cell fate simulation model of gustatory neurons with micrornas … · 100 genome informatics 17(1):...

100 Genome Informatics 17(1): 100–111 (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∗

[email protected] [email protected]

Atushi Doi Kazuko Ueno Satoru [email protected] [email protected] [email protected]

Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shi-rokanedai, Minato-ku, Tokyo 108-8639, Japan

Abstract

Biological regulatory networks have been extensively researched. Recently, the microRNA regu-lation has been analyzed and its importance has increasingly emerged. We have applied the HybridFunctional Petri net with extension (HFPNe) model and succeeded in creating model biologicalpathways, e.g. metabolic pathways, gene regulatory networks, cell signaling networks, and cell-cellinteraction models with one of the HFPNe implementations Cell Illustrator. Thus, we have appliedHFPNe to model regulatory networks that involve a new key regulator microRNA. As a test case, weselected the cell fate determination model of two gustatory neurons of Caenorhabditis elegans—ASEleft (ASEL) and ASE right (ASER). These neurons are morphologically bilaterally symmetric butphysically asymmetric in function. Johnston et al. have suggested that their cell fate is determinedby the double-negative feedback loop involving the lsy-6 and mir-273 microRNAs. Our simulationmodel confirms their hypothesis. In addition, other well-known mutants that are related with thedouble-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 switchingbetween ASEL and ASER without any contradictions. Therefore, the HFPNe-based modeling willbe one of the promising modeling methods and simulation architectures that illustrate microRNAregulatory 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 byenzymatic cleavage, and finally produced as a small RNA (20–24mer) in the cytoplasm. The miRNA ismatured by its incorporation into an RNA-Induced Silencing Complex (RISC). Depending on the typeof miRNA incorporated, the RISC binds to specific mRNAs, degrades them, and accordingly inhibitstheir translation. For example, Wightman et al. reported that the lin-4 miRNA suppresses the lin-14gene in C. elegans [21]. For this functionality, it has been thought that the miRNA sequences shouldperfectly match those of the target mRNAs. Recently, it has been found that miRNA with somemismatched sequences can still suppress the translation [1]. Thus, miRNAs will play an importantrole in studying the gene regulatory network.

∗These authors equally contributed to this study.

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 byorganizing biological knowledge and data. For this software tool, we defined a modeling architecturecalled Hybrid Functional Petri Net (HFPN) with extension (HFPNe), which is based on the theoryof Petri net [24]. Petri net is a kind of graphical programming language invented in the 1960s; it hasbeen extensively studied for modeling concurrent control systems and has been applied to industrialsystems. Petri net is highly applicable to biological systems, and it has been successfully used todevelop and analyze some pathway models for gene regulatory networks, metabolic pathways, andsignaling pathways [4, 5, 12, 13, 14, 20, 22].

In this paper, we concentrate attentions on that the new key factor miRNAs can be effectivelyhandled with the HFPNe to other elements architecture, e.g. miRNA itself can be, its regulations toother elements can be modeled, and regulations can be modeled. In particular, we chose to modelone of the complicated regulations mediated by miRNAs: a double-negative feedback loop (DNFL) ofthe lsy-6 and mir-273 miRNAs that will determine the ASE cell fates in C. elegans, i.e., whether thecells will be ASE left (ASEL) or ASE right (ASER). Johnston et al. proposed that the DNFL of thesemiRNAs determines whether the cells will be ASER or ASEL [8]. The mechanism of differentiation ofASE cells based on the DNFL as follows. For the differentiation of these cells in C. elegans, an NKx-type 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 theASER and ASEL, respectively. For the differentiation, the cog-1 and mir-273 miRNAs regulate themRNAs in the following manner. The cog-1 mRNA contains an lsy-6 complementary site in the3′ untranslated region [9]. In contrast, the die-1 miRNA contains two mir-273 complementary sites inthe 3′ untranslated region [2]. Thus, the actions of cog-1 and die-1 are inhibited under the abundanceof lsy-6 and mir-273, respectively, and differentiation into ASER and ASEL cells cannot occur. Inaddition, 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, and lsy-6 is the DNFL (see Figure 1). However, this modelwas a qualitative one and quantitative aspects of the mechanism were missing. Thus, we created thequantitative ASER-ASEL model with HFPNe and discuss in this paper whether the model of Johnstonet al. is in agreement with the in silico model.

