Reaction-diffusion models of growing plant tips: bifurcations on hemispheres

We study two chemical models for pattern formation in growing plant tips. For hemisphere radius and parameter values together optimal for spherical surface harmonic patterns of index l = 3, the Brusselator model gives an 84% probability of dichotomous branching pattern and 16% of annular pattern, while the hyperchirality model gives 88% probability of dichotomous branching and 12% of annular pattern. The models are two-morphogen reaction-diffusion systems on the surface of a hemispherical shell, with Dirichlet boundary conditions. Bifurcation analysis shows that both models give possible mechanisms for dichotomous branching of the growing tips. Symmetries of the models are used in the analysis.     

Category learning induces position invariance of pattern recognition across the visual field

Human object recognition is considered to be largely invariant to translation across the visual field. However, the origin of this invariance to positional changes has remained elusive, since numerous studies found that the ability to discriminate between visual patterns develops in a largely location-specific manner, with only a limited transfer to novel visual field positions. In order to reconcile these contradicting observations, we traced the acquisition of categories of unfamiliar grey-level patterns within an interleaved learning and testing paradigm that involved either the same or different retinal locations. Our results show that position invariance is an emergent property of category learning. Pattern categories acquired over several hours at a fixed location in either the peripheral or central visual field gradually become accessible at new locations without any position-specific feedback. Furthermore, categories of novel patterns presented in the left hemifield are distinctly faster learnt and better generalized to other locations than those learnt in the right hemifield. Our results suggest that during learning initially position-specific representations of categories based on spatial pattern structure become encoded in a relational, position-invariant format. Such representational shifts may provide a generic mechanism to achieve perceptual invariance in object recognition.     

Flexibility of DNA

A model for the flexibility of DNA is proposed that is based on discrete variations in the direction of propagation in going from one subunit to the next. Expansion of the local free energy in terms of the local bending gives a Gaussian distribution function. The assumption of the independence of local bends on neighbors lead to very simple formulae for the persistence length and the characteristic ratio. Emphasis, however, is placed on the application of the formulae for molecules of finite size where the persistence length and C_∞ are not defined. The formulae are worked out for two models, which should serve as limits for the real physical situation.     

Configurational pattern discrimination responsible for dishabituation in common toads Bufo bufo (L.): Behavioral tests of the predictions of a neural model

Summary Recently, a neural model of visual pattern discrimination for stimulus-specific habituation was developed, based on previous behavioral studies which demonstrated that toads exhibit a dishabituation hierarchy for different worm-like stimuli. The model suggests that visual objects are represented by temporal coding and predicts that the dishabituation hierarchy changes when the stimulus/background contrast direction is reversed or the stimulus size is varied. The behavioral experiments reported in this paper were designed to test these predictions, (1) For a pair of stimuli from the contrast reversal prediction, the experimental results validated the theory. (2) For a pair of stimuli from the size reduction prediction, the experimental results failed to validate the theory. Further experiments concerning size effects suggest that configurai visual pattern discrimination in toads exhibits size invariance. (3) Inspired by the Groves-Thompson account of habituation, we found that dishabituation by a second stimulus has a separate process from habituation to a first stimulus. This paper serves as an example of a fruitful dialogue between experimentation and modeling, crucial for understanding brain functions.Abbreviations a-h worm-like stimulus patterns - AT anterior thalamus - ERF excitatory receptive field - IRF inhibitory receptive field - RF receptive field - R2 to R4 retinal ganglion cell types - vMP posterior ventromedial pallium     

Does sexual conflict contribute to the evolution of novel warning patterns?

Why warning patterns are so diverse is an enduring evolutionary puzzle. Because predators associate particular patterns with unpleasant experiences, an individual's predation risk should decrease as the local density of its warning pattern increases, promoting pattern monomorphism. Distasteful Heliconius butterflies are known for their diversity of warning patterns. Here, we explore whether interlocus sexual conflict can contribute to their diversification. Male Heliconius use warning patterns as mating cues, but mated females may suffer costs if this leads to disturbance, favouring novel patterns. Using simulations, we show that under our model conditions drift alone is unlikely to cause pattern diversification, but that sexual conflict can assist such a process. We also find that genetic architecture influences the evolution of male preferences, which track changes in warning pattern due to sexual selection. When male attraction imposes costs on females, this affects the speed at which novel pattern alleles increase. In two experiments, females laid fewer eggs with males present. However, although males in one experiment showed less interest in females with manipulated patterns, we found no evidence that female colouration mitigates sex-specific costs. Overall, male attraction to conspecific warning patterns may impose an unrecognized cost on Heliconius females, but further work is required to determine this experimentally.     

