From sequence to consequence and back - Core

Progress in Biophysics and Molecular Biology 111 (2013) 75e82

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Progress in Biophysics and Molecular Biology journal homepage: www.elsevier.com/locate/pbiomolbio

Original research

From sequence to consequence and back Stig W. Omholt* Centre for Ecological and Evolutionary Synthesis, Department of Biology, University of Oslo, P.O. Box 1066, Blindern, N-0316 Oslo, Norway

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 25 September 2012

The genotypeephenotype relation is at the core of theoretical biology. It is argued why a mathematically based explanatory structure of this relation is in principle possible, and why it has to embrace both sequence to consequence and consequence to sequence phenomena. It is suggested that the primary role of DNA in the chain of causality is that its presence allows a living system to induce perturbations of its own dynamics as a function of its own system state or phenome, i.e. it capacitates living systems to selftranscend beyond those morphogenetic limits that exist for non-living open physical systems in general. Dynamic models bridging genotypes with phenotypic variation in a causally cohesive way are shown to provide explanations of genetic phenomena that go well beyond the explanatory domains of statistically oriented genetics theory construction. A theory originally proposed by Rupert Riedl, which implies that the morphospace that is reachable by the standing genetic variation in a population is quite restricted due to systemic constraints, is shown to provide a foundation for a mathematical conceptualization of numerous evolutionary phenomena associated with the phenotypic consequence to sequence relation. The paper may be considered a call to arms to mathematicians and the mathematically inclined to rise to the challenge of developing new formalisms capable of dealing with the deep defining characteristics of living systems. Ó 2012 Elsevier Ltd. Open access under CC BY-NC-ND license.

Keywords: Genotypeephenotype relation Open physical systems Systems dynamics Self-transcendence Morphospace Genetic concepts Biological order Systemization Burden

1. Introduction In his thought-provoking book Life Itself (Rosen, 1991), Robert Rosen asks: “What is it that enables living things, apparently so moist, fragile and evanescent, to persist while towering mountains dissolve into dust, and the very continents and oceans dance into oblivion and back?” We are still far from being able to give a full answer to this question. However, I am quite confident that it will encompass a deep understanding of the genotypeephenotype1 relation phrased in mathematical terms. In the following I will outline why I think such a mathematically based explanatory structure is in principle possible, and why it has to embrace both

* Present address: Faculty of Medicine, Norwegian University of Science and Technology, P.O Box 8905, N-7491 Trondheim, Norway. Tel.: þ47 90 94 09 85. E-mail address: [email protected]. 1 The terms genotype and phenotype were introduced by the Danish plant physiologist and geneticist Wilhelm Johannsen in 1909. An individual’s genotype denotes the constitution of parts or all of its genetic material, while its phenotype may comprise anything from a single observable characteristic or trait to all conceivable ones. Thus any morphological, developmental, biochemical or physiological property all the way down to the subcellular level (including epigenetic marks), as well as any of the individual’s behaviour and products of behaviour, is a phenotypic characteristic and belongs to the individual’s phenome. 0079-6107 Ó 2012 Elsevier Ltd. Open access under CC BY-NC-ND license. http://dx.doi.org/10.1016/j.pbiomolbio.2012.09.003

sequence to phenotypic consequence and phenotypic consequence to sequence phenomena. William Bateson coined the term genetics in a letter to Adam Sedgwick in 1905. In 1906 he announced the term publicly in his inaugural address The Progress of Genetic Research to the Third International Conference of Hybridization and Plant Breeding (Punett, 1928): “I suggest for the consideration of this conference the term Genetics, which sufficiently indicates that our labours are devoted to the elucidation of the phenomena of heredity and variation: in other words, to the physiology of descent, with implied bearing on the theoretical problems of the evolutionist and the systematist, and application to the practical problems of breeders whether of animals or plants.” The above quotation is a rare example of a deliberate formulation of the goals of a scientific discipline under establishment, and genetics is still defined as the science of heredity and variation in living organisms. As heredity denotes the transfer of characteristics from parent to offspring through their genes, and variation denotes the change in the form, position, state, or quality of something, it follows that one of the major goals of genetics is to account for observed biological patterns in the wide sense, within and across species, past and present, which in one way or another can be related to hereditary units and principles. Through the phrase “physiology of descent” Bateson apparently envisioned that it fell to

