Mathematical models of important biological phenomena have provided insights about whether and how a verbally stated model can work in an accurate and quantitative sense. Biology has also given mathematicians a variety of challenging math problems that later live a more mathematical life with little biological consequences. However, it was the close combination of the two, in pursuing the unknown facts that would be difficult to achieve without the combination, which made the work of people like Hodgkin-Huxley a big success story. This talk will focus on the efforts of myself and coworkers to use math models, based on a large number of records, to make predictions on issues relevant to the real biological problem. The first part will be on how, by focusing on the whole dose-response scenario instead of a single record in pituitary gonadotrophs, the model predicts that the bell-shaped curve moves to the right as IP3 concentration increases. This prediction has been recently proved by experiments. The second part will be on what the model says about the communication between the cell surface and the endoplasmic reticulum (ER) calcium store in controlling Ca²⁺ entry and store refilling in gonadotrophs that are excitable and relatively small. Our study predicted some seemingly counterintuitive phenomena such as that store refilling occurs at lower than basal [Ca²⁺]_i levels and, most importantly, suggested that in excitable cells that do not express Icrac [Ca²⁺]_i itself plays the role of a messenger between the ER and the plasma membrane. These results indicate that capacitative Ca²⁺ entry in such cells is likely to occur through Ca²⁺-controlled Ca²⁺ entry.

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