Wet-lab experiments, in which the dynamics within living cells are observed, are usually costly and time consuming. This is particularly true if single-cell measurements are obtained using experimental techniques such as flow-cytometry or fluorescenc
e microscopy. It is therefore important to optimize experiments with respect to the information they provide about the system. In this paper we make a priori predictions of the amount of information that can be obtained from measurements. We focus on the case where the measurements are made to estimate parameters of a stochastic model of the underlying biochemical reactions. We propose a numerical scheme to approximate the Fisher information of future experiments at different observation time points and determine optimal observation time points. To illustrate the usefulness of our approach, we apply our method to two interesting case studies.
The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state space, an
alysis techniques based on an exploration of the state space are often not feasible and the integration of the moments of the underlying probability distribution has become a very popular alternative. In this paper the focus is on a comparison of reconstructed distributions from their moments obtained by two different moment-based analysis methods, the method of moments (MM) and the method of conditional moments (MCM). We use the maximum entropy principle to derive a distribution that fits best to a given sequence of (conditional) moments. For the two gene regulatory networks that we consider we find that the MCM approach is more suitable to describe multimodal distributions and that the reconstruction is more accurate if conditional distributions are considered.
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region where the main part of probability mass is located.
