A mathematical perspective on hypothesis-driven model construction: A case study in pea

Mechanistic models in systems biology enable biophysically-backed testing of hypothesised mechanisms. However, determination of their parameter values is highly challenging, and the data available for calibration is frequently qualitative in nature. Acknowledging this, many approaches abandon mechanistic description, avoiding parameterisation and simulating biological network behaviours in a qualitative fashion. Appealing are the methods that capture some of the best of both types of approach, maintaining a qualitative perspective while using mechanistic models that naturally generalise to quantitative data and carry biochemical implications. Here, using a pea branching network model as an exemplar, we demonstrate the conversion of biological hypotheses into simplified, parameter-free mathematical models, elucidating the biophysical assumptions implicitly made by this approach and analysing the exemplar model's behaviour. Using likelihood-free Bayesian calibration, we compare the parameter-free model to the set of plausible calibrations of its parameterised analog, hence demonstrating that almost all of the qualitative conclusions given data - including both suitability of a hypothesised network structure, and sensitivity analysis - are obtained by the parameter-free paradigm. Altogether, our findings highlight the usefulness of parameter-free treatments of quantitative models, and also deepen understanding of branching network function across mutant and grafted plants.