A specific gene or single nucleotide polymorphism or a set of them may increase the
odds of occurrence of a given behavior, but we currently lack sufficient knowledge to determine a complete chain of cause-effect events inevitably leading to that behavior.
The cause-effect link is what might tell something about responsibility or its lack.
Even admitting that some gene pattern may increase the probability that a person may display a given, say, aggressive behavior, there is still no proof that this gene pattern acted to limit the person’s options of behavioral displays at the time the behavior occurred, therefore temporarily limiting her/his freedom of choice and, consequently, responsibility.