lsy-6

cog-1

mir-273

die-1

lim-6

1

23

4

5( )

( )

( )

( )( )

Figure 1: Summary of the DNFL. Thepath involving the steps (1)–(4) formsthe double-negative feedback loop. Theactivation of die-1 (4) leads to the acti-vation of lsy-6 (1) and the suppression ofcog-1 (2) and mir-273 (3). On the otherhand, the activation of cog-1 (2) leads tothe activation of mir-273 (3) and the sup-pression of die-1 (4) and lsy-6 (1).

Entity

Type Discrete

Original symbols of HFPNe Examples of biological images

Cell Illustrator (software)

Continuous Generic Discrete, Continuous, and Generic

ConnectorProcess Association Inhibitation

Process

OUT

degradation

INOUT

Figure 2: Basically, Petri nets are constructed usingthree kinds of symbols for entities, processes, and con-nectors. In Cell Illustrator [15], sets of entities and pro-cesses are both classified into discrete, continuous, andgeneric types; additionally, entities and processes can bereplaced with pictures reflecting the biological images.This replacement makes the HFPNe model of a biologi-cal pathway more comprehensible for biologists (see [16]for details).

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 newexperimental observations can be checked. In order to confirm whether the scheme is also effectivelyapplicable to our miRNA models, the ASER-ASEL model has been updated by including the newfactor lsy-2 in another study by Johnston and Hobert [10]. The new ASER-ASEL model confirmedthat 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 modifyingthe original model (Wild-type model). The various mutant strains are known to the ASE cells. Twomutant 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 modelcan also be sufficiently applicable to the representation of these mutant defects by using a pathwayon 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 compareit with the in vivo results. In section 3.2, we extends the ASER-ASEL model to a new factor lsy-2and discuss the importance of the factor with in silico analysis. In sections 3.3 and 3.4, we create thein silico mutants of ASE cells and compare these results with those observed in vivo. Section 4 is theconcluding remarks.

2 HFPNe Model of DNFL with lsy-6 and mir-273

2.1 Hybrid Functional Petri Net with Extension

Petri net is a network that consists of place, transition, arc, and token. For intuitive notations, in thispaper, we use entity, process, and connector, respectively. An entity (denoted by a circle) can hold to-kens as its content. A process (denoted by a rectangle) is linked to entities by connectors that originatefrom or extend to entities. A process linked with these connectors defines a firing rule in terms of thecontents of the entities to which the connectors are attached or from which they originate. In a modelcreated 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 en-tities 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 morerequirements in modeling, we have defined the principle of HFPNe [16]. Modeling can be realized ina systematic manner by assuming that the object corresponds to the Java class if the process to beillustrated 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 inHFPNe, and a specific value is assigned to each connector as a threshold script. When a processconnector (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 resultof the threshold script is true. The activity rule of an association connector is the same as thatof a process connector in terms of the threshold, but the content of the entity at the source of theassociation connector is not changed by activation. An association connector (a dashed line connectorin Figure 2) can be used to represent enzyme activity since the enzyme itself is not consumed. Aninhibitory connector (a line terminated with the small bar in Figure 2) with a threshold script enablesthe process to be active only if the evaluated result of the threshold script is false. For example,


