scholarly journals Programmable pattern formation in cellular systems with local signaling

2021 ◽  
Author(s):  
Tiago Ramalho ◽  
Stephan Kremser ◽  
Hao Wu ◽  
Ulrich Gerland
Keyword(s):  
Pattern Formation ◽  
Internal State ◽  
Cellular Systems ◽  
Small Subset ◽  
Target Pattern ◽  
Alternative Scheme ◽  
Local Organizer ◽  
Common Principle ◽  
Pattern Forming ◽  
Update Rules

Diverse complex systems, ranging from developing embryos to systems of locally communicating agents, display an apparent capability of "programmable" pattern formation: They reproducibly form a target pattern, but this target can be readily changed. A distinguishing feature of such systems, as compared to simpler physical pattern forming systems, is that their subunits are capable of information processing. Here, we explore schemes for programmable pattern formation within a theoretical framework, in which subunits process discrete local signals to update their internal state according to logical rules. We study systems with different update rules, different topologies, and different control schemes, to assess their ability to perform programmable pattern formation and their susceptibility to errors. Only a small subset of systems permits local organizer cells to dictate any target pattern. These systems follow a common principle, whereby a temporal pattern is transcribed into a spatial pattern, reminiscent of the clock-and-wavefront mechanism underlying vertebrate somitogenesis. An alternative scheme employing several different rules can only form a fraction of patterns but is robust with respect to the timing of organizer cell inputs. Our results establish a basis for the design of synthetic systems, and for more detailed models of programmable pattern formation closer to real systems.

scholarly journals Programmable pattern formation in cellular systems with local signaling

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Tiago Ramalho ◽  
Stephan Kremser ◽  
Hao Wu ◽  
Ulrich Gerland
Keyword(s):  
Pattern Formation ◽  
Cellular Systems ◽  
Target Pattern ◽  
Discrete State ◽  
Alternative Scheme ◽  
Control Schemes ◽  
Local Signaling ◽  
Update Rules ◽  
And Control ◽  
Logical Rules

AbstractComplex systems, ranging from developing embryos to systems of locally communicating agents, display an apparent capability of “programmable” pattern formation: They reproducibly form target patterns, but those targets can be readily changed. A distinguishing feature of such systems is that their subunits are capable of information processing. Here, we explore schemes for programmable pattern formation within a theoretical framework, in which subunits process local signals to update their discrete state following logical rules. We study systems with different update rules, topologies, and control schemes, assessing their capability of programmable pattern formation and their susceptibility to errors. Only a fraction permits local organizers to dictate any target pattern, by transcribing temporal patterns into spatial patterns, reminiscent of the principle underlying vertebrate somitogenesis. An alternative scheme employing variable rules cannot reach all patterns but is insensitive to the timing of organizer inputs. Our results establish a basis for designing synthetic systems and models of programmable pattern formation closer to real systems.

Target Pattern Formation in a Chaotic Medium

1991 ◽  
Vol 60 (8) ◽  
pp. 2485-2488 ◽  
Author(s):  
Hiroyuki Nagashima
Keyword(s):  
Pattern Formation ◽  
Target Pattern

Bifurcation Analysis and Spatiotemporal Patterns in a Diffusive Predator–Prey Model

2014 ◽  
Vol 24 (06) ◽  
pp. 1450081 ◽  
Author(s):  
Guangping Hu ◽  
Xiaoling Li ◽  
Shiping Lu ◽  
Yuepeng Wang
Keyword(s):  
Pattern Formation ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Diffusion System ◽  
Target Pattern ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Impact

In this paper, we consider a species predator–prey model given a reaction–diffusion system. It incorporates the Holling type II functional response and a quadratic intra-predator interaction term. We focus on the qualitative analysis, bifurcation mechanisms and pattern formation. We present the results of numerical experiments in two space dimensions and illustrate the impact of the diffusion on the Turing pattern formation. For this diffusion system, we also observe non-Turing structures such as spiral wave, target pattern and spatiotemporal chaos resulting from the time evolution of these structures.

scholarly journals Self-Organized Crystallization Patterns from Evaporating Droplets of Common Wheat Grain Leakages as a Potential Tool for Quality Analysis

2011 ◽  
Vol 11 ◽  
pp. 1712-1725 ◽  
Author(s):  
Maria Olga Kokornaczyk ◽  
Giovanni Dinelli ◽  
Ilaria Marotti ◽  
Stefano Benedettelli ◽  
Daniele Nani ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Common Wheat ◽  
Seed Quality ◽  
Dark Field ◽  
Quality Analysis ◽  
Wheat Cultivars ◽  
Wheat Kernel ◽  
Self Organized ◽  
Complex Patterns ◽  
Pattern Forming

