Methods of treating or preventing autoimmune diseases with 2,4-pyrimidinediamine compounds

A compound according to the structural formula:

• or a salt and/or N-oxide thereof, wherein:
• R2 is selected from the group consisting of (C1-C6) alkyl optionally substituted with one or more of the same or different R8 groups, (C3-C8) cycloalkyl optionally substituted with one or more of the same or different R8 groups, 3-8 membered cycloheteroalkyl optionally substituted with one or more of the same or different R8 groups and 5-15 membered heteroaryl optionally substituted with one or more of the same or different R8 groups;
• R4 is
• R6a is (C5-C10) aryl optionally substituted with one or more of the same or different R8 groups;
• R8 is selected from the group consisting of Ra, Rb, Ra substituted with one or more of the same or different Ra or Rb, —ORa substituted with one or more of the same or different Ra or Rb, —B(ORa)2, —B(NRcRc)2, —(CH2)m—Rb, —(CHRa)m—Rb, —O—(CH2)m—Rb, —S—(CH2)m—Rb, —O—CHRaRb, —O—CRa(Rb)2, —O—(CHRa)m—Rb, —O—(CH2)m—CH[(CH2)mRb]Rb, —S—(CHRa)m—Rb, —C(O)NH—(CH2)m—Rb, —C(O)NH—(CHRa)m—Rb, —O—(CH2)m—C(O)NH(CH2)m—Rb, —S—(CH2)m—C(O)NH—(CH2)mRb, —O—(CHRa)m—C(O)NH—(CHRa)m—Rb, —S—(CHRa)m—C(O) NH(CHRa)m—Rb, —NH—(CH2)m—Rb, —NH—(CHRa)m—Rb, —NH[(CH2)mRb], —N[(CH2)mRb]2, —NH—C(O)—NH—(CH2)m—Rb, —NH—C(O)—(CH2)m—CHRbRb, and —NH—(CH2)m—C(O)—NH—(CH2)m—Rb;
• each Ra is independently selected from the group consisting of hydrogen, (C1-C6) alkyl, (C3-C8) cycloalkyl, (C4-C11) cycloalkylalkyl, (C5-C10) aryl, (C6-C16) arylalkyl, 2-6 membered heteroalkyl, 3-8 membered cycloheteroalkyl, 4-11 membered cycloheteroalkylalkyl, 5-10 membered heteroaryl and 6-16 membered heteroarylalkyl;
• each Rb is a group independently selected from the group consisting of ═O, —ORd, (C1-C3) haloalkyloxy, ═S, —SRd, ═NRd, ═NORd, —NRcRc, halogen, —CF3, —CN, —NC, —OCN, —SCN, —NO, —NO2, ═N2, —N3, —S(O)Rd, —S(O)2Rd, —S(O)2ORd, —S(O)NRcRc, —S(O)2NRcRc, —OS(O)Rd, —OS(O)2Rd, —OS(O)2ORd, —OS(O)2NRcRc, —C(O)Rd, —C(O)ORd, —C(O)NRcRc, —C(NH)NRcRc, —C(NRa)NRcRc, —C(NOH)Ra, —C(NOH)NRcRc, —OC(O)Rd, —OC(O)ORd, —OC(O)NRcRc, —OC(NH)NRcRc, —OC(NRa)NRcRc, —[NHC(O)]nRd, —[NRaC(O)]nRd, —[NHC(O)]nORd, —[NRaC(O)]nORd, —[NHC(O)]nNRcRc, —[NRaC(O)]nNRcRc, —[NHC(NH)]nNRcRc and —[NRaC(NRa)]nNRcRc;
• each Rc is independently Ra, or, alternatively, each Rc is taken together with the nitrogen atom to which it is bonded to form a 5-8-membered cycloheteroalkyl or heteroaryl which may optionally include one or more of the same or different additional heteroatoms and which is optionally substituted with one or more of the same of different Ra or Rb groups;
• each Rd is independently Ra;
• each m is independently an integer from 1 to 3;
• each n is independently an integer from 0 to 3;
• R35 is a hydrogen or a R8;
• and
• R45 is a (C3-C8) cycloalkyl optionally substituted with one or more of the same or different R8 groups.