Complexity: the organizing principle at the interface of ...

Journal of Genetics , Vol. 96, No. 3, July 2017, pp. 431–444 © Indian Academy of SciencesDOI 10.1007/s12041-017-0793-8

REVIEWARTICLE

Complexity: the organizing principle at the interface of biological (dis)order

RAMRAY BHAT∗ and DHARMA PALLY

Department of Molecular Reproduction Development and Genetics, Indian Institute of Science, Bengaluru 560 012, India*For correspondence. E-mail: [email protected].

Received 8 November 2016; revised 16 March 2017; accepted 21 March 2017; published online 5 July 2017

Abstract. The term complexity means several things to biologists. When qualifying morphological phenotype, on the one hand, itis used to signify the sheer complicatedness of living systems, especially as a result of the multicomponent aspect of biological form.On the other hand, it has been used to represent the intricate nature of the connections between constituents that make up form: amore process-based explanation. In the context of evolutionary arguments, complexity has been defined, in a quantifiable fashion,as the amount of information, an informatic template such as a sequence of nucleotides or amino acids stores about its environment.In this perspective, we begin with a brief review of the history of complexity theory. We then introduce a developmental and anevolutionary understanding of what it means for biological systems to be complex. We propose that the complexity of living systemscan be understood through two interdependent structural properties: multiscalarity of interconstituent mechanisms and excitabilityof the biological materials. The answer to whether a system becomes more or less complex over time depends on the potential for itsconstituents to interact in novel ways and combinations to give rise to new structures and functions, as well as on the evolution ofexcitable properties that would facilitate the exploration of interconstituent organization in the context of their microenvironmentsand macroenvironments.

Keywords. complexity; evo–devo; excitability; multiscale mechanisms.

Introduction

In an interview to Carl Zimmer, published in Discovermagazine, the control systems theorist John Doyle soughtto criticize multidisciplinary efforts aimed at trying tounderstand how complicated systems, biological, natu-ral (such as weather) and man-made (such as the worldwide web) work by collectively referring to these attemptsas ‘emergilent chaoplexity’, a portmanteau of ‘emergent’,‘intelligent’, ‘chaos’ and ‘complexity’ (Zimmer 2007).Doyle’s grouse lay in the fact that these theories seekonly to establish and analyse patterns, the arrangementof interconnected and interrelated components of a sys-tem, without excavating its underlying bulwarks, i.e. thedynamical properties of themechanisms that form the pat-terns in the first place (Li et al. 2014; see also Newman1970). This criticism lies at the heart of the ‘process’ ver-sus ‘pattern’ dichotomy in cell and developmental biology,which arises from the fact that a given pattern cannot beautomatically linked in an ontological fashion with anyone particular process that could give rise to the pattern.Therefore, a biological pattern (and as is often referred

to in three-dimensional terms, biological architecture) canbe idealized as being wrought in more ways than one andcannot by itself, reveal the mechanism that has generatedit. A historical example of this problem is the segmenta-tion in long germ-band insect embryos, such as the fruitfly Drosophila melanogaster: the observation that all thesegments appeared simultaneously separated in a statisti-cally regular manner from each other led early theoriststo propose the involvement of a turing-type reaction-diffusion mechanism, a chemical process that leads tosymmetry breaking in space (Turing 1952; Meinhardt1982; Lacalli et al. 1988; Nagorcka 1988; Hunding et al.1990). Instead, each segment was found to arise relativelyautonomously from others due to an asymmetrical dis-tribution of transcription factors that participated in ahierarchical regulatory network, leading to distinct seg-mental identities (Nusslein-Volhard and Wieschaus 1980;Akam 1989; Gilbert 1991).

Of the terms mentioned above, the ones that have foundthe most favour with biologists have been complexity andemergence (Lee et al. 1997;Hallgrimsson et al. 2002;Eung-damrong and Iyengar 2004). The rationale for this is not

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432 Ramray Bhat and Dharma Pally

hard to guess. Starting from the middle of the 20th cen-tury, the blinding pace of the development of techniquesdevoted to the unraveling of biological systems at themolecular level, ensured that the practicing experimen-tal biologist considered complexity as a metonym for theincredible detail with which they described the genotypeand phenotype of organisms (Rickles et al. 2007; Hay-den 2010). It took a different set of workers in the field topropose that whereas ‘complicatedness’ could emphasizethe number and diversity of components which make upa particular biological system, ‘complexity’ stood more asa measure of the connections between constituents, thatled the ‘whole’ to acquire new properties and performnovel functions (Goodwin 1977; Webster and Goodwin1981; Kauffman 2001; Braha et al. 2006). Accompany-ing this shift from within the realm of biology, theoreticaladvances came from natural and physical sciences, rang-ing from control theory, statistics, and condensed matterphysics, furthering our understanding of how the inter-connections between elements constituting patterns, andimportantly, the mechanisms that forge the interconnec-tivities affect performance and survival of the systems(Adami et al. 2000; Solé andGoodwin 2000;Harmon et al.2015).

In this paper, we initially review the history and devel-opment of complexity theory in the context of biologicalsystems. In the second section,we introduce twopropertiesthat seldomfigure in the commondefinition of complexity,but, as we argue, add a novel and necessary ‘structuralist’dimension to the same. In the third and concluding sec-tion, we discuss how the evolution of properties associatedwith this structural dimension further our understandingof the phylogenetic trajectory of multicellular organismalcomplexity and phenotype.

