Lateral Inhibition Model Research Articles

Looking more masculine among females: Spatial context modulates gender perception of face and biological motion.

Perception of visual information highly depends on spatial context. For instance, perception of a low-level visual feature, such as orientation, can be shifted away from its surrounding context, exhibiting a simultaneous contrast effect. Although previous studies have demonstrated the adaptation aftereffect of gender, a high-level visual feature, it remains largely unknown whether gender perception can also be shaped by a simultaneously presented context. In the present study, we found that the gender perception of a central face or a point-light walker was repelled away from the gender of its surrounding faces or walkers. A norm-based opponent model of lateral inhibition, which accounts for the adaptation aftereffect of high-level features, can also excellently fit the simultaneous contrast effect. But different from the reported contextual effect of low-level features, the simultaneous contrast effect of gender cannot be observed when the centre and the surrounding stimuli are from different categories, or when the surrounding stimuli are suppressed from awareness. These findings on one hand reveal a resemblance between the simultaneous contrast effect and the adaptation aftereffect of high-level features, on the other hand highlight different biological mechanisms underlying the contextual effects of low- and high-level visual features.

Nonlinear manipulation and analysis of large DNA datasets.

Information processing functions are essential for organisms to perceive and react to their complex environment, and for humans to analyze and rationalize them. While our brain is extraordinary at processing complex information, winner-take-all, as a type of biased competition is one of the simplest models of lateral inhibition and competition among biological neurons. It has been implemented as DNA-based neural networks, for example, to mimic pattern recognition. However, the utility of DNA-based computation in information processing for real biotechnological applications remains to be demonstrated. In this paper, a biased competition method for nonlinear manipulation and analysis of mixtures of DNA sequences was developed. Unlike conventional biological experiments, selected species were not directly subjected to analysis. Instead, parallel computation among a myriad of different DNA sequences was carried out to reduce the information entropy. The method could be used for various oligonucleotide-encoded libraries, as we have demonstrated its application in decoding and data analysis for selection experiments with DNA-encoded chemical libraries against protein targets.

A Spike Neural Network Model for Lateral Suppression of Spike-Timing-Dependent Plasticity with Adaptive Threshold

Aiming at the practical constraints of high resource occupancy and complex calculations in the existing Spike Neural Network (SNN) image classification model, in order to seek a more lightweight and efficient machine vision solution, this paper proposes an adaptive threshold Spike Neural Network (SNN) model of lateral inhibition of Spike-Timing-Dependent Plasticity (STDP). The conversion from grayscale image to pulse sequence is completed by convolution normalization and first pulse time coding. The network self-classification is realized by combining the classical Spike-Timing-Dependent Plasticity algorithm (STDP) and lateral suppression algorithm. The occurrence of overfitting is effectively suppressed by introducing an adaptive threshold. The experimental results on the MNIST data set show that compared with the traditional SNN classification model, the complexity of the weight update algorithm is reduced from O(n2) to O(1), and the accuracy rate can still remain stable at about 96%. The provided model is conducive to the migration of software algorithms to the bottom layer of the hardware platform, and can provide a reference for the realization of edge computing solutions for small intelligent hardware terminals with high efficiency and low power consumption.

A model of feedforward, global, and lateral inhibition in the locust visual system predicts responses to looming stimuli.

Detection of looming obstacles is a vital task for both natural and artificial systems. Locusts possess a visual nervous system with an extensively studied obstacle detection pathway, culminating in the lobula giant movement detector (LGMD) neuron. While numerous models of this system exist, none to date have incorporated recent data on the anatomy and function of feedforward and global inhibitory systems in the input network of the LGMD. Moreover, the possibility that global and lateral inhibition shape the feedforward inhibitory signals to the LGMD has not been investigated. To address these points, a novel model of feedforward inhibitory neurons in the locust optic lobe was developed based on the recent literature. This model also incorporated global and lateral inhibition into the afferent network of these neurons, based on their observed behaviour in existing data and the posited role of these mechanisms in the inputs to the LGMD. Tests with the model showed that it accurately replicates the behaviour of feedforward inhibitory neurons in locusts; the model accurately coded for stimulus angular size in an overall linear fashion, with decreasing response saturation and increasing linearity as stimulus size increased or approach velocity decreased. The model also exhibited only phasic responses to the appearance of a grating, along with sustained movement by it at constant speed. By observing the effects of altering inhibition schemes on these responses, it was determined that global inhibition serves primarily to normalize growing excitation as collision approaches, and keeps coding for subtense angle linear. Lateral inhibition was determined to suppress tonic responses to wide-field stimuli translating at constant speed. Based on these features being shared with characterizations of the LGMD input network, it was hypothesized that the feedforward inhibitory neurons and the LGMD share the same excitatory afferents; this necessitates further investigation.

