Text S1
A. Relógio et al. Tuning the Mammalian Circadian Clock
Model design
The model presented for the mammalian circadian clock was designed based on the
information contained on Figure S1. This figure contains the same elements as Figure 1 in the
main text and additionally all parameters and variables indicated on the equations. The model
comprises two major compartments, the nucleus (light grey) and the cytoplasm. There are 20
species represented, including, 5 genes (highlighted in blue boxes); their corresponding
cytoplasmic proteins and cytoplasmic protein complexes (indexed “C” and highlighted in
violet boxes) and nuclear proteins and nuclear protein complexes (indexed “N” and
highlighted in yellow boxes). Dead-end orange lines represent transcription inhibition
reactions,
green
arrows
other
reactions
(transcription,
translation,
import/export,
phosphorylation/dephosphoryplation, and complex formation). The dashed horizontal line
visually divides the model into two large subunits: the RBR loop and the PC loop. All
parameters and variables are given in, Table 2A, 2B and 2C. All time units are given in hours
and concentration units are given as arbitrary units (a.u.). It should be noted that arbitrary
units cannot be compared across different publications according to IUPAC rules [1].
The network in Figure S1 can be translated into the following set of ordinary differential
equations:
CLOCK/BMAL
dx1
 kf x1 x7  kd x1 x1  d x1 x1
dt
(1)
Rev-Erb
dy3
 V3 max
dt
 x1 
1  g  
 kt 3 
 PC 

1  
 ki3 
w
v
v
 x1   x1 
    
 kt 3   kt 3 
v
 d y 3 y3
(2)
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A. Relógio et al. Tuning the Mammalian Circadian Clock
Ror
dy 4
 V4 max
dt
 x1 

1  h
 kt 4 
 PC 

1  
 ki 4 
q
p
p
 x1 
 x1 

  

 kt 4 
 kt 4 
p
 d y4 y4
(3)
REV-ERBC
dz 6
 k p 3 ( y3  y30 )  kiz 6 z 6  d z 6 z 6
dt
(4)
dz 7
 k p 4 ( y 4  y 40 )  kiz 7 z 7  d z 7 z 7
dt
(5)
dx5
 kiz 6 z 6  d x 5 x5
dt
(6)
dx6
 kiz 7 z 7  d x 6 x6
dt
(7)
RORC
REV-ERBN
RORN
Bmal
n
dy5
 V5 max
dt
 x6 
1  i 
 kt 5 
 d y 5 y5
m
n
 x5   x 6 
1      
 ki 5   kt 5 
(8)
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A. Relógio et al. Tuning the Mammalian Circadian Clock
BMALC
dz8
 k p 5 ( y5  y50 )  kiz 8 z8  d z 8 z8
dt
(9)
dx7
 kiz 8 z8  kdx1 x1  kfx1 x7  d x 7 x7
dt
(10)
BMALN
Per
b
dy1
 V1max
dt
 x1 
1  a 
 kt1 
 d y1 y1
c
b
b
 PC   x1   x1 
     
1  
 ki1   kt1   kt1 
(11)
Cry
e
dy 2
 V2 max
dt
 x1 
1  d  
1
 kt 2 
 d y2 y2
f
e
e
f1
 PC   x1   x1 
 x5 
      1  