Figure 3: HFPNe model of the ASEL/ASER pathway. For entities and processes, pictures reflect-ing biological images are used (see Figure 2). Biological meanings of transitions T1, . . ., T25 aresummarized 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 formaldefinition 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 informa-tion on the cell fate determination model of ASEL and ASER in the literature [2, 3, 6, 7, 8, 10, 19]. Wechanged the symbols of the “entity” and “process” to biological images. Although these changes havemathematically 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 adouble circle, but it has been changed to a picture reflecting the biological meaning of the entity; seeFigure 2); this entity reflects the concentration of the substance. In Figure 3, each entity is labeledwith the name of the substance, e.g. die-1, cog-1, and mir-273. In order to indicate the locations ofthe biomolecules, an additional letter (C) or (N) (in the cytoplasm or in the nucleus, respectively) isadded at the end of their names.

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Table 1: Biological facts extracted from the literature [2, 3, 6, 7, 8, 10, 19] and assigned to processesin the HFPNe model in Figure 3. #1: Corresponding processes in the HFPNe. #2: Speed ofthese processes in the HFPNe. The mX(X = 1, . . . , 20) denotes the concentrations of correspondingsubstances (see Table 2). For example, the process T2 has a speed denoted by m12 ∗ 0.1 speed, i.e.,the speed depends on the concentration of lsy-6 in the nucleus (m12).

Biological facts present in the literature (obtained from ex-periments)

#1 #2 Type of biologicalprocess

Literature

Transcription of the lsy-6 gene, produces lsy-6 pri-miRNA,and Drosha processing yields the lsy-6 pre-miRNA.

T1 0.01 Transcription /Drosha processing

[6], [19]

The lsy-6 pre-miRNA is exported from the nucleus to thecytoplasm by exportin-5 and processed by the dicer (lsy-6miRNA) to form miRNA.

T2 m12 ∗ 0.1 Nuclear export /Dicer processing

[6], [19]

The cog-1 mRNA(C) is translated to cog-1(C) under sup-pression by the lsy-6 miRNA (within RISC).

T3 m11 ∗ 0.1 Translation / mi-croRNA inhibition

[9]

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 thecytoplasm (cog-1 mRNA (C)).

T5 m13 ∗ 0.1 Nuclear export –

Cog-1(C) is imported from the cytoplasm to the nucleus(cog-1(N)).

T6 m18 ∗ 0.1 Nuclear import [8]

Cog-1(N) activates transcription of the cog-1 gene, produc-ing the cog-1 mRNA.

T7 m16 ∗ 0.1 Transcription [8]

Cog-1(N) activates the transcription of the mir-273 gene,producing the mir-273 pri-miRNA, and Drosha processingleads to the production of the mir-273 pre-miRNA.

T8 m16 ∗ 0.1 Transcription /Drosha processing

[8]

Transcription of the mir-273 gene yields the mir-273 pri-miRNA, and Drosha processing produces the mir-273 pre-miRNA.

T9 0.01 Transcription /Drosha processing

[6], [19]

The mir-273 pre-miRNA is exported from the nucleus to thecytoplasm by exportin-5 and processed by the dicer (mir-273miRNA) to yield miRNA.

T10 m17 ∗ 0.1 Nuclear export /Dicer processing

[6], [19]

The die-1 mRNA(C) is translated to die-1(C) under sup-pressed by the mir-273 miRNA (within RISC).

T11 m20 ∗ 0.1 Translation / mi-croRNA inhibition

[2]

Transcription of the die-1 gene leads to the production ofthe die-1 mRNA.

T12 0.1 Transcription –

The die-1 mRNA(N) is exported from the nucleus to thecytoplasm (die-1 mRNA(C)).

T13 m3 ∗ 0.1 Nuclear export –

Die-1(C) is imported from the cytoplasm to the nucleus (die-1(N)).


Die-1(N) activates the transcription of the lsy-6 gene, pro-ducing the lsy-6 pri-miRNA, and Drosha processing leads tothe production of the lsy-6 pre-miRNA.


[2]

The expression of lim-6(C) is activated by die-1(C) and sup-pressed by cog-1(C).

