Cell cycle

Caulobacter crescentus is a model organism for the study of asymmetric division and cell type differentiation, as its cell division cycle generates a pair of daughter cells that differ from one another in their morphology and behavior. One of these cells (called stalked) develops a structure that allows it to attach to solid surfaces and is the only one capable of dividing, while the other (called swarmer) develops a flagellum that allows it to move in liquid media and divides only after differentiating into a stalked cell type. Although many genes, proteins, and other molecules involved in the asymmetric division exhibited by C. Crescentus have been discovered and characterized during decades, it remains as a challenging task to understand how cell properties arise from the high number of interactions between these molecular components. This chapter describes a modeling approach based on the Boolean logic framework that provides a means for the integration of knowledge and study of the emergence of asymmetric division. The text illustrates how the simulation of simple logic models gives valuable insight into the dynamic behavior of the regulatory and signaling networks driving the emergence of the phenotypes exhibited by C. crescentus. These models provide useful tools for the characterization and analysis of other complex biological networks.

Background
DNA damage (single or double-strand breaks) triggers adapted cellular responses. These responses are elicited through signalling pathways, which activate cell cycle checkpoints and basically lead to three cellular fates: cycle arrest promoting DNA repair, senescence (permanent arrest) or cell death. Cellular senescence is known for having a tumour-suppressive function and its regulation arouses a growing scientific interest. Here, we advance a qualitative model covering DNA damage response pathways, focusing on G1/S checkpoint enforcement, supposedly more sensitive to arrest than G2/M checkpoint.

Results
We define a discrete, logical model encompassing ATM (ataxia telangiectasia mutated) and ATR (ATM and Rad3-related) pathways activation upon DNA damage, as well as G1/S checkpoint main components. It also includes the stress responsive protein p38MAPK (mitogen-activated protein kinase 14) known to be involved in the regulation of senescence. The model has four outcomes that convey alternative cell fates: proliferation, (transient) cell cycle arrest, apoptosis and senescence. Different levels of DNA damage are considered, defined by distinct combinations of single and double-strand breaks. Each leads to a single stable state denoting the cell fate adopted upon this specific damage. A range of model perturbations corresponding to gene loss-of-function or gain-of-function is compared to experimental mutations.

Conclusions
As a step towards an integrative model of DNA-damage response pathways to better cover the onset of senescence, our model focuses on G1/S checkpoint enforcement. This model qualitatively agrees with most experimental observations, including experiments involving mutations. Furthermore, it provides some predictions.

Direct transcription

This model is a direct transcription of the Boolean model published by Davidich & Bornholdt [1]. Dynamical rules are defined on the basis of the network structure, as the sum of the positive and negative influences exerted on each nodes by its regulators. (Fig. 1, bottom left in [2]; see text for more details).

The model yields a main stable state, corresponding to G0/G1, that gathers most trajectories in the state transition graph; and several alternative, artefactual states.

Adaptation

This model is derived from the Boolean model published by Davidich & Bornholdt [1]. The two Boolean components representing the different levels of activity of Cdc2_Cdc13 have been replaced by a ternary component. In addition, the loops originally placed on Start, SK, PP, and Slp1 nodes have been removed, as they do not represent true auto-regulations, and compensated by the introduction of priorities to account for the maintenance of the start signal and its effect on Rum1 and Ste9.

For proper logical rules, the model has a single stable state, corresponding to the G1 state of Davidich & Bornholdt (with only Ste9, Rum1 and Wee1_Mick1 activated). This means that the other 11 spurious stable states obtained by these authors have been eliminated.

Activation of Start leads to SK inactivation and then to inhibition of Ste9 and Rum 1, launching a to a sequence of state transitions matching that defined by Davidich & Bornholdt [1], as well as available kinetic data (see Model Documentation for proper setting of the logical simulation).

References

This model is a direct transcription of the Boolean model published by Orlando et al. [1]. Synchronous simulation of this model yields a cyclic attractor gathering most trajectories in the state transition graph, which is robust to parameter choice, as reported in [1]. However, asynchronous simulations all lead to a stable state with all variables OFF, whatever the parameter set proposed by the authors, indicating that the oscillations observed in the synchronous simulations may not be sustained. See [2] for more details.

References

This logical model (cf. figure below and [1]) focuses on the network controlling mitotic exit in budding yeast. It is inspired by the work of Queralt et al. (2006) [2], which emphasises the role of PP2A down-regulation by separase in the triggering of Cdc14 activation during anaphase. These authors developed a quantitative model for mitotic exit, integrating evidence on the roles of FEAR (Cdc Fourteen Early Anaphase Release) components Cdc5Polo, PP2ACdc55 and Esp1.

This model was then used to update our model for budding yeast core cycling engine, that relied on an hypothetical inhibitor of Cdc14, called PPX, activated by Pds1, in place of the FEAR reaction. Our logical model qualitatively accounts for available data on the wild-type cell cycle, as well as for nine different cycle perturbations described in Queralt et al, in terms of Cdc14 activation.

See also:

• Core engine
• Morphogenetic checkpoint
• Coupled model combining the budding yeast core cycling engine with the morphogenetic checkpoint and a detailed exit module.

References