A more expressive spline representation for SBML models improves code generation performance in AMICI

Abstract

Spline interpolants are commonly used for discretizing and estimating functions in mathematical models. While splines can be encoded in the Systems Biology Markup Language (SBML) using piecewise functions, the resulting formulas are very complex and difficult to derive by hand. Tools to create such formulas exist but only deal with numeric data and thus cannot be used for function estimation. Similarly, simulation tools suffer from several limitations when handling splines. For example, in the AMICI library splines with large numbers of nodes lead to long model import times. We have developed a set of SBML annotations to mark assignment rules as spline formulas. These compact representations are human-readable and easy to edit, in contrast to the piecewise representation. Different boundary conditions and extrapolation methods can also be specified. By extending AMICI to create and recognize these annotations, model import can be sped up significantly. This allows practitioners to increase the expressivity of their models. While the performance improvement is limited to AMICI, our tools for creating spline formulas can be used for other tools as well and our syntax for compact spline representation may be a starting point for an SBML-native way to represent spline interpolants.