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1.  Hox, Wnt, and the evolution of the primary body axis: insights from the early-divergent phyla 
Biology Direct  2007;2:37.
The subkingdom Bilateria encompasses the overwhelming majority of animals, including all but four early-branching phyla: Porifera, Ctenophora, Placozoa, and Cnidaria. On average, these early-branching phyla have fewer cell types, tissues, and organs, and are considered to be significantly less specialized along their primary body axis. As such, they present an attractive outgroup from which to investigate how evolutionary changes in the genetic toolkit may have contributed to the emergence of the complex animal body plans of the Bilateria. This review offers an up-to-date glimpse of genome-scale comparisons between bilaterians and these early-diverging taxa. Specifically, we examine these data in the context of how they may explain the evolutionary development of primary body axes and axial symmetry across the Metazoa. Next, we re-evaluate the validity and evolutionary genomic relevance of the zootype hypothesis, which defines an animal by a specific spatial pattern of gene expression. Finally, we extend the hypothesis that Wnt genes may be the earliest primary body axis patterning mechanism by suggesting that Hox genes were co-opted into this patterning network prior to the last common ancestor of cnidarians and bilaterians.
Reviewed by Pierre Pontarotti, Gáspár Jékely, and L Aravind. For the full reviews, please go to the Reviewers' comments section.
PMCID: PMC2222619  PMID: 18078518
2.  Symmetrical crypsis and asymmetrical signalling in the cuttlefish Sepia officinalis 
The salience of bilateral symmetry to humans has led to the suggestion that camouflage may be enhanced in asymmetrical patterns. However, the importance of bilateral symmetry in visual signals (and overall morphology) may constrain the evolution of asymmetrical camouflage, resulting in the bilaterally symmetrical cryptic patterns that we see throughout the animal kingdom. This study investigates the cuttlefish (Sepia officinalis), which can control the degree of symmetry in its coloration. Ten juvenile S. officinalis were filmed in two behavioural contexts (cryptic and threatened) to test the prediction that cryptic patterns will be expressed more asymmetrically than an anti-predator signal known as the ‘deimatic display’. Cryptic body patterns, particularly those with a disruptive function, were found to exhibit a high degree of bilateral symmetry. By contrast, the components of the deimatic display were often expressed asymmetrically. These results are contrary to the predicted use of symmetry in defensive coloration, indicating that the role of symmetry in both crypsis and visual signalling is not as straightforward as previously suggested.
PMCID: PMC1560237  PMID: 16627281
symmetry; adaptive coloration; crypsis; cephalopod; Sepia officinalis; deimatic display
3.  Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry 
Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.
We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.
The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.
PMCID: PMC3209460  PMID: 21958045
4.  Molecular insights into the origin of the Hox-TALE patterning system 
eLife  2014;3:e01939.
Despite tremendous body form diversity in nature, bilaterian animals share common sets of developmental genes that display conserved expression patterns in the embryo. Among them are the Hox genes, which define different identities along the anterior–posterior axis. Hox proteins exert their function by interaction with TALE transcription factors. Hox and TALE members are also present in some but not all non-bilaterian phyla, raising the question of how Hox–TALE interactions evolved to provide positional information. By using proteins from unicellular and multicellular lineages, we showed that these networks emerged from an ancestral generic motif present in Hox and other related protein families. Interestingly, Hox-TALE networks experienced additional and extensive molecular innovations that were likely crucial for differentiating Hox functions along body plans. Together our results highlight how homeobox gene families evolved during eukaryote evolution to eventually constitute a major patterning system in Eumetazoans.
eLife digest
Any animal with a body that is symmetric about an imaginary line that runs from its head to its tail is known as a bilaterian. Humans and most animals are bilateral, whereas jellyfish and starfish are not. Bilateral symmetry can take many forms—as demonstrated by the differences between flies, frogs and humans—but all bilaterians express many of the same genes during development.
One of these groups of genes is known as the Hox family. The expression of specific Hox genes at specific times instructs cells in the developing embryo to adopt different fates according to their position along the anterior–posterior (head to tail) axis. The patterning function of Hox genes relies on the presence of two additional cofactors that belong to the so-called TALE family. Although both Hox and TALE proteins were present early on during animal evolution, it is unclear how and when the interactions between them first began to generate symmetrical body plans.
Now, Hudry et al. have provided insights into the origin of the Hox-TALE network by analysing the expression and molecular properties of Hox and TALE proteins from various multicellular and unicellular organisms. These experiments revealed that Hox and TALE proteins of the sea anemone Nematostella, which belongs to a group of animals called cnidarians that have radial rather than bilateral symmetry, interact with one another in a similar manner to the interactions seen in bilaterians.
Hudry et al. then showed that two Nematostella Hox genes were able to substitute for their bilaterian equivalents in fruit flies, and that a Nematostella TALE gene was able to take over neuronal functions of its equivalent in Xenopus frogs. This striking conservation of function between species suggests that Hox and TALE genes were already working together in the common ancestor of all bilaterian and cnidarian animals.
By contrast, TALE members from a unicellular amoeba were unable to interact with Hox proteins, suggesting that Hox–TALE interactions first emerged in multicellular animals. In addition to increasing our knowledge of highly conserved Hox signalling, these data provide insight into the molecular mechanisms that gave rise to the symmetrical body plan that has been adopted, and adapted, by the majority of animals since.
PMCID: PMC3957477  PMID: 24642410
Hox; TALE; evolution; network; transcription factors; Nematostella vectensis; D. melanogaster; other
5.  Dynamic Control of Auxin Distribution Imposes a Bilateral-to-Radial Symmetry Switch during Gynoecium Development 
Current Biology  2014;24(22):2743-2748.
