A simple molecular model of neurulation

Transcription

1 A simple molecular model of neurulation Michel Kerszberg* and Jean-Pierre Changeux Summary A molecular model for the morphogenesis of the central nervous system is built and solved by computer. The formalism rests on molecular biological data gathered from insects and vertebrates during neural differentiation and neuronal fate specification. Two genetic, hierarchically organized switches are introduced, one associated with neural tissue formation, and the other with neuronal specification. The model switches evolve in time, setting up very similar prepatterns of genetic activity in both insects and vertebrates, as observed experimentally. We introduce the hypothesis that cell adhesion and motion are regulated by the switches. If cell motion is turned on by the neural switch, the whole neural tissue (neural plate) thickens, buckles, and folds, ultimately creating a closed neural tube (primary neurulation). When mitoses are more frequent in neural plate tissue, ingression of a neural cell mass takes place instead (secondary neurulation). If cell motions are controlled by the neuronal switch, rather than by the neural one, the differentiation of isolated neuroblasts is observed, which delaminate individually (as in insect neural cord formation). The model thus displays the three major known patterns of neurogenesis; the transition between the vertebrate and insect cases is predicted to result from changes in genetic regulation downstream of the switch genes, and affecting cell adhesion and motility properties. Little is known experimentally about the concerned pathways: their importance as a fruitful area for future investigation is emphasized by our theoretical results. BioEssays 20: , John Wiley & Sons, Inc. Introduction The central nervous system (CNS) of the vertebrates is very different from that of invertebrates such as insects. The former acquire, from dorsal tissue, a closed neural tube, while the latter possess ventral alignments of ganglia, the neural cord. Yet it is becoming clear that development of these structures results in both cases from the action of universal mechanisms. The proteins involved, such as transcription factors, long-range morphogens, membrane receptors, and their ligands, are homologous. The spatial distributions of the Neurobiologie Moléculaire, Institut Pasteur, Paris CNRS URA-1284, France. *Correspondence to: Michel Kerszberg, Neurobiologie Moléculaire, Institut Pasteur, 25, rue du Docteur Roux, F Paris Cedex 15, France. associated genetic activities reflect the overall inversion from ventral to dorsal. (1) This is quite satisfying, of course, but begs the next question: how do these homologous genes and products lead to such different phenotypes, namely, isolated ganglions in one case, and a continuous, closed tube in the other? The construction of a theoretical framework within which such problems can be tackled was initiated during the past few years. The framework is centered around a formal description of gene activity and its control by transcription factors, under the influence of diffusible molecules and intercellular communication channels. It has been applied to gene transcription patterns in the maturing myotube, (2) in the Drosophila syncytial blastoderm (3,4) and to the differentiation of embryonic territories under the influence of retinoic acid. (5) In order to investigate early neurogenesis, the major novel feature we have to introduce in the formalism is cellular motion (in particular cell shape changes). 758 BioEssays 20.9 BioEssays 20: , 1998 John Wiley & Sons, Inc.

2 We define a minimal set of molecular components necessary for neurulation, at three distinct hierarchical levels: (i) cell determination, i.e., permanent fate decisions at the gene level; (ii) cell membrane presentation of ligands and receptors and their intercellular interactions; and (iii) cell responses, i.e., signal transduction followed by biochemical changes, altered gene transcription (back to level i), cellular motion, adhesion, and mitotic activity. The biological premises we adopt are mostly uncontroversial; a major, experimentally verifiable hypothesis is presented, however, which allows us to put forward a tentative understanding of the articulation just discussed between completely different modes of CNS formation. The hypothesis concerns the coupling between genetic activity and cell motion. The model illustrates how current molecular biological data may become progressively incorporated into the logic of computer programs, to help us grapple with the multitude of intercellular and intracellular regulatory networks in morphogenesis. It should be noted that the interpretation of such complex simulations is itself not always straightforward. It is inherent to large computer models that they involve numerous parameters, many of which are ancillary, i.e., they do not bear directly on the issues at hand. For instance, to what degree are the motion of a cell s nucleus and that of its membrane dependent on one another? This connection is not a simple property to evaluate or measure, yet no theoretical treatment of cell motion can be complete without some sort of such linkage. The assumptions underlying ancillary parameters must be thoroughly checked by systematically verifying that their values exert little or no effect on the ensuing predictions. This validation process establishes the model framework, which, in a way, becomes the theoretical equivalent of an experimental preparation. The conviction that the framework has been properly set up is of course difficult to convey in print. As a palliative, and to allow the interested reader to reproduce our results, the computer code will be made available upon request. 