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Restrepo G. Semiotic thoughts on biological sequence representations. Comb Chem High Throughput Screen 2021; 25:349-353. [PMID: 34225612 DOI: 10.2174/1386207324666210705112232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Revised: 04/08/2021] [Accepted: 06/12/2021] [Indexed: 11/22/2022]
Abstract
The deluge of biological sequences ranging from those of proteins, DNA and RNA to genomes has increased the models for their representation, which are further used to contrast those sequences. Here we present a brief bibliometric description of the research area devoted to representation of biological sequences and highlight the semiotic reaches of this process. Finally, we argue that this research area needs further research according to the evolution of mathematical chemistry and its drawbacks are required to be overcome.
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Affiliation(s)
- Guillermo Restrepo
- Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany; Interdisciplinary Center for Bioinformatics, Universität Leipzig, Leipzig, Germany
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Kerr R, Thomson WM, Smith DJ. Mathematical modelling of the vitamin C clock reaction. R Soc Open Sci 2019; 6:181367. [PMID: 31183115 PMCID: PMC6502385 DOI: 10.1098/rsos.181367] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/17/2018] [Accepted: 03/07/2019] [Indexed: 06/09/2023]
Abstract
Chemical clock reactions are characterized by a relatively long induction period followed by a rapid 'switchover' during which the concentration of a clock chemical rises rapidly. In addition to their interest in chemistry education, these reactions are relevant to industrial and biochemical applications. A substrate-depletive, non-autocatalytic clock reaction involving household chemicals (vitamin C, iodine, hydrogen peroxide and starch) is modelled mathematically via a system of nonlinear ordinary differential equations. Following dimensional analysis, the model is analysed in the phase plane and via matched asymptotic expansions. Asymptotic approximations are found to agree closely with numerical solutions in the appropriate time regions. Asymptotic analysis also yields an approximate formula for the dependence of switchover time on initial concentrations and the rate of the slow reaction. This formula is tested via 'kitchen sink chemistry' experiments, and is found to enable a good fit to experimental series varying in initial concentrations of both iodine and vitamin C. The vitamin C clock reaction provides an accessible model system for mathematical chemistry.
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Affiliation(s)
| | | | - D. J. Smith
- Author for correspondence: D. J. Smith e-mail:
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Packwood DM, Reaves KT, Federici FL, Katzgraber HG, Teizer W. Two-dimensional molecular magnets with weak topological invariant magnetic moments: mathematical prediction of targets for chemical synthesis. Proc Math Phys Eng Sci 2013; 469:20130373. [PMID: 24353469 DOI: 10.1098/rspa.2013.0373] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Accepted: 08/27/2013] [Indexed: 11/12/2022] Open
Abstract
An open problem in applied mathematics is to predict interesting molecules that are realistic targets for chemical synthesis. In this paper, we use a spin Hamiltonian-type model to predict molecular magnets (MMs) with magnetic moments that are intrinsically robust under random shape deformations to the molecule. Using the concept of convergence in probability, we show that for MMs in which all spin centres lie in-plane and all spin centre interactions are ferromagnetic, the total spin of the molecule is a 'weak topological invariant' when the number of spin centres is sufficiently large. By weak topological invariant, we mean that the total spin of the molecule depends only upon the arrangement of spin centres in the molecule, and is unlikely to change under shape deformations to the molecule. Our calculations show that only between 20 and 50 spin centres are necessary for the total spin of these MMs to be a weak topological invariant. The robustness effect is particularly enhanced for two-dimensional ferromagnetic MMs that possess a small number of spin rings in the structure.
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Affiliation(s)
- D M Packwood
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan
| | - K T Reaves
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA
| | - F L Federici
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Department of Physics and Astronomy , University College London , Gower Street, London WC1E 6BT, UK
| | - H G Katzgraber
- Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA ; Department of Physics and Astronomy , Texas A&M University , College Station, TX 77843-4242, USA
| | - W Teizer
- WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , Texas A&M University , College Station, TX 77843-3003, USA ; Department of Physics and Astronomy , Texas A&M University , College Station, TX 77843-4242, USA
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