Physical and mathematical modeling in experimental papers: achieving robustness of mathematical modeling studies

Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are more valuable than models which support such theories. Mathematical modeling has been especially strong in physical sciences where theories, based on basic principles, were able to predict energies associated with mass (famous equation E = mc) and existence of fundamental particles (e.g., positron). There have been many applications of mathematical modeling in biology but because it has been harder to come up with basic principles, predictive successes of mathematical theory-based predictions in biology are more modest than that in physics. With the development of novel experimental methods to collect unique data spanning different levels of organization, from gene sequences and intracellular processes in individual cells to populations of organisms, there has been an impressive rise in the number of mathematical modeling studies in biology. Bioinformatics, commonly defined as a science dealing with analysis of sequencing data (but see (1)), and systems biology, commonly defined as a science dealing with intracellular gene networks, are two most well recognized advances driven by the availability of novel datasets. Several recent reviews focus on the usefulness of mathematical modeling for understanding complex biological systems (2–5). Specifically, Möbius & Laan (3) illustrated how mathematical modeling helps to interpret experimental data using example of molecular motors. While Möbius & Laan (3) do describe some pros and cons of mathematical modeling, there was limited discussion on what makes a good mathematical modeling paper and when mathematical modeling can lead to robust conclusions. The authors did not cite and did not discuss an important philosophical paper on the use of mathematical modeling in natural sciences, a paper that every mathematical modeler should read, think about, and discuss with his/her peers (6). In contrast with prevailing