1 The following discussion describes the selected experimental data on which the model is based, followed by a formal introduction to the model itself. Finally, simulation results are presented. Biological premises We now present briefly the experimental basis of our molecular assumptions. (6,7) This evidence is gathered from neural morphogenesis in Drosophila, Xenopus, mouse, and chick. Orthologous gene families are found in all the concerned 1 Inquiries should be directed to M.K. (mkersz@pasteur.fr). The C source code describes thoroughly the model equations and parameter values in a fairly transparent quasimathematical language. For compilation and execution, an X-Window server and the Sun XView graphics library are required. species. We concentrate on morphogenesis along the dorsoventral embryonic axis, and in particular on the formation of the ventralmost neurons and cell types (motor neurons, ventral interneurons and oligodendrocytes). The nervous system begins to form when ectodermal tissue becomes neuroectoderm. Certain cells will then proceed further to acquire proneural identity. This is the province of the proneural genes, which play a central role in neuronal determination. In the peripheral as well as the CNS of Drosophila, the achaete-scute(as-c) gene complex is an early marker of presumptive neural territory (8,9) ; similar evidence accumulates regarding Xenopus neurogenesis. (10 12) What, then, are the upstream factors responsible for the early onset of AS-C gene activity? How is the activity later maintained? What downstream effects do the AS-C transcription factors produce on cell behavior? We address these questions in turn; the discussion is summarized in Figures 1 and 2. Onset of neurulation Orthologous molecules act upstream of AS-C in vertebrates and insects. Figure 1a displays the transverse section of the vertebrate embryo s dorsal ectoderm. Early determination of neuroectoderm is characterized by the expression of a battery of homeobox and paired-box genes. (13) These genes differ according to anteroposterior (AP) location; (14) considering, for instance, the spinal cord, the genes involved include Pax-3, Hox-b9, (15) and Sax-1. (16) Neural plate gene expression is at first antagonized by endogenous repressors, the bone morphogenetic proteins (BMP-2 and/or BMP-4), (17) which favor epidermal fate; the latter are, however, inhibited in turn by chordin, (18,19) an extracellular matrix protein synthesized in the underyling dorsal mesoderm (Spemann s organizer), particularly in the notochord. The reduced inhibition leads to neural induction, (20) and to the formation of the neural plate. This basic mechanism is supplemented by dorsalizing, neuralizing, and antineuralizing contributions from other secreted factors such as activin, (21) noggin, (12,22) fibroblast growth factor (FGF), (23) or the hormone follistatin, (24) all of which originate in or near the notochord as well. After induction, neural plate homeogene expression becomes largely cell autonomous. (25) Under the concentrationdependent control of yet another notochord-secreted polypeptide, Sonic hedgehog(shh), (26,27) and subject to BMPmediated contact interactions with the epidermal ectoderm, homeobox genes such as Msx (7) and Nkx-2 (28) then become expressed and play a role in finer-grained dorsoventral subdivision of the neural plate, as do the Pax genes, whose expression becomes topographically diversified at this time. Along the dorsoventral axis, the situation for insects appears remarkably similar, (7,29) as long as one accepts that the embryo is turned upside down. Thus, in Drosophila, initial dorsoventral patterning occurs under the control of the secreted molecule decapentaplegic; hereafter, the proneural BioEssays

3 genes are activated in each segment of neuroectoderm, at locations precisely defined along the dorsoventral axis by pair-rule and dorsoventral polarity genes. Altogether, the scheme is quite analogous to that in Figure 1, with the orthologous gene name substitutions: Pax=paired, Nkx- 2=ventral nervous system defective (vnd), (30) Msx=muscle segment homeobox (msh), (31) BMP=decapentaplegic (DPP), (32) SHH=hedgehog (hh), and chordin=short gastrulation (sog). (33) It should be apparent from the foregoing discussion that the immediate upstream regulators of AS-C are highly conserved features of neurogenesis. On the other a BMP Pax-3 Nkx-2 BMP hand, the initial determination of neuroectoderm itself is probably a more variable process. DPP, which plays a central role in neural patterning, belongs to the transforming growth factor- (TGF- ) family. It is a morphogen molecule; i.e., (i) its distribution in the embryo is inhomogeneous; and (ii) it exerts differential control on its target genes expression, depending critically on concentration. (34) The extracellularly exported terminal of SHH is also a morphogen, crucial in determining ventral cell fates in the neural tube. (26) Two other molecules implicated in neural induction are proven (or putative) morphogens: activin and noggin. As to the hormone follistatin, its action is a function of concentration and this depends on the distance from its secretion site. Altogether, we consider it a reasonable premise that, in both vertebrates and insects, the initial step of neurogenesis is the net activation of the proneural genes effected by a distributed dorsalizing morphogen activity, modulated, in a second step, by another, ventralizing morpho- AS-C Notch Shh chordin N activin noggin follistatin Figure 1. Signaling in neural morphogenesis. a: Upstream of achaete-scute (AS-C).The AS-C complex of proneural genes occupies a central place in the signalling events leading to neurogenesis. The part of the chain lying upstream of the vertebrate homologues of AS-C is depicted in a simplified way. The proneural genes are turned on in the dorsal part of the epithelium by homeogenes such as Nkx-2, under the probable control of other homeogenes expressed over wide areas of the neural plate, such as Pax-3. The action of these homeogenes is antagonized by signals originating in ectoderm, mediated by members of the bone morphogenetic protein (BMP) family. These, in turn, are themselves inhibited by several factors originating in Spemann s organizer (in or near the notochord N): noggin, chordin, follistatin. Additional factors secreted by the organizer (e.g., activin) also intervene. As a result, a relatively diffuse neural plate (green color) inducing activity is established. The Sonic hedgehog signal, originating partly in the notochord, partly in the floor-plate of the neural plate itself, is involved in defining the ventralmost neuronal territories [(yellow color; medial and dorsal territories (blue) depend on additional ectodermal influences; we deal exclusively here with the ventralmost neurons]. In the case of invertebrates, this illustration should be inverted (ventral is up; otherwise, a similar picture prevails (see text). b: Downstream of AS-C. The hierarchical organization of the two genetic switches, which define the neural plate (green) and its neuronal (yellow) subterritories. The homeodomain proteins whose expression defines the neural plate (e.g., Nkx-2 or Pax-3) interact with other homeodomain proteins. Similarly, the AS-C gene products are bhlh transcription factors that interact with other such factors, in particular, members of the E(Spl) complex, hence a simple model for each switch; a more detailed picture of the neuronal switch is presented as an illustration in c. c: Model of the neuronal genetic switch, based on the observation that continued expression of certain E(spl) genes is incompatible with neural fate (see text), hence the hypothetical scheme presented here. (43) Members of AS-C and E(spl) form dimers among themselves; AS-C homodimers (orange) activate AS-C transcription (autocatalysis) and inhibit E(spl); when this occurs, the cell acquires proneural identity; E(spl) homodimers (purple) act in the opposite way to enforce an ectodermal phenotype. The AS-C and E(spl) promoters include other responsive elements (c,c ), permitting external control of the switch (see Fig. 2). 760 BioEssays 20.9

4 Figure 2. The lateral inhibition pathway. Two cell nuclei, n and n, in which the genetic switches operate as above (see Fig. 1b,1c), separated by cell membranes m and m. Promoters controlling the two switches (labeled Nkx-2 and AS-C) hold the key to the cell s genetic fate. Thus, in addition to including AS-C and E(spl)- responsive elements, the AS-C promoter mediates responses to the dorsalizing morphogen signalling pathway (green), to the the Sonic hedgehog (SHH) pathway (red gradient), and to the Notch receptor pathway (blue and purple). The action of the dorsalizing gradient occurs through the Nkx-2 gene. The neuralizing SHH gradient has an inhibitory effect on AS-C at large, as well as at small concentrations, an activating effect at intermediate concentrations. Notch is a membrane receptor for Delta, a gene activated downstream of AS-C; Notch is expressed over the whole neural plate (see Fig.1). When activated by Delta, Notch in an nearby cell signals an inhibition of the proneural genes, hence of Delta itself. When cells thus interacting are immersed in the two gradients of dorsalizing activity and SHH morphogen, a complex competition arises, leaving either no gene active (not shown, see later), the neural plate switch gene active by itself (green shaded nucleus) or both switches active (yellow shaded nucleus). + Nkx2 N + n' + AS-C dorsalising activity m' Notch Delta m Notch + Nkx2 N + _ Sonic hedgehog n _ AS-C m Notch gen which induces the floor-plate and ventral neuron types. In vertebrates, these morphogens themselves may be produced in the notochord and/or epidermal ectoderm; while in insects, it is more likely that they are released in neuroectoderm before or during mesoderm invagination. The lateral inhibition pathway Initially, transcription of the proneural genes is started over a large area, which is subsequently restricted by a mechanism of intercellular communication, giving rise to lateral inhibition. In Drosophila neurogenesis, synthesis of AS-C activates, directly or indirectly, transcription of Delta, a ligand for the receptor Notch. (35) (In vertebrates, there exists a homologous set of molecules. (36,37) ) It seems safe to assume that expression of the Notch receptor covers more or less uniformly the whole proneural territory; but inevitable local differences in signaling by Notch arise and quickly become amplified. This is because activation of Notch in cell 1 by Delta presented on a nearby cell 2 tends to inhibit AS-C (and Delta) expression in 1. Inhibition on cell 2 will diminish, and Delta signaling from 2 will rise even further. Because of such an intercellular feedback loop, the spatially graded AS-C activity becomes sharpened into a spatial ON/OFF distribution, (38) with topographically separate cells undergoing separate developmental fates: neural (AS-C and Delta expression) or epithelial (no such expression). Genetic determination Neural induction activates a topographically differentiated set of genes (among which the proneural genes) in the neural plate. How is this maintained when the inductive signal has subsided? The key to this problem is quite likely that the genes in question are members of large families of interacting transcription factors. Consider the Drosophila AS-C genes. They are basic helix-loop-helix (bhlh) transcription factors (TFs) and, as such, they are able to interact with other bhlh factors, such as neurod or neurogenin, (39 41) and in particular with TFs encoded by the Enhancer-of-Split (E(spl)) genes. (38,42) It has been suggested that AS-C genes and members of the E(spl) complex, by forming heterodimers and homodimers among themselves, cooperate in establishing proneural identity. One way in which this could happen is by a combination of autocatalysis and mutual inhibition of these genes, (43) which would build up a bistable genetic memory system. This BioEssays

