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Review of cellular biophysics and modeling: a primer on the computational biology of excitable cells

Review of cellular biophysics and modeling: a primer on the computational biology of excitable cells Chaudhry Complex Adapt Syst Model (2020) 8:6 https://doi.org/10.1186/s40294-020-00072-8 BOOK RE VIE W Open Access Review of cellular biophysics and modeling: a primer on the computational biology of excitable cells 1,2* Qasim Ali Chaudhry *Correspondence: Book details chqasim@uet.edu.pk Department Greg Conradi Smith of Mathematics, University of Engineering& Technology, William & Mary, Williamsburg, VA Lahore 54890, Pakistan Cellular Biophysics and Modeling: A Primer on the Computational Biology of Excitable Full list of author information is available at the end of the Cells article Cambridge University Press 2019 © Greg Conradi Smith 2019 DOI: 10.1017/9780511793905 ISBN 978-1-107-00536-5 Hardback ISBN 978-0-521-18305-5 Paperback Keywords: Cellular biophysics, Computational biology, Excitable cells, Mathematical modeling, Dynamical systems Introduction Mathematics is considered to be a difficult subject, and especially this subject and biol - ogy seems immiscible, but this a hard fact that in this era, most of the very important and difficult biological problems are handled with the help of mathematics. This book provides us a sweet mix of biological especially cellular biophysics and mathematical modeling. A mathematical model is a formalized description or an abstract model of a system using tractable mathematical concepts, formulations and language, the mathemati- cal modeling is a process by which a mathematical model is developed. Several books have been written on mathematical modeling for example few of them are (Riaz et  al. 2016; Chaudhry 2016; Dym 2004; Edwards and Edwards 2007; Chaudhry and Al-Mdallal 2019). Mathematical biology is a science and a specialized discipline by which a biologi- cal problem is solved and handled using the concepts and formulation of mathemat- ics. This is one of the most important area of research especially in this era. Many books and research articles have been published where they have solved the complex © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Chaudhry Complex Adapt Syst Model (2020) 8:6 Page 2 of 4 biological problems using mathematics, for example (Bellouquid and Delitala 2006; Herzel and Blüthgen 2008; Hiriart-Urruty 2016). The importance of cell biology cannot be ignored because the origin of life is cell, therefore it is extremely important to study the metabolism, kinetics and other mech- anisms of a cell, and this is the reason that many researches have been done in this area. Cellular biophysics can be termed as the physicochemical and quantitative pro- cess to study the complex and heterogeneous phenomena and processes of cell biol- ogy and in particular the neuroscience, and this book particularly focusses on this topic (Zia and Chaudhry 2016a, b; Gul et  al. 2015; Dreij et  al. 2011; Chaudhry et  al. 2014a, b, c, 2015; Chaudhry and Hanke 2013; Anjum et  al. 2020; Abid et  al. 2014; Khalid and Chaudhry 2019; Chaudhry et al. 2019; Sohail et al. 2018; Khalid and Cha- udrhy 2016). The first chapter of the book is devoted to describe the definitions and basic concepts of the terms which will be later on used throughout this book. The book consists of five parts where each part contains few chapters to discuss the main theme and the details of that part. This book deals with the temporal phenomenon of the biological prob - lems, which were mathematically dealt using ordinary differential equations. Although, it is not difficult to understand that the inclusion of spatial and temporal together not only adds to the difficulty level but also enhances the size of the book, but even than the author of this review article of the book really feels the deficiency of this part in this book, because in order to understand the true metabolism of the cell keeping in view the in vivo and in vitro aspects, spatial part was also desired to be discussed. Part I of the book deals with some basis models where their solutions have been dis- cussed using ordinary differential equations. This part consists of five chapters. In the first