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\renewcommand*\thesubsubsection{\Alph{subsubsection}} + %\renewcommand*\thesubsubsection{\Alph{subsubsection}} \usepackage[titles]{tocloft} \cftsetindents{chapter}{0cm}{.5cm} \cftsetindents{section}{0.5 cm}{0.8cm} \cftsetindents{subsection}{0.5cm}{1.1cm} - \cftsetindents{subsubsection}{0.5 cm}{0.8cm} + \cftsetindents{subsubsection}{0.5 cm}{1.4cm} %\renewcommand{\listfigurename}{\textsc{List of Figures}} %--- Quotes @@ -225,7 +225,7 @@ Cheminformatic has established as a valuable tool in the development and analysis of large chemical networks. Opening the possibility to tackle systemsizes that would not be feasable for a human researcher. The possibilities both for the development of reactions aswell as the the selection and verification of large reaction networks are presented in this thesis. This thesis aims to find sensible synthesis in chemical reaction networks using NMR-spectra and their characteristics. \chapter{Einleitung} - Die Chemieinformatik ist ein aufstrebendes Forschungsfeld, das zum Ziel hat die Beschränkungen der Chemischen Industrie mit der Rechenstärke der Informatik anzugehen. So sollen neue Reaktion und Moleküle entwickelt, bestehende Prozesse optimiert und Eigenschaften analysiert werden. Diese Arbeit thematisiert eine Möglichkeit chemische Reaktionen näher zu analysieren und auf Basis dessen einen Prozess zu optimieren. + Die Chemieinformatik ist ein aufstrebendes Forschungsfeld, das zum Ziel hat die Beschränkungen der Chemischen Industrie mit der Rechenstärke der Informatik anzugehen. So sollen neue Reaktion und Moleküle entwickelt, bestehende Prozesse optimiert und Eigenschaften analysiert werden \cite{cheminformatics}. Die Chemieinformatik eignet sich dabei besonders in der Untersuchung großer Systeme , wie der Entwicklung neuer Medikamente \cite{cheminformatics2}. Diese Arbeit thematisiert eine Möglichkeit chemische Reaktionen näher zu analysieren und auf Basis dessen einen Prozess zu optimieren. Dabei werden zueinander ähnliche Moleküle über ihre zugehörigen NMR-Spektren verglichen. Basierend auf diesen Gemeinsamkeiten und Unterschieden wird eine Synthese bestimmt. \section{ILP und Graphtransformation} Das Ziel bei der Synthese chemischer Moleküle ist die Maximierung der Ausbeute und die Minimierung des nötigen Aufwands. Bekannte Reaktionen können dabei auf eine Vielzahl von Startmolekülen angewandt werden. Aber auch für ein gewähltes Startmolekül ist sowohl in der Auswahl der verwendeten Reaktionen, als auch der gewählten Reihenfolge, große Varianz möglich. Um aus diesem Netzwerk an Reaktionen eine optimale Syntheseplanung zu entwickeln eignet sich das Integer Linear Programming (ILP). Dabei werden alle über die einzelnen Reaktionsschritte bekannten Informationen in einem Reaktionsnetzwerk zusammengefasst. Zu den geeigneten Informationen zählen bevorzugte Stoichiometrien, Energiebarrieren oder Kosten für Katalysatoren und Reaktanten. All diese Informationen können mittels ILP gewichtet zu einem geeigneten Syntheseplan optimiert werden \cite{ilpmot}. Es ist dabei möglich das Reaktionsnetzwerk ausschließlich mit festen Reaktionen zusammenzusetzen. In der Chemie werden Reaktionen aber meistens für Kategorien von Molekülen mit bestimmten Eigenschaften angegeben. Dabei kann das vorliegen einer funktionellen Gruppe oder spezieller Bindungs- und Atomkonfigurationen entscheidend sein, ob eine Reaktion auf die Edukte anwendbar ist und welche Produkte zu erwarten sind. Diese Entscheidung kann bei kleinen Reaktionsnetzwerken händisch durchgeführt werden, steigt in ihrem Aufwand aber schnell an. Eine zeitsparende Alternative ist die Entwicklung des Reaktionsnetzwerks durch Graphtransformationen. Dabei werden Moleküle als Graphen und chemische Reaktionen