Reference Work Entry

Encyclopedia of Complexity and Systems Science

pp 524-548

Biological Development and Evolution, Complexity and Self-organization in

  • Stuart A. NewmanAffiliated withNew York Medical College
  • , Gabor ForgacsAffiliated withUniversity of Missouri

Glossary

Differential adhesion

The capacity of cells to adhere to each other in a cell type‐dependent manner. The strength of adhesion between two cells of type A typically differs from that between cells of type B. This may be due to differences either in the number or type of cell adhesion molecules.

Differential gene expression

The main regulatory basis of cell differentiation . Cells of different type in a given organism carry the same set of genes (the genome) but vary in which of these genes are active, that is, expressed.

Biochemical oscillation

The variation in the concentration of a given molecule in principle either in space or time, although typically the term is reserved for the latter.

Reaction-diffusion mechanism

A  conceptual framework for describing spatiotemporal pattern formation in a system of several interacting and diffusing chemical species.

Canalization

An evolved property of developmental pathways that permits the robust generation of a phenotype in the face of perturbations. The perturbations can be those internal to the organism, in the form of gene mutation or developmental noise, or external to it, in the form of environmental variability.

Definition of the Subject

Much work over the past half‐century in developmental and evolutionary biology has focused on a subset of an organism's components, itsgenes . The hierarchical regulatory relationships among genes have been a major emphasis in studies indevelopment, while the variation of genes has played a corresponding role in evolutionary studies. In the past decade, however, investigators haveincreasingly considered the part played by physical and dynamical properties of cells and tissues, and their molecular components, in producing biologicalcharacteristics over the course of ontogeny and phylogeny. Living cells and tissues encompass numerous interpenetrating multicomponent systems in whichdynamical interactions among intracellular gene products, metabolites, ions, etc., and interactions between cells, directly via theiradhesive surfaces, or indirectly via secreted extracellular matrix (ECM) molecules or diffusible signaling molecules (“morphogens”), generate topologically complex,three‐dimensional self‐perpetuating entities consisting of up to several hundred different cell types in elaborate arrangements. In thisdescription, the systems properties that give rise to organisms and their substructures, however, are nowhere specified in any “geneticprogram”.

While these “generic” (i. e., common to living and nonliving systems) physical and chemical‐dynamic processes contribute tothe production of form and pattern in all modern‐day organisms, it is likely that early in the evolution of multicellular organisms such processeswere even more efficacious in determining organismal forms. In particular, morphologies originally generated by physics and chemicaldynamics could have provided templates for genetic evolution that stabilized and reinforced (rather thaninnovated) multicellular body plans and organ forms. The hierarchical genetic control of development seen in modern organisms can thus be considered anoutcome of this evolutionary interplay between genetic change and generic physicochemical processes.

Introduction

The field of developmental biology has as its major concern embryogenesis : the generation of fully‐formed organisms from a fertilized egg, the zygote. Other issues in this field, organ regeneration and tissue repair in organisms that have already passed through the embryonic stages, have in common with embryogenesis three interrelatedphenomena: cell differentiation , the production of distinct cell types, cell patternformation , the generation of specific spatialarrangements of cells of different types, and morphogenesis, the molding and shaping of tissues [25]. The cells involved in these developmental processes and outcomes generally have the same genetic informationencoded in their DNA, the genome of the organism, so that the different cell behaviors are largely associated withdifferential gene expression.

Because of the ubiquity and importance of differential gene expression during development, and the fact that each type of organism has its own unique genome, a highly gene‐centered view of developmentprevailed for several decades after the discovery of DNA's capacity to encode information. In particular, development was held to be the unfolding ofa “genetic program” specific to each kind of organism and organ, based on differential gene expression. This view became standard despitethe fact that no convincing models had ever been presented for how genes or their products (proteins and RNA molecules) could alone build threedimensional shapes and forms, or even generate populations of cells that utilized the common pool of genetic information in different ways. By“alone” is meant without the help of physics and chemical dynamics, the scientific disciplines traditionally invoked to explain changes inshape, form, and chemical composition in nonliving material systems.

It has long been recognized, however, that biological systems, in addition to being repositories of genes, are also physicochemical systems, andthat phenomena first identified in the nonliving world can also provide models for biological processes. Indeed, at the level of structure and function ofbiomolecules and macromolecular assemblages such as membranes and molecular motors, biology has historically drawn on ideas from chemistry andphysics. More recently there has been intensified cooperation between biological and physical scientists at the level of complex biological systems,including developmental systems. The rise of systems developmental, and evolutionary‐developmental, biology required the generation by physical andinformation scientists of theoretical tools and computational power sufficient to model systems of great complexity. But also, and equally important, hasbeen the growing recognition by modern biologists that organisms are more than programmed expressions of theirgenes , and that the behavior of systems of many interacting components is neither obvious nor predictableon the basis of the behavior of their parts.

Since biology is increasingly studied at the systems level, there has also been new attention to the origination of these complex systems. In manyinstances, it is reasonable to assume that complexity and integration of subsystems in living organisms has evolved in the context of forms and functionsthat originally emerged (in evolutionary history) by simpler physicochemical means. Thus the elaborate system of balanced, antagonistic signalinginteractions that keep cell metabolism homeostatic, and embryogenesis on-track, can be seen as the result of accretion, by natural selection, ofstabilizing mechanisms for simpler physicochemical generative processes that would otherwise be less reliable.

In what follows we will give a fairly wide‐ranging, though hardly comprehensive, survey of the physicochemical processes organizing, andpresumed to have promoted the emergence of the complex systems underlying the multicellular development of animals.

Dynamic Multistability: Cell Differentiation

The early embryos of multicellular organisms are referred to as blastulae . These are typically hollow clusters of several dozen to several hundred cells that arise throughthe cleavage of the zygote (cell divisions without volume increase of the embryo). While the zygote is“totipotent” – it has the potential to give rise to any of the more than 200 specialized cell types (e. g., bone, cartilage,the various kinds of muscle, blood, and nerve cells) of the mature human body – its first few divisions generate cells that are“pluripotent” – capable of giving rise to only a limited range of cell types. These cells, in turn, diversify into ones withprogressively limited potency, ultimately generating all the (generally unipotent) specialized cells of the body [25].

The transition from wider to narrower developmental potency is referred to as determination. This stage of cellspecialization generally occurs with no overt change in the appearance of cells. Instead, subtle modifications, only discernable at the molecular level,set the altered cells on new and restricted developmental pathways. A later stage of cell specialization, referred to as differentiation , results in cells with vastlydifferent appearances and functional modifications – electrically excitable neurons with extended processes up to a meter long, bone andcartilage cells surrounded by solid matrices, red blood cells capable of soaking up and disbursing oxygen, and so forth.

Since each cell of the organism contains an identical set of genes (except for the egg and sperm andtheir immediate precursors, and some cells of the immune system), a fundamental question of development is how the same genetic instructions canproduce different types of cells. This question pertains to both determination and differentiation. Multicellular organisms solve the problem ofspecialization by activating a type‐specific subset of genes in each cell type.

The biochemical state of a cell can be defined as the listof all the different types of molecules contained within it, along with their concentrations. The dynamicalstate of a cell, like that of any dynamical system, residesin a multidimensional space, the “state space”, with dimensionality equal to the number of system variables (e. g.,chemical components) [96]. During the cell division cycle (i. e., the sequence ofchanges that produces two cells from one), also referred to as the cell cycle, the biochemicalstate changes periodically with time. (This, of course, assumesthat cells are not undergoing differentiation). If two cells have the same complement of molecules at corresponding stages of the cell cycle,then, they can be considered to be of the same differentiatedstate . The cell's biochemicalstate also has a spatial aspect – theconcentration of a given molecule might not be uniform throughout the cell. We will discuss an example of this related to Drosophila early development in Sect. “ Evolution of DevelopmentMechanisms”. The state of differentiation of the cell (itstype) can be identified with the collection of proteins it is capable of producing.

Of the estimated 25,000 human genes  [76],a large proportion constitutes the “housekeepinggenes ,” involved in functions common to all or most cellstypes. In contrast, a relatively small number of genes – possibly fewer than a thousand – specify the type of determinedor differentiated cells; these genes are developmentally regulated (i. e., turned on and off in anembryonic stage- and embryonic position‐dependent fashion) during embryogenesis. Cell type diversity is based to a great extent on sharptransitions in the dynamical state of embryonic cells, particularly withrespect to their developmentally‐regulated genes.

When a cell divides it inherits not just a set of genes and a particular mixture of molecular components, but also a dynamicalsystem at a particular dynamical state . Dynamicalstates of many‐component systems can betransient ,stable ,unstable , oscillatory, orchaotic  [96]. Thecell division cycle in the early stages of frog embryogenesis, for example, is thought to be controlled by a limitcycle oscillator [5]. A limit cycle is a continuum of dynamical states that define a stable orbit in the state space surrounding an unstable node, a node being a stationary (i. e., time‐independent) point, or steadystate , of the dynamical system [102]. The fact that cells can inherit dynamicalstates was demonstrated experimentally by Elowitz andLeibler [20]. These investigators used genetic engineering techniques to provide the bacteriumEscherichia coli with a set of feedback circuits involving transcriptional repressor proteins such thata biochemical oscillator not previously found in this organism was produced. Individual cells displayed a chemical oscillation witha period longer than the cell cycle. This implied that the dynamicalstate of the artificial oscillator was inherited across cell generations(if it had not, no periodicity distinct from that of the cell cycle would have been observed). Because the biochemical oscillation was not tied to thecell cycle oscillation, newly divided cells in successive generations found themselves at different phases of the engineered oscillation.

The ability of cells to pass on dynamical states (and not just“informational” macromolecules such as DNA) to their progeny has important implications for developmental regulation, since continuity andstability of a cell's biochemical identity is key to the performance of its role in a fully developed organism. Inheritance which does notdepend directly on genes is called “epigenetic inheritance” [68] and the biological or biochemicalstates inherited in this fashion are called“epigenetic states”. Althoughepigenetic states canbe determined by reversible chemical modifications of DNA [41], they can also represent alternativesteady states of a cell'snetwork of active or expressed genes [46]. The ability of cells to undergo transitions among a limited number of discrete, stable epigeneticstates and to propagate such decisions from one cell generation to the next is essential to the capacityof the embryo to generate diverse cell types.

