, to=8-4] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-3, to=10-3] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-4, to=10-4] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-8, to=8-10] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-8, to=10-8] + \arrow[no head, from=8-10, to=8-11] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-10, to=10-10] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=8-11, to=10-11] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=10-1, to=10-3] + \arrow[no head, from=10-3, to=10-4] + \arrow[no head, from=10-3, to=11-3] + \arrow[no head, from=10-3, to=11-4] + %\arrow[color={rgb,255:red,214;green,92;blue,92}, curve={height=-6pt}, dashed, from=10-3, to=12-5] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=10-4, to=11-6] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=10-8, to=10-10] + \arrow[no head, from=10-10, to=10-11] + \arrow[no head, from=10-10, to=11-10] + \arrow[no head, from=11-1, to=10-1] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=11-1, to=11-3] + \arrow[color={rgb,255:red,214;green,92;blue,92}, dashed, from=11-3, to=13-4] + %\arrow[color={rgb,255:red,92;green,214;blue,92}, curve={height=-6pt}, dashed, from=11-4, to=12-6] + %\arrow[color={rgb,255:red,92;green,92;blue,214}, curve={height=6pt}, dashed, from=11-4, to=13-5] + \arrow[no head, from=11-8, to=10-8] + \arrow[draw={rgb,255:red,214;green,92;blue,92}, dashed, from=11-8, to=11-10] + \arrow[no head, from=12-5, to=11-6] + \arrow[no head, from=12-5, to=12-6] + \arrow[no head, from=12-5, to=13-5] + \arrow[no head, from=13-4, to=12-5] + \end{tikzcd} + + \caption{Beispiel für ein tatsächliches Pushout-Pullback Konstrukt (oben links), ein zu kleines Pushout (oben rechts), ein zu großes Pushout (unten links) und ein zu kleines Pullback (unten rechts). } + \label{pushpullex} \end{figure} Wir betrachten zum Pushout und Pullback vier Beispiele (Abb. \ref{pushpullex}). Im oben rechten Beispiel fügen die Morphismen jeweils eine Horizontale oder vertikale Kant mit Knoten hinzu. Das Pushout hat beides hinzugefügt. Im unten linken Beispiel wird für das Pushout nur insgesamt eine Kante hinzugefügt. Die beiden zuvor erzeugten Kanten werden also kombiniert, weshalb zwei unterschiedliche Morphismusmen $d'':D \rightarrow D''$ mit D'' als tatsächliches Pushout existieren würden. Das Pushout ist in diesem Fall also zu klein. Beim unten linken Beispiel wird für das Pushout eine Kante zu viel eingefügt. Dadurch existieren ebenfalls zwei verschiedene Morphismen (grün und blau) zu einem weiteren vier Stern Graphen. Ebenso existiert kein Morphismus von dem drei Stern Graphen zu dem tatsächlichen Pushout. Das Pushout ist also zu groß. In dem Beispiel unten links wird für das Pullback angenommen, dass wenn die Kante entfernt wird, auch die zugehörigen Knoten entfernt werden. Dadurch ist aber kein Morphismus von dem tatsächlichen Pullback zu diesem Pullback möglich. Ebenso würden, wenn jeweils zwei Knoten mit einer Kante mit $g$ und $f$ hinzugefügt würden, diese im Pushout kombiniert werden. Beides wiederspricht den etablierten Regeln. \paragraph{Pushout Complement} @@ -406,20 +408,922 @@ \end{equation} Die hierfür verwendeten Basisfunktionen können variieren, sind aber meistens Slater oder Gauss-Funktionen \cite{DFTORCA}. \section{Methoden} - \subsection{M\o{}d} - \cite{mod} + \subsection{M\o{}d Derivation Graph} + M\o{}d kurz für Med\O{}lDatschgerl ist ein Python basiertes Graphtransformtions Tool, welches mit dem DPO Ansatz aus Graphtransformationsregeln und aus Startgraphen und den durch Graphtransformation gefundenen neuen Graphen einen Hypergraphen definiert. Die Graphen in M\o{}d können dabei erzeugt werden indem ein SMILE-String geladen wird oder über einen GML-String definiert werden. Im folgenden wird das selbe Molekül Cyclohexan über seinen SMILE und einen GML String definiert. + \begin{verbatim} + cyclohexan = smiles ("C1CCCCC1") + cyclohexan = Graph.fromGMLString( + graph [ + node [ id 0 label "C" ] + node [ id 1 label "H" ] + node [ id 2 label "C" ] + node [ id 3 label "H" ] + node [ id 4 label "C" ] + node [ id 5 label "H" ] + node [ id 6 label "C" ] + node [ id 7 label "H" ] + node [ id 8 label "C" ] + node [ id 9 label "H" ] + node [ id 10 label "C" ] + node [ id 11 label "H" ] + edge [ source 0 target 1 label "-" ] + edge [ source 0 target 2 label "-" ] + edge [ source 2 target 3 label "-" ] + edge [ source 2 target 4 label "-" ] + edge [ source 4 target 5 label "-" ] + edge [ source 4 target 6 label "-" ] + edge [ source 6 target 7 label "-" ] + edge [ source 6 target 8 label "-" ] + edge [ source 8 target 9 label "-" ] + edge [ source 8 target 10 label "-" ] + edge [ source 10 target 11 label "-" ] + edge [ source 10 target 0 label "-" ] + ], name = "Cyclohexan) + \end{verbatim} + Wenngleich die Definition des Moleküls als String deutlich einfacher ist, erlaubt der GML String die Definition nicht chemischer Graphen und auch von Molekülzuständen, die keinen SMILE String zugeordnet haben. Eine Regel kann nur über einen GML String definiert werden. Für eine Regel müssen dabei linke und rechte Seite sowie der Kontext angegeben werden. Um zum Beispiel den Ring des Cyclohexans aufzuspalten um n-Hexan zu erhalten, würde eine Regel benötigt, welche eine C-C Einfachbindung aufspaltet und die Kohlenstoffe mit Wasserstoff sättigt. + \begin{verbatim} + cracking = Rule.fromGMLString( + """rule [ + left [ + edge [ source 1 target 2 label "-" ] + ] + context [ + node [ id 1 label "C" ] + node [ id 2 label "C"] + ] + right [ + node [ id 3 label "H" ] + node [ id 4 label "H" ] + edge [ source 1 target 3 label "-" ] + edge [ source 2 target 4 label "-" ] ] + ] + ) + \end{verbatim} + Alle definierten Graphen werden in der Variable inputGraphs und alle definierten Regeln in der Variable inputRules gespeichert. Mit der Variable inputGraphs kann ein Derivationgraph DG erzeugt werden, auf dem die Regeln mit einer Benutzerdefinierten Abfolge angewendet werden können. Die Variable inputRules kann dabei allgemein oder eine spezifische Regel mit ihrem Variablennamen angewendet werden. Es ist ebenfalls möglich nach jeder Regelanwendung eine restriction Funktion aufzurufen, in welcher unerwünschte Eigenschaften der durch die Regeln erzeugten Graphen abgelehnt werden können. + \begin{verbatim} + dg = DG(graphDatabase=inputGraphs) + dg.build().execute( + addSubset(inputGraphs) + >> rightPredicate[ + restriction + ]( + repeat(inputRules)) + ) + ) + \end{verbatim} + Der durch die Regelanwendung erzeugte Hypergraph kann als über verschiedene print Befehle in einer Latex generierten PDF Datei dargestellt werden. Dafür muss ein FlowPrinter, DGPrinter oder GraphPrinter Objekt erzeugt werden \cite{mod}. + \begin{verbatim} + flowPrinter = FlowPrinter() + flowPrinter.printUnfiltered = False + postSection("Loaded Graphs") + for a in inputGraphs: + a.print() + postSection("Loaded Rules") + for a in inputRules: + a.print() + postSection("Product Graphs") + for a in dg.vertices: + a.graph.print() + \end{verbatim} + M\o{}d wurde verwendet die Einwirkung natürlich auftretenden Reaktionen auf natürliche oder synthetische Moleküle zu untersuchen. + \subsection{networkx} + Networkx ist ein Pythonbasiertes Netzwerk und Graphen Analyse Tool \cite{networkx}. Eine Funktion ist dabei das identifizieren aller sehnen losen Zyklen. Während der laufzeit von M\o{}d wurden verschiedene Analysen dieser sehnen losen Zyklen als restriction verwendet. \subsection{ORCA} - \cite{ORCA} + ORCA ist ein Quantenchemisches Rechnungs Programm auf DFT Basis. Es erlaubt unter anderem Geometrieoptimierung und NMR-Spektren Berechnung von Chemischen Molekülen \cite{ORCA}. Für diese Arbeit wurde ORCA 6.1.1 verwendet. + Für die von M\o{}d generierten Moleküle wurden die Graphen und SMILE Strings bestimmt. + Die zugehörigen XYZ Koordinatendateien wurden aus der RDKit Bibliothek über ihren SMILE String bezogen \cite{rdkit} oder mit dem chemischen Zeichenprogramm Avogadro2 \cite{avogadro} gezeichnet. In beiden Fällen wurde die Geometrie mit ORCA mit den der Dichtefunktion PBE, D4 Dispersionskorrektur und dem Basissatz DEF2-SVP optimiert. Anschließend wurden für die optimierte Struktur mit der Dichtefunktion TPSS, dem Basissatz pcSseg-3 und mit autoaux und tightscf die chemischen Verschiebungen berechnet. + \begin{verbatim} + !PBE D4 DEF2-SVP OPT + + !TPSS pcSseg-3 autoaux tightscf NMR + \end{verbatim} + Für den Vergleich wurden die selben Berechnungen für TMS durchgeführt. Die Kohlenstoff Verschiebung von TMS lag dabei bei 179.73 ppm. Die Bestimmung chemisch Äquivalenter Kerne wurde von Hand durchgeführt. Für jedes mit M\o{}d erzeugte Molekül wurde ein $^{13}$C-NMR berechnet. + \subsection{NMR-Vergleich} + Um die von ORCA berechneten NMR Spektren zu Vergleichen und ihre Ähnlichkeit zu Quantifizieren wurde die Binning Methode mit anschließender Crosscorrelation angewandt \cite{nmrbin}. Jeder Peak $j$ des Spektrums setzt sich aus seiner Intensität $I_{j}$ und seiner Verschiebung $\nu_{j}$ zusammen. Zuerst wird für ein gegebenes NMR Spektrum der Peak mit der größten chemischen Verschiebung $\nu_{max}$ und der kleinsten chemischen Verschiebung $\nu_{min}$ bestimmt und eine Bingröße $b$ festgelegt. Der größte Wert $\nu_{max}$ wird dabei aufgerundet und um eine Bingröße $b$ erhöht (Gleichung \ref{binupper}). Der kleinste Wert $\nu_{min}$ wird abgerundet und um eine Bingröße $b$ verringert (Gleichung \ref{binlower}). + \begin{equation} \label{binupper} + \nu_{max} = ceiling(max) + b + \end{equation} + \begin{equation} \label{binlower} + \nu_{min} = floor(min) - b + \end{equation} + Aus der Obergrenze $\nu_{max}$ und Untergrenze $\nu_{min}$ wird mit der Bingröße die nötige Anzahl an Bins $n$ bestimmt (Gleichung \ref{binnum}). + \begin{equation} \label{binnum} + n = ceiling(\frac{\nu_{max} - \nu_{min}}{b}) + \end{equation} + In welchem Bin $i$ ein Peak $j$ liegt wird bestimmt, indem der kleinste Bin bestimmt wird, dessen unter Grenze kleiner als die chemische Verschiebung des Peaks $\nu_{j}$ ist (Gleichung \ref{binzuor}) + \begin{equation} \label{binzuor} + i = floor((\nu_{j} - \nu{min}) / b) + \end{equation} + Die Intensität des Bins $I_{i}$ ist dabei die Summe aller in ihm liegenden Peaks (Gleichung \ref{binning}). + \begin{equation} \label{binning} + I_{i} = \sum_{b \times i \leq \nu_{j} - \nu_{min} \leq b \times (i + 1)} I_{j} + \end{equation} + Die Intensität wird über alle Bins normalisiert. + Um zwei Spektren zu vergleichen wird anstelle des Randwerte des einen Spektrums gemeinsame Randwerte für beide Spektren nach dem gleichen System bestimmt und die Peaks auf diese Bind aufgeteilt. Anschließend werden die Bins für jedes Spektrum einzelnd normiert. Der Überlapp $O_{i}$ eines Bins des ersten Spektrums $i$ ist dabei mit den Bins des zweiten Spektrums $j$ gleich der Summe beider Bins, sowie des halben Werts der benachbarten Bins (Gleichung \ref{overlap}). + \begin{equation} \label{overlap} + O_{i} = 0.5 \times (I_{i} + I_{j-1}) + (I_{i} + I_{j}) + 0.5 \times (I_{i} + I_{j+1}) : i = j + \end{equation} + Der Gesamtüberlapp $O$ ist die Summe aller Teilüberlappe $O_{i}$ (Gelichung \ref{fulloverlap}) + \begin{equation} \label{fuloverlap} + O_{ij} = \sum_{i} O_{i} + \end{equation} + Aus dieser Crosskorrelation beider Spektren $O_{ij}$ und der Selbstkorrelation beider Spektren $O_{ii}$ und $O_{jj}$, wird der Ähnlichkeitsindex $SI$ berechnet (Gleichung \ref{similarity}) + \begin{equation} \label{similarity} + SI_{ij} = \frac{O_{ij}}{\sqrt{O_{ii} \times O_{jj}}} + \end{equation} + Für alle Moleküle eines aus dem gesamten Derivationgraph ausgewählten Reaktionspfad wurden Literaturspektren recherchiert. + Jedes mit ORCA berechnete $^{13}$C-NMR, wurde mit den Literaturspektren verglichen. Die für ein Literaturspektrum normierten Ähnlichkeitsindices wurden als Wahrscheinlichkeit angenommen, dass beide NMR-Spektren die Gleiche Substanz abbilden. + \subsection{Gurobipy} + Gurobipy \cite{gurobi} ist ein Python basierter ILP-Solver. Zur Bestimmung der Optimalen Parameter wird ein ILP-Baum verwendet. Die bestimmten Wahrscheinlichkeiten wurden mit dem Derivationgraph kombiniert. Darauf basierend wurde Gruobipy verwendet um einen diese Wahrscheinlichkeiten maximierenden Reaktionpfad in dem Derivationgraph zu identifizieren. + \subsection{M\o{}d Zertifikat} + Eine weitere Funktion von M\o{}d ist das Zertifizieren eines bestimmten Reaktionpfades des Hypergraphen mittels Petrinetzen. Dafür müssen die mittels Gurobi bestimmten Parameter für den Derivationgraph in M\o{}d festgelegt werden. + Ein mittels ILP bestimmter Reaktionspfad kann so nähergehend untersucht werden, indem Reaktionen, auf Erfüllbarkeit mit den gegebenen Startmolekülen überprüft werden. \section{Ergebnisse} - \subsubsection{M\o{}d} + \subsection{Ein Molekül Reaktionen} + Für eine einfach Demonstration der Kombination von ILP wurden simple Reaktionen, mit hoher natürlicher Selektivität gesucht. Dabei wurden die natürlichen Synthesen der Stoffe Koffein und Vanillin näher untersucht. Diese Synthesen erfolgen im Wesentlichen durch Reaktionen an einem Zentralen Molekül, wobei die Reaktionspartner nicht weiter Relevant bleiben. Wir bezeichnen sie daher im Folgenden als ein Molekül Reaktionen + \subsubsection{Koffein} + Koffein ist ein dreifach Methyliertes Purin, welches vor allem in Schwarzem Tee und Kaffeebohnen vorkommt. Es wurde erstmals in den 1820 Jahren isoliert. Heute sind Koffeinhaltige Lebensmittel aus dem Alltag nicht mehr wegzudenken, erfüllt aber auch in Zahlreichen Anwendungsfeldern eine signifikante Rolle. In der Natur wird Koffein aus den Nukleotidbasen Adenin und Guanin über die erst Oxidierung zu Xanthosin und anschließende Methylierung der Stickstoffe des Rings hergestellt (Abb.