Symmetry formation is a remarkable feature of biological life forms associated with evolutionary advantages and often with great beauty. Several examples exist in which organisms undergo a transition in symmetry during development [1–4]. Such transitions are almost exclusively in the direction from radial to bilateral symmetry [5–8]. Here, we describe the dynamics of symmetry establishment during development of the Arabidopsis gynoecium. We show that the apical style region undergoes an unusual transition from a bilaterally symmetric stage ingrained in the gynoecium due to its evolutionary origin to a radially symmetric structure. We also identify two transcription factors, INDEHISCENT [9] and SPATULA [10], that are both necessary and sufficient for the radialization process. Our work furthermore shows that these two transcription factors control style symmetry by directly regulating auxin distribution. Establishment of specific auxin-signaling foci and the subsequent development of a radially symmetric auxin ring at the style are required for the transition to radial symmetry, because genetic manipulations of auxin transport can either cause loss of radialization in a wild-type background or rescue mutants with radialization defects. Whereas many examples have described how auxin provides polarity and specific identity to cells in a range of developmental contexts, our data presented here demonstrate that auxin can also be recruited to impose uniform identity to a group of cells that are otherwise differentially programmed.
Graphical Abstract
•Apex of the Arabidopsis gynoecium undergoes a bilateral-to-radial symmetry transition•Transcription factors IND/SPT are necessary and sufficient for organ radialization•IND and SPT regulate auxin transport to achieve radial symmetry•Spatiotemporal auxin dynamics control growth and symmetry of the gynoecium
Symmetry transitions in nature are common and occur almost exclusively via a change from radial to bilateral symmetry. Here, Moubayidin and Østergaard reveal how control of auxin transport by SPATULA and INDEHISCENT imposes a rare bilateral-to-radial symmetry switch during Arabidopsis gynoecium development.
PMCID: PMC4245708  PMID: 25455035
6.  Uniting sex and eukaryote origins in an emerging oxygenic world 
Biology Direct  2010;5:53.
Theories about eukaryote origins (eukaryogenesis) need to provide unified explanations for the emergence of diverse complex features that define this lineage. Models that propose a prokaryote-to-eukaryote transition are gridlocked between the opposing "phagocytosis first" and "mitochondria as seed" paradigms, neither of which fully explain the origins of eukaryote cell complexity. Sex (outcrossing with meiosis) is an example of an elaborate trait not yet satisfactorily addressed in theories about eukaryogenesis. The ancestral nature of meiosis and its dependence on eukaryote cell biology suggest that the emergence of sex and eukaryogenesis were simultaneous and synergic and may be explained by a common selective pressure.
Presentation of the hypothesis
We propose that a local rise in oxygen levels, due to cyanobacterial photosynthesis in ancient Archean microenvironments, was highly toxic to the surrounding biota. This selective pressure drove the transformation of an archaeal (archaebacterial) lineage into the first eukaryotes. Key is that oxygen might have acted in synergy with environmental stresses such as ultraviolet (UV) radiation and/or desiccation that resulted in the accumulation of reactive oxygen species (ROS). The emergence of eukaryote features such as the endomembrane system and acquisition of the mitochondrion are posited as strategies to cope with a metabolic crisis in the cell plasma membrane and the accumulation of ROS, respectively. Selective pressure for efficient repair of ROS/UV-damaged DNA drove the evolution of sex, which required cell-cell fusions, cytoskeleton-mediated chromosome movement, and emergence of the nuclear envelope. Our model implies that evolution of sex and eukaryogenesis were inseparable processes.
Testing the hypothesis
Several types of data can be used to test our hypothesis. These include paleontological predictions, simulation of ancient oxygenic microenvironments, and cell biological experiments with Archaea exposed to ROS and UV stresses. Studies of archaeal conjugation, prokaryotic DNA recombination, and the universality of nuclear-mediated meiotic activities might corroborate the hypothesis that sex and the nucleus evolved to support DNA repair.
Implications of the hypothesis
Oxygen tolerance emerges as an important principle to investigate eukaryogenesis. The evolution of eukaryotic complexity might be best understood as a synergic process between key evolutionary innovations, of which meiosis (sex) played a central role.
This manuscript was reviewed by Eugene V. Koonin, Anthony M. Poole, and Gáspár Jékely.
PMCID: PMC2933680  PMID: 20731852
7.  A diffusion-based neurite length-sensing mechanism involved in neuronal symmetry breaking 
Shootin1, one of the earliest markers of neuronal symmetry breaking, accumulates in the neurite tips of polarizing neurons in a neurite length-dependent manner. Thus, neurons sense their neurites' length and translate this spatial information into a molecular signal, shootin1 concentration.Quantitative live cell imaging of shootin1 dynamics combined with mathematical modeling analyses reveals that its anterograde transport and retrograde diffusion in neurite shafts account for the neurite length-dependent accumulation of shootin1.The neurite length-dependent shootin1 accumulation and shootin1-induced neurite outgrowth constitute a positive feedback loop that amplifies stochastic shootin1 signals in neurite tips.Quantitative mathematical modeling shows that the above positive feedback loop, together with shootin1 upregulation, constitutes a core mechanism for neuronal symmetry breaking.
Cell morphology and size must be properly controlled to ensure cellular function. Although there has been significant progress in understanding the molecular signals that change cell morphology, the manner in which cells monitor their size and length to regulate their morphology is poorly understood. Cultured hippocampal neurons polarize by forming a single long axon and multiple short dendrites (Craig and Banker, 1994; Arimura and Kaibuchi, 2007), and symmetry breaking is the initial step of this process. This symmetry-breaking step reproduces even when the neuronal axon is transected; the longest neurite usually grows rapidly to become an axon after transection, regardless of whether it is the axonal stump or another neurite (Goslin and Banker, 1989). Elongation of an immature neurite by mechanical tension also leads to its axonal specification (Lamoureux et al, 2002). These results suggest that cultured hippocampal neurons can sense neurite length, identify the longest one, and induce its subsequent axonogenesis for symmetry breaking. However, little is known about the mechanism for this process.
