Early papers on biological computing focussed on combinatorial and algorithmic issues, and worked with intentionally oversimpliied chemical models. In this paper, we reintroduce complexity to the chemical model by considering the eeect problem size has on the initial concentrations of reactants, and the eeect this has in turn on the rate of production and quantity of nal reaction products. We give a sobering preliminary analyses of Adleman's technique for solving Hamiltonian path. Even on the simplest problems, the annealling phase of Adleman's technique requires time (n 2) rather than the O(log n) complexity given by a computationally inspired but chemically naive analysis. On more diicult problems, not only does the rate of production of witnessing molecules drop exponentially in problem size, the nal yield also drops exponentially. These issues are not objections to biological computing per se, but rather diiculties to be overcome in its development as a viable technology. 1 Reaction Rates We assume familiarity with Adleman's DNA-based technique Adl94] for solving the hamiltonian path problem. For the present analysis, we will consider the hamiltonian path problem on directed graphs, rather than graphs. We recommend Molecular Cell Biology LBB + 95] as a useful general reference for all chemical and biological concepts not otherwise referenced. We begin by considering a very simple family of directed graphs, the line di-graphs.