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genetics to explain how hereditary units actually cause observed phenotypic patterns in terms of physiological mechanisms. This is supported by the fact that in his book “Mendel’s Principles of Heredity” (Bateson, 1909), he makes several attempts to actually establish an explanatory bridge between hereditary units and phenotypes by referring to physiological and physical principles. When it comes to theoretical population and quantitative genetics, one hundred years of work is still captured by Richard Lewontin’s description in his Genetic Basis of Evolutionary Change almost 40 years ago (Lewontin, 1974). Here he argued how population genetics has been mainly focused on genotype space and the development of mathematical machinery capable of describing changes in this space based on mutation, selection and genetic drift while quantitative genetics has been mainly focused on phenotype space and the development of statistical machinery capable of describing changes in this space based on variance component analysis. By operating in just one space, population genetics has had to make a caricature of phenotype space, while quantitative genetics has had to make a caricature of genotype space. Needless to say, the reason for this situation is the lack of understanding of the genotypeephenotype relation. Better understanding of the genotypeephenotype relation is the key to a mature genetics theory sensu Bateson, capable of linking genotypes, phenotypes and population level genetic phenomena through a causal understanding of biological mechanisms. In order to address the whole range of evolutionary phenomena we need to acknowledge that causality associated with this relation flow in both directions. A theoretical biology, i.e. a theory of organisms, to be taken seriously, must be built upon the genotypeephenotype relation. I firmly believe that the major tool for raising this building is biophysically based systems biology in the wide sense combined with technology enabling massive experimental manipulation and measurement. This work has barely started, but it is the road we have to follow if we are to succeed in meeting Rosen’s challenge. 2. The role of DNA in the chain of causality As the genotypeephenotype relation is of such fundamental importance, and assuming that there is no substitute for mathematics in describing its essence, it is worthwhile to briefly contemplate how we should perceive the function of DNA in a mathematical explanatory framework of biological form in the wide sense. Considering the development of the gene concept over the last hundred years, from an abstract entity though something coding for proteins and then to a curiously elusive object (Beurton and Falk, 2000), it seems appropriate to declare the gene concept to be dysfunctional as a scientific concept because of its ontological fuzziness. The genotype concept is in quite another situation because it has a direct physical interpretation in terms of DNA and there is no particular additional mechanism or effect attributed to it. A genotype may constitute everything from a single base pair to the whole genome of an individual, thus the concept provides the flexibility needed to span the whole spectrum of relationships between DNA information and phenotypic variation. As several people have advocated over many years, DNA is among the most inert and nonreactive of organic molecules. It does not self-replicate and it does not make or do anything in any meaningful sense. And thus it cannot be considered to be a cellular sub-system. This is precisely why it is so biologically useful, and why the cellular machinery works so hard to prevent it from disintegrating (Shapiro, 2011). The terms database and information organelle are frequently used as metaphors for describing the function of genomic DNA and the cell nucleus, respectively. Since

metaphors are very important instruments for thinking, their appropriateness must be evaluated in terms of how well they can be used to reach new understanding through the inferential capacity of the meanings and associations we attach to them. A database may be defined as a comprehensive collection of related data (i.e. pieces of information) organized for convenient access. If we understand information in the restricted technical sense as a sequence of symbols that can be interpreted as a message, the database and the information organelle metaphors are biologically sound. But in my view it is not very useful to just denote DNA as an information storage medium when it comes to assessing its role in the chain of causality in systems theoretical terms. If we interpret information somewhat loosely as any kind of event that affects the state of a dynamic system, it follows that information is created all the time in connection with the emergence of biological form. In mathematical terms creation of biological form is a recursive mapping of form transitions based on successive information generation. In this context DNA is what enables life to play aikido2 with mathematics, physics and chemistry and build order upon order in an unsurpassed way. Open physical systems are sustained non-equilibrium systems exchanging matter and energy with the environment. All living systems are certainly open physical systems, but so are very many inanimate systems that together span immense spatial and temporal scales. The latter group also shows intriguing morphogenetic capacity due to self-organization and emergence (Cross and Greenside, 2009). We are starting to understand some of the mechanisms underlying this capacity (Buka and Kramer, 1996; Hoyle, 2006; Cross and Greenside, 2009; Desai and Kapral, 2009) and how to exploit this knowledge in technology development (Buka and Kramer, 1996; Desai and Kapral, 2009). Living systems do not have exclusive ownership to phenomena like self-assembly, self-organization, emergence, two-way causation between lowerand higher-level system dynamics features, and order creation through local reduction of entropy. The form-generating capacity of living systems dwarfs that of inanimate open systems, however. I think the major reason for this is that the presence of DNA allows a system to induce perturbations of its own dynamics as a function of its own system state or phenome (Fig. 1). This feature, which should not be equated with twoway causality, enables living systems to create order upon order and attain forms in morphospace that are beyond reach for any open physical system that relies on the information generation that follows from the autonomous unfolding of the system per se. In mathematical terms, DNA allows successive within-system state space changes both in terms of state space trajectory changes and reconfiguration of the state space as such. In contrast to non-living open physical systems, the presence of DNA is a systems-structure that capacitates living systems to self-transcend e not beyond the dictums of physics and chemistry, but beyond those morphogenetic limits that exist for non-living open physical systems in general. The term ‘transcendent’ is defined as something going beyond or exceeding usual limits, and I use the term self-transcendence deliberately because here the transcendence is a function of system state. It should be noted that according to the above scheme there is no direct causal arrow from genotype to phenotype in the sense that DNA is responsible for exerting a direct effect as a sub-system on the system dynamics. The causality flows from the system state through a change in use of DNA (as an inert system component) that results in a change in the production of RNA and protein, that in