chapter, compartment modeling approach has been described and some famous compartment models are given. Second chapter discusses the phase diagrams which arise from the solution of differential equations. Third chapter is devoted to discuss about the kinetic rate laws. In fourth chapter, the author discussed some important function families and their characteristic times. In the last chapter of this part, bifurca- tion (fold, transcritical and pitchfork) diagrams have been discussed in details. Part II of this book is concerned with the passive membranes. This part consists of three chapters where first chapter deals with the equilibrium potential whereas in par - ticular the Nernst equilibrium potential. The second chapter of this part deals with the current balance equation. The third and last chapter is discussed on the very famous GHK theory of membrane permeation. Part III of this book is devoted on voltage-gated currents. This part consists of four chapters. The first chapter is written on voltage-gated ionic currents, whereas the second chapters deals with the regenerative ionic currents and bi-stability. In the third chapter, voltage-clamp recording was discussed in detail, where the fourth chapter was focused on Hodgkin-Huxley model of the action potential. In Part IV of this book, the author discussed the excitability and phase planes. This part contains three chapters where the first chapter talks about the Morris-Lecar model, then its reduced model was also discussed. Second chapter is dealt with phase plane analysis, where 2D autonomous ODEs were handled. The last chapter of this part is con - cerned with the very important topic of linear stability analysis. Chaudhr y Complex Adapt Syst Model (2020) 8:6 Page 3 of 4 In the last Part V of the book, oscillations and bursting was discussed in detail. The part consists of four chapters. In the first and second chapters of this part, Hopf Bifurca - tion (Type II excitability and oscillations) and SNIC and SHO Bifurcations (Type I) were discussed respectively. The third chapter deals with the low-threshold calcium spike where the last chapter of this part and book is devoted to describe the synaptic currents. As the concluding remarks, I found this book really interested and informative. I would like to suggest the author to please add the Matlab programs for the given prob- lems in the next edition. Even then, I would recommend the MS and PhD students of the relevant field, mathematicians and researchers for its reading. Acknowledgements QAC acknowledges the support given by University of Ha’il, Saudi Arabia and University of Engineering and Technology, Lahore Pakistan. Authors’ contributions QAC is the sole author of this review article. The author read and approved the final manuscript. Funding No funding was received. Availability of data and materials Not Applicable Competing interests The authors note that there are no competing interests. Author details 1 2 Department of Mathematics, College of Science, University of Ha’il, 2440, Ha’il, Saudi Arabia. Department of Math- ematics, University of Engineering& Technology, Lahore 54890, Pakistan. Received: 25 May 2020 Accepted: 28 May 2020 References Abid N et al (2014) 3D modeling of reaction-diffusion mechanism in heterogeneous cell architecture. Pak J Sci 66(4):331–335 Anjum AUR, Chaudhry QA, Almatroud AO (2020) Sensitivity analysis of mathematical model to study the effect of T cells infusion in treatment of CLL. Mathematics 8(4):564 Bellouquid A, Delitala M (2006) Mathematical modeling of complex biological systems. Springer, Boston Chaudhry QA (2016) An introduction to agent-based modeling modeling natural, social, and engineered complex systems with NetLogo: a review. Complex Adapt Syst Model 4(1):1–2 Chaudhry QA, Al-Mdallal QM (2019) Review of design optimization of fluid machinery: applying computational fluid dynamics and numerical optimization. Complex Adapt Syst Model. https ://doi.org/10.1186/s4029 4-019-0063-0 Chaudhry QA, Hanke M (2013) Study of intracellular reaction and diffusion mechanism of carcinogenic PAHs: using non- standard compartment modeling approach. Toxicol Lett 221:S182 Chaudhry QA et al (2014a) Surface reactions on the cytoplasmatic membranes—Mathematical modeling of reaction and diffusion systems