Abstract
The biological realm has inherited symmetries from the physicochemical realm, but with the increasing complexity at higher phenomenological levels of life, some inherited symmetries are broken while novel symmetries appear. These symmetries are of two types, structural and operational. Biological novelties result from breaking operational symmetries. They are followed by acquisition of regularity and stability, in a recurrent process throughout complexity levels.
The concept of symmetry implies conservation of shape upon rotation or of isomorphic transformation in interactions, retaining one or several parameters invariant in the transformation. These attributes correspond both to topological and operational properties in the stability and evolution of functional structures. In biology the counterpart of these notions has synchronic (e.g., anatomic or physiologic) as well as diachronic (e.g., developmental and evolutionary) connotations. In dealing with these two connotations, I will try to distinguish between topological and operational symmetries, being aware that the use of these terms in the context of biology extends beyond the more precise meaning in the context of physics. Whereas the notion of topological symmetry in biological forms is well documented, that of operational symmetry has been, to my knowledge, hardly considered. As in physics, also in biology, devolving interactions generate breaks of symmetry. Herein I will discuss briefly a few instances of symmetries and its breaks in biology that have played a central role in organic evolution.
Biology deals with forms and their transformations: molecular, cellular, histological, organismal, and ecological. Its structures are grounded in the physical realm and its energetic transactions in the chemical one. In this ascent throughout complexity levels, we cannot discriminate between historical contingency and strict causal determination, although the former seems to play a major role with increasing complexity. Organic evolution devolves from combinatorial propositions that happened to succeed, i.e., were stable and stayed around for us to observe and categorize.
Structural or Topological Symmetries
The formation of anisodiametric molecules by the bonding of isodiametric atoms is the first symmetry break that gives rise to fundamentally asymmetric biological structures.
The first example of a biologically caused break of molecular symmetry paradigmatic for many biological structures was discovered by Pasteur. Whereas molecules of tartaric acid, can exist as two optically active, dextro (d) or levo (l) rotatory isomers, yeast cells can only metabolize the d-isomers. It so happens that all saccharides in biological structures and reactions are similarly dextrorotatory. We now know that the prevalence of d-isomers is due to the asymmetry of the active catalytic sites of the enzymes that recognize saccharides for both their anabolism and catabolism. The reason for the prevalence of saccharide d-isomers and their derivatives (tartaric acid is one) may be that the corresponding metabolic enzymes are encoded by genes all evolutionarily descended from one original prototype. The same may hold for the prevalence of l-phospholipids that are metabolized by many different types of phospholipases. From the predominance of d- over l-isomers of saccharides and of l-phospholipids, we learn two important lessons about biological evolution. Ones in that molecular recognition provides a profound inertia to evolutionary innovation because it demands conservation of forms of proteins and hence of the encoding genes. The other is that the contingent origins of saccharide metabolism amplified asymmetries in the abundance of equally probable, energetically equivalent, isomers.
The same lessons can be draw from the prevalence of l- over d-amino acid isomers in biomolecules. Enzymes involved in amino acid metabolism may have derived from a common prototype that prevailed in the competition between isomeric forms in the primordial organic soup. The consequences were everlasting, since the form of all the proteins whose function requires amino acid recognition must be complementary to the form of the l-isomers. Moreover, the helical rotation of long helical polypeptide chains is derived from the tilt of peptide bonds between l-amino acid residues. And that configuration is, in turn, basic to many of the elastic properties of proteins in structural and functional roles.
Similarly, the two polynucleotide chains in the double-helical DNA molecule have a clockwise axial rotation based on the tilt imposed by the staggering of successive nucleotides. In this case, the degrees of freedom of this rotation are greater than those available to polypeptides chains because the DNA molecule can have an opposite rotational torque under physiological conditions. The primary helicity of the DNA is a consequence of its mode of generation and causes its structural stability that carries on its higher-order organization allowing for protein recognition sites, complex replication and transcription mechanisms, and tertiary folding into chromosomes for cytokinesis. The linear sequence of nucleotide residues in DNA double strands is on the other hand, constrained by purine–pyrimidine base complementarity required for the stability of the double helix. But beyond this, the order of nucleotides can in principle be arbitrary. The same freedom of nucleotide sequence holds for single-stranded RNA molecules. However, in RNA molecules, a new symmetry appears in palindromic nucleotide sequences, at which the single RNA strand folds back on itself by nucleotide base complementarity; pins and four-leafed configurations due to palindromic configurations are responsible for the stability and molecular recognition features of RNA molecules. They correspond to emerging symmetries with profound biological implications. It is precisely these secondary interactions of biological macromolecules (polypeptides and polynucleotides) that have frozen their structural symmetry.
