Turing Systems Research Articles

A general mechanism for “inexact” phase differences in reaction–diffusion–advection systems

‘Inexact’ phase differences that may take any value in the range [0, π], between the chemical morphogens diffusing in an embryo, have been proposed [M.A. Russell, Dev. Biol. 108 (1985) 269] to improve the positional information theory [L. Wolpert, J. Theor. Biol. 25 (1969) 1] by encoding this information with higher resolution than that provided by other mechanisms. Reaction–diffusion systems, including Turing systems, show only ‘exact’ phase differences 0 and/or π. We demonstrate here that inexact phase differences arise naturally in reactive flows described by reaction–diffusion–advection equations and illustrate them by the stationary waves in open flows (flow- and diffusion-distributed structures FDS [R.A. Satnoianu, M. Menzinger, Phys. Rev. E 62 (2000) 113; R.A. Satnoianu, P.K. Maini, M. Menzinger, Physica D 160 (2001) 79] and travelling waves in differential-induced flow systems (DIFI) [A.B. Rovinsky, M. Menzinger, Phys. Rev. Lett. 70 (1993) 778; R.A. Satnoianu, J.H. Merkin, S.K. Scott, Physica D 124 (1998) 345]. The ability of cells in a developing organism to read phase differences in addition to morphogen concentrations would endow them with a robust mechanism for producing segmentation patterns that is richer, shows higher spatial resolution and is more stable than Turing's and Wolpert's positional information mechanisms.

A Two-dimensional Numerical Study of Spatial Pattern Formation in Interacting Turing Systems

For many years Turing systems have beenproposed to account for spatial and spatiotemporal pattern formationin chemistry and biology. We extend the study of Turing systems toinvestigate the rôle of boundary conditions, domain shape,non-linearities, and coupling of such systems. We show thatsuch modifications lead to a wide variety of patterns that bear a strikingresemblance to pigmentation patterns in fish, particularly those involvingstripes, spots and transitions between them. Using the Turing system as ametaphor for activator–inhibitor models we conclude that such amechanism, with the aforementioned modifications, may play a rôlein fish patterning.

Message-Passing Architecture and its Construction in Object-Oriented Rapid Modeling for Automated Manufacturing System Simulation

To develop a simulator for automated manufac turing systems using an object-oriented modeling paradigm, we have researched the message-pass ing architecture and methodology of rapid model construction. For the message-passing methodol ogy, we propose a modified hierarchical control architecture, modified to allow signal paths be tween adjacent job flow-connected resources. Model libraries using the proposed architecture have been described zwith DEVS formalism and have been implemented based on DEVSim++ so that they support the hierarchical and modular concept. In order to support the rapid modeling concept, we have designed a prototype simulator in which the entire message-passing architecture is constructed from limited and partial informa tion in order to reduce modeling overload for us ers. By showing a sample modeling procedure of a system, we demonstrate the interesting features of the developed simulator.

Confined Turing patterns in growing systems

In this paper we address the problem of pattern formation in confined Turing systems in two dimensions, when one assumes the enhancement of the concentration of one of the chemicals at some of the confining surfaces. This model is suitable to study biological systems, such as the skin patterns shown by some marine fish. We also study numerically the dynamical growth of the system by changing the size of the confined region while dynamical diffusion and reaction phenomena take place. This idea is tested in two different models. This allows one to estimate the robustness of stripe formation.

Spatial and spatiotemporal pattern formation in generalised turing systems

Reaction-diffusion, or Turing, models have been proposed to account for a number of pattern formation phenomena in early development. However, there are a number of crucial morphogenetic phenomena that contradict the standard Turing model. Here we review three generalisations of the Turing model and show how they can be applied to two such phenomena. We discuss how these generalisations can provide insight to the processes underlying patterning in these cases.

