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Journal articles on the topic 'Mathematical molecular modelling'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Middleton, A., M. Owen, M. Bennett, and J. King. "Mathematical modelling of gibberellinsignalling." Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology 150, no. 3 (July 2008): S46. http://dx.doi.org/10.1016/j.cbpa.2008.04.023.

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2

Butler, George, Jonathan Rudge, and Philip R. Dash. "Mathematical modelling of cell migration." Essays in Biochemistry 63, no. 5 (October 2019): 631–37. http://dx.doi.org/10.1042/ebc20190020.

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Abstract The complexity of biological systems creates challenges for fully understanding their behaviour. This is particularly true for cell migration which requires the co-ordinated activity of hundreds of individual components within cells. Mathematical modelling can help understand these complex systems by breaking the system into discrete steps which can then be interrogated in silico. In this review, we highlight scenarios in cell migration where mathematical modelling can be applied and discuss what types of modelling are most suited. Almost any aspect of cell migration is amenable to ma

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3

Irfan, Sayed Ameenuddin, and Radzuan Razali. "Mathematical modelling of controlled release fertilizer." Malaysian Journal of Fundamental and Applied Sciences 13, no. 4-1 (December 5, 2017): 372–74. http://dx.doi.org/10.11113/mjfas.v13n4-1.878.

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Controlled release fertilizers (CRFs) are essential for sustainable agriculture system. CRFs are designed to maintain the constant optimum release rate of nutrients from the coated granule. This increase the plant uptake of nutrients hence reduces the soil pollution and decreases the crop expenditure. In the literature, the maximum studies have been done by considering the molecular diffusion as the only phenomenon responsible for nutrient release from CRFs. The molecular diffusion model is solved mostly by using the variable separable methods and Laplace transform as well as finite difference

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4

Leng, G., and D. J. MacGregor. "Mathematical Modelling in Neuroendocrinology." Journal of Neuroendocrinology 20, no. 6 (June 2008): 713–18. http://dx.doi.org/10.1111/j.1365-2826.2008.01722.x.

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5

Vasieva, Olga, Manan'Iarivo Rasolonjanahary, and Bakhtier Vasiev. "Mathematical modelling in developmental biology." REPRODUCTION 145, no. 6 (June 2013): R175—R184. http://dx.doi.org/10.1530/rep-12-0081.

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In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies

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6

MacArthur, B. D., C. P. Please, M. Taylor, and R. O. C. Oreffo. "Mathematical modelling of skeletal repair." Biochemical and Biophysical Research Communications 313, no. 4 (January 2004): 825–33. http://dx.doi.org/10.1016/j.bbrc.2003.11.171.

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7

Zrcek, František, and Milan Horák. "Mathematical modelling of remote detection of molecular air pollutants." Collection of Czechoslovak Chemical Communications 52, no. 6 (1987): 1397–406. http://dx.doi.org/10.1135/cccc19871397.

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A model of remote detection of molecular air pollutants is devised based on the lidar equation. The various kinds of interaction of radiation with matter, viz. absorption, induced fluorescence, and Raman scattering, are taken into account; detection of either scattered or reflected signal is considered. The reflection is assumed to be either axial, using a retroreflector, or omnidirectional from a field target. Based on this model, an algorithm was set up for simulation of the different variants of the experiment, making allowance for a generally variable concentration of the compound along th

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8

Alexander, R. McN. "Modelling approaches in biomechanics." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1437 (August 6, 2003): 1429–35. http://dx.doi.org/10.1098/rstb.2003.1336.

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Conceptual, physical and mathematical models have all proved useful in biomechanics. Conceptual models, which have been used only occasionally, clarify a point without having to be constructed physically or analysed mathematically. Some physical models are designed to demonstrate a proposed mechanism, for example the folding mechanisms of insect wings. Others have been used to check the conclusions of mathematical modelling. However, others facilitate observations that would be difficult to make on real organisms, for example on the flow of air around the wings of small insects. Mathematical m

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9

Head, A. K., S. D. Howison, J. R. Ockendon, and S. P. Tighe. "Mathematical modelling of dislocation plasticity." Physica Scripta T44 (January 1, 1992): 135–36. http://dx.doi.org/10.1088/0031-8949/1992/t44/022.