als Graphentransformation abstrahiert \cite{andersenhyperflow}. So sind Reaktionsnetzwerke mit mehr Reaktionstypen, sowie mehr und größere Moleküle möglich. \section{NMR-Spektroskopie} @@ -233,7 +233,8 @@ \section{Zielsetzung} Das Ziel dieser Masterarbeit ist die Kombination des mathematischen Integer Linear Programming, der Informatischen Methode des Hypergraphen und der chemischen Methode des NMR-Spektrums. Dabei soll für bekannte Reaktionen und Moleküle ein chemisches Reaktionsnetzwerk in der Form eines Hypergraphen entwickelt werden. Für die so gefundenen Moleküle sollen NMR-Spektren bestimmt werden. Diese NMR-Spektren können dabei sowohl durch Quantenchemische Programme berechnet werden, als auch aus den Literaturangaben zu Experimentell bestimmten Spektren stammen. Diese NMR-Spektren sollen miteinander verglichen werden und ihre Ähnlichkeit, sowie ihre charakteristischen Unterschiede, quantifiziert werden. Dieser Grad der Ähnlichkeit soll anschießend genutzt werden um einen Reaktionspfad zu bestimmen, der diese Ähnlichkeit maximiert. Das angestrebte Ziel ist dabei die Automatisierung der Verifizierung unbekannter Moleküle. \chapter{Theoretische Grundlagen} - \section{Graphen Theorie} + Für diese Arbeit werden sowohl Werkzeuge der Graphentheorie (Kapitel \ref{chgraph}), als auch ein Verständnis der NMR-Spektroskopie benötigt (Kapitel \ref{chnmr}) und der quantenchemischen Berechnung selbiger (Kapitel \ref{chdft}), welche im folgenden näher erläutert werden. + \section{Graphen Theorie}\label{chgraph} Die Graphen Theorie befasst sich mit dem Abbilden von Netzwerken und Entitätenbeziehungen. Dabei werden die Netzwerkteilnehmer und Entitäten als Menge von Knoten ($V$) und ihre Verbindungen oder Beziehungen als Menge von Kanten ($E$) abstrahiert. Ein Knoten $v$ ist dabei ein Element der Menge $V$ und eine Kante ein Element der Teilmenge $E \subseteq P_{2}(V)$ Das Tupel $(u,v)$ aus zwei Knoten u und v, mit $u,v \in V$ ist ein Element der Menge $(u,v) \in E$. Ein einfacher Graph ($G$) besteht aus einer Menge von Knoten und Kanten $G = (V, E)$ \cite{bender2006foundations}. Bei einem gerichteten Graph gilt dabei, dass die Kante von Knoten u zu Knoten v gerichtet verläuft. Es gilt $(u,v) \neq (v,u)$, weshalb beide in der Menge von Kanten vorkommen können. In einem ungerichteten Graphen gilt, dass die beiden Tupel dieselbe Kante beschreiben. Es gilt also $(u,v) = (v,u)$. Ein Multigraph ist darüber definiert, dass anders als in einem einfachen Graphen, eine identische Kante mehrmals enthalten ist. Die Kanten sind also keine Menge. Die beiden Kannten haben dann die selbe Repräsentation $(u,v)\stackrel{r}{=}(u,v)$, aber sind nicht die gleiche Kante $(u,v) \neq (u,v)$. Es besteht auch die Möglichkeit, dass eine Kante von einem Knoten zu sich selber führt, also $(v,v)$, was als Schleife bezeichnet wird. Sowohl gerichtete, als auch ungerichtete Graphen können gelabelt sein. Sie werden dann als gelabelter Graph bezeichnet. Dabei lässt sich zwischen Kanten und Knotenlabeln unterscheiden. Für Kantenlabel (\ref{edgelabel}) und Knotenlabel (\ref{verticelabel}) in einem klassischen Gelabelten Graphen gilt, dass jeder Knoten oder jede Kante ein Label aus der Menge der Label $\Omega$ zugeordnet haben muss. \begin{equation} \label{edgelabel} \forall e \in E: \exists label(e) \in \Omega_{E} @@ -252,13 +253,13 @@ \end{itemize} \subsection{Morphismen} \label{chmophisms} Die Definition der Morphismen wurde aus der Doktorarbeit von Jakob Andersen entnommen \cite{andersenphd}. Es seien $G = (V_{G}, E_{G})$ und $H = (V_{H}, E_{H})$, zwei einfache, ungerichtete Graphen. - \paragraph{Morphismus} + \subsubsection{Morphismus} Ein Graphmorphismus $m: G \rightarrow H$ ist dann eine Abbildung von $G$ nach $H$. In dieser Abbildung müssen alle Knoten und