5 establishes the possibility of embryonic cell determination, i.e., persistence of differentiated transcriptional states. Two major genetic switches of this type can be distinguished: the proneural switch just described, and the neuroectodermal switch, which is responsible for the differentiation of the neural plate itself. The latter may be surmised to consist of such genes as Pax-3 or Hox-b9 interacting with other homeobox and paired-box TFs. Mechanical effects: cell adhesion and motion Once their developmental fate is determined, neuroblasts proceed to delaminate. This may happen in several ways. In insects, cells delaminate individually and go on to form the discrete segmental ganglia. In vertebrates, two neurulation modes are known. (44,45) Primary neurulation occurs as neuroblasts form the thickened neural plate, which invaginates while the surrounding epithelium folds over it. The two so-called neural folds ultimately join, closing the neural tube while forming the neural crest. Secondary neurulation consists in the ingression of a neuroblastic cell mass followed by cavitation. Formation of the neural tube by secondary neurulation is observed in some organisms and may sometimes coexist with primary neurulation, occurring then in those parts of the neural tube that form last. The expression of various cell-adhesion molecules shows a characteristic pattern during the invagination process. (44 47) Thus, during neural tube formation, neural tissue progressively ceases presenting the E-cadherin cell adhesion molecule, while beginning the production N-cadherin instead, which plays a role in tube closure. Throughout this process, E-cadherin remains present on outer ectoderm cell membranes. (48) Remarkably, the product of the Hox-b9 gene, which is expressed throughout the posterior portion of the neural plate, has been shown to positively regulate N-CAM, the neural cell adhesion molecule. (49,50) Important differences also appear between the basal and the apical faces of the neuroepithelial cells. Thus, the detected concentrations of a cytoskeletal protein such as vimentin obey a time-dependent basal-to-apical gradient. (51) It can be surmised that, during neurulation, the two faces of the epithelium will acquire and develop very different behavior in terms of their motility. In vertebrates, complex movements of the epithelial cells interact with mechanical tissue properties in generating the neural tube. Such cell movements and rearrangements clearly occur under the influence of forces both intrinsic and extrinsic to the neural plate itself, and are at once coordinated with, and dependent on, the mitotic cycle. (52) We shall not aim here at describing these phenomena in detail. We restrict ourselves instead to a few basic data. Cell motions and shape modifications during neurulation occur both passively (through pushing and pulling by neighbor cells and the extracellular matrix) and by active cytoskeletal action. (51,53) Together with cell division and rearrangement, the resulting movement must generate, among other effects, some at least of the lateral pressure for neural tube buckling. In addition, the folding neural plate presents anchoring and hinge points, (44,52,54) which further enforce and stabilize morphogenesis. Most importantly for this process, epithelial cells form at all times a connected sheet held together by intercellular adherens and other junctions and by cohesive interactions with the basal lamina and extracellular matrix. This cohesiveness is fundamental for the shaping of the forming nervous system. Hypothesis: the connection between neural specification and cell motion How are cell adhesion and motion related to differential gene expression? Very few extant data bear on this question, and therefore the facts must be supplemented with reasonable hypotheses. It turns out that these are critical because the results are highly sensitive to certain aspects of the genemotion coupling. Thus, rather stringent experimental tests will be possible. That there is a link between the Notch Delta complex, cell adhesion, migration, and neuroblast delamination was proposed some time ago. (55) More recently, it has been observed that Notch, in conjunction with the segment polarity gene wingless, is involved in controlling both proliferation (mitosis) and delamination in the ventral neuroectoderm of Drosophila. (56,57) Neuroblast delamination is clearly correlated with the mitotic cycle, as it occurs shortly before cell division, and cytoskeletal changes during delamination resemble closely those seen in mitosis. Thus, there is some evidence that Notch Delta controls delamination in part by intervening in the regulation of the cell cycle itself. As against this, it must be mentioned that disrupting the Notch intracellular pathway does not always seem to affect cell movement. (58) For the sake of simplicity, we shall assume that cell shape changes and movement are regulated, albeit in a possibly very indirect way, either by Notch or by Delta or by both. To simplify matters even further, we consider that cytoskeletal motion is initiated in a cell-autonomous fashion; i.e., cell cell interactions do not intervene in establishing the cell motility, and each cell will tend to move according to its own internal level of expression of Notch and/or Delta. (Of course, the actual movements produced will be the result of an interaction between this cell-autonomous motility and the influence of local adhesion and other forces as produced, in particular, by other cells.) It is known that simple juxtaposition of ectodermal and neuroectodermal cells suffices to generate folding movements, (59) so that the assumption of cell autonomy may not be completely true. We would like to argue, however, that this will be of importance mainly for a detailed investigation of the neural folds, where juxtaposition does occur; and such is not our objective here. 762 BioEssays 20.9

6 Model We now propose a computer model that accounts plausibly for the unfolding of neurulation, based on the cellular and molecular processes just described. It is intended as a minimal, yet sufficient formal framework appropriate to a definite problem of large-scale morphogenesis. From a comparison between the biological premises above and the description below, the simplifications will be apparent. We present successively (i) the critical logical elements of the model as they are used to program a computer; and (ii) the computer simulations, their key parameters, and the results that unfold dynamically in two dimensions. (Full details are available in the program source files referred to earlier.) We begin with the spatial aspects of the model and the way in which cells and molecules are organized in a twodimensional sheet. We then turn to the gene families and their expression in the cell nucleus. Encoded by the genes are (i) transcription factors, which take part in the intracellular regulation networks; and (ii) intercellular signaling molecules, which are presented on the cell membranes. The consequences of