in a cell. J Comput Appl Math 262:244–260 Chaudhry Q, Chaudhry N, Zafar Z (2014b) Numerical approximation of degradation of plasmid DNA in rat plasma. Paki- stan J Sci 66(1):56–59 ChaudhryChaudhry et al (2014c) Mathematical modeling of reaction–diffusion mechanism of pah diol epoxides in a cell. Pakistan J Sci 66(3):209–213 Chaudhry QA et al (2015) Simplified 2d-axisymmetric model for reaction–diffusion mechanism of PAHS in a mammalian cell. JPIChE 43:97–103 Chaudhry QA et al (2019) In silico modeling for the risk assessment of toxicity in cells. Comput Math Appl 77(6):1541–1548 Dreij K et al (2011) A method for efficient calculation of diffusion and reactions of lipophilic compounds in complex cell geometry. PLoS ONE 6(8):e23128 Dym C (2004) Principles of mathematical modeling. Academic press, Cambridge Edwards D, Edwards M (2007) Guide to mathematical modelling. Industrial Press, New York Gul M et al (2015) Simulation of drug diffusion in mammalian cell. J Math 47(2):11–18 (ISSN 1016-2526) Herzel H, Blüthgen N (2008) Mathematical models in mammalian cell biology. Genome Biol 9(7):1 Hiriart-Urruty J-B (2016) Advances in mathematical modeling, optimization and optimal control. Springer, Berlin Khalid S, Chaudhry QA (2019) Quantitative analysis of cancer risk assessment in a mammalian cell with the inclusion of mitochondria. Comput Math Appl 78(8):2449–2467 Chaudhry Complex Adapt Syst Model (2020) 8:6 Page 4 of 4 Khalid S, Chaudrhy Q (2016) Computational modeling of reaction and diffusion processes of toxic PAHs on cellular and mitochondrial DNA. Toxicol Lett 258:S120 Riaz S, Chaudhry QA, Siddiqui S (2016) Mathematical modeling and optimization of complex structures: a review. Springer, Berlin Sohail A et al (2018) Embodied modeling approach to explore tumour cells drug resistance. Complex Adaptive Systems Modeling 6(1):3 Zia M, Chaudhry Q (2016a) Modeling carcinoma reversion using virtual cell. Toxicol Lett 259:S172 Zia M, Chaudhry Q (2016b) In silico modeling of human malignant tumors’ reprogramming. Toxicol Lett 258:S97 Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Complex Adaptive Systems Modeling Springer Journals

Review of cellular biophysics and modeling: a primer on the computational biology of excitable cells

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Chaudhry Complex Adapt Syst Model (2020) 8:6 https://doi.org/10.1186/s40294-020-00072-8 BOOK RE VIE W Open Access Review of cellular biophysics and modeling: a primer on the computational biology of excitable cells 1,2* Qasim Ali Chaudhry *Correspondence: Book details chqasim@uet.edu.pk Department Greg Conradi Smith of Mathematics, University of Engineering& Technology, William & Mary, Williamsburg, VA Lahore 54890, Pakistan Cellular Biophysics and Modeling: A Primer on the Computational Biology of Excitable Full list of author information is available at the end of the Cells article Cambridge University Press 2019 © Greg Conradi Smith 2019 DOI: 10.1017/9780511793905 ISBN 978-1-107-00536-5 Hardback ISBN 978-0-521-18305-5 Paperback Keywords: Cellular biophysics, Computational biology, Excitable cells, Mathematical modeling, Dynamical systems Introduction Mathematics is considered to be a difficult subject, and especially this subject and biol - ogy seems immiscible, but this a hard fact that in this era, most of the very important and difficult biological problems are handled with the help of mathematics. This book provides us a sweet mix of biological especially cellular biophysics and mathematical modeling. A mathematical model is a formalized description or an abstract model of a system using tractable mathematical concepts, formulations and language, the mathemati- cal modeling is a process by which a mathematical model is developed. Several books have been written on mathematical modeling for example few of them are (Riaz et  al. 2016; Chaudhry 2016; Dym 2004; Edwards and Edwards 2007; Chaudhry and Al-Mdallal 2019). Mathematical biology is a science and a specialized discipline by which a biologi- cal problem is solved and handled using the concepts and formulation of mathemat- ics. This is one of the most important area of research especially in this era. Many books and research articles have been published where they have solved the complex © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Chaudhry Complex Adapt Syst Model (2020) 8:6 Page 2 of 4 biological problems using mathematics, for example (Bellouquid and Delitala 2006; Herzel and Blüthgen 2008; Hiriart-Urruty 2016). The importance of cell biology cannot be ignored because the origin of life is cell, therefore it is extremely important to study the metabolism, kinetics and other mech- anisms of a cell, and this is the reason that many researches have been done in this area. Cellular biophysics can be termed as the physicochemical and quantitative pro- cess to study the complex and heterogeneous phenomena and processes of cell biol- ogy and in particular the neuroscience, and this book particularly focusses on this topic (Zia and Chaudhry 2016a, b; Gul et  al. 2015; Dreij et  al. 2011; Chaudhry et  al. 2014a, b, c, 2015; Chaudhry and Hanke 2013; Anjum et  al. 2020; Abid et  al. 2014; Khalid and Chaudhry 2019; Chaudhry et al. 2019; Sohail et al. 2018; Khalid and Cha- udrhy 2016). The first chapter of the book is devoted to describe the definitions and basic concepts of the terms which will be later on used throughout this book. The book consists of five parts where each part contains few chapters to discuss the main theme and the details of that part. This book deals with the temporal phenomenon of the biological prob - lems, which were mathematically dealt using ordinary differential equations. Although, it is not difficult to understand that the inclusion of spatial and temporal together not only adds to the difficulty level but also enhances the size of the book, but even than the author of this review article of the book really feels the deficiency of this part in this book, because in order to understand the true metabolism of the cell keeping in view the in vivo and in vitro aspects, spatial part was also desired to be discussed. Part I of the book deals with some basis models where their solutions have been dis- cussed using ordinary differential equations. This part consists of five chapters. In the first chapter, compartment modeling approach has been described and some famous compartment models are given. Second chapter discusses the phase diagrams which arise from the solution of differential equations. Third chapter is devoted to discuss about the kinetic rate laws. In fourth chapter, the author discussed some important function families and their characteristic times. In the last chapter of this part, bifurca- tion (fold, transcritical and pitchfork) diagrams have been discussed in details. Part II of this book is concerned with the passive membranes. This part consists of three chapters where first chapter deals with the equilibrium potential whereas in par - ticular the Nernst equilibrium potential. The second chapter of this part deals with the current balance equation. The third and last chapter is discussed on the very famous GHK theory of membrane permeation. Part III of this book is devoted on voltage-gated currents. This part consists of four chapters. The first chapter is written on voltage-gated ionic currents, whereas the second chapters deals with the regenerative ionic currents and bi-stability. In the third chapter, voltage-clamp recording was discussed in detail, where the fourth chapter was focused on Hodgkin-Huxley model of the action potential. In Part IV of this book, the author discussed the excitability and phase planes. This part contains three chapters where the first chapter talks about the Morris-Lecar model, then its reduced model was also discussed. Second chapter is dealt with phase plane analysis, where 2D autonomous ODEs were handled. The last chapter of this part is con - cerned with the very important topic of linear stability analysis. Chaudhr y Complex Adapt Syst Model (2020) 8:6 Page 3 of 4 In the last Part V of the book, oscillations and bursting was discussed in detail. The part consists of four chapters. In the first and second chapters of this part, Hopf Bifurca - tion (Type II excitability and oscillations) and SNIC and SHO Bifurcations (Type I) were discussed respectively. The third chapter deals with the low-threshold calcium spike where the last chapter of this part and book is devoted to describe the synaptic currents. As the concluding remarks, I found this