2 A Japanese martial art that is performed by blending with the motion of the attacker and redirecting the attacker’s momentum rather than opposing it directly.


Self-transcendent unfolding of system dynamics and movement in morphospace System state

System state

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/no ing ad Re ding rea

Se pe lf-ind rtu rba uced tio n

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System state

DNA Boundary conditions = Environment Fig. 1. The role of DNA in the chain of causality. DNA is considered as an entity that is part of the system configuration, but is not an autonomous interacting sub-system as such. The system uses DNA to induce perturbations of its own dynamics as a function of system state. This feature makes the system capable of transcending beyond the morphogenetic limits set for other sustained non-equilibrium systems. The morphodynamics of the latter group is to a high degree dictated by the initial conditions and the environment. The figure does not include DNA repair mechanisms or possible changes of DNA as a function of system state. See text for further explanation.

turn perturbs the systems dynamics (Fig. 1). Variation in DNA may or may not cause changes in the perturbation regime. In the case in which it does, it may or may not lead to different systems dynamics and thus system characteristics (i.e. phenotypic variation). When I use the terms genotypeephenotype map, genotypeephenotype relation or sequence to consequence in the following, this should be kept in mind. It is beyond the scope of this paper to elucidate in detail the consequences of this capacity to self-transcend. I would like to point out, however, that the ability of living systems to replicate themselves with high fidelity is one such consequence. Most importantly, the emergence of DNA opened the gates to the Darwinian theatre for open physical systems and thus to the evolution of a variety of forms in space and time. The reproducibility of the genotypeephenotype map is what allows DNA (with its inertness and detachment from the system operations of living matter as such) to bookkeep changes in genotype space that turn out to be beneficial in terms of enhanced individual fitness in a population context. What I think this means is that, while we of course need to acknowledge the key importance of DNA in a future mathematical theory of living systems, we should stop the prevailing practise of using anthropomorphic metaphors that attribute intentions and associated operational capacity to DNA. This practise will not lead us anywhere in terms of theory construction. As Denis Noble so eloquently argued in The Music of Life (Noble, 2006), to understand life we must make a radical switch of perception from the still dominant gene’s eye view to a systems theoretical one. Which also brings us back again to a realm which genetics never should have left, namely physiology. 3. Biology is order and law In her criticism of natural science in The Dappled World, the philosopher Nancy Cartwright introduces the term nomological machine to characterize a fixed arrangement of components, or factors, with stable capacities that in the right kind of stable environment will, with repeated operation, give rise to regular behaviour (Cartwright, 1999). She claims that such machines are

