Donor-Alloantigen-Reactive Regulatory T Cell (darTregs) in Liver Transplantation

Inclusion Criteria: * Subjects who meet all of the following criteria are eligible for enrollment as study participants: * Able to understand and provide informed consent * End-stage liver disease and listed for primary solitary liver transplant * Have a calculated Model for End Stage Liver Disease (MELD) score ≤ 25 at the time of study entry/consent * Female and male subjects with reproductive potential must agree to use effective methods of birth control for the duration of the study. * If history of Hepatitis C Virus (HCV), have completed or are in current treatment for HCV AND have no detectable HCV RNA. * Subjects with HCC meeting Milan criteria. Exclusion Criteria: * Below are exclusion criteria to be assessed at study enrollment, prior to Stage 1 study procedures. Subjects who meet any of these criteria are not eligible for Stage 1 study procedures. Note that subjects in Cohort 1a or 1b will NOT undergo leukapheresis regardless of eligibility. * End stage liver disease secondary to autoimmune etiology (autoimmune hepatitis, primary biliary cirrhosis, or primary sclerosing cholangitis) * History of less than 5 years remission of malignancy, except for 1) HCC or 2) history of adequately treated in-situ cervical carcinoma, or adequately treated basal or squamous cell carcinoma of the skin. * History of previous organ, tissue or cell transplant * Serologic evidence of human immunodeficiency (HIV) 1 or -2 infection * Epstein-Barr Virus (EBV) or cytomegalovirus (CMV) sero-negativity (EBV or CMV naïve candidates) * Chronic use of systemic glucocorticoids or other Immunosuppression (IS), or biologic immunomodulators * Chronic condition requiring anti-coagulation after liver transplantation * Any chronic illness or prior treatment which, in the opinion of the investigator, precludes study participation * Participation in any other studies that involved investigational drugs or regimens in the preceding year * Received any vaccination within 28 days prior to leukapheresis or blood collection for Treg manufacture * Hemoglobin \<9.0 g/dL within 10 days prior to screening * Neutrophils \<1,500/μL within 10 days prior to screening * Platelets \<40,000/μL within 10 days prior to screening * Thymoglobulin Exclusion Criteria B (Stage 2): * Below are exclusion criteria to be assessed prior to administration of Thymoglobulin®. Subjects who meet any of these criteria should not receive Thymoglobulin®: * Calculated Model for End Stage Liver Disease (MELD) score \>25 at the time of deceased donor liver transplant * Last alpha-fetoprotein (AFP) obtained prior to liver transplantation \>400 μg/L for candidates with Hepatocellular Carcinoma (HCC) * Unacceptable Peripheral Blood Mononuclear Cells (PBMC) product for participants enrolled in Cohorts 2, 3, or 4 per the UCSF The Human Islet and Cellular Transplant Facility (HICTF) manufacturing specifications * Absence of donor spleen for any participants * Human leukocyte antigen (HLA)-DR (DR is one of class II antigens) matched to donor at both loci * Subject is \< 21 or \>70 years of age at the time of transplantation * Located in the intensive care unit 72 hours after transplantation * Hemoglobin \<8.0 g/dL * Absolute neutrophil count \<1,200/μL * Platelets \<40,000/μL * Positive pregnancy test for females of child bearing potential * Unexpected histopathology on back table liver biopsy that contraindicates the initiation of Treg supportive IS regimen. * Development of a condition requiring chronic anti-coagulation. * Hypersensitivity to rabbit proteins or any excipient in Thymoglobulin®. * Detectable HCV RNA or less than six months after end of treatment for HCV at the time of transplantation (i.e., does not meet criteria for SVR). * Below are exclusion criteria to be assessed prior to conversion to Everolimus (EVR)-based IS regimen. (Assessed at day 30-44 after transplantation for continuation in the trial) All subjects regardless of eligibility for EVR conversion, with any of the following will not receive darTregs and will move into safety follow up: * Explanted liver with evidence of increased risk of recurrent cancer risk (hepatocellular (HCC) tumor burden exceeding the Milan criteria; presence of vascular invasion; cholangiocarcinoma morphology) * Insufficient depletion of recipient T cells, defined as a nadir CD3 count ≥50 cells μ/L (50 cells /mcL) or total lymphocyte count ≥ 0.1x 109/L if CD3 count is unavailable * Development of a condition requiring chronic anti-coagulation. * Clinical evidence of biliary obstruction * Alanine Aminotransferase (ALT) \>2.0 x upper limit of normal (ULN) * Inability to taper off corticosteroids by 44 days (+/- 2 days) after transplant * Detectable circulating HCV RNA. Everolimus Conversion Criteria C2 (assessed prior to conversion to EVR based IS regimen; EVR cannot be initiated prior to 30 days after liver transplantation). Subjects with any of the following will remain on TAC-based IS regimen. * Evidence of hepatic artery stenosis or thrombosis by Doppler examination or angiography within 7 days prior to conversion * Urine protein/creatinine ratio \>1.0 within 7 days prior to conversion * Calculated GFR less than 30 ml/min per MDRD4 (Modification of Diet in Renal Disease Study) equation within 7 days prior to conversion * Physical examination documentation of abnormal wound healing or uncontrolled wound infection * Hemoglobin \<8.0 g/dL within 7 days prior to conversion * Absolute neutrophil count \<1,200/μL within 7 days prior to conversion * Platelets \<50,000/μL within 7 days prior to conversion \*Below are exclusion criteria to be assessed prior to darTreg infusion for subjects in Cohorts 2, 3, and 4 only. Subjects in Cohort 2, 3, or 4 who meet any of these criteria should not receive a darTreg-infusion: * Inability or unwillingness of participant to give additional written informed consent * Unacceptable darTreg product * Detectible circulating Epstein-Barr Virus (EBV) or cytomegalovirus (CMV) DNA within 10 days prior to darTreg infusion * Detectible Hepatitis B Virus (HBV) DNA within 10 days prior to darTreg infusion * Detectable circulating HCV RNA within 10 days prior to darTreg infusion. * Alanine Aminotransferase (ALT) \>1.5x upper limit of normal within 10 days of darTreg infusion * Most recent, but not greater than 10 days prior to darTreg infusion,12 hour TAC trough levels of \> 8 μg/L for all subjects * Most recent, but not greater than 10 days prior to darTreg infusion,12 hour EVR trough levels of \< 5 μg/L for subjects on EVR * For subjects on EVR-based IS, received Mycophenolate Mofetil (MMF) within 10 days prior to darTreg infusion * Evidence of acute rejection or chronic rejection according to Banff criteria on protocol allograft biopsy based on local assessment * Received any vaccination within 14 days prior to darTreg infusion * Positive pregnancy test for females of child bearing potential * Inability or unwillingness of participant to comply with study protocol or procedures. * Calculated glomerular filtration rate (eGFR) less than 40 ml/min per MDRD4 equation within 10 days prior to infusion.