A brief history of complexity

The development of complexity theory can be consideredto be the result of an intertwining between three contem-poraneous transdisciplinary strands of academic activitiesand research. The first one was cybernetics, defined byNorbert Wiener, one of its arch proponents as ‘the sci-entific study of control and communication in the animaland the machine’ (Heims 1991). Brought together by theMacy conferences, the East Coast cyberneticists, several ofwhom were based in Massachusetts Institute of Technol-ogy (MIT) sought to understand the role of regulation andfeedback in engineered systems and biological problems,specifically neural networks (McCulloch 1989). Cyber-neticists devoted themselves to understand how naturalsystems achieve, and orient themselves towards perform-ing, specific goals as well as how to engineer artificialsystems to do the same (Rosenblueth et al. 1943). Inaddition, the presence of Claude Shannon in this group

ensured the initiation of cyberneticists into the fundamen-tals of entropy and information, showcased by GeorgeGamow’s essay in the Scientific American titled ‘Informa-tion transfer in the living cell’ (Gamow 1955) as well asby Norbert Wiener’s seminal book entitled ‘Cybernetics’(Wiener 1948). In fact, Wiener when dealing with learningin machines, differentiated between learning in biologicalorganisms in an ontogenetic (embryological) versus a phy-logenetic (evolutionary) context, taking it further to positthat the latter is crucial and devoted to establishing theformer in a proper way.The origination of the second transdisciplinary strand,

general systems theory (GST) can be traced for discussionsin the Vienna Circle of philosophers and biologists, andspecifically the efforts of Ludwig von Bertalanffy, whichlaid the foundations of a holistic approach to biologi-cal and physical systems and its extrapolation to socialand cultural constructs (Laszlo 1979;Drack andPouvreau2015). GST was the first to seek a break from the reduc-tionist approach ingrained since Descartes, the idea thatthe structure and function of a system is the sum totalof the structure and functions of its constituents (Berta-lanffy and Laszlo 1972) and emphasized a bottom–upapproach towards understanding the working of naturaland physical systems. Bertalanffy was one of the earliestto suggest that living systems are thermodynamically openand not-at-equilibrium, and that self-regulation is a natu-ral characteristic of such systems (Bertalanffy 1950). GSTwas embraced in principle by Conrad Hal Waddingtonand his Theoretical Biology Group, when von Berta-lanffy visited their meetings in Alpbach. Bertalanffy wroteextensively on evolutionary theory, with one notable inter-vention being his questioning of uniformitarianism, theidea that ‘all change is caused by processes that we cur-rently observe which have worked at the same rate at alltimes’ (Lyell and Deshayes 1830; Bertalanffy 1952; Bakand Paczuski 1995).The third discipline was dynamical systems theory

(DST), a mathematical enterprise that deals with thebehaviour of several interacting elements as a functionof time. The history of DST can be traced since fromthe conceptualization of calculus by Newton and Leib-niz in the 16th century (Mainzer 1997), through the workon nonlinearity of dynamical systems by Henri Poincaréin the 19th century (Poincaré 1899) and continued morerecently with the discovery of chaotic attractors by RalphAbraham (Abraham and Ueda 2000). DST provided themathematical foundation for investigating the behaviourof systems that evolve in time according to specific rules(Abraham and Shaw 1982). Simply put, DST studies theevolution in time of a few variables coupled through dif-ferential equations. The entry of nonlinear mathematicalapproaches in engineering and control systems led to thedevelopment of ‘systems dynamics’ as a result of the workon thedevelopmentofmechanical analog, and later, digitalcomputers by Vannevar Bush, and with the development

Complex biological systems are multiscale and excitable 433

and application of programming to trace the dynamicalproperties of real-world industrial systems by Jay For-rester at the Electrical and Management departments ofMIT respectively (Zachary 1997). The contribution to theunderstanding of deterministic nonlinearity byDSTwas ashot in the arm of complexity theorists who applied theseprinciples towards progressively larger real-world systems.It would be incorrect to assume that the above three

activities of research happened independently of eachother. Ralph Abraham gives a riveting account of howproponents in each strandwere often aware of the develop-ments in, and participatory to, the meetings of their coun-terparts (Abraham 2011). Wiener for instance, acknowl-edges the increasing pervasiveness of nonlinear dynamicalapproaches as a consequence of DST and his prox-imity with Bush and Forrester in the preface to thesecond edition of Cybernetics. The systems dynamicsproject that was started by Forrester and later his stu-dents brought about a synergistic fusion between thephilosophical approaches of GST and the mathemati-cal rigour of DST. Ralph Gerard, a neurophysiologistat Stanford University, participated in the Macy Con-ferences that gave rise to cybernetics and was also acofounder of the Society of General Systems Researchalong with Von Bertalanffy. It is therefore not surpris-ing that the history of complexity also consists of debatesas to whether cybernetics was a specialized form ofGST, or the other way around (Drack and Pouvreau2015).

In 1984, the Santa Fe Institute (SFI) was founded, andopened its doors to a diversity of theoreticians work-ing on problems related to the above streams under theaegis of complexity theory. The founding of SFI was theresult of the vision of George Cowan, a physical chemistemployed at Los Alamos National Laboratory and onceworking for the Manhattan Project. The idea of such aninstitute came about as a result of a lecture Cowan gaveon entropy to a gathering of philosophers, artists andthinkers at Aspen Institute in 1956 (Cowan 2010). TheSFI brought together, through meetings and residence fel-lowships, scientists from a wide range of fields: MurrayGel-Mann, Stuart Kauffmann, Philip Anderson, MarkNewman, Ilya Prigogine, John Holland, Manfred Eigenand others and has strongly contributed to the progressand popularity of complex systems research into the 21stcentury. More recently, institutions such as the New Eng-land Complex Systems Institute have served as a hub forscientists from diverse backgrounds to spearhead effortsof research into, and education about, complex systems ina breadth of fields such as ecology, economics and sociol-ogy.Given that the three strands of research were led mostly

by physical scientists, in collaboration with biological the-orists, the emergence of complexity theory happened inparallel with, and often autonomously from, develop-ments in experimental biology in the 20th century. When