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10

McDonald, Andrew G., Keith F. Tipton, and Gavin P. Davey. "Mathematical modelling of metabolism: Summing up." Biochemist 31, no. 3 (June 1, 2009): 24–27. http://dx.doi.org/10.1042/bio03103024.

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Biochemistry is as much a quantitative subject as qualitative. Initial observations of single- or multicellular organisms have given rise to our discipline, which is the discovery and characterization of the chemistry of all living things. We have moved from Lavoisier's seminal observation of respiration as a form of combustion, to a much more detailed knowledge of the associated biochemistry.

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11

Britton, Nicholas F., and Suzanne M. Skevington. "On the mathematical modelling of pain." Neurochemical Research 21, no. 9 (September 1996): 1133–40. http://dx.doi.org/10.1007/bf02532424.

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12

Huber, Heinrich J., Heiko Duessmann, Jakub Wenus, Seán M. Kilbride, and Jochen H. M. Prehn. "Mathematical modelling of the mitochondrial apoptosis pathway." Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1813, no. 4 (April 2011): 608–15. http://dx.doi.org/10.1016/j.bbamcr.2010.10.004.

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13

Wearing, H. "Mathematical Modelling of Juxtacrine Patterning." Bulletin of Mathematical Biology 62, no. 2 (February 2000): 293–320. http://dx.doi.org/10.1006/bulm.1999.0152.

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14

Smallbone, Kieran, Robert A. Gatenby, and Philip K. Maini. "Mathematical modelling of tumour acidity." Journal of Theoretical Biology 255, no. 1 (November 2008): 106–12. http://dx.doi.org/10.1016/j.jtbi.2008.08.002.

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15

Cohen, David P. A., Loredana Martignetti, Sylvie Robine, Emmanuel Barillot, Andrei Zinovyev, and Laurence Calzone. "Mathematical Modelling of Molecular Pathways Enabling Tumour Cell Invasion and Migration." PLOS Computational Biology 11, no. 11 (November 3, 2015): e1004571. http://dx.doi.org/10.1371/journal.pcbi.1004571.

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16

Murrieta-Rico, Fabian N., Paolo Mercorelli, Oleg Yu Sergiyenko, Vitalii Petranovskii, Daniel Hernández-Balbuena, and Vera Tyrsa. "Mathematical Modelling of molecular adsorption in zeolite coated frequency domain sensors." IFAC-PapersOnLine 48, no. 1 (2015): 41–46. http://dx.doi.org/10.1016/j.ifacol.2015.05.060.

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17

Liebal, Ulf W., Thomas Millat, Imke G. De Jong, Oscar P. Kuipers, Uwe Völker, and Olaf Wolkenhauer. "How mathematical modelling elucidates signalling in Bacillus subtilis." Molecular Microbiology 77, no. 5 (August 25, 2010): 1083–95. http://dx.doi.org/10.1111/j.1365-2958.2010.07283.x.

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18

Rangamani, Padmini, and Ravi Iyengar. "Modelling cellular signalling systems." Essays in Biochemistry 45 (September 30, 2008): 83–94. http://dx.doi.org/10.1042/bse0450083.

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Cell signalling pathways and networks are complex and often non-linear. Signalling pathways can be represented as systems of biochemical reactions that can be modelled using differential equations. Computational modelling of cell signalling pathways is emerging as a tool that facilitates mechanistic understanding of complex biological systems. Mathematical models are also used to generate predictions that may be tested experimentally. In the present chapter, the various steps involved in building models of cell signalling pathways are discussed. Depending on the nature of the process being mod

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19

Owen, Markus R., and Jonathan A. Sherratt. "Mathematical modelling of juxtacrine cell signalling." Mathematical Biosciences 153, no. 2 (November 1998): 125–50. http://dx.doi.org/10.1016/s0025-5564(98)10034-2.

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20

Lemon, Greg, Daniel Howard, Matthew J. Tomlinson, Lee D. Buttery, Felicity R. A. J. Rose, Sarah L. Waters, and John R. King. "Mathematical modelling of tissue-engineered angiogenesis." Mathematical Biosciences 221, no. 2 (October 2009): 101–20. http://dx.doi.org/10.1016/j.mbs.2009.07.003.

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21

Walicki, Edward, and Anna Walicka. "Mathematical modelling of some biological bearings." Smart Materials and Structures 9, no. 3 (June 1, 2000): 280–83. http://dx.doi.org/10.1088/0964-1726/9/3/305.