Pattern formation in generalized Turing systems

Turing's model of pattern formation has been extensively studied analytically and numerically, and there is recent experimental evidence that it may apply in certain chemical systems. The model is based on the assumption that all reacting species obey the same type of boundary condition pointwise on the boundary. We call these scalar boundary conditions. Here we study mixed or nonscalar boundary conditions, under which different species satisfy different boundary conditions at any point on the boundary, and show that qualitatively new phenomena arise in this case. For example, we show that there may be multiple solutions at arbitrarily small lengths under mixed boundary conditions, whereas the solution is unique under homogeneous scalar boundary conditions. Moreover, even when the same solution exists under scalar and mixed boundary conditions, its stability may be different in the two cases. We also show that mixed boundary conditions can reduce the sensitivity of patterns to domain changes.

Drosophila segmentation: Supercomputer simulation of prepattern hierarchy

Spontaneous prepattern formation in a two level hierarchy of reaction-diffusion systems is simulated in three space co-ordinates and time, mimicking gap gene and primary pair-rule gene expression. The model rests on the idea of Turing systems of the second kind, in which one prepattern generates position dependent rate constants for a subsequent reaction-diffusion system. Maternal genes are assumed responsible for setting up gradients from the anterior and posterior ends, one of which is needed to stabilize a double period prepattern suggested to underly the read out of the gap genes. The resulting double period pattern in turn stabilizes the next prepattern in the hierarchy, which has a short wavelength with many characteristics of the stripes seen in actual primary pair-rule gene expression. Without such hierarchical stabilization, reaction-diffusion mechanisms yield highly patchy short wave length patterns, and thus unreliable stripes. The model yields seven stable stripes located in the middle of the embryo, with the potential for additional expression near the poles, as observed experimentally. The model does not rely on specific chemical reaction kinetics, rather the effect is general to many such kinetic schemes. This makes it robust to parameter changes, and it has good potential for adapting to size and shape changes as well. The study thus suggests that the crucial organizing principle in early Drosophila embryogenesis is based on global field mechanisms, not on particular local interactions.

A Simulation Assistant for Modeling Manufacturing Systems

This paper presents a structured approach to modeling manufac turing systems. The structured approach is accomplished through a simulation assistant consisting of a set of predefined GPSS simulation macros, a user interface, and an automatic code generator.

Bifurcations in Turing systems of the second kind may explain blastula cleavage plane orientation.

Spontaneous pattern formation (emergence of Turing structures) may take place in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing biochemical reaction-diffusion systems. Bipolarity in mitosis and cleavage planes in cytokinesis may be related to this formation of prepatterns. Cleavage planes in early blastulas have an apparently well controlled spatial relationship to the polarity known as the animal-vegetal (A-V) axis: the mitotic spindles form perpendicular to this axis in the first two division stages, with cleavage planes going strictly through the A-V poles. The third-stage spindles are parallel to the A-V axis, and cleavage is roughly in the equatorial plane, thus separating the A-V poles. The reason for these phenomena are poorly understood with current mitosis/cytokinesis models based on intrinsic spindle properties. It is shown here by numerical simulation that a simple modification to the usual Turing equations yield selection rules which lead directly to these orientations of the prepatterns, without any further ad hoc assumptions. These results strongly support the prepattern model for mitosis and cytokinesis and the viewpoint that prepatterns play a fundamental role in nature.

An expert system framework based on a simulation generator

Expert Systems (ES) implementations automatically perform tasks for which specially trained or talented people have been re quired. Fifth generation simulation systems integrate the tools developed in the fourth generation and capture the knowledge of the expert programmer as well as that of the simulation model ing expert. Haddock has programmed a user- oriented simula tion generator for the design and control of flexible manufac turing systems (FMS). The development of an ES based on the generator is described in this paper. The system to be described solely requires knowledge of the system to be simulated from the user. FORTRAN written sub routines, incorporated within the software structure of SIMAN, interpret the results of experimental runs and make statistical inferences about the performance measure. Simulation generators can assist simulationists in model develop ment and update, as well as in the analysis of alternative sce narios. A very desirable feature of Intelligent Front Ends (IFEs) is to have the capabilities of analyzing their output. These capa bilities not only reduce the total time required to perform the simulation, but also prevent its misuse.