Temporal evolution of the five dust quantities used to couple the ID radial dust evolution model employed with our MRI-driven turbulence model, for Model IV. These quantities are the representative grain size a_dust,rep (Eq. (16)) in panel a, the representative grain cross-section σ_dust,rep (Eq. (17)), the representative grain mass m_dust,rep (Eq. (18)), the total dust density ρ_dust,_tot (Eq. (8)) in panel d, and the total dust number density n_dust,tot (Eq. (10)) in panel e. Instead of displaying σ_dust,rep and m_dust,_rep, we show the equivalent grain size corresponding to σ_dust,rep (panel b), and the equivalent grain size corresponding to m_dust,_rep (panel c). These equivalent grain sizes better indicate the dominant size when considering the grain cross-section or the grain mass, each of which is important for the MRI calculations (see Sect. 2.3). The panels particularly show the midplane radial profiles. We note that a_dust,rep and a_dust,_m traces the smallest and largest sizes of the dust distribution, respectively, whereas a_dust,σ is the relevant size of the dust distribution involved in the ionization chemistry.