Let R = F 4 + u F 4 , with u 2 = u and S = F 4 + u F 4 + v F 4 , w i t h u 2 = u , v 2 = v , u v = v u = 0 . In this paper, we study F 4 R S -cyclic codes of block length (α , β , γ) and construct cyclic DNA codes from them. F 4 R S -cyclic codes can be viewed as S [ x ] -submodules of F q [ x ] 〈 x α − 1 〉 × R [ x ] 〈 x β − 1 〉 × S [ x ] 〈 x γ − 1 〉 . We discuss their generator polynomials as well as the structure of separable codes. Using the structure of separable codes, we study cyclic DNA codes. By using Gray maps ψ 1 from R to F 4 2 and ψ 2 from S to F 4 3 , we give a one-to-one correspondence between DNA codons of the alphabets { A , T , G , C } 2 , { A , T , G , C } 3 and the elements of R , S , respectively. Then we discuss necessary and sufficient conditions of cyclic codes over F 4 , R, S and F 4 R S to be reversible and reverse-complement. As applications, we provide examples of new cyclic DNA codes constructed by our results. [ABSTRACT FROM AUTHOR]