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22

Rittscher, Jens, Andrew Blake, Anthony Hoogs, and Gees Stein. "Mathematical modelling of animate and intentional motion." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1431 (February 17, 2003): 475–90. http://dx.doi.org/10.1098/rstb.2002.1259.

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Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whethe

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23

Baigent, Stephen, Robert Unwin, and Chee Chit Yeng. "Mathematical Modelling of Profiled Haemodialysis: A Simplified Approach." Journal of Theoretical Medicine 3, no. 2 (2001): 143–60. http://dx.doi.org/10.1080/10273660108833070.

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For many renal patients with severe loss of kidney function dialysis treatment is the only means of preventing excessive fluid gain and the accumulation of toxic chemicals in the blood. Typically, haemodialysis patients will dialyse three times a week, with each session lasting 4-6 hours. During each session, 2-3 litres of fluid is removed along with catabolic end-products, and osmotically active solutes. In a significant number of patients, the rapid removal of water and osmotically active sodium chloride can lead to hypotension or overhydration and swelling of brain cells. Profiled haemodial

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24

Marshall, James A. R., Andreagiovanni Reina, and Thomas Bose. "Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths." PLOS ONE 14, no. 9 (September 30, 2019): e0222906. http://dx.doi.org/10.1371/journal.pone.0222906.

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25

Bruce, David M. "Mathematical modelling of the cellular mechanics of plants." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1437 (July 30, 2003): 1437–44. http://dx.doi.org/10.1098/rstb.2003.1337.

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The complex mechanical behaviour of plant tissues reflects the complexity of their structure and material properties. Modelling has been widely used in studies of how cell walls, single cells and tissue respond to loading, both externally applied loading and loads on the cell wall resulting from changes in the pressure within fluid–filled cells. This paper reviews what approaches have been taken to modelling and simulation of cell wall, cell and tissue mechanics, and to what extent models have been successful in predicting mechanical behaviour. Advances in understanding of cell wall ultrastruc

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26

Vera, Julio, Christopher Lischer, Momchil Nenov, Svetoslav Nikolov, Xin Lai, and Martin Eberhardt. "Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic." International Journal of Molecular Sciences 22, no. 2 (January 7, 2021): 547. http://dx.doi.org/10.3390/ijms22020547.

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In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today’s level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than a

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27

Vera, Julio, Christopher Lischer, Momchil Nenov, Svetoslav Nikolov, Xin Lai, and Martin Eberhardt. "Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic." International Journal of Molecular Sciences 22, no. 2 (January 7, 2021): 547. http://dx.doi.org/10.3390/ijms22020547.

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In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today’s level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than a

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28

Middleton, A. "Mathematical modelling of the Aux/IAA response to Auxin." Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology 150, no. 3 (July 2008): S49. http://dx.doi.org/10.1016/j.cbpa.2008.04.615.

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29

Isaeva, O. G., and V. A. Osipov. "Different Strategies for Cancer Treatment: Mathematical Modelling." Computational and Mathematical Methods in Medicine 10, no. 4 (2009): 253–72. http://dx.doi.org/10.1080/17486700802536054.

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We formulate and analyse a mathematical model describing immune response to avascular tumour under the influence of immunotherapy and chemotherapy and their combinations as well as vaccine treatments. The effect of vaccine therapy is considered as a parametric perturbation of the model. In the case of a weak immune response, neither immunotherapy nor chemotherapy is found to cause tumour regression to a small size, which would be below the clinically detectable threshold. Numerical simulations show that the efficiency of vaccine therapy depends on both the tumour size and the condition of immu

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30

BELLOMO, N., N. K. LI, and P. K. MAINI. "ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES." Mathematical Models and Methods in Applied Sciences 18, no. 04 (April 2008): 593–646. http://dx.doi.org/10.1142/s0218202508002796.

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This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theor

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31

Meades, G., N. K. Thalji, M. de Queiroz, X. Cai, and G. L. Waldrop. "Mathematical modelling of negative feedback regulation by carboxyltransferase." IET Systems Biology 5, no. 3 (May 1, 2011): 220–28. http://dx.doi.org/10.1049/iet-syb.2010.0071.

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32

Bull, Joshua A., Franziska Mech, Tom Quaiser, Sarah L. Waters, and Helen M. Byrne. "Mathematical modelling reveals cellular dynamics within tumour spheroids." PLOS Computational Biology 16, no. 8 (August 18, 2020): e1007961. http://dx.doi.org/10.1371/journal.pcbi.1007961.