Boolean analysis of lateral inhibition

We study Boolean networks which are simple spatial models of the highly conserved Delta–Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. We consider fully asynchronous dynamics over undirected graphs representing the neighbour relation between cells. In this framework, one can show that all attractors are fixed points for the system, independently of the neighbour relation, for instance by using known properties of simplified versions of the models, where only one species per cell is defined. The fixed points correspond to the so-called fine-grained “patterns” that emerge in discrete and continuous modelling of lateral inhibition. We study the reachability of fixed points, giving a characterisation of the trap spaces and the basins of attraction for both the full and the simplified models. In addition, we use a characterisation of the trap spaces to investigate the robustness of patterns to perturbations. The results of this qualitative analysis can complement and guide simulation-based approaches, and serve as a basis for the investigation of more complex mechanisms.

MpFEW RHIZOIDS1 miRNA-Mediated Lateral Inhibition Controls Rhizoid Cell Patterning in Marchantia polymorpha.

Lateral inhibition patterns differentiated cell types among equivalent cells during development in bacteria, metazoans, and plants. Tip-growing rhizoid cells develop among flat epidermal cells in the epidermis of the early-diverging land plant Marchantia polymorpha. We show that the majority of rhizoid cells develop individually, but some develop in linear, one-dimensional groups (chains) of between 2 and 7 rhizoid cells in wild-type plants. The distribution of rhizoid cells can be accounted for within a simple cellular automata model of lateral inhibition. The model predicted that in the absence of lateral inhibition, two-dimensional rhizoid cell groups (clusters) form. These can be largerthan those formed with lateral inhibition. M.polymorpha rhizoid differentiation is positively regulated by the ROOT HAIR DEFECTIVE SIX-LIKE1 (MpRSL1) basic-helix-loop-helix (bHLH) transcription factor, which is directly repressed by the FEW RHIZOIDS1 (MpFRH1) microRNA (miRNA). To test if MpFRH1 miRNA acts during lateral inhibition, we generated loss-of-function (lof) mutants without the MpFRH1 miRNA. Two-dimensional clusters of rhizoids develop in Mpfrh1lof mutants as predicted by the model for plants that lack lateral inhibition. Furthermore, two-dimensional clusters of up to 9 rhizoid cells developed in the Mpfrh1lof mutants compared to a maximum number of 7 observed in wild-type groups. The higher steady-state levels of MpRSL1 mRNA in Mpfrh1lof mutants indicate that MpFRH1-mediated lateral inhibition involves the repression of MpRSL1 activity. Together, the modeling and genetic data indicate that MpFRH1 miRNA mediates lateral inhibition by repressing MpRSL1 during pattern formation in the M.polymorpha epidermis.

Embryonic lateral inhibition as optical modes: An analytical framework for mesoscopic pattern formation.

Cellular checkerboard patterns are observed at many stages of embryonic development. We study an analytically tractable model for lateral inhibition and show that the steady states are analogous to optical phonons at the Γ point, which have the wave number k=0. We study the cases of cells arranged in linear and hexagonal lattices. To determine how the final pattern is selected it is necessary to take into account the granularity of the pattern and, analogously to solid-state physics, to redefine the basis and lattice sites in terms of a periodic crystal. The sites and basis are determined by looking at the symmetries of inhibitory interactions between cells. The redefined basis for cells placed in a linear lattice is composed by two cells which are embedded in another linear lattice, while for cells placed in a hexagonal lattice the redefined basis consists of three cells embedded in another hexagonal lattice. The pattern in hexagonal lattices can be driven into three different states: two of those states are periodic checkerboards and a third in which both periodic states coexist. These observations provides new predictions for experiments.