Shootin1 is one of the earliest markers of neuronal symmetry breaking (Toriyama et al, 2006). During the symmetry-breaking step, it undergoes a stochastic accumulation in neurite tips, and eventually accumulates predominantly in a single neurite that subsequently grows to become an axon. In this study, we demonstrated that shootin1 accumulates in neurite tips in a neurite length-dependent manner, regardless of whether it is the axonal stump or another neurite (Figure 3A, C–F). Thus, morphological information (neurite length) is translated into a molecular signal (shootin1 concentration in neurite tips).
We previously reported that shootin1 is transported from the cell body to neurite tips as discrete boluses and diffuses back to the cell body (Toriyama et al, 2006). The boluses containing variable amounts of shootin1 traveled repeatedly but irregularly along neurites, and their arrival caused large stochastic fluctuations in shootin1 concentration in the neurite tips. To understand the mechanism of length-dependent shootin1 accumulation, we performed quantitative live cell imaging of the anterograde transport and retrograde diffusion of shootin1 and fitted the obtained data into mathematical models of the anterograde transport and retrograde diffusion. The parameters of these two models were derived entirely from quantitative experimental data, without any adjustment. Shootin1 concentration at neurite tips, calculated by integrating the two models, was neurite length dependent (Figure 3B) and showed good agreement with the experimental data (Figure 3A). These results suggest that the neurite length-dependent accumulation of shootin1 is quantitatively explained by its anterograde transport and retrograde diffusion.
This length-dependent shootin1 accumulation constitutes a positive feedback interaction with the previously reported shootin1-induced neurite outgrowth (Shimada et al, 2008). To analyze the functional role of this feedback loop, we quantified shootin1 upregulation (Toriyama et al, 2006) and shootin1-induced neurite outgrowth, and integrated them, together with the above model of length-dependent shootin1 accumulation, into a model neuron (Figure 7A). Furthermore, the parameters of the model components were chosen to give the best fit to the quantitative experimental data without any adjustment. Integrating the three components into a model neuron resulted in spontaneous symmetry breaking (Figure 7B and C). Furthermore, there are a total of 15 agreements between the model predictions and the experimental data, including the neurite length-dependent axon specification and regeneration (Goslin and Banker, 1989; Lamoureux et al, 2002). These data suggest that the three components in our model—namely, diffusion-based neurite length sensing system, shootin1-induced neurite outgrowth and shootin1 upregulation—are sufficient to induce neuronal symmetry breaking.
Bolus-like transport of shootin1 caused large stochastic fluctuations in shootin1 concentration in neurite tips. Interestingly, the generation of continuous shootin1 transport in our model neuron impaired the symmetry-breaking process (Figure 7D). This is consistent with theoretical models in which feedback amplification of fluctuations in signaling can give rise to robust patterns (Turing, 1952; Meinhardt and Gierer, 2000; Kondo, 2002), and underscores the importance of the stochastic fluctuating signals in spontaneous neuronal symmetry breaking.
The combination of quantitative experimentation and mathematical modeling is regarded as a powerful strategy for attaining a profound understanding of biological systems (Hodgkin and Huxley, 1952b; Lewis, 2008; Ferrell, 2009). By focusing on a simple system involving one of the earliest markers of neuronal symmetry breaking, shootin1, we were able to evaluate here the core components of neuronal symmetry breaking on the basis of quantitative experimental data. The present model may thus provide a core mechanism of neuronal symmetry breaking, to which other possible mechanisms can be added to increase the model's complexity in future studies.
Although there has been significant progress in understanding the molecular signals that change cell morphology, mechanisms that cells use to monitor their size and length to regulate their morphology remain elusive. Previous studies suggest that polarizing cultured hippocampal neurons can sense neurite length, identify the longest neurite, and induce its subsequent outgrowth for axonogenesis. We observed that shootin1, a key regulator of axon outgrowth and neuronal polarization, accumulates in neurite tips in a neurite length-dependent manner; here, the property of cell length is translated into shootin1 signals. Quantitative live cell imaging combined with modeling analyses revealed that intraneuritic anterograde transport and retrograde diffusion of shootin1 account for its neurite length-dependent accumulation. Our quantitative model further explains that the length-dependent shootin1 accumulation, together with shootin1-dependent neurite outgrowth, constitutes a positive feedback loop that amplifies stochastic fluctuations of shootin1 signals, thereby generating an asymmetric signal for axon specification and neuronal symmetry breaking.
PMCID: PMC2925530  PMID: 20664640
feedback loop; neuronal polarity; quantitative modeling; shootin1; stochasticity
8.  Human odometer is gait-symmetry specific 
In 1709, Berkeley hypothesized of the human that distance is measurable by ‘the motion of his body, which is perceivable by touch’. To be sufficiently general and reliable, Berkeley's hypothesis must imply that distance measured by legged locomotion approximates actual distance, with the measure invariant to gait, speed and number of steps. We studied blindfolded human participants in a task in which they travelled by legged locomotion from a fixed starting point A to a variable terminus B, and then reproduced, by legged locomotion from B, the A–B distance. The outbound (‘measure’) and return (‘report’) gait could be the same or different, with similar or dissimilar step sizes and step frequencies. In five experiments we manipulated bipedal gait according to the primary versus secondary distinction revealed in symmetry group analyses of locomotion patterns. Berkeley's hypothesis held only when the measure and report gaits were of the same symmetry class, indicating that idiothetic distance measurement is gait-symmetry specific. Results suggest that human odometry (and perhaps animal odometry more generally) entails variables that encompass the limbs in coordination, such as global phase, and not variables at the level of the single limb, such as step length and step number, as traditionally assumed.
