A Study To Evaluate the Pharmacokinetics, Pharmacodynamics, Safety and Tolerability of ASP2408 After Multiple Dose Subcutaneous Injections in Patients With Rheumatoid Arthritis on Methotrexate

Inclusion Criteria: * Subject weighs at least 50 kg. * Subject has a body mass index (BMI) of ≤ 35 kg/m2. * Subject's 12-lead electrocardiogram (ECG) results are normal at Screening and Day 1 prior to study drug dosing or, if abnormal, the abnormality is not clinically significant as determined by the Investigator. * Subject has Rheumatoid Arthritis (RA) that was diagnosed according to the 1987 revised criteria of the American College of Rheumatology (ACR) ≥ 6 months prior to Screening. * Subject meets the ACR 1991 revised criteria for Global Functional Status in RA, Class I, II or III at Screening. * Subject MUST be on concomitant methotrexate (MTX): * for ≥ 3 months prior to Day 1, AND * at a stable dose (10 - 25 mg/week) for ≥ 28 days prior to Day 1 and throughout the study. * Subject's other related medications taken for the treatment of RA at the time of Screening must meet the noted stability requirements and remain on a stable regimen, as follows: * Non-steroidal anti-inflammatory drugs (NSAIDs), selective cyclooxy-genase-2 (COX-2) inhibitors, oral corticosteroids (≤ 10 mg of prednisone, or equivalent, daily) or low dose opioids (≤ 30 mg of oral morphine, or equivalent, daily) must be stable for ≥ 28 days prior to Screening and remain so throughout the Treatment and Observation Period. * Hydroxychloroquine (Plaquenil®) and sulfasalazine must have started ≥ 2 months, and be stable for ≥ 28 days, prior to Day 1. Exclusion Criteria: * Subject has an ongoing infection or has had an infection requiring intravenous antibiotics within 1 month prior to Day 1. * Subject has a past history of serious opportunistic infection. * Subject has a positive Mantoux tuberculin skin or QuantiFERON-TB Gold test within 90 days of, or at Screening, and has not completed an adequate course of antimicrobial therapy per CDC guidelines. * Subject received any live or live-attenuated vaccine within 30 days prior to Day 1. * Subject received any of the following: * Anakinra (Kineret®), etanercept (Enbrel®), or adalimumab (Humira®) within 60 days prior to Day 1. * Rituximab (Rituxan®) or any other anti-CD20 antibody within 180 days prior to Day 1. * Leflunomide (Arava®) within 60 days prior to drug dosing on Day 1, unless the subject has undergone cholestyramine washout at least 30 days prior to Day 1. * Oral or injectable gold, azathioprine, penicillamine, cyclosporine, or tacrolimus within 30 days prior to Day 1. * Cyclophosphamide within 180 days prior to Day 1. * Subject has received any CTLA4-Ig molecule (including, but not limited to abatacept \[Orencia®\] and belatacept \[Nulojix\]). * Subject has participated in a previous clinical study with treatment with ASP2408 or ASP2409 or has participated in another dose cohort of the current trial. * Subject has previously participated in any interventional clinical study, or has received an experimental agent within 56 days or 5 half-lives, whichever is longer, prior to Day 1. * Subject has a history of prolonged QT syndrome.