Robustness, Flexibility, and the Role of Lateral Inhibition in the Neurogenic Network

Meir, Eli; Dassow, George von; Munro, Edwin; Odell, Garrett M.

doi:10.1016/s0960-9822(02)00839-4

Cited by 182 publications

(111 citation statements)

References 21 publications

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“…Analysis and numerical simulation demonstrates another surprising result: even with lateral inhibition in ligand production, patterns of wavelength longer than two or three cells are predicted. It has been suggested recently that lateral inhibition must be combined with other mechanisms to give longer wavelength patterns, such as cell growth [4], long-range filapodial contacts [24], or paracrine signalling [17,33]. However, we have shown that lateral inhibition can be sufficient by itself to predict longer-range patterns without the need for additional long range effects.…”

Section: Discussionmentioning

confidence: 55%

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

Webb

Owen

2004

Journal of Mathematical Biology

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Abstract. We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations-this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor.Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al.[4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses.

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Section: Discussionmentioning

confidence: 55%

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

Webb

Owen

2004

Journal of Mathematical Biology

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“…By necessity, their analysis often focuses on one or a few functions, and robustness of this function does not necessarily mean robustness of other functions. However, the robustness of one function may allow the network to acquire other functions (14,58). Finally, and most importantly, which quantitative oscillator model is the correct one?…”

Section: Discussionmentioning

confidence: 99%

“…Such models help understand processes as different as bacterial chemotaxis (1), circadian rhythms (2-10), organismal development (11)(12)(13)(14)(15), and the behavior of synthetic circuitry (16)(17)(18)(19). Most such models represent biological circuits through differential equations.…”

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confidence: 99%

“…Incessant parameter change and the resulting requirement for robust circuit functioning have one important implication: They render robust circuit architectures or topologies (instead of different parameters within one topology) an important subject of study (12,14,15). The focus of this contribution is such an analysis for several hundred variants of a cellular circuit model that has been successfully used to describe circadian rhythms in different organisms (6,32,33).…”

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confidence: 99%

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Circuit topology and the evolution of robustness in two-gene circadian oscillators

Wagner

2005

Proc. Natl. Acad. Sci. U.S.A.

141

122

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Many parameters driving the behavior of biochemical circuits vary extensively and are thus not fine-tuned. Therefore, the topology of such circuits (the who-interacts-with-whom) is key to understanding their central properties. I here explore several hundred different topologies of a simple biochemical model of circadian oscillations to ask two questions: Do different circuits differ dramatically in their robustness to parameter change? If so, can a process of gradual molecular evolution find highly robust topologies when starting from less robust topologies? I find that the distribution of robustness among different circuit topologies is highly skewed: Most show low robustness, whereas very few topologies are highly robust. To address the second evolutionary question, I define a topology graph, each of whose nodes corresponds to one circuit topology that shows circadian oscillations. Two nodes in this graph are connected if they differ by only one regulatory interaction within the circuit. For the circadian oscillator I study, most topologies are connected in this graph, making evolutionary transitions from low to high robustness easy. A similar approach has been used to study the evolution of robustness in biological macromolecules, with similar results. This suggests that the same principles govern the evolution of robustness on different levels of biological organization. The regulatory interlocking of several oscillating gene products in biological circadian oscillators may exist because it provides robustness. complexity ͉ gene networks

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“…Do cells need genes that function mainly as canalizing agents? Many studies (von Dassow et al 2000;Meir et al 2002;Siegal and Bergman 2002) suggested that complex networks, such as cellular transcription networks, are inherently stable. von Dassow et al (2000) analyzed the segment polarity phenotype, attempting to simulate the 14-stripe pattern in Drosophila development.…”

Section: Do Canalizing Genes Exist?mentioning

confidence: 99%

Evolution under canalization and the dual roles of microRNAs—A hypothesis

Wu¹,

Shen²,

Tang³

2009

Genome Res.

146

167

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Canalization refers to the process by which phenotypes are stabilized within species. Evolution by natural selection can proceed efficiently only when phenotypes are canalized. The existence and identity of canalizing genes have thus been an important, but controversial topic. Recent evidence has increasingly hinted that microRNAs may be involved in canalizing gene expression. Their paradoxical properties (e.g., strongly conserved but functionally dispensable) suggest unconventional regulatory roles. We synthesized published and unpublished results and hypothesize that miRNAs may have dual functions-in gene expression tuning and in expression buffering. In tuning, miRNAs modify the mean expression level of their targets, but in buffering they merely reduce the variance around a preset mean. In light of the constant emergence of new miRNAs, we further discuss the relative importance of these two functions in evolution.Living organisms process as much information and execute as many instructions as any high-power computers normally do. The difference is that living organisms carry out the tasks under extremely variable environments, whereas no computers are made to withstand even moderate fluctuations in voltage input. Living things must be able to dampen variable inputs (in nutrition, temperature, humidity, genetic background, etc.) to achieve the remarkable stability in the output (development, physiological responses, gene expression, etc.). This phenomenon is the essence of biological homeostasis.Darwin's The Origin of Species (Darwin 1859), on the other hand, is about evolutionary changes. On the surface, evolutionary changes and phenotypic stability may seem like antithetical concepts, but in the language of genetics they are really two sides of the same issue. Evolution by natural selection can proceed only when biological systems are reasonably stable. Imagine a system in which phenotypic manifestation is highly variable. In it natural selection cannot easily distinguish one genotype from another and would have low efficacy. The original nongenetic version of the Darwinian theory encountered many difficulties. One of them was the blending of genetic materials, potentially leading to the homogenization of phenotypes. The other resulted from the ignorance of the difference between genotype and phenotype and the puzzle over the existence of phenotypic variation. Fisher (1930) pointed out that, in Darwin's thinking, phenotypic variation should have been purged by natural selection-only the fittest should have remained.The relationship between evolution and biological homeostasis can best be expressed in quantitative genetic terms. Let V g and V e denote phenotypic variance due to genotypic and environmental effect, respectively. V g 3 e is the interactive term between gene and environment. The total phenotypic variance, V t , can be expressed as follows:For simplicity, we assume no dominance here, but the general principle is the same in more complex systems. Any mechanism of biological homeostasis should redu...

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Robustness, Flexibility, and the Role of Lateral Inhibition in the Neurogenic Network

Abstract: The neurogenic network is robust to changes in parameter values, which gives it the flexibility to make new patterns. Our model also offers a possible resolution of a debate on the role of lateral inhibition in cell fate specification.

Cited by 182 publications

References 21 publications

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

Circuit topology and the evolution of robustness in two-gene circadian oscillators

Evolution under canalization and the dual roles of microRNAs—A hypothesis

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