  Biological systems are majorly dependent on their property of bistability in
order to exhibit nongenetic heterogeneity in terms of cellular morphology and
physiology. Spatial patterns of phenotypically heterogeneous cells, arising due
to underlying bistability, may play significant role in phenomena like biofilm
development, adaptation, cell motility etc. While nonlinear positive feedback
regulation, like cooperative heterodimer formation are the usual reason behind
bistability, similar dynamics can also occur as a consequence of host-circuit
interaction. In this paper, we have investigated the pattern formation by a
motif with non-cooperative positive feedback, that imposes a metabolic burden
on its host due to its expression. In a cellular array set inside diffusible
environment, we investigate spatio-temporal diffusion in one dimension as well
as in two dimension in the context of various initial conditions respectively.
Moreover, the number of cells exhibiting the same steady state, as well as
their spatial distribution has been quantified in terms of connected component
analysis. The effect of diffusion coefficient variation has been studied in
terms of stability of related states and time evolution of patterns.