All dividing cells exhibit oscillatory dynamical behavior in the subspace of the full state space whose coordinates are defined by cellcycle‐related molecules. In contrast, cells exhibit alternative stable steady states in the subspace defined by molecules related to states of celldetermination and differentiation . During development, a dividing cell might transmit itsparticular system state to each of its daughter cells, but it is also possible that some internal or external event accompanying cell division could pushone or both daughter cells out of the “basin of attraction” in which the precursor cell resided and into an alternative state. (The basin ofattraction of a stable node is the region of state space surrounding the node, in which all system trajectories, present in this region, terminate atthat node [96].

It follows that not every molecular species needs to be considered simultaneously in modeling a cell's transitions between alternativebiochemical states . Changes in the concentrations of the small moleculesinvolved in the cell's housekeeping functions such as energy metabolism and amino acid, nucleotide, and lipid synthesis, occur much more rapidly thanchanges in the pools of macromolecules such as RNAs and proteins. The latter class of molecules is indicative of the cell'sgene expression profile and can therefore be considered againsta metabolic background defined by the average concentrations of molecules of the former class. Most of a cell's activegenes are kept in the “on” state during the cell's lifetime, sincelike the metabolites they are also mainly involved in housekeeping functions. The pools of these “constitutively active”gene products can often be considered constant, with theirconcentrations entering into the dynamic description of the developing embryo as fixed parameters rather than variables. (See Goodwin [27] for an early discussion of separation of time scales in cell activities).

As mentioned above, it is primarily the regulated genes that areimportant to consider in analyzing determination and differentiation . And of these regulatedgenes , the most important ones for understanding cell type specification are those whose products controlthe activity of other genes.

Genes are regulated by a set of proteins called transcription factors. Like all proteins, these factors arethemselves gene products, in this case having the specific function of turning genes on and off. They do this by binding to specific sequences of DNAusually “upstream” of the gene's transcription start site, called the “promoter”. Transitions between cell types duringdevelopment are frequently controlled by the relative levels of transcription factors. Because the control of most developmentally‐regulated genesis a consequence of the synthesis of the factors that regulate their transcription, cell-type transitions can be driven by changes in the relativelevels of a fairly small number of transcription factors  [14]. We can thus gain insight into the dynamical basis of cell type switching (i. e., determination anddifferentiation ) by focusing on molecular circuits, ornetworks , consisting solely of transcription factors and thegenes that specify them. Networks in which the components mutually regulate one another's expression are termed “autoregulatory”. Althougha variety of autoregulatory transcription factor circuits appear during development, it is clear that such circuits will have different properties depending on their particular “wiringdiagrams”, that is the interaction patterns among their components.

Transcription factors can be classified either as activators, which bind to a site on a gene'spromoter, and enhance the rate of that gene's transcription over its basal rate, or repressors, which decrease the rateof a gene's transcription when bound to a site on its promoter. Repression can be competitive or noncompetitive. In the first case, therepressor will interfere with activator binding and can only depress the gene 's transcription rate to thebasal level. In the second case, the repressor acts independently of any activator and can therefore potentially depress the transcription rate belowbasal levels. The basal rate of transcription depends on constitutive transcription factors , housekeeping proteins which are distinct from those in the autoregulatory circuits that we consider below.

Networks of autoregulatory transcription factors constitute dynamical systems. Like such systems encountered in physics and mathematics they can productively be modeled as systems of ordinarydifferential equations (ODE). A classic approach, exemplified by the work of Keller [47], andmore recently by Cinquin and Demongeot [10], is to set up systems of ODEs representingexperimentally motivated topologies and kinetics of transcription factor interactions. The solutions of these systems of ODEs are then examined withrespect to stationary states, limit cycles , bifurcations, etc., under variations in initialconditions, external inputs and kinetic parameters. When considered a part of a multicellular aggregate, this single‐cell dynamicalsystem can switch between its intrinsic alternative states depending onsignals it experiences from its microenvironment – other such cells, the ECM, or in certain cases the external world.

In his analysis of developmental switching, Keller [47] used simulation methods to investigatethe behavior of several autoregulatory transcription factor networks with a range of wiring diagrams(Fig. 1). Each network was represented by a set of n coupledordinary differential equations – one for the concentration of each factor in the network – and thesteady‐state behaviors of the systems were explored. Thequestions asked were: how many stationary states exist; are they stable orunstable ?

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Figure 1

Six model genetic circuits discussed by Keller [47]. a Autoactivation by monomer X; b autoactivation by dimer X 2; c mutual activation by monomer Y and dimer X 2; d autoactivation by heterodimer XY; e mutual repression by monomers X and Y; f mutual repression by dimer X 2 and heterodimer XY. Activated and repressed states of gene expression are represented respectively by + and –. The various transcription factors (circles for activators and squares for repressors) bind to the promoters of the genes, the colors of which correspond to the transcription factors they specify. Based on Keller [47]; see original paper for details. Figure modified and reprinted, with permission, from [21]

One such network , designated as the “Mutual repression by dimer and heterodimer” (MRDH)(Fig. 1f), comprises the genes encoding the transcriptional repressor, X, and the gene encoding the protein, Y, and thus represents a two component network. Thestationary values of the two components are governed by the following equations:
$$ \frac{\mskip2mu\mathrm{d}[X]}{\text{d} t} = S_{X_B} - \big\{ d_X[X] + 2 d_{X_2} K_{X_2} [X]^2\\ + d_{XY} K_{XY}[X][Y] \big\} = 0 $$
(1)
$$ \frac{\mskip2mu\mathrm{d}[Y]}{\text{d} t} = \frac{1\!+\!\rho K_X K_{X_2} [X]^2}{1 + K_X K_{X_2}[X]^2} S_{Y_B} \\ - \left\{ d_Y [Y]\!+\!d_{XY} K_{XY} [X][Y] \right\}=0 \:, $$
(2)
where \( { [\dots] } \) represents concentrations of the components, the S's synthesis rates, and the d's decay constants for the indicated monomeric \( { ([X], [Y]) } \) and dimeric \( { ([X]^{2}) } \) species. (See Keller [47] for details).

It was found that if in the absence of the repressor X the rate of synthesis of protein Y is high, in its presence, the system described by Eqs. (1)and (2) exhibits three steadystates , as shown in Fig. 2. Steady states 1 and 3 are stable, thus could be considered as defining two distinct cell types, while steady state 2 isunstable. In an example using realistic kinetic constants, the steady‐state values of \( { [X] } \) and \( { [Y]} \) at the two stable steady states differ substantially from one another, showing that the dynamical properties ofthese autoregulatory networks of transcriptionfactors can provide the basis for generating stable alternative cell fates during earlydevelopment.

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Figure 2

The solutions of the steady‐state Eqs. (1) and (2), given in terms of the solutions \( { [X_0] } \) and \( { [Y_0] } \). Here \( { [X_0] } \) is defined as the steady state cellular level of monomer X produced in the presence of steady state cellular level \( { [Y_0] } \) of monomer Y by the rate of transcription \( { S_{X_0} } \). By definition (see Eq. (1)), \( S_{X_0} = d_{X} [X_0] + 2 d_{X_2} K_{X_2} [X_0]^2 + d_{XY} K_{XY} [X_0][Y_0] \). Since along the blue and red lines, respectively, \( { \mskip2mu\mathrm{d}[X]/\text{d} t\equiv [\dot{X}] =0 } \) and \( \mskip2mu\mathrm{d}[Y]/\text{d} t \equiv [\dot{Y}] = 0 \), the intersections of these curves correspond to the steady state solutions of the system of equations, Eqs. (1) and (2). Steady states 1 and 3 are stable , while steady state 2 is unstable . Based on Keller [47]; see original paper for details. Figure modified and reprinted, with permission, from [21]

The biological validity of Keller's model depends on whether switching between these alternativestates is predicted to occur under realistic conditions. By thiscriterion the model works: the microenvironment of a cell, containing an autoregulatory network of transcriptionfactors , could readily induce changes in the rate of synthesis of one or more of the factors viasignal transduction pathways that originate outside the cell (“outside‐in” signaling [24]). Moreover, the microenvironment can also affect the activity of transcriptionfactors in an autoregulatorynetwork by indirectly interfering with their localization in thecell's nucleus, where transcription takes place [59]. In addition, cell division may perturb thecellular levels of autoregulatory transcription factors , particularly if they or their mRNAs are unequally partitionedbetween the daughter cells. Any jump in the concentration of one or more factors in the autoregulatory system can bring it into a new basin ofattraction and thereby lead to a new stable cell state.

The Keller model shows that the existence of multiple steady states in an embryonic cell's state space makes it possible, in principle, for morethan one cell type to arise among its descendents. However this capability does not, by itself, provide the conditions under which such a potentiallydivergent cell population would actually be produced and persist as long as it is required.

Keller's is a single cell analysis. Another, less conventional, approach, acknowledges from the start the multicellular nature of developingorganisms. Here the dynamical attractors sought are ones that pertain to the multicellular system as a whole, which consists of multiple copies ofinitially identical model cells in interaction with one another [43,44].

The need for an inherently multicellular approach to the cell type switching problem is indicated by experimental observations that suggest thatcell differentiation depends on properties of cell aggregates rather than simply those ofindividual cells. For example, during muscle differentiation in the early frog embryo, the muscle precursor cells must be in contact with one anotherthroughout gastrulation (the set of rearrangements that establish the body's main tissue layersreferred to as the “germ layers”, the ectoderm, mesoderm and endoderm) in order to develop into terminally differentiatedmuscle [29].

The need for cells to act in groups in order to acquire new identities during development has been termed the “communityeffect ” [29]. This phenomenon isa developmental manifestation of the general property of cells and other dynamical systems of assuming one or another of their possible internalstates in a fashion that is dependent on inputs from their external environment. In the case noted above the external environment consists of othercells of the same genotype.

