Artificial tissues constructed of cells or polystyrene beads suspended in a solution of type I collagen will, under appropriate conditions, protrude into regions of similar matrices lacking particles, but containing the extracellular glycoprotein fibronectin. This phenomenon has been termed "matrix-driven translocation". Conditions required for the effect include the presence of heparin-like molecules on the cell or bead surfaces, appropriate concentrations of particles and collagen, and physiological ionic strength and pH. Here we consider the idea that the driving force for the concerted movement of matrix and suspended particles is the thermodynamically spontaneous spreading or wetting behavior of two immiscible fluids bounded by common substrata. Wetting theory is shown to be capable of accounting for the behavior of this model system, but this analysis requires that the two matrix regions constitute separate phases at thermodynamic coexistence. We show that one plausible mechanism for the generation of separate phases is the formation of a percolation network of collagen fibers on a lattice of cells or beads. It is argued that the concepts of wetting and percolation apply to properties in common between the model system and living tissues, and may therefore be used to provide a physical account of aspects of tissue morphogenesis.