- Email: [email protected]
Mathematical Aspects of Hodgkin-Huxley Neural Theory.
a variety of subjects, from rather unknown specialties up to such well-studied examples as the frog cornea or renal tubes and the gastric mucosa. The methods applied range from biochemical experiments with various inhibitors to microelectrode studies. It is no wonder that the reviewed data (extracted from more than 1.000 original papers) are controversial and difficult to interpret. This confusion is apparently caused by the existence of different types of chloride transport, reaching from the well-documented co-transport of chloride and sodium ions and the passive exchange against the bicarbonate anion to various types of ATP-driven active uphill transport mechanisms. There is also good evidence for a coupling both to a Na+/K+ pump and - at least in some cases - to a proton gradient. The altogether 14 chapters, written by a well-chosen team of experts, present a wealth of information. Nevertheless, the book must be regarded as a source book for the specialist. The reviewer still has severe doubts whether more than a few selected chapters may be recommended for the “normal” membrane biochemist or physiologist. H. METZNER Tiibingen
Mathematical University US$49.50.
Aspects of Hodgkin-Huxley Neural Theory. J. Cronin. Cambridge Press, Cambridge, 1987, ISBN O-521-33482-9, xi + 261 pp., f35.00,
This book gives an excellent overview of the recent mathematical treatments of the Hodgkin-Huxley equations. Indeed, since the pioneering work of Hodgkin and Huxley in 1952, numerous mathematical models, analytical or numerical, tried to explain important features of nervous conduction (treshold phenomenon, refractory period, traveling waves, . . . ). H owever, severe drawbacks still remain, as indicated in the first chapter of the book. Besides, the author explains why a study of how the solutions behave in general is as important as a numerical study of a particular set of equaitons. The HH equations are difficult to study for two reasons: firstly, they form a system of four strongly non-linear differential equations; and secondly, new mathematical methods (such as singular perturbation analysis) are needed to obtain analytical solutions. In this book, several different models for nerve conduction are reviewed (chapter 3) as well as models for electrically excitable cells other than neurons (chapter 4). Then, the author presents a clear summary of the theory of differential equations (chapter 5), emphasizing the role of periodic solutions, and introducing singular perturbation theory. Finally, the author discusses recent mathematical models derived from voltageclamp experiments (chapter 6). This part of the book is perhaps too short, since it is
210
really the body of the subject. The author chooses the FitzHugh-Nagumo model for nerve conduction, which is a two-dimensional and autonomous system. The singular perturbation method is applied close to the discontinuous solution, and the author concludes that there is a unique stable periodic solution of the singularly perturbed system for each sufficiently small parameter. In the case of the cardiac Purkinje fiber, the Noble model is used, which can be reduced to a three-dimensional system. This three-dimensional system does not have periodic solutions. Finally, the author gives further directions for study of the Noble model and other cardiac models. It may be asked here why the possible apparition of chaotic regimes as the number of differential equations in the system increases is not discussed. In summary, this book should serve as a good introduction to the interdisciplinary subject of the mathematical treatment of nervous conduction for researchers and graduate students in mathematics, physics, biology or medicine. D. GALLEZ BlUSSdS
Immobilized Biocatalysts. W. Hartmeyer. 3-540-16335-2, x + 211 pp., DM39.00.
Springer
Verlag,
Berlin,
1988,
ISBN
Immobilised systems are finding increasing fields of use due to their advantages of higher stability and lower costs. These systems are applied both to industrial biotechnological process because of their cleanliness and to analytical determinations. The most common immobilised systems are biocatalysts: there are enzymes, tissues or bacteria with differences in availability, in stability, or in cost. The first point limiting the use of these systems is evidently related to the support on which the biocatalyst is immobilised and to the immobilisation procedure, which can either be of a chemical nature, with the advantage of stronger bonding but also with the possible risk of less activity, or of a physical one, with the advantage of unmodified chemical structure but with the danger of low stability and thus low activity after short time. All these subjects are treated wisely in the book, both from a theoretical and a practical point of view. The latter is of particular interest, with some practical, experiments being accurately described and able to put the reader in the position to understand clearly the adopted procedures. These experiments fall into the different fields of application: industrial production (aspartic acid, penicillins, aminoacids), analysis (potentiometry, chromatography, enzyme thermistors), medicine (intra- and extra-corporeal therapy, analysis in vivo, artifical organs), basic research (structural studies, enzymes subunits, degeneration and regeration, simulation of natural systems), and special developments and trends (immobilisation of plants cells, organelles, mammallan cells, genetechnology, two-phase systems, multiple immobilisation).
