Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs Double-Negative Feedback Loop by Hybrid Functional Petri Net with Extension

Transcription

1 100 Genome Informatics 17(1): (2006) Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs Double-Negative Feedback Loop by Hybrid Functional Petri Net with Extension Ayumu Saito Masao Nagasaki Atushi Doi Kazuko Ueno Satoru Miyano Human Genome Center, Institute of Medical Science, University of Tokyo, Shirokanedai, Minato-ku, Tokyo , Japan Abstract Biological regulatory networks have been extensively researched. Recently, the microrna regulation has been analyzed and its importance has increasingly emerged. We have applied the Hybrid Functional Petri net with extension (HFPNe) model and succeeded in creating model biological pathways, e.g. metabolic pathways, gene regulatory networks, cell signaling networks, and cell-cell interaction models with one of the HFPNe implementations Cell Illustrator. Thus, we have applied HFPNe to model regulatory networks that involve a new key regulator microrna. As a test case, we selected the cell fate determination model of two gustatory neurons of Caenorhabditis elegans ASE left (ASEL) and ASE right (ASER). These neurons are morphologically bilaterally symmetric but physically asymmetric in function. Johnston et al. have suggested that their cell fate is determined by the double-negative feedback loop involving the lsy-6 and mir-273 micrornas. Our simulation model confirms their hypothesis. In addition, other well-known mutants that are related with the double-negative feedback loop are also well-modeled. The new upstream regulator of lsy-6 (lsy-2) that is mentioned in another paper is also integrated into this model for the mechanism of switching between ASEL and ASER without any contradictions. Therefore, the HFPNe-based modeling will be one of the promising modeling methods and simulation architectures that illustrate microrna regulatory networks. Keywords: microrna, HFPNe, ASE cell, gene regulatory network, dynamic simulation 1 Introduction MicroRNAs (mirnas), which were first discovered by Wightman et al. in Caenorhabditis elegans (C. elegans) in 1993 [21], have recently been found to be important factors in the gene regulatory network. mirna is one of the RNAs that is transcribed from the genome (70mer) in the nucleus, processed by enzymatic cleavage, and finally produced as a small RNA (20 24mer) in the cytoplasm. The mirna is matured by its incorporation into an RNA-Induced Silencing Complex (RISC). Depending on the type of mirna incorporated, the RISC binds to specific mrnas, degrades them, and accordingly inhibits their translation. For example, Wightman et al. reported that the lin-4 mirna suppresses the lin-14 gene in C. elegans [21]. For this functionality, it has been thought that the mirna sequences should perfectly match those of the target mrnas. Recently, it has been found that mirna with some mismatched sequences can still suppress the translation [1]. Thus, mirnas will play an important role in studying the gene regulatory network. These authors equally contributed to this study.

2 Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs DNFL by HFPNe 101 Since 1999, we have been involved in developing a software tool called Cell Illustrator [15, 16, 17, 22, 23] with which biologists can construct pathway models by using tools for creating illustrations by organizing biological knowledge and data. For this software tool, we defined a modeling architecture called Hybrid Functional Petri Net (HFPN) with extension (HFPNe), which is based on the theory of Petri net [24]. Petri net is a kind of graphical programming language invented in the 1960s; it has been extensively studied for modeling concurrent control systems and has been applied to industrial systems. Petri net is highly applicable to biological systems, and it has been successfully used to develop and analyze some pathway models for gene regulatory networks, metabolic pathways, and signaling pathways [4, 5, 12, 13, 14, 20, 22]. In this paper, we concentrate attentions on that the new key factor mirnas can be effectively handled with the HFPNe to other elements architecture, e.g. mirna itself can be, its regulations to other elements can be modeled, and regulations can be modeled. In particular, we chose to model one of the complicated regulations mediated by mirnas: a double-negative feedback loop (DNFL) of the lsy-6 and mir-273 mirnas that will determine the ASE cell fates in C. elegans, i.e., whether the cells will be ASE left (ASEL) or ASE right (ASER). Johnston