At the next higher level of biological complexity, we have cell organelles and cells lipid–protein membranes, which separate internal from external aqueous phases and generate in principle isodiametric spheres with minimal surface energies. However, this symmetry is broken by the appearance of anisotropies. Protista are polarized due to an asymmetric distribution of cytoskeletal proteins defining an anterior–posterior axis, at the end of which in flagella (in bacteria) or budding zones (in fungi and yeast) distinguish heads from tails. This head-to-tail polarity is defined by the intrinsic polarity of actin-like helical proteins or by the self-assembly of asymmetric proteins complexes. Polarity based on molecular anisotropy and molecular recognition has template properties: original polarities guide the formation of subsequent ones. At the organelle level head–tail polarity retaining rotational symmetry is a common feature of virus capsids. They result from the packing, by molecular matching, of anisotropic proteins, as in phage particles, with very few steric degrees of freedom. Alternatively, packing of identical anisotropic proteins gives rise to tubes with helical rotational (left or right handed) symmetry, as in virus capsids or flagella.
The next higher level of complexity is the histological, at which asymmetries appear in cells forming part of monolayered tissues. In this example, in addition to head–tail (apical–basal aspects of cells), new left–right (or medial–lateral) and anterior–posterior polarities produce the overall shape of epithelia through molecular heterogeneities in the cell membrane. In such epithelial cells, the apical–basal polarity is directly observable under the microscope. Other axial asymmetries are manifest by cell behavior in transplantation or cell dissociation-reaggregation experiments. We still do not know how these anisotropies are molecularly represented in the cell membrane but genetic and biochemical arguments suggest that they are due to differences in the molecular composition and molecular recognition of outer membranes of neighboring cells.
Cell differentiation patterns break the monotonic symmetries of epithelia. These diversifications, such as the appearance of sensory elements in epidermis, occur by the differential action of genes responding to heterogeneities in cell proliferation of the epithelium. The observable heterogeneities possibly result from local modifications (elimination or duplication) to regular patterns in evolutionary origin.
Appendages such as arthropod limbs result from outgrowths at fixed positions in the two-dimensional monolayers of the integument. Cell proliferation at these positions leads to two and a half dimensional monolayers of cells that retain their anterior–posterior and dorsal–ventral axial polarities in addition a novel secondary or proximal–distal polarity. Growth occurs by cell proliferation throughout the anlage generating heterogeneities along those two (planar) axes. Similarly local evaginations and invaginations give rise to two one/two-dimensional tissue layers (as in gastrulation), which, in turn, gives rise to the three-dimensional organization of the embryo. Hence, the morphology of the adult organism is derived mainly from two and a half dimensional tissue layers.
True three-dimensional structures arise from delamination of cells perpendicularly to a planar cell sheet surface or from apposition of migrating cells of separate origins. For example, the former occurs in the generation of the nervous system (as in the cerebellum), and the latter occurs in the aggregation and condensation of mesodermal cells to form muscles or bones. That means that the apical–basal axis acquires differential recognition specificities, manifest in the cell membrane, leading to cell sorting and apposition. These mechanisms represent paradigmatic cases of how far recognition of molecular anisotropy leads to the configuration of two one/two- and three-dimensional organs and body plans.
At the next higher or organismic level of biological complexity, we encounter creatures with bilateral, radial, or helical symmetry. As a rule, bilaterally and helically symmetrical organisms are motile (swimming or walking) creatures, while radial symmetry is more often associated with sessile forms. These symmetries are due to the orientation of the mitotic planes of the first zygotic divisions, which in turn may be governed by an intrinsic polarity of the egg or by the entry point of the sperm, thus defining an anterior–posterior axis and/or a dorsal–ventral axis of symmetry. Subsequent cell divisions amplify these symmetries by iteration and linear segmentation. Radial cell cleavage gives rise to metamerism along the circumference (as in polyps) while cleavage along two orthogonal axes gives rise to bilateral forms. Helical symmetry (as in molluscs) results from modified radial cell cleavage retaining the helical staggering of successive zygotic divisions along the anterior–posterior axis. These symmetries must reflect simple structural conditionants because they are easily modified by mutation. Helical forms of gastropods may have a clockwise or anticlockwise rotation different in closely related species and mutation of particular genes can change the helical polarity of the offspring. Bilaterally symmetrical organisms may have secondary asymmetries in the whole animal, as in flat fishes, or in certain organs, like the heart or the genitalia. In this example, too, gene mutations are known that reverse the secondary asymmetry or give rise to a random asymmetry. Moreover, radially or helically (strobilar) symmetrical organization in animals and plants can be modified by the secondary appearance of bilaterality. We are beginning to understand the underlying genetic mechanisms in plants.