PMCID: PMC2817097  PMID: 19740881
Berkeley; idiothetic distance; legged locomotion; odometry; symmetry group
9.  Bipedalism in lizards: whole-body modelling reveals a possible spandrel. 
This paper illustrates how simple mechanical models based on morphological, ethological, ecological and phylogenetic data can add to discussions in evolutionary biology. Bipedal locomotion has evolved on numerous occasions in lizards. Traits that appear repeatedly in independent evolutionary lines are often considered adaptive, but the exact advantages of bipedal locomotion in lizards remain debated. Earlier claims that bipedalism would increase maximal running speed or would be energetically advantageous have been questioned. Here, we use 'whole body' mechanical modelling to provide an alternative solution to the riddle. The starting point is the intermittent running style combined with the need for a high manoeuvrability characterizing many small lizard species. Manoeuvrability benefits from a caudal shift of the centre of mass of the body (body-COM), because forces to change the heading and to align the body to this new heading do not conflict with each other. The caudally situated body-COM, however, might result in a lift of the front part of the body when accelerating (intermittent style), thus resulting in bipedal running bouts. Based on a momentum-impulse approach the effect of acceleration is quantified for a mechanical model, a virtual lizard (three segments) based on the morphometrics of Acanthodactylus erythrurus (a small lacertid lizard). Biologically relevant input (dimensions, inertial properties, step cycle information, etc.) results in an important lift of the front part of the body and observable distances passively covered bipedally as a consequence of the acceleration. In this way, no functional explanation of the phenomenon of lizard bipedalism is required and bipedalism can probably be considered non-adaptive in many cases. This does not exclude, however, some species that may have turned this consequence to their benefit. For instance, instantaneous manipulation of the position of the centre of the body-COM allows stable, persisting bipedal running. Once this was achieved, the bipedal spandrel could be exploited further.
PMCID: PMC1693243  PMID: 14561343
10.  Evolutionary Trends in the Flowers of Asteridae: Is Polyandry an Alternative to Zygomorphy? 
Annals of Botany  2008;102(2):153-165.
Background and Aims
Floral symmetry presents two main states in angiosperms, actinomorphy (polysymmetry or radial symmetry) and zygomorphy (monosymmetry or bilateral symmetry). Transitions from actinomorphy to zygomorphy have occurred repeatedly among flowering plants, possibly in coadaptation with specialized pollinators. In this paper, the rules controlling the evolution of floral symmetry were investigated to determine in which architectural context zygomorphy can evolve.
Floral traits potentially associated with perianth symmetry shifts in Asteridae, one of the major clades of the core eudicots, were selected: namely the perianth merism, the presence and number of spurs, and the androecium organ number. The evolution of these characters was optimized on a composite tree. Correlations between symmetry and the other morphological traits were then examined using a phylogenetic comparative method.
Key Results
The analyses reveal that the evolution of floral symmetry in Asteridae is conditioned by both androecium organ number and perianth merism and that zygomorphy is a prerequisite to the emergence of spurs.
The statistically significant correlation between perianth zygomorphy and oligandry suggests that the evolution of floral symmetry could be canalized by developmental or spatial constraint. Interestingly, the evolution of polyandry in an actinomorphic context appears as an alternative evolutionary pathway to zygomorphy in Asteridae. These results may be interpreted either in terms of plant–pollinator adaptation or in terms of developmental or physical constraints. The results are discussed in relation to current knowledge about the molecular bases underlying floral symmetry.
PMCID: PMC2712368  PMID: 18511411
Floral symmetry; architectural constraints; Asteridae; comparative analysis; composite tree; correlated evolution; evolutionary scenario
11.  Fifteen observations on the structure of energy-minimizing gaits in many simple biped models 
A popular hypothesis regarding legged locomotion is that humans and other large animals walk and run in a manner that minimizes the metabolic energy expenditure for locomotion. Here, using numerical optimization and supporting analytical arguments, I obtain the energy-minimizing gaits of many different simple biped models. I consider bipeds with point-mass bodies and massless legs, with or without a knee, with or without a springy tendon in series with the leg muscle and minimizing one of many different ‘metabolic cost’ models—correlated with muscle work, muscle force raised to some power, the Minetti–Alexander quasi-steady approximation to empirical muscle metabolic rate (from heat and ATPase activity), a new cost function called the ‘generalized work cost’ Cg having some positivity and convexity properties (and includes the Minetti–Alexander cost and the work cost as special cases), and generalizations thereof. For many of these models, walking-like gaits are optimal at low speeds and running-like gaits at higher speeds, so a gait transition is optimal. Minimizing the generalized work cost Cg appears mostly indistinguishable from minimizing muscle work for all the models. Inverted pendulum walking and impulsive running gaits minimize the work cost, generalized work costs Cg and a few other costs for the springless bipeds; in particular, a knee-torque-squared cost, appropriate as a simplified model for electric motor power for a kneed robot biped. Many optimal gaits had symmetry properties; for instance, the left stance phase was identical to the right stance phases. Muscle force–velocity relations and legs with masses have predictable qualitative effects, if any, on the optima. For bipeds with compliant tendons, the muscle work-minimizing strategies have close to zero muscle work (isometric muscles), with the springs performing all the leg work. These zero work gaits also minimize the generalized work costs Cg with substantial additive force or force rate costs, indicating that a running animal's metabolic cost could be dominated by the cost of producing isometric force, even though performing muscle work is usually expensive. I also catalogue the many differences between the optimal gaits of the various models. These differences contain information that might help us develop models that better predict locomotion data. In particular, for some biologically plausible cost functions, the presence or absence of springs in series with muscles has a large effect on both the coordination strategy and the absolute cost; the absence of springs results in more impulsive (collisional) optimal gaits and the presence of springs leads to more compliant optimal gaits. Most results are obtained for specific speed and stride length combinations close to preferred human behaviour, but limited numerical experiments show that some qualitative results extend to other speed-stride length combinations as well.