such signaling upon cellular processes on the receiving side are described in terms of transcriptional control, cell adhesion, motion, and division. a b n' m' m n The embryonic slice For the sake of our computations, we examine the phenomena that take place in a thin slice transverse to the embryo. The model is essentially a digitized image of the slice, a video screen on which color-coded images of cells are projected and move in time. Computing power limits the screen to a definition of pixels. The color code used is described in Figure 3; thus, the color of a cell nucleus reflects the state of genetic activity within it, and the color and luminosity of cell membranes indicate the presence and local concentration of cell cell signaling molecules. Membrane and nuclear molecules are carried along during the motion of the objects bearing them, as the pixels representing the objects change. (The pixels on the slice may be considered to be composing what is technically known as a cellular automaton, whose state is exhibited by the pixel colors.) In addition, molecules may diffuse in the slice, i.e., they may leak to neighboring pixels, but the slice is closed : no material escapes or enters it. (Mathematically, this corresponds to free boundary conditions.) Of course, the two-dimensional transverse nature of the model is at best an approximation, as forces are certainly exerted along the rostrocaudal axis, and cells move along that axis. (60) The full three-dimensional morphogenesis will be dealt with in a forthcoming work. Genetic determination Genes are turned on or off in switch-like manner as described by binary variables G 0 (OFF) or1(on). The probability for a Figure 3. In the model, a two-dimensional transverse embryonic slice is studied in isolation. This slice is projected on a video screen, where cells, their membranes, and nuclei live and move. a: The space of the slice is partitioned in pixels forming a honeybee array. The pixels are color coded. Black pixels are extracellular matrix. Pixels belonging to a cell nucleus such as n or n are beige if no model gene is being transcribed in that nucleus, green if the neural plate gene Notch (see text) is active, and yellow if both the neural plate gene and the neuronal gene Delta are active. Transcription of a gene such as Notch, which encodes a membrane molecule, leads after a translation and translocation delay (arrows), to the presentation of Notch molecules on the membrane. Cell membranes are in various shades of blue (m, m ), the lighter colors indicating larger local concentrations of Delta. Molecules diffuse on the membrane (by hopping to neighboring pixels); receptor-ligand interactions take place between membranes when they come in contact. b: The pixels composing a cell can change in time (white arrows); this is cell motion. Restricting such motion are strong focal attachment points among cells (red circle). These may correspond to adherens junctions or to desmosomes. During membrane displacement, membrane-bound molecules such as receptors and ligands are transported with it. gene to be ON is a sigmoid function of its promoter occupation by TFs. Thus, as the strength of positive regulation overbalances negative regulation by a given amount, gene activity grows rapidly from basal level to saturation. Gene products BioEssays

7 are synthesized at rates proportional to the corresponding activity. The products of the TF genes are assumed to return to the nucleus after a delay caused by transcription, translation, and translocation. Determination of cell fate is under the control of the TFs. Two pairs of TFs are introduced, each composing a genetic switch. Thus, the proneural switch consists of Asc, the proneural factor, and E(spl). (We use underlined mnemonic names for the model genes. This does not imply complete identity with the actual homonymous genes.) Asc and E(spl) products form dimers asc asc, e(spl) e(spl), and asc e(spl). The homodimer asc asc enhances Asc transcription while repressing E(spl). e(spl) e(spl) does the converse, activating E(spl) and inhibiting Asc, while asc e(spl) is not active in this simple formalism. In addition, asc asc positively regulates the gene for a membrane ligand Delta. It is assumed that, at this stage, Delta expression is the hallmark of the neuronal phenotype. The second, neuroectodermal switch, is established by factors Hom neur (the neural plate homeogene) and Hom aux,an auxiliary homeogene. The same interactions are assumed to exist among the products of these genes as between those of Asc and E(spl), so that expression of one prevents expression of the other and conversely. Presentation on the cell membrane of Notch, the receptor for Delta and a marker of the neural plate, is triggered by the product of gene Hom neur. Note that the products of the membrane-bound signaling genes Delta and Notch are uniformly transported to the cell membrane. No distinction of apical and basal membranes will be introduced in this respect (see later). Morphogens Two morphogens act on the genetic switches; their spatially graded, pre-established concentration profiles provide positional information in the system. The setting up of a morphogen concentration gradient has been studied elsewhere. (61) The morphogens are BMPa and Shh. The effect of BMPa ( BMP activity ) is to inhibit transcription of the neuroectodermal gene Hom neur, i.e., to decrease the corresponding gene s ON probability. The concentration of BMPa is high everywhere, except close to the notochord, where it drops smoothly because dorsalizing factors originating in the notochord, such as chordin, antagonize the inhibitory action of BMP. The second morphogen, Shh, is responsible for the initial, relatively widespread, ventralmost region of expression of the proneural gene Asc, which it activates. (We deal solely with the differentiation of the ventralmost neuronal cell types, to the exclusion of those that are dorsal or intermediate.) The concentration of Shh has a peak near the notochord and is interpreted by cells as high, low, or intermediate, according to its value relative to two thresholds, in agreement with experiment. (26) Thus, at the midline (above the notochord), high concentrations