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exceptional. However, to the contrary, they exist in innumerable numbers as living entities. Despite the mind-numbing complexity of living systems, their immense reproducible phenotypic orderliness is precisely the open sesame to the gates of understanding. The simple reason for this is that where there is reproducible order, there is conformity to law. This provides the major rationale for hoping that we will be able to develop a mathematically formulated understanding of biological order and variation, granted a steady improvement of technology for manipulation and measuring. Biology is indeed becoming increasingly mathematized. But the intimate dialogue between mathematics and biology necessary to understand life has barely begun. For several hundred years physics has been the most influential branch of science for the development of mathematics. Considering that the living world dwarfs the inanimate world in terms of order and pattern to be explained, it goes without saying that biology may not just be a major source of inspiration for development of new mathematics, but that all the orderliness of the living world is a major explanandum for an intellectual discipline claiming to be the science of pattern and order. Biology has already been a motivator for novel mathematical development. For example, the topologist René Thom stated very explicitly (Goodwin and Saunders, 1989) that Waddington’s conceptual model of the epigenetic landscape was for him the decisive clue to the discovery of catastrophe-theory models and thus to the writing of Structural Stability and Morphogenesis (Thom, 1975). A biological concept closely related to the mathematical concept structural stability is homeorhesis. Waddington introduced it around 1940 to describe the tendency for developing biological systems to be robust to perturbation while they unfold. In terms of mathematical theory this appears to be a dramatically more challenging phenomenon to deal with than homeostasis. The very modest interest from the mathematical community to develop theory around this concept cannot be attributed to lack of mathematical challenge or biological importance. Rene Thom wrote more than 20 years ago: “I feel that the homeorhesis concept still has much to offer mathematicians” (Goodwin and Saunders, 1989), and in my opinion it still has. In contrast to those that use the term robustness to describe any phenomenon that signify the presence of some sort of stabilization regime in biology, I think we instead need several mathematically well defined concepts to characterize these regimes if we are to succeed in theory development. The homeorhesis concept belongs to this category. The homeorhesis concept is of course intimately linked to the concept of self-transcendence, but the latter involves much more. Our current mathematics of dynamical systems does not seem able to deal properly with the self-transcendence property of living systems that is due to the presence of DNA, i.e. their capacity to induce highly controlled perturbations of their own dynamics as a function of system state. We are of course in a position to do simulations, but I am much looking forward to the development of proper mathematical concepts and machinery addressing this extremely important phenomenon. Hopefully, this development may lead to deep theorems telling us something novel about Life. Another order phenomenon associated with sexually reproducing populations that is most likely to become a key element in the answer to Rosen’s question is the phenomenon of inheritance. By his observation in the Generation of Animals that “they [offspring] resemble their parents more than remoter ancestors, and resemble those ancestors more than any chance individual” (Peck, 1943), Aristotle (c. 340 BC) is one of the earliest recorded investigators of the phenomenon that like begets like. Guided by this observation he addressed the causal mechanisms behind the transmission of biological form, and in terms of identifying the problem he may thus

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be considered to be one of the real founders of genetics. More than 2000 years later the phenomenon of inheritance becomes one of the key premises Charles Darwin used to deduce the principle of natural selection by logical argument (Darwin, 1859). Thus when we rationalise the key concept of evolutionary biology we take this extra dimension to biological order creation for granted, which we should not. There is no a priori reason why an offspring, arising from the random sorting of chromosome pairs plus genetic recombination and the subsequent immense number of highly complex and nonlinear processes making the individual, should on average resemble its parents more than a randomly drawn couple from the population. We have no theory that tells us why this would not give rise to a quite unpredictable parent-offspring relationship. By taking the phenomenon of inheritance for granted we are asserting the existence of an order phenomenon associated with the genotypeephenotype map that currently has no scientific justification. It seems though that the phenomenon is closely connected to the existence of monotonic (i.e. order-preserving) genotypee phenotype maps (Gjuvsland et al., 2011). This implies that the systems dynamics underlying these maps has a predominant tendency to meet mathematical constraints related to monotonicity. This monotonicity is related to the ordering of the parameter space relative to the equilibrium state space (i.e. phenotype space) and is therefore not captured by the current theory of monotonic dynamic systems3 (Smith, 1995); at least new measures and definitions seem to be in demand. In any case, there is no substitute for mathematics to understand the phenomenon of inheritance and numerous other phenomena associated with the genotypeephenotype relation. 4. Modelling of the genotypeephenotype relation e the cGP programme We use DNA information in at least four explanatory settings: as a pure marker where we do not make a direct link to any particular phenotype; when we by statistical means establish an association between one or more chromosomal regions and phenotypic variation; when we can document that a particular DNA variation (natural or imposed) does indeed cause a phenotype; and finally in a causally cohesive setting where we can also explain how the genetic variation causes the observed phenotype in terms of mechanism. Only in the last setting is extensive use of mathematics mandatory for making progress, and it is here the selftranscendence of biological systems due to DNA becomes evident. If a well-validated dynamic model is capable of accounting for the phenotypic variation in a population, the causative genetic variation will manifest in the model parameters. The term parameter denotes here a quantity that is constant over the time-scale of the particular model being studied. However, even the lowest-level model parameters are themselves phenotypes (Rajasingh et al., 2008), whose genetic basis may be mono-, oligo- or poly-genic, and whose physiological basis and variation can be mechanistically modelled at ever deeper levels of detail. The term causally cohesive genotypeephenotype (cGP) modelling was coined to denote an approach where low-level parameters have an articulated relationship to the individual’s genotype, and higher-level phenotypes emerge from the mathematical model describing the causal dynamic relationships between these lowerlevel processes (Rajasingh et al., 2008). This way of modelling