Kaneko, Yomo and co‐workers [43,44]have described a previously unknown chemical‐dynamic process, termed “isologous diversification”, by which replicate copies of thesame dynamical system (i. e., cells of the same initial type) can undergo stabledifferentiation simply by virtue of exchanging chemical substances with one another. This differsfrom Keller's model described above in that the final state achieved exists only in the phase space of the collective “multicellular” system.Whereas the distinct local states of each cell within the collectivity are mutually reinforcing, these local states are not necessarily attractors of thedynamical system representing the individual cell, as they are in Keller's model. The Kaneko–Yomo system thus provides a model for thecommunity effect .

The following simple version of the model, based on Kaneko and Yomo [44], was initiallypresented in Forgacs and Newman [21]. Improvements and generalizations of the model presented insubsequent publications [43] do not change its qualitative features.

Consider a system of originally identical cells with intra- and inter-cell dynamics, which incorporate cell growth, cell division and celldeath (for the general scheme of the model, see Fig. 3a). The dynamical variables are the concentrationsof molecular species (“chemicals”) inside and outside the cells. The criterion by which differentiated cells are distinguished is the averageof the intracellular concentrations of these chemicals (over the cell cycle). Cells are assumed to interact with each other through their effect on theintercellular concentrations of the chemicals A and B (only two areconsidered in this simplified model). Chemicals enter the cells by either active transport ordiffusion . It is further assumed that a source chemical S issupplied by a flow from an external tank to the chamber containing the cells.

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Figure 3

a General scheme of the model of Kaneko and Yomo. The concentrations of each chemical may differ in the various cells (cell i is shown in the center) but some (P in the example) may have a fixed value in the extracellular environment. External chemicals can enter the cells by passive diffusion or active transport. The concentration of any chemical inside a given cell depends on chemical reactions in which other chemicals are precursors or products (solid arrows) or cofactors (dashed arrow). Once cell division has taken place by the synthesis of DNA (one of the “chemicals”) exceeding a threshold, cells communicate with one another by exchange of transportable chemicals. b Schematic representation of the intracellular dynamics of a simple version of the Kaneko–Yomo model. Red arrows symbolize catalysis. The variables \( { x_i^A(t),x_i^B(t),x_i^S(t) } \) and \( { E_i^A, E_i^B, E^S } \) denote respectively the concentrations of chemicals A, B and S and their enzymes in the ith cell, as described in the text. Reprinted, with permission, from [21]

Kaneko and Yomo [44] consider cell division to be equivalent to the accumulation ofa threshold quantity of DNA. To avoid infinite growth in cell number, a condition for cell death has to also be imposed. It is assumed thata cell will die if the amount of chemicals A and B in its interior is below the“starvation” threshold.

The system described can be expressed as the following set of equations (see also Fig. 3b):
$$ \frac{\text{d} x_i^S}{\text{d} t} = -E^S x_i^S + \text{Transp}_i^S + \text{Diff}_i^S $$
(3)
$$ \frac{\text{d} x_i^A}{\text{d} t} = (e_B x_i^B)x_i^B -(e_A x_i^B)x_i^A + E^S x_i^S + \text{Transp}_i^A + \text{Diff}_i^A $$
(4)
$$ \frac{\text{d} x_i^B}{\text{d} t} = (e_A x_i^B)x_i^A -(e_B x_i^B)x_i^B - kx_i^B + \text{Transp}_i^B + \text{Diff}_i^B $$
(5)
$$ \frac{\text{d} X^S}{\text{d} t} = f\left( \overline{X^S} - X^S \right) - \sum\limits_{i=1}^N \left( \text{Transp}_i^S + \text{Diff}_i^S \right) \:, $$
(6)
Here the x i are concentrations of the various chemicals in the ith cell, X S the external concentration of the source chemical. E S is the (constant) concentration in each cell of an enzyme that converts S into A, which in turn is catalyzed by the enzyme (with concentration \( { E_i^A = e_A x_i^B } \)) to produce B. B is catalyzed by an enzyme (with concentration \( { E_i^B =e_B x_i^B } \)) to produce A and it also produces DNA (at a rate k). Transp and Diff are respectively active transport and diffusion functions, which depend on both the intracellular (x i ) and extracellular (X i ) concentrations. (See Forgacs and Newman [21] for details).
Simulations based on the above model and its generalizations, using a larger number of chemicals [43], led to the following general features, which are likely to pertain to real, interacting cells as well:
  1. 1.

    As the model cells replicate (by division) and interact with one another, eventually multiple biochemical states corresponding to distinct cell types appear. The different types are related to each other by a hierarchical structure in which one cell type stands at the apex, cell types derived from it stand at subnodes, and so on. Such pathways of generation of cell type, which are seen in real embryonic systems, are referred to as developmental lineages.

     
  2. 2.

    The hierarchical structure appears gradually. Up to a certain number of cells (which depends on the model parameters), all cells have the same biochemical state (Fig. 4a). When the total number of cells rises above a certain threshold value, the state with identical cells is no longer stable. Small differences between cells first introduced by random fluctuations in chemical concentrations start to be amplified. For example, synchrony of biochemical oscillations in different cells of the cluster may break down (Fig. 4b). Ultimately, the population splits into a few groups (“dynamical clusters”), with the phase of the oscillator in each group being offset from that in other groups, like groups of identical clocks in different time zones.

     
  3. 3.

    When the ratio of the number of cells in the distinct clusters falls within some range (depending on model parameters), the differences in intracellular biochemical dynamics are mutually stabilized by cell-cell interactions.

     
  4. 4.

    With further increase of cell number, the average concentrations of the chemicals over the cell cycle become different (Fig. 4c). That is to say, groups of cells come to differ not only in the phases of the same biochemical oscillations, but also in their average chemical composition integrated over the entire lifetimes of the cells. After the formation of cell types, the chemical compositions of each group are inherited by their daughter cells (Fig. 4d).

     
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Figure 4

Schematic representation of the differentiation scenario in the isologous diversification model of Kaneko and Yomo. When there are N cells and C chemicals (\( { C=3 } \) in the figure), the state space of the multicellular system is \( { N \times C } \) dimensional. A point in this space corresponds to the instantaneous value of all the chemicals and in each cell the orbits represent the evolution of these concentrations in the multicellular system. As long as the biochemical states of the replicating cells are identical, points along the orbit could characterize the synchronous states of the cells. This is illustrated in panel a, where the four circles, representing cells with the same phase and magnitude of their chemicals, overlap. With further replication, cells with differing biochemical states appear. First, chemicals in different cells differ only in their phases, thus the circles in panel b still fall on the same orbit, albeit are well separated in space. With further increase in cell number differentiation takes place: not only the phases but also the magnitudes (i. e., the averages over the cell cycle) of the chemicals in different cells will differ. The two orbits in panel c represent two distinct cell types, each different from the original cell type shown in panels a and b. Panel d illustrates the “breeding true” of the differentiated cells. After the formation of distinct cell types, the chemical compositions of each group are inherited by their daughter cells. That is, chemical compositions of cells are recursive over subsequent divisions as the result of stabilizing interactions. Cell division is represented here by an arrow from a progenitor cell to its progeny. Adapted, with changes, from Kaneko [42]. Reprinted, with permission, from [21]

In contrast to the Keller model in which different cell types represent a choice among basins of attraction fora multi‐attractor system, with external influences having the potential to bias such preset alternatives, in the Kaneko–Yomo modelinteractions between cells can give rise to stable intracellular states, which would not exist without such interactions. Isologous diversification thusprovides a plausible model for the community effect  [29]. It is reasonable to expect that both intrinsic multistability of a dynamical system of the sort analyzed byKeller, and interaction‐dependent multistability, as described by Kaneko, Yomo, and coworkers, based as they are on generic properties of complexdynamical systems, are utilized in initiating developmental decisions in various contexts in different organisms.

Differential Adhesion: Gastrulation

As cells differentiate they become biochemically and structurally specialized and capable of forming multicellular structures with characteristicshapes, such as those of the earliest developmental stages, blastulae and multilayered gastrulae . Later during development tubular vessels, ducts and crypts emerge. The appearance and functionof these specialized structures reflect, among other things, differences in the ability of cells to adhere to each other and the distinct mechanisms bywhich they do so. The distinct adhesion molecules expressed by differentiating cells thus mobilize physical forces to produce stereotypical multicellularstructures.

The organization of tissues is determined not only by the chemical nature of the cells' adhesion molecules but also the distribution of thesemolecules on the cell surface. Epithelioid cells express cell adhesion molecules (CAMs ),such as cadherins, uniformly over their surfaces and tend to form solid cell masses. Epithelial cells, which form two dimensional sheetsmust have CAMs predominantly along their lateral surfaces, whereas substrate adhesion molecules (SAMs), suchas integrins, must populate their basal surfaces, along which interaction with the planar ECM , the basallamina, is carried out. Such distribution of CAMs and SAMs rendersepithelial cells polarized. Finally, mesenchymal cells express SAMs over their surfacesby which they interact with interstitial ECM .

Adhesion enters into the phenomena of embryonic development in several distinct ways. The first, and most straightforward way, is in simply holdingtissues together. Whereas mature tissues contain the definitive, relatively long-lived forms ofCAM ‐containing junctions, during early development the CAM‐containing junctions are present inapparently immature forms [17], consistent with the provisional arrangement of cells and theircapacity to rearrange during these stages.

The other roles for adhesion during development are based on its modulation – the phenomenon of differentialadhesion. The regulated spatiotemporal modulation of adhesion is an important driving force for major morphogenetic transitions duringembryogenesis. The simplest form of this is the detachment of cell populations from existing tissues. This is usually followed by their relocation. Butmodulation of adhesive strength without complete detachment also has morphogenetic consequences,whether it occurs locally, on the scale of the single cell surface, or more globally, on the scale of whole cells within a common tissue.