Kanten in $G$ auch eine Abbildung in $H$ haben. Also gilt: Wenn $e = (u,v) \in E_{G} \implies \exists m(e) = (m(u),m(v)) \in E_{H}$. Die Abbildung muss aber nicht injektiv sein. Ein Beispiel für einen Morphismus, der kein Monomorphismus ist, ist wenn der Graph $G$ aus zwei verbundenen Knoten besteht und der Graph $H$ aus einem Knoten mit einer Schleife besteht (Abbildung \ref{morphisms}). Die Kante kann zwischen beiden Graphen Injektiv abgebildet werden, aber beide Knoten aus Graph $G$ werden auf den selben Knoten in Graph $H$ abgebildet. - \paragraph{Monomorphismus} + \subsubsection{Monomorphismus} Der Monomorphismus ist ein Morphismus, bei dem alle Knoten in $H$ nur von einem Knoten in $G$ abgebildet werden. Die Abbildung muss Injektiv sein. Es gilt: $\forall u,v \in V_{G}, u \neq v \implies m(u) \neq m(v)$. Ein Beispiel für einen Monomorphismus, der aber kein Subgraph Isomorphismus ist, ist wenn der Graph $G$ aus drei in Reihe verbundenen Knoten besteht und der Graph $H$ aus drei Knoten besteht, die alle untereinander verbunden sind. Dadurch würde zwischen Knoten, die Teil der Abbildung sind eine Kante bestehen, die wiederum nicht abgebildet wird. - \paragraph{Subgraph Isomorphismus} + \subsubsection{Subgraph Isomorphismus} Der Subgraph Isomorphismus ist ein Monomorphismus, bei dem zwischen allen abgebildeten Knoten keine nicht abgebildeten Kanten bestehen. Es gilt: $(u,v) \in E_{G} \iff (m(u), m(v)) \in E_{H}$. Ein Beispiel für einen Subgraph Isomorphismus, der kein Isomorphismus ist, ist wenn ein Graph $G$ aus drei linear verbundenen Knoten besteht und Graph $H$ aus einem Graphen mit vier Knoten besteht,wobei drei linear verbunden sind und der letzte beliebig mit den drei anderen verbunden ist. - \paragraph{Isomorphismus} + \subsubsection{Isomorphismus} Der Isomorphismus is ein Subgraph Isomorphismus, bei dem alle Knoten und Kanten jeweils genau einen Knoten und eine Kante haben auf den sie abgebildet werden können. Die Abbildung ist also bijektiv. \begin{figure} [h] \includegraphics[width=\textwidth]{morphismen.png} @@ -289,7 +290,7 @@ \item zwei Morphismen können den selben Start und Endgraphen haben \end{itemize} Auf dieser Kategorie von Graphen lassen sich drei Unterliegende Graphen Typen definieren. - \paragraph{Pushout} + \subsubsection{Pushout} Bei zwei gegebenen Morphismen $g: A \rightarrow C$ und $f: A \rightarrow B$ erzeugen die Morphismen $g': B \rightarrow D$ und $f': C \rightarrow D$ genau dann ein Pushout D von f und g (Abb. \ref{pushout}), wenn: \begin{itemize} \item die Morphismen kommutativ sind: $g' \circ f = f' \circ g$ @@ -300,7 +301,7 @@ \caption{Beispiel für ein kommutatives Diagramm mit einem Pushout D. Die Knoten $A,B,C,D,D'' \in Obj(\textbf{C})$ stellen selber Graphen dar. Die Kanten $g, g', g'',f,f',f'', d'' \in Mor(\textbf{C})$ stellen Morphismen dieser Graphen dar. \cite{andersenphd}. } \label{pushout} \end{figure} - \paragraph{Pullback} + \subsubsection{Pullback} Bei zwei gegebenen Morphismen $g': B \rightarrow D$ und $f': C \rightarrow D$ erzeugen die Morphismen $g: A \rightarrow C$ und $f: A \rightarrow B$ genau dann ein Pulback A von f' und g' (Abb. \ref{pullback}), wenn: \begin{itemize} \item die morphismen kommutativ sind: $g' \circ f = f' \circ g$ @@ -389,9 +390,9 @@ \label{pushpullex} \end{figure} Im folgenden werden zum Pushout und Pullback vier Beispiele näher untersucht (Abb. \ref{pushpullex}). Im oben rechten Beispiel fügen die Morphismen jeweils eine Horizontale oder vertikale Kante 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} + \subsubsection{Pushout Complement} Bei zwei gegebenen Morphismen $g': B \rightarrow D$ und $f: A \rightarrow B$ erzeugen die Morphismen $g: A \rightarrow C$ und $f': C \rightarrow D$ genau dann ein Pushoutcomplement C von f und g', wenn f' und