REVIEW

doi:10.1098/rsif.2006.0173

Published online

*Author for c

Received 9 AAccepted 10 A

Explaining a complex living system:dynamics, multi-scaling and emergence

Irun R. Cohen1 and David Harel2,*

1Department of Immunology, and 2Department of Computer Science and AppliedMathematics, The Weizmann Institute of Science, 76100 Rehovot, Israel

Complex living systems are difficult to understand. They obey the laws of physics andchemistry, but these basic laws do not explain their behaviour; each component part of acomplex system participates in many different interactions and these interactions generateunforeseeable, emergent properties. For example, microscopic interactions between non-living molecules, at the macroscopic level, produce a living cell. Here we discuss how toexplain such complexity in the format of a dynamic model that is mathematically precise, yetunderstandable. Precise, computer-aided modelling will make it easier to formulate novelexperiments and attain understanding and control of key biological processes.

Keywords: biological modelling; reactive animation; emergence properties; reactive system

1. EXPLANATION

Science seeks explanations. To explain, according to thedictionary, is to relieve an idea, event or object of itsobscurity, complexity or difficulty. In other words, toexplain is to make the thing simple. The root meaningof explanation derives from the Latin planus, whichdenotes a plane, a flat and even surface (Oxford EnglishDictionary 1989). Thus, one might say that the idea ofan explanation is to connote the plain and simple, theuncomplicated two-dimensional. The English wordplan also derives from the same Latin planus. Plansneed to be dependable, unchanging and plain—free ofunnecessary complications. Classically, an ideal scien-tific explanation reduces the apparent complexity ofnature to a smooth plane of immutable natural laws(Popper 2000).

The living organism, however, resists smooth expla-nations (Fleck 1979; Efroni & Cohen 2002). Biology hasdone well in its plan to carve living systems into theircomponent parts, but the reductionist program has notuncovered the fundamental laws from which we candeduce how a particular living system actually works.A cell cannot be reduced to a few formative principles,in the way, for example, the behaviour of the SolarSystem can be reduced to the laws of gravity andmotion (Cohen 2000). We even find it difficult toassemble the great amounts of experimental data intoan understandable whole. Most would agree thatcomputer-assisted computational tools are needed todeal with the data in hand (Harel 2003). One’s choice of

orrespondence (dharel@weizmann.ac.il).

pril 2006pril 2006 1

informatic approach, however, depends on one’s view ofthe organism.

2. TRANSFORMATION

The discovery that DNA embodies the genetic code hasdrawn attention to DNA both as the cell’s primaryreservoir of information and as the informatic vehicle forevolutionary change (Mayr 1961). Biologic explanationsoften start with DNA: biological information is seen tooriginate in the genome, and this genomic DNAinformation is translated, by the way ofRNA transcripts,into the diversity of expressed proteins—the proteome.The proteome then fashions the phenotype that definesthe functioning organism. The genome, from such aviewpoint, appears as the master plan—the explana-tion—that encodes the organism (Mayr 1961). This viewhas motivated many to develop bioinformatic algorith-micmethods:first, to readthegenetic program; second, todecipher how genetic information is transformed into aphenotype; and third, to discover hownatural selection ofthe more fit phenotypes, in turn, feeds back to influencethe frequencies of particular genotypes, and thus driveevolution; for example, see Mossel & Vigoda (2005). Thefinal incarnation of DNA information is the transfor-mation of biological processes into ideas by humanminds(exemplified by the way scientists do experiments, deriveconclusions and write papers; Cohen 2006). In theparlance of system design, DNA-based informatics seesthe organism as a transformational system (Harel &Pnueli 1985): the organism transforms DNA sequenceinformation, the genetic ‘program’, into its phenotype, ina series of sub-transformations. Figure 1 depicts this

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This journal is q 2006 The Royal Society

genome

proteome

organism

survival of thefittest

species

transformational system

environmentaltesting

evolution ofvariation

Figure 1. Life as a transformational system. In this scheme,the information encoded in the genome—the DNA—istransformed into the proteome—functional proteins—that,in turn, generate the organism and the species. The fitness ofthe organism and the species in the environment feed back toselect better-adapted genomes and evolution results.