In actual segmented organisms, there are usually local heterogeneities in otherwise homologously iterated metameres. These heterotopies can lead to extreme differences in arthropods. As in the case of cell patterning, these heterotopies result from local genetic differences in gene expression patterns. These patterns correspond to members of genes families conserved since the origin of bilateria.
Thus, it appears that symmetries and asymmetries in biological structures up to the organismal level devolve from molecular structures that compound their symmetry or assymmetry by developmental template mechanisms. The increasing complexity and degrees of freedom of the implementation mechanisms allows for new symmetries from asymmetries or for the generation of novel asymmetries.
Generative or Operational Symmetries
Operational asymmetries though less explored, are more interesting than structural asymmetries because they have driven physiological and morphogenetic evolution.
Chemical reactions are reversible and, hence, operationally symmetrical. Enzyme/proteins (as well as colloids and other polyionic substrates) can accelerate these reactions, they still remaining symmetrical. The symmetry is broken, however, in enzymatic tandem reactions that operate far from equilibrium, when the reactants include a steady source of free energy or the reaction products themselves serve as reactants for further reactions leading to accumulation or use of end products. Directional reactions are at the root of biological syntheses. They locally concentrate free energy into chemical bonds for further use.
We do not know how the coupling of DNA, RNA, and protein first operated in evolution; we can only envisage possible scenarios. One such is that it began as a reinforcing loop in which improved enzymatic efficiency concentrated more energy and, hence, lead to more efficient reactions. Possibly the driving operation improving these energetic transactions was the possibility of self-replication, a spontaneous property of RNA molecules. These molecules are capable of mutating and self-splicing and thus of selecting themselves for higher replication rates. Nucleotide substitutions in RNA molecules represent isomeric alternatives, structurally and energetically equivalent, but from the replication perspective, represent new mutational propositions for further efficiency, leading to further molecular diversity. Since RNA molecules act, in addition, as catalysts of extrinsic reactions, i.e., as enzymes, the end result of the process is more of the same, the reaction going in the direction of increasing synthesis. Through primogenial translation, i.e., transferring sequence specificity to amino acid coupling in peptide bonds, proteins may have appeared with the capability of helping RNA synthesis itself, and vice versa, certain RNA sequences acting as codons (tRNA) for specific amino acid recognition. A new contingent event may have helped to generate molecular diversity–and through it competition and higher efficiency in energy transaction along with further biosynthesis.
Upon the evolutionary invention of reverse transcription of RNA into DNA, the informational stability, through replication fidelity was ensured. The transformational sequence of DNA → RNA → protein represents a magic loop that provided for the efficient use and amplification of the reactants, in the primordial soup. Since the speed of multimolecular reactions is strongly dependent on the concentration of the reactants, their structural association became an obvious step in increasing efficiency. Thus, the membranes of archebacteria may have arisen to enclose loci of association of the reactants involved in the extraction of free energy from incident photons in photosynthesis or from debris scavenged in the primordial soup to self-replicating structures.
In this imaginary process, symmetries become broken. Changes in the linear sequences of nucleotides in RNA and DNA, of amino acid residues in proteins, and of complementary base pairing in double stranded DNA generate diversity. But mutation, a new source of variation, appeared early in evolution. Mutation is a simple isomeric substitution of nucleotides, with enormous implications. The genetic repository of different nucleotide sequences related to amino acid sequences via the genetic code could linearly combine to generate an exploding diversity of stereospecific molecular forms. These associations represent an increase in degrees of complexity at, on, and above the molecular level. In operational terms, isomorphism between nucleotide sequences in DNA and RNA and amino acid sequences in polypeptide chains is a symmetrical phenomenon. The transformation is based on a universal genetic code. As such it is stable, although we do not know whether that stability results from an inertia based on once contingently acquired stereospecific matching maintained because the consequences of changing it would be largely deleterious.