3 It does not necessarily demand u v; t > 0/Ft ðuÞ Ft ðvÞ, where Ft is a semiflow, i.e. the solutions do not need to converge monotonically to a given equilibrium.

bridges the gap between standard population genetic models that simply assign phenotypic values directly to genotypes, and mechanistic physiological models without an explicit genetic basis. This enables a causally coherent depiction of the genotype-tophenotype (GP) map, which can then be placed in a population context (Fig. 2). A few years ago I realized that this research programme idea was actually stated quite explicitly by Jim Burns (1970) in one of the symposia led by Conrad Waddington that resulted in the threevolume work Towards a Theoretical Biology: “It is the quantitative phenotype, arising from the genotypic prescriptions and the environment, which is of critical importance for the cell’s survival and which therefore features in population genetic theory. A study of this synthetic problem would thus, by providing genotypee phenotype mappings for simple synthetic systems, help to connect two major areas of biological theory: the biochemical and the population genetic.” This is to the best of my knowledge also the first time the concept of the genotypeephenotype map appears in print. Almost 20 years earlier in the Symposium of the Society of Experimental Biology in Oxford, Waddington (1953a) made the following critical remark about statistically oriented population genetics theory: “a mathematical treatment may reveal new types of relation and of process, and thus provide a more flexible theory, capable of explaining phenomena which were previously obscure. It is doubtful how far the mathematical theory of evolution can be said to have done this. Very few qualitatively new ideas have emerged from it.” It is thus quite surprising that Waddington apparently did not see the connection when Burns suggested a research programme that could both explain obscure phenomena and generate new ideas. By linking genetics with systems theory the cGP programme opens up a whole new research field that in principle has all phenotypic patterns associated with the genotypeephenotype relation as explananda. We do not know how successful this programme will become in epistemic and instrumental terms. But even though it has barely started, it has already provided some encouraging results that go well beyond the explanatory domains of statistically oriented genetics theory construction. Below I give a few illustrations of this and point to some outstanding challenges that have to be tackled before we can claim substantial progress. Since Gregor Mendel gave us the concepts dominance and recessivity more than 140 years ago (Mendel, 1866), geneticists have invented several additional concepts to describe statistically inferred patterns in their data, like gene action, heritability, epistasis, heterosis, penetrance, expressivity, GxE interaction, pleiotropy and canalization. All these concepts are in active use in production biology, evolutionary biology and medicine, and in terms of underlying mechanisms they are all far from well understood. Alluding to Waddington’s statement above, I claim that most of these phenomena will remain obscure if we do not address them in a cGP-modelling framework. It has already been shown how the cGP modelling approach can be used to explain allele action (Gjuvsland et al., 2010), genetic dominance (Omholt et al., 2000; Gjuvsland et al., 2010), the relationship between additive and epistatic gene action (Gjuvsland et al., 2006; Pumir and Shraiman, 2011), the variation in phenotypic penetrance due to systemic silencing of genetic variation (Plahte et al., 1998; Gjuvsland et al., 2007b), genetic background (Vik et al., 2011) and shape of gene regulatory function (Gjuvsland et al., 2007a), and how the relationship between narrow and broad sense heritability varies as a function of regulatory anatomy (subm.). It has also been used to study response to selection in a mass-action differential equation model of the regulatory switch controlling galactose metabolism in yeast (Peccoud et al., 2004),