studying spatial or temporal pattern formation, theo-rists proposed mechanisms that were grounded in specificphysical theories that incorporated elements of DST andcybernetics such as the propositions of segmental pattern-ing in insect embryos based on reaction-diffusion (Lacalliet al. 1988; Nagorcka 1988), of limb patterning throughreaction-diffusion (Newman and Frisch 1979), and theprocess of sequential somite formation through a clock-and-wavefront model that incorporated a catastrophicchange in fate of cellular oscillators (Thom 1975; Cookeand Zeeman 1976). These attempts to explain patterningof cellular arrangements met with resistance and indif-ference since contemporaneous experimental biologicaltechniques were neither sensitive nor advanced enoughto test the predictions of theoretical models. Therefore,when Kauffman proposed a Boolean model to reconcilethe disproportionation between the number of cell differ-entiation states and the size of the genome proposed inthe day, Lewis Wolpert, acclaimed developmental biolo-gist had the following to say, ‘Totally irrelevant. You findme a developmental biologist who takes Kauffman seri-ously and I’d be very surprised’ (Bentley 2001). It has takendecades for empirical methods to develop to a point wherethey can successfully test predictivemodels (e.g., the clock-and-wavefront model of somite formation is currently anaccepted model for vertebrate segmentation (Baker et al.2006), and reaction-diffusion has been shown to play animportant role in the patterning of limb skeletal elements(Sheth et al. 2012; Glimm et al. 2012, 2014; Raspopovicet al. 2014) and also other repetitive elements (Jiang et al.2004; Maini et al. 2006; Sick et al. 2006; Yamaguchi et al.2007).

In the next section, we start by defining complexity asis accepted in the field. We then work towards building amore structural definition of complexity to use the princi-ple to understand how an organ or organismal phenotypecomes about. The two properties that we argue are crucialto the structural definition of complexity are multiscaleintercomponent relationships, and excitability of the bio-materials that are involved in bringing about a biologicalphenotype.

Dissecting the properties of complex systems

A very stripped down description of a complex systemis that of an entity which is made up of several con-stituents that are interconnected with each other, withcomplexity being ameasure of the number of interconnec-tions between the constituents (Moses 2010). The wordcomplexity itself is derived from the Latin word com-plexus, which means braided together (Gell-Mann 1994).An essential criterion proposed for a system to be com-plex is the acquisition of novel functions or propertiesthat the individual constituents do not perform or possessrespectively. Since these functions are immediate and con-tingent consequences of the interaction of components,


Figure 1. Formation of low complexity ordered and disordered structures: diagram depicting hexagonal structural units arrangedin tessellated geometry (top left). Top right shows an ordered pattern where each blue hexagon is surrounded by six white hexagons.Bottom Left shows a disordered arrangement where there is no discernible pattern in the arrangement of blue and white hexagons.

they are said to be ‘emergent’ properties or functions ofthe system (Gell-Mann 1994). We wish to further add astructural element to the definition of biological complexsystems: complex systems are ensembles of componentsconnected to each other through multiscale interactionswith the resultant organization being regulated by theexcitable nature of the material that constitutes the com-ponents.

Multiscale organization

An implicit assumption of the first description of complexsystems is that a minimum set of interacting constituentsare necessary and sufficient to give rise to a given emer-gent function and/or property. The addition of anotherconstituent to this set may result in a new property butis not required for the earlier one. Therefore, a complexsystem is also relatively autonomous in that the systemachieves a new state as a result of the connectivity betweenits constituents that are in this context relatively insulatedfromother neighbouring potential components.While thisdescription is silent about the nature or arrangement ofthe interconstituent connectivities, theorists have sought tolink the concept of complexity with that of order, definedsometimes as the geometric symmetry inherent within asystem, but more generically by Yagil as the ratio betweenordered and the total coordinates of a given system, where

ordered coordinates are those that remain invariantly andreproducibly instructed fromagiven template (Yagil 2000).A symmetric example of ordered system is the formationof ice crystals and an asymmetric example is the first 200digits of π (pi).Earlier there have been attempts to quantify com-

plexity along informatic lines and to link it with order.Kolmogorov complexity, a measure that was proposedindependently by Andrey Kolmogorov, Ray SolomonoffandGregory Chaitin (Solomonoff 1964a, b; Chaitin 1969;Kolmogorov 1998) has been defined for a given patternto be ‘essentially the length of the shortest computer pro-gram needed to generate that pattern divided by the size ofthe pattern itself ’ (Grassberger 1991).Grassberger’s defini-tion brings the concept of complexity close to informationcontent per pixel or letter, and therefore to the notion ofentropy (Shannon andWeaver 1964). This implies that, themore regular the pattern, the smaller the program neededto describe it and hence the lesser its Kolmogorov com-plexity; also, the more random the pattern, the greater itsKolmogorov complexity (figure 1). AsMurrayGell-Mannpithily put it, this would mean the complexity of the com-plete works of Shakespeare (an example that would fitYagil’s definition of ordered system) would be consider-ably less than the ‘random gibberish of the same lengththat would typically be typed by the proverbial roomful ofmonkeys (and therefore a disordered system) (Gell-Mann1995).


Figure 2. Formation of high complexity intermediately ordered structure: a diagram that depicts the emergence of amulticomponentmultiscale arrangement. Top right shows the emergence of an ordered pattern where each blue hexagon is surrounded by whitehexagons. In the next iteration (centre), each blue hexagon is surrounded by six blue hexagons and a given blue hexagon cluster isseparated from others clusters in a periodic arrangement. Bottom left shows the next iteration which leads to a pattern where eachblue hexagon surrounding the central blue one in the seven hexagon cluster takes on an orange colour. This leads to an arrangementwhere the pattern becomes quasiperiodic with the involvement of further rules of arrangement between blue–blue, blue–orange,orange–orange, blue–white and orange–white interactions (bottom right). The iterations therefore reflect an increase in complexityof the overall multihexagon structure that is reflective of simultaneously existent interactions on divergent spatial scales: not justwithin each ‘orange–blue’ islands but also between the clusters. To predict the formation of the quasiperiodic pattern, it is essentialto unravel the preceding iterative steps and/or the rules that contribute the constitution of the iterative arrangements.

