Nelson joined the MIT Center for Cancer Research (CCR) group of David Housman at the Massachusetts Institute of Technology as a postdoctoral trainee (1986–1989).
From 1984 to 1985, in an intramural National Institutes of Health program at the laboratory of Robert Lazzarini, Nelson studied neuroscience and defined genes encoding neurofilament proteins.
Their findings in FMR1 explained the unusual inheritance in Fragile X syndrome and provided the principles for all subsequent unstable repeat disorders such as myotonic dystrophy, Huntington's disease, and amyotrophic lateral sclerosis.
[5][16][17][18] By studying humans, mice, flies and yeast Nelson's research group has characterized the origins of instability in the repeat, the consequences of "premutation" length expansions, and the function of FMR1 and related FXR1 and FXR2.
Nelson and his research group have defined roles for FMR1 and paralogs in circadian rhythm, energy metabolism, neuronal stem cell development, and microRNA function.
Nelson's research group has used flies and mice to identify and characterize modifiers that showed that the CGG repeat is necessary and sufficient to affect mammalian neurons.