Biological similarity and group theory

Derome, Jean‐Robert

doi:10.1016/0022-5193(77)90331-9

Cited by 12 publications

(5 citation statements)

References 6 publications

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“…In this sense, very diverse contributions can be found in the literature, for instance those based on statistical approaches (Kaitaniemi, 2004;Packard, 2009;Wu et al, 2002), network theory (Furusawa and Kaneko, 2006), and on physical arguments, mainly based on fractality and scaling principles (see Aon et al 2004;Auffray and Nottale, 2008;Demetrius, 2006;West, 1999;West et al 2002;West and Brown, 2005). In addition, some authors have specifically addressed the relevance of group theory and the renormalization group approach (Derome, 1977;West, 2004) in such framework. However, as indicated in the previous subsection, the renormalization group methodology has not yet been applied in the context of powerlaw models (such as S-systems and GMA systems) and power-law rate-laws in order to account for the accuracy of the resulting models.…”

Section: Brief Outline Of the Renormalization Group Methodsmentioning

confidence: 99%

Renormalization group approach to power-law modeling of complex metabolic networks

Hernández‐Bermejo

2010

Journal of Theoretical Biology

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To cite this version:Benito Hernández-Bermejo. Renormalization group approach to power-law modeling of complex metabolic networks.Journal of Theoretical Biology, Elsevier, 2010, 265 (3) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A c c e p t e d m a n u s c r i p t AbstractIn the modeling of complex biological systems, and specially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations.

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Section: Brief Outline Of the Renormalization Group Methodsmentioning

confidence: 99%

Renormalization group approach to power-law modeling of complex metabolic networks

Hernández‐Bermejo

2010

Journal of Theoretical Biology

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“…For much of the 20th century, abstract algebras such as groups and related structures, including rings, group rings, and fields, have been adopted in various fields of natural science [ 1 – 5 ]. Symmetry treatments of dynamic phenomena have been integral to simplifying, unifying, and integrating formal representations of the natural sciences, such as chemistry [ 6 ], physics [ 7 – 10 ], molecular biology [ 11 – 15 ], and anthropology [ 16 ].…”

Section: Introductionmentioning

confidence: 99%

A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors

Sawamura

Morishita

Ishigooka

2016

Theor Biol Med Model

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BackgroundPreviously, we applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings (including laboratory data). To gain a more concrete comprehension, we here apply the concept of matrix representation, which was not explicitly exploited in our previous work.MethodsStarting with a set of orthonormal vectors, called the basis, an operator Rj (an N-tuple patient disease state at the j-th session) was expressed as a set of stratified vectors representing plural operations on individual components, so as to satisfy the group matrix representation.ResultsThe stratified vectors containing individual unit operations were combined into one-dimensional square matrices [Rj]s. The [Rj]s meet the matrix representation of a group (ring) as a K-algebra. Using the same-sized matrix of stratified vectors, we can also express changes in the plural set of [Rj]s. The method is demonstrated on simple examples.ConclusionsDespite the incompleteness of our model, the group matrix representation of stratified vectors offers a formal mathematical approach to clinical medicine, aligning it with other branches of natural science.

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“…In general, when group theory is used in various fields of natural sciences, it plays an important role in describing geometrical or dynamical symmetries of phenomena under consideration; examples include mathematics [3,4], physics [5-8], chemistry [9], molecular/genetic biology [10-22], and anthropology [23]. Moreover, much fertile ground still exists where group theory can display its versatility from a multitude of viewpoints.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, much fertile ground still exists where group theory can display its versatility from a multitude of viewpoints. To our knowledge, one such candidate is molecular/genetic biology where group theory has already provided great contributions [10-22]. …”

Section: Introductionmentioning

confidence: 99%

A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology

Sawamura

Morishita

Ishigooka

2014

Theor Biol Med Model

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BackgroundPreviously, we suggested prototypal models that describe some clinical states based on group postulates. Here, we demonstrate a group/category theory-like model for molecular/genetic biology as an alternative application of our previous model. Specifically, we focus on deoxyribonucleic acid (DNA) base sequences.ResultsWe construct a wallpaper pattern based on a five-letter cruciform motif with letters C, A, T, G, and E. Whereas the first four letters represent the standard DNA bases, the fifth is introduced for ease in formulating group operations that reproduce insertions and deletions of DNA base sequences. A basic group Z5 = {r, u, d, l, n} of operations is defined for the wallpaper pattern, with which a sequence of points can be generated corresponding to changes of a base in a DNA sequence by following the orbit of a point of the pattern under operations in group Z5. Other manipulations of DNA sequence can be treated using a vector-like notation ‘Dj’ corresponding to a DNA sequence but based on the five-letter base set; also, ‘Dj’s are expressed graphically. Insertions and deletions of a series of letters ‘E’ are admitted to assist in describing DNA recombination. Likewise, a vector-like notation Rj can be constructed for sequences of ribonucleic acid (RNA). The wallpaper group B = {Z5×∞, ●} (an ∞-fold Cartesian product of Z5) acts on Dj (or Rj) yielding changes to Dj (or Rj) denoted by ‘Dj◦B(j→k) = Dk’ (or ‘Rj◦B(j→k) = Rk’). Based on the operations of this group, two types of groups—a modulo 5 linear group and a rotational group over the Gaussian plane, acting on the five bases—are linked as parts of the wallpaper group for broader applications. As a result, changes, insertions/deletions and DNA (RNA) recombination (partial/total conversion) are described. As an exploratory study, a notation for the canonical “central dogma” via a category theory-like way is presented for future developments.ConclusionsDespite the large incompleteness of our methodology, there is fertile ground to consider a symmetry model for genetic coding based on our specific wallpaper group. A more integrated formulation containing “central dogma” for future molecular/genetic biology remains to be explored.

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Biological similarity and group theory

Cited by 12 publications

References 6 publications

Renormalization group approach to power-law modeling of complex metabolic networks

Renormalization group approach to power-law modeling of complex metabolic networks

A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors

A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology

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