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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 mathematical modelling from the modelling of intracellular processes such as chemokine receptor signalling and actin filament branching to larger scale processes such as the movement of individual cells or populations of cells through their environment. Two common ways of approaching this modelling are the use of models based on differential equations or agent-based modelling. The application of both these approaches to cell migration are discussed with specific examples along with common software tools to facilitate the process for non-mathematicians. We also highlight the challenges of modelling cell migration and the need for rigorous experimental work to effectively parameterise a model.

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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 methods by different researchers. The release of NPK (nutrient) depends on both molecular diffusions which are expressed by Fick’s second law of diffusion and ionic diffusion, due to the electrolytic behavior of NPK in the soil. In this work, an analytical solution is presented. The obtained solution helps to find the effect of granule coating thickness, nutrient release rate, pH of the soil and temperature of the soil on the nutrient release profiles.

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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 in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

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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 the optical pathway of the light beam. The basic atmospheric processes, viz. radiation absorption by the backround, heat emission, turbulence, and the effect of atmospheric aerosols, are treated, and the last of them is found to play the major role. Aerosols are looked upon as a source of the Mie scattering and they are described by distribution equations with respect to the particle size and the complex refractive index. The variable concentration of the aerosol along the optical pathway and the simultaneous effect of a higher numberof aerosol types are included.

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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 models have been used more often than physical ones. Some of them are predictive, designed for example to calculate the effects of anatomical changes on jumping performance, or the pattern of flow in a 3D assembly of semicircular canals. Others seek an optimum, for example the best possible technique for a high jump. A few have been used in inverse optimization studies, which search for variables that are optimized by observed patterns of behaviour. Mathematical models range from the extreme simplicity of some models of walking and running, to the complexity of models that represent numerous body segments and muscles, or elaborate bone shapes. The simpler the model, the clearer it is which of its features is essential to the calculated effect.

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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 modelled and the scale of the model, different mathematical formulations, ranging from stochastic representations to ordinary and partial differential equations are discussed. This is followed by a brief summary of some recent modelling successes and the state of future models.

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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 whether a particular human action should be captured in a single complex model or whether it is more promising to make extensive use of semantic knowledge and a collection of low–level models that encode certain motion primitives. Scene context plays a crucial role if we intend to give a higher–level interpretation rather than a low–level physical description of the observed motion. A semantic knowledge base is used to establish the scene context. This approach consists of three main components: visual analysis, the mapping from vision to language and the search of the semantic database. A small number of robust visual detectors is used to generate a higher–level description of the scene. The approach together with a number of results is presented in the third part of this article.

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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 haemodialysis, in which the rate of water removal and/or the dialysis machine sodium concentration are varied according to a predetermined profile, can help to prevent wide fluctuations in plasma osmolality, which cause these complications. The profiles are determined on a trial and error basis, and differ from patient to patient. Here we describe a mathematical model for a typical profiled haemodialysis session in which the variables of interest are sodium mass and body fluid volumes. The model is of minimal complexity and so could provide simple guidelines for choosing suitable profiles for individual patients. The model is tested for a series of dialysate sodium profiles to demonstrate the potential benefits of sodium profiling. Next, using the simplicity of the model, we show how to calculate the dialysate sodium profile to model a dialysis session that achieves specified targets of sodium mass removal and weight loss, while keeping the risk of intradia-lytic complications to a minimum. Finally, we investigate which of the model profiled dialysis sessions that meet a range of sodium and fluid removal targets also predict extracellular sodium concentrations and extracellular volumes that lie within “safe” limits. Our model suggests that improvements in volume control via sodium profiling need to be set against potential problems in maintaining blood concentrations and body fluid compartment volumes within “safe” limits.

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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 ultrastructure and the control of cell growth present opportunities for modelling to clarify how growth–related mechanical properties arise from wall polymeric structure and biochemistry.

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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 as a powerful scientific method. This position disregards mathematical thinking as having contributed key discoveries in biology for more than a century, e.g., in the connection between genes, inheritance, and evolution or in the mechanisms of enzymatic catalysis. Here, we discuss the role of computational modelling in the arsenal of modern scientific methods in biomedicine. We list frequent misconceptions about mathematical modelling found among biomedical experimentalists and suggest some good practices that can help bridge the cognitive gap between modelers and experimental researchers in biomedicine. This manuscript was written with two readers in mind. Firstly, it is intended for mathematical modelers with a background in physics, mathematics, or engineering who want to jump into biomedicine. We provide them with ideas to motivate the use of mathematical modelling when discussing with experimental partners. Secondly, this is a text for biomedical researchers intrigued with utilizing mathematical modelling to investigate the pathophysiology of human diseases to improve their diagnostics and treatment.

