Simulation-based validation of the p53 transcriptional activity with hybrid functional Petri net

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Abstract

MDM2 and p19ARF are essential proteins in cancer pathways forming a complex with protein p53 to control the transcriptional activity of protein p53. It is confirmed that protein p53 loses its transcriptional activity by forming the functional dimer with protein MDM2. However, it is still unclear that protein p53 keeps its transcriptional activity when it forms the trimer with proteins MDM2 and p19ARF. We have observed mutual behaviors among genes p53, MDM2, p19ARF and their products on a computational model with hybrid functional Petri net (HFPN) which is constructed based on information described in the literature. The simulation results suggested that protein p53 should have the transcriptional activity in the forms of the trimer of proteins p53, MDM2, and p19ARF. This paper also discusses the advantages of HFPN based modeling method in terms of pathway description for simulations.

Keywords: hybrid functional Petri net, p53, biological pathway, simulation

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Introduction

Molecular interactions are usually summarized in a picture composed of figures of various shapes (e. g. circles and rectangles) and several types of arrows. Graphical images in the picture are important since they reflect the knowledge in biology and medicine. Biological pathway databases such as KEGG [Kanehisa and Goto, 2000] and TRANSPATH [Krull et al., 2003], (http://www.biobase.de/) have compiled many biological molecular interactions, providing invaluable information to researchers in the forms of pictures. However, with such databases, it is not easy to grasp the information about quantitative interactions of molecules, since such databases focus on providing qualitative information of molecular interactions.

On the other hand, the computer simulation has received attentions of researchers in biology and medicine as a useful method to understand biological mechanisms in molecular level of their interests. It is natural to have an idea to use computer simulations for obtaining quantitative information of molecular interactions. However, it is impossible to conduct simulations with only molecular interaction maps stored in these pathway databases because of the lack of information for constructing simulatable computational models.

We have conducted some simulations of biological phenomena including apoptosis signaling pathway [Matsuno et al., 2003b], cell cycles [Fujita et al., 2004; Matsui et al., 2004], and circadian rhythms [Matsuno et al., 2003b], etc. [Matsuno et al., 2000; Doi et al., 2003; Matsuno et al., 2003a; Doi et al., 2004]. Hybrid functional Petri net (HFPN) [Matsuno et al., 2003b] is adopted to construct these computational models for the simulations. These HFPN models are constructed, being based on pictures in the biological literature. Thereafter, parameters of reactions such as the transcription speeds of genes and degradation rates of proteins shall be tuned so that input/output concentration behaviors of substances such as mRNAs and proteins are matched with biological facts which have been obtained from experiments and/or written information in the literature. With this method, we can include information for simulating molecular reactions in the HFPN model while keeping graphical images of the original biological picture.

Proteins p53, MDM2, and p19ARF are proteins closely related to cancer. The protein p53 is a protein which suppresses the formation of tumors, and the protein MDM2 promotes the formation of tumors by decreasing the activity of the protein p53. Understanding of control mechanism of these proteins connects to development of an effective medicine for suppressing the tumor.

In this paper, we present a new HFPN model of a cancer pathway including a tumor suppressor gene p53. As the genes related to p53, genes MDM2 and p19ARF have been identified [Zhang and Xiong, 2001; Iwakuma and Lozano, 2003]. MDM2 works as an inhibitor for p53, and MDM2 is further inhibited by p19ARF. These interactions of these three genes have been described in the existing biological pathway databases including KEGG [Kanehisa and Goto, 2000] and TRANSPATH [Krull et al., 2003] (http://www.biobase.de/). This paper presents an HFPN model of the interaction of p53, MDM2, and p19ARF, and gives simulation results on the HFPN model using Cell Illustrator [Nagasaki et al., 2003], (http://genomicobject.net/~gon/p53/, http://www.fqspl.com.pl/?a=product_view&id=20&lang=en). We also indicate that the facts and data in the biological literature can be interpreted into the HFPN model to construct this dynamic pathway model, while the conventional pathway databases screen out some helpful information for system dynamics.

It is known that protein p53 works as a transcription factor for many genes [el-Deiry, 1998] and its transcriptional activity is controlled by a complex formed with proteins MDM2 and p19ARF [Zhang and Xiong, 2001; Iwakuma and Lozano, 2003]. However, it is still unclear whether protein p53 keeps its transcriptional activity in the form of the trimer with proteins p53, MDM2 and p19ARF. With our HFPN model, we have simulated mutual behaviors between genes p53, MDM2, p19ARF, and their products. The simulation results suggested that protein p53 should have transcriptional activity in the forms of the trimer of proteins p53, MDM2, and p19ARF.