Empiricists from divergent disciplines such as architec-ture, biology and chemistry emphasize the inclusion of‘higher level’ interconstituent relationships in the concep-tion of structural complexity (Crutchfield 1989; EpsteinandPojman1998;Camazine2001;Alexander2002;Alexan-der and Center for Environmental Structure 2004) (fig-ure 2). In this spirit, Kauffman has eloquently describedcomplex systems as lying between highly ordered (lowKolmogorov complex) and disordered (high Kolmogorovcomplex) states (Kauffman 1993). To emphasize the point,completely disordered systems are not complex (figure 1).Yigal’s insight into the relationship between order andcomplexity also allows us to extend it further and link itwith the idea of scale: the number of constituents that canact together at a given instant and point in space. A highlyordered low complexity system differs from intermediatelyordered systems in possessing only one scale. Intermedi-ately ordered (and more complex) systems are multiscale.Modern formalisms that seek to quantify the inter-

relationships between constituents of natural structuresand systems emphasize the requirement of a framework

that incorporates the multiscale nature of real-world net-works and structures. One specific example from the NewEngland Complex Systems Institute is provided by Allenand coworkers, who begin by defining the structure ofa multiconstituent system as ‘the totality of quantifiablerelationships among the components’ comprising it (Allenet al. 2014). Invoking the concept of dependencies: a set ofirreducible interconstituent relationships, it is possible tocome up with two metrics: the complexity profile of thesystem that measures the total information (strength ofdependencies) within a system at scales higher or equal toa given scale, and marginal utility of information, whichmeasures the evolution in the distribution of the informa-tion across the scales of a system, as its informatic contentchanges (marginal utility therefore changes sharply orweakly for systems with strong and weak dependencies,respectively). These two metrics therefore inform us notjust about the information content within a complex sys-tem but how it is distributed across different scales of itsstructure and by extension, help distinguish the informa-tion distribution (or the pattern of dependencies) within


Figure 3. Multiscale and excitable molecular mechanism oftetrapod appendicular condensation morphogenesis: a networkof two avian galectins, Gal-1A and Gal-8, regulate each otherthrough a mutually positive feedback loop at the level of geneexpression. Gal-1A upregulates the expression of its own coun-terreceptor and the interaction between the two upregulatescell adhesion and digital condensations. Intercellular adhesiondecreases cellular motility which decreases the probability ofestablishment of mutually positive galectin gene expression feed-back. The formation of condensations and digits mediated bymultiscale and excitable molecular–cellular architecture is underregulation of tissue microenvironment (the FGF secreting api-cal ectodermal ridge, AER) and the macroenvironment (such astemperature) (based on Sturkie 1943; Moftah et al. 2002; Bhatet al. 2011; Glimm et al. 2014).

a multiscale system from uniscale ordered and disorderedsystems.Let us further the concept of multiscale mechanisms

with a biological example. The tetrapod autopodium rep-resents an evolutionary novelty and the question of howdigits are patterned, i.e. how their sizing and spacing aredetermined has been under investigation for almost a cen-tury (Fell andRobison1929; Saunders 1948;Gilbert 1991).Eachautopodial skeletal element is precededbya cartilagi-nous counterpart that is the result of the differentiationof highly condensed aggregates of precartilage limb budmesenchymal cells, known as digital condensations (Halland Miyake 2000). Each condensation is surrounded bymesenchymal cells that do not participate in condensationformation and eventually apoptose in vivo to give rise tointerdigital spaces.Two independent molecular mechanisms have been

independently proposed to explain how the digits are pat-ternedwithin the developing limb bud. The first mechanis-tic network consists of the expression of the transcriptionfactor Sox9, as a result of its dynamic interaction withtwo diffusible morphogens, BMP and Wnt (Raspopovicet al. 2014). The motivation of this autoregulatory Turing-like reaction diffusion network (called the BSW model)is to ensure peaks in Sox9 expression (one of the earliestmolecular markers of condensations) separated in spaceby troughs in the same expression, leading to digit for-mation in the peak regions. The model proposes, andshows some evidence for autoregulatory negative feed-backs for both BMP andWnt, negative regulation of both

by Sox9, and a positive regulation of Sox9 by BMP. Thesecondmechanismof digital patterning unraveled throughstudies on avian embryonic appendages entails the earlyexpression of two diffusible β lactoside-binding proteinsgalectin-1A (Gal-1A) and Gal-8 and their counterrecep-tors within condensing limbmesenchyme (Bhat et al. 2011;Lorda-Diez et al. 2011). The digital pattern, according tothis mechanism, requires several distinct interactions atmultiple spatiotemporal scales: first, a positive feedbackbetween the expressions of the genes encoding the two dif-fusible galectins; second, the inhibition by Gal-8 protein,of the ability of Gal-1A protein to mediate intercellularadhesion; third, the mediation of intercellular adhesion bythe upregulation by Gal-1A of its own cell surface coun-terreceptor; and fourth, the ability of cells to inherentlyundergo mesenchymal motility. Coordinated interactionsbetween the molecules in the context of motile cells basedon a reaction–diffusion–adhesion scheme leads to the pat-terning of digital condensations within the developingavian limb (Glimm et al.2014) (figure3).Both thesemodelscontrast with a uniscale scheme of ‘positional information’where the limb cells autonomously respond to the coordi-nates of a diffusing morphogen secreted from a localizedcentre, by assuming distinct differentiation fates (Wolpert1969, 1989, 2011).

