Determination of the Microinjected Cytosolic Concentration by Using Mathematical Models of Fluid Dynamics

The precise determination of the intracellular concentration of a drug is a major challenge in drug discovery. Microinjection is a very effective technique for the introduction of macromolecules into single cells. However, due to the large number of parameters that need to be adjusted and the complex physical mechanisms involved, there are currently no means by which the concentration of a microinjected intracellular compound could be theoretically estimated. In this paper, we present a method for the theoretical estimation of intracellular drug concentration, based on the framework of classical fluid mechanism theory - specifically, the modified Bernoulli equation. We introduce into Bernoulli's classical equation the effect of friction due to the non-laminar regimes of the injected fluid. We also study the compatibility of our theoretical estimation model with variations in injection time and concentration of the compound inside the microinjection needle. Finally, microinjected calcium concentrations estimated with the theoretical model were compared with those determined experimentally in several cell types, by using a Fura-2-based Ca²⁺ imaging technique.