PMCID: PMC3024815  PMID: 20542957
legged locomotion; walking and running; optimization and optimal control; minimize energy; gaits; metabolic cost
12.  In Silico Reconstitution of Actin-Based Symmetry Breaking and Motility 
PLoS Biology  2009;7(9):e1000201.
Computational modeling and experimentation in a model system for actin-based force generation explain how actin networks initiate and maintain directional movement.
Eukaryotic cells assemble viscoelastic networks of crosslinked actin filaments to control their shape, mechanical properties, and motility. One important class of actin network is nucleated by the Arp2/3 complex and drives both membrane protrusion at the leading edge of motile cells and intracellular motility of pathogens such as Listeria monocytogenes. These networks can be reconstituted in vitro from purified components to drive the motility of spherical micron-sized beads. An Elastic Gel model has been successful in explaining how these networks break symmetry, but how they produce directed motile force has been less clear. We have combined numerical simulations with in vitro experiments to reconstitute the behavior of these motile actin networks in silico using an Accumulative Particle-Spring (APS) model that builds on the Elastic Gel model, and demonstrates simple intuitive mechanisms for both symmetry breaking and sustained motility. The APS model explains observed transitions between smooth and pulsatile motion as well as subtle variations in network architecture caused by differences in geometry and conditions. Our findings also explain sideways symmetry breaking and motility of elongated beads, and show that elastic recoil, though important for symmetry breaking and pulsatile motion, is not necessary for smooth directional motility. The APS model demonstrates how a small number of viscoelastic network parameters and construction rules suffice to recapture the complex behavior of motile actin networks. The fact that the model not only mirrors our in vitro observations, but also makes novel predictions that we confirm by experiment, suggests that the model captures much of the essence of actin-based motility in this system.
Author Summary
Networks of actin filaments provide the force that drives eukaryotic cell movement. In a model system for this kind of force generation, a spherical bead coated with an actin nucleating protein builds and rockets around on an actin “comet tail,” much like the tails observed in some cellular systems. How does a spherically symmetric bead break the symmetry of the actin coat and begin to polymerize actin in a directional manner? A previous theoretical model successfully explained how symmetry breaks, but suggested that the subsequent motion was driven by actin squeezing the bead forwards—a prediction refuted by experiment. To understand how motility occurs, we created a parsimonious computer model that predicted novel experimental behaviors, then performed new experiments inspired by the model and confirmed these predictions. Our model demonstrates how the elastic properties of the actin network explain not only symmetry breaking, but also the details of subsequent motion and how the bead maintains direction.
PMCID: PMC2738636  PMID: 19771152
13.  The predation costs of symmetrical cryptic coloration 
In psychological studies of visual perception, symmetry is accepted as a potent cue in visual search for cryptic objects, yet its importance for non-human animals has been assumed rather than tested. Furthermore, while the salience of bilateral symmetry has been established in laboratory-based search tasks using human subjects, its role in more natural settings, closer to those for which such perceptual mechanisms evolved, has not, to our knowledge, been investigated previously. That said, the salience of symmetry in visual search has a plausible adaptive rationale, because biologically important objects, such as prey, predators or conspecifics, usually have a plane of symmetry that is not present in their surroundings. We tested the conspicuousness to avian predators of cryptic artificial, moth-like targets, with or without bilateral symmetry in background-matching coloration, against oak trees in the field. In two independent experiments, symmetrical targets were predated at a higher rate than otherwise identical asymmetrical targets. There was a small, but significant, fitness cost to symmetry in camouflage patterns. Given that birds are the most commonly invoked predators shaping the evolution of defensive coloration in insects, this raises the question of why bilateral asymmetry is not more common in cryptic insects.
PMCID: PMC1560277  PMID: 16720401
defensive coloration; bilateral symmetry; bird vision; predation risk; visual search
14.  The basis and significance of pre-patterning in mammals. 
The second polar body (Pb) provides an enduring marker of the animal pole of the zygote, thereby revealing that the axis of bilateral symmetry of the early blastocyst is aligned with the zygote's animal-vegetal axis. That this relationship is biologically significant appeared likely when subsequent studies showed that the equator of the blastocyst tended to correspond with the plane of first cleavage. However, this cleavage plane varies both with respect to the position of the second Pb and to the distribution of components of the fertilizing sperm that continue to mark the point where it entered the egg. It also maps too variably on the blastocyst to play a causal role in early patterning. The zygote has been found transiently to exhibit bilateral symmetry before regaining an essentially spherical shape prior to first cleavage. Marking experiments indicate that the plane of bilateral symmetry of the blastocyst is aligned with, and the plane of first cleavage is typically orthogonal to, the zygote's bilateral plane. The bilateral symmetry of the zygote bears no consistent relationship either to the point of sperm entry or to the distribution of the pronuclei, and may therefore be a manifestation of intrinsic organization of the egg. Finally, the two-cell blastomere inheriting the sperm entry point has not been found to differ consistently in fate from the one that does not.
PMCID: PMC1693237  PMID: 14511479
15.  Genetic Analysis of Floral Symmetry in Van Gogh's Sunflowers Reveals Independent Recruitment of CYCLOIDEA Genes in the Asteraceae 
PLoS Genetics  2012;8(3):e1002628.