T16 m15 ∗ 0.1 Expression [8]

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, pro-ducing the lsy-6 pri-miRNA, and Drosha processing leads tothe production of the lsy-6 pre-miRNA.


[8]

Lim-6(N) activates the transcription of the die-1 gene, pro-ducing the die-1 mRNA.

T19 m1 ∗ 0.1 Transcription [8]

The expression of gcy-7 is activated by die-1 and suppressedby cog-1.

T20 m15 ∗ 0.1 Expression [8], [3]

The expression of gcy-6 is activated by die-1 and suppressedby cog-1.

T21 m15 ∗ 0.1 Expression [8], [3]

Lim-6 suppresses the expression of the gcy-5 gene. T22 0.1 Expression [3], [7]Lim-6 suppresses the expression of the gcy-22 gene. T23 0.1 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]


Table 2: Entities in the HFPNe model of Fig-ure 3. Variable (mX(X = 1, . . . , 20)) indicatesthe concentration of each substance. Initialvalue 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

Twenty-five biological events related to the ASEL-ASER pathway are summarized in the first column ofTable 1; these events have been extracted from theliterature [2, 3, 6, 7, 8, 10, 19]. Each of these is repre-sented by an HFPNe element “process” (originally, anunfilled rectangle, but it has been changed to a pic-ture reflecting the biological meaning of the process;see Figure 2); a process speed has been assigned tothe events. Each event is assigned to the processesTi(i = 1, . . . , 25), as shown in the second column ofTable 1. The third column indicates the speeds ofthese processes. An additional 22 biological eventsare also assigned to the processes (dj(j = 1, . . . , 22)in Figure 3). All of them denote the natural degra-dation of mRNA, miRNA, and protein (not listed inTable 1). No kinetic parameters of these processeshave been documented and measured in any litera-ture. Thus, we simplified the kinetic parameters tothe extent possible. The same speed mX ∗ 0.1 (mXindicates the concentration of the corresponding sub-stance) is assigned for (i) translation and transcrip-tion with active regulations (association connectors),(ii) nuclear export, and (iii) nuclear import. The tran-scription speeds of mRNA and miRNA are the samevalue 0.1 and 0.01, respectively. The types of biolog-ical processes are described in the fourth column ofTable 1, and the literature referred to is listed in thefifth column. Table 2 summarizes the variable andinitial values of entities used in Figure 3.

By means of these processes and notations of molecules, the molecular interactions in the pathwaycan be described as follows.

The lsy-6 gene is transcribed to produce the lsy-6 pri-miRNA, which is then processed to producethe pre-miRNA by the protein Drosha (T1); the pre-miRNA then migrates to the outside of thenucleus via exportin-5, and is processed by the dicer to yield the lsy-6 miRNA (T2). The lsy-6miRNA 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) suppressesthe expression of the gcy-6 (T21) and gcy-7 (T20) genes, and the die-1 (T16) activates the expressionof the lim-6 gene (Figure 1 (2)).

The mir-273 gene is transcribed to produce the mir-273 pri-miRNA; this, in turn, is processedby the Drosha protein to produce the pre-miRNA (T9), migrated to the outside of the nucleus viaexpotrin 5, and is processed by the dicer to yield the mir-273 miRNA (T10). The mir-273 miRNAsuppresses 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 ofthe nucleus (T13), and translated to the protein die-1(C) (T11). When the die-1(C) activates theexpression of the protein lim-6 (T16), it migrates to the nucleus (T14) and activates the transcriptionof the lsy-6 (T15) gene (Figure 1 (4)).

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Time Time

ASEL-reportergenes

ASER-reportergenes

mir-273 (m17)initial value

=10 =0

Figure 4: Simulation results of reporter gene ex-pression by controlling the initial concentration ofmir-273.

