A 42-year-old man with known valvular heart disease develops a fever for 1 week. He appears unwell; findings include a pansystolic murmur at the apex that radiates to the axilla and a soft S1 sound. He has petechiae on his conjunctival sac, linear hemorrhages under a few fingernails, and painful, tender, and erythematous nodules on some of the distal fingertips. Which of the following is the most responsible mechanism for these physical findings?