NEW YORK — Alzheimer’s researchers and drug companies have for years concentrated on one hallmark of Alzheimer’s disease: the production of toxic shards of a protein that accumulate in plaques on the brain.

But now, in a surprising coincidence, two groups of researchers working from entirely different starting points have converged on a mutated gene involved in another aspect of Alzheimer’s disease: the immune system’s role in protecting against the disease. The mutation is suspected of interfering with the brain’s ability to prevent the buildup of plaque.