There is a gene that encodes the enzyme COMT which is responsible for degrading dopamine, epinephrine and norepinephrine neurotransmitters. Some people have a polymorphism (SNP) which is called Val158Met and in case of Met/Met mutation COMT enzyme will be less active which allows dopamine and norepinephrine to accumulate. There are multiple researches and COMT is quite well studied already - it's linked to certain psychological traits (also good ones) and some psychiatric deceases if a person has other mutations (like in the MTHFR gene). ​ I believe, based on own experience, COMT can significantly contribute to stuttering if there are other mutations in the genes.