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cyclical transformation of DNA information. The expla-nation of the living system, from this viewpoint, isobtained not by reducing its complexity to a simpleunderlying ‘one-dimensional’ genetic code, but rather byreducing its complexity to an orderly, sequentialtransformation of information from genes to phenotypes(Mayr 1961).This transformational plan is not static, buthomeostatic—the transformation of information fromgenome to phenotype, with the help of controllingfeedback loops, generates the evolution of a stable,balanced adaptation of the living system to its changingenvironment (Segel & Bar-Or 1999).

3. REACTION

But there is another way of explaining the livingsystem; not as a hierarchical, sequential transformationalsystem, but as a highly concurrent reactive system(Harel & Pnueli 1985; Harel 2003). A reactive system,in contrast to a transformational system, does not behaveaccording to a pre-programmed chain of linked instruc-tions. Rather, such a system reacts in parallel to manyconcurrent inputs, and its behaviours, outputs andeffects, are not just a function of the values of its inputsbut also of their variety, of the order inwhich they arrive,of their timing, of their arrival speeds and so forth.A reactive systemexpresses a dynamic narrative inwhichthe DNA code is one of the many formative inputs(figure 2). Structural proteins, enzymes, carbohydrates,lipids, intracellular signals, hormones and othermolecules play key roles in forming and informing thesystem. The environment of the living system is a mostcritical source of information (Cohen 2006). True, DNAserves as a special repository of information because it isreplicated and transmitted across generations, but DNAis meaningless without the proteins and other moleculesthat selectively activate segments of theDNAsequence in

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variable and alternative ways to create genes. Theactivation of specific genes emerges from the dynamicstate of the cell.One could argue thatDNA is just asmucha servant of the cell’s state as it is the cell’smaster; there isno hierarchical master plan (Cohen & Atlan 2006).

Note that, unlike a transformational system, areactive system does not seek equilibrium, has no setpoint and no state of rest (Cohen 2000). A reactivesystem holds itself together as a system just by reacting.A reactive system succeeds not by reaching homeostasis;a brain in homeostasis is clinically dead. A reactivesystem succeeds by being both robust and resilient. Thereactive system responds to simultaneous perturbationsand continues to survive; thanks to its reactivedynamics. It is true that organisms feature sub-systemsthat can be described nicely by homeostatic principles;some examples are the thermoregulatory system thatmaintains your internal temperature at 378C, yourwater balance system and blood glucose regulation. Butthese systems act only like the transformational systemswhenviewed as awhole; internally, each of these systemsis fashioned by collectives of concurrently reactive,never-resting cells.

4. EMERGENCE ACROSS SCALES

Reactive systems call our attention to their emergentproperties. An emergent property of a system is abehaviour of the system, taken as whole, that is notexpressed by any one of the lower-scale componentsthat comprise it. Life, for example, is an emergentproperty; none of the component molecules of a cell arealive, only a whole cell lives. Emergence is difficult todefine in biological terms. A recent survey lists fivedifferent definitions of emergence (Deguet et al. 2006).The notion of ‘levels’, however, is shared by all the fivedefinitions (Deguet et al. 2006). Emergence, in otherwords, is a matter of scale.

A cell emerges from the structured interactions ofthe molecules that comprise the cell. But the cell isorders of magnitude larger than its component molecu-lar interactions. Obviously, you cannot see a cell fromthe inside at the molecular scale. The cell emerges onlywhen you step back—zoom out—and look at thecellular system at a scale appropriate to seeing anentire cell. The cell emerges from its componentinteractions at the scale at which the cell functions asan object with its own interactions with other cells andmolecules. In other words, interactions at one scalecreate objects at a higher scale; that is, transition frominteraction to object is the essence of emergence(figure 3). Molecular interactions create higher-scalecells, cellular interactions create higher-scale organs,and so on from organisms to societies. The microscopicactivities of your neurons, for example, give rise to themacroscopic behaviour of your brain only when we viewthe brain; at lower scales of observation we see onlycells or molecules. Indeed, reading this article emergesat the scale of a whole human (who has learned to read)from underlying interactions at the cellular scale of eyeand brain. Obviously, the capacity to read cannot bededuced merely by cataloguing all the neurons andtheir connections in your eye and brain. A human brain

reactive system

organism

species

DNAsequence

expressed genessRNA protein expression;

modifications

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environment

history

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Figure 2. The living organism as a reactive system. According to this view, the cell, the organism and the species are not meresequential transformations of information encoded in the genome—a DNA master program. Living cells, organisms and speciesemerge from a web of ongoing concurrent interactions of various entities and processes; DNA is only one of the manyparticipating informational entities.

scales interactions

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emergence:

interactions at a lower scale formobjects at a higher scale

Figure 3. The emergence of objects. Objects emerge at higherscales from interactions at lower scales. Molecularinteractions at one scale give rise to a cell at a higher scale:interactions between cells generate an organ; interactionsbetween organs generate an organism; and interactionsbetween organisms generate a society.