The genetic basis of floral symmetry is a topic of great interest because of its effect on pollinator behavior and, consequently, plant diversification. The Asteraceae, which is the largest family of flowering plants, is an ideal system in which to study this trait, as many species within the family exhibit a compound inflorescence containing both bilaterally symmetric (i.e., zygomorphic) and radially symmetric (i.e., actinomorphic) florets. In sunflower and related species, the inflorescence is composed of a single whorl of ray florets surrounding multiple whorls of disc florets. We show that in double-flowered (dbl) sunflower mutants (in which disc florets develop bilateral symmetry), such as those captured by Vincent van Gogh in his famous nineteenth-century sunflower paintings, an insertion into the promoter region of a CYCLOIDEA (CYC)-like gene (HaCYC2c) that is normally expressed specifically in WT rays is instead expressed throughout the inflorescence, presumably resulting in the observed loss of actinomorphy. This same gene is mutated in two independent tubular-rayed (tub) mutants, though these mutations involve apparently recent transposon insertions, resulting in little or no expression and radialization of the normally zygomorphic ray florets. Interestingly, a phylogenetic analysis of CYC-like genes from across the family suggests that different paralogs of this fascinating gene family have been independently recruited to specify zygomorphy in different species within the Asteraceae.
Author Summary
The evolution of flower shape and symmetry is of great interest to plant biologists, because it can affect pollinator behavior. Species in the flowering plant family Asteraceae exhibit flower heads that can contain both bilaterally and radially symmetric flowers. In this study, we identify a CYCLOIDEA-like gene that is responsible for determining flower symmetry in sunflower. Mis-expression of this gene causes a double-flowered phenotype, similar to those captured in Vincent van Gogh's famous nineteenth-century paintings, whereas loss of gene function causes radialization of the normally bilaterally symmetric ray florets. Interestingly, this gene is not orthologous to the CYCLOIDEA-like gene responsible for floral symmetry in other members of the Asteraceae, providing evidence of the parallel recruitment of different members of the same gene family for the same function.
PMCID: PMC3315478  PMID: 22479210
16.  Facial attractiveness, symmetry and cues of good genes. 
Cues of phenotypic condition should be among those used by women in their choice of mates. One marker of better phenotypic condition is thought to be symmetrical bilateral body and facial features. However, it is not clear whether women use symmetry as the primary cue in assessing the phenotypic quality of potential mates or whether symmetry is correlated with other facial markers affecting physical attractiveness. Using photographs of men's faces, for which facial symmetry had been measured, we found a relationship between women's attractiveness ratings of these faces and symmetry, but the subjects could not rate facial symmetry accurately. Moreover, the relationship between facial attractiveness and symmetry was still observed, even when symmetry cues were removed by presenting only the left or right half of faces. These results suggest that attractive features other than symmetry can be used to assess phenotypic condition. We identified one such cue, facial masculinity (cheek-bone prominence and a relatively longer lower face), which was related to both symmetry and full- and half-face attractiveness.
PMCID: PMC1690211  PMID: 10535106
17.  Microscopic Symmetry Imposed by Rotational Symmetry Boundary Conditions in Molecular Dynamics Simulation 
A large number of viral capsids, as well as other macromolecular assemblies, have icosahedral structure or structures with other rotational symmetries. This symmetry can be exploited during molecular dynamics (MD) to model in effect the full viral capsid using only a subset of primary atoms plus copies of image atoms generated from rotational symmetry boundary conditions (RSBC). A pure rotational symmetry operation results in both primary and image atoms at short range, and within nonbonded interaction distance of each other, so that nonbonded interactions can not be specified by the minimum image convention and explicit treatment of image atoms is required. As such an unavoidable consequence of RSBC is that the enumeration of nonbonded interactions in regions surrounding certain rotational axes must include both a primary atom and its copied image atom, thereby imposing microscopic symmetry for some forces. We examined the possibility of artifacts arising from this imposed microscopic symmetry of RSBC using two simulation systems: a water shell and human rhinovirus 14 (HRV14) capsid with explicit water. The primary unit was a pentamer of the icosahedron, which has the advantage of direct comparison of icosahedrally equivalent spatial regions, for example regions near a 2-fold symmetry axis with imposed symmetry and a 2-fold axis without imposed symmetry. Analysis of structural and dynamic properties of water molecules and protein atoms found similar behavior near symmetry axes with imposed symmetry and where the minimum image convention fails compared with that in other regions in the simulation system, even though an excluded volume effect was detected for water molecules near the axes with imposed symmetry. These results validate the use of RSBC for icosahedral viral capsids or other rotationally symmetric systems.
PMCID: PMC3215146  PMID: 22096451
18.  Anisotropy of Fibrous Tissues in Relation to the Distribution of Tensed and Buckled Fibers 
Fibrous tissues are characterized by a much higher stiffness in tension than compression. This study uses microstructural modeling to analyze the material symmetry of fibrous tissues undergoing tension and compression, to better understand how material symmetry relates to the distribution of tensed and buckled fibers. The analysis is also used to determine whether the behavior predicted from a microstructural model can be identically described by phenomenological continuum models. The analysis confirms that in the case when all the fibers are in tension in the current configuration, the material symmetry of a fibrous the tissue in the corresponding reference configuration is dictated by the symmetry of its fiber angular distribution in that configuration. However, if the strain field exhibits a mix of tensile and compressive principal normal strains, the fibrous tissue is represented by a material body which consists only of those fibers which are in tension; the material symmetry of this body may be deduced from the superposition of the planes of symmetry of the strain and the planes of symmetry of the angular fiber distribution. Thus the material symmetry is dictated by the symmetry of the angular distribution of only those fibers which are in tension. Examples are provided for various fiber angular distribution symmetries. In particular, it is found that a fibrous tissue with isotropic fiber angular distribution exhibits orthotropic symmetry when subjected to a mix of tensile and compressive principal normal strains, with the planes of symmetry normal to the principal directions of the strain. This anisotropy occurs even under infinitesimal strains and is distinct from the anisotropy induced from the finite rotation of fibers. It is also noted that fibrous materials are not stable under all strain states due to the inability of fibers to sustain compression along their axis; this instability can be overcome by the incorporation of a ground matrix. It is concluded that the material response predicted using a microstructural model of the fibers cannot be described exactly by phenomenological continuum models. These results are also applicable to non-biological fiber-composite materials.