\ref{coffsynth}). Insbesondere die Methylierung erfolgt erst in der 7, dann in der 3 und zuletzt in der 1 Position. Diese geordnete Methylierung erfolgt mit hoher Spezifität und eignet sich so für eine nähere Untersuchung \cite{caffeinesynth}. + \begin{figure} [h] + \includegraphics[width=\textwidth]{coffeinesynthesis.png} + \caption{Synthese von Koffein in Pflanzen aus den Nukleotiden Adenin und Guanin. Erst werden die Purin Ringstrukturen Oxidiert und nach der Abspaltung der Ribose die Stickstoffe Methyliert. Die Methylierung erfolgt in der 7, 3 und zuletzt der 1 Position \cite{caffeinesynth}. } + \label{coffsynth} + \end{figure} + \subsubsection{Vanillin und 3,4-Dihydroxyaldehyd} + Vanillin ist die einer der beliebtesten Aromatischen Moleküle mit hoher Verwendung in Lebensmitteln, wobei der überwiegende Teil synthetisch hergestellt wird. In der Natur wird Vanillin in Vanille Orchideen aus Phenylalanin synthetisiert. Zuerst wird dabei der Aminrest in einer Eliminierung Reaktion zu Zimtsäure umgewandelt. Die Zimtsäure wird dann in der 3 und 4 Position des Phenylrests Hydroxiliert und zu einem Aldehyd oxidiert (Abb. \ref{vansynth}). Die Hydroxylierung und oxidation zu einem Aldehyd eignet sich dabei für eine nähere Untersuchung \cite{vanillinesynth}. + \begin{figure} [h] + \includegraphics[width=\textwidth]{vanillsynth.png} + \caption{Synthese von Vanilline in der Vanille Orchidee. Die Synthese erfolgt aus der Aminosäure Phenylalanin. Dabei wird zuerst die Aminogruppe eliminiert, anschließend der Phenylrest hydroxyliert und die aus der Eliminierung entstandene Doppelbindung oxidiert (rot). Der letzte Schritt ist die Methylierung des 4-Hydroxyrests \cite{vanillinesynth}. } + \label{vansynth} + \end{figure} + \subsection{M\o{}d: Ein Molekül Reaktionen} + Für die ein Molekül Reaktionen wurden zuerst in M\o{}d Transformationsregeln definiert. Diese Regeln wurden dann auf ein Startmolekül angewandt, welches Teil des natürlichen Syntheseprozesses ist. Dabei wurde insbesondere darauf geachtet, dass möglichst wenige und möglichst einfache Regeln deinen Teil der Synthese darstellen. + \subsubsection{M\o{}d: Koffein} + Für die Synthese von Koffein wurde mit dem Purin Ring Xanthine gestartet (Abb. \ref{xanthine}) + \begin{figure} [h] + \includegraphics[width=\textwidth]{xanthine.png} + \caption{Darstellung von Xanthin in M\o{}d.} + \label{xanthine} + \end{figure} + Ebenso wurde für die Transformationsregel zum Austausch eines an einen Stickstoff gebundenen Wasserstoff, durch eine Methylgruppe definiert. + (Abb. \ref{nmeth}). + \begin{figure} [h] + \includegraphics[width=\textwidth]{nmeth.png} + \caption{Darstellung der Regel zum Methylieren eines protonierten Stickstoffs in M\o{}d.} + \label{nmeth} + \end{figure} + Durch das wiederholte anwenden der Regel auf Xanthine konnte ein Reaktionsnetzerk entwickelt werden, an dessen Ende die Synthese von Koffein steht (Abb. \ref{coffsynthmod}). Dabei wurden die folgenden Zwischenprodukte bestimmt: + \begin{itemize} + \item $p_{0,0}$: 1-Methylxanthin + \item $p_{0,1}$: 3-Methylxanthin + \item $p_{0,2}$: 7-Methylxanthin + \item $p_{0,3}$: 1,3-Dimethylxanthin oder Theophyllin + \item $p_{0,4}$: 1,7-Dimethylxanthin oder Paraxanthin + \item $p_{0,5}$: 3,7-Dimethylxanthin oder Theobromin + \end{itemize} + \begin{figure} [h] + \includegraphics[width=\textwidth]{coffsynthmod.png} + \caption{Darstellung aller Synthesepfade von Koffein aus Xanthine in M\o{}d. Die Graphen $p_{0,0}$ bis $p_{0,5}$ stellen dabei die Zwischenprodukte 1-Methylxanthin, 3-Methylxanthin, 7-Methylxanthin, 1,3-Dimethylxanthin oder Theophylline, 1,7-Dimethylxanthin oder Paraxanthin und 3,7-Dimethylxanthin oder Theobromin dar.} + \label{coffsynthmod} + \end{figure} + \subsubsection{M\o{}d: Vanillin und 3,4-Dihydroxyaldehyd} + Für die Synthese von Koffein wurde mit Zimtsäure gestartet (Abb. \ref{zimt}). Das natürliche Produkt ist dabei E-Zimtsäure. + \begin{figure} [h] + \includegraphics[width=\textwidth]{zimt.png} + \caption{Darstellung von Zimtsäure in M\o{}d.} + \label{zimt} + \end{figure} + Zur Umsetzung der Zimtsäure zu dem Vanillin Zwischenprodukts, 3,4-Dihydroxybenzaldehyd, wurde eine Regel zur Hydroxylierung der aromatischen Kohlenstoffe (Abb. \ref{hydrox}) und zur Oxidierung einer Doppelbindung mit Carboxylgruppe zu einem Aldehyd (Abb. \ref{aldhyd}) definiert. + \begin{figure} [h] + \includegraphics[width=\textwidth]{hydrox.png} + \caption{Darstellung der Regel zum Hydroxylieren des Phenylrests in M\o{}d.} + \label{hydrox} + \end{figure} + \begin{figure} [h] + \includegraphics[width=\textwidth]{aldehyd.png} + \caption{Darstellung der Regel zum oxidieren der Zimtsäure Doppelbindung zu einem Aldehyd in M\o{}d.} + \label{aldhyd} + \end{figure} + Durch das wiederholte anwenden beider Regeln auf Zimtsäure konnte ein Reaktionsnetzerk entwickelt werden, an dessen Ende die Synthese von 3,4-Dihydroxybenzaldehyd steht (Abb. \ref{vanisynthmod}). Die breite Regelanwendung bedeutet die Ermittlung vieler Moleküle, welche nicht mehr zu dem Zielmolekül umgesetzt werden können. Darum wurden die Zwischenprodukte auf die Moleküle beschränkt, die tatsächlich Zwischenprodukte darstellen. Dabei wurden die folgenden Zwischenprodukte bestimmt: + \begin{itemize} + \item $p_{0,4}$: 3-Hydroxzimtsäure oder m-Coumarsäure + \item $p_{0,5}$: 4-Hydroxzimtsäure oder p-Coumarsäure + \item $p_{0,6}$: Benzaldehyd + \item $p_{0,13}$: 3,4-Dihydroxzimtsäure oder Kaffesäure + \item $p_{0,16}$: 3-Hydroxybenzaldehyd + \item $p_{0,17}$: 4-Hydroxybenzaldehyd + \end{itemize} + \begin{figure} [h] + \includegraphics[width=\textwidth]{vanisynthmod.png} + \caption{Darstellung aller Synthesepfade von 3,4-Dihydroxybenzaldehyd aus Zimtsäure in M\o{}d. Nur ein Teil aller Zwischenprodukte wird dabei tatsächlich zu dem gewünschten Produkt.} + \label{vanisynthmod} + \end{figure} + \subsection{NMR: Ein Molekül Reaktionen} + Für alle Zwischenprodukte wurde mit ORCA ein $^{13}$C-NMR berechnet und ein dazugehöriges Literaturspektrum recherchiert. + \subsubsection{NMR: Koffein} + Für alle Xanthinringe lässt sich sagen, dass ausschließlich die Protonen der Methygruppen chemisch Äquivalent zueinander sind. In einem $^{13}$C-NMR weisen also alle Kohlenstoffe ein eigenes Signal mit Intensität 1 auf. Die von ORCA berechneten NMR Spektren wurden den recherchierten Literaturspektren gegenübergestellt (Tabellen \ref{tabelxanthin},\ref{tabel1xanthin},\ref{tabel3xanthin},\ref{tabel7xanthin},\ref{tabel13xanthin},\ref{tabel17xanthin},\ref{tabel37xanthin},\ref{tabel137xanthin}) und ihre Verschiebung zueinander bestimmt. + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Xanthin mit einem Literatur Spektrum \cite{xanthinnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.14 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabelxanthin} + ORCA & Exp & Differenz\\ + \hline + 112.57 & 108.8 & 3.77 \\ + 138.61 & 137.2 & 1.41000000000003 \\ + 151.03 & 140.5 & 10.53 \\ + 152.87 & 152.4 & 0.469999999999999 \\ + 155.64 & 156.1 & -0.460000000000008 \\ + & & 3.144 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für 1-Methylxanthin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.71 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabel1xanthin} + ORCA & Exp & Differenz \\ + \hline + 30.18 & 27 & 3.18 \\ + 112.28 & 106.4 & 5.88 \\ + 137.88 & 140.6 & -2.72 \\ + 150.37 & 147 & 3.37 \\ + 153.13 & 151.2 & 1.93000000000001 \\ + 157.91 & 155.2 & 2.71000000000001 \\ + & & 2.39166666666667 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für 3-Methylxanthin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.35 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabel3xanthin} + ORCA & Exp & Differenz \\ + \hline + 31.34 & 28.8 & 2.54 \\ + 112.87 & 106.9 & 5.97 \\ + 138.12 & 140.5 & -2.38 \\ + 153.46 & 149.4 & 4.06 \\ + 154.78 & 151.2 & 3.58000000000001 \\ + 155 & 154.7 & 0.300000000000011 \\ + & & 2.345 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für 7-Methylxanthin mit einem Literatur Spektrum \cite{7xanthinnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.73 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabel7xanthin} + ORCA & Exp & Differenz \\ + \hline + 36.69 & 33.03 & 3.66 \\ + 113.78 & 106.9 & 6.88 \\ + 143.18 & 143.01 & 0.170000000000016 \\ + 151.13 & 149.3 & 1.82999999999998 \\ + 153.94 & 151.35 & 2.59 \\ + 157.1 & 155.85 & 1.25 \\ + & & 2.73 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Theophyllin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.61 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabel13xanthin} + ORCA & Exp & Differenz \\ + \hline + 29.23 & 27.7 & 1.53 \\ + 32.05 & 29.7 & 2.35 \\ + 112.36 & 106.4 & 5.95999999999999 \\ + 137.43 & 140.5 & -3.06999999999999 \\ + 152.62 & 147.8 & 4.81999999999999 \\ + 155.4 & 151.2 & 4.20000000000002 \\ + 156.89 & 154.4 & 2.48999999999998 \\ + & & 2.61142857142857 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Paraxanthin mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.19 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabel17xanthin} + ORCA & Exp & Differenz \\ + \hline + 28.59 & 26.7 & 1.89 \\ + 36.8 & 32.9 & 3.9 \\ + 113.44 & 106.5 & 6.94 \\ + 142.72 & 143 & -0.280000000000001 \\ + 151.81 & 147.4 & 4.41 \\ + 153.04 & 151.1 & 1.94 \\ + 158.8 & 155.3 & 3.5 \\ + & & 3.18571428571428 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Theobromin mit einem Literatur Spektrum \cite{theobrominnoMenmr}. Die Methylsignale (ca. 30 ppm) wurden aus einem anderen Spektrum genommen, da diese Angabe fehlte \cite{theobrominnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.63 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabel37xanthin} + ORCA & Exp & Differenz \\ + \hline + 30.96 & 29.3 & 1.66 \\ + 36.7 & 33.9 & 2.8 \\ + 114.14 & 108.1 & 6.04000000000001 \\ + 142.73 & 142.6 & 0.129999999999995 \\ + 153.39 & 150 & 3.38999999999999 \\ + 155.92 & 153.1 & 2.81999999999999 \\ + 156.49 & 154.9 & 1.59 \\ + & & 2.63285714285714 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Koffein mit einem Literatur Spektrum \cite{manyxanthinesnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.77 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{tabel137xanthin} + ORCA & Exp & Differenz \\ + \hline + 28.8 & 27.5 & 1.3 \\ + 31.72 & 29.3 & 2.42 \\ + 36.86 & 33.1 & 3.76 \\ + 113.66 & 106.6 & 7.06 \\ + 142.13 & 142.8 & -0.670000000000016 \\ + 153.86 & 148.1 & 5.76000000000002 \\ + 155.29 & 151 & 4.28999999999999 \\ + 158.29 & 154.5 & 3.78999999999999 \\ + & & 3.77285714285714 \\ + \hline + \end{tabular} + \end{center} + \end{table} + Die Methylwasserstoff lassen sich dabei den Signalen um ca. 30 ppm zuordnen, wobei das 1-Methyl Signal mit 28.6 bis 30.18 bei ORCA und 26.7 bis 27.7 in den experimentellen Spektren den niedrigsten Wert aufweist. Die mittlere Verschiebung weißt das 3-Methylsignal mit 31.0 bis 32.1 in ORCA und 28.8 bis 29.7 in den experimentellen Spektren auf. Die größte Verschiebung ist dem 7-Methylsignal mit 36.7 bis 36.9 in ORCA und 32.9 bis 33.9 in den experimentellen Spektren zuzuordnen. Die Signale des Purinrings sind für den größten Teil konstant über alle Moleküle, wobei Xanthin mit 151.03 in ORCA zu 140.5 im Experiment eine besonders große Differenz aufweist. Die größten Unterschiede sind über alle Xanthine bei dem Kohlenstoff neben dem 7-Stickstoff. Über alle Moleküle gemittelt lässt sich bestimmen, dass die von ORCA ermittelten Spektren im Durchschnitt um 2.5 ppm nach oben verschoben sind. + \subsubsection{NMR: Vanillin und 3,4-Dihydroxyaldehyd} + Für 3-hydroxylierte Zwischenprodukte lässt sich sagen, dass keine Kerne chemisch Äquivalent zueinander sind. Wenn nicht oder nur in der 4-Position hydroxyliert ist, sind jeweils die im Phenylrest gegenüberliegenden Wasserstoffe und Kohlenstoff zueinander chemisch Äquivalent. In einem $^{13}$C-NMR weisen also alle Kohlenstoffe in 3-hydroxilierten Moleküle ein eigenes Signal mit Intensität 1 auf. In nicht oder 4-hydroxylierten Molekülen verschmelzen jeweils zwei Signale zu insgesamt zwei Signalen mit Intensität 2. Die von ORCA berechneten NMR Spektren wurden den recherchierten Literaturspektren gegenübergestellt (Tabellen \ref{tabelzimt},\ref{tabelmcoum},\ref{tabelpcoum},\ref{tabelald},\ref{tabelcafac},\ref{tabel3ald},\ref{tabel4ald},\ref{tabel34ald}) und ihre Verschiebung zueinander bestimmt. + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Zimtsäure