Is teaching a requirement for the Neuroscience Ph.D. program?

Yes. All students are expected to teach for two semesters.

How could someone with a strong interest in Physics/Math/Engineering/Computer Science fit into the Neuroscience Ph.D. program?

We strongly encourage such students to apply. Our program aims to draw undergraduates with strong quantitative backgrounds (e.g., majors in mathematics, physics, engineering and computer science, in addition to well-trained biology and psychology majors) into neuroscience. We aim to do that in a way that allows them to continue to develop their quantitative skills in the context of a rigorous training in neuroscience. Students in the Quantitative and Computational Neuroscience track within the Neuroscience Ph.D. must fulfill all the requirements of the Neuroscience Ph.D. In addition, their electives should be in quantitative courses, and their Ph.D. research should be in quantitative and/or computational neuroscience.

What is the Joint Degree Program in Neuroscience?

The joint graduate degree program in Neuroscience is designed for students that want to do a Ph.D. primarily based on another discipline, but with a neuroscience component. Students graduate with a Ph.D. degree in X and Neuroscience where X is their home department-- for example, Psychology and Neuroscience, or Molecular Biology and Neuroscience, or Philosophy and Neuroscience. 
The program is designed for maximum flexibility. Students apply to a home department and follow the Ph.D. rules and requirements of that home department. Further requirements to qualify for the Joint Degree in Neuroscience are very simple: (1) one of the student's thesis committee members must be a member of the core PNI faculty; (2) the students' Ph.D. thesis research must have a significant neuroscience component; and (3) the PNI faculty member on the students' thesis committee and the Directors of Graduate Studies of both the home department and Neuroscience should indicate their approval. Students normally register for the Joint Degree when they pass their general exams.

Which should I apply to? The Ph.D. in Neuroscience or the Joint Degree Program?

The Ph.D. in Neuroscience is designed as an integrative Ph.D., running all the way from molecules to the human mind. Following this philosophy, students are required to take a year-long, very intensive, Core Course that goes from synapses and electrophysiology to human fMRI. If you are interested in being trained across the breadth of neuroscience, then the Neuroscience Ph.D. is for you. In contrast, if you are only interested in parts of this -- for example, you are studying viruses that infect neurons, your primary interest is in neurovirology, and it would be far better for you to learn how viruses infect cells that to learn about the difference between episodic memory and semantic memory, then the Joint Degree Program, with Molecular Biology as your home department, would be for you.