Biology Reference
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deterministic models [18], several groups recently started to investigate the role of noise in cell cycle
regulation through stochastic modeling [19-21]. Some of these models use the measured molecule
numbers of critical cell cycle regulators [15,16,22] and reproduce the fluctuations in their level through
the Gillespie stochastic simulation algorithm [23].
The model of Kar
et al.
[20] is built on the deterministic model of Tyson and Novak [24] and unpacks
the original system into elementary reactions. The stochastic model is capturing the experimental
findings that the coefficient of variation (
CV
=
standard deviation/mean) of the cell cycle period is
approximately 14% while the
CV
of the cell size at cell division is about the half of this value [25,26].
The authors could get a good fit to these low fluctuations by assuming that the half-lives of the key cell
cycle regulator mRNAs are approximately 12 seconds, which is much shorter than any earlier measured
value (4-70 minutes in [27]). Kar
et al.
[20] commented on this discrepancy that the originally fitted
mRNA levels [15] might come from experiments that underestimated the real average number of mRNA
molecules, as suggested in [28], but even with higher values of mRNA levels they could not fit the data
with realistically long mRNA half-lives.
Most previous models of protein synthesis considered transcription, translation and degradation of
mRNAs as first order chemical reactions [6], neglecting the observed multiple steps of transcriptional and
translational complex formation and senescence by deadenylation of mRNAs [29] or polyubiquitination
of proteins [30]. Kar
et al.
[20] followed these same lines and assumed that production of cell cycle
regulatory proteins are made up of first order elementary reactions of transcription, translation and
degradations of mRNAs and proteins. They found that with realistic mRNA half-lives the period of
the cell cycle and the cell size at division showed too large fluctuations compared to experimental
observations. In this work, we started to investigate how this large noise can be reduced by taking into
account the multi-step gestation and senescence of mRNAs, which have been shown to have a role in
this variability reduction [10]. We did not incorporate mRNA bursting into the model since it increases
noise [3] and we neglected the effects of extrinsic noise that originates from the uneven partitioning of
cell mass and molecular content at cell division [20,31], rather focusing on the intrinsic noise coming
from the fluctuations in molecule numbers [4].
MATERIALS AND METHODS
Our
in silico
approach is based on a Petri net representation of the model of stochastic molecular
dynamics presented in [20], which we modified and extended to represent the multi-step gestation and
senescence processes of mRNAs. Our choice of the modeling formalism stems from the intuitive mapping
existing between reaction-oriented description of biochemical systems and the modeling elements of Petri
nets, a correspondence that we already exploited in a previous work [21] still dealing with a cell-cycle
regulation network. We encoded the model of Kar
et al.
[20] as a stochastic Petri net [32]. The model
in [20], which we do not report here entirely for the sake of conciseness, describes the regulatory network
of cell cycle in yeast through a set of coupled reactions involving 19 distinct biochemical entities (genes,
mRNAs and proteins). Figure 1 provides a diagram of a small portion of the overall model, which we use
to explain the rationale of the encoding with stochastic Petri nets. The diagram shows some of the key
reactions involving the cell cycle core regulator CyclinB-Cdk1 complex and one of its antagonists, the
anaphase promoting complex related protein Cdh1 [18]. The model includes synthesis and degradation
of the mRNAs and translation and degradation of the proteins of these two key regulators. The kinetics
of all reactions shown in figure1, as well as that of the reactions appearing in the model in [20] that are
not reported here, follow mass-action law.