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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 as a powerful scientific method. This position disregards mathematical thinking as having contributed key discoveries in biology for more than a century, e.g., in the connection between genes, inheritance, and evolution or in the mechanisms of enzymatic catalysis. Here, we discuss the role of computational modelling in the arsenal of modern scientific methods in biomedicine. We list frequent misconceptions about mathematical modelling found among biomedical experimentalists and suggest some good practices that can help bridge the cognitive gap between modelers and experimental researchers in biomedicine. This manuscript was written with two readers in mind. Firstly, it is intended for mathematical modelers with a background in physics, mathematics, or engineering who want to jump into biomedicine. We provide them with ideas to motivate the use of mathematical modelling when discussing with experimental partners. Secondly, this is a text for biomedical researchers intrigued with utilizing mathematical modelling to investigate the pathophysiology of human diseases to improve their diagnostics and treatment.

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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 immune system as well as on the response of the organism to vaccination. In particular, we found that vaccine therapy becomes more effective when used without time delay from a prescribed date of vaccination after surgery and is ineffective without preliminary treatment. For a strong immune response, our model predicts the tumour remission under vaccine therapy. Our study of successive chemo/immuno, immuno/chemo and concurrent chemoimmunotherapy shows that the chemo/immuno sequence is more effective while concurrent chemoimmunotherapy is more sparing.

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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 theory of tumour onset and evolution.

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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 bounds of the aforesaid TIs for the generalized F -sum graphs. The foresaid TIs are also obtained for some particular classes of the generalized F -sum graphs as the consequences of the obtained results. At the end, 3 D -graphical presentations are also included to illustrate the results for better understanding.

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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 organic compound. Before we can utilize models for such purposes, we must define their mathematical structure and identify suitable parameter values. Because nature has not provided us with guidelines for selecting the best model design, the choice of the most useful model is not trivial. In the present chapter I show that power-law modelling within BST (Biochemical Systems Theory) offers guidance for model selection, construction and analysis that is otherwise difficult to find.

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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 geometries like a circle. In this minireview, we focus on recent research which aims at coupling the biochemistry with cellular mechanics and modelling cell shape changes. In particular, we want to contrast two principal modelling approaches: (1) interface tracking where the cell membrane, interfacing cell interior and exterior, is explicitly represented by a set of moving points in 2D or 3D space and (2) interface capturing. In interface capturing, the membrane is implicitly modelled analogously to a level line in a hilly landscape whose topology changes according to forces acting on the membrane. With the increased availability of high-quality 3D microscopy data of complex cell shapes, such methods will become increasingly important in data-driven, image-based modelling to better understand the mechanochemistry underpinning cell motion.

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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 and continuous time models and (iii) representing continuous and discrete state processes. We then discuss the task of calibrating the models using information available in web-based databases. For situations in which the data are not available from existing sources we discuss model calibration based upon measured data and system identification methods. Such methods, together with mathematical modelling databases and computational tools, are often available in standard packages. We therefore make explicit mention of a range of popular and useful sites. As an example of the whole modelling and calibration process, we discuss a study of the cross-talk between the IL-1 (interleukin-1)-stimulated NF-κB (nuclear factor κB) pathway and the TGF-β (transforming growth factor β)-stimulated Smad2 pathway.

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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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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 (semi-spherical) coordinates. Several key parameters including an injection velocity, a diffusion coefficient, thickness of subcutaneous tissue, and a permeability factor at the tissue-blood boundary were estimated from experimental data in rats. With reference to analytical solutions in a simplified model without convection, numerical solutions revealed that the diffusion coefficient and thickness of subcutaneous tissue determined the timing of the peak concentration in the plasma, and its magnitude was dictated by the permeability factor. Furthermore, the initial velocity, induced by needle injection, elevated an immediate transport of salubrinal at t < 1h. The described analysis with a combination of partial and ordinary differential equations contributes to the prediction of local and systemic effects and the understanding of the transportation mechanism of salubrinal and other agents.

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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 vitro studies have proposed that TDF and FTC act synergistically within an HIV-infected cell. However, it is unclear whether, and which, direct drug–drug interactions mediate the apparent synergy. The goal of this work was to refine a mechanistic model for the molecular mechanism of action (MMOA) of nucleoside analogues in order to analyse whether putative direct interactions may account for the in vitro observed synergistic effects. Our analysis suggests that depletion of dNTP pools can explain apparent synergy between TDF and FTC in HIV-infected cells at clinically relevant concentrations. Dead-end complex (DEC) formation does not seem to significantly contribute to the synergistic effect. However, in the presence of non-nucleoside reverse transcriptase inhibitors (NNRTIs), its role might be more relevant, as previously reported in experimental in vitro studies.

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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 of siderophore function related to fungi. Initially, a set of partial differential equations are calibrated and integrated numerically to generate quantitative predictions on the spatio-temporal distributions of siderophores and related populations. This model is then reduced to a simpler set of equations that are solved algebraically giving rise to solutions that predict the distributions of siderophores and resultant compounds. These algebraic results require the calculation of zeros of cross products of Bessel functions and thus new algebraic expansions are derived for a variety of different cases that are in agreement with numerically computed values. The results of the modelling are consistent with experimental data while the analysis provides new quantitative predictions on the time scales involved between siderophore production and iron uptake along with how the total amount of iron acquired by the fungus depends on its environment. The implications to bio-technological applications are briefly discussed.

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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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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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