The most important symmetry break in biology is the contingent consequence of mutation because it led to diversity and higher complexity with more efficient ways of replicating faithfully and capturing more surrounding available energy. Thus, photosynthesis in biosynthesis and the oxidation–reduction processes in metabolism were efficient consequences in prokaryotic cells. Eukaryotic cells appeared as compounds of three prokaryotic symbionts, some reduced to cell nuclei, others reduced to plastids for photosynthesis or to mitochondria for oxidative-reductive chemical reactions. This prokaryotic symbiosis represents another instance of symmetry breaking, which leads to a further increase in the phenomenological levels of complexity. The origin of multicellular eukaryota lies in yet another symmetry break that leads to a higher level of biological complexity. By comparison the subsequent appearance of a large diversity of multiple metazoa and metaphyta is a trivial step representing combinatorial variations of conserved generative mechanisms.
When 700 million years ago evolution put multicellular organisms on the scene, the fundamental problems of energy fixation and transaction, metabolism, and biosynthesis had already been solved. Since then the expenditure of free energy in driving chemical reactions is minimal because all the intermediate steps catalyzed by particular enzymes have already been tested and selected for maximal efficiency. Organisms can now deal with multiple sources of energy. The outcome of this wealth was the explosion in morphological diversity. The main limitations to diversity are internal generative ones. Multicellular diploblastic metazoans gave rise at the beginning of the Cambrian (580 million years ago) to triploblastic metazoa whose three blastoderm layers allow for a variety of internal tissues and organs, a supporting skeleton, sensory and motor nervous systems, specialized sexual organs, and sexual dimorphisms. In addition, segmentation, i.e., iteration of metameric modules, did allow body-size increase and longitudinal specialization. Appendages provided for locomotory, bucal respiratory, and sensory organs. Epithelial specializations gave rise to defense spines and plates and digestive organs. Within 50 million years, the Cambrian explosion led to the appearance of the major extant phyla: platyhelminths, arthropods, annelids, molluscs, echinoderms, and chordates. There also arose some groups with different body plans that have since become extinct.
Molecular comparisons of genes performing similar functions in extant organisms (animals or plants) of diverse taxanomic groups reveals a surprising degree of nucleotide sequence conservation from the Cambrian ancestors. Thus, we may ask, which novel genetic operations and which symmetry breaks can account for the Cambrian explosion of morphological diversity modes? Molecular and developmental genetic analysis in a few organisms has uncovered a modular nature of the structure of genes, of their functional interactions within cells, and of the morphologies to which they give rise. This modularity is helping us to understand morphogenetic evolution. Genes contain in their protein-coding regions amino acid sequence motifs that upon translation correspond to protein folds or structural domains. These domains serve particular types of molecular recognition in enzymatic reactions with substrates or between proteins or between proteins and cis-regulatory DNA sequences of genes (consisting of several short polynucleotide motifs that condition its transcription). It so happens that there is only a limited number of protein domains, on the order of 1000–2000 domains, and hence of molecular recognition features. These domains remain conserved in evolution possibly because mismatches between protein partners in their transaction leads to failures in function. This necessity for conservation represents a large inertial component of evolution.
One way to generate diversity in the face of this inertia is to duplicate the gene modules, followed by slight modification of their individual structure and secondary modulation of their function. Another way is to reshuffle these modules (exons) and generate chimeric transcriptional units giving rise to complex proteins. In addition, reshuffling of cis-acting promoter regions of a gene can bring it under the control of novel trans-acting regulatory protein. While gene duplication followed by mutation can give rise to diversity in the number of related functions of the original protein, differential splicing of exons encoded in the same gene can give rise to several different proteins. Thus, a large fraction of the vertebrate genome encode for numerous (up to a thousand) members of the same protein family. Yet the total genome complexity has increased very little in number of genes, from about 4000–5000 in bacteria, to 6000 in yeast, to 15,000–18,000 in nematodes and insects, and about 60,000 in primates. The apparent increase in morphological complexity from monocellular eukaryotes to metazoa was attended by a less than 10-fold increase of magnitude in the number of genes.
High mutation rates, attributable to both nucleotide substitutions and DNA segment rearrangement, such as translocations and a gene conversion, provide a continuous source of novel genetic propositions for evolution. The viability of these propositions is limited only by their immediate phenotypic effects. A dysfunctional type of mutation in the protein-coding regions may set off a rapid selection for a compensatory mutation in that protein’s interacting partner (so called coevolution). A mutation in the regulatory region of a gene, in contrast, resolves in the disappearance of one phenotypic character in the cell lineage in which the gene is normally acting; the appearance by mutation of a new short sequence in the regulatory region of a gene may result in the appearance of a new phenotypic character in a new cell lineage or at later branchings of it. The later types of genetic changes leave overall development unperturbed but provide an opportunity for the appearance of large morphogenetic novelties. The latter type of genetic changes surely constitutes the most important driving operation in organic evolution.
