  We investigate a stochastic version of the synthetic multicellular clock
model proposed by Garcia-Ojalvo, Elowitz and Strogatz. By introducing dynamical
noise in the model and assuming that the partial observations of the system can
be contaminated by additive noise, we enable a principled mechanism to
represent experimental uncertainties in the synthesis of the multicellular
system and pave the way for the design of probabilistic methods for the
estimation of any unknowns in the model. Within this setup, we investigate the
use of an iterative importance sampling scheme, termed nonlinear population
Monte Carlo (NPMC), for the Bayesian estimation of the model parameters. The
algorithm yields a stochastic approximation of the posterior probability
distribution of the unknown parameters given the available data (partial and
possibly noisy observations). We prove a new theoretical result for this
algorithm, which indicates that the approximations converge almost surely to
the actual distributions, even when the weights in the importance sampling
scheme cannot be computed exactly. We also provide a detailed numerical
assessment of the stochastic multicellular model and the accuracy of the
proposed NPMC algorithm, including a comparison with the popular particle
Metropolis-Hastings algorithm of Andrieu {\em et al.}, 2010, applied to the
same model and an approximate Bayesian computation sequential Monte Carlo
method introduced by Mari\~no {\em et al.}, 2013.