Review I. R. Cohen and D. Harel 3

at the neuronal scale looks pretty much like the brain ofa chimpanzee, and the DNA of chimpanzees andhumans differ by only a few per cent (Olson & Varki2003). But still only humans will read this article;reading emerges from human cultures that have usedhuman brains to invent reading.

A major goal of systems biology is to learn how theconcurrent reactions and interactions of the lower-scalecomponents of a cell, organism or society generateemergent properties visible at higher scales and higherlayers of reality. In particular, we want to know aboutthe factors responsible for a system’s robustness (whichgenes, for example, can be knocked out withoutchanging the phenotype and which cannot) and for asystem’s resilience (which molecules are critical incontrolling the system’s behaviour). We would liketo know, for example, which neuronal interactionsgenerate reading.

The larger-scale system we need for observing wholecells, for example, canbevariedaccording to theobjectiveof the study; we can observe cells through an electronmicroscope, through their secretions, shape or move-ment, through their interactions in tissue culture, in anorganism, and so forth. Likewise, the organism emergeswhen we observe collections of cells at a scale at whichthe collective—the organism—performs collectiveinteractions with other organisms (Cohen 2006). Biologicentities, like Russian Babushka dolls, are formed byembedded interactions at various scales and variouslayers. Interactions at a lower scale emerge as objectsexpressing their own properties at a higher scale. Scalingis the key to emergence; emergent properties arise as newobjects from one scale to the next (figure 3).

To see emergence and study it, one has to be able toobserve and manipulate the system at more than onescale. One has to cross scales to see how lower-scalemolecular interactions create and affect higher-scalecellular interactions; one would like to know the effects

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of molecular experiments (lower-scale manipulations)on cellular behaviours (higher-scale outcomes). Thus, acomputer methodology that would allow us to zoomback and forth between lower-scale data and higher-scale behaviour while experimenting in silico is an idealway—possibly the only way—to study emergencecomputationally.

5. REACTIVE ANIMATION

One of the techniques we have used in our own study ofemergence in reactive systems is what we call reactiveanimation (RA; Efroni et al. 2003, 2005). RA is aprecise representation of a complex system, but it doesnot search for orderly organizing principles imposed bythe informed biologist top-down. Rather, RA begins

4 Review I. R. Cohen and D. Harel

bottom-up by translating the actual database gener-ated by experiments and observations into a precisedynamic notation legible to computers and executableby computers. RA then proceeds to exhibit theexecuted simulations transformed into a realisticallyanimated front end, easily recognized and compre-hended by biologists. RA is thus fashioned in two tiers:specification and animation.

We have achieved precise specification of experi-mental data using the visual computer language ofStatecharts as an example of choice (Harel 1987; Harel &Gery 1997).1 The Statecharts language was initiallydeveloped to create and study reactive systems designedby human brains, such as aerospace and automotivesystems, telecommunication and control applications,interactive software and so forth. We have discovered,however, that Statecharts suits natural systems too(Kam et al. 2001).

The object-oriented version of Statecharts isembedded in a structural definition of classes of objectsand the connections between them; a statechart isconstructed for each object class, to specify the precisestate-based behaviour and the behavioural mani-festations of the connections of any object in that class(see top portion of figure 4). This notation, composed ofobject class, states and connections, is most suitable forbiology, which deals with many classes of objects(molecules, cells, organisms, societies, etc.) and withthe connections between them (interactions, inheri-tance, causal influences, etc.). Also, biologists thinkexperimentally in terms of the states of molecules, cellsand populations. So Statecharts is a well-suited mediumfor dealing with living systems.

Statecharts are modular and hierarchical, and so isthe underlying structure of the objects; you can add orremove objects, connections, states and transitions atany level. There are ample means to specify rich kindsof behaviour such as concurrency, stochasticity, chainreactions and time-dependent or time-constrainedactions. The multi-level, hierarchical nature ofStatecharts is most important to emergence: you canbuild any object (a cell, for example) from the lower-scale objects (molecules or organelles, for example) thatcreate it, and you can view behaviour on any level youchoose—molecular or cellular. The Statechartslanguage comes complete with a mathematicallyprecise dynamic semantics legible to computers,rendering it amenable to execution/simulation.

