Microbial world is critically governed by population dynamics. Inter- and intra-species regulation by quorum sensing (QS) and quorum sensing inhibition (QSI) orchestrates such behavior. These signals mediated by small molecules called auto-inducers (AI), can induce functions that may not be observed in planktonic forms. This is best exemplified by bioluminescence, virulence and biofilm formation \citep{9th149,ncbib}. Different mathematical models were developed to understand the biofilm phenomenon, three-dimensional restraints and transport parameters on autoinducer (Table 1). The review of mathematical models on QS indicate that complexity involved in understanding QS necessitates equally appropriate equipment and new technology. Mathematical models and technological developments have contributed in parallel with traditional experiments \citep{rats,review}. Some of the recent developments have been touched upon here. Considering a priori assumptions to develop mathematical models may not be realistic, Brown developed a simple model to link molecular and population processes \cite{archipelago}. Herein, models were proposed for homogeneous populations of Gram-positive and Gram-negative QS-QSI signalling structures. These systems were targeted towards molecular and population dynamics. The results add a dimension to framework required for understanding complex system-specific models. In another work, Pai and group used a kinetic model to develop a generic metric “sensing potential” that quantifies QS activation \citep[see][]{infection}. This potential limits to a lone stretch of time that represents the prevailing QS-controlled target activation. The predicted were confirmed in artificial QS circuits based on Escherichia coli. These experiments, performed through synthetic QS, provide a structure to characterize diverse QS systems. Working on different organism - Vibrio harveyi, Fan and Bressloff developed population based models \citep{pathways}. Single-cell models were used to understand signal integration while population-based models were used for interpreting responses to multiple environmental stimuli. Another report found that there are critical autoinducer regulation mechanisms in bacteria wherein, phenotypic heterogeneity causes selected cells (and not all) to produce AI \cite{afe4h}. This was further probed through a theoretical model in which, cells generated and utilized AIs as per physiological and environment induced requirements (Bauer et al., 2017). When the ecological and population dynamics were coupled and mediated by QS, it prompted generation of phenotypic heterogeneity within population. These results indicate existence of a system that is not governed by bistable gene regulatory circuitry.
Biofilm formation is controlled by QS and its prevention is crucial for anti-microbial drug action. Ghasemi et al. proposed a nonlinear system of partial differential equations based model of biofilm in response to antibiotics \cite{simulation}. The study suggested that QS mechanism controlled the switch between aggressive growth coupled with low biofilm formation and sustainable growth coupled with high biofilm formation, with respect to environmental conditions. This has important therapeutic implications. Limited volume systems like microfluidic devices have recently gained momentum as experimental systems of choice in QS studies (Table 2).