Impact of changing cell-cell communication network in models of epithelial pattern formation

When modelling multi-cellular systems, one has to account for cell-cell signalling in addition to the molecular networks driving cell behaviours. Here, we aim at exploring how the topology of the cell-cell communication network impacts the behaviour of the whole multicellular system. More precisely, we focus on epithelial pattern formation, on which our question can be rephrased in terms of cell sizes and shapes. Relying on a logical modelling framework, and using a simple lateral inhibition model over a population of epithelial cells, we assess the model behaviours considering a variety of communication networks. This study suggests that reasonable deviations from a fixed grid (with regular hexagonal shaped cells) do not change much the resulting patterns. We further explore the impact of cell shapes and show that characteristics such as network regularity and number of shared neighbours of contacting cells are relevant to qualify such deviations.

Enhanced Delta-Notch Lateral Inhibition Model Incorporating Intracellular Notch Heterogeneity and Tension-Dependent Rate of Delta-Notch Binding that Reproduces Sprouting Angiogenesis Patterns

Endothelial cells adopt unique cell fates during sprouting angiogenesis, differentiating into tip or stalk cells. The fate selection process is directed by Delta-Notch lateral inhibition pathway. Classical Delta-Notch models produce a spatial pattern of tip cells separated by a single stalk cell, or the salt-and-pepper pattern. However, classical models cannot explain alternative tip-stalk patterning, such as tip cells that are separated by two or more stalk cells. We show that lateral inhibition models involving only Delta and Notch proteins can also recapitulate experimental tip-stalk patterns by invoking two mechanisms, specifically, intracellular Notch heterogeneity and tension-dependent rate of Delta-Notch binding. We introduce our computational model and analysis where we establish that our enhanced Delta-Notch lateral inhibition model can recapitulate a greater variety of tip-stalk patterning which is previously not possible using classical lateral inhibition models. In our enhanced Delta-Notch lateral inhibition model, we observe the existence of a hybrid cell type displaying intermediate tip and stalk cells’ characteristics. We validate the existence of such hybrid cells by immuno-staining of endothelial cells with tip cell markers, Delta and CD34, which substantiates our enhanced model.

側抑制に基づく図形の解析 : 景観の図形認識の立場からの解明と評価に関する研究(4)

側抑制に基づく図形の解析 : 景観の図形認識の立場からの解明と評価に関する研究(4)

An Enhanced Delta-Notch Lateral Inhibition Model Incorporating Intracellular Notch Heterogenity and Tension-Dependent Rate of Delta-Notch Binding to Explain Cellular Patterning during Sprouting Angiogenesis

During sprouting angiogenesis, endothelial cells take on a spatial pattern of unique cell fates, becoming either the tip cell or the stalk cell. This process of fate selection is guided by lateral inhibition via the Delta-Notch signalling pathway. Classical Delta-Notch lateral inhibition models generate the salt-and-pepper pattern where tip cells are separated exactly by one stalk cell. However, it has been observed during angiogenesis that other forms of tip-stalk patterning are present, such as two or three stalk cells spaced between consecutive tip cells. To reproduce the diverse forms of angiogenic patterns, we develop a mathematical model that incorporates both intracellular Notch heterogeneity and tension-dependent rate of Delta-Notch binding into the classical lateral inhibition model. We first provide experimental evidence to justify the inclusion of these additional mechanisms. Next, we present our computational analysis where we demonstrate that unlike classical lateral inhibition models, our enhanced Delta-Notch lateral inhibition model is capable of explaining a larger range of cellular patterning during sprouting angiogenesis. A pivotal prediction in our enhanced Delta-Notch lateral inhibition model is the existence of intermediate cell states, i.e., cells that exhibit moderate Delta or Notch levels thus manifesting both tip cell and stalk cell traits. We provide experimental evidence that such intermediate cell states do exist by staining of endothelial cell cultures with CD34, a known tip cell marker, thus substantiating our enhanced model.

Diversity of fate outcomes in cell pairs under lateral inhibition

Cell fate determination by lateral inhibition via Notch/Delta signalling has been extensively studied. Most formalised models consider Notch/Delta interactions in fields of cells, with parameters that typically lead to symmetry breaking of signalling states between neighbouring cells, commonly resulting in salt-and-pepper fate patterns. Here, we consider the case of signalling between isolated cell pairs, and find that the bifurcation properties of a standard mathematical model of lateral inhibition can lead to stable symmetric signalling states. We apply this model to the adult intestinal stem cell (ISC) of Drosophila, the fate of which is stochastic but dependent on the Notch/Delta pathway. We observe a correlation between signalling state in cell pairs and their contact area. We interpret this behaviour in terms of the properties of our model in the presence of population variability in contact areas, which affects the effective signalling threshold of individual cells. Our results suggest that the dynamics of Notch/Delta signalling can contribute to explain stochasticity in stem cell fate decisions, and that the standard model for lateral inhibition can account for a wider range of developmental outcomes than previously considered.