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HFPN model of protein interactions of p53, MDM2, and p19ARF

Hybrid functional Petri net

A Petri net is a network consisting of places, transitions, arcs, and tokens. A place (depicted as a circle) can hold tokens as its content. At a transition (depicted as a filled rectangle), arcs coming from places and those going out from the transition to some places can be connected. A transition with these arcs defines a firing rule with regard to the contents of the places to which the arcs are attached.

HFPN was defined by Matsuno et al. [Matsuno et al., 2003b] as an extension of a hybrid Petri net. [Alla and David, 1998] HFPN has two kinds of places, namely, discrete and continuous (depicted as a double circle) and two kinds of transitions, discrete and continuous (depicted as an unfilled rectangle). The concepts of discrete place and discrete transition are the same as those in the traditional discrete Petri net ^{Footnote 1}. A continuous place can hold a real number as its content. A continuous transition fires continuously at the speed of the parameter assigned to the continuous transition. The traditional symbols of these places and transitions are shown in Fig. 1.

Three types of arcs are used in HFPN. A specific value is assigned to each arc as a weight. When a normal arc (a solid arc in Fig. 1) with weight w is attached to a discrete/continuous transition, a certain number of tokens are transferred through the normal arc only if the content of the place at the source of the normal arc exceeds the weight w. The firing rule of a test arc is the same as that of a normal arc in terms of the weight, but the content of the place at the source of the test arc is not consumed by firing. A test arc (a dashed line arc in Fig. 1) can be used to represent enzyme activity since the enzyme itself is not consumed. An inhibitory arc (a line terminated with the small bar in Fig. 1) with weight w enables the transition to fire only if the content of the place at the source of the arc is less than or equal to w. For example, an inhibitory arc can be used to represent repressive activity in gene regulation (inhibitory arcs are not used in this paper).

HFPN model construction based on the literature

Fig. 2 shows an HFPN model which has been constructed by compiling and interpreting the information of p53-MDM2 interactions in the literature [Barak et al., 1993; Miyashita and Reed, 1995; Honda et al., 1997; Kamijo et al., 1998; Pomerantz et al., 1998; Zhang et al., 1998; Tao and Levine, 1999; Zhang and Xiong, 1999]. We changed the symbols of "place" and "transition" to biological images. Although these changes have no effect on mathematical meaning, it is helpful for biologists to understand the pathway. Each substance such as protein or mRNA corresponds to an HFPN element "place" (originally a double circle, but it is changed to a picture reflecting the biological meaning of the place: see Fig. 1 ), which holds the concentration of the substance. In Fig. 2 , each place is labeled with the name of the substance (e. g. p53 mRNA, p19ARF). The name of a complex of two proteins A and B is represented as A_B, where places for proteins A and B are labeled with A and B. An additional name (C) or (N) is attached at the tail of a substance name, when we need to distinguish locations of the substances in the cytoplasm or in the nucleus.

Twenty-one biological events related to p53-MDM2 interactions are summarized in the second column of Table 1, which have been extracted from the literature [Barak et al., 1993; Miyashita and Reed, 1995; Honda et al., 1997; Kamijo et al., 1998; Pomerantz et al., 1998; Zhang et al., 1998; Tao and Levine, 1999; Zhang and Xiong, 1999]. Each of these events is represented by an HFPN element "transition" (originally an unfilled rectangle, but it is changed to a picture reflecting the biological meaning of the transition: see Fig. 1), where the reaction speed of the event is assigned. Twenty biological events are assigned to the transitions T_i (i = 1,...,20) as shown in the third column of Table 1. Types of biological processes are described in the fourth column of Table 1 with the literature in the fifth column. Table 2 summarizes variable and initial value of the place in the Fig. 2. Note that the transitions d_j (j = 1, ..., 15) represent natural degradation of the corresponding substances. We define the speed of natural degradation as mX*0.01(mX indicates the concentration of a corresponding substance).

