  Ordinary differential equations (ODE) are widely used for modeling in Systems
Biology. As most commonly only some of the kinetic parameters are measurable or
precisely known, parameter estimation techniques are applied to parametrize the
model to experimental data. A main challenge for the parameter estimation is
the complexity of the parameter space, especially its high dimensionality and
local minima.
  Parameter estimation techniques consist of an objective function, measuring
how well a certain parameter set describes the experimental data, and an
optimization algorithm that optimizes this objective function. A lot of effort
has been spent on developing highly sophisticated optimization algorithms to
cope with the complexity in the parameter space, but surprisingly few articles
address the influence of the objective function on the computational complexity
in finding global optima. We extend a recently developed multiple shooting for
stochastic systems (MSS) objective function for parameter estimation of
stochastic models and apply it to parameter estimation of ODE models. This MSS
objective function treats the intervals between measurement points separately.
This separate treatment allows the ODE trajectory to stay closer to the data
and we show that it reduces the complexity of the parameter space.
  We use examples from Systems Biology, namely a Lotka-Volterra model, a
FitzHugh-Nagumo oscillator and a Calcium oscillation model, to demonstrate the
power of the MSS approach for reducing the complexity and the number of local
minima in the parameter space. The approach is fully implemented in the COPASI
software package and, therefore, easily accessible for a wide community of
researchers.
