Glenn Ernest Cullen served two terms as president of the American Society of Biological Chemists from 1937 to 1938. In 1914, he joined the Rockefeller Institute of Medical Research as an assistant in the Department of Chemistry. There, he collaborated with Donald D. Van Slyke on enzymatic studies, with a particular emphasis on urease. Cullen and Van Slyke eventually approximated the reaction catalyzed by urease, which came to be known as the Van Slyke–Cullen constant. Cullen also participated in the development of quantitative methods of analysis, which were widely used by investigators engaged in studying different phases of the chemical disturbances of disease. In 1918, Cullen's research at Rockefeller was interrupted while he served as a lieutenant in the Sanitary Corps. Later that year, he was appointed an associate of the Institute.
In 1921, Cullen left the Rockefeller Institute for the John Herr Musser Department of Research Medicine at the University of Pennsylvania. Continuing his research on quantitative methods, Cullen worked with J. N. Austin, and they published a monograph on the hydrogen ion concentration of blood in health and disease. Cullen also became interested in chemical disturbances found in infants with gastroenteritis and began a collaboration with Graeme Mitchell. Cullen remained at Pennsylvania for several years, after which he joined the Department of Biochemistry at the Vanderbilt University School of Medicine in Nashville, Tennessee, where he eventually became head of the department. At Vanderbilt, Cullen maintained an active interest in clinical problems. His time at Vanderbilt ended in 1931 when Cullen was recruited by Mitchell to become director of laboratories in the Research Foundation and professor of Research Pediatrics in the College of Medicine at the University of Cincinnati. He retained this position until his death in 1940.