Mathematical University US$49.50.
Aspects of Hodgkin-Huxley Neural Theory. J. Cronin. Cambridge Press, Cambridge, 1987, ISBN O-521-33482-9, xi + 261 pp., f35.00,
This book gives an excellent overview of the recent mathematical treatments of the Hodgkin-Huxley equations. Indeed, since the pioneering work of Hodgkin and Huxley in 1952, numerous mathematical models, analytical or numerical, tried to explain important features of nervous conduction (treshold phenomenon, refractory period, traveling waves, . . . ). H owever, severe drawbacks still remain, as indicated in the first chapter of the book. Besides, the author explains why a study of how the solutions behave in general is as important as a numerical study of a particular set of equaitons. The HH equations are difficult to study for two reasons: firstly, they form a system of four strongly non-linear differential equations; and secondly, new mathematical methods (such as singular perturbation analysis) are needed to obtain analytical solutions. In this book, several different models for nerve conduction are reviewed (chapter 3) as well as models for electrically excitable cells other than neurons (chapter 4). Then, the author presents a clear summary of the theory of differential equations (chapter 5), emphasizing the role of periodic solutions, and introducing singular perturbation theory. Finally, the author discusses recent mathematical models derived from voltageclamp experiments (chapter 6). This part of the book is perhaps too short, since it is
210
really the body of the subject. The author chooses the FitzHugh-Nagumo model for nerve conduction, which is a two-dimensional and autonomous system. The singular perturbation method is applied close to the discontinuous solution, and the author concludes that there is a unique stable periodic solution of the singularly perturbed system for each sufficiently small parameter. In the case of the cardiac Purkinje fiber, the Noble model is used, which can be reduced to a three-dimensional system. This three-dimensional system does not have periodic solutions. Finally, the author gives further directions for study of the Noble model and other cardiac models. It may be asked here why the possible apparition of chaotic regimes as the number of differential equations in the system increases is not discussed. In summary, this book should serve as a good introduction to the interdisciplinary subject of the mathematical treatment of nervous conduction for researchers and graduate students in mathematics, physics, biology or medicine. D. GALLEZ BlUSSdS
Immobilized Biocatalysts. W. Hartmeyer. 3-540-16335-2, x + 211 pp., DM39.00.
Springer
Verlag,
Berlin,
1988,
ISBN
Immobilised systems are finding increasing fields of use due to their advantages of higher stability and lower costs. These systems are applied both to industrial biotechnological process because of their cleanliness and to analytical determinations. The most common immobilised systems are biocatalysts: there are enzymes, tissues or bacteria with differences in availability, in stability, or in cost. The first point limiting the use of these systems is evidently related to the support on which the biocatalyst is immobilised and to the immobilisation procedure, which can either be of a chemical nature, with the advantage of stronger bonding but also with the possible risk of less activity, or of a physical one, with the advantage of unmodified chemical structure but with the danger of low stability and thus low activity after short time. All these subjects are treated wisely in the book, both from a theoretical and a practical point of view. The latter is of particular interest, with some practical, experiments being accurately described and able to put the reader in the position to understand clearly the adopted procedures. These experiments fall into the different fields of application: industrial production (aspartic acid, penicillins, aminoacids), analysis (potentiometry, chromatography, enzyme thermistors), medicine (intra- and extra-corporeal therapy, analysis in vivo, artifical organs), basic research (structural studies, enzymes subunits, degeneration and regeration, simulation of natural systems), and special developments and trends (immobilisation of plants cells, organelles, mammallan cells, genetechnology, two-phase systems, multiple immobilisation).