PMCID: PMC2805028  PMID: 17408329
19.  A simple model for the early events of quorum sensing in Pseudomonas aeruginosa: modeling bacterial swarming as the movement of an "activation zone" 
Biology Direct  2009;4:6.
Quorum sensing (QS) is a form of gene regulation based on cell-density that depends on inter-cellular communication. While there are a variety of models for bacterial colony morphology, there is little work linking QS genes to movement in an open system.
The onset of swarming in environmental P. aeruginosa PUPa3 was described with a simplified computational model in which cells in random motion communicate via a diffusible signal (representing N-acyl homoserine lactones, AHL) as well as diffusible, secreted factors (enzymes, biosurfactans, i.e. "public goods") that regulate the intensity of movement and metabolism in a threshold-dependent manner. As a result, an "activation zone" emerges in which nutrients and other public goods are present in sufficient quantities, and swarming is the spontaneous displacement of this high cell-density zone towards nutrients and/or exogenous signals. The model correctly predicts the behaviour of genomic knockout mutants in which the QS genes responsible either for the synthesis (lasI, rhlI) or the sensing (lasR, rhlR) of AHL signals were inactivated. For wild type cells the model predicts sustained colony growth that can however be collapsed by the overconsumption of nutrients.
While in more complex models include self-orienting abilities that allow cells to follow concentration gradients of nutrients and chemotactic agents, in this model, displacement towards nutrients or environmental signals is an emergent property of the community that results from the action of a few, well-defined QS genes and their products. Still the model qualitatively describes the salient properties of QS bacteria, i.e. the density-dependent onset of swarming as well as the response to exogenous signals or cues.
This paper was reviewed by Gáspár Jékely, L. Aravind, Eugene V. Koonin and Artem Novozhilov (nominated by Eugene V. Koonin).
PMCID: PMC2660287  PMID: 19216743
20.  Visual signalling by asymmetry: a review of perceptual processes. 
Individual levels of asymmetry in traits that display fluctuating asymmetry could be used as visual signals of phenotypic (and perhaps genotypic) quality, as asymmetry can often be negatively related to fitness parameters. There are some data to support this hypothesis but the experimental protocols employed have commonly resulted in asymmetries far larger than those observed in nature. To date, there has been little consideration of the ability of animals to accurately discriminate small asymmetries (of the magnitude observed in the wild) from perfect symmetry. This is key to assessing the plausibility of the asymmetry-signalling hypothesis. Here, I review the perceptual processes that may lead to the discrimination of asymmetry and discuss a number of ecologically relevant factors that may influence asymmetry signalling. These include: signal orientation, distance of trait elements from the axis of symmetry, trait complexity, trait contrast and colour, and the behaviour of both signaller and receiver. I also discuss the evolution of symmetry preferences and make suggestions as to where researchers should focus attention to examine the generality of asymmetry-signalling theory. In highly developmentally stable signalling systems the magnitude of asymmetry may be too small to be detected accurately and reliably, hence asymmetry signalling is unlikely to have evolved in these situations.
PMCID: PMC1692659  PMID: 10515000
21.  The metabolic and mechanical costs of step time asymmetry in walking 
Animals use both pendular and elastic mechanisms to minimize energy expenditure during terrestrial locomotion. Elastic gaits can be either bilaterally symmetric (e.g. run and trot) or asymmetric (e.g. skip, canter and gallop), yet only symmetric pendular gaits (e.g. walk) are observed in nature. Does minimizing metabolic and mechanical power constrain pendular gaits to temporal symmetry? We measured rates of metabolic energy expenditure and calculated mechanical power production while healthy humans walked symmetrically and asymmetrically at a range of step and stride times. We found that walking with a 42 per cent step time asymmetry required 80 per cent (2.5 W kg−1) more metabolic power than preferred symmetric gait. Positive mechanical power production increased by 64 per cent (approx. 0.24 W kg−1), paralleling the increases we observed in metabolic power. We found that when walking asymmetrically, subjects absorbed more power during double support than during symmetric walking and compensated by increasing power production during single support. Overall, we identify inherent metabolic and mechanical costs to gait asymmetry and find that symmetry is optimal in healthy human walking.
PMCID: PMC3574372  PMID: 23407831
symmetry; biomechanics; energetics; locomotion; limb work
22.  Cortical Factor Feedback Model for Cellular Locomotion and Cytofission 
PLoS Computational Biology  2009;5(3):e1000310.
Eukaryotic cells can move spontaneously without being guided by external cues. For such spontaneous movements, a variety of different modes have been observed, including the amoeboid-like locomotion with protrusion of multiple pseudopods, the keratocyte-like locomotion with a widely spread lamellipodium, cell division with two daughter cells crawling in opposite directions, and fragmentations of a cell to multiple pieces. Mutagenesis studies have revealed that cells exhibit these modes depending on which genes are deficient, suggesting that seemingly different modes are the manifestation of a common mechanism to regulate cell motion. In this paper, we propose a hypothesis that the positive feedback mechanism working through the inhomogeneous distribution of regulatory proteins underlies this variety of cell locomotion and cytofission. In this hypothesis, a set of regulatory proteins, which we call cortical factors, suppress actin polymerization. These suppressing factors are diluted at the extending front and accumulated at the retracting rear of cell, which establishes a cellular polarity and enhances the cell motility, leading to the further accumulation of cortical factors at the rear. Stochastic simulation of cell movement shows that the positive feedback mechanism of cortical factors stabilizes or destabilizes modes of movement and determines the cell migration pattern. The model predicts that the pattern is selected by changing the rate of formation of the actin-filament network or the threshold to initiate the network formation.
