T-Regulatory Cell Infusion Post Umbilical Cord Blood Transplant in Patients With Advanced Hematologic Cancer

OBJECTIVES: Primary * Determine the maximum tolerated dose (MTD) of umbilical cord blood (UCB)-derived T-regulatory (Treg) cells. Secondary * Estimate the proportion of patients with detectable circulating Treg cells at 0, 1, 3, 7, and 14 days after infusion. * Estimate the risk of grades II-IV and III-IV acute graft versus host disease (GVHD) at day +100 with the infusion of Treg cells. * Estimate the proportion of patients with sustained donor engraftment. * Estimate the proportion of patients with double chimerism at 6 months and 1 year. * Determine the speed and cumulative incidence of neutrophil recovery by day 42 and platelet recovery by 6 months after UCB transplantation. * Estimate the risk of chronic GVHD at 1 year. * Estimate the probability of disease-free survival at 100 days and 1 year. * Estimate the risk of fungal and viral infections at 1 year * Estimate the risk of relapse at 1 year * Characterize the pattern of immune cell recovery over 1 year OUTLINE: This is a dose-escalation study of umbilical cord blood (UCB)-derived T-regulatory (Treg) cells. Patients receive nonmyeloablative UCB transplantation and post-transplant immunosuppression as in protocol UMN-2005LS036 (without antithymocyte globulin during conditioning regimen). * Nonmyeloablative conditioning and UCB transplantation: Patients receive allopurinol on days -7 to day 0, fludarabine phosphate intravenously (IV) over 1 hour on days -6 to -2 and cyclophosphamide IV over 2 hours on day -6; undergo total-body irradiation (TBI) once on day -1; and undergo UCB transplantation on day 0. * Immunosuppression therapy: Beginning on day -3 and continuing until day +100, patients receive sirolimus intravenously (IV) with 8-12 mg oral loading dose followed by a single dose of 4mg/day with a target serum concentration of 3-12 mg/mL with a taper until day +180. Patients also receive mycophenolate mofetil IV or orally every 8 hours on days -3 to +30. * Radiation therapy: total body irradiation is administered on Day -1 of 200 cGy. * UCB Treg cell infusion: Patients receive escalating doses of UCB-derived CD4+ CD25+ Treg cells IV on day +1 (and Day +15 for dose level 5 only) until the maximum tolerated dose is obtained. After completion of study treatment, patients are followed at day 180, 360, and 720.