Trial of AB-110 in Adults With Hematologic Malignancies Undergoing Cord Blood Transplantation

Inclusion Criteria: * Patients must have received some immunosuppressive chemotherapy in the preceding 3 months. * Acute myelogenous leukemia (AML): 1. Complete first remission (CR1) at high risk for relapse 2. Complete second remission (CR2). 3. No documented myelofibrosis at screening marrow biopsy * Acute lymphoblastic leukemia (ALL): 1. Complete first remission (CR1) at high risk for relapse 2. Complete second remission (CR2). * Other acute leukemias that are of ambiguous lineage or of other types * Any acute leukemia with marrow aplasia or without adequate count recovery. * Myelodysplastic Syndrome (MDS) * Karnofsky score \> 70 %. * Calculated creatinine clearance \> 60 ml/min. * Bilirubin \< 1.5 mg/dL, ALT \< 3 x upper limit of normal * Pulmonary function (FVC, FEV1 and corrected DLCO) \> 50% predicted. * Left ventricular ejection fraction \> 50%. * Albumin \> 3.0 g/dL. * Negative antiviral serology: * Negative human immunodeficiency virus (HIV) antibody. * Negative human T-lymphotropic virus (HTLV)-1 and 2 antibodies. * Negative hepatitis B surface antigen (HBsAg) and undetectable hepatitis B virus (HBV) DNA * Negative hepatitis C virus (HCV) antibody or negative HCV ribonucleic acid (RNA) * For female subjects of childbearing potential: 1. A negative serum pregnancy test 2. Willing to use contraception throughout the study period. * Male subjects must be willing to use a recommended method of contraception throughout the study period, and to refrain from sperm donation throughout the study period. * Two appropriate CB units identified for the subject. * In the judgment of the investigator, participation in the protocol offers an acceptable benefit-to-risk ratio when considering current disease status, medical condition, and the potential benefits and risks of alternative treatments for the subject's cancer. * Willingness and ability to comply with scheduled visits, drug administration plan, protocol-specified laboratory tests, other study procedures, and study restrictions. * Evidence of a signed informed written consent Exclusion Criteria: * Pregnancy or breastfeeding. * Current active, uncontrolled bacterial, viral, or fungal infection * Prior allogeneic or autologous HCT at any time. * Active malignancy other than the one for which AB-110 transplant is being performed within 12 months of enrollment. * Any identified and available 10/10 HLA-matched related donor or 10/10 HLA-matched unrelated donor. * Have evidence of recipient donor specific anti-HLA antibodies. * Active central nervous system (CNS) disease at time of screening. * Documented allergy to DMSO, mouse or bovine proteins, or iron. * Subject has other conditions that in the opinion of the investigator would place the subject at increased risk for toxicity by participation in the study. * Psychiatric condition making the patient unlikely to comply with protocol therapy, required tests and follow-up.