Lambert-Eaton myasthenic syndrome (named for the two scientists who first reported it in 1956) is a rare neuromuscular disease affecting around 0.5...

 Lambert-Eaton myasthenic syndrome (named for the two scientists who first reported it in 1956) is a rare neuromuscular disease affecting around 0.5 people per million population. Patients with LEMS present with proximal weakness in the legs which progressively spreads to proximal weakness in the arms, distal weakness in both the arms and legs and finally weakness involving the hands, feet and cranial muscles. Patients also report autonomic disturbances including constipation, dry eyes and increased sweating. 

It is now known that the cause of this condition is the presence of antibodies to voltage gated calcium channels (VGCC) in the serum of affected individuals. These antibodies target the channels and lead to their destruction. 

The first line therapy for LEMS is treatment with a voltage gated K+ channel blocker such as amifampridine (3,4-diaminopyridine). Why do you think that this would be effective? In your answer, include where you would find voltage gated K+ channels, what role they play in the nervous system and how their inhibition would improve symptoms of LEMS.