A 24-year-old woman presents to the clinic with complaints of frequent joint dislocations, easy skin bruising, and persistent joint pain. She reports that even minimal trauma causes her skin to bruise, and she has experienced multiple joint dislocations over the past few years, particularly in her shoulders and knees. On physical examination, her skin is noted to be unusually soft and hyperextensible, and she displays hypermobile joints. She mentions that her mother and younger sister have similar symptoms.

Given the likely underlying genetic defect, which of the following is the most likely cause of this patient's condition?