Chapter

Similarity in Chemical Reaction Networks: Categories, Concepts and Closures

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  • Corporación SCIO, Colombia
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Abstract

Similarity studies are important for chemistry and their applications range from the periodic table to the screening of large databases in the searching for new drugs. In this later case, it is assumed that similarity in molecular structure is related to similarity in reactivity. However, we state that structural formulas can be regarded as abstract representations emerging from the analysis of large amounts of data upon chemical reactivity. Hence, chemical formulas such as organic functions are not direct pictures of the atomic constitution of matter, but signs used to represent similarity in the reactivity of a class of substances. Therefore, reactivity, rather than molecular structure, becomes the fundamental feature of chemical substances. As reactivity is important, chemical identity is given by the relations substances establish with each other, giving place to a network of chemical reactions. We explore similarity in the network rather than in molecular structure. By characterising each substance in terms of the related ones, we show how Category Theory helps in this description. Afterwards, we study the similarity among substances using topological spaces, which leads us to concepts such as closure and neighbourhood, which formalise the intuition of things lying somewhere near around. The second focus of the chapter is the exploration of the potential of closure operators, and of topological closures in particular, as more general descriptors of chemical similarity. As we introduce the formalism, we develop a worked example, concerning the analysis of similarity among chemical elements regarding their ability to combine into binary compounds. The results show that several of the trends of chemical elements are found through the current approach. © 2015 Bentham Science Publishers Ltd Published by Elsevier Inc. All rights reserved.

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... Historical supporters of the ontology of reactions are Geoffroy [54], Brodie [76], and more recently Earley [77,78,79,80], van Brakel [81], and Stein [82], with Schummer providing an interesting ontology for chemistry based on substances and reactions in a network of dynamical relations, where substances and reactions mutually define each other at the experimental and theoretical level [75]. This is the approach we take here, which can be formalised through category theory, 31 where objects are defined by their relations [84]. ...
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Chemistry shapes and creates the disposition of the world's resources and exponentially provides new substances for the welfare and hazard of our civilisation. Over the history chemists-driven by social, semiotic and material forces-have shaped the discipline, while creating a colossal corpus of information and knowledge. Historians and sociologists, in turn, have devised causal narratives and hypotheses to explain major events in chemistry as well as its current status. In this Perspective we discuss the approaches to the evolution of the social, semiotic and material systems of chemistry. We critically analyse their reaches and challenge them by putting forward the need of a more holistic and formal setting to modelling the evolution of chemical knowledge. We indicate the advantages for chemistry of considering chemical knowledge as a complex dynamical system, which, besides casting light on the past and present of chemistry, allows for estimating its future, as well as the effects of hypothetical past events. We describe how this approach turns instrumental for forecasting the effects of material, semiotic and social perturbations upon chemical knowledge. Available data and the most relevant formalisms to analyse the different facets of chemical knowledge are discussed.
... In fact, random knowledge of about half of the space would have led to about half of the similarities resulting from the space, mainly for main group elements. This justifies the almost invariable resemblances among chemical elements reported by Meyer and Mendeleev and others [20] and the difficulty in finding stable similarities for transition metals [16,21,22], characterised by few compounds, therefore requiring a more complete knowledge of the space. ...
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Mendeleev came across with his first attempt to a periodic system by classifying and ordering the known elements by 1869. Order and similarity were based on knowledge of chemical compounds, which gathered together constitute the chemical space by 1869. Despite its importance, very little is known about the size and diversity of this space and even less is known about its influence upon Mendeleev's periodic system. Here we show, by analysing 11.484 substances reported in the scientific literature up to 1869 and stored in Reaxys database, that 80\% of the space was accounted by 12 elements, oxygen and hydrogen being those with most compounds. We found that the space included more than 2,000 combinations of elements, of which 5\%, made of organogenic elements, gathered half of the substances of the space. By exploring the temporal report of compounds containing typical molecular fragments, we found that Meyer's and Mendeleev's available chemical space had a balance of organic, inorganic and organometallic compounds, which was, after 1830, drastically overpopulated by organic substances. The size and diversity of the space show that knowledge of organogenic elements sufficed to have a panoramic idea of the space. We determined similarities among the 60 elements known by 1869 taking into account the resemblance of their combinations and we found that Meyer's and Mendeleev's similarities for the chemical elements agree to a large extent with the similarities allowed by the chemical space.
... In fact, random knowledge of about half of the space would have led to about half of the similarities resulting from the space, mainly for main group elements. This justifies the almost invariable resemblances among chemical elements reported by Meyer and Mendeleev and others [20] and the difficulty in finding stable similarities for transition metals [16,21,22], characterised by few compounds, therefore requiring a more complete knowledge of the space. ...