By means of these transitions and notations for molecules, the molecular interactions in the pathway can be described as follows: Protein p53 in the nucleus (p53(N)) forms complex with MDM2(N) (T₁), migrating to the outside of the nucleus (T₇) (p53_MDM2(C)). Then with ubiquitin, p53_MDM2(C) produces p53[Ub] (T₈) which will be decomposed by proteasome (T₉). Hence, the complex formation of p53_MDM2(N) decreases the concentration of protein p53 in the nucleus (p53(N)). In contrast, p19ARF(N) forms trimer p53_MDM2_p19ARF with proteins p53(N) and MDM2(N), thereby preventing p53(N) from decreasing. There are two pathways to form the trimer p53_MDM2_p19ARF: One is the case that p19ARF(N) is bound to complex p53_MDM2(N) (T₃) after forming the complex of p53(N) and MDM2(N) (T₁), and the other is the case that p53(N) is bound to complex MDM2_p19ARF (T₄) after forming the complex of MDM2(N) and p19ARF(N) (T₂). Consequently, p19ARF(N) prevents p53(N) from decreasing because p53_MDM2_p19ARF can not be transferred to the cytoplasm, not being marked with ubiquitin. After degradation of protein p53 of the heterodimer p53_MDM2(C) by proteasome (T₈ and T₉), the remaining MDM2(C) migrates (T₁₀) to the inside of the nucleus (MDM2(N)).

Gene p53 is transcribed (T₅) and translated (T₆) to produce protein p53(C), then it is migrated (T₁₁) to the inside of the nucleus (p53(N)). The fact that p53(N) can contribute to the transcription of gene MDM2 is expressed in this HFPN model by describing a test arc from place p53(N) to transition T₁₈. Transitions T₁₂ and T₁₄ are used for expressions of MDM2 and p19ARF, respectively. Translations of genes MDM2 and p19ARF are represented by transitions T₁₃ and T₁₅, respectively. Transition T₁₆ represents the nuclear import of protein p19ARF.

Activation of gene Bax by protein p53(N) is represented by a test arc from place p53(N) to transition T₁₇. Experimentally, the transcriptional activity of protein p53 is detected by the concentration of Bax mRNA, and this is a reason why gene Bax appears in Fig. 2.

Our HFPN pathway model involves knowledge about protein subcellular localization, process of forming protein complexes, and functional molecular interaction. Starting from a qualitative pathway model, we manually tuned the parameters for the transitions and initial conditions on places in the HFPN model so that the model is consistent with the data in [Pomerantz et al., 1998]. Thus it also involves knowledge about system dynamics. The HFPN model in Fig. 2 is available from http://genomicobject.net/, http://genomicobject.net/~gon/p53/ including all parameters in the model and can be simulated on Cell Illustrator 2.0 (http://www.fqspl.com.pl/?a=product_view&id=20&lang=en).

Transcriptional activity of p53-MDM2-p19ARF complex on MDM2 and Bax

For the transcriptional activity of the complex p53-MDM2-p19ARF, two cases opposite to each other can be considered: the p53-MDM2-p19 complex can activate MDM2 and Bax or can not activate them.

It is confirmed that the complex of proteins p53 and MDM2 has no transcriptional activity on MDM2 and Bax [Oliner et al., 1993; Honda et al., 1997], while protein p53 itself has transcriptional activity on them [Barak et al., 1993; Miyashita and Reed, 1995]. This change on the p53 transcriptional activity results from the binding of protein MDM2 to the site of protein p53 which is also the transactivation domain for downstream genes. From this fact, it is natural to consider that protein p53 loses its transcriptional activity by forming the complex with protein MDM2. However, we find the following observations in the literature which are contradictory to the above fact:

1. Protein p53 accumulates in the nucleus when both proteins p19ARF and MDM2 exist in the cell [Pomerantz et al., 1998; Zhang and Xiong, 1999; Zhang and Xiong, 2001].
   
2. When plenty of protein p53 exist in the nucleus, an increase of p53 transcriptional activity can be observed [Pomerantz et al., 1998].

On the assumption that p53 itself and the complex p53-MDM2 do not accumulate enough to have transcriptional activity through translocation of the p53-MDM2 complex from the nucleus to the cytoplasm, we may consider that in A)-B), protein p53 forms the complex p53-MDM2-p19ARF with proteins MDM2 and p19ARF. This may mean that the complex p53-MDM2-p19ARF has transcriptional activity on genes MDM2 and Bax.

The next section shows simulations on the HFPN model of Fig. 2. The simulation results suggested that the complex p53-MDM2-p19ARF should have the transcriptional activity on genes MDM2 and Bax.