Can we generalize our idea of multiscale interconsti-tutent relationships to biological examples and devel-opmental mechanisms that do not necessarily involvediffusible morphogens? One of us has earlier proposedthat mechanisms of multicellular development comprisemolecules acting at two or more distinct spatial or tem-poral scales with one spatial scale that is equal to, orexceeding, the spatial scale of single cells (Newman andBhat 2009). In the above example, the morphogens (BMPandWnt and galectins) diffuse across a multicellular field.Upon examination, severalmembers of the developmentalgenetic toolkit in animals mediate distinct physicochem-ical changes across specific spatial scales (Newman andBhat 2008; Engler et al. 2009). Cell adhesion moleculeswhen expressed uniformly, can convert a population ofcells into adheredmulticellular structures.When expressedacross molecular thresholds, this leads to sorting betweenmore adhesive and relatively less adhesive multicellularpopulations (Duguay et al. 2003). Juxtacrine signallingmechanisms mediated by transmembrane receptor andtransmembrane ligand couples result in lateral inhibitionat the spatial scale of single cells, i.e. a single cell adoptsa different fate from those surrounding it (Simpson 1997).Recent work on oscillation in gene expression of cyto-plasmic proteins and transcription factors downstream ofNotch, Wnt and FGF pathways shows how cell fates canbe coordinated by juxtacrine cell interactions over largermulticellular scales such as the presomitic mesoderm, thetissue that gives rise to the somites during vertebrate seg-mentation (Aulehla and Pourquie 2006; Dequeant et al.2006). Juxtacrine molecules that are involved in the planar


cell polarity, upon stimulation by extracellular Wnt gra-dients are able to establish and synchronize the polarityof cells across tissue fields altering their pattern (Axel-rod and Tomlin 2011). The production of ECM proteinswithin proliferating cells and their arrangement into pro-tein superstructures such as basal laminae results in aheterogeneity of physical and chemical cues dynamicallytransmitted to those cells that are proximal to the lami-nae, relative to those that are distal, altering the signallingwithin, andpatterningof, cellular collectives (Spencer et al.2010). It is however important to note that the moleculesthat act at, and mediate such functions across, distinct cel-lular scales, do not do so in isolation from one another,but are wired to each other through gene regulatory net-works or transcription factors. For example, the formationof somites is brought about by a spatially variable regula-tion of phase synchronization of cyclic gene expressionby a morphogen gradient (FGF) (Aulehla and Pourquie2006).

A second example is the postnatal branching mor-phogenesis in murine mammary glands that requires thecoordinated expression and activation of transmembranemolecules through the interaction of the cells with theirsurrounding matrix: integrins, and cytoplasmic signallingcues for cell proliferation: Erk1/2 pathway (Whyte et al.2009). Their coordinated expression is mediated by agalectin, which gets secreted to the extracellular mileu,only to repartition into apposite cellular compartmentsand pattern the mammary epithelia (Bhat et al. 2016a).Specification of the rostrocaudal axis in the early ver-tebrate embryos is guided by coordinated expression ofmembers of the bone morphogenetic proteins, their dif-fusible antagonists, matrix metalloproteinases and decoycytoplasmic receptors, creating robust spatially regulatedgradients of signalling that specify cell fates across mul-ticellular fields (Reversade and De Robertis 2005). Inall the three examples stated above, molecules mediat-ing discrete functions across diverse scales combine inunique ways to form regulatory networks that mediatedevelopmental pattern formation.We have earlier codifiedan ontogenetic framework, wherein we describe entitiesknownasdynamical patterningmodules (DPMs) that con-tribute in discrete ways tomulticellular patterning throughthe deployment of physical or chemical processes suchas diffusion, adhesion, lateral inhibition, matrix forma-tion, cell division and death,multicellular polarization etc.(Newman and Bhat 2008, 2009). DPMs therefore rep-resent a lens for understanding the formation of tissues,organs and organisms not just through the expression ofgenes but through the deployment of specific gene prod-ucts that contribute to discrete intercellular behaviour,forming and transforming tissue-specificmulticellular pat-terns.Having advocated a multiscale interconstituent archi-

tecture for complex systems, we also ask if there are

generic rules to the global topologies of intercompo-nent connectivities. Widely communicated observationsby Albert-László Barabási and coworkers relate to thetopology of real-world networks, proposing them to begenerically ‘scale-free’, which means that the degree ofdistribution (as in the number of nodes to which a givennode is connected) follows a power law: more connectednodes are fewer in number and relatively less connectednodes are greater in number (Barabási 2002;Newman et al.2006a). Barabasi’s model asserts that the scale-free net-work topology is not incidental to (or a consequence of)network functions, but rather causal to the maintainedfunctioning of the system. Simply put, the most denselyconnected nodes act as hubs connected to a large numberof sparsely connected nodes, and also, importantly, holdtogether the network’s integrity, so much so that removingthese hubs (or rewiring them) has the highest probability ofdisrupting the entire network. Therefore scale-freeness iscrucial in rendering the network robust-yet-fragile: Bar-Yam and Epstein have argued that scale-free networkswithin specific limits on the scaling exponents exhibithigher sensitivity to cues when compared to random topo-logical counterparts, while retaining robustness to otherstimuli (Bar-Yam and Epstein 2004).

The essentiality of scale-freeness to the performance ofreal-world complex systems is critiqued on the groundsthat it represents one of the various existent real-worldnetwork topologies (Li et al. 2006). Secondly, an examina-tion of those networks that exhibit an approximate versionof power law-like distribution, reveals that the robust-yet-fragile property is not causal to scale-free connectivity, i.e.thehighest-connectedhubs are thenotweakest ‘links in thechain’ (Bollobás 1998). In fact, using a dynamical networkmodel, networks with scaling components significantlylesser than that for ideal scale-free counterpartswere foundto be relatively more sensitive to environmental stimuli(Bar-Yam and Epstein 2004). Some analyses carried outon the world wide web infrastructure seem to show thatthe network architecture is centred on a mesh-like distri-bution of moderately-connected high-bandwidth routersand is sensitive to real-world constraints such as contem-poraneous router technologies and link costs (Aldersonet al. 2005).Whether multiscale intercomponent interaction net-

works that are responsible for the establishment of multi-cellular phenotypes during development have a scale-freeor optimized architecture is still far from clear. In fact,studies on hierarchically organized excitable networks inbiological systems indicate that their dynamical behaviourcould depend on hub-like nodes or subcentralized con-nectedmodules, depending on the biological system underinvestigation (Muller-Linow et al. 2008). A more crucialquestion is whether such architectures are evolvable? Inother words, how easy (or not) is it for suboptimally per-forming molecular architectures exploring configuration


phase spaces to traverse to subspaces where they can per-form optimally (Braha et al. 2006). In the subsequent twosections, we endeavor to answer this question.