Polar expression of CAMs can lead rather directly tomorphogenetic change, as illustrated in Fig. 5. Inthe process of differentiation some of the originally non‐polarized cells may lose theirCAMs along part of their surface, thus preventing them from adhering to one another at thosesites [98]. If the cells move around randomly, maximizing their contacts with one another inaccordance with this constraint, a hollow region (a lumen ) will naturally arise.

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Figure 5

Schematic illustration of lumen formation by polarized cells expressing cell adhesion molecules only on restricted parts of their surface. The shading in the eight cells in the middle panel represents the lack of adhesion molecules on corresponding regions of the cells. As a consequence, if minimization of configurational energy is the driving force in cell rearrangement, a lumen , shown on the right is bound to appear. (Based on Newman [62]) Reprinted, with permission, from [21]

One of the most dramatic morphogenetic processes exhibited by embryonic cells is sorting, theability of cells of distinct types to segregate into distinct tissues which do not intermix at their common boundary. Steinberg postulated that cells ofdifferent origin adhere to each other with different strengths and, in analogy with immiscible liquids such as oil and water, undergo a process ofphase separation in which the final configuration corresponds to the minimum of interfacial and surface free energies [93]. (Here the different tissues play a role analogous to liquids and the constituent cells mimic the moleculesof the liquid). This “differential adhesion hypothesis” (DAH) was expressed inquantitative terms by Phillips [77] based on geometric analysis of surface and interfacialtensions of immiscible droplets of liquids. According to the DAH, thefinal “phase‐separated” state of two adjacent tissues is an equilibrium configuration not dependent on the pathway by which it wasachieved. That is, it will be the same whether arrived at by fusion of two intact fragments of tissue or by the sorting out of their respective cells froma binary mixture (Fig. 6). Another implication of theDAH is that tissue engulfment relationships should form a hierarchy: if tissue A engulfs tissue B and B engulfs C in separate experiments, it follows that A will engulf Cif that experiment is performed. Finally, the DAH predicts that the values of tissue surfacetensions should fall in a quantitative order that corresponds to theengulfment hierarchy. Each of these predictions of the DAH has been amply confirmedexperimentally [19,21,22,93].

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Figure 6

Different paths by which two immiscible liquids or cell aggregates (composed of cells with differing adhesive properties) may arrive at the same equilibrium state . The path on the left shows sorting or nucleation, which proceeds through the gradual coalescence of groups of cells. The path on the right corresponds to engulfment, which occurs through spreading. Reprinted, with permission, from [21]

By the time the blastula has formed, the embryo already contains, or begins to generate,a number of differentiated cell types. Insofar as these cell types have or acquire distinct adhesive properties, compartmentalization or other formsof regional segregation start taking place. This regionalization, accompanied by the collective movement of the resulting cell masses – that iscommon to all forms of gastrulation  – gives rise to embryos consisting of two or threegerm layers along with some subsidiary populations of cells.

To understand how cells can rearrange by differential adhesion it is useful to describe the notion of the “work of adhesion”. Considera unit interfacial area between two materials A and B immersed ina medium, denoted by M (which in particular could be vacuum or, in the case of tissues, the extracellular mediumor tissue culture medium). We define the work of adhesion w AB as the energy input required to separate A and B across the unit area inmedium M. We can imagine such a unit area to be formed in the following way. First, we separatea rectangular column of A and B to produce two free unit surfaces ofeach substance (Fig. 7). This requires w AA and w BB amounts ofwork, respectively. These quantities are called the works of cohesion. (Note that the magnitudes of the work of adhesion and cohesion depend on themedium). We then combine these pieces to end up with two unit interfacial areas between A and B as shown in Fig. 7. Thus the total work, \( { \Delta _{AB} } \), needed to produce a unitinterfacial area between A and B is given by
$$ \Delta_{AB} =\tfrac{1}{2}(w_{AA} +w_{BB})-w_{AB} $$
(7)
The quantity \( { \Delta_{AB} } \) is called the interfacial energy and Eq. (7) is known as the Dupré equation [39]. If the interface is formed by two immiscible liquids then Eq. (7) can readily be expressed in terms of liquid surface and interfacial tensions . By its definition the surface tension is the energy required to increase the surface of the liquid by one unit of area. Since the works w AA and w BB create two units of area, we obtain
$$ \sigma_{AB} =\sigma_{AM} +\sigma_{BM} -w_{AB}\:, $$
(8)
where \( { \sigma_{AM}, \sigma_{BM} } \) and \( { \sigma_{AB} } \) are respectively the surface tensions of liquids A and B and their mutual interfacial tension [39]. (Whereas for solids \( { \Delta_{AB} } \) depends on the amount of interfacial area between A and B already formed, for liquids, \( { \sigma_{AB} } \) does not). Note that immiscibility of A and B implies \( { \sigma_{AB} > 0 } \). If, on the contrary, \( { \sigma_{AB}\le 0 } \), it is energetically more beneficial for the molecules of liquid A to be surrounded by molecules of liquid B, and vice versa; that is, A and B are miscible.
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Figure 7

Schematic illustration of creation of an interface between two materials A and B, immersed in a common medium. In the two-step process shown, first free interfaces of materials A or B are produced (middle panel), which requires the separation of their corresponding subunits (molecules, cells) from one another, and thus involves the works of cohesion, \( { w_{AA} } \) and w BB . In the second step the free interfaces are combined to form the AB interface (by rearranging the A and B blocks; right panel). The separation of A and B requires the work of adhesion, w AB . If the cross‐sectional area of columns A and B is of unit magnitude, then the operation shown results in two units of interfacial area between A and B. Reprinted, with permission, from [21]

If we now invoke the liquid‐like behavior of tissues, we can apply Eq. (7) orEq. (8) to obtain the conditions for sorting in terms of the w's orσ's. We imagine the cells of tissues A and B to be initially randomlyintermixed and surrounded by tissue culture medium and allow them to sort, as discussed above. Let us assume that tissue A is the more cohesive one. This implies that w AA is the largest of the three quantities on the right hand side of Eq. (7). In the energetically most favorable configuration at the end of the sorting process cells of tissue A form a sphere, the configuration in which they have minimal contact with their environment and maximal contact with eachother. Then, depending on the relative magnitudes of the w's, the sphere oftissue B may completely or partially envelop the sphere of tissue A or thetwo spheres may separate (Fig. 8) [21,93].

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Figure 8

Geometric configurations of immiscible liquids A (represented by the interior smaller sphere in the left panel) and B (represented by the larger sphere in the left panel, and the corresponding relations between the works of cohesion and adhesion. It is assumed that A is more cohesive than B: \( { w_{AA} >w_{BB} } \) and \( { \sigma_{AM} >\sigma _{BM} } \) (M denotes the surrounding medium). The left and middle panels correspond respectively to complete and partial envelopment. Figure modified and reprinted, with permission, from [21]

Biochemical Oscillations: Segmentation

A wide variety of animal types, ranging across groups as diverse as insects, annelids (e. g., earthworms), and vertebrates, undergo segmentation early indevelopment, whereby the embryo, or a major portion of it, becomes subdivided into a series of tissue modules [25]. These modules typically appear similar to each other when initially formed; later they may follow distinctdevelopmental fates and the original segmental organization may be all but obscured in the adult form. Somite formation (or somitogenesis) isa segmentation process in vertebrate embryos in which the tissue to either side of the centralaxis of the embryo (where the backbone will eventually form) becomes organized into parallel blocks of tissue.

Somitogenesis takes place in a sequential fashion. The first somite begins forming as a distinct cluster of cells in the anterior region(towards the head) of the embryo's body. Each new somite forms just posterior (towards the tail) to the previous one, budding off from the anteriorportion of the unsegmented presomitic mesoderm (PSM) (Fig. 9). Eventually, 50 (chick), 65 (mouse), or asmany as 500 (certain snakes) of these segments will form.

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Figure 9

Model proposed by Pourquié for segment formation in vertebrates, based on mouse and chick data. A gradient of \( { FGF8 } \) (see text), shown in black, regresses posteriorly during somitogenesis. The anterior boundary of the gradient defines the determination front, which corresponds to the position of the wavefront (thick black line). (A coordinately‐expressed gradient of \( { Wnt3A } \) plays a similar role; Aulehla et al. [2]). Oscillatory (i. e., waxing and waning with developmental stage) expression of chairy1 and related genes is shown in red. Expression of genes of the Mesp family, which encode transcription factors involved in somite boundary formation, is shown in green. (Reprinted, with permission, from Pourquié [78]; see original paper for details)

In the late nineteeth century the biologist William Bateson speculated that the formation of repetitive blocks of tissue, such as the somites ofvertebrates or the segments of earthworms might be produced by an oscillatory process inherent to developing tissues [2,65]. More recently, Pourquié and coworkers made the significantobservation that the gene c‑hairy1, which specifies a transcription factor, is expressed in the PSM of avianembryos in cyclic waves whose temporal periodicity corresponds to the formation time of one somite [72,78] (Fig. 9).The c‑hairy1 mRNA and protein product are expressed in a temporally‐periodic fashion in individualcells, but since the phase of the oscillator is different at different points along the embryo's axis, the areas of maximal expression sweep along theaxis in a periodic fashion.

Experimental evidence suggests that somite boundaries form when cells which have left a posterior growth zone move sufficiently far away froma source of a diffusible protein known as fibroblast growth factor 8 (FGF8) in the tailbud at the posterior end of the embryo [18]. The FGF gradient thus acts as a “gate” that, when its low end coincides with a particularphase of the segmentation clock, results in formation of a boundary [18,78]. The general features of this mechanism (called the “clock and wavefront” model) were predicted on thebasis of dynamical principles two decades before there was any direct evidence for a somitic oscillator [13].

