Simplification traps
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OPINION PAPER
Simplification traps Heino Prinz
Received: 2 November 2011 / Accepted: 14 November 2011 / Published online: 7 December 2011 # Springer-Verlag 2011
Abstract When experiments are analyzed with simple functions, one gets simple results. A trap springs when experiments show deviations from the expected simplicity. When kinetic experiments do not follow exponential curves, they simply are not of the first or pseudofirst order. They can and have to be calculated on the base of plausible reaction schemes. When dose–response curves are analyzed with logistic functions (“4-parameter fit”) and give Hill coefficients different from one, this is an experimental result stating that more than one molecule is involved in eliciting the response. If one ignores that result, one usually finds forgiving referees, but one will loose real money when one tries to develop such an unspecific compound into a drug. Keywords Numerical methods . Multiexponential fits . Dose–response curves . 4PL . Logistic function . Systematic deviations Biochemical analysis requires the calculation of theoretical values. The current approach for enzyme kinetics, dose– response curves, binding kinetics or equilibrium binding studies is based on analytical solutions [3] with explicit functions like: y ¼ f ðxÞ:
ð1Þ
x is the independent variable (for example, the time or the concentration of a compound) and the function f(x) may be rather complex. Even though analytical solutions have been Electronic supplementary material The online version of this article (doi:10.1007/s12154-011-0069-3) contains supplementary material, which is available to authorized users. H. Prinz (*) Max-Planck-Institut für molekulare Physiologie, Otto-Hahn-Str. 11, 44227 Dortmund, Germany e-mail: [email protected]
developed over more than a century, they are limited to only few well-documented examples. Biochemical observations often reveal more complexity. Problems arise when the complexities are ignored or when simple analytical solutions are extended by unjustified means. An entirely different approach to the calculation of theoretical values is possible with numerical methods, where any theoretical value y can be calculated from any reaction scheme. One simply translates a given scheme into a set of equations and lets the computer solve them. x ! computer with a set of instructions ! y:
ð2Þ
The procedure (Eq. (2)) also is a mathematical function [8] but not an explicit one. It is well-suited to a huge variety of biochemical reaction schemes because it does not impose limits. Unfortunately, numerical methods are taught in Mathematics departments but usually have no part of the curriculum in life sciences. An introductory textbook to numerical methods for life scientists has been published recently [7]. The main principles of numerical approaches are straight forward: one simply writes down plausible reaction schemes, translates them step by step into a set of ordinary or differential equations and let the computer solve them. This approach can be used
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