The protein lim-6 activates the expression ofthe flp-4 (T24) and flp-20 (T25) genes and sup-presses that of the gcy-5 (T22) and gcy-22 (T23)genes; subsequently, it migrates to the inside ofthe nucleus (T17), and lim-6 (N) activates thetranscription of the lsy-6 (T18) and die-1 (T19)genes (Figure 1 (5)).

Our HFPNe pathway model involves theknowledge of protein subcellular localization, theprocess of forming protein complexes, and func-tional molecular interactions. Beginning from aqualitative pathway model, we manually tunedthe parameters for the processes and initial con-ditions of entities in the HFPNe model in orderthat the model is consistent with the data in ref-erence [8]. Thus, it also involves the knowledgeof system dynamics. The HFPNe model in Fig-ure 3, including all parameters in the model, isavailable in reference [25] and can be simulatedusing Cell Illustrator 2.0 [26].

3 Simulation and Results

3.1 ASEL-ASER Pathway Model

The ASER cell expresses gcy-6 and gcy-7, and the ASER cell expresses the gcy-5 gene. In adultanimals, two of these genes—gcy-6 and gcy-7—are stereotypically expressed only in the ASEL cell,whereas gcy-5 and cgy-22 are expressed only in the ASER cell [8]. Moreover, two genes—flp-4 andflp-20—that code for the FMRFamide-type neuropeptides, are only expressed in ASEL cells [8]. Thesedifferences can be used to distinguish between these two cells. If the initial concentration of mir-273 ishigh, the reporter proteins of ASEL, i.e., flp-4, flp-20, gcy-6, and gcy-7, are upregulated; further, thereporter proteins of ASER, i.e., gcy-5 and gcy-22 are not observed. In contrast, if the concentrationof mir-273 is low or zero, the results are completely reversed (see Figure 4). Thus, by controlling theinitial concentration of mir-273, the cell fate determination of gustatory neurons in vivo can be alsoobserved 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 withnew information. The ASER-ASEL model is no exception. Recently, Johnston and Hobert have foundthat lsy-2 is another key regulator that activates the transcription of lsy-6 by transporting it from thecytoplasm to the nucleus [10]. Figure 3 shows the compiled model containing this information. Theentities lsy-2(C) and lsy-2(N) and the processes T26, T27, d23, and d24 surrounded with the dottedrectangle are added to the original model in Section 2. Lsy-2(C) is transported from the cytoplasmto the nucleus (lsy-2(N)) via the process T16. Lsy-2(N) activates the transcription of lsy-6 via theprocess T17. The natural degradation of lsy-2(C) and lsy-2(N) is represented with d16 and d17. Thedetailed 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, wherethe 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


Table 3: Elements added to the new ASER-ASEL model in Section 3.2. (a) The additional biologicalevents and their reaction speeds. Other events are the same as those listed in Table 1. (b) Theadditional entities and their initial values. Other entities are the same as those listed in Table 2.(a)

Biological phenomena on the literature (obtainedby experiments)

#1 #2 Type of biological pro-cess

Literature

Protein lsy-2(C) is imported from the cytoplasm tothe nucleus (lsy-2(N)).


Lsy-2(N) activates transcription of gene lsy-6, pro-ducing lsy-6 pri-miRNA, and the drosha processesto produce lsy-6 pre-miRNA.

T27 m22 ∗ 0.1 Transcription / Droshaprocessing

[10], [6], [19]