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Simulation and results

Fig. 3 shows the results of simulations, where concentration behaviors of p53(N), MDM2(N), p19ARF(N), p53_MDM2_p19ARF, and Bax mRNA are observed in the following combinations of three genes expressions; p53, MDM2, and p19ARF. We introduced gene Bax in the HFPN model in order to detect the expression level of gene p53. We suppose that a cell is rich in an amount of ubiquitin (the initial value of the place for ubiquitin is set to be 100). We considered the following cases:

1. All genes p53, MDM2, and p19ARF are not expressed (transitions T₅, T₁₂, and T₁₄ are deleted).
2. Only gene p53 is expressed (transitions T₁₂ and T₁₄ are deleted).
3. Genes p53 and MDM2 are expressed (transition T₁₄ is deleted).
4. The complex p53-MDM2-p19ARF can not activate genes MDM2 and Bax, while all of genes p53, MDM2, and p19ARF are expressed (transitions T₁₉ and T₂₀ are deleted).
5. The complex p53-MDM2-p19ARF can activate genes MDM2 and Bax, while all of genes p53, MDM2, and p19ARF are expressed.

When none of three genes p53, MDM2, and p19ARF is expressed, the concentrations of p53(N), MDM2(N), p19ARF(N), p53_MDM2_p19ARF, and Bax mRNA do not grow (Fig. 3 (1)). When gene p53 is expressed, protein p53 in the nucleus (p53(N)) shows a temporal high concentration, and thereafter keeps its concentration at a lower level (Fig. 3(2)). Low accumulation of MDM2(N) in the nucleus and low expression of Bax mRNA are also observed.

Fig. 3(3) shows that MDM2(N) accumulates more in the nucleus compared to that of Fig. 3(2) when genes MDM2 and p53 are expressed. In contrast, the concentration of protein p53(N) becomes lower compared to its concentration in Fig. 3(2).

On the assumption that gene MDM2 is not knocked out in our model, protein MDM2 is accumulated (Fig. 3(2)) in the nucleus due to the activation of MDM2 by p53 in the nucleus (T₁₈). As shown in Fig. 3(2), although protein p53 concentrates in the nucleus, it rapidly decreases after reaching the peak. This decrease is caused by protein MDM2 that ubiquitinates protein p53 exported to the cytoplasm from the nucleus. This low concentration of protein p53 causes the low level expression of gene Bax. In Fig. 3(3), we can observe that protein p53 keeps at lower concentration level in the nucleus than Fig. 3(2). This reduction of protein p53 results from the expression of gene MDM2.

Fig. 3(4) and Fig. 3(5) show the case when all of genes p53, MDM2, and p19ARF are expressed under two different assumptions on the transcriptional activity of the complex p53-MDM2-p19ARF.

• High accumulation of the complex p53_MDM2_p19ARF is observed under the assumption that the complex p53-MDM2-p19ARF has no transcriptional activity for genes MDM2 and Bax (Fig. 3(4)). Besides, both of the accumulation of protein p53(N) and the expression of Bax mRNA keep in low level.
• In contrast, when we assume the transcriptional activity of the complex p53-MDM2-p19ARF for MDM2 and Bax genes (Fig. 3(5)), lower accumulation of p53_MDM2_p19ARF is observed. In addition, both of the accumulation of MDM2(N) and the expression of Bax mRNA grow rapidly and keep in higher level in comparison with the case of Fig. 3(4).

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Other descriptions on p53, MDM2 and p19ARF interactions

Fig. 4 is the part of molecular interactions in KEGG [Kanehisa and Goto, 2000], (http://www.genome.jp/kegg/pathway/hsa/hsa04110.html) which shows the relationship between p53 and MDM2 ^{Footnote 2}. In general, biological interactions to repress gene products are not restricted to one kind of effect: a protein A represses the expression of a gene B, and a protein A represses the activities of a protein B and so on. Fig. 4 does not give any specific information for the repression of p53 by MDM2.

Fig. 5 is the part of the pathway about p53 in TRANSPATH [Krull et al., 2003], (http://www.biobase.de/). Although this map describes the information on the complex formation of MDM2 and ARF, ubiquitination of p53 by the complex of MDM2 and ARF is not involved in this map while the effect of tetramer formation of protein p53 is involved ^{Footnote 3}.

Fig. 6 shows the relationships among proteins p53, MDM2, and p19ARF in the description proposed by Kohn [Kohn, 1999], (http://discover.nci.nih.gov/mim/index.jsp). The arc terminated with the short bar in this map represents repression of p53 degradation by the complex MDM2-p19ARF. The same function as this repression of p53 degradation is involved in the HFPN model of Fig. 2, while this function of repression is not modeled using such symbol of arc for repression. That is, the HFPN model of Fig. 2 realizes this repression by transition T₄ in Fig. 2, to which two arcs from places p53(N) and MDM2_p19ARF connect, and from which an arc to place p53_MDM2_p19ARF connects. It is easily seen that this complex formation of p53-MDM2-p19ARF prevents the protein p53 from degrading if we notice the fact that p53 is degraded through the complex formation with protein MDM2. Hence, the HFPN of Fig. 2 involves more exact description than Fig. 6 about the interactions of proteins p53, MDM2, and p19ARF.