mit einem Literatur Spektrum \cite{cinamnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 4.02 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabelzimt} + Height & Exp & ORCA & Differenz \\ + \hline + 1 & 117.33 & 120.33 & 3 \\ + 2 & 128.39 & 133.48 & 5.09 \\ + 2 & 128.98 & 134.2 & 5.22 \\ + 1 & 130.77 & 135.91 & 5.13999999999999 \\ + 1 & 134.04 & 140.47 & 6.43000000000001 \\ + 1 & 147.14 & 151.41 & 4.27000000000001 \\ + 1 & 172.6 & 171.56 & -1.03999999999999 \\ + & & & 4.01571428571429 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für m-Coumarsäure mit einem Literatur Spektrum \cite{mcoumnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.51 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabelmcoum} + Height & Exp & ORCA & Differenz \\ + \hline + 1 & 115.3 & 118.6 & 3.3 \\ + 1 & 118.6 & 121.09 & 2.49000000000001 \\ + 1 & 119.2 & 121.69 & 2.49 \\ + 1 & 120.8 & 122.36 & 1.56 \\ + 1 & 131 & 134.46 & 3.46000000000001 \\ + 1 & 137.1 & 141.29 & 4.19 \\ + 1 & 146.5 & 153.69 & 7.19 \\ + 1 & 159.1 & 164.15 & 5.05000000000001 \\ + 1 & 170.5 & 172.55 & 2.05000000000001 \\ + & & & 3.53111111111111 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für p-Coumarsäure mit einem Literatur Spektrum \cite{pcoumnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.35 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabelpcoum} + Height & Exp & ORCA & Differenz \\ + \hline + 1 & 115.41 & 117.18 & 1.77000000000001 \\ + 2 & 115.83 & 118.65 & 2.82000000000001 \\ + 1 & 125.36 & 132.76 & 7.39999999999999 \\ + 2 & 130.17 & 135.75 & 5.58000000000001 \\ + 1 & 144.27 & 149.67 & 5.39999999999998 \\ + 1 & 159.67 & 166.09 & 6.42000000000002 \\ + 1 & 168.05 & 171.61 & 3.56 \\ + & & & 4.70714285714286 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Benzaldehyd mit einem Literatur Spektrum \cite{aldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 4.80 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabelald} + Height & Exp & ORCA & Differenz \\ + \hline + 2 & 128.9 & 133.45 & 4.54999999999998 \\ + 2 & 129.5 & 135.86 & 6.36000000000001 \\ + 1 & 134.2 & 139.15 & 4.95000000000002 \\ + 1 & 136.4 & 141.47 & 5.06999999999999 \\ + 1 & 192 & 195.09 & 3.09 \\ + & & & 4.804 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für Kaffesäure mit einem Literatur Spektrum \cite{caffacdnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 2.18 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabelcafac} + Heigt & Exp & ORCA & Differenz \\ + \hline + 1 & 147.9 & 155.79 & 7.88999999999999 \\ + 1 & 146.5 & 149.88 & 3.38 \\ + 1 & 129.3 & 132.99 & 3.69 \\ + 1 & 123.1 & 131.94 & 8.84 \\ + 1 & 121.7 & 118.15 & -3.55 \\ + 1 & 116.4 & 116.16 & -0.240000000000009 \\ + 1 & 141.5 & 149.28 & 7.78 \\ + 1 & 114.6 & 110.95 & -3.64999999999999 \\ + 1 & 176.2 & 171.66 & -4.53999999999999 \\ + & & & 2.17777777777778 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für 3-Hydroxybenzaldehyd mit einem Literatur Spektrum \cite{mhydaldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.83 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabel3ald} + Height & Exp & ORCA & Differenz \\ + \hline + 1 & 115 & 122.95 & 7.95 \\ + 1 & 122 & 123.33 & 1.33 \\ + 1 & 123 & 124.61 & 1.61 \\ + 1 & 131 & 133.96 & 2.96000000000001 \\ + 1 & 138 & 143.41 & 5.41 \\ + 1 & 158 & 164.39 & 6.38999999999999 \\ + 1 & 194 & 195.16 & 1.16 \\ + & & & 3.83 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für 4-Hydroxybenzaldehyd mit einem Literatur Spektrum \cite{phydaldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt 3.348 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabel4ald} + Height & Exp & ORCA & Differenz \\ + \hline + 2 & 116.5 & 118.46 & 1.95999999999999 \\ + 1 & 130.3 & 135.08 & 4.78 \\ + 2 & 132.7 & 137.69 & 4.99000000000001 \\ + 1 & 163.8 & 168.28 & 4.47999999999999 \\ + 1 & 191 & 191.53 & 0.530000000000001 \\ + & & & 3.348 \\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table}[htb] + \caption{Vergleich des von ORCA berechneten Spektrum für 3,4-Dihydroxybenzaldehyd mit einem Literatur Spektrum \cite{mphydaldhnmr}. Die Werte sind in ppm angegeben. Die durchschnittliche Differenz beträgt -3.81 ppm.} + \begin{center} + \begin{tabular}{ |c|c|c|c| } + \label{tabel34ald} + Height & Exp & ORCA & Differenz \\ + \hline + 1 & 113.1 & 114.22 & 1.12 \\ + 1 & 117.79 & 115.21 & -2.58000000000001 \\ + 1 & 133.4 & 124.59 & -8.81 \\ + 1 & 134.66 & 130.13 & -4.53 \\ + 1 & 149.32 & 145.44 & -3.88 \\ + 1 & 158.08 & 151.27 & -6.81 \\ + 1 & 191.41 & 190.26 & -1.15000000000001 \\ + & & & -3.80571428571429 \\ + \hline + \end{tabular} + \end{center} + \end{table} + Bei den Zwischenprodukten der 3,4-Dihydroxybenzaldehyd Synthese lässt sich im Vergleich zu den Koffein Synthese Zwischenprodukten weniger ein Muster erkennen. Das ist unter anderem darauf zurückzuführen, dass der deutliche Elektronegativitäten Unterschied zwischen Sauerstoff und Wasserstoff einen großen Einfluss auf das Ringsystem erwirkt. Dadurch sind die Signale des Kerngerüsts deutlich weniger Konstant. Das Endprodukt 3,4-Dihydroxybenzaldehyd sticht dabei aber trotzdem heraus, da es im Gegensatz zu allen anderen Spektren durchschnittlich eine größere chemische Verschiebung aufweist. Über alle Spektren gemittelt haben die ORCA Spektren trotzdem eine um 2.8 ppm größere chemische Verschiebung. + \subsection{NMR SI: Ein Molekül Reaktionen} + Es wurden bereits Analysen zu der Genauigkeit von berechneten NMR-Spektren im Vergleich zu Experimentellen Spektren durchgeführt. Dabei wurde besonders festgestellt, dass einfache DFT Methoden die Effekte von schweren Atomen wie dem in TMS enthaltenden Silizium nicht akkurat bestimmen können. Insbesondere kann davon ausgegangen werden, dass die Frequenz des TMS-Kohenstoff zu gering ausfällt \cite{heavyateff1,heavyatef2}. Das führt wiederum dazu, dass die chemische Verschiebung der Signale im ORCA Spektrum zu hoch ausfällt. Dieser Wert ist systematisch, weshalb er als ungefähres Mittel der Unterschiede zwischen den von ORCA berechneten und experimentellen Spektren quantifiziert wurde. Auf alle Peaks der experimentellen Spektren wurden 2.5 ppm hinzuaddiert. Die Bingröße $b$ variiert in Literaturangaben zwischen 1 und 0.1 ppm \cite{nmrbin,nmrbinsize} mit einer Genauigkeit von 0.1 ppm. Deshalb wurde die Bingröße $b \in \{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0\}$ variiert und der resultierende Ähnlichkeitsindex $SI$ über alle sinnvollen Werte gemittelt. + \subsubsection{NMR SI: Koffein} + Den Erwartungen entsprechend weißt das ORCA Spektrum von 7-Methylxanthine eine hohe Ähnlichkeit zu dem experimentellen Spektrum von 7-Methylxanthin auf. Das Spektrum von Paraxanthin ist jedoch noch etwas ähnlicher. Die Spektren von Theobromin haben im Vergleich dazu die größten Übereinstimmungen, wobei Koffein am zweit ähnlichsten ist. Allgemein scheint eine Identifikation des 7-Methylrest gut zu funktionieren, jedoch keine einfache Unterscheidung der Restlichen Methylgruppen möglich zu sein. Da in allen Molekülen das xanthine Grundgerüst vorliegt und die Addition einer Methylgruppe dieses nicht zu sehr verändert, haben alle Moleküle eine signifikante Ähnlichkeit zueinander (Tabelle \ref{nmrsimcoff}). + \begin{table}[htb] + \caption{Resultierende Wahrscheinlichkeiten beim Vergleich aller Zwischenprodukte der Koffeinsynthese, sowie Xanthin und Koffein mit den natürlichen Zwischenprodukten 7-Methyxanthin und Theobromin} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{nmrsimcoff} + Molekül & 7-Methylxanthin & Theobromin\\ + \hline + Xanthin & 0.12 & 0.25\\ + 1-Methylxanthin & 0.18 & 0.16\\ + 3-Methylxanthin & 0.12 & 0.2\\ + 7-Methylxanthin & 0.25 & 0.21\\ + Theophylline & 0.18 & 0.16\\ + Paraxanthin & 0.3 & 0.18\\ + Theobromin & 0.1 & 0.31\\ + Koffein & 0.3 & 0.29\\ + \hline + \end{tabular} + \end{center} + \end{table} + + \subsubsection{NMR SI: Vanillin und 3,4-Dihydroxyaldehyd} + Bei der Vanillin Synthese liegen die chemischen Verschiebungen des Grundgerüsts weiter auseinander, weshalb manche Moleküle, wie 3-Hydroxybenzaldehyd nur eine sehr geringe Ähnlichkeit zu den natürlich Zwischenprodukten aufweisen. p-Coumarsäure hat die größte Ähnlichkeit zu sowohl seinem eigenen experimentellen Spektrum, sowie zu dem von 4-Hydoxybenzaldehyd. Die zweitgrößte Ähnlichkeit zu dem experimentellen Spektrum von p-Coumarsäure hat Kaffeesäure. Bei dem experimentellen Spektrum von 4-Hydroxybenzaldehyd hat das richtige Molekül die zweit größte Ähnlichkeit (Tabelle \ref{nmrsimvani}). + \begin{table}[htb] + \caption{Resultierende Wahrscheinlichkeiten beim Vergleich aller Zwischenprodukte der Vanillesynthese mit den natürlichen Zwischenprodukten p-Coumarsäure und Theobromin} + \begin{center} + \begin{tabular}{ |c|c|c| } + \label{nmrsimvani} + Molekül & p-Coumarsäure & 4-Hydroxybenzaldehyd\\ + \hline + Zimtsäure & 0.09 & 0.17\\ + p-Coumarsäure & 0.38 & 0.44\\ + m-Coumarsäure & 0.12 & 0.12\\ + Benzaldehyd & 0.09 & 0.18\\ + Kaffesäure & 0.34 & 0.15\\ + 3-Hydroxybenzaldehyd & 0.02 & 0.03\\ + 4-Hydroxybenzaldehyd & 0.34 & 0.26\\ + 3,4-Dihydroxybenzaldehyd & 0.17 & 0.17\\ + \hline + \end{tabular} + \end{center} + \end{table} + \subsection{ILP: Ein Molekül Reaktionen} + Der Hypergraph der komplett explorierten Synthese wurde an Gurobi übergeben und um eine Kante die in das Ausgangsprodukt hineinfließt und aus dem Zielmolekül herausfließt erweitert. Die Wahrscheinlichkeiten wurden als konstante Werte $p_{i,e}$ den Kanten $e$ des Hypergraphen zugeordnet. Die Kante 4 von Zimtsäure zu Benzaldehyd hat also die Wahrscheinlichkeit $p_{1,4} = 0.09$ das diese Reaktion dem ersten Referenzspektrum mit p-Coumarsöure entspricht. Die Wahrscheinlichkeit wurde der Kante zugeordnet, welche in den Knoten fließt. + Für jede Kante werden vier ganzzahlige Variablen $x_{e}$, $b_{e}$, $n_{1,e}$ und $n_{2,e}$ definiert. Die Variable $b_{e}$ ist dabei eine Wahrheitsvariable, die definiert ob eine Kante verwendet wird. Die Variable $x_{e}$ beschreibt wie oft die selbe Kante verwendet wird. Die Variablen $n_{1,e}$ und $n_{2,e}$ sind ebenfalls Wahrheitsvariablen und legen fest, welche zwei Reaktionen den Referenz NMR-Spektren entsprechen und deswegen zu der Zielfunktion da zuzählen. Dabei ist $n_{1,e}$ die Zuordnungsvariable zu dem ersten Referenz NMR-Spektrum mit 7-Methylxanthin oder p-Coumarsäure und $n_{2,e}$ die Zuordnungsvariable zu dem zweiten Referenz NMR-Spektrum mit 3,7-Methylxanthin oder 4-Hydroxybenzaldehyd. + Die Variablen unterliegen den Beschränkungen, dass: + \begin{itemize} + \item $x_{e} \geq b_{e}$ + \item $b_{e} \geq n_{1,e}$ + \item $b_{e} \geq n_{2,e}$ + \item flow ([], [Startmolekül]) = 1 + \item flow ([Zielmolekül], []) = 1 + \item Für jedes Molekül: inflow = outflow + \item $n_{1,e} + n_{2,e} \leq 1$ + \item $\sum_{e} n_{1,e} = 1$ + \item $\sum_{e} n_{2,e} = 1$ + \end{itemize} + Unter diesen Beschränkungen soll ein Pfad durch den Hypergraphen bestimmt werden, welcher ein geordnetes Paar von Molekülen auswählt, welche zusammen die größte Wahrscheinlichkeit aufweisen und zusammen alle Zwischenprodukte der Synthese darstellen. Die ausgehenden Kanten sind nicht in die Zielfunktion eingeflossen (Gleichung \ref{objective}). + \begin{equation} \label{objective} + max Obj = \sum_{e} 1000 \times (p_{1,e} \times n_{1,e} + p_{2,e} \times n_{2,e}) \newline - \frac{x_{e}}{ max(p_{1,e}, p_{2,e})} + \end{equation} + \subsubsection{ILP: Koffein} + Der Hypergraph für die Koffeinsynthese wird in Tabelle \ref{hypergraphcaffsynth} dargestellt. + \begin{table} + \caption{Der für die Koffeinsynthese definierte Hypergraph in Gurobi.} + \begin{center} + \begin{tabular}{ |c|c|c|c|c| } + \label{hypergraphcaffsynth} + Index & Edukt & Produkt & $n_{\text{7-Methylxanthin},e}$ & $n_{\text{3,7-Dimethylxanthin},e}$\\ + \hline + 1 & & Xanthin & 0.12 & 0.25\\ + 2 &Xanthin & 1-Methylxanthin & 0.18 & 0.16\\ + 3 &Xanthin & 3-Methylxanthin & 0.12 & 0.2\\ + 4 &Xanthin & 7-Methylxanthin & 0.25 & 0.21\\ + 5 &1-Methylxanthin & Theophyllin & 0.18 & 0.16\\ + 6 &1-Methylxanthin & Paraxanthin & 0.3 & 0.18\\ + 7 &3-Methylxanthin & Theophyllin & 0.18 & 0.16\\ + 8 &3-Methylxanthin & Theobromin & 0.1 & 0.31\\ + 9 &7-Methylxanthin & Paraxanthin & 0.3 & 0.18\\ + 10 &7-Methylxanthin & Theobromin & 0.1 & 0.31\\ + 11 &Theophyllin & Koffein & 0.3 & 0.29\\ + 12 &Paraxanthin & Koffein & 0.3 & 0.29\\ + 13 &Theobromin & Koffein & 0.3 & 0.29\\ + 14 &Koffein & & 0.0 & 0.0\\ + \hline + \end{tabular} + \end{center} + \end{table} + Die beste gefundene Lösung ist für die Kanten 1, 4, 10, 13 und 14 jeweils ein flow von 1 und alle anderen Kanten ein flow von 0. Dies entspricht der natürlich auftretenden Lösung. + \subsubsection{ILP: Vanillin und 3,4-Dihydroxyaldehyd} + Der Hypergraph für die Vanillinsynthese wird in Tabelle \ref{hypergraphcaffsynth} dargestellt. + \begin{table} + \caption{Der für die Vanillesynthese definierte Hypergraph in Gurobi.