We studied the evaporation-induced pattern formation in droplets of common wheat kernel leakages prepared out of ancient and modern wheat cultivars as a possible tool for wheat quality analysis. The experiments showed that the substances which passed into the water during the soaking of the kernels created crystalline structures with different degrees of complexity while the droplets were evaporating. The forms ranged from spots and simple structures with single ramifications, through dendrites, up to highly organized hexagonal shapes and fractal-like structures. The patterns were observed and photographed using dark field microscopy in small magnifications. The evaluation of the patterns was performed both visually and by means of the fractal dimension analysis. From the results, it can be inferred that the wheat cultivars differed in their pattern-forming capacities. Two of the analyzed wheat cultivars showed poor pattern formation, whereas another two created well-formed and complex patterns. Additionally, the wheat cultivars were analyzed for their vigor by means of the germination test and measurement of the electrical conductivity of the grain leakages. The results showed that the more vigorous cultivars also created more complex patterns, whereas the weaker cultivars created predominantly poor forms. This observation suggests a correlation between the wheat seed quality and droplet evaporation patterns.

Applications of a Theory of Biological Pattern Formation Based on Lateral Inhibition

1974 ◽  
Vol 15 (2) ◽  
pp. 321-346 ◽  
Author(s):  
H. MEINHARDT ◽  
A. GIERER
Keyword(s):  
Pattern Formation ◽  
Lateral Inhibition ◽  
Molecular Mechanisms ◽  
Positional Information ◽  
Cell Types ◽  
Model Calculations ◽  
Slime Moulds ◽  
Biological Pattern Formation ◽  
Pattern Forming ◽  
Differentiation And Proliferation

Model calculations are presented for various problems of development on the basis of a theory of primary pattern formation which we previously proposed. The theory involves short-range autocatalytic activation and longer-range inhibition (lateral inhibition). When a certain criterion is satisfied, self-regulating patterns are generated. The autocatalytic features of the theory are demonstrated by simulations of the determination of polarity in the Xenopus retina. General conditions for marginal and internal activation, and corresponding effects of symmetry are discussed. Special molecular mechanisms of pattern formation are proposed in which activator is chemically converted into inhibitor, or an activator precursor is depleted by conversion into activator. The (slow) effects of primary patterns on differentiation can be included into the formalism in a straightforward manner. In conjunction with growth, this can lead to asymmetric steady states of cell types, cell differentiation and proliferation as found, for instance, in growing and budding hydra. In 2 dimensions, 2 different types of patterns can be obtained. Under some assumptions, a single pattern-forming system produces a ‘bristle’ type pattern of peaks of activity with rather regular spacings on a surface. Budding of hydra is treated on this basis. If, however, gradients develop under the influence of a weak external or marginal asymmetry, a monotonic gradient can be formed across the entire field, and 2 such gradient-forming systems can specify ‘positional information’ in 2 dimensions. If inhibitor equilibrates slowly, a spatial pattern may oscillate, as observed with regard to the intracellular activation of cellular slime moulds. The applications are intended to demonstrate the ability of the proposed theory to explain properties frequently encountered in developing systems.

scholarly journals Fluid dynamic instabilities: theory and application to pattern forming in complex media

2017 ◽  
Vol 375 (2093) ◽  
pp. 20160155 ◽  
Author(s):  
François Gallaire ◽  
P.-T. Brun
Keyword(s):  
Stability Analysis ◽  
Pattern Formation ◽  
Fluid Dynamic ◽  
Fluid Flows ◽  
Review Article ◽  
Media Theory ◽  
Complex Media ◽  
Theoretical Methods ◽  
Pattern Forming ◽  
Potential Use

In this review article, we exemplify the use of stability analysis tools to rationalize pattern formation in complex media. Specifically, we focus on fluid flows, and show how the destabilization of their interface sets the blueprint of the patterns they eventually form. We review the potential use and limitations of the theoretical methods at the end, in terms of their applications to practical settings, e.g. as guidelines to design and fabricate structures while harnessing instabilities. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications’.

scholarly journals Emergence of evolutionary driving forces in pattern-forming microbial populations

2018 ◽  
Vol 373 (1747) ◽  
pp. 20170106 ◽  
Author(s):  
Jona Kayser ◽  
Carl F. Schreck ◽  
QinQin Yu ◽  
Matti Gralka ◽  
Oskar Hallatschek
Keyword(s):  
Natural Selection ◽  
Pattern Formation ◽  
Genetic Drift ◽  
Cell Biology ◽  
Evolutionary Dynamics ◽  
Driving Forces ◽  
Population Level ◽  
Microbial Populations ◽  
Random Genetic Drift ◽  
Pattern Forming

