Natalizumab (BG00002, Tysabri) Study in Japanese Participants With Relapsing-Remitting Multiple Sclerosis (RRMS)

Part A Key Inclusion Criteria: * Must give written informed consent and any authorizations required by local law. * Must have a diagnosis of relapsing-remitting MS, as defined by the revised McDonald criteria 1 through 4 (Polman et al, 2005). All other possible neurologic diagnoses must have been reasonably excluded by means of laboratory and/or imaging studies, in the opinion of the Investigator. * Japanese men and women aged 18 to 65, inclusive, at the time of informed consent. * All male subjects and female subjects of childbearing potential must practice effective contraception during the study and be able to continue contraception for 12 weeks after their last dose of study treatment. * Must have an Expanded Disability Status Scale (EDSS) score between 0.0 and 6.0, inclusive. * Must have experienced at least 1 medically documented clinical exacerbation within 12 months of enrollment. * Must be willing to remain free from concomitant immunosuppressive or immunomodulatory treatment (including interferon beta \[IFNβ\] and chronic systemic corticosteroids) for the duration of the study. * Must have a baseline MRI, conducted within 35 calendar days prior to enrollment. Key Exclusion Criteria: * Diagnosis or history of neuromyelitis optica (NMO), e.g., a long spinal lesion extending over 3 or more vertebral bodies was detected, or the subject has a history of positive tests for anti-aquaporin-4 (anti-AQP4) antibodies. * The subject is considered by the Investigator to be immunocompromised, based on medical history, physical examination, laboratory testing, or prior immunosuppressive or immunomodulating treatment. * An MS exacerbation (relapse) within 30 days prior to enrollment or, in the opinion of the Investigator, the subject has not stabilized from a relapse prior to enrollment at Week 0. * History of malignancy. * Known history of, or positive test result for human immunodeficiency virus (HIV) infection. * Known history of or positive test result for hepatitis C virus or hepatitis B virus within the year prior to enrollment. * History of severe allergic or anaphylactic reactions or known drug hypersensitivity. * A clinically significant infectious illness within 30 days prior to enrollment. * Abnormal liver function test results at screening: alanine aminotransferase (ALT), or aspartate aminotransferase (AST) \>2 times of the upper limit of normal (ULN) or bilirubin \>1.5 times of the ULN during screening. * Previous treatment with natalizumab, any murine protein, or any other therapeutic monoclonal antibody. * Any prior treatment with any of the following medications: total lymphoid irradiation, cladribine, T-cell or T-cell receptor vaccination. * Treatment with immunosuppressant medications, e.g., azathioprine, cyclophosphamide, methotrexate, and fingolimod within 6 months prior to enrollment, or mitoxantrone and cyclosporine within 12 months prior to enrollment. * Treatment with any of the following medications or procedures within 6 months prior to enrollment: intravenous immunoglobulin (IVIg), plasmapheresis, or cytapheresis. * Treatment with immunomodulatory medications (including IFNβ and glatiramer acetate \[GA\]) within 2 weeks of enrollment. * Treatment with any of the following medications within 30 days of enrollment: intravenous corticosteroid treatment, systemic corticosteroid treatment, 4-aminopyridine or related products. * Participation in any other investigational treatment within the 6 months prior to enrollment or concurrent with this study. Part B Key Inclusion Criteria: * Must give written informed consent and any authorizations required by local law. * Must have a diagnosis of relapsing-remitting MS, as defined by the revised McDonald criteria 1 through 4 (Polman et al, 2005). All other possible neurologic diagnoses must have been reasonably excluded by means of laboratory and/or imaging studies, in the opinion of the Investigator. * Japanese men and women aged 18 to 65, inclusive, at the time of informed consent. * All male subjects and female subjects of childbearing potential must practice effective contraception during the study and be able to continue contraception for 12 weeks after their last dose of study treatment. * Must have an EDSS score between 0.0 and 5.5, inclusive. * Must have experienced at least 1 medically documented clinical exacerbation within 12 months of enrollment. * Must be willing to remain free from concomitant immunosuppressive or immunomodulatory treatment (including IFNβ and chronic systemic corticosteroids) for the duration of the study. * Prior to enrollment all subjects must have: a screening MRI, or documentation of an MRI within the subject's medical record within 1 year of the screening visit, which reveals 3 or more T2 hyperintense lesions consistent with MS, and a baseline MRI, conducted within 7 calendar days prior to enrollment, which reveals at least 1 MRI lesion consistent with MS. Key Exclusion Criteria * Diagnosis or history of NMO, e.g., a long spinal lesion extending over 3 or more vertebral bodies was detected, or the subject has a history of positive tests for anti-AQP4 antibodies. * The subject is considered by the Investigator to be immunocompromised, based on medical history, physical examination, laboratory testing, or prior immunosuppressive or immunomodulating treatment. * An MS exacerbation (relapse) within 30 days prior to enrollment or, in the opinion of the Investigator, the subject has not stabilized from a relapse prior to enrollment at Week 0. * History of malignancy. * Known history, or positive test result of HIV infection. * Known history of or positive test result for hepatitis C virus or hepatitis B virus within the year prior to Enrollment. * History of severe allergic or anaphylactic reactions or known drug hypersensitivity. * A clinically significant infectious illness within 30 days prior to Enrollment. * Abnormal liver function test results at screening: ALT or AST \>2 times of the ULN or bilirubin \>1.5 times of the ULN during screening. * Previous treatment with natalizumab, any murine protein, or any other therapeutic monoclonal antibody. * Any prior treatment with any of the following medications: total lymphoid irradiation, cladribine, T-cell or T-cell receptor vaccination. * Treatment with immunosuppressant medications, e.g., azathioprine, cyclophosphamide, methotrexate, and fingolimod within 6 months prior to enrollment, or mitoxantrone and cyclosporine within 12 months prior to enrollment. * Treatment with any of the following medications or procedures within 6 months prior to enrollment: IVIg, plasmapheresis, or cytapheresis. * Treatment with immunomodulatory medications (including IFNβ and GA) within 2 weeks of enrollment. * Treatment with any of the following medications within 30 days of enrollment: intravenous corticosteroid treatment, systemic corticosteroid treatment, 4-aminopyridine or related products. * Participation in any other investigational treatment within the 6 months prior to enrollment or concurrent with this study. NOTE: Other protocol defined inclusion/exclusion criteria may apply.