(b)Entity name Variable (mX) Initial value

lsy-2(C) m21 1.00 / 0.40 / 0.36 / 0lsy-2(N) m22 0

0.0. If the initial concentration of lsy-2(C) is zero, the ASER reporter genes—gcy-22 and gcy-5—areexpressed and the ASEL reporter genes—gcy-7, gcy-6, flp20, and flp4—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-22and gcy-5—are not expressed and ASEL reporter genes—gcy-7, gcy-6, flp20, and flp-4—are expressed(Figure 5 (1)). With the in silico simulation of the new ASER-ASEL model, the qualitative hypothesisof Johnston et al. that the lsy-2 should be the upstream regulator of the ASER-ASEL cell fatedetermination is confirmed quantitatively. In the in silico model, the initial concentration of lsy-2that switches from ASER to ASEL is approximately 0.38. As shown in Figure 5 (2), if the initialvalue of lsy-2 is slightly high (0.40), the expression time of the ASER reporter genes is slower thanthat if this value is considerably high. However, the final concentrations of the reporter genes arenot 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, thefinal concentrations of the reporter genes are not different between these two cells. Thus, we couldquantitatively 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 modifi-cations in the original model, and it confirms whether in vivo results can also be obtained with thein silico mutant model. If the in vivo and in silico results are different, it implies that the originalmodel in silico is incomplete, e.g. new regulation factors exist or some regulations in the model areincorrect. 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 ot71.

3.3.1 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, and gcy-6 reporters are ectopically activated in ASER, whereas theexpression of the ASER marker gcy-22 is lost [8]. In order to deactivate the transcription of the cog-1gene, 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, theASER-specific cell fate markers are not expressed on both left and right cells. This implies that theleft and right cells of the in silico mutant differentiate into ASEL cells. This result confirms that thein silico model is well organized to a mutant model.

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Initial concentrationof lsy-2

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(2) (4)(3)(1)

0.40 00.361.00

lsy-2(C)

lsy-6(C)

cog-1(C)

mir-273(C)

die-1(C)

lim-6(C)

gcy-7

gcy-6

flp-20

flp-4

gcy-22

gcy-5

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, gcy-5, flp-20, and flp-4) and miRNAs (lsy-6(C) and mir-273(C)).The initial parameters and their speeds are described in Tables 1–3.


3.3.2 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 toverify this fact, all transcriptions of lsy-6 are nullified, e.g. the activities of T1, T15, T18, and T27are changed from true to false.

The simulation result is presented in Figure 6 (2). The ASER-specific cell fate markers are ex-pressed on the right as well as left cells; in addition, the ASER-specific cell fate markers are notexpressed on both left and right cells. This implies that the left and right cells of the in silico mutantdifferentiate into ASER cells. This result confirms that the in silico model is well organized to themutant model.

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(1) (2)

sy607 ot71wild type

ASEL mode:

lsy-2(C) = 1.0

ASER mode:

lsy-2(C) = 0

Figure 6: Simulation results of the concentration behaviors of the reporter proteins. Each solid lineindicates gcy-5 and gcy-22; the dotted line, flp-4 and flp-20; and the dashed line; gcy-6 and gcy-7behaviors.

4 Discussion and Conclusion

In this paper, we have concentrated on that the new key factor miRNAs can be effectively handledwith 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 bemodeled. In particular, we have chosen to model one of the complicated regulations mediated bymiRNAs: 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-273miRNA can be modeled with m4, m12, m17, and m19, respectively. With respect to (ii), the factthat 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, and T27 and the association connectors liked tothese, respectively. Additionally, the fact that the transcription and Drosha processing of the mir-273pre-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) areinhibited by the lsy-6 miRNA and the mir-273 miRNA is modeled with T3 and T11 and the inhibitoryconnector linked to that, respectively. Thus, the HFPNe can naturally integrate the new key factormiRNA to a model illustrating biological pathways involving mRNAs and proteins. Using the simple

110 Saito et al.

quantitative model (ASER-ASEL model), we have simulated and confirmed the qualitative modelproposed by Johnston et al. The ASER-ASEL model was also updated with the lsy-2 regulations tolsy-6. With the updated model, we have also confirmed that their hypothetical qualitative model isapplicable for quantitative illustration as well. In addition, we performed in silico mutant analyses toconfirm 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 quantitativemodel, we have adopted the simple model with following manners; (i) the same translation speedamong 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 simplemodel 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.

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