Motivated by the formation of certain link types during Hin-mediated DNA recombination
experiments, we consider tangle equations where one of the products is a
connect-sum of 2-bridge links. We are thus led to study Dehn surgeries on knots in
lens spaces that yield connect-sums of lens spaces. Using 3-manifold methods, we
prove, for certain classes of knot exteriors, a distance bound on Dehn surgery slopes.
(This proof complements an algebraic-geometric proof of a more general statement
due to Boyer and Zhang [6]). Analysing the known examples of connect-sums of
lens spaces surgeries, together with some sample calculations, we conjecture that if
surgery on a knot K [Symbol appears here. To view, please open pdf attachment] L(p, q), with p, q [Symbol appears here. To view, please open pdf attachment]1, 2, yields L(p, q)#L(t, 1), then the knot
has reducible exterior. Using Heegaard Floer homology, we prove a special case of the
conjecture, as well as some surgery obstructions. We then apply our results, in the
spirit of the tangle model of Ernst and Sumners [67], to the problem of Hin-mediated
DNA recombination, where we characterise its distributive recombination step.