Excitability

Excitability is a property of spatially extended dynami-cal systems by which a perturbing input evokes an outputwhose strength is disconnected to the strength of the input,but which can be propagated through the spatial distri-bution of the system, often with a following refractoryperiod (Mikhailov 1990). A suprathreshold stimulus isthus able to nudge the system out of a steady state, allow-ing it to undergo excursions and then return back to thesteady state. Therefore, excitability is more than just thecontinuity of, or interconnectivity between, components;the latter are coupled in a manner so as to allow thepropagation of energy or information within the system(Zykov 1987). Excitability results in nonlinear dynamicalbehaviourwhich is characteristic of a large variety ofmate-rials and media. Because of the distribution of the energysource within excitable media, such systems are able toexhibit unique patterns such as wave trains, spiral andscroll waves (Winfree 2001).

Excitable chemical systems show spatial or temporaloutput patterns. A specific class of chemical reactions wasdiscovered in the early 20th century that could exhibitspontaneous spatial and temporal patterns of colour.Chemical components, common to these reactions wouldbe an acid and a halogen, such as bromine or iodine. Thefirst such reaction was described by the Soviet chemistBorisBelousov (Zhang et al.1993).The full chemical inves-tigation of Belousov’s reaction (consisting ofmalonic acid,cerium sulphate and potassium bromate) was carried outby Anatol Zhabotinsky and hence the reaction is namedBelousov–Zhabotinsky (or B–Z) reaction (Tyson 1976).TheBriggs–Rauscher reaction shows temporal oscillationsinstead of spatial patterns (Briggs and Rauscher 1973;Weigel 1981). Combining iodate with hydrogen peroxideusing starch as an indicator leads to a stirred solution thatperiodically oscillates between dark blue and colourlessseveral times before turning blue finally. The oscillationsare dependent on temperature: the higher the latter, thefaster the oscillations. B–Z reactions are examples of opennonequilibrium thermodynamic systems that store anddissipate energy with respect to their environment.The nonlinear excitable nature of dissipative systems

is also responsible for the property of self-organization:the ‘spontaneous appearance of large-scale organizationthrough limited interactions among simple components’(Braha et al. 2006). Self-organization entails the emergenceof symmetry or correlation in a disordered system. Natureis replete with examples of self-organization, from galax-ies to tornadoes, and from increasing examples of cyclicalchanges in temporal to spatial properties and regimes. Notjust within abiotic chemical systems, self-organization is

also evidenced in, and in fact characteristic of, biologicalsystems. For example, spiral waves similar to B–Z reac-tions, taking place at different spatial and temporal scaleshave been observed for dictyosteliid amoeba that can orga-nize to form fruiting bodies by signalling to each otherusing cAMP(Palsson et al.1997).Evenwithin themulticel-lular mound formation, propagating chemotactic waves,both in concentric ring formaswell as spiral type havebeenobserved in distinct strains andguide the orientationof cellmovement accordingly (Siegert and Weijer 1995). Tempo-ral oscillations have been observed over several scales inbiology. Oscillation in expression of genes and periodic-ity in Notch signalling within the presomitic mesodermof embryos guides the formation of somites in vertebrates(Palmeirim et al. 1997). Oscillations in expression of periodgene and its product drive the circadian rhythms of activityand development in animals (Hardin et al. 1990).The dynamical properties of excitable systems have

often been modelled using multiscale mathematical mod-els such as reaction diffusion (Petrov et al. 1995; Merkinet al. 1996; Forgács and Newman 2005). This is reflec-tive of the self-organizational aspect of excitable systems:Gierer and Meinhardt describe self-organization as thebalance between positive and negative feedbacks (Mein-hardt 1982), with reaction diffusion being a special caseof the larger locally autoactive lateral inhibitory class ofmechanisms (Meinhardt and Gierer 2000). This suggeststhat multiscale excitable systems achieve organizationthrough reciprocal interactions involving feedbacks.Not unlike chemical excitable media, self-organizing

biological media are not insulated from their microenvi-ronment ormacroenvironment. In fact, they exhibit a greatdeal of plasticity in response to external cues. However,the ability to self-organize in a robust manner is intrinsicto the system with the microenvironment or macroenvi-ronment serving to modulate the pattern. Reinvoking theexample of limb development, investigators have shownthat the digital mesenchyme when dissected out and dis-sociated and inserted back under limb ectodermal jacketsor cultured in vivo were able to form rudimentarily pat-terned digits (Zwilling 1964; Ros et al. 1994), suggestingthat the ability ofmesenchymal cells to self-organize them-selves into condensations (surrounded by noncondensingmesenchyme) is intrinsic to them and is regulated by ecto-dermal signals (Newman and Bhat 2007) (figure 3).

The excitability of biological systems is also a functionof their material properties: both cells and extracellularmatrix can act as recipients and propagators of chemi-cal and mechanical cues. Biological tissues share anotherproperty with complex chemical systems: they are ‘softmatter’, i.e. materials that are deformable often viscoelas-tic and show organizing properties at scales intermediatebetween macroscopic and microscopic scales (Hamley2000, 2007). These properties are therefore common tocells, tissues and organs as well as complex abiotic flu-ids such as gels, foam, copolymers and liquid crystals


(De Gennes 1975, 1992; Epstein and Pojman 1998). Thediversity in physicochemical compositions of ECMs andthe cells embedded within the latter enhances the modali-ties of signal propagation within such systems in the formof paracrine and juxtacrine signals, or through mechan-ical traction and compression forces making them moreexcitable. Thematerial properties of ECMhas for instance,been shown to alter cell differentiation fates (Engleret al. 2006; Alcaraz et al. 2008) as well as their polar-ity and morphogenesis (Aragona et al. 2013; Ranga et al.2016).

