細胞や組織における時間空間パターン形成の数理

柴田達夫理化学研究所 発生・再生科学総合研究センター

2013 理研 CDB-連携大学院 集中レクチャー 2013/8/28

細胞中の時空間パタン形成

(Figure 3E), this suggests that Lgl inhibits the cortical localizationof Baz.

In epithelial cells, Lgl competes with Baz for interaction withPar-6 and aPKC (Yamanaka et al., 2003, 2006). In Drosophila,distinct Lgl/Par-6/aPKC and Baz/Par-6/aPKC complexes (here-after referred to as Lgl and Baz complexes, respectively) areassembled in vivo (Figure 6A). To test whether the interactionof Baz with Par-6 and aPKC is inhibited by Lgl, we analyzedPar-6 immunoprecipitates from larval brains expressing Baz-GFP. Par-6 immunoprecipitates from wild-type brains containedboth Lgl and Baz (Figure 4C). However, an excess of Baz wascoimmunoprecipitated with Par-6 from lgl mutant brains (Fig-ure 4C), whereas overexpression of Lgl reduces the amountsof coimmunoprecipitated Baz (Figure 4D). Interestingly, Par-6

Figure 4. AurA Regulates the Subunit Composition of the ParComplex(A and B) Cortical release of Lgl regulates the localization of Baz to the

posterior lateral cortex. Baz-GFP was coexpressed with either Lgl-RFP

or His-RFP in pupal SOP cells. NEBD is t = 0. Anterior is oriented toward

the left. (A) In prophase, Baz-GFP localizes to the posterior lateral cortex,

as Lgl-RFP is released from this side. (B) Posterior lateral localization of

Baz-GFP fails in aurA37/37 mutants.

(C and D) AurA promotes and Lgl inhibits the assembly of the Baz com-

plex. Immunoprecipitates (IP) from larval brains expressing Baz-GFP

were analyzed. (C0 ) Quantification of (C). The IP signal was adjusted to

the corresponding input signal and normalized for wild-type (WT) (set

to 1). Averages and standard deviations are shown (n = 5). Differences

to WT are significant (p < 0.05). (D) Immunoprecipitates from brains

expressing Baz-GFP alone (control) or together with either LglWT-myc or

Lgl3A-myc were analyzed. (D0 ) Quantification of (D). The IP signal was

adjusted to the corresponding input signal and normalized for control

(set to 1). Averages and standard deviations are shown (n = 3 for Baz;

n = 6 for Lgl). Baz levels are significantly different from the control, and

Lgl levels are significantly different from each other (p < 0.05).

immunoprecipitates from aurAmutants contained an excessof Lgl at the expense of Baz (Figure 4C). This was phenocop-ied by expression of Lgl3A (Figure 4D), demonstrating thatentry of Baz into the Par complex requires AurA to initiatethe phosphorylation-dependent release of Lgl from the cellcortex. Thus, AurA triggers a remodeling of the Par complexfrom the Lgl configuration into the Baz configuration byactivating aPKC at the onset of mitosis.

Numb Localization Requires AppropriateLevels of Baz ComplexIf a failure to assemble the Baz complex is responsible for themislocalization of Numb in aurA mutants, then restoring thelevels of Baz complex should rescue aurA mutants. To testthis, we constructed a Baz-Par-6 fusion protein to forceBaz into the Par complex. Indeed, expression of this con-struct in aurA mutant SOP cells rescued the asymmetriclocalization of the Numb reporter GFP-Pon (Lu et al., 1999)(Figures 5A–5C; Movies S7–S9). Overexpression of Bazalone failed to rescue GFP-Pon asymmetry in aurA mutantSOP cells (Figure 5D; Movie S10), although it affected theapical-basal distribution of GFP-Pon (Figure S4D0). We

conclude that AurA induces the asymmetric localization ofNumb by promoting the interaction of Baz with Par-6.We show that lgl mutants contain an excess amount of Baz

complex. If this is responsible for Numb mislocalization in thesemutants, they should be rescued by lowering Baz levels. Indeed,moderate knockdown of Baz (Figures S5AC–S5AE) rescued theasymmetric localization of Numb (Figures 5E–5G) in lgl mutantneuroblasts. We conclude that the role of Lgl in the asymmetriclocalization of Numb is to inhibit the assembly of the Bazcomplex.Excess or insufficient levels of Baz complex both disrupt the

asymmetric localization of Numb. Since AurA and Lgl act in anantagonistic manner on the formation of the Baz complex, weanalyzed Numb localization in lgl aurA double mutants. As