et al. proposed that the DNFL of these mirnas determines whether the cells will be ASER or ASEL [8]. The mechanism of differentiation of ASE cells based on the DNFL as follows. For the differentiation of these cells in C. elegans, an NKxtype homeobox gene cog-1 and a zinc-finger transcription factor die-1 are the part of key factors [2, 9]. The cog-1 and die-1 genes are gradually expressed and then promote the differentiation into the ASER and ASEL, respectively. For the differentiation, the cog-1 and mir-273 mirnas regulate the mrnas in the following manner. The cog-1 mrna contains an lsy-6 complementary site in the 3 untranslated region [9]. In contrast, the die-1 mrna contains two mir-273 complementary sites in the 3 untranslated region [2]. Thus, the actions of cog-1 and die-1 are inhibited under the abundance of lsy-6 and mir-273, respectively, and differentiation into ASER and ASEL cells cannot occur. In addition, die-1 promotes the expression of lsy-6 and cog-1 promotes the expression of mir-273. Thus, the loop formed by cog-1, mir-273, die-1, andlsy-6 is the DNFL (see Figure 1). However, this model was a qualitative one and quantitative aspects of the mechanism were missing. Thus, we created the quantitative ASER-ASEL model with HFPNe and discuss in this paper whether the model of Johnston et al. is in agreement with the in silico model. ( 5) 4 ( ) lsy-6 1 ( ) Type Cell Illustrator (software) Original symbols of HFPNe Examples of biological images Discrete Continuous Generic Discrete, Continuous, and Generic die-1 cog-1 Entity Process OUT degradation lim-6 3 ( ) mir ( ) Connector Process Association Inhibitation OUT IN Figure 1: Summary of the DNFL. The path involving the steps (1) (4) forms the double-negative feedback loop. The activation of die-1 (4) leads to the activation of lsy-6 (1) and the suppression of cog-1 (2) and mir-273 (3). On the other hand, the activation of cog-1 (2) leads to the activation of mir-273 (3) and the suppression of die-1 (4) and lsy-6 (1). Figure 2: Basically, Petri nets are constructed using three kinds of symbols for entities, processes, and connectors. In Cell Illustrator [15], sets of entities and processes are both classified into discrete, continuous, and generic types; additionally, entities and processes can be replaced with pictures reflecting the biological images. This replacement makes the HFPNe model of a biological pathway more comprehensible for biologists (see [16] for details).

3 102 Saito et al. One of the merits of the in silico model with HFPNe is as follows: once the model is created, it can be easily updated with new information; further, the consistency of the new model with new experimental observations can be checked. In order to confirm whether the scheme is also effectively applicable to our mirna models, the ASER-ASEL model has been updated by including the new factor lsy-2 in another study by Johnston and Hobert [10]. The new ASER-ASEL model confirmed that lsy-2 is the key upstream regulator of the ASE cell fate determination on a quantitative basis. Another merits of the in silico model is that mutant analyses can be easily performed by modifying the original model (Wild-type model). The various mutant strains are known to the ASE cells. Two mutant types are selected, and we discuss how to create the mutant models from the original model. Moreover, these mutant models are simulated, and they confirmed that the new ASER-ASEL model can also be sufficiently applicable to the representation of these mutant defects by using a pathway on a quantitative basis. Section 2 discusses the HFPNe architecture and describes the ASER-ASEL model with HFPNe. In section 3.1, we present the result of the in silico simulation of the ASER-ASEL model and compare it with the in vivo results. In section 3.2, we extends the ASER-ASEL model to a new factor lsy-2 and discuss the importance of the factor with in silico analysis. In sections 3.3 and 3.4, we create the in silico mutants of ASE cells and compare these results with those observed in vivo. Section 4 is the concluding remarks. 