Abstract: A microfluidic system includes a matrix structure having a plurality of wells, each of the wells being accessible via at least one microfluidic path connectable via an interface to at least one droplet input for receiving one or more sets of droplets from one or more droplet sources, wherein a droplet enters a well based on one or more of: buoyancy, gravity, hydrodynamic force, and/or mechanical capturing, and wherein contents of a particular well are determinable based on a position of the particular well in the matrix structure and on inputs to the matrix structure. Methods using the matrix structure.

Abstract: A system includes a plurality of drug libraries, at least one comprising multiple droplets of multiple drugs, each drug associated with a corresponding unique drug identifier in the system, and a live cell library comprising multiple live cells or live cell lines, each live cell associated with a corresponding unique cell or cell line identifier in the system. A plurality of junctions combining drug droplets from the drug libraries and a live cell from the live cell library. At least one of said drug libraries produces a random stream of heterogenous drug droplets, the drug droplets corresponding to drugs in said drug libraries.