166 Cell 135, 161–173, October 3, 2008 ª2008 Elsevier Inc.

! Wirtz-Peitz F, Nishimura T, Knoblich JA (2008) Linking cell cycle to asymmetric division: Aurora-A phosphorylates the Par complex to regulate Numb localization. Cell 135:161–173.

neuroblast

589Lateral diffusion of PAR proteins • Goehring et al.

!laments using latrunculin (Severson and Bowerman, 2003) or by compromising cortical contractility through the use of a fast-acting mutation in nmy-2 (Liu et al., 2010). Similar to Liu et al. (2010), we observed that as embryos lacking a functional cortex entered anaphase, the PAR-2 domain contracted, accompanied by a corresponding expansion of the anterior PAR domain (Fig. 4, G and I). This contraction coincided with removal of PAR-2 from the cortex to the centrosome through what appeared to be membrane invaginations arising because of microtubule

network to associate with the membrane, and their dynamics on the membrane appear to be largely independent of the acto-myosin cortex during the maintenance phase. Consequently, the cortical actin network is unlikely to be providing the required spatial asymmetries in attachment and detachment required for maintenance of the PAR boundary.

These results super!cially disagree with two reports that disruption of the actomyosin cortex during maintenance phase destabilizes PAR domains, either by depolymerization of actin

Figure 4. PAR domain maintenance does not require an intact actin cytoskeleton. (A and B) Treatment of permeable embryos with CD or latrunculin A leads to rapid disruption of the actomyosin cortex as visualized with NMY-2–GFP (A) or LifeAct–GFP (B) using spinning disk confocal microscopy of a cortical plane taken before and 2–3 min after drug treatment. (C) Treatment of permeable embryos expressing fluorescently tagged PAR-2 (green)/PAR-6 (red) with CD or latrunculin A does not lead to loss of PAR domains. Select wide-field images of the embryo midplane are shown (Videos 1 and 2). (D) PAR distributions several minutes after treatment with CD are similar to untreated embryos (compare with Fig. 2 A). Mean ± SD is shown (n = 6 anterior to posterior profiles). Similar measurements for latrunculin A are provided in Fig. S2. (E) The recovery of GFP–PAR-2 during FRAP is similar in embryos left untreated compared with embryos treated with either CD or latrunculin A. Box size was 4.1 ! 4.1 µm. In each case, two to four FRAP curves were averaged and normalized to allow comparison (see Materials and methods). (F) Same as E, but for GFP–PAR-6 embryos with a 6.9 ! 6.9–µm box size. (G) A kymo-graph of GFP–PAR-2 in a CD-treated embryo shows that the domain remains relatively stable until anaphase (Ana, dashed white line), when it undergoes a dramatic contraction. Time is relative to nuclear envelope breakdown. Distance is relative to the center of the PAR-2 domain. Select images show a PAR-2 domain before and after anaphase. The PAR-2 invaginations that accompany domain contraction are indicated (white arrow; Video 3). Black lines indicate the extent of the PAR-2 domain at the beginning of time series and are shown above and below the kymograph to facilitate size comparisons. (H) Same as G, but including nocodazole plus CD. Disruption of microtubules eliminates both PAR-2 invaginations and anaphase PAR-2 domain contraction. (I) After anaphase onset, the boundaries of both mCherry–PAR-2 (green) and GFP–PAR-6 (red) shift to the posterior in CD-treated embryos. Images of a CD-treated embryo before (Metaphase) and after anaphase onset (Anaphase) illustrate the posterior migration of both PAR-2 and PAR-6 domain boundaries as a result of invaginations. In the insets, identical 25 ! 25–µm regions encompassing the boundary region are taken from images before and after anaphase as indicated, and channels are shown individually to demonstrate the shift of both domain boundaries. Bars: (A–C) 5 µm; (G–I) 10 µm.

