Maltosyltransferase that uses maltose 1-phosphate (M1P) as the sugar donor to elongate linear or branched alpha-(1->4)-glucans. Maltooligosaccharides with a degree of polymerization (DP) superior or equal to 4 are efficient acceptors, with DP6 being optimal in the GlgE-catalyzed polymerization with M1P. Is specific for the alpha-anomer of M1P as substrate, since the beta-anomer of M1P gives no activity. Alpha-D-glucose 1-phosphate cannot serve as a donor substrate, but alpha-maltosyl fluoride is an efficient donor in vitro. Exhibits an alpha-retaining catalytic mechanism, with evidence that maltooligosaccharide acceptors are extended at their non-reducing ends. Is also able to catalyze the reverse reaction in vitro, releasing M1P from glycogen or maltoheptaose in the presence of inorganic phosphate. Also catalyzes disproportionation reactions through maltosyl transfer between maltooligosaccharides. Is probably involved in a branched alpha-glucan biosynthetic pathway from trehalose, together with TreS, Mak and GlgB. [(1->4)-alpha-D-glucosyl](n) + alpha-maltose 1-phosphate = [(1->4)-alpha-D-glucosyl](n+2) + phosphate Is competitively inhibited by alpha-, beta- and gamma-cyclodextrins (cyclic maltooligosaccharides), unlike GlgE from M.tuberculosis. Optimum pH is 7.0 with maltohexaose as acceptor substrate. Optimum temperature is 30 degrees Celsius with maltohexaose as acceptor substrate. Homodimer. Belongs to the glycosyl hydrolase 13 family. GlgE subfamily.