  The hematopoietic system has a highly regulated and complex structure in
which cells are organized to successfully create and maintain new blood cells.
Feedback regulation is crucial to tightly control this system, but the specific
mechanisms by which control is exerted are not completely understood. In this
work, we aim to uncover the underlying mechanisms in hematopoiesis by
conducting perturbation experiments, where animal subjects are exposed to an
external agent in order to observe the system response and evolution.
Developing a proper experimental design for these studies is an extremely
challenging task. To address this issue, we have developed a novel Bayesian
framework for optimal design of perturbation experiments. We model the numbers
of hematopoietic stem and progenitor cells in mice that are exposed to a low
dose of radiation. We use a differential equations model that accounts for
feedback and feedforward regulation. A significant obstacle is that the
experimental data are not longitudinal, rather each data point corresponds to a
different animal. This model is embedded in a hierarchical framework with
latent variables that capture unobserved cellular population levels. We select
the optimum design based on the amount of information gain, measured by the
Kullback-Leibler divergence between the probability distributions before and
after observing the data. We evaluate our approach using synthetic and
experimental data. We show that a proper design can lead to better estimates of
model parameters even with relatively few subjects. Additionally, we
demonstrate that the model parameters show a wide range of sensitivities to
design options. Our method should allow scientists to find the optimal design
by focusing on their specific parameters of interest and provide insight to
hematopoiesis. Our approach can be extended to more complex models where latent
components are used.