The multiscale nature of component architectures andthe excitability of biological tissues play crucial roles inmulticellular pattern formation. Spatiotemporal multicel-lular patterns represent order/organization at mesoscopicscales (Wagoner Johnson and Harley 2011). This allowsus to liken mesoscopically patterned cellular collectives topartially ordered structures that lie between ordered anddisordered systems (as referred to in the previous section).Developmental pattern formation brings into relevancethe emergence of organization at spatial scales in additionto already existing ones. The emergence is contingent onthe formation of novel multiscale architectures that are theresult of the expression and physicochemical properties ofthe specific gene products, but also the context of excitableand soft nature of the tissue (comprising the cells and theirsurrounding ECM) wherein the molecular components ofsuch multiscale architectures are expressed.

The evolution of complexity

We now turn to the most speculative association of thisperspective: the relationship between the evolution ofmor-phological phenotype and the criteria we have proposedabove that are central to the notion of complexity, i.e.multiscalarity and excitability. It is challenging to ascer-tain in a quantifiable manner if molecular mechanisms ofphenotypic determination have become more multiscaleover phylogenetic time periods, given the discontinuousand punctuated nature of the evolution of multicellularphenotypes. It is nevertheless interesting to note that anexamination of the genomes of representatives of extantphyla shows a gradational increase in acquisition of thosegene products, which contribute to multiscale pattern for-mation we described above. For example, the sequencedgenome of Monosiga brevicollis, a unicellular holozoanchoanoflagellate (and closest living relatives ofmetazoans)lacks Notch, Delta, and Fringe family of genes, whichare essential for juxtacrine cell communication witnessedin lateral inhibition-based and temporal synchronization-based patterning of cell state specification (Gazave et al.2009). In addition, its genome also lacks genes that codefor classical morphogens Wnts and TGF-β and theirreceptors, pathways involved in polarity and epithelial-to-mesenchymal transitions (King et al. 2008).Representative

placozoans and sponges, metazoans with indeterminatebody plans, lack genes that encode for proteins medi-ating planar cell polarity (involved in cell intercalationand convergent extension) as well as proteins that con-stitute epithelial-specific extracellular matrices (Newman2012). Diploblast phyla such as cnidaria and ctenophoraexpress proteins constituting basal lamina, but may lacksomemesenchymal-specificECMglycoproteins character-istic of chordates, or their cognate-binding proteins suchas lectins (Jeeva andZalik 1996). Therefore, key patterningmodules that individually, or in combination, give rise todiversity in body plans seem to have been added on andretained along the evolutionary trajectory of multicellularanimals.Coming from a generic angle, it is pertinent to men-

tion that work done on real-world nonbiological networkarchitecture emphasizes theneed for solution-rich configu-ration spaces (Braha et al. 2006): wide ‘non-rare’ paramet-ric regimes, which allow for robust self-organization andeven tolerate parametric variation with noncatastrophicconsequences, and allow excursions out of subspacesthat represent suboptimally organized or functioningarchitectures. A recent example of the presence of such‘solution-rich configuration spaces’ is the galectin-basedmechanism of digital pattern formation in tetrapod limbs(Bhat et al. 2016b). The identified parametric phase sub-space permissive for endoskeletal element number andpattern typical of tetrapod autopodium is continuous withsubspaceswhich are representative of patterns of nontetra-pod ancestral appendicular endoskeleta. Interestingly, themolecular architecture on which the parametric space wasconstructed is both multiscale in nature as well as accom-modates excitable properties of appendicular mesenchyme(such as the ability to secrete and react to galectins, whileundergoing mesenchymal motility and intercellular adhe-sion) (Bhat et al. 2016b).Can we arrive at a metric for complexity based on our

understanding of development occurring within excitablebiomaterial systems with multiscale architectures? Wepropose that the complexity of a given morphologicalphenotype is a function of the interlinkage or intercon-nectivity between the DPMs involved in giving rise tothe phenotype. A close link between DPMs increases thepotential of an excitable system to give rise to intricatemulticellular architectures. This linkage could be estab-lished along both developmental and evolutionary timearrows. In developmental time, a connected deploymentof two DPMs leads to the formation of heterogeneousmulticellular arrangements and patterns within a homoge-neous field of cells. Inmacroevolutionary time, the numberand combinations of codeployed DPMs could be cru-cial to the determination of diversity in, and innovationof, body-plans and organ-plans. Complexity also helpsaccount for a greater diversity of tissue-types and pattern-types of triploblasts (from relatively stiff types like bone,through relatively viscoelastic types such as tendons and


ligaments, to liquid-like epitheloid and liquid (blood) tis-sues) compared with diploblasts, sponges and transientlymulticellular organisms. In fact, the repertoire of extracel-lular matrix proteins, which can contribute significantly tothe rheological properties of tissues, is greater in deuteros-tomes and especially vertebrates as a result of duplicationsand domain shuffling and recombinations (Ozbek et al.2010; Hynes 2012).

On the other hand, in microevolutionary time, thestrength in the interlinkage of the molecular componentsof DPMs could play an important role in constrainingor biasing the evolution of morphological phenotypesand patterns. Therefore, in the example used recurrentlyin this essay, i.e. the evolution of the tetrapod appen-dicular skeleton, a constraint in the values of Gal-8expression rate (which determines the excitable posi-tive feedback loop between Gal-1A and Gal-8) and thebinding affinity of Gal-8 to its glycoligands (which regu-lates cell adhesivity) are imperative to the determinationof the tetrapod endoskeletal pattern. This shows howexcitable multiscale developmental mechanisms influencethe evolution of a complex morphological skeletal pat-tern.It is worth mentioning that previous attempts to seek

a gradient of complexity in evolutionary time employa nonstructural genomic criterion. Work by ChristophAdami, Charles Ofria and Richard Lenski uses a defi-nition of complexity as the information that a sequencestores about its environment (Adami 2002). Using an insilico environment, where digital organisms with genomesact as Darwinian populations, Adami and others ele-gantlydemonstrate that complexity increasesprogressively(Adami et al. 2000). Digital organisms evolve to increasetheir genomic size consistent with an attempt to assimi-late further information about their environment.Watkinsuses a similar definition of complexity to come up withan information theoretic model of its evolution, observ-ing that in sexually reproducing organisms, complexity (interms of novel behaviour and adaptation) can be maxi-mized if the organismal genomes are long enough such thatgenomic variation persists within populations (Watkins2009).

