A specialized ODE integrator for the efficient computation of parameter sensitivities

We present a novel integration algorithm that is based on second derivatives and contains other unique features such as improved error estimates. These features allow the integrator to take larger time steps than other methods. In practical applications, i.e. systems biology models of different sizes and behaviors, the method competes well with established integrators in solving the system equations, and it outperforms them significantly when local parameter sensitivities are evaluated. For ease-of-use, the solver is embedded in a framework that automatically generates the integrator input from an SBML description of the system of interest.For future applications, comparatively ‘cheap’ parameter sensitivities will enable advances in solving large, otherwise computationally expensive parameter estimation and optimization problems. More generally, we argue that substantially better computational performance can be achieved by exploiting characteristics specific to the problem domain; elements of our methods such as the error estimation could find broader use in other, more general numerical algorithms.In systems biology, mathematical models often take the form of system of ordinary differential equations (ODEs). These are approximations of the underlying mechanisms such as enzyme-catalyzed biochemical reactions that are applicable when molecule numbers are sufficiently high, and when the spatial distributions of components in a cell can be neglected. More specifically, ODE models consider the rate of change in a set of states (e.g. species concentrations) as a function of the system’s current state, its inputs, and its inherent kinetic parameters that capture, for instance, affinities of molecular interactions [1].In contrast to systems modeling in domains such as physics, however, model parameters and initial conditions for systems biology models are often not known, or they can only be roughly approximated. As few kinetic parameters can be measured directly, paramet