on May 24, 2011

jcb.rupress.orgD

ownloaded from

Published April 25, 2011

Goehring NW, Hoege C, Grill SW, Hyman AA (2011) PAR proteins diffuse freely across the anterior-posterior boundary in polarized C. elegans embryos. The Journal of Cell Biology 193:583–594.

C. elegans

(Dictyostelium)

Arai Y, Shibata T et al. (2010) PNAS 107:12399–12404.

Chemotaxis cell

PIP3/PTEN

(Asymmetric cell division) (Asymmetric cell division)

Cell polarity and asymmetry

組織の中のパタン形成

0 Introduction

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dorsal view (St25)

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ventral view (St25)

In Xenopus, proportional pattern of the dorsal-ventral axis is robustly formed, despite the variation in the embryonic size (Fig. A-C), and even in the half-size embryo after bisection experiments (Fig. D-F). What is the mechanism that dynamically adjusts the DV pattern to embryonic size?

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The positional information along the DV axis is given by local concentration of a morphogen. In Xenopus, BMP is primarily the morphogen. In Fig. G and H, the BMP activity is quantified by the nuclear phospho-Smad1 (pSmad1) signal.

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! Inomata, H., et al. Cell 153, 1296–1311 (2013).

Fig S2

Wolpert’s “French !ag” model (1969)

• Concentration gradient can convey positional information.

• Such a molecule is called “morphogen”

•Question:

What mechanism can produce a gradient ?

alleles, indicating that SCW is required for maximal DPPactivity19. Similarly, in the imaginal disc, the glass bottomboat (gbb, also known as 60A) gene is expressed through-out the wing pouch of the disc (Fig. 2a, top), and the patterning defects observed in hypomorphic gbb mutantwings are exacerbated by a small reduction of dpp activ-ity, suggesting that GBB elevates DPP signaling within thedisc20.

Furthermore, genetic analysis of TGF! receptor func-tion revealed that signals must be integrated downstreamof multiple receptors. The heteromeric TGF! receptorcomplex consists of two types of serine–threoninekinases21. Upon ligand binding, the type II kinase phos-phorylates the type I kinase, which then transduces the sig-nal to downstream components22. While the type II recep-tor, Punt (PUT), and the type I receptor, Thick veins(TKV), are essential for all DPP signaling23–27, a secondtype I receptor, Saxophone (SAX), is also necessary fornormal patterning in each tissue. In the embryo, SAX isrequired to obtain the highest levels of DPP signaling tospecify amnioserosal cell fates, and in the wing disc SAXfunction is required to obtain normal levels of DPP signal-ing across the entire DPP activity gradient23–25,28.Overexpression of TKV can bypass the requirement forSAX (Ref. 25), suggesting that the two receptors could usethe same intracellular signal-transduction machinery.

Three reports3–5 have now clarified the interrelation-ships among these BMP ligands and receptors. In embryoscompletely lacking dpp expression, injection of increasingamounts of an mRNA encoding a mutated, constitutivelyactivated form of the TKV receptor (TKV-A) induces the full complement of dorsal cell fates in a dose-depend-ent fashion3,4. Thus, signaling downstream of TKV reca-pitulates the embryonic response to DPP (Ref. 3). Inmarked contrast, injection of a constitutively activatedSAX (SAX-A) mRNA has no biological effect3,4. However,when SAX-A mRNA is co-injected with low or moderatelevels of TKV-A mRNA, SAX-A mRNA elevates the biological response to a given level of TKV-A mRNA(Refs 3, 4). A similar synergistic effect of ectopic TKV-Aand SAX-A signaling is observed in the wing disc5.Together, these results indicate that in both tissues, SAXand TKV transmit distinct intracellular signals that mustbe integrated for the accurate interpretation of positionalvalues.

