structure of heterotic strings[1, 2, 19–21]. In fact, in heterotic string theories, gauge degrees of freedom are taken by Lorentz singlets in one sector of closed strings. There is another way to incorporate gauge degrees of freedom into string theory. In theories containing open strings such as Type I theory, one can add Chan-Paton factors[1, 2, 22, 23] to the ends of open strings. The interactions between closed and open strings at tree-level are on D$_{2}$ . In the field theory limits of this case, the tree amplitudes for gauge- gravity interaction and those for pure gauge field are connected via D$_{2}$ relations. Then a question arises: In what kind of theory for gauge-gravity interactions do the field limits of D$_{2}$ relations hold? Or do the field theory alimits of D$_{2}$ relations also hold in minimal coupling theory of gauge and gravity? In this paper, we study the amplitudes in minimal coupling theory of gauge field and gravity. We find though the KLT factorization relations and the D$_{2}$ relations hold on worldsheets with different topologies in string theory, the field theory limits of D$_{2}$ relations also hold in minimal coupling theory of gauge field and gravity. D$_{2}$ relations in minimal coupling theory of gauge field and gravity are based on the disk structure. They give a new understanding on gauge-gravity interaction. The structure of this paper is as follows. In Section II, we give an introduction to KLT relations and D$_{2}$ relations. We also give the low energy limits of D$_{2}$ relations for amplitudes with three and four legs. In Section III, we use the low energy limits of D$_{2}$ relations to give the tree amplitudes for gauge-gravity interaction. We find the amplitudes given by D$_{2}$ relations are same with those given by KLT factorization relations. Then the D$_{2}$ relations give the amplitudes in minimal coupling theory of gauge field and gravity. In Section IV, we consider the D$_{2}$ relations for general tree amplitudes where gluons are minimally coupled to gravitons. We first study the mixed amplitudes where all the legs take positive helicity or 3