g' der Pushout von f und g ist oder f und g der Pullback von f' und g' ist. - \paragraph{Double Pushout} + \subsubsection{Double Pushout} Eine Graphtransformation lässt sich mit dem Double Pushout (DPO) Ansatz realisieren. Der DPO ist dabei eine Kombination aus den Morphismen l, r, l', r', m, m' (Abbildung \ref{dpo}) und einer Transformations Regel $p = (L \stackrel{l}{\leftarrow} K \stackrel{r}{\rightarrow} R)$. Die Regel besteht aus dem Kontext $K$, den zwei Morphismen $l$ und $r$. Bei einer angenommen Transformation von links nach rechts stellt $L$ die Vorbedingung, $R$ die Folgebedingung, $G$ den Vorzustand und $H$ den Folgezustand dar. Die Graphransformation eines Graphen $G$ zu einem Graphen $H$ mit der Regel $p$ und dem Morphismus $m$ wird über den Ausdruck $G \stackrel{p,m}{\implies} H$ dargestellt. Die nötigen Schritte lauten: \begin{itemize} \item Finde einen Morphismus $m: L \rightarrow G$ von der Vorbedingung $L$ zum Startgraphen $G$ @@ -516,9 +517,10 @@ \label{petrinetmarkedfree} \end{figure} Die Feststellung, welche Sequenziellen Übergänge und Gesamtzustände aus einem Initialen Marking oder der Initialen Tokenverteilung $mu$ möglich ist, wird \textit{Reachability} genannt. Ein Zustand $\mu'$ ist direkt erreichbar, wenn er durch das auslösen eines möglichen Übergangs erzeugt wird. Ein Zustand $\mu$ ist allgemein erreichbar, wenn er durch einen Zustand direkt erreichbar ist, welcher selber allgemein oder direkt erreichbar ist. Eine \textit{Reachability} Menge $R(M)$ kann für ein Petrinetz $M = (P, T, I, O, \mu)$ mit der Zustandsmenge $P$, der Übergangsmenge $T$, der Menge von Input und Output Funktionen für Übergänge $I$ und $O$ und dem Initialen Marking $\mu$ definiert werden, als die Menge aller Markings, die durch den Markierten Petrinetz erreicht werden können \cite{petrinets}. Mit Blick auf den zuvor definierten Hypergraphen \ref{hypergraph} können die Zustände in einem Petrinetz als Knoten in einem Hypergraphen und die Übergänge als Hyperkanten verstanden werden. Dann erlaubt es die etablierte Nutzung von Petrinetzten um die Erfüllbarkeit einer Abfolge von Hyperkanten Übergängen zu untersuchen. Insbesondere bei Reaktionsnetzwerken, kann so durch ein Initiales Marking der Startmoleküle oder eine erzeugende Kante ohne Input, gewährleisten, dass nur Reaktionen stattfinden, für die alle nötigen Edukte vorliegen. - \section{NMR-Spektroskopie} + \section{NMR-Spektroskopie}\label{chnmr} + Um die im Hypergraphen entwickelten organischen Moleküle zu untersuchen eignet sich NMR-Spektroskopie. Für die Erklärung der Grundlagen der NMR-Spektroskopie wurde das Lehrbuch Organische Chemie von Peter Vollhardt \cite{ocwiley} verwendet. \subsection{Spektren} - Um die im Hypergraphen entwickelten organischen Moleküle zu untersuchen eignet sich NMR-Spektroskopie. Für die Erklärung der Grundlagen der NMR-Spektroskopie wurde das Lehrbuch Organische Chemie von Peter Vollhardt \cite{ocwiley} verwendet. Spektroskopie (lat. Erscheinung, Sichtbarwerden) befasst sich mit der Darstellung realer Eigenschaften durch eine Auftragung einer kontinuierlichen oder kleinschrittig gestaffelten Größe gegen die Intensität. In der organischen Chemie werden vor allem vier Spektroskopie Typen verwendet. Als kleinschrittig gestaffeltes Spektrum die Massenspektroskopie, bei der ein Molekül in kleinere geladene Fragmente geteilt wird. Diese Fragmente können über ein ganzzahliges Masse-Ladungs-Verhältnis und ihre Häufigkeit Charakterisiert werden. Zerstörungsfrei hingegen sind die kontinuierlichen, auf elektromagnetischen Wellen basierenden Absorptions- oder Resonanzspektren. Die verbreitetsten Resonanzspektren sind dabei UV/Vis und Infrarot. Die verwendeten Elektromagnetische Strahlung ist dabei im UV/Vis (200 - 800 nm) und Infrarot (800 nm - 1 