Preprint
Full-text available
Meyer and Mendeleev came across with their periodic systems by classifying and ordering the known elements by about 1869. Order and similarity were based on knowledge of chemical compounds, which gathered together constitute the chemical space by 1869. Despite its importance, very little is known about the size and diversity of this space and even less is known about its influence upon Meyer's and Mendeleev's periodic system. Here we show, by analysing 11,484 substances reported in the scientific literature up to 1869 and stored in Reaxys database, that 80% of the space was accounted by 12 elements, oxygen and hydrogen being those with most compounds. We found that the space included more than 2,000 combinations of elements, of which 5%, made of organogenic elements, gathered half of the substances of the space. By exploring the temporal report of compounds containing typical molecular fragments, we found that Meyer's and Mendeleev's available chemical space had a balance of organic, inorganic and organometallic compounds, which was, after 1830, drastically overpopulated by organic substances. The size and diversity of the space show that knowledge of organogenic elements sufficed to have a panoramic idea of the space. We determined similarities among the 60 elements known by 1869 taking into account the resemblance of their combinations and we found that Meyer's and Mendeleev's similarities for the chemical elements agree to a large extent with the similarities allowed by the chemical space.
... Así, realizamos un nuevo estudio basado en compuestos considerando aspectos históricos del sistema periódico, especialmente su dependencia de los compuestos, valencias y estequiometrías, más que de las propiedades de los elementos aislados (sustancias simples). El estudio (Leal et al. 2012) es influenciado por las ideas de Schummer (1998) de que la química tiene sus raíces en el carácter relacional de las sustancias (Bernal & Daza 2010), lo que combinado con conceptos de teoría de categorías (Bernal et al. 2015) y análisis de redes sociales (Restrepo 2015b) lleva a la idea de que una sustancia química (no necesariamente un elemento) no solamente es caracterizada por propiedades medidas para la sustancia aislada, sino, más importante, por las otras sustancias con las cuales la sustancia en cuestión está relacionada, e.g. por reactividad química. ...
Chapter
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Antes de analizar las aproximaciones desde la semejanza al sistema periódico, definimos "ley periódica", "tabla periódica" y "sistema periódico" y criticamos algunas confusiones que se dan en estos términos. Resaltamos la importancia de sustancias "simples" y "básicas" como lados realista y trascendental del concepto de elemento químico. Además, resaltamos que los compuestos, más que los elementos como sustancias simples, son los portadores de información importante para la clasificación de los elementos. Una discusión sobre la estructura matemática del sistema periódico es introducida usando la conjetura de Villaveces, que formalizamos a través de la noción de relaciones de orden y de semejanza. Posteriormente se discuten seis aproximaciones fenomenológicas a la semejanza de los elementos químicos, las cuales conducen al concepto de tipo natural como grupo de la tabla periódica y a la pregunta por el mínimo número de propiedades necesarias para la caracterización de los elementos químicos. Los estudios varían en sus metodologías para evaluar la semejanza y en el tipo de información (física o química) usada para caracterizar los elementos químicos. Se encuentra que las semejanzas de los grupos cercanos a los gases nobles son frecuentes al comprarse con las semejanzas de los metales de transición. Se resalta la importancia de conceptos topológicos como clausura, frontera e interior para explorar los detalles de las semejanzas de los elementos químicos. Se estudia la aplicación particular de estas ideas a los semimetales para los seis estudios de semejanza. Finalmente, se analizan varias preguntas abiertas sobre estudios matemáticos del sistema periódico.
... Thus, considering historical aspects of the periodic system, especially its reliance on chemical compounds, valences, and stoichiometries of compounds, rather than on properties of isolated elements (simple substances); we ran a novel study based only on compounds. The study (Leal et al. 2012) is influenced by Schummer's (1998) idea that chemistry is rooted on the relational character of substances (Bernal & Daza 2010), which combined with concepts from category theory (Bernal et al. 2015) and social network analysis (Restrepo 2017) leads to the idea that a chemical substance (not necessarily an element) is not only characterized by properties measured upon the isolated substance, but, most important, by the other substances with which the substance in question is related, for example by chemical reactivity. Schummer (1998) leads to the claim that (1) two substances belong to the same substance class if they are chemically similar and (2) they are similar if each of them react under the same conditions to form product substances of a common substance class. ...
Chapter
We explore the meaning of the periodic table and of some of its related terms. In so doing we highlight a few common mistakes that arise from confusion of those terms and from misinterpretation of others, e.g. element, periodic system, table and law. An approach to the structure of the periodic system we follow in this chapter is through similarity. In so doing we review seven works addressing the similarity of chemical elements accounting for different number of elements and using different properties, either chemical or physical ones.
... Thus, considering historical aspects of the periodic system, especially its reliance on chemical compounds, valences, and stoichiometries of compounds, rather than on properties of isolated elements (simple substances); we ran a novel study based only on compounds. The study (Leal et al. 2012) is influenced by Schummer's (1998) idea that chemistry is rooted on the relational character of substances (Bernal & Daza 2010), which combined with concepts from category theory (Bernal et al. 2015) and social network analysis (Restrepo 2017) leads to the idea that a chemical substance (not necessarily an element) is not only characterized by properties measured upon the isolated substance, but, most important, by the other substances with which the substance in question is related, for example by chemical reactivity. Schummer (1998) leads to the claim that (1) two substances belong to the same substance class if they are chemically similar and (2) they are similar if each of them react under the same conditions to form product substances of a common substance class. ...
