Mathematical modelling helps clarify the theoretical basis of physiochemical and biological phenomena

Experiments provide scientists with a real-world glimpse into a particular physical or biological phenomenon under study. This is the fundamental basis on which many areas of science are built. But, there is also an equally important area of scientific research that complements, and in some cases, underpins experimental research: i.e., theoretical research. Specifically, a firm theoretical foundation provides the basis on which hypothesis is formulated and experiments are designed. In essence, experiments cannot be conjured without borrowing some help from theoretical insights promulgated in the scientific literature. But, this concerns hypothesis formulation and experimental design. There is also an increasingly important use of theoretical research: i.e., to explain experimental data. Theoretical research applied in this way typically utilise the tools and techniques of mathematical modelling to help explain physical and biological phenomena. While well-designed experiments should be able to provide some clues to the underlying mechanisms at play, there are many instances where myriad factors impact on a phenomenon and which thus preclude the use of experiments to decode its mechanistic basis. For example, understanding the surface charge characteristics of bacterial cells under different solution pH requires an understanding of the chemical groups on the cell surface as well as their surface distribution. Using the tools of different surface complex formation models, scientists would be able to fit the experimental data to different models and thus deduce the most likely mechanism underpinning the observed phenomenon. The above example represents a use of mathematical modelling for deciphering which theoretical models best describes a physical phenomenon. But, this is not confirmative. Compared to this, a more fundamental approach utilizes theoretical reasoning and mathematical modelling to derive first principles models that explains physical phenomenon. Such models form the basis on which experiments could be designed to either validate or invalidate them. This approach is currently most applicable to physics, chemistry and engineering, while remaining at a nascent stage in biological research due to our incomplete understanding of many biological processes. Collectively, experimental science has seen increasing use of theoretical reasoning and mathematical modelling to derive greater fundamental insights into physical and chemical phenomena. Such efforts can be classified into two main approaches. The first approach utilizes mathematical modelling as a tool to discern the most probable theoretical framework that describes a phenomenon. While laudable, these efforts are not confirmative, but represents an important first step in deriving a deeper understanding of an experimentally observed phenomenon. On the other hand, the second approach builds a theoretical model based on first principles on which hypothesis can be formulated and experiments designed to either validate or invalidate the model. Overall, using the complementary tools of theory and experiments would provide more perspectives into a problem; thereby, providing more experimental or model readouts that either validates our understanding or which seeds further research.