A more structural definition of complexity, especiallyone that incorporates excitability as a fundamental com-ponent of the definition assumes that change in phenotypecan be brought about by (i) genetic change, (ii) envi-ronmental change, (iii) interaction between genotype andenvironment, and (iv) noise or other inexplicable factors.Factor 2 is known as phenotypic plasticity and is the prop-erty of a single genotype to undergo alteration in responseto an environmental difference (Nanjundiah 2003). It iswell accepted that organisms alter their anatomy, phys-iology and behaviour in response to alterations in theirenvironment and the known variation in any given trait inresponse to the corresponding environmental alteration isknown as reaction norm.

Phenotypic plasticity can be, but is not necessarily,adaptive. The influence of phenotypic plasticity on theevolvability of form and function (more specifically, theextent of its influence) has been a subject of rich debate(Müller andPigliucci 2010;Laland et al.2014) and is oneofthe central questions of the field of evolutionary develop-mental biology (Müller andPigliucci 2010)West-Eberhardhas argued that plasticity plays a central role in pheno-typic evolution (West-Eberhard 1989). Her framework isone of the strongest attempts to integrate nonadaptiveplasticity (the direct and noninherited effect of plasticityon excitable biological form) with the modern synthesisby asserting that the alteration in phenotypic traits asa plastic response to environmental cues takes place inthe context of, and permissive to, associated coexpressedphenotypic traits. If the plastic response enhances fitness,such trait combinations could get selected during evolu-tion, resulting in shifts of developmental reaction norm,or the variability of the original trait to environment. Inthis way, phenotypic plasticity, and hence environment,could contribute to the evolutionary trajectories of organ-isms. Therefore, interlinked trait ‘dependencies’, throughWest-Eberhard’s framework, ensure that plastic responsesget accommodated within the genotype and fixed withinevolving populations. Theoretical extensions by Kanekoand coworkers, using simulations of catalytic reaction net-works (Kaneko and Furusawa 2006) and gene regulatorynetworks (Kaneko 2007, 2008), in fact show a positivecorrelation between phenotypic plasticity, evolvability andrate of evolution.The innovationof signallingmolecules thatwere required

to render biological tissue soft and excitable (i.e. thosethat comprise DPMs), facilitated by radical macroenvi-ronmental changes, potentially brought about a hecticperiod of evolutionary origination of organismal bodyplans coincidentwith theCambrian period (Newman et al.2006b). Subsequently, the stabilization, possibly throughaccommodative mechanisms described in the previousparagraph, aswell as through evolution of further genomicregulation, led to a decrease in both the phylogenetic plas-ticity of existent phenotypes and innovation of furthernovel phenotypes, at least at the level of body plans ina ‘post-Cambrian’ world.

Conclusion

An important dimension missing from our essay is a dis-cussion on complexity in relation to populations that areable to evolve through natural selection and are able toacquire novel phenotypic traits. This philosophical think-ing forwarded recently by Peter Godfrey-Smith under theconcept of ‘Darwinian populations’ explores a multidi-mensional population-based approach to understandinghow complex (sensu Adami) adaptive traits originate andevolve (Godfrey-Smith 2009). Godfrey-Smith associates


the latterwith the requirement of a combinationof featuresas smoothness of fitness landscapes, bottlenecks, special-ization etc. We hope to integrate this aspect within ourpresentation of complexity in later extensions of this per-spective. In this perspective, we have also not extendedour analyses tomultispecies ecological systems, where oth-ers have sought to search for candidate laws (Jorgensen1992). Of these, the metric known as ascendancy hasbeen proposed byUlanowicz to includemutually exclusiveparameters signifying the (multidimensional) organiza-tion of trophic interactions and what he denotes as theoverhead, a measure of the system’s strength in reserve,linked directly to its organizing ability in the face of per-turbation (Ulanowicz 2003). The similarity between thesetwo sub-metrics on the one hand, and multiscalarity andexcitability on the other, is hard to miss.In conclusion, we present a narrative of complexity of

biological form which moves beyond an informatic under-standing of the same, into a structural one. Therefore,complex forms are no longer ‘simply’ multicomponent(and hence complicated) but also multiscale. Multiscalemulticomponent biological systems additionally need tobe excitable in order to self-organize and exhibit pheno-typic complexity.Why is such a structural understanding of complexity

important? Deeper investigations into the molecular–cellularmechanisms of diseases such as cancer suggest thatthe latter do not invariably witness a loss in tissue architec-ture (Nelson and Bissell 2006) but also transiently acquirenew multicellular patterns and morphologies (Lengyel2010; Aceto et al. 2014). Our analysis of complexity wouldnow allow us to make some testable predictions regard-ing the generic principles of complex morphogenesis evenin the unlikeliest of pathophysiological contexts, suchas a reestablishment of multiscale architecture in metas-tasizing cancer cells that would tie key morphogeneticproperties such as polarity, adhesion and secretion ofmor-phogens andECM,making them excitable and sensitive totheir new extracellular microenvironments. We anticipatethat future theoretical efforts to model organ-complexitiesand organismal-complexities would better accommodatethe material properties of multicellular collectives withinextant multiscale cellular–molecular networks in the spiritof thequest laidout in an influential essay ‘Molecular vital-ism’ at the beginning of the 20th century: to understandthe chemistry behind evolvable but robust organized (and,may we add, complex) morphogenetic systems (Kirschneret al. 2000).

Acknowledgements

R.B. would like to thank the organizers of 3rd Foundations ofBiologymeeting held at the Indian Institute of ScienceEducationand Research, Pune, where an intense dialogue with the partici-pants on complexity led to several of the ideas proposed in thismanuscript. We would also like to thank Stuart A. Newman,

Tilmann Glimm, Christopher Rose, I. S. Mian and three anony-mous reviewers for providing valuable criticisms on earlier draftsof this manuscript.

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