Image retrieval via balance-evolution artificial bee colony algorithm and lateral inhibition

Image retrieval is a fundamental issue in pattern recognition. In this work, lateral inhibition (LI) model is adopted as a pre-processing step, which widens the gray level gradients so as to facilitate the image retrieval scheme. In searching for a perfect match between a predefined template and a reference image, we adopt metaheuristic algorithms for good seach capability. Artificial bee colony (ABC) algorithm is a bio-inspired optimization technique, which imitates the foraging behavior of honey bee swarms. It is well known that the algorithm is good at exploration but poor at exploitation. We present balance-evolution artificial bee colony (BE-ABC) algorithm that aims to strike a balance between exploration and exploitation rather than just focusing on improving the latter. BE-ABC algorithm adaptively manipulates the search intensity at the exploration and exploitation stages during the iterations. Besides that, it incorporates an overall degradation procedure to prevent premature convergence. Simulation results confirm that BE-ABC algorithm is more capable than several state-of-the-art metaheuristic algorithms in this image retrieval scheme.

Homeostasis, singularities, and networks

Homeostasis occurs in a biological or chemical system when some output variable remains approximately constant as an input parameter [Formula: see text] varies over some interval. We discuss two main aspects of homeostasis, both related to the effect of coordinate changes on the input-output map. The first is a reformulation of homeostasis in the context of singularity theory, achieved by replacing 'approximately constant over an interval' by 'zero derivative of the output with respect to the input at a point'. Unfolding theory then classifies all small perturbations of the input-output function. In particular, the 'chair' singularity, which is especially important in applications, is discussed in detail. Its normal form and universal unfolding [Formula: see text] is derived and the region of approximate homeostasis is deduced. The results are motivated by data on thermoregulation in two species of opossum and the spiny rat. We give a formula for finding chair points in mathematical models by implicit differentiation and apply it to a model of lateral inhibition. The second asks when homeostasis is invariant under appropriate coordinate changes. This is false in general, but for network dynamics there is a natural class of coordinate changes: those that preserve the network structure. We characterize those nodes of a given network for which homeostasis is invariant under such changes. This characterization is determined combinatorially by the network topology.

Signaling Delays Preclude Defects in Lateral Inhibition Patterning.

Lateral inhibition represents a well-studied example of biology's ability to self-organize multicellular spatial patterns with single-cell precision. Despite established biochemical mechanisms for lateral inhibition (e.g., Delta-Notch), it remains unclear how cell-cell signaling delays inherent to these mechanisms affect patterning outcomes. We investigate a compact model of lateral inhibition highlighting these delays and find, remarkably, that long delays can ensure defect-free patterning. This effect is underscored by an interplay with synchronous oscillations, cis interactions, and signaling strength. Our results suggest that signaling delays, though previously posited as a source of developmental defects, may in fact be a general regulatory knob for tuning developmental robustness.

Pattern formation in discrete cell tissues under long range filopodia-based direct cell to cell contact

Pattern formation via direct cell to cell contact has received considerable attention over the years. In particular the lateral-inhibition mechanism observed in the Notch signalling pathway can generate a regular periodic pattern of differential cell activity, and has been proposed to explain the emergence of patterns in various tissues and organs. The majority of models of this system have focussed on short-range contacts: a cell signals only to its nearest neighbours and the resulting patterns tend to be of fine-scale “salt and pepper” nature. The capacity of certain cells to extend signalling filopodia (cytonemes) over multiple cell lengths, however, inserts a long-range or non-local component into this process. Here we explore how long range signalling can impact on pattern formation. Specifically, we extend a standard model for Notch-like lateral inhibition to include cytoneme-mediated signalling, and investigate how pattern formation depends on the spatial distribution of signal from the signalling cell. We show that a variety of patterns can be obtained, ranging from a sparse pattern of single isolated cells to larger clusters or stripes.