Ligand specificities of the TKV and SAX receptors havebeen established by functional criteria, primarily by deter-mining whether dominant-negative forms of each receptor(TKV-DN and SAX-DN) can block the phenotypes causedby ectopic (or elevated) ligand activity in vivo3–5. In theembryo and the wing disc, expression of TKV-DN blocksthe activity of DPP as well as the activity of SCW or GBB(depending on the tissue examined). By contrast, expres-sion of SAX-DN blocks the activity of SCW and GBB, buthas no effect on DPP activity. A separate experimentdemonstrated that, in the embryo, scw function is essentialfor the activity of a chimeric receptor composed of theextracellular domain of SAX and the intracellular domainof TKV (Ref. 3). Moreover, SCW and GBB have full bio-logical activity, even when expressed in cells that do notexpress DPP (Refs 3–5), indicating that signaling by SCWor GBB does not require the formation of heterodimerswith DPP. These findings strongly suggest that SCW andGBB are necessary components of the ligand for the SAXreceptor.

Taken together, these results modify the previous paradigm of DPP action. Although experimental manipu-lations indicate that DPP, acting through TKV, can specifyall positional values in the field in a dose-dependent fashion, the ability of DPP to specify positional valuesacross a cell field in vivo requires synergistic signalingfrom a second ligand, SCW or GBB, acting through theSAX receptor (Fig. 3). While the mechanism(s) by whichthe SAX signal is integrated into the TKV signaling path-way are presently unknown, some predictions can bemade from recent biochemical analyses of signaling down-stream of the vertebrate homologs of the two receptors(Fig. 3).

Although synergistic signaling between TKV and SAXis required for the elucidation of positional information inboth cell fields, the biological mechanism used to specifypositional information within each cell field differs. In the wing disc, diffusion of DPP from its source probablyprovides the necessary positional information, whereasGBB signaling provides a constant level of elevation of the DPP signal across the wing disc (Fig. 2a). By contrast, positional information in the embryonic ecto-derm is specified by the spatially restricted modulation

ReviewsDPP gradient formation and interpretation

TIG October 1999, volume 15, No. 10 397

FIGURE 1. The ‘French flag’ model of positional information

(Top) A morphogen, produced in a restricted domain within a field of cells (left panel, black stripe),mediates the organization of the entire field into a set of discrete domains (right panel, red, white andblue stripes), which could represent either differentiation of particular cell types or the expressionpatterns of individual genes. (Bottom) The morphogen conveys positional information by forming anextracellular gradient (curved black line) as the result of diffusion from its source and subsequenttitration or consumption within the field. Cells within the field determine their position by interpretingthe morphogen concentration, resulting in their activation of specific programs of target geneexpression at discrete morphogen thresholds.

French FlagFrench Flag

trends in Genetics

morphogen

gradient

position

1.!Wolpert, L. Positional information and the spatial pattern of cellular differentiation. J Theor Biol 25, 1–47 (1969).

© 1970 Nature Publishing Group

1.! Crick, F. Diffusion in embryogenesis. Nature 225, 420–422 (1970).

米沢富美子「ブラウン運動」共立出版

インクは拡散する拡散 (Diffusion)

Movie S1

たんぱく質は組織中を拡散する拡散 (Diffusion)

! Inomata, H., et al. Cell 153, 1296–1311 (2013).

ものは濃度の低い方に流れる(Fickの法則)

J = −D ∂C∂x

流れ 濃度の勾配

D > 0 : 係数

• 流れ J は濃度の勾配の低い方向に流れる

∂C∂x

> 0∂C∂x

< 0

C C

物質の保存則

(Cの時間変化率)=(輸送による正味の流入)

∂C∂t

= − ∂J∂x

x x+Δxx-Δx

C(x,t)

J(x −Δx,t) J(x,t)

