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Using agar plates hosting a 2D cell population stimulated with signalingmolecules is crucial for experiments such as gene regulation and drug discoveryin a wide range of biological studies. In this paper, a biophysical model isproposed that incorporates droplet soaking, diffusion of molecules within agar,cell growth over an agar surface, and absorption of signaling molecules bycells. The proposed model describes the channel response and provides valuableinsights for designing experiments more efficiently and accurately. Themolecule release rate due to droplet soaking into agar, which is characterizedand modeled as the source term for the diffusion model, is derived.Furthermore, cell growth is considered over the surface, which dictates thedynamics of signaling molecule reactions and leads to a variable boundarycondition. As a case study, genetically-modified $E.\,coli$ bacteria are spreadover the surface of agar and Isopropyl-beta-D thiogalactopyranoside (IPTG) isconsidered as a signaling molecule. IPTG droplets are dropped onto thebacteria-covered agar surface. The parameters for the IPTG molecule releaserate as a diffusion source into the agar are estimated from this experiment.Then, a particle-based simulator is used to obtain the spatio-temporal profileof the signaling molecules received by the surface bacteria. The resultsindicate that the number of molecules reacting with or absorbed by bacteria atdifferent locations on the surface could be widely different, which highlightsthe importance of taking this variation into account for biological inferences.

Biophysical Model for Signal-Embedded Droplet Soaking into 2D Cell Culture