Quantifying time-varying cellular secretions with local linear models

Extracellular protein concentrations and gradients initiate a wide range of cellular responses, such as cell motility, growth, proliferation and death. Understanding inter-cellular communication requires spatio-temporal knowledge of these secreted factors and their causal relationship with cell phenotype. Techniques which can detect cellular secretions in real time are becoming more common but generalizable data analysis methodologies which can quantify concentration from these measurements are still lacking. Here we introduce a probabilistic approach in which local-linear models and the law of mass action are applied to obtain time-varying secreted concentrations from affinity-based biosensor data. We first highlight the general features of this approach using simulated data which contains both static and time-varying concentration profiles. Next we apply the technique to determine concentration of secreted antibodies from 9E10 hybridoma cells as detected using nanoplasmonic biosensors. A broad range of time-dependent concentrations was observed: from steady-state secretions of 230 pM near the cell surface to large transients which reached as high as 56 nM over several minutes and then dissipated.