A re-examination of the selection of the sensory organ precursor of the bristle sensilla of Drosophila melanogaster.

The bristle sensillum of the imago of Drosophila is made of four cells that arise from a sensory organ precursor cell (SOP). This SOP is selected within proneural clusters (PNC) through a mechanism that involves Notch signalling. PNCs are defined through the expression domains of the proneural genes, whose activities enables cells to become SOPs. They encode tissue specific bHLH proteins that form functional heterodimers with the bHLH protein Daughterless (Da). In the prevailing lateral inhibition model for SOP selection, a transcriptional feedback loop that involves the Notch pathway amplifies small differences of proneural activity between cells of the PNC. As a result only one or two cells accumulate sufficient proneural activity to adopt the SOP fate. Most of the experiments that sustained the prevailing lateral inhibition model were performed a decade ago. We here re-examined the selection process using recently available reagents. Our data suggest a different picture of SOP selection. They indicate that a band-like region of proneural activity exists. In this proneural band the activity of the Notch pathway is required in combination with Emc to define the PNCs. We found a sub-group in the PNCs from which a pre-selected SOP arises. Our data indicate that most imaginal disc cells are able to adopt a proneural state from which they can progress to become SOPs. They further show that bristle formation can occur in the absence of the proneural genes if the function of emc is abolished. These results suggest that the tissue specific proneural proteins of Drosophila have a similar function as in the vertebrates, which is to determine the time of emergence and position of the SOP and to stabilise the proneural state.

Signaling Delays Preclude Defects in Lateral Inhibition Patterning

Developmental biology is extraordinarily robust in its ability to self-organize exquisite spatio-temporal patterns despite an intrinsically noisy set of parts. Lateral inhibition is one mechanism commonly implicated in the formation of such precise emergent behavior. Models of lateral inhibition's patterning capabilities usually implicitly assume, however, that cells receive expression signals from their neighbors without delay. Here we explicitly investigate the effects of signaling delays as well as their relation to cis-interactions in lateral inhibition patterning. We find that rather than being a source of error, signaling delays counter-intuitively allow biology to ensure defect-free patterning, which together with cis-interactions can be both fast and robust to noise and parameter variation. This suggests that overlooking time delays in developmental signaling does not just ignore a potential source of error, but rather ignores a knob with which evolution may tune patterning robustness in general.

Notch3 is necessary for neuronal differentiation and maturation in the adult spinal cord.

Notch receptors are key regulators of nervous system development and promoters of neural stem cells renewal and proliferation. Defects in the expression of Notch genes result in severe, often lethal developmental abnormalities. Notch3 is generally thought to have a similar proliferative, anti-differentiation and gliogenic role to Notch1. However, in some cases, Notch3 has an opposite, pro-differentiation effect. Here, we show that Notch3 segregates from Notch1 and is transiently expressed in adult rat and mouse spinal cord neuron precursors and immature neurons. This suggests that during the differentiation of adult neural progenitor cells, Notch signalling may follow a modified version of the classical lateral inhibition model, involving the segregation of individual Notch receptors. Notch3 knockout mice, otherwise neurologically normal, are characterized by a reduced number of mature inhibitory interneurons and an increased number of highly excitable immature neurons in spinal cord laminae I–II. As a result, these mice have permanently lower nociceptive thresholds, similar to chronic pain. These results suggest that defective neuronal differentiation, for example as a result of reduced Notch3 expression or activation, may underlie human cases of intractable chronic pain, such as fibromyalgia and neuropathic pain.

Modeling Notch signaling: a practical tutorial.

Theoretical and computational approaches for understanding different aspects of Notch signaling and Notch dependent patterning are gaining popularity in recent years. These in silico methodologies can provide dynamic insights that are often not intuitive and may help guide experiments aimed at elucidating these processes. This chapter is an introductory tutorial intended to allow someone with basic mathematical and computational knowledge to explore new mathematical models of Notch-mediated processes and perform numerical simulations of these models. In particular, we explain how to define and simulate models of lateral inhibition patterning processes. We provide a Matlab code for simulating various lateral inhibition models in a simple and intuitive manner, and show how to present the results from the computational models. This code can be used as a starting point for exploring more specific models that include additional aspects of the Notch pathway and its regulation.