of Shh repress the proneural gene; at intermediate levels (on both sides), activation takes place; while even further from the midline, repression is again assumed. Lateral inhibition pathway Cell membranes read at all times the state of neighboring membranes, for adhesion, motion, and signal transduction purposes. Transduction occurs as each membrane pixel i is examined for neighboring pixels j belonging to different cells. The amounts of ligand Delta in these neighbors are added up. The sum is then multiplied by the concentration of receptor Notch in i: it is assumed that the local activated receptor Notch* is proportional to this product. Notch* is finally summed over the whole cell membrane, and the resulting signal causes a reduction in the expression of the proneural gene Asc. Cell adhesion and motion Cell motion is introduced in the following manner. At the membrane, pixels may cease to belong to a cell (retraction) or may be added to it (launching exploratory filopodia ). The probabilities of these processes of subtraction or addition are adjusted according to the conditions encountered locally. It is assumed that neuroepithelial and presumptive neuronal cells each express a particular homophilic adhesion molecule. The membrane concentrations of these are proportional to the activities of the switch genes Notch and Delta, respectively. (In fact, Notch and Delta are themselves involved in cell adhesion (55) and are thus good candidates as the posited molecules.) Consider a cell 1, which displays, on its membrane, a particular adhesion molecule. Assume now that cell 1 has the possibility to grow by adding a particular pixel to itself, and that this addition results in cell 1 making contact with another cell 2. If 2 displays, on its membrane, a sufficient concentration of the same adhesion molecule as displayed by 1, the probability of effectively adding the pixel will be increased, relative to the probability of other possible pixel moves. The net result is an adhesion force, which acts on cells and parts of cells to bring and keep them together. (46) Epidermal cells, which do not express Notch, are restricted to a horizontal layer. On the other hand, neural plate and neuronal cells move more freely. Movement toward the basal side is favored. Cells are joined pairwise by strong focal adhesion points, and form a string of beads, much like actual epithelia when seen in transverse section. Pair relationships established at the beginning of a simulation cannot be rearranged. The adhesion points demarcate apical and basal faces in each cell. This distinction serves as a starting point for our modeling of cytoskeletal movement. Several cell biology models of motion have been proposed that potentially lead to epithelial invagination. (62) Here we limit ourselves to a single, simple mechanism that posits that neural plate and/or neuronal cells tend to undergo cortical contraction of their apical face, while they simultaneously expand their basal 764 BioEssays 20.9

8 face. These processes are implemented in the program by biasing the probabilities for pixel addition or subtraction from a cell. Thus, when pixels belonging to the apical face of a cell are removed from it with increased probability, apical constriction progressively ensues as the surface of the face diminishes, simulating the effects of an actual contraction force. In conformity with our major hypothesis, we assume that control over cell-cortical motion is ultimately exerted by the neural plate switch gene Notch and/or the proneural gene Asc. We shall see that which gene is dominant has dramatic implications for morphogenesis. The nucleus of each cell is periodically translated in order to coincide with the center of gravity of the cell. As all changes in the identities of those pixels composing a given cell arise from surface changes, this nucleus adjustment can be seen as a way to propagate surface movement to the nucleus by cytoplasmic viscosity and cytoskeletal dynamics. Cell Division In cell division (mitosis), the pixels previously occupied by the mother cell are split into two sets belonging each to a daughter. An important feature of cell division is anisotropy; i.e., the axis defined by the two daughter nuclei is not oriented in random fashion; instead, the axis has a greater probability of lying parallel to the line joining the two focal adhesion points on the mother cell membrane. Consequently, the new cells lie automatically in the plane of the epithelial sheet. Division itself occurs with a probability which is a function of cell size and type (depending on the expression of the switch genes Notch and Asc or lack thereof). As division occurs, all molecular species present must be distributed among daughters; this is done on the basis of equipartition. Note that a rudimentary mechanism for epigenetic inheritance must be implemented, so that each cell bequeaths to its daughters the transcriptional state of its nucleus. (Of course, we do not want to model here chromatin configurations or gene methylation.) This is particularly important just after division, when the complement of TF s in a daughter may not be sufficient yet to ensure continued expression or repression of the proper genes. As noted earlier, our model is two-dimensional, while it is well known that the neuroepithelium is rather fluid and that cells migrate along the rostrocaudal axis of the forming neural tube. (52,60) Division as introduced here can be seen in part as mitosis proper, and in part as a simplified way to model cell influx from the third (rostrocaudal) dimension. Computer simulations and results Two main sets of simulations have been performed. They differ essentially by the coupling of cell motion to the genetic switches. When cell movement is activated and modulated by the neuroectodermal switch, which is turned over the relatively widespread neural plate region, we observe the analogue of vertebrate primary or secondary neurulation, depending on the rate of cell division; coupling of cell motion to the proneural switch,on the other hand, gives rise to the delamination of discrete neuroblasts, as happens in the formation of the insect neural cord. The vertebrate neural tube: primary neurulation Consider the model embryo in transverse section (Fig. 4). We first study the case in which cell motion is turned on by the neural plate gene. It turns out that the observed phenomena will then appropriately describe the dorsal part of a vertebrate. Figure 4a shows the distribution of morphogenetic activities over the section, as postulated in the model. The green curve corresponds to BMPa, i.e., the activity that inhibits neural plate formation. BMPa is distributed in a shallow midline-centered gradient. Its concentration is high when far from the midline (in presumptive non-neural tissue), and is depressed near the midline (in the presumptive neural plate) by a chordin-type activity. The yellow curve indicates the (Sonic hedgehog-style) neurogenic gradient Shh. The remainder of Figure 4 shows simulated snapshots of the system, taken at successive times during a typical simulation. Cells start as a homogeneous epithelial sheet (Fig. 4b). As the morphogens act, neural plate genes are turned on (in cells in which this occurs, nuclei are depicted in green). Note that, while the inhibition gradient is shallow, the gene expression boundary is sharp. All neural plate cells express the Notch receptor. The neural plate cells are released from the molecular forces which maintain them in a sheet; they thus grow, and the epithelium thickens in a neural plate. Apical side membrane constriction and basal side expansion also take place, whose consequences will become clear shortly. Meanwhile (Fig. 4c), the neurogenic gradient acts and turns on the proneural genes (nuclei shown in yellow). This occurs in two patches which are, however, very close to one another in our simulations, and thus rapidly appear as a single one. These genes control neuronal identity, entailing a buildup in the concentration of Delta, the ligand for Notch, on their membrane (high Delta concentration on cell membranes is depicted by a light color). In cells that express Notch and bind Delta from neighbors, the proneural genes are then down-regulated, leading to a precise topographical assignment of isolated cells to neuronal fate (Fig. 4d). Thus, the model achieves accurate and reliable genetic determination of single cells at locations defined precisely by morphogenetic fields (yellow arrows). At this moment, the morphogen distribution has decayed, but the activity or inactivity of the neural plate genes and of the proneural genes is self-maintained through autocatalytic loops. Cells are committed at the genetic level. Hence, cells where, say, Asc is not expressed at this stage are not even responsive to the Shh morphogen. This is not because they BioEssays

9 Figure 4. Simulated formation of a neural tube (primary neurulation). The dorsal part of a transverse embryonic section is shown at successive times (dorsal is up). a: The morphogenetic activities involved. Green, inhibition of dorsalization. This is in a shallow gradient, weaker at the midline. Red, the Sonic hedgehog-type signal. The latter is interpreted relative to two threshold levels (see text), hence a signal for ventralmost neuron formation, which is maximal at the location of the yellow arrows. b: Reading the first gradient, under the influence of the dorsalization signal, the initial epithelial layer of cells breaks up into a central portion (the prospective neural plate) and non-neural ectoderm. Green, nuclei expressing Notch; blue, cell membranes; red, adherens junctions between adjacent cells. c: Reading the second (neuralizing) morphogen gradient. Yellow, nuclei expressing both Notch and its ligand Delta, the marker of presumptive neuronal territory. Light blue, membranes displaying the Delta ligand. The proneural territory is seen to become sharply delineated. Two proneural patches form, one near each maximum (yellow arrows), but they appear adjacent because the system examined is small. Trace of the maxima is not lost, however, as will become apparent below. The neural plate cells also begin to thicken, forming the neural plate. d: Sharper definition of neuronal territories due to lateral inhibition. Two isolated neuroblasts have become differentiated. Morphogen has decayed and the neural precursors are now autonomously committed. The neural plate starts invaginating because its cells constrict their apical face while expanding their basal face. e: Neural ingression proceeds, while epithelial cells grow over the neural cells, forming the neural folds. f: Tube folding begins under the joint effects of neural cells pulling downward and epithelial cells dividing and pushing the neural folds inward. g: Cells at the folds deform under the sheer mechanical forces they are subjected to. h: Folding almost complete. i: The neural tube is closed. j: The process described here is somewhat variable. The outcome of a different simulation, with all parameters assuming the same values, is depicted (cf. i). lack the appropriate receptor(s), (although the turning off of such receptor(s) may be part of the non-neuronal fate), but because the concentration of the concerned TFs is too large to be overturned. These TF high expression levels are transmitted to daughter cells, as is genetic commitment. Because of cell membrane differential expansion and contraction, neuroepithelium ingression starts (Fig.4e,f). Neural ingression is accompanied by a progressive further thickening near the edge of the neural plate, as ectoderm covers the plate (Fig. 4g,h). Because ectodermal cell movement here is limited to a horizontal layer, the model does not lead to very accentuated neural folds, but a refined version of it could clearly accommodate them. In Figure 4f i, we observe how the folds become closer, until the gap between them 766 BioEssays 20.9

