Two chemically active spheres in an infinite medium, one a zeroth-order reactant source and the other a first-order sink, are considered for various sphere size ratios, center-to-center distances, and sink strengths from chemical to diffusion controlled conditions. This source-sink model simulates some aspects of biological mutualism interactions between different cells. Infinite series expansions in a single index n are obtained for the sink reaction rate and reactant concentration profiles using the bispherical expansion. Each of the coefficients, generated exactly by a matrix elimination method, is expressed in terms of nested, continued fractions easily evaluated for the given n. At intermediate and larger sink-source separation distances the sink reaction rate decays harmonically. For smaller sink-source separations with a highly reactive small sink, a local maximum in the sink reaction rate is found. (C) 2003 American Institute of Physics.