During somitogenesis in the zebrafish a pair of transcription factors known as her1 and her7, which are related to chicken hairy1 (see above), oscillate in the PSM in a similarfashion, as does the cell surface signaling ligand delta C. Lewis [52] has suggested that her1 and her7 constitute an autoregulatory transcriptionfactor gene circuit of the sort treated byKeller [47] (see Sect. “ Dynamic Multistability: CellDifferentiation”, above), and are the core components of the somitic oscillator inzebrafish. He also hypothesizes that deltaC, whose signaling function is realized by activating the Notch receptors on adjacent cells, isa downstream effector of this oscillation. The two her genes negatively regulate their ownexpression [33,71] and are positively regulated bysignaling via Notch [71]. Certain additional experimental results [34] led Lewis to the conclusion that signaling by the Notch pathway, usually considered to act in the determination ofcell fate [1] in this case acts to keep cells in the segment‐generating growth zone insynchrony [52]. Such synchrony has been experimentally confirmed in chickenembryos [79,94].

Lewis [52] and Monk [58] haveindependently provided a simple mechanism for the oscillatory expression of the her1 and her7 genes, which we briefly summarize here. The model is based on the assumption,mentioned above, that there exists a feedback loop in which the Her1 and Her7 proteins directly bind to the regulatory DNA of their own genes toinhibit transcription. Also incorporated into the model is the recognition that there is always a delay between the initiation of transcription andthe initiation of translation, \( { T_m } \)(since it takes time for the mRNA molecule to translocate into the cytoplasm), as well as between the initiation of translation and the emergence ofa complete functional protein molecule, \( { T_p } \) (see Fig. 10a).

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Figure 10

Cell autonomous gene expression oscillator for zebrafish somitogenesis. a Molecular control circuitry for a single gene, her1, whose protein product acts as a homodimer to inhibit her1 expression. b Computed behavior for the system in a (defined by Eqs. (9) and (10)) in terms of the number of mRNA molecules per cell in red and protein molecules in blue. Parameter values were chosen appropriate for the her1 homodimer oscillator based on experimental results. (Reprinted from Lewis [52] with permission from Elsevier; see original paper for details)

These ingredients are put into mathematical language in the following way. For a given autoregulatory gene, let m(t) be the number of mRNA molecules in a cell at time t and let p(t) be the number of the corresponding proteinmolecules. The rate of change of m and p, are then assumed to obey thefollowing equations
$$ \frac{\text{d} p(t)}{\text{d} t} = am(t-T_p)-bp(t) $$
(9)
$$ \frac{\text{d} m(t)}{\text{d} t} = f\left[ p(t-T_m ) \right]-cm(t)\:. $$
(10)
Here the constants b and c are the decay rates of the protein and its mRNA, respectively, a is the rate of production of new protein molecules and f(p) is the rate of production of new mRNA molecules. The function f(p) is assumed to be a decreasing function of the amount of protein (for its form see Lewis [52]. The results of simulations turned out to be quite insensitive to the specific form of f(p)).

The above delay differential equations were numerically solved for her1 and her7 (for which Lewis was able to estimate the values of all the model parameters in Eqs. (9) and (10) using experimental results). The solutions indeed exhibitsustained oscillations in the concentration of Her1 and Her7, with the predicted periods close to the observed ones (Fig. 10b). In a subsequent study Lewis and his coworkers have experimentally confirmed the main features of thisoscillatory model forsegmentation  [26].

Reaction-Diffusion Mechanisms: Body AxisFormation

The nonuniform distribution of any chemical substance, whatever the mechanism of its formation, can clearly provide spatial information tocells. For at least a century embryologists have considered models for pattern formation and its regulation that employdiffusion gradients [25]. Only in the last decade, however, has convincing evidence been produced that this mechanism is utilized in earlydevelopment. The prime evidence comes from studies of mesoderm induction, a key event precedinggastrulation in the frog Xenopus. Nieuwkoop [69] originally showed that mesoderm (the middle of the three germ layers in the three‐layeredgastrula – the one that gives rise to muscle, skeletal tissue, and blood) only appeared when tissue from the upper half of an early embryo(“animal cap”) was juxtaposed with tissue from the lower half of the embryo (“vegetal pole”). By themselves, animal cap andvegetal pole cells, respectively, only produce ectoderm, which gives rise to skin and nervous tissue, and endoderm, which gives rise to the intestinallining. Later it was found that several released, soluble, factors of the TGF-β protein superfamily and the FGF protein family could substitute forthe inducing vegetal pole cells [28]. Both TGF-β [55] and FGFs [9] can diffuse over several cell diameters.

While none of this proves beyond question that simple diffusion of such released signal molecules(called “morphogens”) between and among cells, rather than some other, cell‐dependent mechanism, actually establishes the gradients inquestion, work by Lander and co‐workers, among others [49], has shown thatdiffusion‐like processes, mediated by secreted molecules interacting with cell surfaces and ECMs , arelikely to be involved in much developmental patterning. Analysis of such effects can best be performed by considering generalized reaction‐diffusionsystems, which we now describe (see [21] for additional details).

The rate of change in the concentrations of n interacting molecular species (c i , \( { i=1,2,\dots,n } \)) is determined by their reaction kinetics and can be expressed in termsof ordinary differential equations
$$ \frac{\text{d} c_i }{\text{d} t}=F_i (c_1 ,c_2,\dots,c_n )\:. $$
(11)
The explicit form of the functions F i in Eq. (11) depends on the details of the reactions. Spatial inhomogeneities also cause time variations in the concentrations even in the absence of chemical reactions. If these inhomogeneities are governed by diffusion , then in one spatial dimension,
$$ \frac{\partial c_i }{\partial t} = D_i \frac{\partial^2 c_i }{\partial x^2}\:. $$
(12)
Here D i is the diffusion coefficient of the ith species. In general, both diffusion and reactions contribute to the change in concentration and the time dependence of the c i 's is governed by reaction‐diffusion equations
$$ \frac{\partial c_i }{\partial t} = D_i \frac{\partial^2 c_i }{\partial x^2} + F_i(c_1 ,c_2,\dots,c_n)\:. $$
(13)
Reaction‐diffusion systems exhibit characteristic parameter‐dependent bifurcations (the “Turing instability”), which are thought to serve as the basis for pattern formation in several embryonic systems, including butterfly wing spots, stripes on fish skin, distribution of feathers on the skin of birds, the skeleton of the vertebrate limb, and the primary axis of the developing vertebrate embryo [21].

Gastrulation in the frog embryo is initiated by the formation of an indentation, the“blastopore”, through which the surrounding cells invaginate, or tuck into, to the hollowblastula . Spemann and Mangold [91] discovered thatthe anterior blastopore lip constitutes an organizer: a population of cells that directs the movement of othercells. The action of the Spemann–Mangold organizer ultimately leads to the formation of the notochord, the rod of connective tissue that firstdefines the anteroposterior body axis, and to either side of which the somites later appear (see Sect. “ BiochemicalOscillations: Segmentation”, above). These investigators also found that an embryo with an organizer from another embryo at the samestage transplanted at some distance from its own organizer would form two axes, and conjoined twins would result. Other classes of vertebrates havesimilarly acting organizers.

A property of this tissue is that if it is removed, adjacent cells differentiate into organizer cells and take up its role. This indicates thatone of the functions of the organizer is to suppress nearby cells with similar potential from exercising it. This makes the body axis a partlyself‐organizing system. The formation of the body axis in vertebrates also exhibits another unusual feature: while it takes place in an apparentlysymmetrical fashion, with the left and right sides of the embryo seemingly equivalent to one another, at some point the symmetry is broken. Genes such asnodal and lefty start being expressed differently on the two sides of theembryo [90], and the whole body eventually assumes a partly asymmetric morphology, particularlywith respect to internal organs, such as the heart.

Turing [99] first demonstrated thatreaction‐diffusion systems like that represented in Eq. (12) will, with appropriate choice of parameters and boundary conditions, generate self‐organizing patterns, witha particular propensity to exhibit symmetry breaking across more than one axis. Using this class of models, Meinhardt [56] has presented an analysis of axis formation in vertebrates and the breaking of symmetry around these axes.

The first goal a model of axis formation has to accomplish is to generate an organizer de novo. For this high local concentrations and gradeddistributions of signaling molecules are needed. This can be accomplished by the coupling of a self‐enhancing feedback loop acting overa short range with a competing inhibitory reaction acting over a longer range. The simplest system that can produce such a molecularpattern in the \( { x-y } \) plane consists ofa positively autoregulatory activator (with concentration \( { A(x,y;t) }\)) and an inhibitor (with concentration \( {I(x,y;t) } \)). The activator controls the production of the inhibitor, which in turn limits the production of theactivator. This process can be described by the following reaction‐diffusion system [56]
$$ \frac{\partial A}{\partial t} = D_A \left( {\frac{\partial^2 A}{\partial x^2}+\frac{\partial^2 A}{\partial y^2}} \right)+s\frac{A^2+I_A }{I\left( {1+s_A A^2} \right)}-k_A A $$
(14)
$$ \frac{\partial I}{\partial t} = D_I \left( {\frac{\partial^2 I}{\partial x^2}+\frac{\partial^2 I}{\partial y^2}} \right)+sA^2-k_I I+I_I $$
(15)
The A 2 terms specify that the feedback of the activator on its own production and that of the inhibitor in both cases is non‐linear. The factor \( { s > 0 } \) describes positive autoregulation, the capability of a factor to induce positive feedback on its own synthesis. This may occur by purely chemical means (“autocatalysis”), which is the mechanism assumed by Turing [99] when he first considered systems of this type. More generally, in living tissues, positive autoregulation occurs if a cell's exposure to a factor it has secreted causes it to make more of the same factor [100]. The inhibitor slows down the production of the activator (i. e., the 1/I factor in the second term in Eq. (14)). Both activator and inhibitor diffuse (i. e., spread) and decay with respective diffusion (\( { D_A,D_I } \)) and rate constants (\( { k_A,k_I } \)). The small baseline inhibitor concentrations, I A and I I can initiate activator self‐enhancement or suppress its onset, respectively, at low values of A. The factor s A , when present, leads to saturation of positive autoregulation. Once the positive autoregulatory reaction is under way, it leads to a stable, self‐regulating pattern in which the activator is in dynamic equilibrium with the surrounding cloud of the inhibitor.

