MLN4924 for the Treatment of Acute Myelogenous Leukemia, Myelodysplastic Syndrome, and Acute Lymphoblastic Leukemia

Inclusion Criteria: * Age greater than or equal to 18 years * Have the following diagnosis: * AML or ALL (for the dose escalation phase only)including leukemia secondary to prior chemotherapy or resulting from an antecedent hematologic disorder, who have failed to achieve complete response (CR) or who have relapsed after prior therapy and are not candidates for potentially curative treatment. * Acute Promyelocytic Leukemia (APL) patients are not eligible * AML or ALL patients who are over age 60 and have not received prior therapy are also eligible if they are not candidates for standard induction chemotherapy * High-grade MDS, defined as \> 10% blasts on bone marrow examination * Low-grade MDS, defined as \< 10% blasts on bone marrow examination (Schedule B expansion cohort only) * Patients who are willing to refrain from donating blood for at least 90 days after their final dose of MLN4924 and (for male patients) willing to refrain from donating semen for at least 4 months after their final dose of MLN4924 * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * Female patients who are postmenopausal, surgically sterile, or agree to practice 2 effective methods of contraception or abstain from heterosexual intercourse * Male patients who agree to practice 2 effective methods of contraception or abstain from heterosexual intercourse * Voluntary written consent * Suitable venous access * Adequate clinical laboratory values during the screening period as specified in the protocol * Patients who are on hydroxyurea may be included in the study and may continue on hydroxyurea while participating in this study. Exclusion Criteria: * Female patients who are lactating or have a positive serum pregnancy test during the screening period * Any serious medical or psychiatric illness * Treatment with any investigational products * Systemic antineoplastic therapy or radiotherapy within 14 days before the first dose of study drug, except for hydroxyurea * Major surgery within 14 days before the first dose of study drug * Life-threatening illness unrelated to cancer * Clinically uncontrolled central nervous system (CNS) involvement * Known human immunodeficiency virus (HIV) positive * Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection * Evidence of uncontrolled cardiovascular conditions as specified in the protocol * Diarrhea \> Grade 1, based on the NCI CTCAE categorization * Systemic treatment with prohibited medications * Ongoing anticoagulant therapy (eg, aspirin, Coumadin, heparin) that cannot be held to permit bone marrow sampling * Use of acetaminophen, acetaminophen-containing products, and statins are not permitted on the day before dosing, day of dosing, and day after dosing with MLN4924