} + \begin{center} + \begin{tabular}{ |c|c|c|c|c| } + \label{hypergraphvanilsynth} + Index & Edukt & Produkt & $n_{\text{p-Coumarsäure},e}$ & $n_{\text{4-Hydroxybenzaldehyd},e}$\\ + \hline + 1 & & Zimtsäure & 0.09 & 0.17\\ + 2 &Zimtsäure & p-Coumarsäure & 0.38 & 0.44\\ + 3 &Zimtsäure & m-Coumarsäure & 0.12 & 0.12\\ + 4 &Zimtsäure & Benzaldehyd & 0.09 & 0.18\\ + 5 &p-Coumarsäure & Kaffesäure & 0.34 & 0.15\\ + 6 &p-Coumarsäure & 4-Hydroxybenzaldehyd & 0.34 & 0.26\\ + 7 &m-Coumarsäure & Kaffesäure & 0.34 & 0.15\\ + 8 &m-Coumarsäure & 3-Hydroxybenzaldehyd & 0.02 & 0.03\\ + 9 &Benzaldehyd & 3-Hydroxybenzaldehyd & 0.02 & 0.03\\ + 10 &Benzaldehyd & 4-Hydroxybenzaldehyd & 0.1 & 0.31\\ + 11 &Kaffesäure & 3,4-Dihydroxybenzaldehyd & 0.17 & 0.17\\ + 12 &3-Hydroxybenzaldehyd & 3,4-Dihydroxybenzaldehyd & 0.17 & 0.17\\ + 13 &4-Hydroxybenzaldehyd & 3,4-Dihydroxybenzaldehyd & 0.17 & 0.17\\ + 14 &3,4-Dihydroxybenzaldehyd & & 0.0 & 0.0\\ + \hline + \end{tabular} + \end{center} + \end{table} + Die beste gefundene Lösung ist für die Kanten 1, 2, 6, 13 und 14 jeweils ein flow von 1 und alle anderen Kanten ein flow von 0. Dies entspricht der natürlich auftretenden Lösung. + \subsection{Fazit: Ein Molekül Reaktionen} + Bei den bisher betrachteten ein Molekül Reaktionen wurde immer nur ein festgelegtes Startmolekül in das System gegeben. Dieses Startmolekül wurde nach Transformationsregeln variiert, wobei jedoch nach dem natürlichen Vorbild auch genau ein Zielmolekül synthetisiert werden sollte. In dem Koffein Beispiel gab es dabei keine Enantiomere oder E/Z-Isomere. In dem Vanille Beispiel gab es keine Enatiomere. Es gab mit Zimtsäure, Coumarsäure und Kaffesäure zwar E/Z-Isomere, welche aber durch die natürliche Vorgabe von E-Zimtsäure bereits vorgegeben waren. Außerdem entstande keine neue Doppelbindung mit einem E/Z-Isomer durch Graphtransformation. Der Schluss von dem Graphen auf eine Geometrie war deswegen immer eindeutig. \newline Für die Synthesen waren immer genau drei Reaktionen nötig, welche mittels des ILP nur bezüglich ihrer Reihenfolge variiert werden konnte. Das Problem ließe sich daher ebenfalls durch die einfache Addition zweier Moleküle entlang eines ausgewählten Pfades lösen. Der Raum möglicher Lösungen ist mit 6 pro Beispiel stark begrenzt. Trotzdem eigneten sich beide Beispiele mit der natürlich auftretenden Selektivität der Reihenfolge, der guten Differenzierbarkeit der NMR-Spektren und Kompaktheit der Synthese als Graphtransformationsregeln als Demonstration des Konzeptes. + \subsection{Multi Molekül Reaktionen} + Um die Grenzen der Möglichkeiten des ILP weiter auszureizen betrachten wir im Folgenden Reaktionen, die ebenfalls mit einfachen Reaktionsregeln ein hochvernetztes Reaktionsnetzwerk erzeugen. + \subsection{Olefin Metathese und Diels Alder} + Die zwei Reaktionen Olefin Metathese in Kombination mit der Diels-Alder-Reaktion erlaubt mit dem richtigen Ausgangsmolekülen die Entwicklung eines hochvernetzten Reaktionsnetzerks und unterliegenden Hypergraphen. + \subsubsection{Olefin Metathese} + Die Olefin Metathese ist eine vergleichbar neuere Reaktion \cite{olefinmetathese}. Mit meistens einem organischen Ruthenium-Katalysator werden dabei die Reste zweier Doppelbindungen rekombiniert. Dar Ruthenium-Katalysator hat dabei eine offene Bindungsstelle an die eine Hälfte der C-C-Doppelbundung als Carben bindet (A und E). Eine Olefin (B und F) bindet an diesen Komplex (C und G). Aus diesem Komplex wird ein Olefin abgespalten, welches entweder das eingehende Olefin ist oder eine beliebige Kombination beider Olefine (D) (Abb. \ref{olefinmetathese}). + \begin{figure} [h] + \includegraphics[width=\textwidth]{olefinmetathese.png} + \caption{Katalysezyklus der Olefinmetathese \cite{olefinmetathese}. } + \label{olefinmetathese} + \end{figure} + In der Forschung wurde dieser Katalytische Prozess zu immer gezielteren Ausbeuten durch spezialisierte Katalysatoren weiterentwickelt. Dabei wurde neben der generellen Selektivität der Produkte auch eine gezielte Selektivität hin zu E-Isomeren erzielt. Für die Anwendung auf ein Reaktionsnetzwerk ist eine Produktspezialisierung jedoch weniger interessant. Die E/Z-Selektivität ist dabei insbesondere im Hinblick auf den chemischen Molekül als Graphen nicht umsetzbar, wenngleich sie bei der Geometirerealisierung berücksichtigt werden kann. Die Möglichkeiten der Olefinmetathese sind jedoch begrenzt, wenn es um die Queervernetzung geht. Bei einer Olefin Metathese bleibt die Gesamtzahl an Einfach und Doppelbindungen gleich. + \subsubsection{Diels Alder} + Die Diels Alder Reaktion ist eine ohne Katalysator natürlich auftretende Reaktion, bei der zwei Doppelbindungen enthaltenden Moleküle verbunden werden. Dabei wird eine Vinylgruppe und zwei mit einer Einfachbindung verbundenen Vinylgruppen zu einem Cyclohexen Ring (Abb. \ref{dielsalder}). Wenn diese Bedingungen in einer Lösung vorhanden sind, kommt es zu dieser Kombination, mit nur geringer Rückreaktion \cite{dielsalder}. + \begin{figure} [h] + \includegraphics[width=\textwidth]{dielsalder.png} + \caption{Die Diels Alder Reaktion \cite{dielsalder}. } + \label{dielsalder} + \end{figure} + Die Diels Alder Reaktion ist einfach und sorgt dafür, dass Doppelbindungen zu Einfachbindungen werden. In der Kombination mit der Olefin Metathese sollten so viele verschiedene Produkte möglich werden. + \subsubsection{Butadien} + Der gewählte Ausgangsstoff ist Butadien. Das vorliegen von Zwei Doppelbindungen erlaubt es der Olefinmetathese Kohlenstoffketten mit alternierenden Einfach und Doppelbindungen aufzubauen. Diese können wiederum mit der Diels Alder Reaktion untereinander Kombiniert werden und so zu einer Großen Menge an unterschiedlichen Molekülen führen, welche alle untereinander kombinierbar sind. + \subsection{M\o{}d: Multi Molekül Reaktionen} + Bei der Definition der Transformationsregeln für mehr Molekül Reaktionen müssen auf der linken und rechten Seite, sowie im Kontext die gleichen Atome vorliegen. Bei den meisten mehrstufigen, chemischen Synthesen wird ein Zentrales Molekül betrachtet. Es kommt zwar vor, dass für eine Reaktion zwei Moleküle zusammen geführt werden, aber Teile des Moleküls, die in Reaktionen abgespalten werden, werden in der Restlichen Synthese nicht weiter erwähnt. Bei einem Multi Molekül sollen diese abgespaltenen Moleküle potenziell wieder miteinander Reagieren. Es ist also wichtig, dass eine Transformationsregel in hinsicht auf Multi Molekül Reaktionen, alle Teile vollständig weiterführt. + \subsubsection{M\o{}d: Olefin Metathese und Diels Alder} + In M\o{}d wurde mit dem Molekül Butadien (Abb. \ref{butadienmod}) gestartet. Auf dieses wurden wiederholt die Olefin Metathese (Abb. \ref{olmetmod}) und die Diels Alder Reaktion (Abb. \ref{dialdmod}) angewendet. + \begin{figure} [h] + \includegraphics[width=\textwidth]{butadienmod.png} + \caption{Butadien in M\o{}d. } + \label{butadienmod} + \end{figure} + \begin{figure} [h] + \includegraphics[width=\textwidth]{olmetmod.png} + \caption{Olefin Metathese in M\o{}d.. } + \label{olmetmod} + \end{figure} + \begin{figure} [h] + \includegraphics[width=\textwidth]{dialmod.png} + \caption{Diels Alder Reaktion in M\o{}d.} + \label{dialdmod} + \end{figure} + Bei dieser Reaktion ist es anders als bei den bisherigen Reaktionen möglich, dass der Ergebnisraum unbegrenzt wachsen kann. Darum sind Beschränkungen des Ergebnisraums nötig. Die einfachste Beschränkung der Ergebnisse ist eine Obergrenze für die Anzahl an Atomen. Damit Butadien als Startmolekül diese Begrenzung erfüllt, müssen mindestens 4 Kohlenstoffe zugelassen werden. Damit die Diels Alder Reaktion stattfinden kann müssen 6 Kohlenstoffe erlaubt sein. Die Regeln zeigen einen diversen Raum an gefundenen Molekülen bei 10 Kohlenstoffen. Da dies die Computerleistung stark beansprucht muss der Raum weiter eingeschränkt werden. Die Olefin Metathese ist bekannt dafür, Ringe mit großer Ringspannung aufzubrechen \cite{olefinmetathese}. Besonders strapaziert sind kleine Ringe mit der Größe 3 und 4, sowie große Ringe. Ein Kohlenstoff Ring der Größe 6 ist am stabilsten \cite{ringstrain}. Da die Olefin Metathese mit hoher Selektivität Ringe mit hoher Spannung aufbricht, ist davon auszugehen, dass zu große und zu kleine Ringe nicht Teil des Ergebnisraums sind. Insbesondere ist nur der 6 Ring als die stabilste Ringgröße zu erwarten. Deshalb wurden für jedes gefundene Molekül alle sehnenlosen Ringe gefunden und alle Ringe, die nicht die Größe 6 hatten aus dem Ergebnis Raum entfernt. Eine weitere Quelle der Ringspannung sind überlappende Ringe. Norbornan wird zum Beispiel aus drei überlagernden Ringen gebildet. Da auch in diesen Molekülen hohe Ringspannung vorliegt wurden alle Moleküle mit Ringen, die mehr als zwei gemeinsame Atome haben aus dem Ergebnisraum entfernt. Die letzte Begrenzung für Ringspannung ist, dass kein Atom in vier Ringen sein kann. \newline + Mit der Beschränkung durch wurden durch die Regelanwendung 19 Moleküle mit etwa 200 Transformationen aus Butadien entwickelt. + Die Moleküle und ihre SMILE-Strings lauten: + \begin{itemize} + \item Butadien: C=CC=C + \item Ethylen: C=C + \item Hexatrien: C=CC=CC=C oder C=C/C=C/C=C + \item 4-Vinyl-Cyclohex-1-en: C1CCC(C=C)CC=1 + \item 4-Vinyl-Octa-1,7-Dien: C(CCC(C=C)CC=C)=C + \item Octatetraen: C=CC=CC=CC=C oder C=C/C=CC=C/C=C + \item 4-Butadienyl-Cyclohex-1-en: C1CCC(C=CC=C)CC=1 + \item 3-Vinyl-Cyclohex1en: C=CC1C=CCCC1 + \item Cyclohexen: C1CCCCC=1 + \item 4,5-Divinyl-Cyclohex-1-en: C=CC1CC=CCC1C=C + \item 3,4-Divinyl-Cyclohex-1-en: C1CCC(C=C)C(C=C)C=1 + \item 3,5-Divinyl-Cyclohex-1-en: C(C1CC(C=C)C=CC1)=C + \item Benzol: C1C=CC=CC=1 + \item 5-Butan-1-enyl-Cyclo-1,3-dien: C(CCC1C=CC=CC1)=C + \item 3-Butadienyl-Cyclohex-1-en: C1C(C=CC=C)CCCC=1 + \item 3-Vinyl-Octa-1,7-Dien: C=CC(C=C)CCCC=C + \item Okta-1,7-dien: C=CCCCCC=C + \item 3,6-Divinyl-Cyclohex1en: C=CC1C=CC(C=C)CC1 + \item 1,2,3,4,4a,5,6,7,8,8a-Octahydronaphthalin: C1CC2CCCCC2CC=1 + \item 1,4,4a,8a-Tetrahydronaphthalin: C1CC2C=CC=CC2CC=1 + \end{itemize} + Wenn die Startmoleküle mit einem generischen Olekinmetathese Katalysator zum reagieren gebracht wird ist zu erwarten, dass alle Moleküle in verschiedenen Enantiomeren und E/Z-Isomeren synthetisiert werden würden. Daher ist es ohne das tatsächliche durchführen dieses Experiments schwierig einen Reaktionspfad herauszusuchen, der von dem ILP bestätigt werden soll. Es wurde sich für die Synthese von Benzol entschieden, da die hohe Symmetrie im Vergleich zu den anderen Spektren zu einem sehr markanten Spektrum führt (Abb. \ref{benzsynthmod}). + \begin{figure} [h] + \includegraphics[width=\textwidth]{benzsynthmod.png} + \caption{Benzolsynthese in M\o{}d. Erst Olefin Metathese von zwei Butadien zu Hexatrien und Ethylen. Dann Olefin Metathese von Hexatrien und Butdien zu Ethylen und Octatetraen. Zuletzt eine Ringschluss Olefin Metathese von Octatetraen zu Bensol und Ethylen.} + \label{benzsynthmod} + \end{figure} + Die direkteste Synthese ist dabei die Olefin Metathese von zwei Butadien zu Hexatrien und Ethylen. Anschließend die Olefin Metathese von Hexatrien mit Butadien zu Octatetraen. Zuletzt eine Ringschluss Olefin Metathese von Octatretraen zu Benzol und Ethylen. Es werden drei Butadien eingesetzt um mit drei Olefin Metathesen ein Benzol und drei Ethylen zu erhalten. + \subsection{NMR: Multi Molekül Reaktionen} + \subsubsection{NMR: Olefin Metathes und Diels Alder} + Die generierten Graphen wiesen anders als zuvor verschiedene Enantiomere, sowie E/Z-Isomere auf. Es ist daher notwendig diese zu unterscheiden. In den Fällen Hexatrien und Octatetraen wurde speziell die Konfiguration gewählt, bei der alle Doppelbindungen in der E-Konfiguration sind. Bei den Verbindungen mit Cyclohexanring und angehängten Vinylgruppen, wurde die Position so gewählt, dass die Reste Äquatorial zum Ring stehen. Bei den beiden Hydronaphtalinen wurde die Konfiguration gewählt, bei der beide Ringe in der Äquatorialen Konfiguration liegen. Verallgemeinert wurde die Konfiguration mit der größten Symmetrie und dadurch mit den meisten chemisch Äquivalenten Kohlenstoffen gewählt. + \subsection{NMR SI: Multi Molekül Reaktionen} + In der Literatur werden NMR-Spektren bevorzugt für einen vollständig aufgereinigten Stoff angegeben. Daher wurde entschieden, dass jedes Molekül NMR mit dem Kombinierten NMR aller Edukte der vorangegangenen Reaktionen verglichen werden. + \subsubsection{NMR SI: Olefin Metathes und Diels Alder} + Die Referenzspektren der Benzolsynthese sind: + \begin{itemize} + \item Hexatrien und Ethylen + \item Octatetraen und Ethylen + \item Benzol und Ethylen + \end{itemize} + Für den Vergleich der NMR Spektren wurden die Bingrößen $b \in \{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0\}$ verwendet. Der Ähnlichkeitsindex wurde als Mittelwert des Ähnlichkeitsindex für alle Bingrößen genommen. Die finale Wahrscheinlichkeit entspricht dem Ähnlichkeitsindex normalisiert für jedes Referenzspektrum. + \begin{table} + \caption{Resultierende Wahrscheinlichkeiten für den Vergleich aller aus Butadien Entwickelten Moleküle mit Hexatrien und Ethylen, Octatetraen und Ethylen und Benzol und Etylen.