Table 1 Mathematical model describing key parameters that regulate daily rhythms of protein O-GlcNAcylation.

G1_t = 0.60006-0.23683*C_t-0.36690*C_t-1

(1)

G2_t = -0.15959 + 0.64048*F_t-1 + 0.88571*F_t-2

(2)

G_t = 0.4 + a*3*G1_t + 2*G2_t-2

(3)

U1_t = 31.742-5.597*G_t-4.992*G_t-1

(4)

U2_t = 32.915-34.274*F_t-36.579*F_t+1

(5)

U_t = U1_t-2 + U2_t-1

(6)

ogt_t = 0.06982-a*(0.19496*F_t + 0.43217*F_t-2 + 0.53953*F_t-3)

(7)

OGT1_t = 0.73589-0.75087*ogt_t+1-0.68392*ogt_t

(8)

OGT2_t = 1.06818 + 0.17796*C_t + 0.28562*C_t-1

(9)

OGT_t = 2.5*OGT1_t + a*OGT2_t-1-1

(10)

oga1_t = 0.23416-0.24845*F_t + 0.29379*F_t-1 + 0.18123*F_t-2

(11)

oga2_t = 1.3542-1.1107*C_t-0.9980*C_t-3

(12)

oga_t = a*b*(oga1_t-2*oga2_t-0.2)

(13)

OGA_t = 0.3379-4.3531*oga_t+1 + 1.9031*oga_t-1

(14)

OGTAct_t = c*OGT_t + d

(15)

OGAAct_t = e*OGA_t + f

(16)

OXU_t = 0.4167*U_t*OGTAct_t/OGAAct_t

(17)

O_t = 0.2008750-0.0051100*OXU_t + 0.0071568*OXU_t-2 + 0.0036060*OXU_t-3

(18)

Variables

Description

G1_t

Clock-controlled post-transcriptional regulation on GFAT activity

C_t

Clock-controlled mechanism(s)

G2_t

Daily gfat2 mRNA level

F_t

Daily feeding pattern of flies

a

Parameter to indicate whether flies have an intact circadian clock. WT flies (w¹¹¹⁸): a = 1; clock mutant flies (per⁰): a = 0

G_t

Daily GFAT activity level

U1_t

Level of UDP-GlcNAc calculated using GFAT activity

U2_t

Level of UDP-GlcNAc calculated using feeding activity

U_t

Overall daily UDP-GlcNAc level

ogt_t

Daily ogt mRNA level

OGT1_t

OGT protein level regulated by ogt mRNA

OGT2_t

Translational regulation of OGT protein by clock

OGT_t

Daily OGT protein level

oga1_t

Feeding-regulated ogt mRNA level

oga2_t

Clock-regulated ogt mRNA level

oga_t

Daily oga mRNA level

b

Parameter to indicate whether flies eat at natural feeding time. RF21-3: b = 1; RF9-15: b = 0

OGA_t

Daily OGA protein level

OGTAct_t

Daily OGT activity

c, d

Parameters to predict OGT activity from OGT protein level. In this model, c = 1 and d = 0

OGAAct_t

Daily OGA activity

e, f

Parameters to predict OGA activity from OGA protein level. In this model, e = 0.1 and f = 1

OXU_t

Interaction between daily UDP-GlcNAc level, OGT activity and OGA activity

O_t

Daily O-GlcNAcylation level