Evolutionary dynamics are controlled by a number of driving forces, such as natural selection, random genetic drift and dispersal. In this perspective article, we aim to emphasize that these forces act at the population level, and that it is a challenge to understand how they emerge from the stochastic and deterministic behaviour of individual cells. Even the most basic steric interactions between neighbouring cells can couple evolutionary outcomes of otherwise unrelated individuals, thereby weakening natural selection and enhancing random genetic drift. Using microbial examples of varying degrees of complexity, we demonstrate how strongly cell–cell interactions influence evolutionary dynamics, especially in pattern-forming systems. As pattern formation itself is subject to evolution, we propose to study the feedback between pattern formation and evolutionary dynamics, which could be key to predicting and potentially steering evolutionary processes. Such an effort requires extending the systems biology approach from the cellular to the population scale. This article is part of the theme issue ‘Self-organization in cell biology’.

Designing modular reaction-diffusion programs for complex pattern formation

TECHNOLOGY ◽  
2014 ◽  
Vol 02 (01) ◽  
pp. 55-66 ◽  
Author(s):  
Dominic Scalise ◽  
Rebecca Schulman
Keyword(s):  
Pattern Formation ◽  
Cell Fate ◽  
Spatial Patterns ◽  
Control Cell ◽  
Reaction Diffusion ◽  
Tissue Growth ◽  
Complex Pattern ◽  
Target Pattern ◽  
Synthetic Dna ◽  
Integrated Programs

Cells use sophisticated, multiscale spatial patterns of chemical instructions to control cell fate and tissue growth. While some types of synthetic pattern formation have been well studied1-6, it remains unclear how to design chemical processes that can reproducibly create similar spatial patterns. Here we describe a scalable approach for the design of processes that generate such patterns, which can be implemented using synthetic DNA reaction-diffusion networks7,8. In our method, black-box modules are connected together into integrated programs for arbitrarily complex pattern formation. These programs can respond to input stimuli, process information, and ultimately produce stable output patterns that differ in size and concentration from their inputs. To build these programs, we break a target pattern into a set of patterning subtasks, design modules to perform these subtasks independently, and combine the modules into networks. We demonstrate in simulation how programs designed with our methodology can generate complex patterns, including a French flag and a stick figure.

Why patterns appear spontaneously in dissipative systems?

1999 ◽  
Vol 4 ◽  
pp. 113-118
Author(s):  
K. Staliūnas
Keyword(s):  
Growth Rate ◽  
Pattern Formation ◽  
Energy Flow ◽  
Temporal Patterns ◽  
Conservative System ◽  
Dissipative Systems ◽  
Spatial And Temporal Patterns ◽  
Flow Through ◽  
Pattern Forming ◽  
Entropy Growth

It is proposed that the spatial (and temporal) patterns spontaneously appearing in dissipative systems maximize the energy flow through the pattern forming interface. In other words – the patterns maximize the entropy growth rate in an extended conservative system (consisting of the pattern forming interface and the energy bathes). The proposal is supported by examples of the pattern formation in different systems. No example contradicting the proposal is known.

scholarly journals An MBO Scheme for Minimizing the Graph Ohta–Kawasaki Functional

2018 ◽  
Vol 30 (5) ◽  
pp. 2325-2373 ◽  
Author(s):  
Yves van Gennip
Keyword(s):  
Pattern Formation ◽  
Variational Model ◽  
Lyapunov Functionals ◽  
Copolymer Melts ◽  
Mass Constraint ◽  
The Subject ◽  
Pattern Forming ◽  
Mathematical Literature ◽  
Special Case ◽  
Standard Graph

Abstract We study a graph-based version of the Ohta–Kawasaki functional, which was originally introduced in a continuum setting to model pattern formation in diblock copolymer melts and has been studied extensively as a paradigmatic example of a variational model for pattern formation. Graph-based problems inspired by partial differential equations (PDEs) and variational methods have been the subject of many recent papers in the mathematical literature, because of their applications in areas such as image processing and data classification. This paper extends the area of PDE inspired graph-based problems to pattern-forming models, while continuing in the tradition of recent papers in the field. We introduce a mass conserving Merriman–Bence–Osher (MBO) scheme for minimizing the graph Ohta–Kawasaki functional with a mass constraint. We present three main results: (1) the Lyapunov functionals associated with this MBO scheme $$\Gamma $$ Γ -converge to the Ohta–Kawasaki functional (which includes the standard graph-based MBO scheme and total variation as a special case); (2) there is a class of graphs on which the Ohta–Kawasaki MBO scheme corresponds to a standard MBO scheme on a transformed graph and for which generalized comparison principles hold; (3) this MBO scheme allows for the numerical computation of (approximate) minimizers of the graph Ohta–Kawasaki functional with a mass constraint.

Sign in / Sign up

Export Citation Format

Share Document