Boolean modeling of mammalian cell cycle and cancer pathways

The cell division cycle is controlled by a complex molecular network: a recent model of the cell cycle and cancer pathways includes close to a hundred genes [Fumiã and Martins, 2013]. To cope with such complexity, different approaches have been used by modelers. Recently, Deritei et al [2016] have emphasized modularity as a key organizational principle. Their model however, includes only 21 components. This raises the question how the approach would fare on larger models such as the one published by Fumiã and Martins.To explore that question we first convert these two models to a common modeling framework [Naldi et al., 2009]. Preliminary results show that there is only limited overlap between the two models, with shared variables being controlled by different regulators. This suggests that at this stage module definition may still depend on the modeler and thus may not yet reflect actual biological organization.


Introduction
When the same system is modeled by different authors, to the extent that the system is well understood and the modeling approaches are consistent, we should expect converging results.The mammalian cell cycle, due to its fundamental and practical importance in various areas of biology and medicine, is a heavily studied biological system.Yet a single look at two recent logical models [ [1] Deriteiet al., [2] Fumiã et al.] reveals important differences in terms of complexity.Our aim is to evaluate the origin, extent and significance of these differences.
In this paper, we first convert the two models to a common modeling framework [ [3] GINsim] and check that the transposed models are equivalent to the original models.This preliminary study reveals discrepancies within one of the models, as described in the original paper in terms of logical equations, or in terms of regulatory graph and simulation results [1].Then we compare the converted models focusing on the common elements.We hoped that the common elements have common logical expression; however, this is not what we found.This suggests that module definition may still depend on the modeler and thus may not yet reflect actual biological organization.

Cell cycle
The mammalian cell cycle functions as an excellent case study for coordination between closely connected bistable circuits.It consists in a series of events that take place within the cell, leading to division and duplication of DNA to produce two daughter cells [4].The cell cycle consists of the following two phases, named inter-phase and M phase (Mitotic phase).Inter-phase consists of the following three phase, named G1 phase (Gap 1 phase), S phase (Synthesis phase), and G2 phase (Gap 2 phase).In G1 phase, the cell gets big for replication and the enzyme required in the next S phase is synthesized.This phase is called preparation phase by researchers.
At the end of G1 phase there is a cell cycle checkpoint.This is a series of safety mechanisms to confirm that the DNA is defect free and that the function of the cell is normal.The G1 checkpoint is known as the restriction point, and requires the presence of growth factors.Cells that proceed through this checkpoint are committed to entering the S phase, during which chromosomal DNA is replicated.When DNA synthesis is completed and all chromosomes have been replicated, S phase is terminated.During the S phase, the amount of intracellular DNA doubles.The period from the completion of DNA replication to P -507 the entry into M phase is called the G2 period.In the G2 phase, active protein synthesis is again performed, and microtubules necessary for mitosis are mainly produced.In the M phase, mitosis and cytokinesis are performed.It is a relatively short period of the cell cycle.
In addition to these four phases, there is a G0 phase which leaves the cell cycle and stops dividing.The cell cycle starts with this phase.Fig. 1. shows the cell cycle.

Method
GINsim (Gene Interaction Network simulation) is a computer tool based on a logical formalism for simulation and analysis of regulatory networks [3].In GINsim, regulatory networks are modeled as logical regulatory graphs (LRG), and state transition graphs represent dynamical behaviors.Nodes in a logical regulatory graph represent the components system such as protein and mRNA, etc. Arrows connect the nodes, and represent the relationship and effect between the nodes.To complete the logical regulatory graph, we have to be expressed the relationship between each node using the logical expression.Operator AND, OR and NOT in logical expression are represented by &, | and !respectively.Dynamic movement is represented by a State Transition Graph (STG).In this type of graph, node represents the state to give a value of the logical variable for each component.Variables are arranged in the order defined at the modeling stage.The values of 0 represent inactive and 1 represent active state of each components.We have two types of simulation: asynchronous and synchronous.In asynchronous graph, each value is updated individually.Conversely, in synchronous graph, all values will be updated at the same time.The authors the paper that we use are used synchronous simulation.So in this paper, we use also synchronous simulation to confirm their results.

The mammalian cell cycle model
First, we convert the three models proposed by Deritei et al., namely the restriction switch, the phase switch and the full cell cycle model, [3] into GINsim's fromalism.

The restriction switch
This restriction switch works between G1 phase and S phase in the cell cycle.The restriction point is the point of the G1 phase of the animal cell cycle where the cells are involved in the cell cycle and then extracellular proliferation stimulants are no longer required.This switch model consists of 6 nodes.

The phase switch
The phase switch is the network responsible for toggling the cell from G2 into mitosis, then past the spindle assembly checkpoint into cytokinesis.This switch consists of 11 nodes.