1  
k
k
k
k
 i2   t 2   t 2 
 i 21 
(12)
CRYC
dz1
 k p 2 ( y 2  y 20 )  kdz 4 z 4  kdz 5 z5  kfz 5 z1z 2  kfz 4 z1z3  d z1 z1
dt
(13)
dz 2
 k p1 ( y1  y10 )  kdz 5 z 5  kd phz3 z 3  kfz 5 z 2 z1  kphz 2 z 2  d z 2 z 2
dt
(14)
PERC
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PERC*
dz 3
 kphz 2 z 2  kdz 4 z 4  kd phz3 z 3  kfz 4 z 3 z1  d z 3 z 3
dt
(15)
PERC*/CRYC
dz 4
 kfz 4 z1z 3  kex 2 x 2  kiz 4 z 4  kdz 4 z 4  d z 4 z 4
dt
(16)
dz 5
 kfz 5 z1z 2  kex 3 x3  kiz 5 z 5  kdz 5 z 5  d z 5 z 5
dt
(17)
PERC/CRYC
PER*N/CRYN
dx 2
 kiz 4 z 4  kex 2 x 2  d x 2 x 2
dt
(18)
dx3
 kiz 5 z 5  kex 3 x3  d x 3 x3
dt
(19)
PC  x2  x3
(20)
PERN/CRYN
PER/CRYpool
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A. Relógio et al. Tuning the Mammalian Circadian Clock
List of Variables
Variable [a.u.]
x1
x2
x3
PC
x5
x6
y1
y2
y3
y4
y5
z1
z2
z3
z4
z5
z6
z7
z8
Table 1. List of Variables
Name
CLOCK/BMAL
PER*N/CRYN
PERN/CRYN
PER/CRYpool
REV-ERBN
RORN
Per
Cry
Rev-Erb
Ror
Bmal
CRYC
PERC
PERC*
PERC*/CRYC
PERC/CRYC
REV-ERBC
RORC
BMALC
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List of Parameters
Parameters
Name
Value
Degradation rates for nuclear proteins or nuclear protein complexes [hour-1]
CLOCK/BMAL
0.08
dx1
*
PER N/CRYN
0.06
dx2
PERN/CRYN
0.09
dx3
REV-ERBN
0.17
dx5
RORN
0.12
dx6
BMALN
0.15
dx7
-1
Degradation rates for mRNAs [hour ]
Per
0.3
dy1
Cry
0.2
dy2
Rev-Erb
2
dy3
Ror
0.2
dy4
Bmal
1.6
dy5
-1
Degradation rates for cytoplasmic proteins [hour ]
CRYC
0.23
dz1
PERC
0.25
dz2
*
PERC
0.6
dz3
*
PERC /CRYC
0.2
dz4
PER
/CRY
0.2
dz5
C
C
REV-ERBC
0.31
dz6
RORC
0.3
dz7
BMALC
0.73
dz8
Reaction rates for complex formation/dissociation
CLOCK/BMAL-complex formation [hour-1]
2.3
kfx1
-1
CLOCK/BMAL-complex dissociation [hour ]
0.01
kdx1
*
kfz4
1
PERC /CRYC-complex formation [(a.u.hour)-1]
*
PERC /CRYC-complex dissociation [hour-1]
1
kdz4
-1
kfz5
1
PERC/CRYC-complex formation [(a.u.hour) ]
-1
PERC/CRYC-complex dissociation [hour ]
1
kdz5
-1
Phosphorylation/dephosphorylation reaction rates [hour ]
PERC-phosphorylation rate
2
kphz2
*PERC dephosphorylation rate
0.05
kdphz3
-1
Transcription rates [a.u.hour ]
Per
1
V1max
Cry
2.92
V2max
Rev-Erb
1.9
V3max
Ror
10.9
V4max
Bmal
1
V5max
Table 2A. List of Parameters
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Parameters
Name
Activation/inhibition rates [a.u.]
Per-activation rate
kt1
Per-inhibition rate
ki1
Cry-activation rate
kt2
Cry-inhibition rate
ki2
Cry-inhibition rate
ki21
Rev-Erb-activation rate
kt3
Rev-Erb-inhibition rate
ki3
Ror-activation rate
kt4
Ror-inhibition rate
ki4
Bmal-activation rate
kt5
Bmal-inhibition rate
ki5
Transcription fold activation (dimensionless)
Per
a
Cry
d
Rev-Erb
g
Ror
h
Bmal
i
Production rates [hour-1]
PERC
kp1
CRYC
kp2
REV-ERBC
kp3
RORC
kp4
BMALC
kp5
Import/Export rates [hour-1]
PERC*/CRYC
kiz4
PERC/CRYC
kiz5
REV-ERBC
kiz6
RORC
kiz7
BMALC
kiz8
PER*N/CRYN
kex2
PERN/CRYN
kex3
Table 2B. List of Parameters
Value
3
0.9
2.4
0.7
5.2
2.07
3.3
0.9
0.4
8.35
1.94
12
12
5
5
12
0.4
0.26
0.37
0.76
1.21
0.2
0.1
0.5
0.1
0.1
0.02
0.02
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Parameters
Name
Hill coefficients of transcription (dimensionless)
Per-activation
b
Per-inhibition
c
Cry-activation rate
e
Cry-inhibition
f
Cry-inhibition
f1
Rev-Erb-activation
v
Rev-Erb-inhibition
w
Ror-activation
p
Ror-inhibition
q
Bmal-activation
n
Bmal-inhibition
m
Exogenous RNA [a.u.]
y10
Per
y20
Cry
y30
Rev-Erb
y40
Ror
y50
Bmal
Table 2C. List of Parameters
Value
5
7
6
4
1
6
2
6
3
2
5
0
0
0
0
0
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References
1. Olesen H (1995) Properties and units in the clinical laboratory sciences. I. Syntax and semantic
rules (recommendation 1995). International Union of Pure and Applied Chemistry (IUPAC)
and International Federation of Clinical Chemistry (IFCC). Eur J Clin Chem Clin Biochem 33:
627-636.
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