} + \begin{center} + \scriptsize + \begin{tabular}{ |c|c|c|c| } + \label{nmrsimbenz} + Molekül & Hexatrien und Ethylen & Octatetraen und Ethylen & Benzol und Etylen \\ + \hline + Butadien & 0.11 & 0.11 & 0.0\\ + Ethylen & 0.18 & 0.15 & 0.17\\ + Hexatrien & 0.31 & 0.21 & 0.0\\ + 4-Vinyl-Cyclohex-1-en & 0.0 & 0.0 & 0.0\\ + 4-Vinyl-Octa-1,7-Dien & 0.04 & 0.04 & 0.0\\ + Octatetraen & 0.21 & 0.31 & 0.0\\ + 4-Butadienyl-Cyclohex-1-en & 0.02 & 0.02 & 0.03\\ + 3-Vinyl-Cyclohex1en & 0.0 & 0.0 & 0.0\\ + Cyclohexen & 0.0 & 0.0 & 0.0\\ + 4,5-Divinyl-Cyclohex-1-en & 0.0 & 0.0 & 0.01\\ + 3,4-Divinyl-Cyclohex-1-en & 0.0 & 0.0 & 0.0\\ + 3,5-Divinyl-Cyclohex-1-en & 0.0 & 0.0 & 0.16\\ + Benzol & 0.0 & 0.0 & 0.51\\ + 5-Butan-1-enyl-Cyclo-1,3-dien & 0.0 & 0.0 & 0.09\\ + 3-Butadienyl-Cyclohex-1-en & 0.03 & 0.03 & 0.0\\ + 3-Vinyl-Octa-1,7-Dien & 0.0 & 0.0 & 0.0\\ + Okta-1,7-dien & 0.0 & 0.0 & 0.0\\ + 3,6-Divinyl-Cyclohex1en & 0.06 & 0.07 & 0.0\\ + 1,2,3,4,4a,5,6,7,8,8a-Octahydronaphthalin & 0.0 & 0.0 & 0.0\\ + 1,4,4a,8a-Tetrahydronaphthalin & 0.03 & 0.04 & 0.03\\ + \hline + \end{tabular} + \end{center} + \end{table} + Das Referenzspekrtrum mit Hexatrien und Ethylen weißt eine große Ähnlichkeit mit den beiden tatsächlichen Molekülen auf. Die Ähnlichkeit zum Referenzspektrum liegt für Ethylen bei 0.18 und für Hexatrien bei 0.31. Die Moleküle Butadien mit 0.11 und Octatetraen mit 0.21 weisen ebenfalls eine hohe Ähnlichkeit zum Referenzspektrum auf. Da es sich bei Octatetraen, Hexatrien und Butadien um Kohlenstoffketten mit alternierenden Einfach- und Doppelbindungen ist diese Ähnlichkeit zu erwarten. Alle drei haben ein Signal bei ca. 122 ppm, und ein Signal bei ca. 145 ppm. Die längeren Ketten haben dabei ein Signal bei ca. 140 ppm zusätzlich, weshalb der Überlapp bei Hexatrien und Octatetraen etwas größer ist. + Das Referenzspektrum mit Octatetraen und Ethylen weißt eine große Ähnlichkeit mit beiden tatsächlichen Molekülen auf. Die Ähnlichkeit zum Referenzspektrum liegt für Ethylen bei 0.15 und für Octatetraen bei 0.31. Die Moleküle butadien mit 0.11 und Hexatrien mit 0.21 weisen ebenfalls eine hohe Ähnlichkeit zum Referenzspektrum auf. Die Gründe dafür sind wie beim ersten Referenzsspektrum, da der Ähnlichkeitsindex $SI$ zweier Moleküle Symmetrisch ist. + Das Referenzspektrum mit Benzol und Etyhlen hat die größte Ähnlichkeit mit den beiden tatsächlich im Spektrum enthaltenden Stoffen, Ethylen mit 0.17 und Benzol mit 0.51. Es gibt aber auch einige weitere Stoffe wie 5-Butan-1-enyl-Cyclo-1,3-dien und 3,5-Divinyl-Cyclohex-1-en, welche mit 0.09 und 0.16 ebenfalls eine deutliche Ähnlichkeit aufweisen. Diese Ähnlichkeit liegt daran, dass der eine Benzolpeak bei ca. 132.96 ppm mit Peaks aus den anderen beiden Spektren überlagert. Beide Moleküle haben einen Peak bei 132.93 und 133.29 ppm respektive. Da der Peak von 5-Butan-1-enyl-Cyclo-1,3-dien näher liegt ist die Ähnlichkeit größer. + Diese Vergleiche demonstrieren die Limitationen eines simpleren Ansatz wie dem Binning mit Crosskorrelation. Ähnliche Moleküle mit vergleichbaren chemischen Verschiebungen können einen hohen Ähnlichkeitsindex $SI$ aufweisen, auch wenn die Anzahl der Peaks nicht zum Molekül passt. Die tiefer gehenden chemischen Informationen können so verloren gehen. + \subsection{ILP: Multi Molekül Reaktionen} + Für die Definition des ILP Problems wurde der Hypergraph über alle mit M\o{}d entwickelten Reaktionen definiert. Dabei besteht eine Kante, die den Ausgangsstoff in das System einführen kann und für jedes andere Molekül eine Kante, die es aus dem System entfernt. Die Kanten, bei der die Edukte und Produkte identisch zueinander sind wurden aufgrund ihrer Redundanz entfernt. + \subsubsection{ILP: Olefin Metathes und Diels Alder} + \paragraph{Kantenwahrscheinlichkeit} + Die Wahrscheinlichkeiten wurden als konstante Werte $p_{i,e}$ den Kanten $e$ des Hypergraphen zugeordnet. Die Wahrscheinlichkeit wurde der Kante zugeordnet, welche in den Knoten fließt. Im der Olefinmetathese fließt jede Kante entweder in keine, ein oder zwei Edukte. Augehende Kanten, die ins nichts fließen sollten in der Zieflunktion nicht berücksichtigt werden. Die chemischen Reaktionen sind also nur die Kanten mit ein oder zwei Produkten. Da den Produkten Wahrscheinlichkeitswerte zugewiesen sind liegt nahe, dass die Gesamtwahrscheinlichkeit dem Produkt beider Einzelwahrscheinlichkeiten der Produkte entspricht. Da die Wahrscheinlichkeiten kleiner als 1 sind, wird dies bei Kanten mit zwei Edukten zu kleineren Wahrscheinlichkeiten führen als bei Kanten mit nur einem Edukt. Ein weiterer Ansatz ist den Mittelwert beider Produkte zu wählen. Diese Lösung sorgt dafür, dass eine Kante mit einem sehr unwahrscheinlichen und einem sehr wahrscheinlichen Produkt trotzdem eine mittlere Gesamtwahrscheinlichkeit hat. Wir betrachten zur demonstration der Kantenwahrscheinlichkeit zwei Kanten im Hypergraphen bezüglich ihrer Wahrscheinlichkeit für das dritte Referenzspektrum. + \begin{itemize} + \item 42: Octatetraen $\rightarrow$ Benzol + Ethylen + \item 44: 4-Butadienyl-Cyclohex-1-en $\rightarrow$ 5-Butan-1-enyl-Cyclo-1,3-dien + \end{itemize} + Die Wahrscheinlichkeiten für Kanten mit nur einem Produkt entsprechen der Wahrscheinlichkeit für dieses Produkt. Demnach hat die Kante 44 für das dritte Referenzspektrum die Wahrscheinlichkeit $p_{3,44}$ für Durchschnitt und Produkt. Kante 42 hingegen hat die Wahrscheinlichkeit 0.0876 für das Produkt (Gleichung \ref{pprod}) und 0.34 (Gleichung \ref{pavg}). + \begin{equation} \label{pprod} + p_{3,42} = 0.51 \times 0.17 = 0.0876 + \end{equation} + \begin{equation} \label{pavg} + p_{3,42} = \frac {0.51 + 0.17} {2} = 0.34 + \end{equation} + Für jede Kante werden fünf ganzzahlige Variablen $x_{e}$, $b_{e}$, $n_{1,e}$, $n_{2,e}$ und $n_{3,e}$ definiert. Die Variable $b_{e}$ ist dabei eine Wahrheitsvariable, die definiert ob eine Kante verwendet wird. Die Variable $x_{e}$ beschreibt wie oft die selbe Kante verwendet wird. Die Variablen $n_{1,e}$, $n_{2,e}$ und $n_{3,e}$ sind ebenfalls Wahrheitsvariablen und legen fest, welche drei Reaktionen den Referenz NMR-Spektren entsprechen und deswegen zu der Zielfunktion da zuzählen. Dabei ist $n_{1,e}$ die Zuordnungsvariable zu dem ersten Referenz NMR-Spektrum mit Hexatrien und Ethylen, $n_{2,e}$ die Zuordnungsvariable zu dem zweiten Referenz NMR-Spektrum mit Octatetraen und Ethylen und $n_{3,e}$ die Zuordnungsvariable zum dritten Referenz NMR-Spektrum mit Benzol und Ethylen. Da das ILP aus den Startmolekülen die den NMR Spektren nach Wahrscheinlichste Lösung zu finden, ist kein Molekül als Zielmolekül definiert. + Die Variablen unterliegen den Beschränkungen, dass: + \begin{itemize} + \item $x_{e} \geq b_{e}$ + \item $b_{e} \geq n_{1,e}$ + \item $b_{e} \geq n_{2,e}$ + \item $b_{e} \geq n_{3,e}$ + \item flow ([], [Startmolekül]) = 3 + \item Für jedes Molekül: inflow = outflow + \item Für jedes Kantenpaar: i: head $\rightarrow$ tail und j: tail $\rightarrow$ $\sum b_{i} + b_{j} \leq 1$ + \item $n_{1,e} + n_{2,e} + n_{3,e} \leq 1$ + \item $\sum_{e} n_{1,e} = 1$ + \item $\sum_{e} n_{2,e} = 1$ + \item $\sum_{e} n_{3,e} = 1$ + \item wenn die größte Wahrscheinlichkeit einer nicht ausgehenden Kante $p_{max,e} = 0$ ist, wird diese stattdessen auf $p_{max,e} = 0.0001$ gesetzt um einen Wertfehler zu verhindern + \end{itemize} + Unter diesen Beschränkungen soll ein Pfad durch den Hypergraphen bestimmt werden, welcher die drei Wahrscheinlichsten Kanten für die drei Referenzspektren auswählt dabei möglichst wenige unwahrscheinliche Kanten beinhaltet. Die ausgehenden Kanten sind nicht in die Zielfunktion eingeflossen (Gleichung \ref{objectivebutadien}). + \begin{equation} \label{objectivebutadien} + max Obj = \sum_{e} 1000 \times (p_{1,e} \times n_{1,e} + p_{2,e} \times n_{2,e} + p_{3,e} \times n_{3,e}) \newline - \frac{x_{e}}{ max(p_{1,e}, p_{2,e}, p_{3,e})} + \end{equation} + Für beide Kantenwahrscheinlichkeitsdefinitionen wurden jeweils die 10 besten Lösungen gesucht. + \paragraph{Knoten Auswahl} + Ein Ansatz der unabhängig von der Auswahl der Kantenwahrscheinlichkeitsberechnung ist, aus den NMR-Spektren Zielmoleküle zu wählen und einen Pfad zu finden, der diese synthetisiert. Dafür wurde jedem Molekül $v$ die Wahrscheinlichkeit $p_{i,v}$ direkt zugeordnet. Für jede Kante des Hypergraphen werden zwei Variablen $x_{e}$ und $b_{e}$ definiert. Die Variable $b_{e}$ ist dabei eine Wahrheitsvariable, die definiert ob eine Kante verwendet wird. Die Variable $x_{e}$ beschreibt wie oft die selbe Kante verwendet wird. Für jeden Knoten des Hypergraphen werden drei Variablen $n_{1,e}$, $n_{2,e}$ und $n_{3,e}$ definiert. Diese drei Variablen sind ebenfalls Wahrheitsvariablen und legen fest, welche drei Moleküle den drei Referenzspektren entsprechen. Dabei ist $n_{1,e}$ die Zuordnungsvariable zu dem ersten Referenz NMR-Spektrum mit Hexatrien und Ethylen, $n_{2,e}$ die Zuordnungsvariable zu dem zweiten Referenz NMR-Spektrum mit Octatetraen und Ethylen und $n_{3,e}$ die Zuordnungsvariable zum dritten Referenz NMR-Spektrum mit Benzol und Ethylen. + Die Variablen unterliegen den Beschränkungen, dass: + \begin{itemize} + \item $x_{e} \geq b_{e}$ + \item Hilfsvariable: $m_{v} = \sum{e} b_{e}: v \in head(b_{e})$ + \item $m_{v} \geq n_{1,v}$ + \item $m_{v} \geq n_{2,v}$ + \item $m_{v} \geq n_{3,v}$ + \item flow ([], [Startmolekül]) = 3 + \item Für jedes Molekül: inflow = outflow + \item Für jedes Kantenpaar: i: head $\rightarrow$ tail und j: tail $\rightarrow$ $\sum b_{i} + b_{j} \leq 1$ + \item $n_{1,v} + n_{2,v} + n_{3,v} \leq 1$ + \item $\sum_{v} n_{1,v} = 1$ + \item $\sum_{v} n_{2,v} = 1$ + \item $\sum_{v} n_{3,v} = 1$ + \end{itemize} + Dabei soll die Wahrscheinlichkeit der ausgewählten Moleküle maximiert werden (Gleichung \ref{objspecmain}) + \begin{equation} \label{objspecmain} + \sum_{v}\sum_{i} n_{i,v} \times p_{i,v} + \end{equation} + Wenn es mehrere Lösungen gibt, die den gleichen Wert für die Zielfunktion $z$ haben, werden diese erst danach sortiert, welche Lösung die geringste Anzahl an Reaktionen hat (Gleichung \ref{objspecsec}) und bei der gleichen Anzahl an Reaktionen, nach dem geringsten flow (Gleichung \ref{objtrd}). + \begin{equation} \label{objspecsec} + \sum_{e} b_{e} + \end{equation} + \begin{equation} \label{objspectrd} + \sum_{e} x_{e} + \end{equation} + Für die Lösung des ILP wurden die beiden besten Lösungen bestimmt. + \begin{table} + \caption{Lösung 1 für die Knotenauswahl beim ILP vom Butadien Beispiel mit $z = 3$.} + \begin{center} + \scriptsize + \begin{tabular}{ |c|c|c|c| } + \label{ilpspec1} + Flow & Kante & Edukt & Produkt \\ + \hline + 3 & 1 & Ethylen & \\ + 1 & 4 & 2 Butadien & Hexatrien + Ethylen\\ + 1 & 23 & Butadien + Hexatrien & Octatetraen + Ethylen\\ + 1 & 41 & Benzol & \\ + 1 & 42 & Octatetraen & Benzol + Ethylen\\ + 3 & 213 & & Butadien\\ + \hline + \end{tabular} + \end{center} + \end{table} + \begin{table} + \caption{Lösung 2 für die Knotenauswahl beim ILP vom Butadien Beispiel mit $z = 4$.} + \begin{center} + \scriptsize + \begin{tabular}{ |c|c|c|c| } + \label{ilpspec2} + Flow & Kante & Edukt & Produkt \\ + \hline + 3 & 1 & Ethylen & \\ + 2 & 4 & 2 Butadien & Hexatrien + Ethylen\\ + 1 & 18 & 2 Hexatrien & Octatetraen + Butadien\\ + 1 & 41 & Benzol & \\ + 1 & 42 & Octatetraen & Benzol + Ethylen\\ + 3 & 213 & & Butadien\\ + \hline + \end{tabular} + \end{center} + \end{table} + Beide Lösungen die aus der Auswahl der besten Knoten resultieren ergeben chemisch Sinn. Die erste Lösung (Tabelle \ref{ilpspec1}) ist die erwartete Lösung. Die zweite Lösung (Tabelle \ref{ilpspec2}) verwendet viele der gleichen Kanten, aber Produziert mit Kante 18, Octatetraen aus zwei Hexatrien. Diese Variation ist ebenfalls erwartbar. + \subsection{Petrinetz Zertifikat: Multi Molekül Reaktionen} + Durch den einfachen Optimierungsprozess des ILP wird die Zielfunktion maximiert und eine Menge an Kanten zurückgegeben. Diese Kanten haben keine Reihenfolge oder Zusammenhang abseits der Definition des ILP. Darum kommt es oft vor, dass die Reaktionen in Sequenz ein Molekül für eine Reaktion benötigen, welches erst durch eine andere Reaktion erzeugt wird. Beide Reaktioen ließen sich so nur chemisch Durchführen, wenn die jeweils andere zuvor stattgefunden hat. Um solche Lösungen des ILP Problems auszuschließen wurde für jede Lösung ein Petrinetzzertifikat erstellt. + \subsubsection{Petrinetz Zertifikat: Olefin Metathes und Diels Alder} + \paragraph{Produkt} + Nach der Untersuchung mit einem Petrinetz basierend auf dem Hypergraphen konnte nur eine Lösung zertifiziert werden (Tabelle \ref{ilpprodzert}) + \begin{table} + \caption{Lösung 10 für die Kantenwahrscheinlichkeit als Produkt beim ILP vom Butadien Beispiel mit $z = 197.08$.} + \begin{center} + \scriptsize + \begin{tabular}{ |c|c|c|c| } + \label{ilpprodzert} + Flow & Kante & Edukt & Produkt \\ + \hline + 1 & 1 & Ethylen & \\ + 1 & 4 & 2 Butadien & Hexatrien + Ethylen\\ + 1 & 36 & 3,5-Divinyl-Cyclohex-1-en & \\ + 1 & 37 & Butadien + Ethylen & 3,5-Divinyl-Cyclohex-1-en\\ + 3 & 213 & & Butadien\\ + \hline + \end{tabular} + \end{center} + \end{table} + Diese Lösung entspricht nicht der erwarteten Synthese von Benzol aus Butadien (Abb. \ref{benzsynthmod}). + \paragraph{Durchschnitt} + \begin{table} + \caption{Lösung 5 für die Kantenwahrscheinlichkeit als Durchschnitt beim ILP vom Butadien Beispiel mit $z = 798.54$.