Learning Contrast-Invariant Cancellation of Redundant Signals in Neural Systems

Cancellation of redundant information is a highly desirable feature of sensory systems, since it would potentially lead to a more efficient detection of novel information. However, biologically plausible mechanisms responsible for such selective cancellation, and especially those robust to realistic variations in the intensity of the redundant signals, are mostly unknown. In this work, we study, via in vivo experimental recordings and computational models, the behavior of a cerebellar-like circuit in the weakly electric fish which is known to perform cancellation of redundant stimuli. We experimentally observe contrast invariance in the cancellation of spatially and temporally redundant stimuli in such a system. Our model, which incorporates heterogeneously-delayed feedback, bursting dynamics and burst-induced STDP, is in agreement with our in vivo observations. In addition, the model gives insight on the activity of granule cells and parallel fibers involved in the feedback pathway, and provides a strong prediction on the parallel fiber potentiation time scale. Finally, our model predicts the existence of an optimal learning contrast around 15% contrast levels, which are commonly experienced by interacting fish.     

Warning signals are seductive: Relative contributions of color and pattern to predator avoidance and mate attraction in Heliconius butterflies

Visual signaling in animals can serve many uses, including predator deterrence and mate attraction. In many cases, signals used to advertise unprofitability to predators are also used for intraspecific communication. Although aposematism and mate choice are significant forces driving the evolution of many animal phenotypes, the interplay between relevant visual signals remains little explored. Here, we address this question in the aposematic passion‐vine butterfly Heliconius erato by using color‐ and pattern‐manipulated models to test the contributions of different visual features to both mate choice and warning coloration. We found that the relative effectiveness of a model at escaping predation was correlated with its effectiveness at inducing mating behavior, and in both cases wing color was more predictive of presumptive fitness benefits than wing pattern. Overall, however, a combination of the natural (local) color and pattern was most successful for both predator deterrence and mate attraction. By exploring the relative contributions of color versus pattern composition in predation and mate preference studies, we have shown how both natural and sexual selection may work in parallel to drive the evolution of specific animal color patterns.     

A model of visual perception

In this paper we propose a model of visual perception in which a positive feedback mechanism can reproduce the pattern stimulus on a neurons screen. The pattern stimulus reproduction is based on informations coming from the spatial derivatives of visual pattern. This information together with the response of the feature extractors provides to the reproduction of the visual pattern as neuron screen electric activity. We simulate several input patterns and prove that the model reproduces the percept.     

Regulated transport as a mechanism for pattern generation: Capabilities for phyllotaxis and beyond

Large-scale pattern formation is a frequently occurring phenomenon in biological organisms, and several local interaction rules for generating such patterns have been suggested. A mechanism driven by feedback between the plant hormone auxin and its polarly localized transport mediator PINFORMED1 has been proposed as a model for phyllotactic patterns in plants. It has been shown to agree with current biological experiments at a molecular level as well as with respect to the resulting patterns. We present a thorough investigation of variants of models based on auxin-regulated polarized transport and use analytical and numerical tools to derive requirements for these models to drive spontaneous pattern formation. We find that auxin concentrations in neighboring cells can feed back either on exocytosis or endocytosis and still produce patterns. In agreement with mutant experiments, the active cellular efflux is shown to be more important for pattern capabilities as compared to active influx. We also find that the feedback must originate from neighboring cells rather than from neighboring walls and that intracellular competition for the transport mediator is required for patterning. The importance of model parameters is investigated, especially regarding robustness to perturbations of experimentally estimated parameter values. Finally, the regulated transport mechanism is shown to be able to generate Turing patterns of various types.     

On the analysis of the cat's pattern recognition system

The objective of the paper is to determine in abstract terms the algorithms used by the cat detecting simple patterns and to quantify the contributions of the visual areas 17, 18, 19 for this task. The data incorporated in the algorithm are collected from behavioral experiments where the animals had to distinguish between two patterns. The patterns were superimposed with gaussian noise and the detection probability was measured. The resulting model describes pattern recognition in two steps: first extraction of features and second classification. The test of the validity of the model system was to predict the outcome of similar experiments but with different patterns. With the help of the model it is possible to describe the effect of a lesion in parametric form. This in turn gives some hints about the functions of the visual areas 17, 18, 19 for the specific fask, tested in the experiments.     

Maintenance of heterocyst patterning in a filamentous cyanobacterium

In the absence of sufficient combined nitrogen, some filamentous cyanobacteria differentiate nitrogen-fixing heterocysts at approximately every 10th cell position. As cells between heterocysts grow and divide, this initial pattern is maintained by the differentiation of a single cell approximately midway between existing heterocysts. This paper introduces a mathematical model for the maintenance of the periodic pattern of heterocysts differentiated by Anabaena sp. strain PCC 7120 based on the current experimental knowledge of the system. The model equations describe a non-diffusing activator (HetR) and two inhibitors (PatS and HetN) that undergo diffusion in a growing one-dimensional domain. The inhibitors in this model have distinct diffusion rates and temporal expression patterns. These unique aspects of the model reflect recent experimental findings regarding the molecular interactions that regulate patterning in Anabaena. Output from the model is in good agreement with both the temporal and spatial characteristics of the pattern maintenance process observed experimentally.     