Author Summary
Actin is a globular protein, assembling (polymerizing) into filaments. This process is called actin polymerization. Cell biologists have revealed that actin polymerization plays a central role in eukaryotic cell locomotion. Stimulated by internal/external molecular signals, actin polymerization occurs just beneath the cellular membrane. Such actin polymerization gives rise to pressure to push the cellular membrane outwards, which pulls the cell body and induces cell locomotion. Here, an important question on the mechanism is how the area of actin polymerization in cell is determined. To answer this question, we introduce a simple computational model that includes actin and a control factor of actin polymerization, which we call “cortical factor”'. Cell shape deformation induces heterogeneous distribution of cortical factor, leading to the heterogeneous actin polymerization in cell, which further enhances cell shape deformation. This feedback mechanism consistently explains a variety of modes of spontaneous cell movement, including both cell locomotion and cell division-like behaviors. Those different modes of movement emerge depending on the rate of actin polymerization and the threshold of concentration of cortical factor to control actin polymerization.
PMCID: PMC2645504  PMID: 19282961
23.  Anthropometric, Gait and Strength Characteristics of Kenyan Distance Runners 
This study intended to take a biomechanical approach to understand the success of Kenyan distance runners. Anthropometric, gait and lower extremity strength characteristics of six elite Kenyan distance runners were analyzed. Stride frequency, relative stride length and ground contact time were measured at five running speeds (3.5 - 5.4 m/s) using a motion capture system. Isometric knee extension and flexion torques were measured at six angles and hamstrings and quadriceps (H:Q) ratios at three angular velocities were determined using an isokinetic dynamometer. These runners were characterized by a low body mass index (20.1 ± 1.8 kg·m- 2), low percentage body fat (5.1 ± 1.6%) and small calf circumference (34.5 ± 2.3 cm). At all running speeds, the ground contact time was shorter (p ¼ 0.05) during right (170 - 212 ms) compared to left (177 - 220 ms) foot contacts. No bilateral difference was observed in other gait or strength variables. Their maximal isometric strength was lower than other runners (knee extension: 1.4 - 2.6 Nm·kg-1, knee flexion: 1.0 - 1.4 Nm·kg-1) but their H:Q ratios were higher than athletes in other sports (1.03 ± 0.51 at 60o/s, 1.44 ± 0.46 at 120o/s, 1.59 ± 0.66 at 180o/s). The slim limbs of Kenyan distance runners may positively contribute to performance by having a low moment of inertia and thus requiring less muscular effort in leg swing. The short ground contact time observed may be related to good running economy since there is less time for the braking force to decelerate forward motion of the body. These runners displayed minor gait asymmetry, though the difference may be too small to be practically significant. Further investigations are needed to confirm whether the bilateral symmetry in strength and high H:Q ratios are related to genetics, training or the lack of injuries in these runners.
Key pointsThis is the first study in the literature to analyze the biomechanical characteristics of elite Kenyan distance runners, potentially providing insight into their success in distance running.Their slim limbs may positively contribute to performance by having a low moment of inertia and thus requiring less muscular effort in leg swing.Overall, short ground contact time was observed with the right leg shorter than the left leg. This may be related to good running economy since there is less time for the braking force to decelerate forward motion of the body.These runners displayed symmetry in strength between the left and right legs and possessed high hamstrings to quadriceps ratios compared to athletes in other sports.
PMCID: PMC3761913  PMID: 24149957
Stride length; stride frequency; ground contact time; isometric torque; hamstrings to quadriceps ratio; asymmetry
24.  Passive appendages generate drift through symmetry breaking 
Nature Communications  2014;5:5310.
Plants and animals use plumes, barbs, tails, feathers, hairs and fins to aid locomotion. Many of these appendages are not actively controlled, instead they have to interact passively with the surrounding fluid to generate motion. Here, we use theory, experiments and numerical simulations to show that an object with a protrusion in a separated flow drifts sideways by exploiting a symmetry-breaking instability similar to the instability of an inverted pendulum. Our model explains why the straight position of an appendage in a fluid flow is unstable and how it stabilizes either to the left or right of the incoming flow direction. It is plausible that organisms with appendages in a separated flow use this newly discovered mechanism for locomotion; examples include the drift of plumed seeds without wind and the passive reorientation of motile animals.
Passive mechanisms without energy input are the only way for non-motile organisms to disperse in fluids. Here, the authors use the analogue of the inverted pendulum motion upon gravity to explain the passive drift of a body with a protrusion to the sides of an incoming fluid stream.
PMCID: PMC4220513  PMID: 25354545
25.  Floral symmetry: pollinator-mediated stabilizing selection on flower size in bilateral species 
Pollinator-mediated stabilizing selection (PMSS) has been proposed as the driver of the evolutionary shift from radial to bilateral symmetry of flowers. Studies have shown that variation in flower size is lower in bilateral than in radial species, but whether bilateral flowers experience more stabilizing selection pressures by employing fewer, more specialized pollinators than radial flowers remains unclear. To test the PMSS hypothesis, we investigate plant–pollinator interactions from a whole community in an alpine meadow in Hengduan Mountains, China, to examine: (i) variance in flower size and level of ecological generalization (pollinator diversity calculated using functional groups) in 14 bilateral and 13 radial species and (ii) the role pollinator diversity played in explaining the difference of variance in flower size between bilateral and radial species. Our data showed that bilateral species had less variance in flower size and were visited by fewer pollinator groups. Pollinator diversity accounted for up to 40 per cent of the difference in variance in flower size between bilateral and radial species. The mediator effect of pollinator diversity on the relationship between floral symmetry and variance in flower size in the community is consistent with the PMSS hypothesis.
PMCID: PMC2825790  PMID: 19710062
bilateral and radial; variance in flower size; pollinator diversity; ecological specialization; pollinator-mediated stabilizing selection; mediator effect

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