2 HFPNe Model of DNFL with lsy-6 and mir Hybrid Functional Petri Net with Extension Petri net is a network that consists of place, transition, arc, and token. For intuitive notations, in this paper, we use entity, process, and connector, respectively. An entity (denoted by a circle) can hold tokens as its content. A process (denoted by a rectangle) is linked to entities by connectors that originate from or extend to entities. A process linked with these connectors defines a firing rule in terms of the contents of the entities to which the connectors are attached or from which they originate. In a model created using Petri net, an entity represents the amount/density of some biological molecule/object, and a process defines the speed/condition/mechanism of interaction/reaction/transfer among the entities linked by the connectors. The conventional Petri net can be used to model only the discrete features in biological pathways, e.g. logical regulatory relationships between genes. Due to this limitation of the Petri net and more requirements in modeling, we have defined the principle of HFPNe [16]. Modeling can be realized in a systematic manner by assuming that the object corresponds to the Java class if the process to be illustrated is a more detailed biological pathway such as alternative splicing, ribosomal frameshifting, and the regulation of subcellular localization information [16]. We use HFPNe for illustrating an mirna-related DNFL. Three types of connectors are used in HFPNe, and a specific value is assigned to each connector as a threshold script. When a process connector (a solid connector in Figure 2) with a threshold script is attached to a discrete, continuous, or generic process (depicted as a single circle, double circle, or a single circle with a cross, respectively), a certain number of tokens are transferred though the process connector only if the evaluated result of the threshold script is true. The activity rule of an association connector is the same as that of a process connector in terms of the threshold, but the content of the entity at the source of the association connector is not changed by activation. An association connector (a dashed line connector in Figure 2) can be used to represent enzyme activity since the enzyme itself is not consumed. An inhibitory connector (a line terminated with the small bar in Figure 2) with a threshold script enables the process to be active only if the evaluated result of the threshold script is false. For example,

4 Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs DNFL by HFPNe 103 Figure 3: HFPNe model of the ASEL/ASER pathway. For entities and processes, pictures reflecting biological images are used (see Figure 2). Biological meanings of transitions T1,..., T25 are summarized in Table 1; T26 and T27 are summarized in Table 3. an inhibitory connector can be used to represent repressive activity in gene regulation. The formal definition has been provided by Nagasaki et al. [16]. 2.2 HFPNe Model Based on the Literature Figure 3 shows an HFPNe model that has been constructed by compiling and interpreting the information on the cell fate determination model of ASEL and ASER in the literature [2, 3, 6, 7, 8, 10, 19]. We changed the symbols of the entity and process to biological images. Although these changes have mathematically no effect, they are helpful for biologists to understand the pathway. Each substance, such as a protein, an mrna, and mirna, corresponds to an HFPNe element entity (originally a double circle, but it has been changed to a picture reflecting the biological meaning of the entity; see Figure 2); this entity reflects the concentration of the substance. In Figure 3, each entity is labeled with the name of the substance, e.g. die-1, cog-1, and mir-273. In order to indicate the locations of the biomolecules, an additional letter (C) or (N) (in the cytoplasm or in the nucleus, respectively) is added at the end of their names.

5 104 Saito et al. Table 1: Biological facts extracted from the literature [2, 3, 6, 7, 8, 10, 19] and assigned to processes in the HFPNe model in Figure 3. #1: Corresponding processes in the HFPNe. #2: Speed of these processes in the HFPNe. The mx(x = 1,...,20) denotes the concentrations of corresponding substances (see Table 2). For example, the process T2 has a speed denoted by m speed, i.e., the speed depends on the concentration of lsy-6 in the nucleus (m12). Biological facts present in the literature (obtained from experiments) Transcription of the lsy-6 gene, produces lsy-6 pri-mirna, and Drosha processing yields the lsy-6 pre-mirna. The lsy-6 pre-mirna is exported from the nucleus to the cytoplasm by exportin-5 and processed by the dicer (lsy-6 mirna) to form mirna. The cog-1 mrna(c) is translated to cog-1(c) under suppression by the lsy-6 mirna (within RISC). #1 #2 Type of biological process T Transcription / Drosha processing T2 m Nuclear export / Dicer processing T3 m Translation / microrna inhibition Transcription of the cog-1 gene yields the cog-1 mrna. T4 0.1 Transcription The cog-1 mrna(n) is