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33

Ward, J. P. "Mathematical modelling of quorum sensing in bacteria." Mathematical Medicine and Biology 18, no. 3 (September 1, 2001): 263–92. http://dx.doi.org/10.1093/imammb/18.3.263.

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34

Herrero, Miguel A., and José M. López. "Bone Formation: Biological Aspects and Modelling Problems." Journal of Theoretical Medicine 6, no. 1 (2005): 41–55. http://dx.doi.org/10.1080/10273660412331336883.

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In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological experimentation.

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35

Du, Yansong, Yang Zheng, Shangzhi Xie, and Xu Bo. "Mathematical modelling of a crystal spatial light mixer." Journal of Optics 22, no. 2 (January 21, 2020): 025704. http://dx.doi.org/10.1088/2040-8986/ab6424.

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36

Grassly, Nicholas C., Margarita Pons-Salort, Edward P. K. Parker, Peter J. White, Neil M. Ferguson, Kylie Ainslie, Marc Baguelin, et al. "Comparison of molecular testing strategies for COVID-19 control: a mathematical modelling study." Lancet Infectious Diseases 20, no. 12 (December 2020): 1381–89. http://dx.doi.org/10.1016/s1473-3099(20)30630-7.

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37

Li, Dawang, Long-yuan Li, and Xianfeng Wang. "Mathematical modelling of concrete carbonation with moving boundary." International Communications in Heat and Mass Transfer 117 (October 2020): 104809. http://dx.doi.org/10.1016/j.icheatmasstransfer.2020.104809.

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38

Bartel, Thomas, and Hermann-Georg Holzhütter. "Mathematical modelling of the purine metabolism of the rat liver." Biochimica et Biophysica Acta (BBA) - General Subjects 1035, no. 3 (September 1990): 331–39. http://dx.doi.org/10.1016/0304-4165(90)90097-g.

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39

Liu, Jia Bao, Sana Akram, Muhammad Javaid, Abdul Raheem, and Roslan Hasni. "Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs." Discrete Dynamics in Nature and Society 2021 (March 2, 2021): 1–17. http://dx.doi.org/10.1155/2021/8821020.

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A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total π -electron energy of the molecules, respectively. For molecular graphs, the general sum-connectivity and general Randić are well-studied fundamental topological indices (TIs) which are considered as degree-based molecular descriptors. In this paper, we obtain the

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40

Voit, Eberhard O. "Modelling metabolic networks using power-laws and S-systems." Essays in Biochemistry 45 (September 30, 2008): 29–40. http://dx.doi.org/10.1042/bse0450029.

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Mathematical modelling has great potential in biochemical network analysis because, in contrast with the unaided human mind, mathematics has no problems keeping track of hundreds of interacting variables that affect each other in intricate ways. The scalability of mathematical models, together with their ability to capture all imaginable non-linear responses, allows us to explore the dynamics of complicated pathway systems, to study what happens if a metabolite, gene or enzyme is altered, and to optimize biochemical systems, for instance toward the goal of increased yield of some desired organ

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41

Brumen, Milan, Aleš Fajmut, Andrej Dobovišek, and Etienne Roux. "Mathematical Modelling of Ca2+ Oscillations in Airway Smooth Muscle Cells." Journal of Biological Physics 31, no. 3-4 (December 2005): 515–24. http://dx.doi.org/10.1007/s10867-005-2409-4.

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42

Kambam, P. K. R., M. A. Henson, and L. Sun. "Design and mathematical modelling of a synthetic symbiotic ecosystem." IET Systems Biology 2, no. 1 (January 1, 2008): 33–38. http://dx.doi.org/10.1049/iet-syb:20070011.

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43

Stinner, Björn, and Till Bretschneider. "Mathematical modelling in cell migration: tackling biochemistry in changing geometries." Biochemical Society Transactions 48, no. 2 (April 2, 2020): 419–28. http://dx.doi.org/10.1042/bst20190311.