Morphological diversity devolves from combinatorial associations of a few genes acting in discrete groups in cells, along cell lineages in development. Combinations of modular elements is the basis for the formation of protein complexes acting as stable cell structures (such as the cytoskeleton) or as “agglomerates” (such as ribosomes and transcription and replication complexes). Because of the constraints imposed by molecular recognition, these complexes remained largely invariant in the course of evolution. Transient associations between genes and proteins are combinatorial devices, assigning several formerly independent acting genes to one working team (“syntagma”) by subjecting them to the control of the same regulatory genes operating on their common DNA promoter regions. Individual syntagmata are conserved functional entities, modules, performing the same genetic operation throughout evolution. The DNA motifs of these common promoter regions can be several in number, thus exposing a single gene to several controlling genes. Cell proliferation during development allows novel uses of these syntagmata in different cell lineages (positions) and at different developmental times, while always retaining the same basic molecular recognition specificity. A given cell of a particular lineage may thus be under the control of several active syntagmata. Cell–cell interactions may induce those syntagmata and hence differential cell behavior as defined by combinatorials of syntagmata.
The genetic operations defined by active syntagmata correspond to functional modules in developmental operations. Thus, cell division, cell differentiation, cell adhesion, cell recognition, signal transduction, nerve growth guidance, and even sexual dimorphism are the work of syntagmata. In a growing number of cases, we find that members of syntagmata have remained the same since Cambrian times.
Cambrian organisms devised supracellular modules, segments, and developmental compartments. The locally differentiated properties of body parts along the anterior–posterior and the dorsal–ventral axes as well as features of organs (such as heart and eye) are now known to be controlled by members of gene families that have been conserved from the ancestors of the modern triploblast grade (including both deutero- and protostomia). These “selector” genes implement topographical differentiation by locally controlling syntagmata of histodifferentiation genes. Cell groups become isolated in modular entities (developmental compartments) associated with the specific expression of those territorial (“selectors”) genes in all their cells. These cell groups are polyclonal in origin and become established making use of specific cell recognition labels, adhesion modules of complementarily matching specific ligands and receptors (selector dependent) of neighboring cells.
Cell proliferation within modules is indeterminate but the cells cannot cross module borders, which later correspond to segmental or subsegmental entities in the adult patterns. Cell lineage borders become major organizative entities. Exchange of signals at either side of these borders drive differential gene activity and the release of growth factors (acting as diffussible morphogens or as ligands) operating on the receptors of next cells in transmission cascades. Thus, the territorial specification of cells by “selector” genes is implemented in cell behavior and hence in developmental operations. Following further cell proliferation, a new subdivision of territories appear, each specified by new selector genes. In this way, genetic specification of modules results from combinations of syntagmata operating in the same cells. Segmental or periodic diversity, already recognizable in Cambrian taxa, must have used these genetic operations because the selector genes involved are present in the derived forms of common ancestors. Local modifications of these genetic–developmental operations, fundamentally by combinatorial displacements, have since directed the currently observable morphological diversity. Their association and dissociation of syntagmata in cells of different cell lineages determined the fantastic morphological diversity of the Cambrian explosion. Hence, the extant morphological world is then the result of combinatorial diversification of a few, functionally successful, molecular interactions.
The evolution across several levels of complexity from atoms to molecules, to cells, to organs, and to organisms is an iterated symmetry break. And possibly new breaks of symmetry underlie the emergence of new organic properties like the organization of neurons in brains, behavior of animals conforming societies, or groups of species interacting in ecosystems. It is a mystery how the increase in complexity levels occurred, what the driving force of organic evolution was, and in particular how amplification in morphological diversity happened to arise. The Cambrian explosion took place within only 20–50 million years and in a rather homogeneous marine world. Selection from or adaptation to new niches seems to have been of little importance. Rather it seems that the generation of new morphologies through new genetic associations, i.e., the propositional aspect of selection, may have played the dominant role. Since molecular recognition encoded by genes appears to override physical or external specifications. Organisms seem to be more dependent on their generative mechanisms than on the external morphologies to which they give rise.