A Safety Study of Human Cord Blood Derived, Culture Expanded Natural Killer Cell (PNK-007) Infusion With Subcutaneous Recombinant Human IL-2 (rhIL-2) in Adults With Relapsed and/or Refractory Acute Myeloid Leukemia (AML)

Inclusion Criteria: Subjects must satisfy the following criteria to be enrolled in the study: 1. Subject has an eligible disease: * Primary Acute myeloid leukemia (AML) induction failure: no Complete Remission (CR) after 2 or more induction attempts or * Relapsed AML: not in CR after 1 or more cycles of standard re-induction chemotherapy * For relapsed subjects \> 60 years of age, the 1 cycle of standard re-induction chemotherapy is not required if either of the following criteria is met: * relapse within 6 months of last chemotherapy * blast count \<30% within 10 days of starting this protocol therapy or * Secondary AML (MDS transformation or treatment related): or • AML relapsed \> 2 months after transplant Subjects with prior central nervous system (CNS) involvement are eligible provided that it has been treated and Cerebrospinal fluid (CSF) is clear for at least 2 weeks prior to Visit 1. 2. Subject is ≥ 18 and ≤ 70 years of age at the time of signing the informed consent form (ICF). 3. Subject must understand and voluntarily sign an ICF prior to any study-related assessments/procedures being conducted. 4. Subject is willing and able to adhere to the study schedule and other protocol requirements. 5. Karnofsky Performance Status \> 50%. 6. Ability to be off prednisone and other immunosuppressive drugs for at least 3 days prior to the PNK-007 cell infusion. 7. Female of childbearing potential (FCBP) must: a. Have two negative pregnancy tests as verified by the Investigator prior to starting study therapy. She must agree to ongoing pregnancy testing during the course of the study, and after the end of study treatment. This applies even if the subject practices true abstinence from heterosexual contact. 8. Either commit to true abstinence from heterosexual contact or agree to use, and be able to comply with, effective contraception without interruption, 28 days prior to starting PNK-007, during the study therapy (including dose interruptions), and for 28 days after discontinuation of study therapy. Male subjects must: a. Practice true abstinence or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential while participating in the study, during dose interruptions and for at least 28 days following PNK-007 discontinuation, even if he has undergone a successful vasectomy. Exclusion Criteria: The presence of any of the following will exclude a subject from enrollment: 1. Subject has any significant medical condition, laboratory abnormality, or known psychiatric illness that would prevent the subject from participating in the study. 2. Subject has any condition including the presence of laboratory abnormalities which places the subject at unacceptable risk if he or she were to participate in the study. 3. A subject has any condition that confounds the ability to interpret data from the study. 4. Subject has a body weight exceeding 120kg. 5. Subject has aspartate aminotransferase (AST), alanine aminotransferase (ALT), or alkaline phosphatase ≥ 2.5 x the upper limit of normal (ULN) at screening. 6. Estimated glomerular filtration rate (eGFR) \< 30 mL/min/1.73 m2 at screening calculated using the Modification of Diet in Renal Disease Study equation or history of an abnormal eGFR \< 60 and a decline of \> 15 mL/min/1.73 m2 below normal in the past year. 7. Subject has a bilirubin level \> 2 mg/dL (unless subject has known Gilbert's disease) at screening. 8. Subject has had prior treatment with biologic antineoplastic agents no less than 7 days before PNK-007 infusion and at least 5 half lives. For agents that have known Adverse Events (AEs) occurring beyond 7 days after administration (ie, monoclonal antibodies), this period must be extended beyond the time during which acute AEs are known to occur. An exception to this criteria is hydroxyurea which can be given throughout the Screening/Baseline Period up to the time of the pre-conditioning treatment. 9. Subject has bi-phenotypic acute leukemia. 10. Subject has had a transplant \< 60 days prior to Visit 1 (Screening/Baseline visit). 11. Subject has had treatment for graft-versus-host disease \< 30 days prior to Visit 1 (Screening/Baseline visit). 12. Subject is pregnant or breastfeeding. 13. Subject has new or progressive pulmonary infiltrates or pleural effusion large enough to be detected by chest x-ray or Computed tomography (CT) scan. 14. Subject has active autoimmune disease other than controlled connective tissue disorder or those who are not on active therapy. 15. Subject is HIV positive. 16. Subject has a history of malignancy except primary, secondary, or relapsed Acute myeloid leukemia (AML), or excised and cured non-melanoma skin cancer, or cervical carcinoma in situ that was surgically ablated more than 5 years prior to PNK-007 infusion. 17. Subject has a history of severe asthma and is presently on chronic medications or has a history of other symptomatic pulmonary disease. 18. Untreated chronic infection or treatment of any infection with systemic antibiotics within 2 weeks prior to dosing with PNK-007. 19. Subject has any other organ dysfunction (CTCAE Version 4.03 Grade 3) that will interfere with the administration of the therapy according to this protocol. 20. Subject has a resting left ventricular ejection fraction (LVEF) of \< 35% obtained by echocardiography or multigated acquisition scan (MUGA).