Safety and Efficacy Study of OMS721 in Patients With Atypical Hemolytic Uremic Syndrome

Inclusion Criteria: 1. Are age \>= 12 years old at screening (Visit 1). 2. Have a primary aHUS, diagnosed clinically, and have ADAMTS13 activity \> 5% in plasma. Participants are eligible with or without a documented complement mutation or anti-CFH antibody. Participants are categorized according to their response to plasma therapy (plasma exchange or plasma infusion): * Plasma therapy-resistant aHUS participants must have all of the following: * Screening platelet count \< 150,000/μL despite at least four plasma therapy treatments in a 7-day period prior to screening * Evidence of microangiopathic hemolysis (at least one of: 1. presence of schistocytes, 2. serum LDH \> 1.5 times upper limit of normal (ULN), and 3. haptoglobin \< LLN) * Serum creatinine \> ULN * Plasma therapy-responsive aHUS participants must have all of the following: * Have a documented history of requiring plasma therapy to prevent aHUS exacerbation defined as all of the following: * decrease in platelet count \> 25% when plasma therapy frequency has been decreased (including discontinuation of plasma therapy) * LDH \> 1.5 times ULN when plasma therapy frequency has been decreased (including discontinuation of plasma therapy) * Have received plasma therapy at least once every 2 weeks at an unchanged frequency for at least 8 weeks before first dose of OMS721 3. If sexually active and of childbearing potential, must agree to practice a highly effective method of birth control until the end of the study, defined as one that results in a low failure rate (i.e., less than 1% per year) when used consistently and correctly, such as implants, injectables, combined oral contraceptives, some intrauterine devices, sexual abstinence or vasectomized partner. 4. Do not have access to eculizumab treatment, have not derived therapeutic benefit from eculizumab treatment, or have not been able to tolerate eculizumab treatment. Exclusion Criteria: 1. Have STEC-HUS. 2. Have a positive direct Coombs test. 3. Have a history of hematopoietic stem cell transplant. 4. Have HUS from an identified drug. 5. History of vitamin B12 deficiency-related HUS. 6. History of Systemic Lupus Erythematosus. 7. History of antiphospholipid syndrome. 8. Active cancer or history of cancer (except non-melanoma skin cancers) within 5 years of screening. 9. Have been on hemodialysis or peritoneal dialysis for ≥ 12 weeks. 10. Have an active systemic bacterial or fungal infection requiring systemic antimicrobial therapy (prophylactic antimicrobial therapy administered as standard of care is allowed). 11. Baseline resting heart rate \< 45 beats per minute or \> 115 beats per minute. 12. Baseline QTcF \> 470 milliseconds. 13. Have malignant hypertension (diastolic blood pressure \[BP\] \> 120 mm Hg with bilateral hemorrhages or "cotton-wool" exudates on funduscopic examination). 14. Have a poor prognosis with a life expectancy of less than three months in the opinion of the Investigator. 15. Are pregnant or lactating. 16. Have received treatment with an investigational drug or device within four weeks of the screening visit. 17. Have abnormal liver function tests defined as ALT or AST \> five times ULN. 18. Have HIV infection. 19. History of cirrhosis of the liver. 20. Are an employee of Omeros, an Investigator, a study staff member, or their immediate family member. 21. Have a known hypersensitivity to any constituent of the product. 22. Presence of any condition that the Investigator believes would put the subject at risk or confound the interpretation of the data. 23. Have previously completed treatment in an OMS721study. 24. Have received intravenous immunoglobulin (IVIG) treatment within 8 weeks of screening visit. 25. Have received rituximab within 24 weeks of screening visit.