Tetany is caused by hypocalcemia, thus the question can be rephrased as 'How does alkaosis cause hypocalcemia?'. Roughly about half of serum calcium (%40) is bound to albumin. Most of the rest is ionized calcium, which is the active form. As the serum pH concentration increases, the amount of H+ available to bind albumin decreases, so more sites on albumin become available for calcium to bind. As more calcium binds to albumin, ionized portion dwindles, which causes hypocalcemia.
A 50 year woman presents to ED with diminished conciousness. Her vitals are: T: 35,6 C, BP: 90/50 mm Hg, HR: 50/min SaO2: %89 (ambient air). You take the medical history from her sister, who says that she was recovering from "flu" and she had been using an antibiotic, but she can't recall its name. Upon further questioning, she says her sister started to have medical problems 6 months ago: she had gained about 5 kg since then, she was having bowel problems ("Always spending too much time in there", she says) and stopped attending the local book club because she was always "tired". You notice her skin is cold and dry upon examination. What are the typical antibodies associated with her condition?