mm). Die meist verbreitetste Spektroskopie hingegen ist die Kern-Magnet-Resonanz-Spektroskopie (Nucleus-Magnetic-Resonance, kurz NMR-Spektroskopie). UV-Resonanzspektroskopie ist möglich, wobei die Menge von Molekülen, die dafür verwendbar sind, sehr gering ist. Die elektromagnetischen Wellen für NMR sind im Radiowellenbereich (über 100 mm) \cite{ocwiley}. + Spektroskopie (lat. Erscheinung, Sichtbarwerden) befasst sich mit der Darstellung realer Eigenschaften durch eine Auftragung einer kontinuierlichen oder kleinschrittig gestaffelten Größe gegen die Intensität. In der organischen Chemie werden vor allem vier Spektroskopie Typen verwendet. Als kleinschrittig gestaffeltes Spektrum die Massenspektroskopie, bei der ein Molekül in kleinere geladene Fragmente geteilt wird. Diese Fragmente können über ein ganzzahliges Masse-Ladungs-Verhältnis und ihre Häufigkeit Charakterisiert werden. Zerstörungsfrei hingegen sind die kontinuierlichen, auf elektromagnetischen Wellen basierenden Absorptions- oder Resonanzspektren. Die verbreitetsten Resonanzspektren sind dabei UV/Vis und Infrarot. Die verwendeten Elektromagnetische Strahlung ist dabei im UV/Vis (200 - 800 nm) und Infrarot (800 nm - 1 mm). Die meist verbreitetste Spektroskopie hingegen ist die Kern-Magnet-Resonanz-Spektroskopie (Nucleus-Magnetic-Resonance, kurz NMR-Spektroskopie). UV-Resonanzspektroskopie ist möglich, wobei die Menge von Molekülen, die dafür verwendbar sind, sehr gering ist. Die elektromagnetischen Wellen für NMR sind im Radiowellenbereich (über 100 mm) \cite{ocwiley}. \subsection{Kernspin} Die im Atomkern befindlichen Neutronen und Protonen können sich in einem von zwei für NMR relevanten Zuständen befinden. Diese Zustände des Kernspins sind die $\alpha$ und $\beta$ Konfiguration. Dieser Kernspin ist keine Visuelle Rotation, hat aber die Eigenschaft, wie Ladung in Bewegung, ein Magnetfeld zu erzeugen. Die verschiedenen Zustände unterscheiden sich dabei in der theoretischen Drehrichtung und damit auch in der Richtung des induzierten Magnetfeldes. Unter normalen Umständen treten beide Konfigurationen im Verhältnis 1:1 auf. Durch das induzierte Magnetfeld kann ein entgegen gerichtetes, externes Magnetfeld diese Konfiguration energetisch hindern. Dadurch befinden sich deutlich weniger Kerne in diesem Zustand. Die Temperatur der Teilchen erlaubt jedoch einen Wechsel Abhängig vom Energieunterschied. Es ist ebenfalls möglich diesen Konfigurationswechsel durch Radiowellen einer zu dem Kern gehörigen Charakteristischen Wellenlänge zu erzwingen, wobei die Rückänderung der Konfiguration, auch Relaxation genannt, nach kurzer Zeit eintritt. Diese Relaxation emittiert dabei eine für den Kern charakteristische Wellenlänge. Sowohl die absorbierte, als auch die emittiert Wellenlänge hängen von der Energiedifferenz der beiden Konfigurationen ab, welche wiederum von der Umgebung des Kerns, aber auch von dem angelegten Magnetfeld abhängen. Die Frequenz der Strahlung ist dabei linear proportional zur Stärke des Magnetfeld. \subsection{NMR aktive Kerne} @@ -595,7 +597,7 @@ \end{figure} \subsection{Schreibweise} In einem wissenschaftlichen Kontext wird nicht immer das gesamte Spektrum als Bild angegeben. Um trotzdem eine Angabe zu machen, die das Spektrum ausreichend beschreibt, muss ein aussagekräftiger String verwendet werden. Für Chlorethan, wäre dass zum Beispiel $^{1}$H-NMR (300 MHz): $\delta$ 1.488 (-CH$_{3}$, 3, t, $^{3}J = 7.232$), 1.488 (-CH$_{2}$-, 2, q, $^{3}J = 7.232$). Für jeden Kern wird dabei, in der Reihenfolge, die Verschiebung in ppm, eine kurze Zuordnung zum Kern, die Intensität, die Multiplettaufspaltung und die Stärke der Aufspaltung genannt. Für die Stärke der Aufspaltung wird zudem angegeben, über wie viele Bindungen diese Interaktion stattfindet. Für das ganze