The various organizers and subsequent inductions leading to symmetry breaking, axis formation and the appearance of the three germ layers inamphibians during gastrulation , can all, in principle, be modeled by thereaction‐diffusion system in Eqs. (14)and (15), or by the coupling of several such systems. The biological relevance of suchreaction‐diffusion models depends on whether there exist molecules that can beidentified as activator‐inhibitor pairs. Meinhardt's model starts with a default state, which consists of ectoderm. Patch-like activationgenerates the first “hot spot”, the vegetal pole organizer, which induces endoderm formation (simulation inFig. 11a). A candidate for the diffusible activator in the corresponding self‐enhancing loopfor endoderm specification is the TGF-β-like factor Derriere, which activates the VegT transcription factor [97].

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Figure 11

Pattern formation in the reaction‐diffusion model of Meinhardt. a Induction of the vegetal pole organizer . Left: The interaction of an autocatalytic activator, the TGF-β-like factor Derriere (red), with a long‐ranging inhibitor (whose production it controls, and which in turn, limits the activator's production), creates an unstable state in an initially near‐uniform distribution of the substances (inhibitor not shown). Middle and right: Small local elevation in the activator concentration above steady‐state levels triggers a cascade of events governed by Eqs. (14)–(15): further increase of the activator due to autocatalysis, spread of the concomitantly produced surplus of inhibitor into the surrounding, where it suppresses activator production (middle), and the establishment of a new stable state, in which the activator maximum (hot spot) is in a dynamic equilibrium with the surrounding cloud of inhibitor (right). The right panel also shows the near‐uniform distribution of the activator (green) in the second reaction‐diffusion system discussed in b. b Induction of the Nieuwkoop center. Once the first hot spot has formed, it activates a second self‐enhancing feedback loop. The production of the activator (green) in this reaction is inhibited by the vegetal pole organizer itself. As a consequence, the Nieuwkoop center is displaced from the pole. c Zonal separation of ectoderm, endoderm and mesoderm. The competition of several positive feedback loops assures that in one cell only one of these loops is active. As the results indicate, reaction‐diffusion systems can produce not only spot-like organizers, but also zones. Endoderm (red) forms as shown from a default ectodermal state (blue). The mesodermal zone (green; which forms by the involvement of the FGF/brachyury feedback loop) develops a characteristic width by an additional self‐inhibitory influence in Eqs. (14) and (15). d Induction of the Spemann–Mangold organizer . The activation of an organizing region (yellow) within the still symmetric mesodermal zone would imply a competition over relatively long distances. In such a case, Eqs. (14) and (15) lead to the occurrence of two organizing regions, a biologically unacceptable result. The strong asymmetry shown in b prevents this and suggests a reason for the existence of the Nieuwkoop center. (Reprinted from Meinhardt [56] with permission from the University of the Basque Country Press; see original paper for details)

VegT expression remains localized to the vegetal pole, but not because of lack of competence of the surrounding cells to produceVegT [11]. These findings provide circumstantial evidence for the existence of the inhibitorrequired by the reaction‐diffusion model. Subsequently, a second feedback loopforms a second hot spot in the vicinity of the first, in the endoderm. This is identified with the “Nieuwkoop center”, a secondorganizing region, which appears in a specific quadrant ofthe blastula . A candidate for the second self‐enhancing loop is FGF together withBrachyury [87]. Interestingly, the inhibitor for this loop is hypothesized to be the first loopitself (i. e., the vegetal pole organizer), which acts as local repressor for the second. As a result of this local inhibitory effect, theNieuwkoop center is displaced from the pole (simulation in Fig. 11b). With the formation of theNieuwkoop center the spherical symmetry of the embryo is broken. In Meinhardt's model this symmetry breaking “propagates” and thus forms thebasis of further symmetry breakings, in particular the left-right asymmetry.

By secreting several diffusible factors, the Nieuwkoop center induces the formation of the Spemann–Mangoldorganizer  [31] (If the second feedback loop, responsible for the Nieuwkoopcenter is not included in the model, two Spemann–Mangold organizersappear symmetrically with respect to the animal‐vegetal axis and no symmetry breaking occurs). The organizer triggersgastrulation , in the course of which the germ layers acquire their relative positions and thenotochord forms. This long thin structure marks the midline of the embryo, which itself inherits organizer function and eventually establishes the primary(AP) embryonic axis. A simulation of midline formation, based on Meinhardt's model is shown in Fig. 12.

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Figure 12

Formation of the midline and enfolding of the anteroposterior (AP) axis according to the reaction‐diffusion model of Meinhardt. a Schematics of the hypothesized processes involved in axis formation. Cells close to the blastopore (red annulus) move towards the Spemann–Mangold organizer (blue). The spot-like organizer redirects the cells in its vicinity: initially they are drawn to the organizer, but then lose their attraction to it, so that they leave as a unified stripe‐like band. Stem cells in the organizer region may contribute to this band to form the most central element of the midline (green). Such highly coordinated cellular motion and strong positional specification along the enfolding AP axis requires the simultaneous action of several feedback loops. bd Simplified simulation of the scenario described in a. A reaction‐diffusion system tuned to make stripes (green; compare with zone formation in Fig. 11) is triggered by the organizer (blue). The organizer itself is the result of a self‐enhancing system, activated in a spot-like manner. (In bd the blastopore is shown in yellow.) Repulsion between the spot system (the organizer) and the stripe system (the notochord) causes the elongation of the latter. Saturation in self‐enhancement (due to the factor s A in Eq. (14)) ensures that the stripe system does not disintegrate into individual patches and thus establishes the midline. This, in turn, acts as a sink for a ubiquitously produced substance (pink), which could be the product of BMP-4. The local concentration of this substance (shades of pink) is a measure of the distance from the midline. This simulation is simplified in that the actual movement of cells toward the organizer is not considered; instead, the midline elongates by the addition of lines of new cells next to the blastopore. (a redrawn, and bd reprinted, from Meinhardt [56] with permission from the University of the Basque Country Press; see original paper for details)

Evolution of Developmental Mechanisms

Many key gene products that participate in and regulate multicellular development emerged over several billions of years of evolution ina world containing only single‐celled organisms. Less than a billion years ago multicellular organisms appeared, and the gene productsthat had evolved in the earlier period were now raw material to be acted upon by physical and chemical‐dynamic mechanisms on a more macroscopicscale [62]. The mechanisms described in the previous sections – chemical multistability,chemical oscillation , changes in cell adhesive differentials (both between cell types and across the surface of individual cells), andreaction‐diffusion ‐based symmetry breaking, would have caused these ancient multicellular aggregates to take on a wide range ofbiological forms. Any set of physicochemical activities that generated a new form in a reliable fashion within a genetically uniformpopulation of cell aggregates would have constituted a primitive developmental mechanism.

But any developmental process that depends solely on physical mechanisms of morphogenesis would have been variable in its outcome – subject to inconstant external parameters such as temperature and the chemicalmicroenvironment [67]. Modern‐day embryos develop in a more rigidly programmed fashion:the operation of cell type- and pattern‐generating physical and chemical‐dynamic mechanisms is constrained and focused by hierarchical systemsof coordinated gene activities. These developmental‐genetic programs are the result of eons ofmolecular evolution that occurred mainly after the origination of multicellularity.

The relation between physical mechanisms of morphogenesis and hierarchical developmental programs can be appreciated by considering a majorpuzzle in the field of evolutionary developmental biology (“EvoDevo”): the disparity between the mechanisms of segment formation in“short germ‐band” insects such as beetles and “long germ‐band” insects such as fruit flies. As we will see, onesolution to this conundrum touches on all categories of multicomponent dynamical behaviors discussed in earlier sections.

Similarly to somitogenesis in vertebrates (see Sect. “ Biochemical Oscillations:Segmentation”), in short germ-band insects [75], as well as in other arthropods,such as the horseshoe crab [40], segmental primordia are added in sequence from a zone of cellproliferation (“growth zone”) (Fig. 13). In contrast, in long germ-band insects, such as thefruit fly Drosophila, a series of chemical stripes (i. e., parallel bands of high concentration ofa molecule) forms in the embryo, which at this stage is a syncytium, a large cell with singlecytoplasmic compartment containing about 6000 nuclei arranged in a single layer on the inner surface of the plasma membrane [50]. These stripes are actually alternating, evenly‐spaced bands of transcription factors of the“pair‐rule” class. The pair-rule genes include even‐skipped, fushi tarazu, and hairy, which is theinsect homolog of the c‑hairy1 gene expressed in a periodic fashion during vertebrate somitogenesis (seeSect. “Biochemical Oscillations: Segmentation”). When cellularization (the enclosure of eachnucleus and nearby cytoplasm in their own complete plasma membrane) takes place shortly thereafter, the cells of the resulting blastoderm will haveperiodically‐distributed identities, determined by the particular mix of transcription factors they have incorporated. The different cell states are later transformed into states of differentialadhesivity [36], and morphological segments form as a consequence.

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Figure 13

Comparison of sequential and parallel segmentation modes in short and long germ-band insects. Left: In short germ-band insects (the embryo of the grasshopper, Schistocerca gregaria, is shown schematically) one or groups of a few segments appear in succession. Brown stripes indicate expression of a segment polarity gene such as engrailed . With further development additional segments appear sequentially from a zone of proliferation that remains posterior to the most recently‐added segment. Right: In long germ-band insects (the embryo of the fruit-fly, Drosophila melanogaster, is shown) gradients of maternal gene products (e. g., bicoid and nanos) are present in the egg before cellularization of the blastoderm (see text). As development proceeds, the maternal gene products induce the expression of gap genes (e. g., hunchback, Krüppel), the products of which, in turn, induce the expression of pair-rule genes in a total of 14 stripes (e. g., eve, fushi tarazu, hairy). Each pair-rule gene is expressed in a subset of the stripes: eve, for example, is expressed in seven alternating stripes, shown in green. The pair-rule gene products provide a prepattern for the alternating bands of nuclear expression of segment polarity genes. Once cellularization has occurred (bottom panel), these are distributed similarly to that in short germ-band embryos. (Schistocerca series after Patel [73]; Drosophila series after Ingham [36]. Reprinted, with permission, from [21]

The formation of overt segments in both short (e. g., grasshoppers [75], Patel [74] and beetles [6]) and long germ-band insects [45] requires the prior expression of a stripe of the product of the engrailed(en) gene , a transcription factor, in the cells of the posterior border of each of the presumptive segments. InDrosophila, the positions of the engrailed stripes are largely determined by the activity of the pair-rule geneseven‐skipped (eve) and fuhsi tarazu(ftz), which, as mentioned above, exhibit alternating, complementary seven stripe patterns prior to the formation of theblastoderm [23,35].

