We investigate the participation of male and female applicants to a competition for research funding, using an original dataset with detailed information on both successful and unsuccessful applicants to 21 calls by a mission-oriented funding agency. We use this information to construct a fictitious pool of 277,464 potential applicants and to model their probability to submit an application. We find that, even after controlling for productivity, quality of research, seniority, years of career discontinuity, number of prior applications, affiliation, and ethnicity, women were still less likely to apply than men. The lower likelihood of females to apply was not explained by the use of masculine language in the text of the calls. Instead, women's research interests were more distant from the topics of the calls than men's. Topic proximity fully mediated female penalization in the likelihood to apply for research funding. These results are an important heads-up, in view of the increasing focus of governments in mission-oriented programs.