The study investigates the cooperative action of calcium ions (Ca²⁺) in the release of neurotransmitters at the neuromuscular junction. Ca²⁺ is essential for neuromuscular transmission, controlling the amount of transmitter released by nerve impulses. The authors re-examine the quantitative dependence of transmitter release on Ca²⁺ and test the hypothesis that a cooperative action of multiple Ca²⁺ ions is involved. Methods: Experiments were conducted on frog sartorius nerve-muscle preparations at room temperature (19-24°C). Solutions were isotonicized by replacing NaCl with KCl, allowing variation in Ca²⁺ and Mg²⁺ concentrations while maintaining constant e.p.p. (end-plate potential) amplitude. The nerve was stimulated at a rate of 0.5 Hz, and end-plate potentials were recorded using microelectrodes. Theory: The basic assumption is that two parallel reactions occur on the nerve terminal: Ca²⁺ binding to a critical receptor site X to form CaX, and Mg²⁺ binding to MgX. The fraction of sites occupied by Ca²⁺ is given by a mathematical expression. The non-linear relationship between e.p.p. and Ca²⁺ concentration suggests that a higher power of Ca²⁺ is necessary for release, indicating a cooperative action. Results: The amplitude of e.p.p. increases approximately quadratically with Ca²⁺ concentration. This non-linear relationship is more pronounced at low Ca²⁺ concentrations. The fourth power relationship between e.p.p. and Ca²⁺ is supported by Lineweaver-Burk plots and double-logarithmic plots. Discussion: The cooperative action of four Ca²⁺ ions is proposed to explain the non-linear dependence of e.p.p. on Ca²⁺ concentration. The physical basis for this cooperative action is unknown but may involve a stoichiometric reaction or a stochastic model where multiple CaX molecules are required for release. The study suggests that the probability of release depends on a membrane process involving about four Ca²⁺ ions simultaneously occupying a critical position. The authors acknowledge valuable discussions and technical assistance from Professor B. Katz and Professor R. Miledi.The study investigates the cooperative action of calcium ions (Ca²⁺) in the release of neurotransmitters at the neuromuscular junction. Ca²⁺ is essential for neuromuscular transmission, controlling the amount of transmitter released by nerve impulses. The authors re-examine the quantitative dependence of transmitter release on Ca²⁺ and test the hypothesis that a cooperative action of multiple Ca²⁺ ions is involved. Methods: Experiments were conducted on frog sartorius nerve-muscle preparations at room temperature (19-24°C). Solutions were isotonicized by replacing NaCl with KCl, allowing variation in Ca²⁺ and Mg²⁺ concentrations while maintaining constant e.p.p. (end-plate potential) amplitude. The nerve was stimulated at a rate of 0.5 Hz, and end-plate potentials were recorded using microelectrodes. Theory: The basic assumption is that two parallel reactions occur on the nerve terminal: Ca²⁺ binding to a critical receptor site X to form CaX, and Mg²⁺ binding to MgX. The fraction of sites occupied by Ca²⁺ is given by a mathematical expression. The non-linear relationship between e.p.p. and Ca²⁺ concentration suggests that a higher power of Ca²⁺ is necessary for release, indicating a cooperative action. Results: The amplitude of e.p.p. increases approximately quadratically with Ca²⁺ concentration. This non-linear relationship is more pronounced at low Ca²⁺ concentrations. The fourth power relationship between e.p.p. and Ca²⁺ is supported by Lineweaver-Burk plots and double-logarithmic plots. Discussion: The cooperative action of four Ca²⁺ ions is proposed to explain the non-linear dependence of e.p.p. on Ca²⁺ concentration. The physical basis for this cooperative action is unknown but may involve a stoichiometric reaction or a stochastic model where multiple CaX molecules are required for release. The study suggests that the probability of release depends on a membrane process involving about four Ca²⁺ ions simultaneously occupying a critical position. The authors acknowledge valuable discussions and technical assistance from Professor B. Katz and Professor R. Miledi.