The cross linkage school:
A necessary pragmatism

Arthur Guyton in the preface of his Textbook of Medical Physiology, 8th edition (1991) writes, “Each time I revise this Textbook... I think that someday physiology will become a completely mature subject without change from year to year.” “However”, he admits, “this always proves to be far from the truth... and only now are we beginning to make inroads into many of its fundamental secrets.  Most importantly, within past few years many new techniques for learning cellular and molecular physiology have become available.” Then he adds his conviction; “Therefore, more and more can we present principles in molecular and physical term, rather than merely as of separate biological phenomenon." Clearly, increasing bulk of information from cellular and molecular biology demands for efficacious categorization and distribution of data towards unified pattern generation.  Thus, there is a necessity for cross hybridization between biomedical sciences and science of pattern generation.  However, both biomedical sciences and mathematics are so vast that there are specialties and sub-specialties in them.  Historically, the notions of specialization, specialist and authority have frequently yielded the feelings of insider and outsider making healthy cross hybridization and inter-disciplinary interaction a difficult task, especially in the core applications. By core application, we mean, the use of mathematics to unify concepts by which a great mass of biological experimental results can be brought into a coherent whole.  This is obviously different from fringe applications which include the design of special purpose software and computer programs for clinical and research uses like medical and research data keeping, interpretation of data, patterning of EEG, ECG and other recordings, calculation of radiation doses, etc. Some examples of core applications of hybridization between mathematics and biological sciences are given below.

 

The analysis of control complex is very often an essential prerequisite to understanding the pattern of feedback and adaptation as well the purpose of physiological systems.  It may involve linear and nonlinear programmes.  It is in this core area where linking between mathematics and biomedical sciences call yield significant leads.  In recent times, the introduction of matrix-valued analytical functions, based on advanced theories of interpolation has been providing means of analysing and designing complex and flexible control systems with multiple inputs and outputs, and with linear and nonlinear processes involved.

 

The concept of knot theory is also promising, to the life scientist.  The theory of operator was developed about five decades ago at least partly to achieve mathematical model of quantum mechanics.  It has recently been suggested that there exists interesting relationships between operator algebras and classification of knots, meaning that a scheme to encode the pattern of a knot in algebric elements is possible.  In this case algebric manipulations will correspond to physical actions on the knot.  Then it will also be possible to project a scheme in algebric terms how the physical configurations of a knot can be changed to another configuration, or to remove the knot.  This appears highly promising to many DNA researchers.  Cellular DNA in a eukaryotic cell remains in supercoil formation and thus forms a complex knotlike structure.  During DNA replication, however, the knot is pulled apart with high order.  The underlying mechanics is enigmatic.  Nevertheless, a strong possibility is there that the knot theory may provide a lead in this respect very soon.

 

The language of fractals is attracting more and more attention of scientists engaged in all fields including biological and biomedical sciences.  Fractal geometry is the dialect of the fractal language, and fractal geometry is non-Euclidean, but it describes natural shapes and forms more elegantly.  It is in fact an emerging notion that the patterns of neural network, beating of a heart, chaotic properties of turbulence caused from cardiovascular disorders etc. can be held in fractal dimensions and Mandelbrot set, enabling the construction of their realistic patterns.

 

A comment on the use of computers is required at this point.  No one does confuse between the science of pattern and the computer science.  Each is a highly powerful tool and is mutually interactive but the individual power lies in different bearings.  Mathematics provides abstract modeling of natural phenomenon, and it also provides algorithms for such models to be computerized.  Computer, on the other hand, provides opportunity for conceptualizing an abstract mathematical pattern.  For optimizing localization and mapping strategies, linkage analysis and system dynamics with which physiological sciences are so intricately bound, computer is essential.  However, the mathematical encoding forms the heart of this computational realization.  Consider the potentiality of computer graphics of iterative maps or so called fractal picture.  This perhaps could not be achieved by only analytic means if there would be no computer graphics.  Computer graphics not only involve mathematical pattern and computer algorithm, but also their synchronized intersection with geometric presentation.  Examples of uses of computer aided modeling and mapping and fractal pictures in the process of approaching biomedical problems are rather widespread now.  A quick survey of journals like Science and Nature amply indicates a rapid increase of such uses in the different fields of biomedical research, ranging from DNA research, gene analysis, genetic engineering, protein analysis to ecology, pharmacology and structural biology, from neurophysiology to virology, from pathophysiology to computer-assisted diagnosis.

 

 

Along with increasing versatility of computer, newer concepts in statistical sciences have improved the handling and interpretation of biomedical data.  Now techniques in statistical analysis like spatial statistics, boot-strap and jack-knife statistics are of high potential value to be employed in life sciences.  Boot-strap statistics is an innovative method of generating data using limited data, however, with statistical characteristics being preserved.  Jack-Knife statistics relates to boot-strap and is used to reduce the bias by repeatedly cutting away a part of data.  It is now being suggested that this statistical manipulation can be used in several fields of' biomedical studies where available data sets are genuinely limited.  Data may often be of mixed nature: mixed of discrete and continuous variables, and information is often partly parametric and partly nonparametric.  Hence classical nonparametric assumptions and computations, though extensively in use as yet, have their own limitations.  It is now possible to   use methods of nonparametric modeling to assess statistically the data sets of mixed variables.  Likewise, the implication of spatial statistics in biomedical and life sciences will appear wide and in-depth in short run with increasing use of video and scanner type devices.  The spatial statistics will have implications in advanced analysis of data with spatial characteristics and information, in the enhancement of' blurred image and hidden pattern and in many other similar ways.

 

Time has now come when syngamy between biomedical sciences and the science of pattern making is becoming a need.  New waves are urging upon the theoretical and applied biology.  Undisputedly, marriage between structure and function, patterns and properties, mathematics and biology will make this sojourn healthier.  It is therefore, essential that we support this endeavor carefully. In other words, Chester Hyman’s 'let us be tolerant to each other's research' is no longer sufficient.  Promotion of conscious, organized and structured cross hybridization is to be encouraged.  To this effect, we publish in the following pages two debate articles written by two budding scientists.