Representation of Faces in Longtailed Macaques (Macaca fascicularis)

The experiments described in this study were intended to increase our knowledge about social cognition in primates. Longtailed macaques (Macaca fascicularis) had to discriminate facial drawings of different emotional expressions. A new experimental approach was used. During the experimental sessions social interactions within the group were permitted, but the learning behaviour of individual monkeys was analysed. The procedure consisted of a simultaneous discrimination between four visual patterns under continuous reinforcement. It has implications not only for simple tasks of stimulus discrimination but also for complex problems of internal representations and visual communication. The monkeys learned quickly to discriminate faces of different emotional expressions. This discrimination ability was completely invariant with variations of colour, brightness, size, and rotation. Rotated and inverted faces were recognized perfectly. A preference test for particular features resulted in a graded estimation of particular facial components. Most important for face recognition was the outline, followed by the eye region and the mouth. An asymmetry in recognition of the left and right halves of the face was found. Further tests involving jumbled faces indicated that not only the presence of distinct facial cues but the specific relation of facial features is essential in recognizing faces. The experiment generally confirms that causal mechanisms of social cognition in non-human primates can be studied experimentally. The behavioural results are highly consistent with findings from neurophysiology and research with human subjects.     

Invariance of visual operations at the level of receptive fields

The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.     

Neural network model of the primary visual cortex: From functional architecture to lateral connectivity and back

The role of intrinsic cortical dynamics is a debatable issue. A recent optical imaging study (Kenet et al., 2003) found that activity patterns similar to orientation maps (OMs), emerge in the primary visual cortex (V1) even in the absence of sensory input, suggesting an intrinsic mechanism of OM activation. To better understand these results and shed light on the intrinsic V1 processing, we suggest a neural network model in which OMs are encoded by the intrinsic lateral connections. The proposed connectivity pattern depends on the preferred orientation and, unlike previous models, on the degree of orientation selectivity of the interconnected neurons. We prove that the network has a ring attractor composed of an approximated version of the OMs. Consequently, OMs emerge spontaneously when the network is presented with an unstructured noisy input. Simulations show that the model can be applied to experimental data and generate realistic OMs. We study a variation of the model with spatially restricted connections, and show that it gives rise to states composed of several OMs. We hypothesize that these states can represent local properties of the visual scene. Action Editor: Jonathan D. Victor     

The significance of wing pattern diversity in the Lycaenidae: mate discrimination by two recently diverged species

Closely related species of lycaenid butterflies are determinable, in part, by subtle differences in wing pattern. We found that female wing patterns can act as an effective mate‐recognition signal in some populations of two recently diverged species. In field experiments, we observed that males from a Lycaeides idas population and an alpine population of L. melissa preferentially initiate courtship with conspecific females. A morphometric study indicated that at least two wing pattern elements were important for distinguishing the two species: hindwing spots and orange crescent‐shaped pattern elements called aurorae. We deceived male L. idas into initiating courtship with computer generated paper models of heterospecific females when these pattern elements were manipulated, indicating that the wing pattern elements that define the diversity of this group can be effective mate recognition signals.     

Chromosome inversions and ecological plasticity in the main African malaria mosquitoes

Chromosome inversions have fascinated the scientific community, mainly because of their role in the rapid adaption of different taxa to changing environments. However, the ecological traits linked to chromosome inversions have been poorly studied. Here, we investigated the roles played by 23 chromosome inversions in the adaptation of the four major African malaria mosquitoes to local environments in Africa. We studied their distribution patterns by using spatially explicit modeling and characterized the ecogeographical determinants of each inversion range. We then performed hierarchical clustering and constrained ordination analyses to assess the spatial and ecological similarities among inversions. Our results show that most inversions are environmentally structured, suggesting that they are actively involved in processes of local adaptation. Some inversions exhibited similar geographical patterns and ecological requirements among the four mosquito species, providing evidence for parallel evolution. Conversely, common inversion polymorphisms between sibling species displayed divergent ecological patterns, suggesting that they might have a different adaptive role in each species. These results are in agreement with the finding that chromosomal inversions play a role in Anopheles ecotypic adaptation. This study establishes a strong ecological basis for future genome‐based analyses to elucidate the genetic mechanisms of local adaptation in these four mosquitoes.     