book really interested and informative. I would like to suggest the author to please add the Matlab programs for the given prob- lems in the next edition. Even then, I would recommend the MS and PhD students of the relevant field, mathematicians and researchers for its reading. Acknowledgements QAC acknowledges the support given by University of Ha’il, Saudi Arabia and University of Engineering and Technology, Lahore Pakistan. Authors’ contributions QAC is the sole author of this review article. The author read and approved the final manuscript. Funding No funding was received. Availability of data and materials Not Applicable Competing interests The authors note that there are no competing interests. Author details 1 2 Department of Mathematics, College of Science, University of Ha’il, 2440, Ha’il, Saudi Arabia. Department of Math- ematics, University of Engineering& Technology, Lahore 54890, Pakistan. Received: 25 May 2020 Accepted: 28 May 2020 References Abid N et al (2014) 3D modeling of reaction-diffusion mechanism in heterogeneous cell architecture. Pak J Sci 66(4):331–335 Anjum AUR, Chaudhry QA, Almatroud AO (2020) Sensitivity analysis of mathematical model to study the effect of T cells infusion in treatment of CLL. Mathematics 8(4):564 Bellouquid A, Delitala M (2006) Mathematical modeling of complex biological systems. Springer, Boston Chaudhry QA (2016) An introduction to agent-based modeling modeling natural, social, and engineered complex systems with NetLogo: a review. Complex Adapt Syst Model 4(1):1–2 Chaudhry QA, Al-Mdallal QM (2019) Review of design optimization of fluid machinery: applying computational fluid dynamics and numerical optimization. Complex Adapt Syst Model. https ://doi.org/10.1186/s4029 4-019-0063-0 Chaudhry QA, Hanke M (2013) Study of intracellular reaction and diffusion mechanism of carcinogenic PAHs: using non- standard compartment modeling approach. Toxicol Lett 221:S182 Chaudhry QA et al (2014a) Surface reactions on the cytoplasmatic membranes—Mathematical modeling of reaction and diffusion systems in a cell. J Comput Appl Math 262:244–260 Chaudhry Q, Chaudhry N, Zafar Z (2014b) Numerical approximation of degradation of plasmid DNA in rat plasma. Paki- stan J Sci 66(1):56–59 ChaudhryChaudhry et al (2014c) Mathematical modeling of reaction–diffusion mechanism of pah diol epoxides in a cell. Pakistan J Sci 66(3):209–213 Chaudhry QA et al (2015) Simplified 2d-axisymmetric model for reaction–diffusion mechanism of PAHS in a mammalian cell. JPIChE 43:97–103 Chaudhry QA et al (2019) In silico modeling for the risk assessment of toxicity in cells. Comput Math Appl 77(6):1541–1548 Dreij K et al (2011) A method for efficient calculation of diffusion and reactions of lipophilic compounds in complex cell geometry. PLoS ONE 6(8):e23128 Dym C (2004) Principles of mathematical modeling. Academic press, Cambridge Edwards D, Edwards M (2007) Guide to mathematical modelling. Industrial Press, New York Gul M et al (2015) Simulation of drug diffusion in mammalian cell. J Math 47(2):11–18 (ISSN 1016-2526) Herzel H, Blüthgen N (2008) Mathematical models in mammalian cell biology. Genome Biol 9(7):1 Hiriart-Urruty J-B (2016) Advances in mathematical modeling, optimization and optimal control. Springer, Berlin Khalid S, Chaudhry QA (2019) Quantitative analysis of cancer risk assessment in a mammalian cell with the inclusion of mitochondria. Comput Math Appl 78(8):2449–2467 Chaudhry Complex Adapt Syst Model (2020) 8:6 Page 4 of 4 Khalid S, Chaudrhy Q (2016) Computational modeling of reaction and diffusion processes of toxic PAHs on cellular and mitochondrial DNA. Toxicol Lett 258:S120 Riaz S, Chaudhry QA, Siddiqui S (2016) Mathematical modeling and optimization of complex structures: a review. Springer, Berlin Sohail A et al (2018) Embodied modeling approach to explore tumour cells drug resistance. Complex Adaptive Systems Modeling 6(1):3 Zia M, Chaudhry Q (2016a) Modeling carcinoma reversion using virtual cell. Toxicol Lett 259:S172 Zia M, Chaudhry Q (2016b) In silico modeling of human malignant tumors’ reprogramming. Toxicol Lett 258:S97 Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Complex Adaptive Systems ModelingSpringer Journals

Published: Jun 8, 2020

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