Foundations that support systems and computational neuroscience
This list is not exhaustive but it is a good start for young scientists seeking funding for risky projects that are unlikely to receive support from NIH and NSF. Check them for grant opportunities.
Simons Foundation
Whitehall Foundation
Brain and Behavior Research Foundation
Ziegler Foundation for the Blind
Human Frontier Science Program
MQ: Transforming Mental Health
The New York Academy of Sciences (Blavatnik Award)
For an extensive list of funding sources for post-doctoral fellowships see this list.