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Rule Book: Guidelines to a Mathematical Biology


When faced with challenging research problems, nothing may be more comforting than having access to a collection of helpful guidelines.  This explains the appearance of a Rule Book.

Biomedical research is the art of reaching into biology, pulling something out, putting numbers on it, and then telling a credible story.  A rule book calls attention to what we are actually doing and frequently explains things we need to know.  Consider, if you will, the following examples. 

  • In a mathematical biology, practically everything is done with equations running on the best available research data.  Why?  Only equations can deal successfully with the hierarchical nature of biology and the remarkable relationships that ensue there from.  Just as parts are embedded parts, so too are complexities embedded in complexities.  Equations allow us to dig our way into these complexities and then return safely by the same route.
  • Stereology needs biochemistry and molecular biology just as much as these disciplines need stereology.  Why? Because they can supply gold standards only when working together in the same equations. 
  • A sizable portion of modern day research in biology is built on a foundation of semiquantitative data.  By learning to look at these data - and the assumptions behind them - through the lens of a mathematical biology you will see how quickly this shaky foundation collapses when put to the test.  Why?  Semiquantitative data are not trustworthy because they don't play by the rules.

Table of Contents

  1. Conceptual Framework

  2. Sampling

  3. Hierarchical Parts

  4. Experiments as Equations

  5. Optimal Data

  6. Interpretations

  7. Gold Standards

  8. Connections

  9. Change

  10. Bias and Animal Variability

  11. Counting Molecules

  12. Complexity

  13. Reverse and Forward Engineering

  14. Integrating Data

  15. Mathematical Phenotypes

  16. Dimensional Consistency

  17. Standardization

  18. Universal Databases

  19. Semiquantitative Data

The Rule Book comes with an interesting piece of software called the Concentration Trap.  With it you will quickly discover how easy it is to deprive semiquantitative data of one of its most treasured perks - the ability to gain the appearance of respectability by attaching itself to a statistical significance.  By learning to run the program, you will be able to show that the appearance of an increase is - in reality - often a decrease or a decrease an increase.  Consider a real-life scenario.  If semiquantitative data can get it right only about 50% of the time, then a significant difference (P<0.05) will also get it right only 50% of the time.  In other words, semiquantitative data invariably carry a hidden probability layer that undermines the validity of a statistical outcome.  Using the concentration trap program, you will be able to estimate the effects of this hidden layer on the results coming from a wide range of published studies.