C(x,t +Δt)−C(x,t)Δt

= − J(x,t)Δx

+ J(x −Δx,t)Δx

or

C(x):位置xにおける濃度J(x): 位置xにおける流れ密度

拡散方程式

J = −D ∂C∂x

Fickの法則

∂C∂t

= − ∂J∂x

物質の保存則

∂C(x,t)∂t

= D ∂2C(x,t)∂x2

D : 拡散係数 (μm2/sec)

反応がある場合の物質の保存則

(Cの時間変化率)=(正味の生成率)+(輸送による正味の流入)

x x+Δxx-Δx

C(x,t)

J(x −Δx,t) J(x,t)C(x):位置xにおける濃度J(x): 位置xにおける流れ密度f(x) : 位置xにおける反応

∂C∂t

= f − ∂J∂x

C(x,t +Δt)−C(x,t)Δt

= f (x,t)− J(x,t)Δx

+ J(x −Δx,t)Δx

or

f (x,t)

反応拡散方程式

∂C∂t

= f − ∂J∂x物質の保存則

∂C(x,t)∂t

= f (x,t)+D ∂2C(x,t)∂x2

J = −D ∂C∂x

Fickの法則

D : 拡散係数 (μm2/sec)

離散的に考える∂C(x,t)

∂t= f (x,t)+D ∂2C(x,t)

∂x2

C(x,t +Δt)−C(x,t)Δt

= f (x,t)+DC(x+Δx,t)−C(x,t)[ ]− C(x,t)−C(x −Δx,t)[ ]

(Δx)2

= f (x,t)+DC(x+Δx,t)+C(x −Δx,t)−2C(x,t)(Δx)2

C(x,t +Δt)=C(x,t)+Δt f (x,t)+DC(x+Δx,t)+C(x −Δx,t)−2C(x,t)(Δx)2

⎛⎝⎜

⎞⎠⎟

反応拡散方程式

微分を離散化する

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x x+Δxx-Δx

or

離散的に考える∂C(x,t)

∂t= f (x,t)+D ∂2C(x,t)

∂x2

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⎛⎝⎜

⎞⎠⎟

反応拡散方程式

t

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細胞の相互作用

C1 C2

細胞1 細胞2

細胞の相互作用

C1 C2

細胞1 細胞2∂C1(t)∂t

=αC2 (t)−βC1(t)

細胞2の中の濃度C2に応じて細胞1の発現量が決まる

∂C2 (t)∂t

=αC1(t)−βC2 (t)

同様に

Ci Ci+1

細胞i 細胞i+1

細胞の相互作用

∂Ci (t)∂t

=αCi−1(t)+αCi+1(t)−βCi (t)

隣の細胞の中の濃度に応じて細胞iの発現量が決まる

Ci Ci+1

細胞i 細胞i+1

細胞の相互作用

∂Ci (t)∂t

=αCi−1(t)+αCi+1(t)−βCi (t)

=α Ci−1(t)+Ci+1(t)−2Ci (t)( )− (β +2α)Ci (t)

隣の細胞の中の濃度に応じて細胞iの発現量が決まる

∂C(x,t)∂t

=α(Δx)2 ∂2C(x,t)∂x2

− (β +2α)Ci (t)

~細胞サイズ

まとめ１

• 拡散方程式は物質の拡散を表わす• 反応拡散方程式は反応効果が加わっている• 細胞間の相互作用によって組織中を拡がる反応も反応拡散方程式で表わされる

濃度勾配をつくる

モルフォゲン(morphogen)の生成

∂C(x,t)∂t

= D ∂2C(x,t)∂x2

−λC(x,t)

濃度の時間変化 拡散 分解反応

反応拡散方程式

= D λ (µm) C(x)=C0e−x/濃度の空間分布 特徴長さ

拡散距離

• 特徴長さ ℓ は、分子が分解されるまでに移動する平均距離

まとめ２• 指数関数で表わされる勾配が作られる• 因子がある領域で作られる• 拡散によって拡がる• 分解される

• 空間の濃度勾配は拡散係数と分解レートで決まる

What is the mechanism that dynamically adjusts the DV pattern to embryonic size?

! Inomata, H., et al. Cell 153, 1296–1311 (2013).