Note that the information interpreted into the HFPN model in Fig. 2 has been extracted by human experts from the literature and it involves various biological facts as mentioned in section of HFPN model. However, such information is not fully included in these molecular interaction maps.

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Discussion and conclusion

Through simulation, we discussed whether the complex p53-MDM2-p19ARF has transcriptional activity for genes Bax and MDM2 or not.

Pomerantz et al. [Pomerantz et al., 1998] provided the result that protein p53 accumulates in a HeLa cell after injecting gene p19ARF in the cell. In addition, they reported that protein p19ARF injection increases protein p53 and the amount of products which are activated by protein p53. Fig. 3(4) shows an observation corresponding to that by Pomerantz et al. [Pomerantz et al., 1998]. In this figure, the complex p53-MDM2-p19ARF concentration keeps high level due to the complex formation between p53, MDM2 and p19ARF, which allows protein p53 to escape from its ubiquitination by protein MDM2. The increase of protein p53 (the part of p53-MDM2-p19ARF complex) coincides with the experimental observation reported in [Pomerantz et al., 1998]. However, for gene Bax, which is activated by protein p53, the simulation result shows low expression while the gene expression of Bax is high in [Miyashita and Reed, 1995]. Recall that we have assumed that the complex p53-MDM2-p19ARF has no transcriptional activity for genes Bax and MDM2. This means that, in the HFPN simulation model, only protein p53 in the nucleus (p53(N)) can activate Bax and MDM2. On the other hand, the simulation result of Fig. 3(5) shows high expression of gene Bax as well as a certain amount of concentration of protein p53, being consistent with the experimental observation in the literature [Pomerantz et al., 1998]. Note that the increase of p53-MDM2-p19ARF complex promotes not only the expression of gene Bax but also the production of protein MDM2 in the nucleus. The increased MDM2 accelerates the decomposition of p53 exported to the cytoplasm from the nucleus. Thereby a lower concentration of Fig. 3(5) than that of Fig. 3(4) is induced. The simulation results suggested that protein p53 should have the transcriptional activity in the forms of the trimer of proteins p53, MDM2, and p19ARF.

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Further remarks

Most existing pathway databases present many biological maps of molecular interactions. However, in order to conduct simulations based on these maps, more biological facts such as reaction speeds of complex formation and protein degradations have to be included to these maps. This means that we have to reconstruct computational pathway maps for simulations after careful reading of papers of the interest. In other words, these pathway databases have not been constructed on the assumption that pathways included in them will be used for simulations.

The HFPN model of the complex p53-MDM2-p19ARF has been constructed based on biological knowledge being extracted by careful reading of the literature. Of course, with no proof by biological experiments, we could not conclude that the complex p53-MDM2-p19ARF has transcriptional activity for genes Bax and MDM2. However, without the help of simulations, it is hard to get insights into the systematic behavior of the genes and proteins forming the complex p53-MDM2-p19ARF, as demonstrated in this paper. Simulations can reduce the number of biological experiments and save the costs from both sides of expense and time.

As demonstrated in this paper, the description of biological pathways with HFPN allows the biological pathways to be simulated directly, since HFPN includes dynamic elements (transitions) at which reaction speeds are assigned as well as static elements (places) which represent the states of substances such as concentration. We have developed the automatic conversion systems of biological pathways in KEGG and TRANSPATH into HFPN models [Nagasaki et al., 2004]. By incorporating dynamic parameters such as reaction speeds of translation and complex formation from the knowledge of biologists and/or information in the literature into the converted HFPN models, the HFPN models become simulatable on Cell Illustrator (http://www.fqspl.com.pl/?a=product_view&id=20&lang=en).

We have recently developed a new biological pathway description format in XML called Cell System Markup Language (CSML) (http://www.csml.org/). By using the CSML and this conversion system, we are now working on the construction of a simulatable pathway database.

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Acknowledgements

This work is partially supported by the Grand-in-Aid for Scientific Research on Priority Areas 17014067 and 17017007 from the Ministry of Education, Culture, Sports, Science and Technology in Japan.