Mathematical modelling of juxtacrine patterning

Spatial pattern formation is one of the key issues in developmental biology. Some patterns arising in early development have a very small spatial scale and a natural explanation is that they arise by direct cell—cell signalling in epithelia. This necessitates the use of a spatially discrete model, in contrast to the continuum-based approach of the widely studied Turing and mechanochemical models. In this work, we consider the pattern-forming potential of a model for juxtacrine communication, in which signalling molecules anchored in the cell membrane bind to and activate receptors on the surface of immediately neighbouring cells. The key assumption is that ligand and receptor production are both up-regulated by binding. By linear analysis, we show that conditions for pattern formation are dependent on the feedback functions of the model. We investigate the form of the pattern: specifically, we look at how the range of unstable wavenumbers varies with the parameter regime and find an estimate for the wavenumber associated with the fastest growing mode. A previous juxtacrine model for Delta-Notch signalling studied by Collier et al. (1996, J. Theor. Biol. 183, 429–446) only gives rise to patterning with a length scale of one or two cells, consistent with the fine-grained patterns seen in a number of developmental processes. However, there is evidence of longer range patterns in early development of the fruit fly Drosophila. The analysis we carry out predicts that patterns longer than one or two cell lengths are possible with our positive feedback mechanism, and numerical simulations confirm this. Our work shows that juxtacrine signalling provides a novel and robust mechanism for the generation of spatial patterns.     

A model of neural network for spatiotemporal pattern recognition

A model of neural network to recognize spatiotemporal patterns is presented. The network consists of two kinds of neural cells: P-cells and B-cells. A P-cell generates an impulse responding to more than one impulse and embodies two special functions: short term storage (STS) and heterosynaptic facilitation (HSF). A B-cell generates several impulses with high frequency as soon as it receives an impulse. In recognizing process, an impulse generated by a P-cell represents a recognition of stimulus pattern, and triggers the generation of impulses of a B-cell. Inhibitory impulses with high frequency generated by a B-cell reset the activities of all P-cells in the network.Two examples of spatiotemporal pattern recognition are presented. They are achieved by giving different values to the parameters of the network. In one example, the network recognizes both directional and non-directional patterns. The selectivities to directional and non-directional patterns are realized by only adjusting excitatory synaptic weights of P-cells. In the other example, the network recognizes time series of spatial patterns, where the lengths of the series are not necessarily the same and the transitional speeds of spatial patterns are not always the same. In both examples, the HSF signal controls the total activity of the network, which contributes to exact recognition and error recovery. In the latter example, it plays a role to trigger and execute the recognizing process. Finally, we discuss the correspondence between the model and physiological findings.     

Generalized spectral light scatter models of diverse bacterial colony morphologies

An optical forward‐scatter model was generalized to encompass the diverse nature of bacterial colony morphologies and the spectral information. According to the model, the colony shape and the wavelength of incident light significantly affect the characteristics of a forward elastic‐light‐scattering pattern. To study the relationship between the colony morphology and the scattering pattern, three‐dimensional colony models were generated in various morphologies. The propagation of light passing through the colony model was then simulated. In validation of the theoretical modeling, the scattering patterns of three bacterial genera, Staphylococcus, Exiguobacterium and Bacillus, which grow into colonies having convex, crateriform and flat elevations, respectively, were qualitatively compared to the simulated scattering patterns. The strong correlations observed between simulated and experimental patterns validated the scatter model. In addition, spectral effect on the scattering pattern was studied using the scatter model, and experimentally investigated using Staphylococcus, whose colony has circular form and convex elevation. Both simulation and experiment showed that changes in wavelength affected the overall pattern size and the number of rings.     

Visual Cues in Mate Recognition by Males of the Damselfly, Coenagrion puella (L.) (Odonata: Coenagrionidae)

Coenagrion puella males search actively for mates and are not aggressive to other males. To study the role of visual cues in male–female discrimination, four types of models were used: (1) bodies of intact insects, (2) models of painted males, (3) models of male–female chimerae, and (4) models of female body parts. Abdomen coloration pattern and presence of wings were the most important cues for sexual recognition by males. Step-by-step elimination of male coloration pattern leads to an increase in the tandem response rate. A female model painted as a male repelled males like the intact male model. The absence of either the head or the thorax slightly decreased the number of tandem responses, but models without both the head and the thorax were not recognized as a mate. Abdomen thickness larger than that of a normal female decreased the attractiveness of the model. Models of the gynochrome female were significantly more attractive than models of the androchrome one. Female models containing male parts were less attractive than models without any structure at this place. Using principal-components analysis, it is shown that models repelling males usually were those containing an intact male abdomen or a female abdomen painted with blue. The results indicate that C. puella males can distinguish males from females visually by morphological structures and coloration pattern.