exported from the nucleus to the cytoplasm (cog-1 mrna (C)). Cog-1(C) is imported from the cytoplasm to the nucleus (cog-1(n)). Cog-1(N) activates transcription of the cog-1 gene, producing the cog-1 mrna. Cog-1(N) activates the transcription of the mir-273 gene, producing the mir-273 pri-mirna, and Drosha processing leads to the production of the mir-273 pre-mirna. Transcription of the mir-273 gene yields the mir-273 primirna, and Drosha processing produces the mir-273 premirna. The mir-273 pre-mirna is exported from the nucleus to the cytoplasm by exportin-5 and processed by the dicer (mir-273 mirna) to yield mirna. The die-1 mrna(c) is translated to die-1(c) under suppressed by the mir-273 mirna (within RISC). Transcription of the die-1 gene leads to the production of the die-1 mrna. The die-1 mrna(n) is exported from the nucleus to the cytoplasm (die-1 mrna(c)). Die-1(C)isimportedfromthecytoplasmtothenucleus(die- 1(N)). Die-1(N) activates the transcription of the lsy-6 gene, producing the lsy-6 pri-mirna, and Drosha processing leads to the production of the lsy-6 pre-mirna. The expression of lim-6(c) is activated by die-1(c) and suppressed by cog-1(c). Lim-6(C) is imported from the cytoplasm to the nucleus (lim-6(n)). Lim-6(N) activates the transcription of the lsy-6 gene, producing the lsy-6 pri-mirna, and Drosha processing leads to the production of the lsy-6 pre-mirna. Lim-6(N) activates the transcription of the die-1 gene, producing the die-1 mrna. The expression of gcy-7 is activated by die-1 and suppressed by cog-1. The expression of gcy-6 is activated by die-1 and suppressed by cog-1. T5 m Nuclear export Literature [6], [19] [6], [19] [9] T6 m Nuclear import [8] T7 m Transcription [8] T8 m Transcription / Drosha processing T Transcription / Drosha processing T10 m Nuclear export / Dicer processing [8] T11 m Translation / microrna [2] inhibition T Transcription T13 m3 0.1 Nuclear export T14 m Nuclear import [8] T15 m Transcription / Drosha processing [6], [19] [6], [19] [2] T16 m Expression [8] T17 m2 0.1 Nuclear import [8] T18 m1 0.1 Transcription / Drosha processing [8] T19 m1 0.1 Transcription [8] T20 m Expression [8], [3] T21 m Expression [8], [3] Lim-6 suppresses the expression of the gcy-5 gene. T Expression [3], [7] Lim-6 suppresses the expression of the gcy-22 gene. T Expression [8] Lim-6 activates the expression of the flp-4 gene. T24 m2 0.1 Expression [8] Lim-6 activates the expression of the flp-20 gene. T25 m2 0.1 Expression [8]

6 Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs DNFL by HFPNe 105 Twenty-five biological events related to the ASEL- ASER pathway are summarized in the first column of Table 1; these events have been extracted from the literature [2, 3, 6, 7, 8, 10, 19]. Each of these is represented by an HFPNe element process (originally, an unfilled rectangle, but it has been changed to a picture reflecting the biological meaning of the process; see Figure 2); a process speed has been assigned to the events. Each event is assigned to the processes Ti(i =1,...,25), as shown in the second column of Table 1. The third column indicates the speeds of these processes. An additional 20 biological events are also assigned to the processes (dj(j = 1,...,20) in Figure 3). All of them denote the natural degradation of mrna, mirna, and protein (not listed in Table 1). No kinetic parameters of these processes have been documented and measured in any literature. Thus, we simplified the kinetic parameters to the extent possible. The same speed mx 0.1 (mx indicates the concentration of the corresponding substance) is assigned for (i) translation and transcription with active regulations (association connectors), (ii) nuclear export, and (iii) nuclear import. The transcription speeds of mrna and mirna are the same value 0.1 and0.01, respectively. The types of biological processes are described in the fourth column of Table 1, and the literature referred to is listed in the fifth column. Table 2 summarizes the variable and initial values of entities used in Figure 3. Table 2: Entities in the HFPNe model of Figure 3. Variable (mx(x = 1,...,20)) indicates the concentration of each substance. Initial value is the initial content of an entity. Entity Name Variable (mx) Initial value lim-6(n) m1 0 lim-6(c) m2 0 die-1 mrna(n) m3 0 lsy-6 (C) m4 0 gcy-7 m5 0 gcy-6 m6 0 gcy-22 m7 0 gcy-5 m8 0 flp-20 m9 0 flp-4 m10 0 cog-1 mrna(c) m11 0 lsy-6(n) m12 0 cog-1 mrna(n) m13 0 die-1(n) m14 0 die-1(c) m15 0 cog-1(n) m16 0 mir-273(n) m17 0 cog-1(c) m18 0 mir-273(c) m19 0 die-1 mrna(c) m20 0 By means of these