The Statecharts visual language is itself multi-scalar, but the part of RA that makes scale crossingboth more vivid and more revealing is the connectionbetween the Statecharts simulations (tier one) andtrue animation (tier two). Technically, RA involvesconnecting the Statecharts simulation tool (in ourcase, Rhapsody from I-Logix) to an animation toolthrough an interface that empowers the simulation toconstruct an animated representation (see figures 4and 5, which illustrate RA using a recent model of the

1We have used Statecharts because we are familiar with it—one of usinvented it. Other languages, however, and not only Statecharts, canbe used bottom-up to catalogue and simulate biologic data at variousscales simultaneously.

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lymph node; Swerdlin et al. submitted). We initiallydeveloped RA to study the differentiation of stemcells into mature T cells in the thymus, a criticalprocess in the development of the immune system(Efroni et al. 2003). For that study, we primed theFlash animation tool2 with visual motifs representingthe cells and parts of cells (receptors and markers)relevant to the thymus. Animation motifs, however,can be fashioned to reflect any dynamic system ofinterest: a traffic system; an operating army; aneconomic system; a political system; and so forth. RAembodies two defining features: the simulation toolinstructs the animation tool to deploy its motifsaccording to the actual simulation and one can interactwith the model and experiment with it, by the way ofeither the underlying statecharts or the front-endanimation. In our RA study of the thymus, the resultingFlash animation expressed the properties of cells thatemerged from the molecular-scale interactions fed intothe Statecharts simulation tool (Efroni et al. 2003,2005). However, the animated representation can beconstructed to suit any imaginable scale crossing, fromatoms or less (less than 10K12 m) to galaxies andbeyond (greater than 10C25 m). It is only necessarythat lower-scale reactions produce and direct a movingpicture of higher-scale objects and their behaviours(figures 4 and 5). Emergent properties are disclosed inthe animated transition from one scale to another.

We did not intend to study emergence when we builtRA, but we realized that RA created a new platform foremergence when we noticed that the RA animationdisclosed cell behaviours that were not overtly pre-programmed in the molecular data we included in theStatecharts simulation. Unexpectedly, RA revealed finedetails of cell movements in defined anatomic compart-ments in both the lymph node (Swerdlin et al. submitted)and the thymus (Efroni et al. in press), and competitionbetween individual T cells for critical stimulatoryinteractions with other cell types, selection of T cells fortheir velocity, and other high-scale behaviours hidden inthe molecular data of T-cell development in the thymus(Efroni et al. in press). These emergent properties becamenoticeable only through the transition of simulation toanimation (figure 5); the Statechart representation alonedid not disclose them. The role of competition in thephysiology of T-cell development in the thymus was notpreviously studied, or even discussed, by immunologists;the animation of T-cell behaviour in the thymus in factsimulated by RA alerted us to study the phenomenon(Efroni et al. in press). RA has thus served to catalysenovel thinking and, ultimately, experimentation.

RA not only alerts, but also empowers the observer.We built the RA interface in a way that allows theobserver to become an experimenter in silico andknockout, add or modify cells, molecules or whateverelse on the fly. The animation tool communicates themodification to the simulation tool, and the simulationgenerates a modified animation (Efroni et al. in press;

2In our RA work, we use a number of animation tools; in the thymusproject of [EHC03] and the lymph node project of [SCH06], fromwhich figures 4 and 5 are taken, we used FLASH from MACROMEDIA.

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Figure 4. From a model of the lymph node [SCH06]. Snapshots of a Statechart simulation in Rhapsody, carried out understandard conditions, together with the animated outcomes presented in Flash. The left-hand statechart describes part of thebehaviour of a B cell, which undergoes many changes as the organ evolves; the right-hand statechart describes four of the manycell receptors that play an important role in the immune response. Below the statecharts is a snapshot of the resulting animationin Flash showing the various elements in the various parts of the lymph node; see [SCH06].

Review I. R. Cohen and D. Harel 5

Swerdlin et al. submitted).Emergent properties thus canbe studied as well as revealed computationally by RA(figure 5). RA made it possible both to investigate the

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role of competition and to predict the outcomeof experimentation (Efroni et al. in press). RA combinesmodelling for explanation withmodelling for prediction.

