Securing an individual predoctoral fellowship is one of the most impressive ways to demonstrate your scientific independence. It readily places you in a stronger negotiating position when hunting for research-related jobs after graduation.
Funding opportunities for graduate students are often offered as individual fellowships or training grants, as exemplified by the National Science Foundation Graduate Research Fellowship Program and the National Research Service Award Individual Predoctoral Fellowship (F31) offered by the National Institutes of Health (NIH). To be eligible for these federal grants, the applicant has to be a US citizen or permanent resident enrolled in a research doctoral degree program. Advanced graduate students considering transitioning into postdoctoral positions should consider the Predoctoral to Postdoctoral Fellows Transition Award (F99/K00), a new program launched by the National Cancer Institute that aims to facilitate the transition of talented graduate students into successful careers as independent scientists.
Opportunities are also offered by private research foundations, and they may have less stringent requirements for citizenship. Therefore, international students who hold F1 visas may be eligible. See individual awards for requirements. For graduate students majoring in biophysics, the American Heart Association is a good fit given the many common research interests shared by biophysicists and cardiovascular researchers. A comprehensive list of non-NIH funding opportunities for predoctoral and graduate researchers can be found here.
A critical part of writing a successful grant application is having a thorough understanding of the mission of the funding agencies and the types of projects they support. A careful study of the funding opportunity announcement as well as direct contact with the program staff is strongly recommended prior to the submission of your application. An application for a typical predoctoral fellowship contains not only the research plan for the project, but also two or three letters of recommendation, a personal statement of your career goals, and a detailed mentoring plan that you need to work out carefully with your mentor. In addition to a well-thought-out research plan consolidated by compelling preliminary data, an impressive mentoring plan indicating strong support from your mentor(s) and collaborators is equally important to convince the reviewers that you are a worthy candidate. Though it varies by funding agency, the success rate of predoctoral fellowships is in the range of 10 to 35 percent.