Fig.4.2. The Phase Switch
When we run simulation, this switch has three stable states.This result is also the same result as them.In the phase switch, multi stability is also essential.

The full cell cycle model
The cell cycle model is a combination of the restriction switch and the phase switch.These cell cycle switches mutually toggle to generate cyclic dynamics.These two switches within the cell are tightly bound to form a control network of the mammalian cell cycle.This model is formed by four nodes plus two switches.These nodes represent regulatory sub-networks rather than molecular species.The restriction switch has two stable states, and the phase switch has four stable states.These restriction switch and phase switch drive the mammalian cell cycle.So these switches are important for cell cycle.In order to drive the cell cycle of mammals, because the multi-stablility is essential, we can confirm that it meets the conditions.

Boolean network model for cancer pathways
The cancer network proposed, although highly simplified by Fumiã et al [2].But this model has 96 nodes.So we think this model is complicated and difficult.These equations are update rules of the model. (1) It includes proteins related to oncogenes, tumor suppressor genes and stability genes, which are the three major classes of mutation targets involved in tumorigenesis.These nodes represent a significant subset of the proteins involved in the cancer and the network edge represents a number of parallel pathways in which the transformed cells maintain an aberrant gene expression pattern and survive and develop further malignancies.The network has input nodes for applying to cells, different environmental stimuli and stresses such as hypoxia, carcinogens, nutrient depletion, proliferation and growth suppression signaling.Here, threshold function is given by these equation.
This kind of expression can also be represented as logical rules in the formalism used by GINsim.Here, when σ=1 the protein is functionally active.On the contrary, when σ=0 the protein is inactive.We calculate the logical expression for each node and input it.As a P -509 Next we focused on the common parts of these models.As a result, were 12 common elements between the cell cycle model and the cancer pathways.Further, all of the elements were also common in the restriction switch.We found that many of these elements has received a lot of influence from the common node.For example, all elements affected by UbcH10 are in common.But this result is not expected.We hoped that all nodes of cell cycle model would be in common with cancer pathways.From this result, we have to examine the logical expression.But the logical expression was not the same.Because it contains elements that are not in common.All affected elements are the same UbcH10 also the logical expression is different.This suggests that at this stage module definition may still depend on the modeler and thus may not yet reflect actual biological organization.

Conclusion
The primary purpose of this study was to create a boolean model based on a recent paper on cell cycle and cancer pathway.
In chapter 3, we describe to convert the models to a common modeling framework .We used GINsim as a common framework.We converted it into a common framework using logical regulatory graph.After that, we use state transition graphs for checking operation etc.
Further, GINsim has circuit analyze and expression of stable state that is useful for analysis of biological systems.
In chapter 4, we describe the cell cycle model.Deritei et al [1] have emphasized modularity as a key organizational principle.This cell cycle model is a combination of the restriction switch and the phase switch.Here, we explained the timing of working and the number of nodes in each parts.In the two switches, we confirmed that there are multi stable state.This is a required condition.
In chapter 5, we describe the boolean network model for cancer pathways.First, we show the equations.There are 96 equations.These equations are update rules of the model.We used these equations and thresholds function to decide the logical expressions.
Comparing the cell cycle model and cancer pathways, it appears to differ.However, these models have the same parts.Some elements were common.Further, we found that many of these elements has received a lot of influence from the common elements.From this result, many cell models can be presumed to have common parts.
Finally, future tasks of this study are comparison of behaviors of these models and compare them with other cell cycle models.In this time, we run synchronous simulation only.We have to run asynchronous simulation.

Fig. 4 . 1 .
Fig.4.1.The Restriction SwitchWhen we run simulation, this switch has two stable states, consistent with the original results.This restriction point is a switch-like transition controlled by a bistable molecular control circuit.In the restriction switch, multi stability is essential.

Fig. 4 . 3 .
Fig.4.3.The full cell cycle model5.Boolean network model for cancer pathwaysThe cancer network proposed, although highly simplified by Fumiã et al[2].But this model has 96 nodes.So we think this model is complicated and difficult.These equations are update rules of the model.
Fig.5.1.The cancer pathways 6.Comparison of the models A recent model of the cell cycle and cancer pathways includes close to a hundred genes [2].To cope with such complexity, different approaches have been used by modelers.So we did a comparison of the model of the Cell Cycle model and Boolean Network Model for Cancer Pathways.These models represent the cell cycle.So we examined the same or different parts of these models.First, we have focused on the elements.Looking at these graph, There is a big difference in the number of elements.The cell cycle model has 21 elements and the cancer pathways has 96 elements.In cell cycle model made by Deritei et al [1] have emphasized modularity as a key principle.So there is a big difference.Next we focused on the common parts of these models.As a result, were 12 common elements between the cell cycle model and the cancer pathways.

Table 1 .
Stable state of the restriction switch

Table 2 .
Stable state of the phase switch Name

Table 3 .
Common elements