Inclusion Criteria:  Diagnosis of UC at least 3 months prior to screening. Mildly to severely active UC. Inadequate response, loss of response, or intolerance to at least 1 prior conventional therapy, and no more than 2 prior advanced therapies.  Participants at risk for colorectal cancer must have a colonoscopy prior to or at screening as follows:  Participants > 50 years of age must have documentation of a colonoscopy within 3 years of the screening visit to exclude adenomatous polyps. Participants whose adenomas have been completely excised at screening are eligible. Participants with extensive colitis for ≥ 8 years, or disease limited to the left side of the colon for ≥ 10 years, must either have had a full colonoscopy to assess for the presence of dysplasia within 1 year before first administration of study drug or a full colonoscopy to assess for the presence of malignancy at the screening visit. No evidence of active tuberculosis (TB), latent TB, or inadequately treated TB. Women of childbearing potential (WOCBP) and males with female partners of childbearing potential must utilize highly effective contraceptive methods beginning 4 weeks prior to first dose of study drug and continue for the duration of the study. Body mass index (BMI) 18 to 35 kg/m^2 inclusive and weight ≥ 50 kg.  Exclusion Criteria:  Prior treatment with recombinant IL-2 or modified IL-2 therapy, including MK-6194 (PT101). Known sensitivity to MK-6194 (PT101) or its excipients. Known history of hypersensitivity to interleukin-2 (IL-2). Disease limited to the rectum (i.e., within 15 cm of the anal verge). Diagnosis of toxic megacolon. Suspected or known colon stricture or stenosis. Diagnosis of Crohn's disease, or indeterminant colitis.  Has severe colitis as evidenced by:  Current hospitalization for the treatment of UC Likely to require a colectomy within 12 weeks of baseline in the opinion of the Investigator Symptom complex at screening or baseline visits that includes at least 4 of the following: diarrhea with ≥ 6 bowel movements/day with macroscopic blood in stool; focal severe or rebound abdominal tenderness; persistent fever (≥ 37.5°C); tachycardia (> 90 beats/minute); anemia (hemoglobin < 8.5 g/dL). Previously had surgery for UC (e.g., subtotal colectomy with ileo-rectal anastomosis or colectomy with ileoanal pouch, Koch pouch, or ileostomy) or in the opinion of the Investigator, likely to require surgery for UC during the study period. History of abnormal thallium stress test or functional cardiac function test. History of significant cardiac, pulmonary, renal, hepatic, or central nervous system (CNS) impairment. Active clinically significant infection, or any infection requiring hospitalization or treatment with intravenous anti-infectives within 8 weeks of randomization, or any infection requiring oral anti-infective therapy within 6 weeks of randomization. History of opportunistic infection. History of symptomatic herpes zoster within 16 weeks of randomization, or any history of disseminated herpes simplex, disseminated herpes zoster, ophthalmic zoster, or central nervous system (CNS) zoster. Currently on any chronic systemic (oral or IV) anti-infective therapy for chronic infection (such as pneumocystis, cytomegalovirus, herpes zoster, or atypical mycobacteria). Currently receiving lymphocyte depleting therapy. History of abnormal pulmonary function tests. Participants with organ or tissue allograft. Participants who have HIV infection (positive antibody test) regardless of virologic status are excluded from the study. Known history of drug or alcohol abuse within 1 year of screening. Malignancy within 5 years of screening, with the exception of adequately treated or excised non-metastatic basal cell or squamous cell cancer of the skin. Participants with a malignancy that occurred > 5 years prior to screening are eligible with documentation of disease-free state since treatment. Immunosuppressive therapy with either cyclosporine A, tacrolimus, or mycophenolate mofetil within 2 weeks of the Day 1 visit. Exposure to advanced therapy within 5 half-lives of the Day 1 visit, or documentation of detectable drug during screening. Participants receiving concomitant medications for UC (i.e., oral probiotics, aminosalicylates, thiopurines, and/or oral corticosteroids) that have not been administered at stable doses 2 weeks prior to the screening endoscopy or participants unable or unwilling to maintain stable doses of medications through Week 12 of the study period. Participants taking oral prednisone or equivalent not greater than 20 mg per day, or budesonide 9 mg per day are eligible. Participants unable to discontinue topical enemas within 2 weeks prior to endoscopy. Received a live attenuated vaccine < 1 month prior to screening or is planning to receive a live attenuated vaccine during the study period or within 12 weeks of the end of participation in the study. Currently enrolled in another investigational device or drug study, or it has been less than 30 days or 5 half lives since ending another investigational device or drug study, or receiving another investigational agent. Is pregnant or nursing or is planning to become pregnant during the study. Any uncontrolled or clinically significant concurrent systemic disease other than UC. Any condition or disease that, in the opinion of the Investigator, would pose a risk to participant safety or interfere with study evaluation, procedures or completion.