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Fig. 2. The cGP programme: integrating genetics, genomics, and multiscale models in a population context. In the illustration, a gene codes for ion-channel parameters, which affect transmembrane currents and the action potential of a heart cell. Genetically determined variation in low-level parameters propagates through multiple levels of electrophysiological, mechanical and fluid dynamic processes. Phenotypic variation emerges at each level of organization. A cGP model integrates a multiscale model of this biological system with a linkage map through the genes encoding ion channels, thus the cGP model describes the creation of new genotypes as a result of meiosis and mating as well the phenotypes arising from these genotypes. By linking genetics with systems theory the cGP programme opens up a whole new research field that in principle has all phenotypic patterns associated with the genotypeephenotype relation within its explanatory domain. The figure was made by Arne Gjuvsland.

and, based on a model of the gene regulatory network that controls flowering time in Arabidopsis thaliana, to show how additive gene action could arise from highly nonlinear biological processes. Further, it has been shown how the approach allows us to perform genome-wide association studies on low-level phenotypes serving as parameters in dynamic models (Wang et al., 2012) in order to uncover subtle genetic variation underlying complex trait variation and explain how this variation actually causes phenotypic effects in mechanistic terms. There is no limit to the complexity of biological models that can be used in a cGP context. The steady progress in multiscale modelling (Hunter and Borg, 2003) will hopefully soon allow us to start describing how genetic variation propagates through the phenotypic hierarchy from subcellular phenotypes and up to the whole organism, including new ways for pattern description (Martens et al., 2009). Epistemically very important results have already been obtained in linking ion-channel molecular dynamics to models of cardiomyocyte function (Silva et al., 2009). In the not too far future, the cGP programme in a multiscale setting will probably give us an extensive understanding of how different types of genetic variation propagate and manifest as a function of regulatory architecture, physiological setting and genetic background. And this endeavour will most likely drive the development of a phenomics technology in a very rational way (Houle et al., 2010). Hopefully, it will also hone our methodological and conceptual weapons to start to make real headway in describing the ontogeny (and associated themes) of organisms in a cGP context (Alberch, 1991; Pigliucci, 2010). One particular sequence to consequence phenomenon that is associated with both embryonic and post-embryonic regulatory biology is phenotypic plasticity, i.e. that a given genotype may produce different phenotypes due to environmental change. The concept was introduced by James M. Baldwin (Baldwin, 1896): “The creatures which can stand the ‘storm and stress’ of the physical influences of the environment, and of the changes which occur in the environment, by undergoing modifications of their congenital functions or of the structures which they get congenitallydthese

creatures will live; while those which cannot, will not”. And it is given substantial attention by evolutionary biologists (Schlichting and Pigliucci, 1993; Fusco and Minelli, 2010; Reed et al., 2010; Snell-Rood et al., 2010). The concept of genetic assimilation, introduced by Waddington (1953b), has received renewed attention in recent years due to the rapid expansion of our understanding of how the environment influences the distribution of epigenetic markers affecting phenotypic variation (where variation in the markers also represent phenotypic variation). It describes the evolutionary process by which a phenotype produced specifically in response to some environmental stimulus, becomes stably expressed independently of the evoking environmental effect (Braendle and Flatt, 2006). Many consider this to be a very important evolutionary mechanism for genetic change in populations, and if this is the case, phenotypic plasticity steps to the fore also as a strategy for enhancing evolvability. To develop cGP descriptions of phenotypic plasticity is going to be a major undertaking that will involve most of what we know about regulatory biology, and several things we do not yet know. As organismal phenotypic plasticity in Metazoans is a result of phenotypic plasticity of cells in tissues and organs, the mathematical description of cellular phenotypic plasticity should become a major focus. We have to admit that “there is not yet any deep theoretical understanding of the basic principles of cell informatics” (Shapiro, 2011), but my hope is that a concerted theoretical-experimental effort to find the regulatory principles underlying cellular phenotypic plasticity will bring us much further towards such deep theoretical understanding. Cellular phenotypic plasticity involves a whole range of phenomena, and I will just provide one specific example here. Experimental data on excitable cells produced over the last 20 years point to the existence of a regulatory language that ensures maintenance of cellular function as a function of environmental change by concerted regulation of ion channel density. In models of neurons and cardiomyocytes, we describe variation in an ion conductance by variation of one or more parameters. This

