Meristematic tissues are virus free because:
Meristematic tissues remain virus free because virus multiplication and movement are inhibited in rapidly dividing apical dome cells. Most plant viruses rely on plasmodesmata intercellular connections and phloem sieve tubes for systemic translocation from source leaves to sinks; meristem dome lacks differentiated phloem and contains narrow plasmodesmata with high callose deposition limiting viral cell to cell trafficking. Additionally mitotic cycle of meristem cells is significantly shorter than time required for virus replication and assembly, so daughter cells produced outrun infection front resulting in exclusion. High metabolic rate leads to elevated endogenous auxin levels and high oxygen radical scavenging antioxidant activity creating unfavorable environment for viral polymerase function. Molecular evidence indicates strong RNA silencing response in meristem with high expression of Dicer like proteins DCL1-4 and RNA dependent RNA polymerase RDR6 generating small interfering RNAs that degrade viral genomes. Consequently even severely infected mother plant harbors distal 0.1 millimeter virus free zone exploitable for phytosanitation, providing basis for meristem culture combined with heat therapy for eradication of persistent viruses in vegetatively propagated crops.
Ref: Cassells 1991 virus free meristem; Lodish Chap. 8 viral movement.