Book
Since 1969, the international chemistry community has only held conferences on the topic of the Periodic Table three times, and the 2012 conference in Cusco, Peru was the first in almost a decade. The conference was highly interdisciplinary, featuring papers on geology, physics, mathematical and theoretical chemistry, the history and philosophy of chemistry, and chemical education, from the most reputable Periodic Table scholars across the world. Eric Scerri and Guillermo Restrepo have collected fifteen of the strongest papers presented at this conference, from the most notable Periodic Table scholars. The collected volume will contain pieces on chemistry, philosophy of science, applied mathematics, and science education.
... From a methodological viewpoint there were two important steps for finding similarity classes, namely the construction of neighbourhoods and their clustering. In Bernal et al. it has been shown that those neighbourhoods can be further explored through an interesting connection with Formal Concept Analysis, a mathematical technique based on the finding of closed sets of objects (51). There, objects are characterised by their attributes and, for the particular case of binary compounds, objects are chemical elements and their attributes are those chemical elements belonging to their neighbourhoods. ...
Chapter
Similarity is one of the key concepts of the periodic table, which was historically addressed by assessing the resemblance of chemical elements through that of their compounds. A contemporary approach to the similarity among elements is through quantum chemistry, based on the resemblance of the electronic properties of the atoms involved. In spite of having two approaches, the historical one has been almost abandoned and the quantum chemical oversimplified to free atoms, which are of little interest for chemistry. Here we show that a mathematical and computational historical approach yields well-known chemical similarities of chemical elements when studied through binary compounds and their stoichiometries; these similarities are also in agreement with quantum chemistry results for bound atoms. The results come from the analysis of 4,700 binary compounds of 94 chemical elements through the definition of neighbourhoods for every element that were contrasted producing similarity classes. The method detected classes of elements with different patterns on the periodic table, e.g. vertical similarities as in the alkali metals, horizontal ones as in the 4th-row platinum metals and mixed similarities as in the actinoids with some transition metals. We anticipate the methodology here presented to be a starting point for more temporal and even more detailed studies of the periodic table.
... All scien tists working in mathematical chemistry, perhaps without knowing it, are looking for fundamental rules or trends underlying chemistry: for example, when study ing how the encoding of the molecular structure may also encode features of the substances the characterized molecules represent; or when considering that the molecular structure may be used to estimate properties of substances by order ing their molecules; or when giving insight on the number of possible substances based on the complexity of the molecular structure. There are also examples of mathematization of chemistry where the molecular structure (understood as a collection of atoms related by bonds) is not the central point, such as approaches using category theory (Bernal 2012, Bernal et al. 2015 and topology (Stadler and Stadler 2002, Restrepo et al. 2004, Flamm et al. 2015, to look for patterns such as functional groups or families of chemicals in chemical networks. Or, for ex ample, the study of the network of organic chemistry (Fialkowski et al. 2005), which despite its apparent complexity shows a welldefined topological structure (Grzybowski et al. 2009). ...
Chapter
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Chemical atomism in the nineteenth century: from Dalton to Cannizzaro
  • A Rocke
Rocke, A. Chemical atomism in the nineteenth century: from Dalton to Cannizzaro; Ohio University Press, 1984.
The Chemical Core of Chemistry I: A Conceptual Approach
  • J Schummer
  • Hyle
Schummer, J. HYLE. The Chemical Core of Chemistry I: A Conceptual Approach. Int J Philos Sci 1998, 4, 129-162.
Effective but Costly, Evolved Mechanisms of Defense against a Virulent Opportunistic Pathogen in Drosophila melanogaster
  • S Klamt
  • U Haus
  • Fabian
Klamt, S.; Haus, U.; Fabian. Effective but Costly, Evolved Mechanisms of Defense against a Virulent Opportunistic Pathogen in Drosophila melanogaster. Theis PLos Biology 2009, 5, e1000385.
On the covering generalized rough sets
  • W Bartol
  • K Pioro
  • F Rossello
Bartol, W.; Pioro, K.; Rossello, F. On the covering generalized rough sets. Inf Sci, 2004, 166, 193-211.
Chapter Similarity searching using 2D structural finger-prints
  • P Willett
  • Chemoinformatics
  • J Bajorath
  • Ed
Willett, P. Chemoinformatics and computational chemical biology; Bajorath, J., Ed.; Humana Press, 2011; Chapter Similarity searching using 2D structural finger-prints, pp 133-158.
Concept data analysis
  • C Carpineto
  • G Romano
Carpineto, C.; Romano, G. Concept data analysis;