hong1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000216). Biomodels notes: The figure 2C of the reference publication is reproduced. To reproduce figure 2C, the following initial conditions were used (as per the authors suggestion). This is different from that of the model. M=1.35; CP=0.039; CP2=0.088; TF=0.06; IC=0.44 (TFtot=0.5 & IC=TFtot-TF). JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes.

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Minimum criteria for DNA damage-induced phase advances in circadian rhythms.

  • Christian I Hong
  • Judit Zámborszky
  • Attila Csikász-Nagy
PLoS Comput. Biol. 2009; 5 (5):
Abstract
Robust oscillatory behaviors are common features of circadian and cell cycle rhythms. These cyclic processes, however, behave distinctively in terms of their periods and phases in response to external influences such as light, temperature, nutrients, etc. Nevertheless, several links have been found between these two oscillators. Cell division cycles gated by the circadian clock have been observed since the late 1950s. On the other hand, ionizing radiation (IR) treatments cause cells to undergo a DNA damage response, which leads to phase shifts (mostly advances) in circadian rhythms. Circadian gating of the cell cycle can be attributed to the cell cycle inhibitor kinase Wee1 (which is regulated by the heterodimeric circadian clock transcription factor, BMAL1/CLK), and possibly in conjunction with other cell cycle components that are known to be regulated by the circadian clock (i.e., c-Myc and cyclin D1). It has also been shown that DNA damage-induced activation of the cell cycle regulator, Chk2, leads to phosphorylation and destruction of a circadian clock component (i.e., PER1 in Mus or FRQ in Neurospora crassa). However, the molecular mechanism underlying how DNA damage causes predominantly phase advances in the circadian clock remains unknown. In order to address this question, we employ mathematical modeling to simulate different phase response curves (PRCs) from either dexamethasone (Dex) or IR treatment experiments. Dex is known to synchronize circadian rhythms in cell culture and may generate both phase advances and delays. We observe unique phase responses with minimum delays of the circadian clock upon DNA damage when two criteria are met: (1) existence of an autocatalytic positive feedback mechanism in addition to the time-delayed negative feedback loop in the clock system and (2) Chk2-dependent phosphorylation and degradation of PERs that are not bound to BMAL1/CLK.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
system system 3.0 1.0
Id Name Initial quantity Compartment Fixed
CP Monomer clock proteins (PER) system (system)
CP2 Dimer form of clock proteins (PER/PER) system (system)
M Messenger RNA of the clock proteins (Per mRNA) system (system)
TF Transcription factor (BMAL1/CLK) system (system)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
CP = initialValue_CP
CP2 = initialValue_CP2
M = initialValue_M
TF = initialValue_TF
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
r1 r1 ∅ > M

system * function_4_r1
r10 r10 ∅ > TF + CP2

system * kicd * IC
r11 r11 CP2 > ∅

system * kcp2d * CP2
r12 r12 TF + CP2 > ∅

system * kica * CP2 * TF
r13 r13 CP2 > ∅

system * function_4_r13
r14 r14 CP2 > ∅

system * chk2 * CP2
r15 r15 ∅ > TF

system * kcp2d * IC
r16 r16 ∅ > TF

system * chk2c * IC
r17 r17 ∅ > TF

system * function_4_r17
r2 r2 ∅ > M

system * function_4_r2
r3 r3 M > ∅

system * kmd * M
r4 r4 ∅ > CP

system * function_1
r5 r5 CP > ∅

system * kcpd * CP
r6 r6 {2.0}CP > CP2

system * ka * pow(CP, 2)
r7 r7 CP2 > {2.0}CP

system * kd * CP2
r8 r8 CP > ∅

system * function_4_r8
r9 r9 CP > ∅

system * chk2 * CP

Global parameters

Id Value
CPtot 0.0
Dex 0.0
IC 0.0
ICtot 1.0
IR_pulse_duration 2.0
J 0.3
Jp 0.05
TFtot 0.5
chk2 0.0
chk2ToggleOnOff 1.0
chk2_value 0.25
chk2c 0.0
chk2c_value 0.1
chk2pulseactive 1.0
chk2pulseactive_elim 1.0
chk2pulseactive_elim_elim 0.0
chk2pulseonoff 0.0
function_1 0.0
function_4_r1 0.0
function_4_r13 0.0
function_4_r17 0.0
function_4_r2 0.0
function_4_r8 0.0
initialValue_CP 0.039
initialValue_CP2 0.088
initialValue_M 1.35
initialValue_TF 0.06
ka 100.0
kcp2d 0.0525
kcpd 0.525
kcps 0.5
kd 0.01
kica 20.0
kicd 0.01
kmd 0.1
kms 1.0
kp1 10.0
kp2 0.1
n 2.0
trigOFFtime 0.0
trigONtime 4.0

Local parameters

Id Value Reaction

Assignment rules

Definition
IC = TFtot - TF
function_1 = kcps * M
function_4_r17 = kp2 * IC / (Jp + CP + 2.0 * CP2 + 2.0 * IC) / system
function_4_r2 = kms * pow(TF, n) / (pow(J, n) + pow(TF, n)) / system
chk2pulseonoff = chk2pulseactive - (chk2pulseactive_elim_elim + chk2pulseactive_elim)
function_4_r8 = kp1 * CP / (Jp + CP + 2.0 * CP2 + 2.0 * IC) / system
function_4_r13 = kp2 * CP2 / (Jp + CP + 2.0 * CP2 + 2.0 * IC) / system
function_4_r1 = Dex / system
CPtot = CP + 2.0 * CP2 + 2.0 * IC
trigOFFtime = trigONtime + IR_pulse_duration
chk2c = chk2ToggleOnOff*(chk2pulseonoff * (chk2c_value / IR_pulse_duration))
chk2 = chk2ToggleOnOff*(chk2pulseonoff * (chk2_value / IR_pulse_duration))

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments
geq(time, trigONtime) chk2pulseactive_elim = 0
geq(time, trigOFFtime) chk2pulseactive_elim_elim = 1