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Figure 5. Illustrating reactive animation in the lymph nodemodel [SCH06]. In the top portion of the figure, the statechart transitionfrom figure 4 that allows a B cell to differentiate to a plasma cell has been removed (top right) and as a result no plasma cells can becreated. This can be seen in the animation snapshot (top left), which shows that B cells that were fated to become plasma cells(represented in the animation as yellow circles, secreting antibodies) stay undifferentiated (blue circles). In the bottom portion, thetransition that allows receptor CXCR5 to be expressed has been removed (bottom right), thus preventing cells from expressing it.CXCR5 is necessary for cell migration as it responds to the chemokine signal BLC, which is secreted from the PF regions (primaryfollicles) and attracts cells to these regions. The animation snapshot shows that no cells are present in these areas (bottom left).

6 Review I. R. Cohen and D. Harel

Others have developed or employed visualizationtechniques for modelling complex systems: Petri nets(Reisig 1998) are one example and the compound UMLset of languages is another (UML). These approachesdiffer from RA in that they are either stand-alonelanguages (in the case of the former) or a multitude of

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loosely connected languages (in the latter); they do not,in and of themselves, feature the ability to both specifyand model visually and see the system in operation ina visual fully animated fashion. However, a detaileddiscussion of these other visual simulation technologiesis beyond the scope of the present paper. Indeed, any

Review I. R. Cohen and D. Harel 7

technology or combination of technologies that wouldsupport bottom-up specification linked to an interac-tive animated front end would serve.

6. DYNAMICS

The animation tool in RA should not be viewed merelyas an amusement or computational virtuosity. RAconveys dynamics—the capacity to change withtime—and dynamics is the essence of a reactive system.Consider, for example, the distinction between a livingcell and a dead cell: at a single instant, a living cell and adead cell may contain precisely the same catalogue ofcomponent molecules in the same concentrations; theparts catalogue is the same for both the living and thedead. It is not the parts themselves, but the dynamicsof their interactions that distinguish the living fromthe dead (Cohen 2000). The living cell goes oninteracting as a reactive system and the dead celldecays into disintegration.

A computer is a tool for realizing dynamics, andliving systems, as dynamic systems, are aptly describedby computer simulation of their dynamics. Many kindsof mathematical-looking formulations are staticstatements, even though (as in the case of differentialequations, for example) they often describe change overtime. However, a formulation such as RA, whose verynature is to give rise to moving and realistic computersimulations, is dynamic in its essence; just like a livingcell, a computer simulation has no existence but for itsvariation in time.

7. LIVE MODELLING

Reduction alone is not an explanation in biology; thecomplex living system cannot be explained merely bydigging deeper into the system; the essence of thesystem includes its higher-scale emergent properties aswell as its fundamental component parts (Cohen 2000).Explanation requires combining classical scientificreduction (to a lower scale) with extension (to a higherscale), which we have illustrated in developing RA.Extension, in addition to reduction, is needed because acomplex system, such as a living organism, revealsdifferent features at different scales of observation(Cohen 2006).

Even the non-living physical world is sensitive toscale and frame of reference. Different scales ofphysical observation clearly reveal material realitiesthat fit radically different physical descriptions—witness the varied worldviews of classical mechanics,relativity and quantum mechanics (Feynman 1988).Fortunately for the physicist, however, each of thesephysical views of material reality can usually be fixedat one scale of observation; hence, most physicalexplanations can be adequately reduced to the laws ofnature that pertain to a particular scale. Physicistscan deal with one scale at a time. Hence, physics isserved well by immutable mathematics. The math forthe physicist is the explanation.

The complexity of living systems, however, is suchthat biologists are obliged to attend simultaneously tomore than one scale of observation. Higher-scale

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extension must complement lower-scale reduction.Most importantly, living systems are essentiallydynamic, and so are best represented by methodsthat, from the very start, are geared towards realistic,multi-scale computer simulations.

In summary, we might say that RA redefines theconcept of a model as used by biologists. A biologicalmodel traditionally functions as a representation of abiological theory (or proto-theory); one’s model rep-resents the way one understands the real system.Classically, we build a biological model to test thevalidity of our understanding by seeing how well themodel accounts for the known behaviour of the realsystem, or how accurately the model predicts theresults of new experiments. Tradition says, first under-stand, and then make a model to explain what youunderstand. RA, at least for complex living systems,turns the process around: first make a dynamic modelthat integrates the data, then you will understand.A model that represents faithfully the dynamic crossingof scales and layers is itself an explanation of the livingsystem’s emergent properties (Efoni et al. 2005).

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