Spektrum wird auch angegeben, mit welcher Frequenz oder Feldstärke das Spektrometer eingestellt wurde. - \subsection{Kohlenstoff NMR} + \subsection{Kohlenstoff NMR}\label{chdft} Der neben Wasserstoff am häufigsten untersuchte Kern ist Kohlenstoff. Für sein NMR wird $^{13}$C verwendet und ein Lösungsmittel mit $^{12}$C eingesetzt. Das Spektrum verhält sich dabei größtenteils genauso, wie das von Wasserstoff, mit der Ausnahme, dass $^{13}$C fast nie nebeneinander vorliegt, also keine $^{13}$C,$^{13}$C Multiplett Interaktion stattfindet. $^{13}$C kann aber durchaus mit $^{1}$H interagieren. Diese Kopplung wird häufig gezielt neutralisiert, da der $^{13}$C Kern weniger leicht angeregt wird und so ein schlechteres Signal/Rausch-Verhältnis vorliegt. Kleinere Peaks können so leichter im Rauschen untergehen. Darum wird oft ein $^{1}$H Breitband entkoppeltes $^{13}$C Spektrum aufgenommen. Die Notation dafür ist $^{13}$C{$^{1}$H}. Um dies zu erreichen, wird ein breites Wasserstofffrequenz Signal während der gesamten Messung eingestrahlt. Das resultierende Spektrum weist für jeden chemisch äquivalenten Kohlenstoff nur einen Peak auf. Die Peak Fläche wird dabei je nach ausgeblendeten Kern unterschiedlich beeinflusst, weshalb die Intensität nur noch als Richtwert und nicht mehr als absolute Größe betrachtet werden kann. \section{Dichte Funktional Theorie (DFT)} Die Dichte Funktional Theorie (DFT) vereinfach die Quantenchemischen Atomorbitale als eine über den Raum verteilte Elektronendichtefunktion $\rho[r]$. Für ein gegebens Molekül lässt sich daraus die Kinetische Energie $T$ (Gleichung \ref{dftkin}), die Energie der Elektronen-Protonen-Wechselwirkung $V_{eN}$ (Gleichung \ref{dftpotn}), sowie die die Energie der Elektronen-Protonen-Wechselwirkung $V_{ee}$ (Gleichung \ref{dftpote}) also Integral dieser Dichtefunktion über den gesamten Raum $r$ bestimmen. @@ -619,7 +621,8 @@ \end{equation} Die hierfür verwendeten Basisfunktionen können variieren, sind aber meistens Slater oder Gauss-Funktionen \cite{DFTORCA}. \chapter{Methoden und Tools} - \section{Graptransformation Derivation Graph} + Für die Entwicklung der Reaktionsnetzwerke (Kapitel \ref{chmod}), die Beschränkung der entstehenden Graphen (Kapitel \ref{chnetx}), die Berechnung der NMR-Spektren (Kapitel \ref{chorca}) und die Lösung (Kapitel \ref{chgurobi}) und Verifikation (Kapitel \ref{chmodpet}) des ILP wurden verschiedene Programme verwendet, welche im Folgenden näher erläutert werden. Ebenso wird die Methode definiert, mit der die NMR-Spektren untereinander verglichen werden (Kapitel \ref{chnmrsi}). + \section{Graptransformation Derivation Graph}\label{chmod} 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 SMILES-String geladen wird oder über einen GML-String definiert werden. Im folgenden wird das selbe Molekül Cyclohexan über seinen SMILES und einen GML String definiert. \begin{lstlisting}[language=Python] cyclohexan = smiles ("C1CCCCC1") @@ -702,9 +705,9 @@ a.graph.print() \end{lstlisting} M\o{}d wurde verwendet die Einwirkung natürlich auftretenden Reaktionen auf natürliche oder synthetische Moleküle zu untersuchen. - \section{networkx} + \section{networkx}\label{chnetx} Networkx ist ein Pythonbasiertes Netzwerk und Graphen Analyse Tool \cite{networkx}. Eine Funktion ist dabei das identifizieren aller sehnen losen Zyklen. Während der laufzeit des Graptransformationstools wurden verschiedene Analysen dieser sehnen losen Zyklen als restriction verwendet. - \section{ORCA} + \section{ORCA}\label{chorca} 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 durch das Graptransformationstool 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. @@ -714,7 +717,7 @@ !TPSS pcSseg-3 autoaux tightscf NMR \end{lstlisting} 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 dem