It’s about time: Analysing an alternative approach for reductionist modelling of linear pathways in systems biology

Thoughtful use of simplifying assumptions is crucial to make systems biology models tractable while still representative of the underlying biology. A useful simplification can elucidate the core dynamics of a system. A poorly chosen assumption can, however, either render a model too complicated for making conclusions or it can prevent an otherwise accurate model from describing experimentally observed dynamics.\n\nHere, we perform a computational investigation of linear pathway models that contain fewer pathway steps than the system they are designed to emulate. We demonstrate when such models will fail to reproduce data and how detrimental truncation of a linear pathway leads to detectable signatures in model dynamics and its optimised parameters.\n\nAn alternative assumption is suggested for simplifying linear pathways. Rather than assuming a truncated number of pathway steps, we propose to use the assumption that the rates of information propagation along the pathway is homogeneous and instead letting the length of the pathway be a free parameter. This results in a three-parameter representation of arbitrary linear pathways which consistently outperforms its truncated rival and a delay differential equation alternative in recapitulating observed dynamics.\n\nOur results provide a foundation for well-informed decision making during model simplifications.\n\n1 Author summaryMathematical modelling can be a highly effective way of condensing our understanding of biological processes and highlight the most important aspects of them. Effective models are based on simplifying assumptions that reduce complexity while still retaining the core dynamics of the original problem. Finding such assumptions is, however, not trivial.\n\nIn this paper, we explore ways in which one can simplify long chains of simple reactions wherein each step is linearly dependent on its predecessor. After generating synthetic data from models that describe such chains in explicit detail, we compare how well different simplifications retain the original dynamics. We show that the most common such simplification, which is to ignore parts of the chain, often renders models unable to account for time delays. However, we also show that when such a simplification has had a detrimental effect, it leaves a detectable signature in its optimal parameter values. We also propose an alternative assumption which leads to a highly effective model with only three parameters. By comparing the effects of these simplifying assumptions in thousands of different cases and for different conditions we are able to clearly show when and why one is preferred over the other.