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O W N L O A DCircadian Rhythms in Drosophila melanogaster
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O W N L O A D
Figure 1 is the control mechanism of autoregulatory feedback loops of
Drosophila m. participating five genes, period (per), timeless
(tim), Drosophila Clock (dClk), cycle (cyc) and double-time
(dbt). We shall model this mechanism with HFPN and discuss its simulation
results by following the observations in [1,2,3].
Roughly speaking, PER and TIM proteins collaborate in the regulation of their
own expression in Drosophila, assembling in PER-TIM complexes that permit
nuclear translocation, inactivation of per and tim transcription
in a cycling negative feedback loop, and activation of dClk transcription
which participates in the dCLK-CYC negative feedback loop. The dCLK and
the CYC form heterodimers that activate per and tim transcriptions
and inhibit dClk transcription. Refer to [1]
for the details of the mechanism.
Figure 1: A graphical model of the gene regulation in the Drosophila
circadian oscillator.
Among these five genes, three genes, per, tim, and dClk, are rhythmically expressed (Figure 2): per and tim mRNA levels begin to rise in the subjective day and to peak early in the subjective evening, and dClk mRNA level peaks late at night to early in the morning. Although per and tim mRNAs reach peak levels in the evening, PER and TIM levels do not peak until late evening. It is considered that this delay results from the initial destabilization of PER by DBT-dependent phosphorylation followed by the stabilization of PER by dimerization with TIM [2,3].
Figure 2: Behaviors of the per, tim, dClk, and cyc genes and proteins.
By using Genomic Object Net, we designed a HFPN shown in Figure 3 which naïvely represents this gene regulatory mechanism of Drosophila circadian rythm, where the functions for continuous transitions are tuned so that the simulation results will coincide with the observations in [1,2,3] and the expressions in Figure 2. More details shall be give in the sequel along with biological discussions.
Figure 3: A HFPN representation of Drosophila circadian mechanism in which five genes per, tim, dClk, cyc, and dbt participate. The complex forming rate m11*m10/20 (m4*m5/20, m4*m7/20) of the proteins dCLK (m11) and CYC (m10) (the proteins PER (m4) and TIM (m5), the proteins PER (m4) and DBT(m7)) is assigned to transition T1 (T2, T3). Transitions T4, T5, and T6 represent the degradation rates of complexes of the corresponding proteins.
Figure 4 (a) indicates that this HFPN model representing two negative feedback loops, the PER-TIM feedback and the dCLK-CYC feedback, successfully produce periodic oscillations of per mRNA (m2), tim mRNA (m3), and dClk mRNA (m13), while the concentration of cyc mRNA (m12) keeps constant expression.
Figure 4 (a): Behaviors of concentrations of four mRNAs simulated on Genomic Object Net
Figure 4 (b): Time difference around four hours is observed between the peaks of concentrations of per mRNA and PER.
It is known that the protein TIM stabilizes phosphorylated PER by dimerizing
with it [1]. This phenomenon is
reflected to the firing speed of transition T5, that is, the firing
speed of transition T5 (m8/15) is set to be slower than the one of
transition T7 (m4/10). Moreover, it is suggested in [3]
that the normal function of protein DBT is to reduce the stability and thus
the level of accumulation of monomeric PER proteins. This function is realized
in Figure 3 in transition T3. It is clearly expressed in Figure 4
(b) that there is time difference around five hours between the peaks of concentrations
of per mRNA and PER which is believed to be arisen from the above two
facts. This indicates that the result of simulation is in good agreement with
the experimental observation in [1].
Figure 5: Concentration behaviors of per mRNA. (a) dbtL
mutant (b) Wild type (c) dbtS mutant.
View larger version of this image
Figure 6: A HFPN realization of the circadian rhythm model due to Ueda et al. [4]. A series of ten ODEs
are realized in this network, where Perm(CCn, PTn) represents the concentration
of per mRNA (dCLK-CYC complex in the nuleus, PER-TIM complexin the nucleus)
and C1 = 0nM/h, S1 =1.4nM/h,A1 = 0.45nM/h, B1 = 0, L1 = 0.3nM/h, D0 = 0.012nM/h,D1
= 0.94nM/h, R1 = 1.02nM/h.
References
[1] Hardin P.E. (2000) From biological clock to biological rhythms. Genome Biology 2000, 1(4), reviews1023.1-1023.5. Hofestädt, R. (1994). A Petri Net Application of Metabolic Processes. Journal of System Analysis, Modelling and Simulation 16, 113-122.
[2] Kloss, B., Price, J.L., Saez, L., Blau, J., Rothenfluh, A., Wesley, C.S. and Young, M.W. (1998) The Drosophila clock gene double-time encodes a protein closely related to human casein Kinase Ie. Cell, 94, 97-107.
[3] Price, J.L., Blau, J., Rothenfluh A., Adobeely, M., Kloss, B. and Young, M.W. (1998) double-time is a novel Drosophila clock gene that regulates PERIOD protein accumulation, Cell , 94, 83-95.
[4] Ueda, H. R., Hagiwara, M., and Kitano, H. (2001) Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm, J. Theor. Biol., 210 (4), 401-406.