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Directed cell migration poses a rich set of theoretical challenges. Broadly, these are concerned with (1) how cells sense external signal gradients and adapt; (2) how actin polymerisation is localised to drive the leading cell edge and Myosin-II molecular motors retract the cell rear; and (3) how the combined action of cellular forces and cell adhesion results in cell shape changes and net migration. Reaction–diffusion models for biological pattern formation going back to Turing have long been used to explain generic principles of gradient sensing and cell polarisation in simple, static geomet

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44

Sreenath, Sree N., Kwang-Hyun Cho, and Peter Wellstead. "Modelling the dynamics of signalling pathways." Essays in Biochemistry 45 (September 30, 2008): 1–28. http://dx.doi.org/10.1042/bse0450001.

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In the present chapter we discuss methodologies for the modelling, calibration and validation of cellular signalling pathway dynamics. The discussion begins with the typical range of techniques for modelling that might be employed to go from the chemical kinetics to a mathematical model of biochemical pathways. In particular, we consider the decision-making processes involved in selecting the right mechanism and level of detail of representation of the biochemical interactions. These include the choice between (i) deterministic and stochastic chemical kinetics representations, (ii) discrete an

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45

Khatibi, R. H., R. Lincoln, D. Jackson, S. Surendran, C. Whitlow, and J. Schellekens. "Systemic data management for mathematical modelling of environmental problems." Management of Environmental Quality: An International Journal 15, no. 3 (June 2004): 318–30. http://dx.doi.org/10.1108/14777830410531289.

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46

Chen, Andy, Ping Zhang, Zhiyao Duan, Guofeng Wang, and Hiroki Yokota. "Modelling the Molecular Transportation of Subcutaneously Injected Salubrinal." Biomedical Engineering and Computational Biology 3 (January 2011): BECB.S7050. http://dx.doi.org/10.4137/becb.s7050.

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For the subcutaneous administration of a chemical agent (salubrinal), we constructed a mathematical model of molecule transportation and subsequently evaluated the kinetics of diffusion, convection, and molecular turnover. Salubrinal is a potential therapeutic agent that can reduce cellular damage and death. The understanding of its temporal profiles in local tissue as well as in a whole body is important to develop a proper strategy for its administration. Here, the diffusion and convection kinetics was formulated using partial and ordinary differential equations in one- and three-dimensional

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47

Iannuzzi, Sara, and Max von Kleist. "Mathematical Modelling of the Molecular Mechanisms of Interaction of Tenofovir with Emtricitabine against HIV." Viruses 13, no. 7 (July 13, 2021): 1354. http://dx.doi.org/10.3390/v13071354.

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The combination of the two nucleoside reverse transcriptase inhibitors (NRTI) tenofovir disoproxil fumarate (TDF) and emtricitabine (FTC) is used in most highly active antiretroviral therapies for treatment of HIV-1 infection, as well as in pre-exposure prophylaxis against HIV acquisition. Administered as prodrugs, these drugs are taken up by HIV-infected target cells, undergo intracellular phosphorylation and compete with natural deoxynucleoside triphosphates (dNTP) for incorporation into nascent viral DNA during reverse transcription. Once incorporated, they halt reverse transcription. In vi

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48

Choudhury, M. Jabed A., Philip M. J. Trevelyan, and Graeme P. Boswell. "Mathematical modelling of fungi-initiated siderophore–iron interactions." Mathematical Medicine and Biology: A Journal of the IMA 37, no. 4 (July 14, 2020): 515–50. http://dx.doi.org/10.1093/imammb/dqaa008.

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Abstract Nearly all life forms require iron to survive and function. Microorganisms utilize a number of mechanisms to acquire iron including the production of siderophores, which are organic compounds that combine with ferric iron into forms that are easily absorbed by the microorganism. There has been significant experimental investigation into the role, distribution and function of siderophores in fungi but until now no predictive tools have been developed to qualify or quantify fungi-initiated siderophore–iron interactions. In this investigation, we construct the first mathematical models o

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49

Ruiz-Baier, R., A. Gizzi, S. Rossi, C. Cherubini, A. Laadhari, S. Filippi, and A. Quarteroni. "Mathematical modelling of active contraction in isolated cardiomyocytes." Mathematical Medicine and Biology 31, no. 3 (June 10, 2013): 259–83. http://dx.doi.org/10.1093/imammb/dqt009.

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50

Brown, L. E., A. M. Middleton, J. R. King, and M. Loose. "Multicellular Mathematical Modelling of Mesendoderm Formation in Amphibians." Bulletin of Mathematical Biology 78, no. 3 (March 2016): 436–67. http://dx.doi.org/10.1007/s11538-016-0150-8.

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