} + \begin{center} + \scriptsize + \begin{tabular}{ |c|c|c|c| } + \label{ilpavgzert} + Flow & Kante & Edukt & Produkt \\ + \hline + 3 & 1 & Ethylen & \\ + 1 & 4 & 2 Butadien & Hexatrien + Ethylen\\ + 1 & 23 & Butadien + Hexatrien & Octatetraen + Ethylen\\ + 1 & 41 & Benzol & \\ + 1 & 42 & Octatetraen & Benzol + Ethylen\\ + 3 & 213 & & Butadien\\ + \hline + \end{tabular} + \end{center} + \end{table} + Diese Lösung entspricht der erwarteten Synthese von Benzol aus Butadien (Abb. \ref{benzsynthmod}). + \paragraph{Knoten Auswahl} + Beide Lösungen der Knotenauswahlmethode erfüllen ein Petrinetzzertifikat. - - - - - \newpage + \section{Ziel Moleküle} + Eine Methode um die Wahl zur Berechnung der Kantenwahrscheinlichkeit zu umgehen, ist durch die NMR-Spektren Moleküle auszuwählen und den Flow zu diesen Molekülen zu + \section{Ausblick} + \clearpage \printbibliography - \newpage + \clearpage \section{Eigenständigkeitserklärung} Hiermit versichere ich, dass ich die vorliegende Arbeit selbstständig angefertigt und keine anderen als die angegebenen Hilfsmittel benutzt habe. Alle Stellen, die dem Wortlaut oder dem diff --git a/Report/refs.bib b/Report/refs.bib index 59310c5..f0e01f4 100644 --- a/Report/refs.bib +++ b/Report/refs.bib @@ -202,5 +202,438 @@ primaryClass={cs.FL}, url={https://arxiv.org/abs/1603.02481}, } +@inproceedings{networkx, + abstract = {NetworkX is a Python language package for exploration + and analysis of networks and network algorithms. + The core package provides data structures + for representing many types of networks, or graphs, + including simple graphs, directed graphs, and graphs + with parallel edges and self-loops. The nodes in NetworkX + graphs can be any (hashable) Python object + and edges can contain arbitrary data; this flexibility + makes NetworkX ideal for representing networks + found in many different scientific fields. + In addition to the basic data structures many graph + algorithms are implemented for calculating network + properties and structure measures: shortest paths, + betweenness centrality, clustering, and degree distribution + and many more. NetworkX can read and + write various graph formats for easy exchange with + existing data, and provides generators for many + classic graphs and popular graph models, such as + the Erdos-Renyi, Small World, and Barabasi-Albert + models. + The ease-of-use and flexibility of the Python programming + language together with connection to the + SciPy tools make NetworkX a powerful tool for scientific + computations. We discuss some of our recent + work studying synchronization of coupled oscillators + to demonstrate how NetworkX enables research in + the field of computational networks.}, + added-at = {2008-09-24T13:11:32.000+0200}, + address = {Pasadena, CA USA}, + author = {Hagberg, Aric A. and Schult, Daniel A. and Swart, Pieter J.}, + biburl = {https://www.bibsonomy.org/bibtex/272096c6553d7057409fe78ca698eb332/mschuber}, + booktitle = {Proceedings of the 7th Python in Science Conference}, + editor = {Varoquaux, Ga\"el and Vaught, Travis and Millman, Jarrod}, + interhash = {7a78aca0e0e5adfc4d7e882e4635435f}, + intrahash = {72096c6553d7057409fe78ca698eb332}, + keywords = {2008 analysis network python tool}, + pages = {11 - 15}, + timestamp = {2008-09-24T13:11:32.000+0200}, + title = {Exploring Network Structure, Dynamics, and Function using NetworkX}, + url = {http://conference.scipy.org/proceedings/SciPy2008/paper_2/}, + year = 2008 +} +@article{rdkit, + added-at = {2017-04-11T06:11:47.000+0200}, + author = {Landrum, Greg}, + biburl = {https://www.bibsonomy.org/bibtex/28d01fceeccd6bf2486e47d7c4207b108/salotz}, + description = {Release 2016_09_4 (Q3 2016) Release · rdkit/rdkit}, + interhash = {ee9a4ddeff3121aa622cf35709fa6e21}, + intrahash = {8d01fceeccd6bf2486e47d7c4207b108}, + keywords = {chemoinformatics drug-design pharmacophores software}, + timestamp = {2017-04-11T06:11:47.000+0200}, + title = {RDKit: Open-Source Cheminformatics Software}, + url = {https://github.com/rdkit/rdkit/releases/tag/Release_2016_09_4}, + year = 2016 +} +@article{avogadro, + author={Hanwell, Marcus D. + and Curtis, Donald E. + and Lonie, David C. + and Vandermeersch, Tim + and Zurek, Eva + and Hutchison, Geoffrey R.}, + title={Avogadro: an advanced semantic chemical editor, visualization, and analysis platform}, + journal={Journal of Cheminformatics}, + year={2012}, + month={Aug}, + day={13}, + volume={4}, + number={1}, + pages={17}, + abstract={The Avogadro project has developed an advanced molecule editor and visualizer designed for cross-platform use in computational chemistry, molecular modeling, bioinformatics, materials science, and related areas. It offers flexible, high quality rendering, and a powerful plugin architecture. Typical uses include building molecular structures, formatting input files, and analyzing output of a wide variety of computational chemistry packages. By using the CML file format as its native document type, Avogadro seeks to enhance the semantic accessibility of chemical data types.}, + issn={1758-2946}, + doi={10.1186/1758-2946-4-17}, + url={https://doi.org/10.1186/1758-2946-4-17} +} +@article{nmrbin, + title = {A novel spectra similarity measure}, + journal = {Chemometrics and Intelligent Laboratory Systems}, + volume = {85}, + number = {1}, + pages = {1-8}, + year = {2007}, + issn = {0169-7439}, + doi = {https://doi.org/10.1016/j.chemolab.2005.10.002}, + url = {https://www.sciencedirect.com/science/article/pii/S0169743905001620}, + author = {Lorant Bodis and Alfred Ross and Ernö Pretsch}, + keywords = {Spectra comparison, NMR spectra, Quality control}, + abstract = {A new method is described for calculating the similarity degree of two spectra. Its performance is optimized with similar, computer-generated 1H NMR spectra. The method is compared with a recently proposed local cross-correlation method. Using a test set, its power to discriminate between related and unrelated 1H NMR spectra is better than with the cross-correlation method. Better results are also obtained when comparing measured spectra of a database with the corresponding estimated ones or with estimated spectra of randomly assigned structures. Although, so far, it has only been tested with 1H NMR spectra, due to the generality of the approach, the novel procedure can be applied to comparing other spectra or patterns as well.} +} +@misc{gurobi, + author = {{Gurobi Optimization, LLC}}, + title = {{Gurobi Optimizer Reference Manual}}, + year = {2026}, + url = {https://www.gurobi.com} +} +@Article{caffeinesynth, + AUTHOR = {Lin, Zhipeng and Wei, Jian and Hu, Yongqiang and Pi, Dujuan and Jiang, Mingguo and Lang, Tao}, + TITLE = {Caffeine Synthesis and Its Mechanism and Application by Microbial Degradation, A Review}, + JOURNAL = {Foods}, + VOLUME = {12}, + YEAR = {2023}, + NUMBER = {14}, + ARTICLE-NUMBER = {2721}, + URL = {https://www.mdpi.com/2304-8158/12/14/2721}, + PubMedID = {37509813}, + ISSN = {2304-8158}, + ABSTRACT = {Caffeine is a metabolite derived from purine nucleotides, typically accounting for 2–5 Percent of the dry weight of tea and 1–2 Percent of the dry weight of coffee. In the tea and coffee plants, the main synthesis pathway of caffeine is a four-step sequence consisting of three methylation reactions and one nucleosidase reaction using xanthine as a precursor. In bacteria, caffeine degradation occurs mainly through the pathways of N-demethylation and C-8 oxidation. However, a study fully and systematically summarizing the metabolism and application of caffeine in microorganisms has not been established elsewhere. In the present study, we provide a review of the biosynthesis, microbial degradation, gene expression, and application of caffeine microbial degradation. The present review aims to further elaborate the mechanism of caffeine metabolism by microorganisms and explore the development prospects in this field.}, + DOI = {10.3390/foods12142721} +} +@Article{vanillinesynth, + AUTHOR = {Tazon, Arnold William and Awwad, Fatima and Meddeb-Mouelhi, Fatma and Desgagné-Penix, Isabel}, + TITLE = {Biotechnological Advances in Vanillin Production: From Natural Vanilla to Metabolic Engineering Platforms}, + JOURNAL = {BioChem}, + VOLUME = {4}, + YEAR = {2024}, + NUMBER = {4}, + PAGES = {323--349}, + URL = {https://www.mdpi.com/2673-6411/4/4/17}, + ISSN = {2673-6411}, + ABSTRACT = {Vanillin, an aromatic aldehyde, is one of the most popular flavors worldwide, extensively used in the food, cosmetics, pharmaceutical, and agrochemical industries. Despite its widespread use, less than 1 Percent of the total vanillin production is natural, with the majority being synthesized chemically. While chemical synthesis can help to meet the growing demand for vanillin, a strong market trend has rapidly developed for products created from natural ingredients, including natural vanillin. Given the labor-intensive process of extracting vanillin from vanilla pods, there is a critical need for new metabolic engineering platforms to support the biotechnological production of nature-identical vanillin. This review highlights the significance of vanillin in various markets, its diverse applications, and the current state of bio-engineered production using both prokaryotic and eukaryotic biological systems. Although recent advancements have demonstrated successful vanillin production through biocatalytic approaches, our focus was to provide a current and innovative overview of vanillin bioengineering across various host systems with special consideration placed on microalgae, which are emerging as promising platforms for vanillin production through metabolic engineering. The use of these systems to support the biotechnological production of vanillin, while leveraging the photosynthetic capabilities of microalgae to capture CO2 and convert it into biomass, can significantly reduce the overall carbon footprint.}, + DOI = {10.3390/biochem4040017} +} +@article{xanthinnmr, + author = {Benoit, Robert L. and Fréchette, Monique}, + title = {Protonation of hypoxanthine, guanine, xanthine, and caffeine}, + journal = {Canadian Journal of Chemistry}, + volume = {63}, + number = {11}, + pages = {3053-3056}, + year = {1985}, + doi = {10.1139/v85-506}, + URL = { + https://doi.org/10.1139/v85-506 + }, + eprint = { + https://doi.org/10.1139/v85-506 + } + , + abstract = { The protonation equilibria of three hydroxypurines, hypoxanthine, guanine, and xanthine, and of related caffeine have been studied by 1H and 13C nmr and uv spectroscopies in aqueous sulfuric or perchloric acids. The results have been interpreted on the basis of the excess acidity method. The values and the protonation sites are discussed and comparisons are made with results of recent theoretical calculations. } +} +@article{manyxanthinesnmr, + author = {Mueller, Christa E. and Shi, Dan and Manning, Malcolm, Jr. and Daly, John W.}, + title = {Synthesis of paraxanthine analogs (1,7-disubstituted xanthines) and other xanthines unsubstituted at the 3-position: structure-activity relationships at adenosine receptors}, + journal = {Journal of Medicinal Chemistry}, + volume = {36}, + number = {22}, + pages = {3341-3349}, + year = {1993}, + month = {10}, + issn = {0022-2623}, + doi = {10.1021/jm00074a015}, + url = {https://doi.org/10.1021/jm00074a015}, + eprint = {https://pubs.acs.org/jmcmar/article-pdf/36/22/3341/7236147/jm00074a015.pdf}, +} +@article{7xanthinnmr, + author = {Jayantha, Bhagya and Zhang, Shuyuan and Summers, Ryan M. and Mendis, Gamini P. and Jayakody, Lahiru N.