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modelling practise is in many situations absolutely sound. But because a cell can take down or up the density of an ion channel in minutes (Royle and Murrell-Lagnado, 2002; Sorkin and von Zastrow, 2009), the ion channel density is a state space variable under strict regulatory control. The existence of this control becomes very apparent when for example stomatogastric ganglion neurons of the spiny lobster are plated in a primary cell culture (Turrigiano et al., 1995). After plating these neurons lose most of their active properties. Over a period of 3e4 days, however, they adjust their magnitudes of ion conductances such that they become bursting neurons when depolarized, resembling the original in vivo phenotype. Besides being able to mimic this behaviour by computational models imposing covariance structures between various conductances (Turrigiano et al., 1995; Ball et al., 2010; Soofi et al., 2012), the underlying regulatory system responsible for this behaviour totally eludes us. My guess is that when we start to understand it, a new chapter in theoretical regulatory biology and thus cGP modelling will be opened. 5. From phenotypic consequence to sequence When we talk about the consequence to sequence relation we have to distinguish between direct change of the genome for adaptive purposes and change of genomic organization due to adaptation that in turn has consequences for the type of adaptive genetic variation that may later arise. The first phenomenon is direct causation and the latter is indirect causation. Direct causation challenges the current dictum of the Neo-Darwinian programme saying there is no link between the type of variation that arises in a germline and adaptational needs, while indirect causation does not. Considering that in recent years parts of the biological community have become sensitized to the idea of creating a Lamarckian twist to evolutionary biology in order to explain nonDNA based trans-generational inheritance, it is worthwhile to recollect that in The variation of animal and plants under domestication (Darwin, 1868), Charles Darwin suggested an inheritance mechanism allowing for the propagation of acquired traits based on pangenes that could circulate from the body to the germ cells. If we exchange pangenes with non-coding RNA we are immediately at the research front of current biology (Daxinger and Whitelaw, 2012). We already know from several studies that mutation rates may increase substantially in prokaryotes and yeast as a response to environmental change. The evolutionary biology textbook mantra stating that the process of mutation is not an adaptation but a consequence of unrepaired damage (Futuyma, 2009) is thus not entirely correct. In Evolution: A view from the 21st century James Shapiro argues convincingly that that the natural genetic engineering apparatus of cells may have some further tricks up their sleeves to which the evolutionary biology community have not given enough consideration (Shapiro, 2011). Having said that, I would like to emphasise that this does not imply that living systems have an anticipatory capacity and an associated molecular machinery that puts them in a position where they can make deliberate adaptive genomic changes, either directly or through epigenetic changes that later may lead to genomic change through genetic assimilation or other mechanisms. The fact that extinction is one of the most predominant patterns in the history of life should represent enough of a warning sign for attributing too much direct anticipatory capability to life. In his delightful book The Black Swan, Nassim N. Taleb distinguishes between two realms, Mediocristan and Extremistan (Taleb, 2007). Mediocristan is where normality resides. The normal distribution is a major characteristic of Mediocristan and the impacts of events are rather small. Extremistan is a very different