On theoretical [4] and experimental [51]grounds it has long been recognized that the kinetic properties that give rise to a chemicaloscillation (Sect. “ Biochemical Oscillations:Segmentation”), can, when one or more of the components is diffusible, also give rise to standing or traveling spatial periodicitiesof chemical concentration (Sect. “Reaction‐Diffusion Mechanisms: Body Axis Formation”). (SeeFig. 14 for a simple dynamical system that exhibits temporaloscillation or standing waves, depending on whether or not diffusion is permitted). This connectionbetween oscillatory andreaction‐diffusion mechanisms can potentially unify the differentsegmentation mechanisms found in short and long germ-band insects. This would be quitestraightforward if the Drosophila embryo were patterned by a reaction‐diffusion system, which can readilygive rise to a series of chemical standing waves (“stripes”).

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Figure 14

Example of a network that can produce (for the same parameter values) sequential stripes when acting as an intracellular biochemical clock in a one‐dimensional cellularized blastoderm with a posterior proliferative zone, and simultaneously forming stripes when acting in a one‑dimensional diffusion‐permissive syncytium. The network is shown in the central box. Arrows indicate positive regulation; lines terminating in circles, negative regulation. In the upper boxes, the equations governing each of the two behaviors are shown. The four genes involved in the central network diagram, as well as their levels of expression, are denoted by \( { g_1, g_2, g_3 } \), and g 4. In the reaction‐diffusion case, g 1 and g 2 can diffuse between nuclei (note that the two sets of equations differ only in the presence of a diffusion term for the products of genes 1 and 2). The lower boxes indicate the levels of expression of gene 2 for the two systems. For the intracellular clock the x‑axis represents time, and the indicated time variation of the gene's expression level refers to a single nucleus. In the reaction‐diffusion system this axis represents space, the distance along a chain of 81 nuclei. In the pattern shown on the right, the initial condition consisted of all gene product levels set to zero except gene 1 in the central of 81 nuclei, which was assigned a small value (the exact quantity did not affect the pattern). All parameters (except for D 1 and D 2) had the same value when generating the two patterns (for details see Salazar‐Ciudad et al. [85], from which the figure was redrawn). Figure modified and reprinted, with permission, from [21]

While the stripe patterns of the pair-rule genes in Drosophila indeed have the distinct appearance of being produced by a reaction‐diffusion system(Fig. 13), at least one of the stripes is generated instead by a complex set of interactions amongtranscription factors in the syncytial embryo. The formation of eve stripe number 2 requires the existence of sequences in the eve promotor that switch on theeve gene in response to a set of spatially‐distributedmorphogens that under normal circumstances have the requisite values only at the stripe 2 position(Fig. 15) [88,89]. In particular, these promoter sequences respond to specific combinations of products of the “gap”genes (e. g., giant, knirps, the embryonically‐produced version of hunchback). These proteins aretranscription factors that are expressed in a spatially‐nonuniform fashion and act as activators and competitive repressors of the pair-rulegene promoters (also see discussion of the Keller model inSect. “Dynamic Multistability: Cell Differentiation”). The patterned expression of the gap genes,in turn, is controlled by the responses of their own promoters to particular combinations of products of “maternal”genes (e. g., bicoid, staufen), which are distributed as gradients along the embryo at even earlier stages (Fig. 13). As the category name suggests, the maternalgene products are deposited in the egg during oogeneis.

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Figure 15

a Schematic representation of a portion of the even‐skipped gene, including the promoter and transcription start site. Contained within the promoter is a subregion (“stripe 2 enhancer”) responsible for the expression of the second eve stripe. This sequence contains binding sites for gap gene –class transcription factors that positively (hunchback, red) or negatively (giant, blue; Krüppel, orange) regulate eve expression. b Illustration of Drosophila syncytial blastula , showing distribution of giant, hunchback and Krüppel proteins in region of first six prospective parasegments. At the position of prospective parasegment 3 (the posterior half of the last head segment plus the anterior half of the first thoracic – upper body – segment) the levels of the activator hunchback is high and those of the inhibitors giant and Krüppel are low. This induces eve stripe 2. To either side of this position giant and Krüppel are high, restricting expression of eve to a narrow band. (a based on Small et al. [88]; b after Wolpert [104], 2002. Reprinted, with permission, from [21])

While the expression of engrailed along the posterior margin of each developing segment is a constant themeduring development of arthropods, the expression patterns of pair-rule genes is less well‐conserved over evolution [15]. The accepted view is that the short germ-band “sequential” mode is the more ancient way of makingsegments, and that the long germ-band “simultaneous” mode seen in Drosophila, which employs pair-rulestripes, is more recently evolved [53].

No intracellular oscillations have thus far been identified during segmentation of invertebrates, unlike the case in vertebrates such as the mouse,chicken, and zebrafish. However, the sequential appearance of gene expression stripes from the posterior proliferative zone of short germ-band insects andother arthropods such as spiders, has led to the suggestion that these patterns in fact arise from a segmentation clock like that found to controlvertebrate somitogenesis [95].

Based on the experimental findings, theoretical considerations and evolutionary inferences described above, it has been hypothesized that theancestor of Drosophila generated its segments by a reaction‐diffusion system [60,85], built upon the presumed chemical oscillator underlying shortgerm-band segmentation . Modern‐day Drosophila contains (retains, according to the hypothesis) the ingredients forthis type of mechanism. Specifically, in the syncytial embryo several of the pair-rule proteins (e. g., eve, ftz) diffuse over short distances amongthe cell nuclei that synthesize their mRNAs, and positively regulate their own synthesis [30,38].

The hypothesized evolutionary scenario can be summarized as follows: the appearance of the syncytial mode of embryogenesis converted the chemicaloscillation ‐dependent temporal mechanism found in the more ancient short germ-band insects into the spatial standing wave mechanism seen in the morerecently evolved long germ-band forms. The pair-rule stripes formed by the proposed reaction‐diffusion mechanism would have been equivalent to oneanother. That is, they would have been generated by a single mechanism acting in a spatially‐periodic fashion, not bystripe‐specific molecular machinery (see above). Thus despite suggesting an underlying physical connection between modern short germ-bandsegmentation and segmentation in the presumed anscestor of long germ-band forms, this hypothesis introduces a new puzzle of its own: Why doesmodern‐day Drosophila not use a reaction‐diffusion mechanism to produce its segments?

Genes are always undergoing random mutation, but morphological change does not always track genetic change. Particularly interesting are those casesin which the outward form of a body plan or organ does not change, but its genetic “underpinning” does. One example of this is seen inthe role of the transcription factor sloppy‐paired (slp) in the beetle Tribolium and Drosophila. In relation to, but in contrast with the paired (prd) protein, which activates engrailed and wingless in the same odd-even parasegmental register in both species, slp has anopposite parasegmental register in Tribolium and Drosophila [8].

This situation can result from a mechanism that is initially “plastic”, i. e., having variable morphological outcomes despiteutilizing the same genes (as physically based mechanisms would typically be), followed by a particular kind of natural selection, termed“canalizing selection” by Waddington [101] (see also [86]). Canalizing selection will preserve those randomly acquired genetic alterations that happen to enhance thereliability of a developmental process. Development would thereby become more complex at the molecular level, but correspondingly more resistant(“robust”) to external perturbations or internal noise that could disrupt non‐reinforced physical mechanisms ofdetermination.

If the striped expression of pair-rule genes in the ancestor of modern Drosophila was generated bya reaction‐diffusion mechanism, this inherently variable developmental system would have been a prime candidate for canalizingevolution. The elaborate systems of multiple promoter elements responsive to pre‐existing, nonuniformly distributed molecular cues (e. g.,maternal and gap gene products), seen in Drosophila is therefore not inconsistent with this pattern having originatedas a reaction‐diffusion process.

In light of the discussion in the previous paragraphs, a tentative answer to why modern‐day Drosophiladoes not use a reaction‐diffusion mechanism to produce its segments is that such pattern‐forming systems are inherently unstable toenvironmental and random genetic changes, and would therefore, under pressure of natural selection, have been replaced, or at least reinforced, by morehierarchically‐organized genetic control systems. We do not know, at present, whether the short germ-band mode of segmentation is similarlyhierarchically reinforced.

This evolutionary hypothesis has been examined computationally in a simple physical model by Salazar‐Ciudad andcoworkers [84]. The model consists of a fixed number of nuclei arranged in a row withina syncytium. Each nucleus has the same genome (i. e., the same set of genes ), and the same epigenetic system (i. e.,the same activating and inhibitory relationships among these genes). The genes in thesenetworks specify receptors or transcriptionfactors that act within the cells that produce them, or paracrine factors that diffuse between cells(Fig. 16). These genes interact with each other according to a set of simple rules that embodyunidirectional interactions in which an upstream gene activates a downstream one, as well as reciprocal interactions, in whichgenes feed back (via their products) on each other's activities. This formalism was based on a similarone devised by Reinitz and Sharp [80], who considered the specific problem ofsegmentation in the Drosophila embryo.

