Scenarii of division and apoptosis in a virtual cell: a compositional approach

Laurence Calzone, François Fages
Cours C-2-19 Bio-informatique formelle
MPRI 2004-2005



These pages describe a modeling/programming project for the students of the Formal Bio-informatics course of the MPRI.

Each student is invited to choose one of the five projects presented below and work in a team of two or three people per project.

Note that the fourth project consists mainly in assembling the models developed in project 1, 2 and 3, checking the behaviour of the composite model with scenarios of signal_induced cell division or apoptosis, and possibly asking modifications of these models to the other teams. Project 4 thus requires good coordination skills. Project 5 should be developed independently of the other projects but the results should be discussed in comparison with the results of project 4.

The deliverable of each project should be composed of a Biocham model with execution traces and a report (in French or English) describing the choices made in the model, its capabilities and limits, and a general discussion for possible improvements of the overall approach.


November 22th: indicate your project choice by e-mail to Laurence Calzone.

December 22nd: each team sends a brief summary of its achievements to Laurence Calzone.

January 17th: end of the project and delivery of the results.


Biochemical reactions in Biocham

See the documentation at

Shortcuts to some useful infos on how to write biochemical reactions in Biocham:

Let A be a protein made at a rate ks, with the help of a transcription factor TF, and degraded at a rate kd.
Let A~{p1} be the phosphorylated and active form of the protein A.
Let B be the kinase (here, the catalyst of the reaction) that phosphorylates A, and PPA, the phosphatase that dephosphorylates A~{p1}.
A and B associate to form a complex A-B. The formation of the complex can be reversible and A-B can break apart or A-B can also release two molecules: A~{p1} and B. The association of A and B occurs at a rate a (for association) and the dissociation at a rate d (for dissociation). A is phosphorylated at a rate k.

The same kinetics can be observed for the reverse reaction involving A~{p1} and the phosphatase PPA.

Since A is a reserved keyword for the CTL path quantifier in Biocham, we write mA for molecule A, and the reactions are written as follows:

% synthesis:
ks*[TF] for _=[TF]=>mA.

% degradation:
kd*[mA] for mA=>_.

% phosphorylation by B:
(a*[mA]*[B], d*[mA-B]) for mA+B <=> mA-B.
k*[mA-B] for mA-B => mA~{p1} + B.

% dephosphorylation by PPA:
(a'*[mA~{p1}]*[PPA], d'*[mA~{p1}-PPA]) for mA~{p1}+PPA <=> mA~{p1}-PPA.
k'*[mA~{p1}-PPA] for mA~{p1}-PPA => mA + PPA.

where ks, kd, a, d, k, a', d', and k' are parameters. Parameters are defined as follows:


The variables mA, B, TF, mA-B, mA~{p1} and PPA have set initial values. In some cases, such as PPA, for example, some species are defined as variables even though their activity does not change. PPA is still defined like the other variables:




By definition (online Webster dictionary), signaling can be any kind of communication that encodes a message. In cell biology, it can be interpreted as the conversion of any kind of signal into another, and mediated by enzymes.

Events such as cell growth, cell motility, cell adhesion, cell differentiation or cell proliferation are regulated by diverse signal transduction pathways. Disfunctioning in signal transduction pathways is the cause of many diseases such as cancer, inflammatory diseases ...

We consider here only the case of extracellular signaling. Molecules (such as hormones) or ligands bind to transmembrane receptors and trigger biological responses (through activation of intermediate molecules) inside the cell. The signal can be either activating or inhibitory.

MAP kinase pathways mainly control cell proliferation, differentiation and embryogenesis. They are composed of three kinases that are activated in series by dual phosphorylation. Through this cascade, the message is amplified and the response is switchlike (e.g. it activates abruptly but ignores the small stimuli).

Introductory concepts of cell cycle

During a cell cycle, a cell grows and divides into two daughter cells containing the same genetic information. Before each division, all the components of the cell need to be duplicated. The cell cycle is divided in four phases.

Phases of the cell cycle

DNA replication
DNA replication must occur only once per cycle. To ensure that DNA does not re-replicate before mitosis, there exits a network of proteins that controls DNA synthesis. In late mitosis and early G1 phase, some proteins prepare for DNA synthesis. ORC (origin recognition complexes) and MCM (Mini-chromosome maintenance) associate into a pre-RC complex. In early S phase, a family of proteins, the Cdk/cyclins, phosphorylates the complex which allows the opening of a replication fork. Once DNA synthesis has occurred, the same proteins, that promoted DNA replication, inhibit the reformation of the pre-RC complexes. When these proteins degrade at the end of mitosis, the pre-RC complexes can reform.

Cell division is an event for which many mistakes are fatal. In order to avoid catastrophic failure, the cell verifies that proper conditions are satisfied at crucial steps in the division process. As it progresses through the division cycle, the cell halts at some checkpoints and verifies that it can continue. The checkpoints can be: size, undamaged DNA, completion of DNA synthesis, alignment of the chromosomes on the metaphase plate...

Regulation of cell cycle by cyclin dependent kinase
The proper alternation between the two phases S (DNA synthesis) and M (Mitosis) is coordinated by a complicated network that regulates the activity of a family of key proteins. These proteins are composed of two subunits: a catalytic subunit, the cyclin-dependent kinase, Cdk, and a regulatory subunit, a cyclin. Cdk has to associate with a cyclin partner to form a dimer and has to be appropriately phosphorylated in order to be active.
The Cdk/cyclin dimers have a central role in the cell cycle.
On top of ensuring S/M alternation, the dimers also control cell size, and DNA replication. The progression through cell cycle is orchestrated by the rise and fall of the Cdk/cyclin dimers. There are different ways to regulate the activity of the dimers: through synthesis of the cyclins by transcription factors, through degradation of the cyclins, through association with stoichiometric inhibitors, and through phosphorylation and dephosphorylation of Cdk.


"apoptosis"= programmed cell death; from the Greek "falling off or dropping off".

Apoptosis is an irreversible process triggering cell death in response to DNA damage, viral infection, starvation, growth factor deprivation, heat shock, hypoxia, etc... It is a destruction of cellular organelles by proteases (caspases). The destruction occurs by the fragmentation of DNA and the nucleus, chromatin condensation, the formation of apoptotic elements, the disruption of the membrane and the reduction of the cellular volume. Pieces of the dead cell are then surrounded by a membrane and "eaten" by the macrophages.


Project 1: The MAP kinase pathway  

Project 2: The entry into the cell cycle /G1-S transition

Project 3: The p53 pathway

Project 4: Putting the pieces together

Project 5: Qualitative analysis of networks regulating cell cycle and apoptosis