A 59-year-old male is found to have a 3.5-cm mass in the right upper lobe of his lung. A biopsy of this mass is diagnosed as a moderately differentiated squamous cell carcinoma. Workup reveals that no bone metastases are present, but laboratory examination reveals that the man's serum calcium levels are 11.5 mg/dL. This patient's paraneoplastic syndrome is most likely the result of ectopic production of