10 Figure 5. Formation of a neuroblastic cell mass (secondary neurulation). The conditions are the same as in Fig. 4, except that the spatial range over which neural plate inhibition is weak has been decreased by a factor 2 (to reduce the neural plate size) and the rate of mitoses in neural plate tissue is 5 times higher. a: The extent of presumptive neural territory at the end of the initial phase is diminished. b: Neuronal and other cells begin to delaminate. c: The gap left by delaminating cells is reduced by epithelial cell divisions. Neural cells also divide, rapidly increasing the size of the invaginating cell mass. d: This mass remains at first homogeneous. e: The neural cells begin to cavitate (form an inner hollow space, or ependymal canal). f: This goes on, but extremely slowly; clearly, the model is too simple to encompass full cavitation. heals completely. Note too how cell shapes are affected at the folds, due to the mechanical stresses applied there by the combined ectodermal expansion (because of cell divisions) and neural tube movements. It is important to stress that the whole process, reproducible as it is in its global features, is nevertheless subject to quite a bit of variability in the details, as illustrated in Figure 4j (compare with Fig. 4i). Because of the small dimensions of the system we use for computation (in particular, the artificially small number of cells involved), it is clear that our simulations exaggerate such diversity effects. The sharpness of gradient reading that we observe leaves little doubt that variability would be greatly reduced in larger-scale simulations. The vertebrate neural tube: secondary neurulation We now divide the range of the neural disinhibition activity by a factor of 2 (the extent of the neural plate is thus reduced, as is appropriate for the caudal part of the embryo), and increase by a factor of about 5 the rate of division of the neural plate cells. The resulting behavior is shown in Figure 5. In sharp contrast to our previous simulations, we now observe the ingression of a neuroblastic mass. This resembles the initial steps of secondary neurulation. The model as it stands does not encompass the full subsequent cavitation of this mass, although a tendency to cavitation can be observed in Figure 5e,f. The insect neural cord Let us now assume that cell motion is coupled, not to the neural plate switch genes, but to those that signal a neuronal fate (i.e., Asc). The results are remarkably different (Fig. 6). At first, everything proceeds as in neurulation. A group of cells at the center of the system start to express the neural plate signal (Fig. 6a); in two nearby subgroups, the proneural genes then become active (Fig. 6b,c). This again turns on the lateral inhibition pathway for these genes; hence some cells progressively stop producing the neuronal signal. Ultimately, two discrete neuroblasts differentiate, whose membrane motions become specialized (i.e., they perform apical contraction and basal expansion). This leads to their delamination, at locations that are symmetric with respect to the midline (Fig. 6d f). Such behavior bears a close resemblance to the delamination of one line of ganglion precursors during neurogenesis in insects (provided the embryo is seen ventral side up). (In actuality there are, on each side of the embryo, three lines of delaminating ganglions, but our model is set up to encompass only one of these.) Just as in the vertebrate BioEssays

11 Figure 6. Formation of the neural cord of insects. Dorsal is down. a: Initial definition of proneural territory. b: Beginning of neuronal gene transcription in one cell (yellow). c: The same phenomenon occurs in two additional cells. d: The patches of neuronal territory are refined, under the effect of lateral inhibition. Transcription of Delta in the middle cell becomes inhibited: this cell reverts to ectodermal fate and ceases to delaminate. Two isolated neuroblasts remain and continue to delaminate. e: Neuroblasts delaminate further. f: The integrity of the ectodermal sheet is restored. neural tube case, variations of pattern can sometimes be observed from one experiment to the other, indicating that our simple model cannot quite account for the near-perfect reproducibility of the insect segmental ganglion pattern. These variations include imperfections in the symmetry of the pattern and/or delamination of neuroblast groups, rather than single, isolated cells. A brief discussion of neural tube defects in mammals and in human pathology One way to test the basic features of the model is to check whether it can generate some of the defective neural tube phenotypes observed in naturally occurring mutations, or in experimentally induced ones in particular gene knockout experiments. Among spontaneous mutations, those that have homologues in human congenital diseases are of course particularly interesting. A case in point is provided by the Pax-3 mutations giving rise to the splotch phenotypes in mouse (63) ; the affected animal s most conspicuous malformation is a failure of neural tube closure in the lumbosacral region. Mutations in the human homologue PAX-3 are implicated in Waardenburg syndrome type I. (64) Many of the defects in Waardenburg patients are similar to those of splotch mice. Among other effects, the mutations apparently alter the rate of cell division in neural epithelium. From the results we have presented, it is clear that, in our model, differences in mitotic rates can affect the success of neural tube closure. During the course of our simulations, we have observed many cases in which failure to close the tube was due to a lack of proper matching of the mitotic rates in neural and non-neural tissue (data not shown). The other defects we have observed as parameters varied (data not shown) were (i) absence of a neural plate (due to weak morphogen action); (ii) excess or absence of neurons (according to the strength of lateral inhibition); and (iii) failure to close due to excessive extent of the neural plate (because of excessive morphogen action, or excessive mitotic rate in neural tissue). The recent construction of a null mutant for HES-1, (65) a murine homologue of E(spl), is highly relevant in this context, for the mutant phenotype indeed presents an excess of neural tissue, and abnormalities of neural tube closure. The interpretation of these observations in the framework of our model is relatively straightforward: if the bending forces acting on the neural plate remain unchanged, and mitotic rates in the surrounding epithelium do not vary appreciably, it will be more problematic to bend a wider neural plate enough to achieve closure. 768 BioEssays 20.9