processes and notations of molecules, the molecular interactions in the pathway can be described as follows. The lsy-6 gene is transcribed to produce the lsy-6 pri-mirna, which is then processed to produce the pre-mirna by the protein Drosha (T1); the pre-mirna then migrates to the outside of the nucleus via exportin-5, and is processed by the dicer to yield the lsy-6 mirna (T2). The lsy-6 mirna suppresses the translation of the cog-1 mrna(c) within the RISC (T3) (Figure 1 (1)). The cog-1 gene is transcribed to form the cog-1 mrna (T4), migrates to the outside of the nucleus (T5), and is translated into the protein cog-1(c) (T3). When cog-1(c) migrates to the nucleus (T6), cog-1(n) activates the transcription of the cog-1 (T7) and mir-273 (T8) genes. Cog-1(C) suppresses the expression of the gcy-6 (T21) and gcy-7 (T20) genes, and the die-1 (T16) activates the expression of the lim-6 gene (Figure 1 (2)). The mir-273 gene is transcribed to produce the mir-273 pri-mirna; this, in turn, is processed by the Drosha protein to produce the pre-mirna (T9), migrated to the outside of the nucleus via expotrin 5, and is processed by the dicer to yield the mir-273 mirna (T10). The mir-273 mirna suppresses the translation of the die-1 mrna(c) within the RISC (T11) (Figure 1 (3)). The die-1 gene is transcribed to yield the die-1 mrna (T12); this is exported to the outside of the nucleus (T13), and translated to the protein die-1(c) (T11). When the die-1(c) activates the expression of the protein lim-6 (T16), it migrates to the nucleus (T14) and activates the transcription of the lsy-6 (T15) gene (Figure 1 (4)).

7 106 Saito et al. The protein lim-6 activates the expression of the flp-4 (T24) andflp-20 (T25) genes and suppresses that of the gcy-5 (T22)andgcy-22 (T23) genes; subsequently, it migrates to the inside of the nucleus (T17), and lim-6 (N) activates the transcription of the lsy-6 (T18) and die-1 (T19) genes (Figure 1 (5)). Our HFPNe pathway model involves the knowledge of protein subcellular localization, the process of forming protein complexes, and functional molecular interactions. Beginning from a qualitative pathway model, we manually tuned the parameters for the processes and initial conditions of entities in the HFPNe model in order that the model is consistent with the data in reference [8]. Thus, it also involves the knowledge of system dynamics. The HFPNe model in Figure 3, including all parameters in the model, is available in reference [25] and can be simulated using Cell Illustrator 2.0 [26]. 3 Simulation and Results ASEL-reporter genes ASER-reporter genes lsy-6 (m12) initial value mir-273 (m17) initial value Concentration Concentration =0 =10 =10 =0 Figure 4: Simulation results of reporter gene expression by controlling the initial concentrations of lsy-6 and mir ASEL-ASER Pathway Model The ASEL cell expresses gcy-6 and gcy-7, and the ASER cell expresses the gcy-5 and gcy-22 genes. In adult animals, two of these genes gcy-6 and gcy-7 are stereotypically expressed only in the ASEL cell, whereas gcy-5 and gcy-22 are expressed only in the ASER cell [8]. Moreover, two genes flp-4 and flp-20 that code for the FMRFamide-type neuropeptides, are only expressed in ASEL cells [8]. These differences can be used to distinguish between these two cells. If the initial concentration of lsy-6/mir-273 is high/low (or zero), the reporter proteins of ASEL, i.e., flp-4, flp-20, gcy-6, andgcy- 7, are upregulated; further, the reporter proteins of ASER, i.e., gcy-5 and gcy-22 are not observed. In contrast, if the concentration of lsy-6/mir-273 is low (or zero)/high, the results are completely reversed (see Figure 4). Thus, by controlling the initial concentration of lsy-6 and mir-273, the cell fate determination of gustatory neurons in vivo can be also observed in silico. 3.2 The Updated Model: A Bifurcation Using the New Factor lsy-2 One of the merits of the in silico model is that once the model is created, it can be easily updated with new information. The ASER-ASEL model is no exception. Recently, Johnston and Hobert have found that lsy-2 is another key regulator that activates the transcription of lsy-6 by transporting it from the cytoplasm to the nucleus [10]. Figure 3 shows the compiled model containing this information. The entities lsy-2(c) and lsy-2(n) and the processes T26, T27, d21, and d22 surrounded with the dotted rectangle are added to the original model in Section 2. Lsy-2(C) is transported from the cytoplasm to the nucleus (lsy-2(n)) via the process T26. Lsy-2(N) activates the transcription of lsy-6 via the process T27. The natural degradation of lsy-2(c) and lsy-2(n) is represented with d21 and d22. The detailed parameters in this updated model are summarized in Table 3. The result of the simulation result of the new ASER-ASEL model is presented in Figure 5, where the concentration behaviors of lsy-6(c), cog-1(c), mir-273(c), die-1(c), gcy-7, gcy-6, flp-20, flp-4, gcy-22, and gcy-5 are observed with four initial concentrations of lsy-2(c), i.e., 1.00, 0.40, 0.36, and