Graptransformationstool erzeugte Molekül wurde ein $^{13}$C-NMR berechnet. - \section{NMR-Vergleich} + \section{NMR-Vergleich}\label{chnmrsi} Um die von dem quatntenchemischen 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 @@ -749,13 +752,14 @@ \end{equation} Für alle Moleküle eines aus dem gesamten Derivationgraph ausgewählten Reaktionspfad wurden Literaturspektren recherchiert. Jedes mit dem Quantenchemischen Programm 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. - \section{Gurobipy} + \section{Gurobipy}\label{chgurobi} 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. - \section{Petrinetz Zertifikat} + \section{Petrinetz Zertifikat}\label{chmodpet} 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. \chapter{Ergebnisse} - \section{Ein-Molekül-Reaktionen} + Mit den erläuterten Werkzeugen und Methoden werden drei Beispiel Reaktionsnetzwerke analysiert. Dabei werden zwei natürlich auftretende Ein-Molekül-Reaktionen (Kapitel \ref{chonmolre}) und eine Multi-Molekül-Reaktion (Kapitel \ref{chmultmore}) aus der Organischensynthesechemie. Die Beispiele sind dabei nicht erschöpfend und dienen lediglich als Demonstration der Methode und als ein mögliches Anwendungsschema. + \section{Ein-Molekül-Reaktionen}\label{chonmolre} 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. Sie werden im Folgenden als Ein-Molekül-Reaktionen bezeichnet. \subsection{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}. @@ -1338,7 +1342,7 @@ \FloatBarrier \section{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 entstand keine neue Doppelbindung mit einem E/Z-Isomer durch Graphtransformation. Der Schluss von dem Graphen auf eine Geometrie war deswegen immer eindeutig. \newline Die Berechnung der NMR Spektren war trotzdem fehleranfällig. Dabei konnten bestimmte Molekülveränderungen besser in dem NMR-Berechnungstool abgebildet werden. Eine Methylierung erzeugte dabei nur eine geringe Veränderung im Xanthingrundgerüst, weshalb die Zuordnung vor allem in dem Signal der Methylgruppe lag. Die Hydroxylierung und Oxidierung zum Aldehyd resultierten in deutlichen Veränderungen der Phenylgruppe, weshalb das Grundgerüst selber verändert wurde. \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 Hypergraph 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. Es ist anzumerken, dass die erwartete Synthese über die Auswahl der Referenzspektren festgelegt wurde. Diese Synthese wurde über NMR-Spektren abstrahiert. Es lässt sich so sagen, dass die NMR-Spektren in dieser Analyse die Struktur hinreichend Codieren, aber nicht eine Unbekannte Synthese vollständig hergeleitet wurde. \newline Für ausgewählte Literaturspektren von nicht in der natürlichen Synthese erwarteten Molekülen wurden ebenfalls die Crossskorrelationen mit den berechneten Spektren ermittelt. Dabei konnte ebenfalls eine erhöhte Korrelation mit dem zugehörigen berechneten Spektrum bestimmt werden. Das ILP konnte dabei den neuen Syntheseplan ebenfalls zuverlässig zuordnen. Die Auswahl eines Syntheseplans basierend auf der Ähnlichkeit von NMR-Spektren ist daher gerechtfertigt und stellt eine Verbesserung gegenüber der Auswahl ohne selbige dar. - \section{Multi-Molekül-Reaktionen} + \section{Multi-Molekül-Reaktionen}\label{chmultmore} Die bisherigen Ein-Molekül-Reaktionen lassen sich durch ein ILP lösen, erfordern die Verwendung jedoch nicht. Um die Grenzen des ILP weiter auszureizen, wird ein komplexerer Hypergraph entwickelt. Dieser Hypergraph wird mit wenigen, einfachen Transformationsregeln und mit einem Ausgangsmolekül erzeugt. Das Ziel ist ein hochvernetztes Reaktionsnetzwerk. \section{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. @@ -1518,11 +1522,11 @@ \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}) + Dabei soll die Wahrscheinlichkeit der