Study of ProTmune for Allogeneic HCT in Adult Patients With Hematologic Malignancies

Key Inclusion Criteria: 1. Male and female patients aged 18 years and older, inclusive; 2. Patients must have a hematologic malignancy for which allogeneic hematopoietic peripheral blood cell transplantation is deemed clinically appropriate. Eligible diseases and stages include the following: 1. Acute myeloid leukemia 2. Acute lymphoblastic leukemia, including T lymphoblastic lymphoma with a history of marrow involvement 3. Myelodysplastic Syndrome 4. Chronic myelogenous leukemia 3. Availability of a suitable 8/8 HLA-A, -B, -C, and -DRB1-matched unrelated mPB donor; 4. mBP donor collection that meets protocol specifications; 5. Adequate performance status, defined as Karnofsky score greater than or equal to 70%; 6. For female patients of childbearing potential, all of the following criteria must be met: * They are not pregnant (i.e., female patients must have a negative serum pregnancy test at screening); * They are not breastfeeding; * They do not plan to become pregnant during the study; and * They are using an effective method of contraception from screening to the end of the study, unless their sexual partner is surgically sterile. 7. For male patients, agreement to use condoms with spermicide during sexual intercourse from screening to the end of study; and 8. Willingness and ability to sign an IRB/IEC-approved ICF before performance of any study-specific procedures or tests and to comply with protocol visits, and study procedures. Key Exclusion Criteria: 1. Phase 1 only: Known bone marrow fibrosis; Phase 2 only: Bone marrow fibrosis grade 3 (severe) or greater; 2. Positive serology for human immunodeficiency virus (HIV) or human T-cell lymphotropic virus (HTLV) at any time prior to enrollment; 3. Currently uncontrolled bacterial, viral, or fungal infection (progression of clinical symptoms despite therapy); 4. Prior autologous or allogeneic HCT; 5. Active malignancy, other than the one for which the allogeneic mPB transplant is being performed, within 12 months of enrollment, excluding superficial basal cell and carcinoma in situ cervical cancer; 6. Pulmonary disease, renal dysfunction, hepatic disease, cardiac disease, neurologic disease; 7. Participation in another clinical trial involving an investigational product within 30 days prior to screening; or 8. Any condition or therapy, which, in the opinion of the Investigator, might pose a risk to the patient or make participation in the study not in the best interest of the patient.