Combined effects of two drugs present simultaneously are usually expressed as summation, synergism or potentiation, and antagonism. When the sum of the effects of each drug present separately equals the combined effect of the two drugs present simultaneously, the action is called additive or summation. However, the expected value of the sum of each effect of drugs present alone has not been well defined. In this report, the theoretical value of the expected sum of each effect of two inhibitors is given and a graphical metho is presented to visualize summation, synergism, and antagonism. The inhibitory effects of a dissociable local anesthetic, tetracaine, and an undissociable local anesthetic, benzyl alcohol, upon a soluble firefly luminescent system were analyzed according to the above theory. The results clearly indicate that the action of these two classes of local anesthetics is pure additive or summation.Local anesthetics inhibit propagation of nerve impulses at synapses and at axons. A number of dissociable and undissociable compounds of diverse structure show local anesthetic activities.Clinically used local anesthetics possess a lipophilic benzene at one end and a tertiary amine on the other. The amine terminal is protonated to form a quaternary nitrogen and becomes highly hydrophilic with its positive charge. The extent of the positive charge is a function of the pka of the compound and the pH of the medium. At physiological pH these compounds exist in both uncharged and charged forms. It has been a matter of discussion as to which is the pharmacologically active form.Alcohols and volatile general anesthetics do not form charged molecules and show local anesthetic activities in excised nerve preparations. Barbiturates dissociate into negatively charged and uncharged molecules and show local anesthetic activities. The uncharged molecule should interact with nerve cells hydrophobically, whereas the charged molecule should bind to nerve cells electrostatically or by hydrogen bonding.Ritchie and Greengard (1) and later Narahashi et al. (2) proposed that local anesthetics penetrate the nerve cell membrane in its uncharged form and inhibit the nerve action by binding to the effector sites from the inside of the cell membrane in its positively charged form. This theory suggests that there are at least two separate modes of action among agents that show local anesthetic action: the predominant force of interaction of dissociable anesthetics is ionic, whereas the mode of action of undissociable local anesthetics is not. However, Agin et al. (3) and Hersh (4) suggested that dissociable and undissociable local anesthetics may interact with living and model systems in an identical way.We have previously shown that volatile general anesthetics (5) and dissociable local anesthetics (6) inhibit flash intensities of firefly luminescence in vitro. Firefly luciferin and luciferase can be solubilized from the tail lantern of fireflies and emit light in vitro when ATP is added. The flash intensity and total light o...