ausgewählten Moleküle maximiert werden (Gleichung \ref{objspecmain}). Nachdem drei Zielmoleküle ausgewählt wurden wird der Fluss in diese Moleküle als Bedingung gesetzt. \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{objspectrd}). + Alle Lösungen, die positiven Fluss $b_{e} = 1$ in die Zielmoleküle haben, werden 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{objspectrd}). \begin{equation} \label{objspecsec} \sum_{e} b_{e} \end{equation} diff --git a/Report/refs.bib b/Report/refs.bib index ef1d85f..26b1134 100644 --- a/Report/refs.bib +++ b/Report/refs.bib @@ -672,6 +672,38 @@ keywords = {Calibration-curve method, Electronic referencing, Metabolomics, NMR spectroscopy, Nuclear magnetic resonance (NMR), Pharmaceutical analysis, Quantitative NMR (qNMR), Referencing technique, Standard-addition method, Validation}, abstract = {This review illustrates the need to use nuclear magnetic resonance (NMR) spectroscopy for the quantitative analysis of small molecules in their crude forms and in mixtures. We provide the basic concepts of quantitative NMR (qNMR), a brief description of important acquisition and processing parameters responsible for obtaining high-quality, reproducible NMR spectra in order to maximize accuracy, and the latest referencing techniques used for quantitative analysis. We also describe methods that are used for quantitative analysis including calibration-curve and standard-addition methods. Further, we briefly address validation of qNMR spectroscopy and its major applications in various scientific disciplines.} } +@article{cheminformatics, + author = {Wegner, J. K. and Sterling, A. and Guha, R. and Bender, A. and Faulon, J.-L. and Hastings, J. and O'Boyle, N. and Overington, J. and Van Vlijmen, H. and Willighagen, E.}, + title = {Cheminformatics}, + year = {2012}, + issue_date = {November 2012}, + publisher = {Association for Computing Machinery}, + address = {New York, NY, USA}, + volume = {55}, + number = {11}, + issn = {0001-0782}, + url = {https://doi.org/10.1145/2366316.2366334}, + doi = {10.1145/2366316.2366334}, + abstract = {Open-source chemistry software and molecular databases broaden the research horizons of drug discovery.}, + journal = {Commun. ACM}, + month = nov, + pages = {65–75}, + numpages = {11} +} +@article{cheminformatics2, + author = {Chen, H. and Kogej, T. and Engkvist, O.}, + title = {Cheminformatics in Drug Discovery, an Industrial Perspective}, + journal = {Molecular Informatics}, + volume = {37}, + number = {9-10}, + pages = {1800041}, + keywords = {Cheminformatics, Machine Learning, Library Design, High-Throughput Screening}, + doi = {https://doi.org/10.1002/minf.201800041}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/minf.201800041}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/minf.201800041}, + abstract = {Abstract Cheminformatics has established itself as a core discipline within large scale drug discovery operations. It would be impossible to handle the amount of data generated today in a small molecule drug discovery project without persons skilled in cheminformatics. In addition, due to increased emphasis on “Big Data”, machine learning and artificial intelligence, not only in the society in general, but also in drug discovery, it is expected that the cheminformatics field will be even more important in the future. Traditional areas like virtual screening, library design and high-throughput screening analysis are highlighted in this review. Applying machine learning in drug discovery is an area that has become very important. Applications of machine learning in early drug discovery has been extended from predicting ADME properties and target activity to tasks like de novo molecular design and prediction of chemical reactions.}, + year = {2018} +}