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Figure 16

Schematic of the gene-gene interactions in the model of Salazar‐Ciudad et al. [84]. A line of cells is represented at the top. Below, types of genes are illustrated. Genes whose products act solely on or within the cells that produce them (receptors: r, transcription factors : f) are represented by squares; diffusible factors (paracrine factors or hormones: h) that pass between cells and enable genes to affect one another's activities, are represented by circles. Activating and inhibitory interactions are denoted by small arrows and lines terminating in circles, respectively. Double‐headed green arrows denote diffusion. (After Salazar‐Ciudad et al. [84]) Reprinted, with permission, from [21]

One may ask whether a system of this sort, with particular values of the gene-gene coupling and diffusion constants, can form a spatialpattern of differentiated cells. Salazar‐Ciudad and coworkers performed simulations on systems containing 25 nuclei, and a pattern wasconsidered to arise if after some time different nuclei stably expressed one or more of the genes at different levels. The system was isolated fromexternal influences (“zero‐flux boundary conditions” were used, that is the boundaries of the domain were impermeable to diffusiblemorphogens ), and initial conditions were set such that at \( { t=0 }\) the levels of all gene products had zero value except for that of an arbitrarily chosen gene, which hada non-zero value in the nucleus at the middle position.

Isolated single nuclei, or isolated patches of contiguous nuclei expressing a given gene, are the one‐dimensional analogue of isolatedstripes of gene expression in a two‐dimensional sheet of nuclei, such as those in the Drosophila embryoprior to cellularization [84]. Regardless of whether a particular system initially gives riseto a pattern, if within the model it evolves by random changes in the values of the gene -gene coupling constants it may acquire or losepattern‐forming ability over subsequent “generations”. Salazar‐Ciudad and coworkers therefore used such systems to performa large number of computational “evolutionary experiments”. Here we will describe a few of these that are relevant to the questionsraised by the evolution of segmentation in insects, discussed above.

It had earlier been determined that the core mechanisms responsible for all stable patterns fell into two non‐overlapping topologicalcategories [83]. These were referred to as “emergent” and“hierarchical”. Mechanisms in which reciprocal positive and negative feedback interactions give rise to the pattern, are emergent. Incontrast, those that form patterns by virtue of the unidirectional influence of one gene on the next, in an ordered succession(“feed‐forward” loops [54]), as in the “maternal gene induces gap geneinduces pair-rule gene” scheme described above for early steps of Drosophila segmentation,are hierarchical. Emergent systems are equivalent to excitable dynamical systems, like the transcription factor networks discussed in Sect. “Dynamic Multistability: Cell Differentiation”and the reaction‐diffusion systems discussed in Sect. “ Reaction‐Diffusion Mechanisms: Body AxisFormation”.

In their computational studies of the evolution of developmental mechanisms the investigators found that randomly‐chosen emergent networks were much more likely than randomly‐chosen hierarchical networks to generate complex patterns, i. e., patterns with three or more(one‐dimensional) stripes. This was taken to suggest that the evolutionary origination of complex forms, such as segmented body plans, would havebeen more readily achieved in a world of organisms in which dynamical (e. g., multistable, reaction‐diffusion , oscillatory ) mechanismswere also active [84] and not just mechanisms based on genetic hierarchies.

Following up on these observations, Salazar‐Ciudad and co‐workers performed a set of computational studies on the evolution ofdevelopmental mechanisms after a pattern had been originated. First they identified emergent and hierarchical networks that produceda particular pattern – e. g., three “stripes” [84]. (Note that patternsthemselves are neither emergent nor hierarchical – these terms apply to the mechanisms that generate them). They next asked if given networks would“breed true” phenotypically, despite changes to their underlying circuitry. That is, would their genetically‐altered“progeny” exhibit the same pattern as the unaltered version? Genetic alterations in these model systems consisted of point mutations(i. e., changes in the value of a gene-gene coupling constants), duplications, recombinations (i. e., interchange of coupling constantvalues between pairs of genes), and the acquisition of new interactions (i. e., a coupling constant that was initially equal to zero wasrandomly assigned a small positive or negative value).

It was found that hierarchical networks were much less likely to diverge from the original pattern (after undergoing simulated evolution asdescribed) than emergent networks [84]. That is to say, a given pattern would be more robust(and thus evolutionarily more stable) under genetic mutation if it were generated by a hierarchical , than an emergent network . Occasionally it wasobserved that networks that started out as emergent were converted into hierarchical networks with the same number of stripes. The results ofSalazar‐Ciudad and coworkers on how network topology influences evolutionary stability imply that these “converted” networks wouldproduce the original pattern in the face of further genetic evolution. Recall that this is precisely the scenario that was hypothesized above to haveoccurred during the evolution of Drosophila segmentation  [84].

Subject to the caveats to what is obviously a highly schematic analysis, the possible implications of these computational experiments for theevolution of segmentation in long germ-band insects are the following: (i) if the ancestral embryoindeed generated its seven‐stripe pair-rule protein patterns by a reaction‐diffusion mechanism, and (ii) if this pattern was sufficientlywell‐adapted so as to provide a premium on breeding true, then (iii) genetic changes that preserved the pattern but converted the underlyingnetwork from an emergent one toa hierarchic one (as seen in present‐day Drosophila) would have been favored.

As this discussion of the short germ-band/long germ-band puzzle suggests, developmental mechanisms can change over the course of evolution whiletheir morphological outcomes remain constant. While forms (few tissue layers, segments, tubes, and so forth) remain simple and reminiscent of structuresthat can be generated by generic physical processes, the associated gene‐expression networks canbecome increasingly more complex. This is because the latter tend to evolve so as to bring about a developmental result in a fashion protectedagainst perturbation from external and internal variability, including, in the latter case, mutation and noise.

The evolutionary changes that will lead to increasingly canalized or robust outcomes can include genetic redundancies [70,103] such as duplication of developmental controlgenes [32] and multiplication of their regulatory elements [88,89], as well as the utilization of chaperone proteins as“phenotypic capacitors” [81]. The effect of this mode of evolution is to convertorganisms into more stable types that are less morphologically plastic than ones molded by relatively unconstrained physical mechanisms(Fig. 17).

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Figure 17

Schematic representation of evolutionary partitioning of a morphologically plastic ancestral organism into distinct morphotypes associated with unique genotypes. a A hypothetical primitive metazoan is shown with a schematic representation of its genome in the box below it. Specific genes are shown as colored geometric objects; interactions between them by lines. Determinants of the organism's form include the materials provided by expression of its genes (light blue arrows) and the external environment, including physical causes (purple arrows) acting on its inherent physical properties. At this stage of evolution the organism is highly plastic, exhibiting several condition‐dependent forms that are mutually interconvertible (dark blue arrows). b Descendents of organism in a after some stabilizing evolution. Gene duplication, mutation, etc. have led to non‐interbreeding populations that are biased toward subsets of the original morphological phenotypes. Determinants of form are still gene products and the physical environment, but the effect of the latter has become attenuated (smaller, fainter purple arrows) as development has become more programmatic. There is also causal influence of the form on the genotype (orange arrows), exerted over evolutionary time, as ecological establishment of forms filters out those variant genotypes that are not compatible with the established form. Some morphotypes remain interconvertible at this stage of evolution. c Modern organisms descended from those in b. Further stabilizing evolution has now led to each morphotype being uniquely associated with its own genotype. Physical causation is even more attenuated. Note that in this idealized example the forms have remained unchanged while the genes and mechanisms for generating the forms have undergone extensive evolution. (From Newman et al. [67]; with permission from the University of the Basque Country Press)

Future Directions

While all living systems are part of the physical world and thus must obey its physical laws, it is not self‐evident that all biologicalproblems can be adequately addressed by the concepts of physics as we know them today. On a fundamental level this is because whereas the laws ofphysics have not changed during the lifetime of the Earth, living systems have. Evolution is the hallmark of life, but has little relevance forphysics. As living systems evolved, some lineages transformed from single cells into multicellular organisms with a myriad of different interactingcomponents organized on multiple levels. Such systems are considerably more complex than even the most elaborate materials studied by physicists. Thus, onthe practical level, the tools of present day physics do not make it possible to study a fully developed adult organism with all its parts or eventhe subcellular economy of intracellular biochemical networks .

The developing embryo, however, considered at the appropriate level of resolution, is not beyond physical comprehension of its main episodes andtransitions. Each of the processes discussed in the previous sections, multistability of dynamical systems, differentialadhesion and interfacialtension , chemicaloscillation and symmetry‐breaking byreaction‐diffusion interaction, have their counterparts in the world of nonlivingchemically and mechanically excitable [57] “soft matter” [16]. These descriptions of the behavior of matter at an intermediate scale (i. e., between molecules and bulkmaterials), represent elegant simplifications of highly complex many-body interactions. They are based on models developed by physicists usingsophisticated mathematical techniques and systems‐level approaches (nonlinear dynamics, and scaling and renormalization group theory, to namea few), which, for the most part, were unavailable before the mid-20th century.

Embryos are approachable by these physical principles because they are, to a major extent, chemically and mechanically excitable soft matter. Developing tissues consist of cells containing complex biochemicalnetworks which are capable of switching between a limited numberof stationary or oscillatory states . Their cells are mobile with respect to one another, giving themliquid‐like properties, and they secrete diffusible signal molecules, permitting them to become spatially heterogeneous by straightforward physicalmeans.

As we have seen, the forms generated by self‐organizing physical processes of soft matter will become increasingly regulated by genetichierarchies over the course of evolution. But the major structural motifs of the animal body and its organs (hollow, multilayered cell masses, segments,tubes) had their origin more than 500 million years ago [12,61,68]. During this period “beforeprograms” [67], certain molecules of the “developmental‐genetictoolkit ” [7] – cadherins, Notch and its ligands, secreted molecules such as Wnt, BMP,hedgehog, FGF – though having evolved in the world of single cells, took on, when present in a multicellular context, the role of mediatingintermediate‐scale physical effects [66]. Once this new set (for organisms) of physicalprocesses was thus mobilized, morphological evolution, unconstrained in this early period by highly integrated programs, could proceed very rapidly. Theotherwise puzzling high degree of conservation, in disparate animal forms, of the toolkit genes for morphological development is to be expected underthese circumstances [64].

Although multicellular forms are relatively simple, and the physical processes that likely first brought them about comprehensible, the molecularmechanisms of development in modern‐day organisms are enormously complex. The challenge for both developmental and evolutionary studies in thefuture, then, will be to experimentally disentangle and conceptually reintegrate the roles physics and developmental genetics in modern organisms andtheir ancestors.

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