8 Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs DNFL by HFPNe 107 Table 3: Elements added to the new ASER-ASEL model in Section 3.2. (a) The additional biological events and their reaction speeds. Other events are the same as those listed in Table 1. (b) The additional entities and their initial values. Other entities are the same as those listed in Table 2. (a) Biological phenomena on the literature (obtained by experiments) Protein lsy-2(c) is imported from the cytoplasm to the nucleus (lsy-2(n)). Lsy-2(N) activates transcription of gene lsy-6, producing lsy-6 pri-mirna, and the drosha processes to produce lsy-6 pre-mirna. (b) Entity name Variable (mx) Initial value lsy-2(c) m /0.40/0.36/0 lsy-2(n) m22 0 #1 #2 Type of biological process T26 m Nuclear import [10] T27 m Transcription / Drosha processing Literature [10], [6], [19] 0.0. If the initial concentration of lsy-2(c) is zero, the ASER reporter genes gcy-22 and gcy-5 are expressed and the ASEL reporter genes gcy-7, gcy-6, flp-20 (chart not shown), and flp-4 (chart not shown) are not expressed (Figure 5 (4)). In contrast, if the initial concentration of lsy-2(c) is high (1.0), the ASER reporter genes gcy-22 and gcy-5 are not expressed and ASEL reporter genes gcy-7, gcy-6, flp-20, andflp-4 are expressed (Figure 5 (1)). With the in silico simulation of the new ASER-ASEL model, the qualitative hypothesis of Johnston et al. that the lsy-2 should be the upstream regulator of the ASER-ASEL cell fate determination is confirmed quantitatively. In the in silico model, the initial concentration of lsy-2 that switches from ASER to ASEL is approximately As shown in Figure 5 (2), if the initial value of lsy-2 is slightly high (0.40), the expression time of the ASER reporter genes is slower than that if this value is considerably high. However, the final concentrations of the reporter genes are not different between ASER and ASEL. On the other hand, if the initial value of lsy-2 is slightly low (0.36), the expression time of the ASEL reporter genes is slower than that if it is zero. However, the final concentrations of the reporter genes are not different between these two cells. Thus, we could quantitatively conclude that lsy-2 is a key regulator of ASER and ASEL cell fate determination. 3.3 In Silico Mutant Models Another merit of the in silico model is that mutant models can be easily created with minor modifications in the original model, and it confirms whether in vivo results can also be obtained with the in silico mutant model. If the in vivo and in silico results are different, it implies that the original model in silico is incomplete, e.g. new regulation factors exist or some regulations in the model are incorrect. Many mutants that related with the ASER-ASEL model are known, e.g. sy607, nr2073, and ot71 [2, 3, 9, 11, 18]. From these mutants, we select two major mutants sy607 and ot Mutant sy607: The Lack of cog-1 The mutant sy607 lacks the cog-1 homeobox gene. The detection is normally performed as follows: the ASEL-specific flp-4, flp-20, andgcy-6 reporters are ectopically activated in ASER, whereas the expression of the ASER marker gcy-22 is lost [8]. In order to deactivate the transcription of the cog-1 gene, the activity of the T5 process is changed from true to false. With this minor modification, the original model becomes the sy607 mutant model. The simulation result is shown in Figure 6 (1). The ASEL-specific cell fate markers are expressed on the left as well as right cells; in addition, the ASER-specific cell fate markers are not expressed on both left and right cells. This implies that the

9 108 Saito et al. Initial concentration of lsy lsy-2(c) Concentration lsy-6(c) cog-1(c) mir-273(c) die-1(c) lim-6(c) gcy-7 gcy-6 gcy-22 gcy-5 Concentration Concentration Concentration Concentration Concentration Concentration Concentration (1) (2) (3) (4) Figure 5: Simulation results of the concentration behaviors of the proteins (lsy-2(c), cog-1(c), die- 1(C), lim-6(c), gcy-7, gcy-6, gcy-22, andgcy-5) and mirnas (lsy-6(c) and mir-273(c)). The initial parameters and their speeds are described in Tables 1 3.