place. Here, events that seemed unlikely, impossible and even unthinkable occur frequently and have a dramatic impact. Black Swan events occur in Extremistan. Even though Taleb focuses mainly on human systems, I think these two metaphors are very apt for evolutionary biology too. Species become extinct also in Mediocristan, but extinctions seem predominantly to happen in Extremistan. Most species appear to die out because they are unlucky in terms of being exposed to stresses not anticipated in their prior evolution (Raup, 1992). Thus in terms of adaptation, Life cannot deal with Extremistan very well, but the way organisms respond to directional selection shows that they are tuned to adapt to abiotic and biotic changes in Mediocristan. Living in Mediocristan has consequences that are directly connected to the indirect causation between the phenome and genome mentioned above. I allude here to the thinking of Rupert Riedl as it is spelt out in his book Order in Living Organisms (Riedl, 1978). Riedl constructed an explanatory apparatus to address a wide range of evolutionary phenomena associated with the biological order he considered to be beyond explanatory reach of classical NeoDarwinism. They include the four types of biological order we observe: standard part, hierarchical, interdependent and traditive order. Standard part order denotes that the same building blocks across biological scales are used over and over again, such as giant molecules, regulatory modules, organelles, cells and body parts. Hierarchical order describes those patterns characterised by features that do not overlap, but form a ranked organisation where lower ranking features receive meaning from the higher ones, and the higher-ranking features receive content from the lower ones. Interdependent order denotes orderly patterns characterised by functional connections between features of equal rank, manifested for example by synorganization where separate features develop coordinated adaptations, and synformation where there is harmonious change of a complex of features. Finally, traditive order involves time and characterises patterns associated with embryogenesis, how new structures are built upon older structures and the fact that development recapitulates the most important steps in evolution. The build-up of these four types of order leads to static and dynamic phenomena that are not explained by the rather meagre explanatory core of Neo-Darwinism. The static phenomena include homology and homonomy and the dynamic ones include homodynamy, coadaptation, parallel evolution, orthogenesis, Cartesian transformation, heteromorphosis, systemic mutation and spontaneous atavism. As these phenomena define the lion’s share of directed phenomena in macroevolution, they are certainly explananda for a mature evolutionary theory. Lack of space prevents me from outlining the contents of Order in Living Organisms at the level of detail it deserves, and I will just state its major claims concerning the consequence to sequence relation in order to hopefully invoke some interest. The theory does not challenge the Neo-Darwinian dictum that there is no link between which mutations that arise and adaptive needs. But it challenges the conception that mutations that are actually played within the Darwinian theatre are in principle uniformly distributed in terms of phenotypic effects, i.e. it says that the morphospace that is reachable by the standing genetic variation in a population is quite restricted due to systemic constraints. According to the theory, information flows from DNA through the epigenetic system to phenotypes in the normally conceived way. However, the chances of successful adaptation increase if the epigenetic system through systemization imitates the functional dependencies of phenotypes. This leads to higher adaptive speed within a single adaptive direction through a positive feedback loop. But this comes at a price, as the possibility for evolution in other


directions becomes more restrained due to the systemic conditions developed by the organization of the organism. The systemization of the epigenotype (sensu Waddington (1942))4 leads to build-up of burden on decisions. The concept denotes the number of other decisions the decision in question implies, and also on the number of features that it results in. The burden increases due to systemization and new features built on the basis of old ones. This leads to preservation of established order. Mutations with low burden lead to small changes of the order that has already been established, i.e. they belong to Mediocristan. Features with high burden get fixated and new inventions happen elsewhere. Homologues are conserved because they have high burden. Body plans arise from the fixation of features due to burden. Mutations in highly burdened genes are often lethal and are seldom tested by environmental selection. The evolvability increases with systemization, but decreases with burden. This causes the cementing of structures, functions and pathways beyond and often in opposition to new functional requirements dictated by new selection pressures. The systemization of the epigenotype due to functional requirements may be viewed as indirect anticipation of what is to come. It would be most helpful if the mathematicians could start embedding the systemization and burden phenomena in a systems dynamics framework. When we start to come to grips with modelling embryonic development in a cGP context we will be able to mathematically conceptualize the systemization process and the associated generation of burden and the four types of biological order. Then we will be in position to assess the importance of Riedl’s contribution to the conceptual foundation of evolutionary biology. 6. Concluding remarks Stephen Toulmin considered scientific problems of a discipline to be equal to its explanatory ideals minus current capacities (Toulmin, 1977). I definitely think we will be able to fulfil the explanatory ideals of genetics laid down by William Bateson more than one hundred years ago through mathematization of the genotypeephenotype relation in a causally cohesive way. But even though our capacities have increased tremendously since 1906, we are still lacking proper mathematics (in the wide sense) for describing life, in particular its capacity for self-transcendence. We are also lacking technology for massive non-invasive measurement of phenotypes. Thus there is no substitute for extensive collaboration between numerous scientific competences within a systemstheoretical framework if we are to drastically reduce the distance between explanatory ideals and explanatory capacities. Several people seem to think that we are at the beginning of the end of epistemically breath-taking biological research. I think we instead are at the end of the beginning, and my conjecture is that our endeavour will lead to a theoretical biology with a much simpler and more coherent structure than that of the intellectual grocery store we currently have. Acknowledgements I thank Jonathan Bard, Keith Baverstock, Barbara Eriksen, Thomas Flatt, Peter Hunter, Kjetill Jakobsen and Denis Noble for their comments on the manuscript. I am also grateful to my colleagues Arne Gjuvsland and Jon Olav Vik for several helpful

4 “We certainly need to remember that between genotype and phenotype, and connecting them to each other, there lies a whole complex of developmental processes. It is convenient to have a name for this complex: ‘epigenotype’ seems suitable”.

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