}, + title = {Engineered Pseudomonas putida monoculture system for green synthesis of 7-methylxanthine}, + journal = {Green Chemistry}, + volume = {27}, + number = {37}, + pages = {11365-11379}, + year = {2025}, + month = {10}, + abstract = { 7-Methylxanthine (7-MX) is a clinically proven safe drug to treat myopia. The chemical synthesis of 7-MX is hindered due to low specificity, demanding sustainable biological production using renewable, cost-effective feedstocks. To this end, we systematically engineered robust P. putida EM42 to produce 7-MX using caffeine and glycerol in minimal salt media. Removing the transcriptional repressor (glpR), genome integration of heterologous N-demethylase and its reductase, ndmABD, and overexpression of native fdhA to balance the redox cofactors enabled the selective conversion of caffeine to 7-MX with 100\% yield. We discovered a native transporter, PP\_RS18750, that efficiently takes up caffeine, facilitating the conversion in glycerol-containing media. We achieved 9.2 ± 0.42 g L−1 of 7-MX in a 3-L bioreactor by process-level optimization, the highest titer reported to date. Our techno-economic analysis indicates that this novel engineered monoculture approach can produce pharmaceutical-grade 7-MX commercially for \$328 per kg, with remarkably low E-factor and Process Mass Intensity (PMI) values, demonstrating the sustainable green valorization of caffeine into high-value methylated xanthine. }, + issn = {1463-9262}, + doi = {10.1039/d5gc02883c}, + url = {https://doi.org/10.1039/d5gc02883c}, + eprint = {https://pubs.rsc.org/gc/article-pdf/27/37/11365/10400487/d5gc02883c.pdf}, +} +@article{theobrominnoMenmr, + author = {Bouzková, Kateřina and Babinský, Martin and Novosadová, Lucie and Marek, Radek}, + title = {Intermolecular Interactions in Crystalline Theobromine + as Reflected in Electron Deformation Density and 13C NMR + Chemical Shift Tensors}, + journal = {Journal of Chemical Theory and Computation}, + volume = {9}, + number = {6}, + pages = {2629-2638}, + year = {2013}, + month = {06}, + abstract = {An understanding of the role of intermolecular + interactions in + crystal formation is essential to control the generation of diverse + crystalline forms which is an important concern for pharmaceutical + industry. Very recently, we reported a new approach to interpret the + relationships between intermolecular hydrogen bonding, redistribution + of electron density in the system, and NMR chemical shifts (Babinský + et al. J. Phys. Chem. A, 2013, 117, 497). Here, we employ this approach to characterize + a full set of crystal interactions in a sample of anhydrous theobromine + as reflected in 13C NMR chemical shift tensors (CSTs). + The important intermolecular contacts are identified by comparing + the DFT-calculated NMR CSTs for an isolated theobromine molecule and + for clusters composed of several molecules as selected from the available + X-ray diffraction data. Furthermore, electron deformation density + (EDD) and shielding deformation density (SDD) in the proximity of + the nuclei involved in the proposed interactions are calculated and + visualized. In addition to the recently reported observations for + hydrogen bonding, we focus here particularly on the stacking interactions. + Although the principal relations between the EDD and CST for hydrogen + bonding (HB) and stacking interactions are similar, the real-space + consequences are rather different. Whereas the CHX + hydrogen bonding influences predominantly and significantly the in-plane + principal component of the 13C CST perpendicular to the + HB path and the CH hydrogen bonding modulates + both in-plane components of the carbonyl 13C CST, the stacking + modulates the out-of-plane electron density resulting in weak deshielding + (2–8 ppm) of both in-plane principal components of the CST + and weak shielding (ca. 5 ppm) of the out-of-plane component. + The hydrogen-bonding and stacking interactions may add to or subtract + from one another to produce total values observed experimentally. + On the example of theobromine, we demonstrate the power of this approach + to identify and classify the intermolecular forces that govern the + packing motifs in crystals and modulate the NMR CSTs.}, + issn = {1549-9618}, + doi = {10.1021/ct400209b}, + url = {https://doi.org/10.1021/ct400209b}, + eprint = {https://pubs.acs.org/jctcce/article-pdf/9/6/2629/8808212/ct400209b.pdf}, +} +@article{theobrominnmr, + author = {Thevis, Mario and Opfermann, Georg and Krug, Oliver and Schänzer, Wilhelm}, + title = {Electrospray ionization mass spectrometric characterization and quantitation of xanthine derivatives using isotopically labelled analogues: an application for equine doping control analysis}, + journal = {Rapid Communications in Mass Spectrometry}, + volume = {18}, + number = {14}, + pages = {1553-1560}, + doi = {https://doi.org/10.1002/rcm.1518}, + url = {https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/abs/10.1002/rcm.1518}, + eprint = {https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/pdf/10.1002/rcm.1518}, + abstract = {Abstract Isotope-dilution mass spectrometry has been employed successfully in numerous fields of analytical chemistry enabling the establishment of fast and reliable procedures. In equine sports, xanthine derivatives such as caffeine and theobromine are prohibited, and doping control laboratories analyze horse urine specimens regarding these illicit performance-enhancing drugs. Theobromine has to exceed a threshold level of 2 μg/mL, hence a robust and reliable quantitation is required. Stably deuterated theobromine and caffeine were synthesized by the reaction of xanthine or theobromine with iodomethane-d3 in the presence of N-methyl-N-trimethylsilyltrifluoroacetamide or potassium carbonate in acetonitrile, respectively. Both compounds were characterized by nuclear magnetic resonance spectroscopy and electrospray ionization tandem mass spectrometry, and a robust and fast assay for the qualitative and quantitative analysis of theobromine in equine urine samples was validated. Urine specimens were extracted by means of solid-phase extraction cartridges, and concentrated extracts were analyzed by liquid chromatography interfaced to a triple-quadrupole mass spectrometer. In addition, the dissociation behavior of deuterated analogues to caffeine and theobromine allowed proposals for fragmentation routes of xanthine derivatives after atmospheric pressure ionization and collisionally activated dissociation. Copyright C 2004 John Wiley and Sons, Ltd.}, + year = {2004} +} +@article{cinamnmr, + title = {A comparative vibrational and NMR study of cis-cinnamic acid polymorphs and trans-cinnamic acid}, + journal = {Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy}, + volume = {57}, + number = {3}, + pages = {513-519}, + year = {2001}, + issn = {1386-1425}, + doi = {https://doi.org/10.1016/S1386-1425(00)00401-7}, + url = {https://www.sciencedirect.com/science/article/pii/S1386142500004017}, + author = {Kazuhiko Hanai and Akio Kuwae and Takatomo Takai and Hitoshi Senda and Ko-Ki Kunimoto}, + keywords = {-Cinnamic acid, -Cinnamic acid, Polymorphism, IR/Raman spectra, NMR spectra}, + abstract = {The IR and Raman spectra of the two polymorphic forms (58°- and 68°-forms) of cis-cinnamic acid were measured, and the spectral differences discussed on the basis of the crystal structures of the two forms. The IR bands related to the COOH group differ in the frequencies and band shape, reflecting differences in the hydrogen bonding between the two modifications. These spectra were compared with those of trans-cinnamic acid. The IR, Raman, and NMR spectra of the isotopic compounds, including the deuterated and 13C analogs of the cis and trans acids, were also recorded in the solid state and in solution to confirm the spectral assignments.} +} +@article{mcoumnmr, + author = {Nakazawa, Takahiro and Ohsawa, Keisuke}, + title = {Metabolism of Rosmarinic Acid in Rats}, + journal = {Journal of Natural Products}, + volume = {61}, + number = {8}, + pages = {993-996}, + year = {1998}, + month = {08}, + abstract = {The urine of rats administered rosmarinic acid (7) orally contained seven metabolites, which + were identified as trans-caffeic acid 4-O-sulfate (1), trans-m-coumaric acid 3-O-sulfate (2), trans-ferulic acid 4-O-sulfate (3), trans-caffeic acid (4), m-hydroxyphenylpropionic acid (5), trans-m-coumaric acid (6), and unchanged rosmarinic acid (7) by spectroscopic and chemical data. The + total cumulative amount of 1−7 excreted in the urine 48 h after the oral administration of + rosmarinic acid was approximately 31.8 Percent of the dose administered. On the other hand, the + metabolites attributed to rosmarinic acid could not be found in the bile. Orally administered + rosmarinic acid may thus be concluded to be excreted in the urine rather than in the bile, with + cleavage of ester bonds, selective para-dehydroxylation, methylation, and sulfate-conjugation. + Metabolites 2, 3, 5, and 6 were also detected in the plasma. }, + issn = {0163-3864}, + doi = {10.1021/np980072s}, + url = {https://doi.org/10.1021/np980072s}, + eprint = {https://pubs.acs.org/jnprdf/article-pdf/61/8/993/13045095/np980072s.pdf}, +} +@article{pcoumnmr, + author = {Świsłocka, Renata and Kowczyk-Sadowy, Małgorzata and Kalinowska, Monika and Lewandowski, Włodzimierz}, + title = {Spectroscopic (FT-IR, FT-Raman, 1H and 13C NMR) and theoretical studies of p-coumaric acid and alkali metal p-coumarates}, + journal = {Journal of Spectroscopy}, + volume = {27}, + number = {1}, + pages = {546146}, + keywords = {p-Coumaric acid, alkali metal p-coumarates, IR, Raman, NMR spectra}, + doi = {https://doi.org/10.3233/SPE-2012-0568}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.3233/SPE-2012-0568}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.3233/SPE-2012-0568}, + abstract = {The evaluation of the electronic charge distribution in metal complexes enables more precise interpretation of mechanism by which particular metal ions affect biochemical properties of ligands [J. Inorg. Biochem. 99 (2005), 1407–1423, J. Mol. Struct. 919 (2009), 284–289]. In this paper we investigated the influence of alkali metal cations (lithium, sodium, potassium, rubidium and cesium) on the electronic structure of p-coumaric acid (p-CA). It allowed to observe the systematic changes in the spectra of investigated complexes depending on the position of the element in the periodic table. p-Coumaric acid is a derivative of cinnamic acid that occurs in several plant species. Li, Na, K, Rb and Cs p-coumarates were synthesized and the experimental and theoretical FT-IR, FT-Raman, 1H and 13C NMR spectra of p-coumaric acid and its salts were registered and analyzed. The structures, atomic charges, infrared and NMR spectra of p-coumaric acid and Li, Na, K salts were calculated by B3LYP/6-311++G** method.}, + year = {2012} +} +@article{aldhnmr, + author = {Kuan, Fu-Hua and Inoue, Yoshio and Chûjô, Riichiro}, + title = {Structure and molecular dynamics of solid-state inclusion complexes of cyclodextrin and permethylated cyclodextrin with benzaldehyde studied by high-resolution CP/MAS13C NMR}, + journal = {Journal of inclusion phenomena}, + volume = {4}, + number = {3}, + pages = {281–290}, + doi = {https://doi.org/10.1007/BF00658002}, + eprint = {https://link.springer.com/article/10.1007/BF00658002}, + abstract = {The structure and molecular dynamics of the benzaldehyde inclusion-complexes with alpha-andbeta-cyclodextrins and permethylated alpha-cyclodextrin in the solid state have been studied by high-resolution cross-polarization/magic angle sample-spinning13C NMR spectroscopy. It is shown that the guest benzaldehyde molecule undergoes motion in the host cyclodextrin cavity and the rate of motion depend on the cavity size. In the alpha-cyclodextrin complex, compared to beta-and permethylated alpha-cyclodextrin complexes, the benzaldehyde motion is severely restricted, but under high-vacuum benzaldehyde is released more easily from the cavity.}, + year = {1986} +} +@Article{caffacdnmr, + AUTHOR = {Yu, Jiahui and Xie, Jingchen and Sun, Miao and Xiong, Suhui and Xu, Chunfang and Zhang, Zhimin and Li, Minjie and Li, Chun and Lin, Limei}, + TITLE = {Plant-Derived Caffeic Acid and Its Derivatives: An Overview of Their NMR Data and Biosynthetic Pathways}, + JOURNAL = {Molecules}, + VOLUME = {29}, + YEAR = {2024}, + NUMBER = {7}, + ARTICLE-NUMBER = {1625}, + URL = {https://www.mdpi.com/1420-3049/29/7/1625}, + PubMedID = {38611904}, + ISSN = {1420-3049}, + ABSTRACT = {In recent years, caffeic acid and its derivatives have received increasing attention due to their obvious physiological activities and wide distribution in nature. In this paper, to clarify the status of research on plant-derived caffeic acid and its derivatives, nuclear magnetic resonance spectroscopy data and possible biosynthetic pathways of these compounds were collected from scientific databases (SciFinder, PubMed and China Knowledge). According to different types of substituents, 17 caffeic acid and its derivatives can be divided into the following classes: caffeoyl ester derivatives, caffeyltartaric acid, caffeic acid amide derivatives, caffeoyl shikimic acid, caffeoyl quinic acid, caffeoyl danshens and caffeoyl glycoside. Generalization of their 13C-NMR and 1H-NMR data revealed that acylation with caffeic acid to form esters involves acylation shifts, which increase the chemical shift values of the corresponding carbons and decrease the chemical shift values of the corresponding carbons of caffeoyl. Once the hydroxyl group is ester, the hydrogen signal connected to the same carbon shifts to the low field (1.1~1.6). The biosynthetic pathways were summarized, and it was found that caffeic acid and its derivatives are first synthesized in plants through the shikimic acid pathway, in which phenylalanine is deaminated to cinnamic acid and then transformed into caffeic acid and its derivatives. The purpose of this review is to provide a reference for further research on the rapid structural identification and biofabrication of caffeic acid and its derivatives.