10 Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs DNFL by HFPNe 109 left and right cells of the in silico mutant differentiate into ASEL cells. This result confirms that the in silico model is well organized to a mutant model Mutant ot71: The Lack of lsy-6 Ot71 is the lsy-6 null mutant. It is normally detected by the expression of the ASEL markers flp-4, flp-20; gcy-6 is lost in ASEL, with a concomitant gain of the ASER marker gcy-22 [8]. In order to verify this fact, all transcriptions of lsy-6 are nullified, e.g. the activities of T1, T15, T18, andt27 are changed from true to false. The simulation result is presented in Figure 6 (2). The ASER-specific cell fate markers are expressed on the right as well as left cells; in addition, the ASER-specific cell fate markers are not expressed on both left and right cells. This implies that the left and right cells of the in silico mutant differentiate into ASER cells. This result confirms that the in silico model is well organized to the mutant model. wild type sy607 ot71 ASEL mode: lsy-2(c) = 1.0 Concentration ASER mode: lsy-2(c) = 0 Concentration (1) (2) Figure 6: Simulation results of the concentration behaviors of the reporter proteins. Each solid line indicates gcy-5 and gcy-22; the dotted line, flp-4 and flp-20; and the dashed line; gcy-6 and gcy-7 behaviors. 4 Discussion and Conclusion In this paper, we have concentrated on that the new key factor mirnas can be effectively handled with the HFPNe architecture from the following viewpoints: (i) mirna itself can be modeled, (ii) its regulations from other elements can be modeled, and (iii) regulations to other elements can be modeled. In particular, we have chosen to model one of the complicated regulations mediated by mirnas: a DNFL of the lsy-6 and mir-273 mirnas that will determine the ASE cell fates in C. elegans. For viewpoint (i), the lsy-6 pre-mirna, lsy-6 mirna, mir-273 pre-mirna, and mir-273 mirna can be modeled with m4, m12, m17, and m19, respectively. With respect to (ii), the fact that the transcription and Drosha processing of the lsy-6 pre-mirna is activated by die-1(n), lim- 6(N), and lsy-2(n) is represented by T15, T18, andt27 and the association connectors liked to these, respectively. Additionally, the fact that the transcription and Drosha processing of the mir-273 pre-mirna is activated by cog-1(n) is represented by T8 and the association connector linked to it. With regard to (iii), the fact that the translation of the cog-1 mrna(c) and the die-1 mrna(c) are

11 110 Saito et al. inhibited by the lsy-6 mirna and the mir-273 mirna is modeled with T3 and T11 and the inhibitory connector linked to that, respectively. Thus, the HFPNe can naturally integrate the new key factor mirna to a model illustrating biological pathways involving mrnas and proteins. Using the simple quantitative model (ASER-ASEL model), we have simulated and confirmed the qualitative model proposed by Johnston et al. The ASER-ASEL model was also updated with the lsy-2 regulations to lsy-6. With the updated model, we have also confirmed that their hypothetical qualitative model is applicable for quantitative illustration as well. In addition, we performed in silico mutant analyses to confirm whether the simulation model is consistent with the observed results of mutants in vivo. However, with the lack of detailed parameters that are necessary for sophisticated quantitative model, we have adopted the simple model with following manners; (i) the same translation speed among processes, (ii) the same transcription speed among processes, (iii) the same activation strength, and (iv) the same inhibition strength. Thus, for creating a sophisticated in silico model in the future, we might be required to cooperate with other in vivo/in vitro laboratories. Nevertheless, this simple model has reconstructed the qualitative features of the ASEL-ASER model without lsy-2, an ASEL- ASER model with lsy-2, and the mutant models of sy607 and ot71. References [1] Bagga, S., Bracht, J., Hunter, S., Massirer, K., Holtz, J., Eachus, R., and Pasquinelli, A. E., Regulation by let-7 and lin-4 mirnas results in target mrna degradation, Cell, 122(4): , [2] Chang, S., Johnston, R. J. Jr., Frokjaer-Jensen, C., Lockery, S., and Hobert, O., MicroRNAs act sequentially and asymmetrically to control chemosensory laterality in the nematode, Nature, 430: , [3] Chang, S., Johnston, R. J. Jr., and Hobert, O., A transcriptional regulatory cascade that controls left/right asymmetry in chemosensory neurons of C. elegans, Genes Dev., 17(17): , [4] Doi, A., Fujita, S., Matsuno, H., Nagasaki, M., and Miyano, S., Constructing biological pathway models with hybrid functional Petri nets, In Silico Biol., 4(3): , [5] Doi, A., Nagasaki, M., Fujita, S., Matsuno, H., and Miyano, S., Abstract Genomic Object Net: II. Modelling biopathways by hybrid functional Petri net with extension, Appl. Bioinformatics, 2(3): , [6] Filipowicz, W., Jaskiewicz, L., Kolb, F. A., and Pillai, R. S., Post-transcriptional gene silencing by sirnas and mirnas, Curr. Opin. Struct. Biol., 15:1 11, [7] Hobert, O., Tessmar, K., and Ruvkun, G., The Caenorhabditis elegans lim-6 LIM homeobox gene regulates neurite outgrowth and function of particular GABAergic neurons, Development, 126: , [8] Johnston, R. J. Jr., Chang, S., Etchberger, J. F., Ortiz, C. O., and Hobert, O., MicroRNAs acting in a double-negative feedback loop to control a neuronal cell fate decision, Proc. Natl. Acad. Sci. USA, 102(35): , [9] Johnston, R. J. Jr. and Hobert, O., A microrna controlling left/right neuronal asymmetry in Caenorhabditis elegans, Nature, 426: , [10] Johnston, R. J. Jr. and Hobert, O., A novel C. elegans zinc finger transcription factor, lsy-2, required for the cell type-specific expression of the lsy-6 microrna, Development, 132(24): , 2005.

12 Cell Fate Simulation Model of Gustatory Neurons with MicroRNAs DNFL by HFPNe 111 [11] Kim, K. and Li, C., Expression and regulation of an FMRFamide-related neuropeptide gene family in Caenorhabditis elegans, J. Comp. Neurol. 475(4): , [12] Matsuno, H., Doi, A., Nagasaki, M., and Miyano, S., Hybrid Petri net representation of gene regulatory network, Pac. Symp. Biocomput., 5: , [13] Matsuno, H., Murakami, R., Yamane, R., Yamasaki, N., Fujita, S., Yoshimori, H., and Miyano, S., Boundary formation by notch signaling in Drosophila multicellular systems: experimental observations and gene network modeling by Genomic Object Net, Pac. Symp. Biocomput., 8: , [14] Matsuno, H., Tanaka, Y., Aoshima, H., Doi, A., Matsui, M., and Miyano, S., Biopathways representation and simulation on hybrid functional Petri net, In Silico Biol., 3(3): , [15] Nagasaki, M., Doi, A., Matsuno, H., and Miyano, S., Genomic Object Net: I. A platform for modelling and simulating biopathways, Appl. Bioinformatics, 2(3): , [16] Nagasaki, M., Doi, A., Matsuno, H., and Miyano, S., A versatile petri net based architecture for modeling and simulation of complex biological processes, Genome Inform., 15(1): , [17] Nagasaki, M., Doi, A., Matsuno, H., and Miyano, S., Bioinformatics Technologies, Computational modeling of biological processes with Petri net based architecture, Springer Press, Chen, Y. P. Ed., [18] Palmer, R. E., Inoue, T., Sherwood, D. R., Jiang, L. I., and Sternberg, P. W., Caenorhabditis elegans cog-1 locus encodes GTX/Nkx6.1 homeodomain proteins and regulates multiple aspects of reproductive system development, Dev. Biol., 252(2): , [19] Tang, G., sirna and mirna: an insight into RISCs, Trends Biochem. Sci., 30: , [20] Troncale, S., Tahi, F., Campard, D., Vannier, J. -P., and Guespin, J., Modeling and simulation with hybrid functional Petri nets of the role of interleukin-6 in human early haematopoiesis, Pac. Symp. Biocomput. 11, 2006 (in press). [21] Wightman, B., Ha, I., and Ruvkun, G., Posttranscriptional regulation of the heterochronic gene lin-14 by lin-4 mediates temporal pattern formation in C. elegans., Cell, 75(5): , [22] [23] [24] [25] [26]