}, + DOI = {10.3390/molecules29071625} +} +@article{mhydaldhnmr, + author = {Mart, H. and Sökmen, T. and Yürük, H.}, + title = {The synthesis and thermal properties of oligo-3-hydroxybenzaldehyde synthesized by oxidative polycondensation}, + journal = {Journal of Applied Polymer Science}, + volume = {101}, + number = {2}, + pages = {892-897}, + keywords = {oxidative polycondensation, polyaromatics, polyphenols, oligomers}, + doi = {https://doi.org/10.1002/app.23537}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/app.23537}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/app.23537}, + abstract = {Abstract Polymerization of 3-hydroxybenzaldehyde was investigated by oxidative polycondensation (OP) method. No polycondensation reaction was observed both in acidic (in CH3COOH) and organic (in THF) media. Polycondensation was carried out with hydrogenperoxide (H2O2) in an aqueous alkaline medium at 90°C. The product was characterized by 1H NMR, 13C NMR, FTIR, UV–vis, and elemental analysis. The number average molecular weight, mass average molecular weight, and polydispersity index values of O-3HBA were found to be 3600, 8000 g mol−1, and 2.22, respectively. The product (O-3HBA) with reactive aldehyde and hydroxyl group was soluble in most polar organic solvents and was composed of phenylene units. Thermal properties of the oligomer were investigated by thermogravimetric analyses under an air atmosphere. The weight loss of O-3HBA was found to be 5 and 50 Percent at 231 and >1000C, respectively. The carboneous residue of the O-3HBA was 54 Percent at 1000C. C 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 892–897, 2006}, + year = {2006} +} +@article{phydaldhnmr, + author = {Jha, Anjali and Kumar, B.Rajesh and Kumar Ch, RaviShankar}, + title = {Synthesized Novel Schiff Base of 4-Hydroxybenzaldehyde with Anilines for Optoelectronic + Applications}, + journal = {SSRN Preprint Server}, + pages = {46}, + keywords = {Schiff base, Spectral studies, Computational studies, Energy gap, Refractive index.}, + url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4934411}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/app.23537}, + abstract = {Optical materials organic in nature are leading materials exhibiting semiconducting properties is trend of present technology in optical and electronic applications. Active organic materials of Schiff bases are of vital importance in terms of their molecular properties, band gap, refractive index and dielectric operated at room temperature than compared to inorganic materials at elevated temperatures during synthesis. The present article focuses on the development of thin films with the synthesis of Schiff base of 4-hydroxy benzaldehydes and substituted anilines using the green synthesis method. The formation of the Schiff base compounds was confirmed with spectroscopic methods with shifts in wavenumbers in infrared spectra, transition with optical band gap with ultraviolet spectra and chemical environment with chemical shifts using proton NMR. Powdered XRD provide information of structure, composition and crystalline proximity of the synthesized Schiff base compounds. Optical properties refractive index and dielectric constant were attributed with spectroscopic ellipsometer. Computational studies were performed using the Gaussian 16 package with the B3LYP method basis set 6-311++** for all molecular compounds to confirm the molecular structures, optimized geometry, and electronic and optical properties. The insights of these properties are best visualized in terms of quantum mechanical descriptors responsible due to changes in electron density. Studies of these Schiff base compounds with nitro groups proved to exhibit optical properties and as an excellent organic semiconducting material with an energy gap of 3.08 eV; refractive index of 2.074, and dielectric constant of 4.303. }, + year = {2024} +} +@article{mphydaldhnmr, + author = {Syfani, Nova and Putra, Deddi Prima and Arbani, Dayar}, + title = {3,4-DIHYDROXYBENZOIC ACID AND 3,4-DIHYDROXYBENZALDEHYDE FROM THE FERN + Trichomanes chinense L.; ISOLATION, ANTIMICROBIAL AND ANTIOXIDANT PROPERTIES}, + journal = {Indo. J. Chem.,}, + volume = {12}, + number = {3}, + pages = {273-278}, + keywords = {Trichomanes chinense L.; 3,4-dihydroxybenzoic acid; 3,4-dihydroxybenzaldehyde; antioxidant; + antimicrobial}, + url = {https://academia-edu-documents.ada3b51d29be5ae5c31d26340608fd48.r2.cloudflarestorage.com/76337429/62cb66d00830376d6243dfc70e9c9c13f07a-libre.pdf?response-content-disposition=inline%3B%20filename%3D3_4_DIHYDROXYBENZOIC_ACID_AND_3_4_DIHYDR.pdf&response-content-type=application%2Fpdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=62bb68dcc7da7de029ac4fdac624cee9%2F20261018%2Fauto%2Fs3%2Faws4_request&X-Amz-Date=20261018T014804Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=2d857d9fd2556313a486db1447aa14a97dca8a72ac8aa120ff8d3c255860bd06}, + abstract = {3,4-dihydroxybenzoic acid (1) and 3,4-dihydroxybenzaldehyde (2) have been isolated from ethyl acetate + fraction of methanolic fractions of leaves, stems and roots of the fern Trichomanes chinense L. (Hymenophyllaceae). + These two compounds also showed significant antioxidant using DPPH and antimicrobial activities using the disc + diffusion assay.}, + year = {2012} +} +@article{heavyateff1, + author = {Lodewyk, Michael W. and Siebert, Matthew R. and Tantillo, Dean J.}, + title = {Computational Prediction of 1H and 13C Chemical Shifts: A Useful Tool for Natural Product, Mechanistic, and Synthetic Organic Chemistry}, + journal = {Chemical Reviews}, + volume = {112}, + number = {3}, + pages = {1839-1862}, + year = {2012}, + month = {03}, + issn = {0009-2665}, + doi = {10.1021/cr200106v}, + url = {https://doi.org/10.1021/cr200106v}, + eprint = {https://pubs.acs.org/chreay/article-pdf/112/3/1839/8644981/cr200106v.pdf}, +} +@article{heavyatef2, + author = {Jonas, Eric and Kuhn, Stefan and Schlörer, Nils}, + title = {Prediction of chemical shift in NMR: A review}, + journal = {Magnetic Resonance in Chemistry}, + volume = {60}, + number = {11}, + pages = {1021-1031}, + keywords = {chemical shift prediction, graph neural network, machine learning, NMR}, + doi = {https://doi.org/10.1002/mrc.5234}, + url = {https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/abs/10.1002/mrc.5234}, + eprint = {https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/pdf/10.1002/mrc.5234}, + abstract = {Abstract Calculation of solution-state NMR parameters, including chemical shift values and scalar coupling constants, is often a crucial step for unambiguous structure assignment. Data-driven (sometimes called empirical) methods leverage databases of known parameter values to estimate parameters for unknown or novel molecules. This is in contrast to popular ab initio techniques that use detailed quantum computational chemistry calculations to arrive at parameter estimates. Data-driven methods have the potential to be considerably faster than ab inito techniques and have been the subject of renewed interest over the past decade with the rise of high-quality databases of NMR parameters and novel machine learning methods. Here, we review these methods, their strengths and pitfalls, and the databases they are built on.}, + year = {2022} +} +@article{nmrbinsize, + author = {Schripsema, Jan}, + title = {Similarity and differential NMR spectroscopy in metabolomics: application to the analysis of vegetable oils with 1H and 13C NMR}, + journal = {Metabolomics}, + volume = {15}, + number = {39}, + pages = {1573-3890}, + doi = {https://doi.org/10.1007/s11306-019-1502-9}, + abstract = {In NMR based metabolomics there is a need for tools to easily compare spectra and to extract the maximum of information from the data.}, + year = {2019} +} +@article{olefinmetathese, + author = {Connon, Stephen J. and Blechert, Siegfried}, + title = {Recent Developments in Olefin Cross-Metathesis}, + journal = {Angewandte Chemie International Edition}, + volume = {42}, + number = {17}, + pages = {1900-1923}, + keywords = {cross-metathesis, homogeneous catalysis, olefins, ring-opening metathesis, synthetic methods}, + doi = {https://doi.org/10.1002/anie.200200556}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.200200556}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.200200556}, + abstract = {Abstract Among the many types of transition-metal-catalyzed CC bond-forming reactions, olefin metathesis has come to the fore in recent years owing to the wide range of transformations that are possible with commercially available and easily handled catalysts. Consequently, olefin metathesis is now widely considered as one of the most powerful synthetic tools in organic chemistry. Until recently the intermolecular variant of this reaction, cross-metathesis, had been neglected despite its potential. With the evolution of new catalysts, the selectivity, efficiency, and functional-group compatibility of this reaction have improved to a level that was unimaginable just a few years ago. These advances, together with a better understanding of the mechanism and catalyst–substrate interactions, have brought us to a stage where more and more researchers are employing cross-metathesis reactions in multistep procedures and in the synthesis of natural products. The recent inclusion of alkynes and hindered bicyclic olefins as viable substrates for bimolecular metathesis coupling, the discovery of enantioselective cross-metathesis and cross-metathesis in water, and the successful marriage of metathesis and solid-phase organic synthesis has further widened the scope of this versatile reaction.}, + year = {2003} +} +@article{dielsalder, + author = {Sauer, Jürgen and Wiest, Hubert and Mielert, Albrecht}, + title = {Eine Studie der DIELS-ALDER-Reaktion, I. Die Reaktivität von Dienophilen gegenüber Cyclopentadien und 9.10-Dimethyl-anthracen}, + journal = {Chemische Berichte}, + volume = {97}, + number = {11}, + pages = {3183-3207}, + doi = {https://doi.org/10.1002/cber.19640971129}, + url = {https://chemistry-europe.onlinelibrary.wiley.com/doi/abs/10.1002/cber.19640971129}, + eprint = {https://chemistry-europe.onlinelibrary.wiley.com/doi/pdf/10.1002/cber.19640971129}, + abstract = {Abstract Die Additionsgeschwindigkeiten verschiedener Dienophile an Cyclopentadien und 9.10-Dimethyl-anthracen werden in wasserfreiem Dioxan als Solvens durch kinetische Messungen ermittelt und in Hinsicht auf den Mechanismus der DIELS-ALDER-Reaktion diskutiert.}, + year = {1964} +} +@article{ringstrain, + author = {Wiberg, Kenneth B.}, + title = {The Concept of Strain in Organic Chemistry}, + journal = {Angewandte Chemie International Edition in English}, + volume = {25}, + number = {4}, + pages = {312-322}, + keywords = {Strained molecules}, + doi = {https://doi.org/10.1002/anie.198603121}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.198603121}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/anie.198603121}, + abstract = {Abstract “Die Ringschließung ist offenbar diejenige Erscheinung, welche am meisten über die räumliche Anordnung der Atome Auskunft geben kann. Wenn eine Kette von 5 und 6 Gliedern sich leicht, eine von weniger oder mehr Gliedern sich schwierig oder auch gar nicht schließen läßt, so müssen dafür offenbar räumliche Gründe vorhanden sein.… Die vier Valenzen des Kohlenstoffatoms wirken in den Richtungen, welche den Mittelpunkt der Kugel mit den Tetraederecken verbinden, und welche miteinander einen Winkel von 109°28′ machen. Die Richtung der Anziehung kann eine Ablenkung erfahren, die jedoch eine mit der Größe der Letzteren wachsende Spannung zur Folge hat,”[ Ring formation is evidently the reaction that can provide the most important information on the spatial arrangement of atoms. Steric reasons should explain the observation that 5- or 6-membered chain undergoes ready closure, whereas a shorter or longer chain undergoes difficult or no closure.… The four valences of the carbon atom act in the directions that connect the center of a sphere with the corners of a tetrahedron and form angles of 109°28′ with one another. The direction of the attraction can deviate, but this in increasing strain as the sizes of the latter increase. ] This is the quintessence of the “ring-strain theory” formulated by Adolf von Baeyer over one hundred years ago. Although it is today only one facet of the many aspects of strain theory, it has repeatedly stimulated experimental and theoretical chemists. Among the most spectacular of the recent successes in synthetic chemistry are the syntheses of tetra-tert-butyltetrahedrane and [1.1.1]propellane. The reasons for the great stability of these two highly strained compounds are completely different. The experimental findings as well as the results of theoretical analysis by means of molecular mechanics and ab initio calculations have contributed decisively to our present state of knowledge of the structure, energy, and reactivity of organic compounds.}, + year = {1986} +} + +

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