A pattern formation mechanism to control spatial organization in the embryo of Drosophila melanogaster

It is known that cells are already committed to a particular segment at the cellular blastoderm stage during embryogenesis of Drosophila melanogaster. Recently, several segmentation genes have been observed to be expressed in a sequence of banded spatial patterns in the syncytial blastoderm, prior to the formation of the cellular blastoderm. It is demonstrated in this paper that a two component reaction-diffusion (RD) system with net production functions which are antisymmetric with respect to the uniform steady-state values, is capable of producing a sequence of seven spatial patterns in the syncytial blastoderm. The sequence of patterns obtained exhibit a strong preference for banded or striped patterns. The first pattern is a simple anteroposterior gradient while the second is a gradient in the dorsoventral direction. The next five patterns are a sequence of banded patterns which exhibit frequency doubling, i.e. the number of bands in each pattern tend to be double the number in the previous pattern. The predicted pattern sequence is comparable to that observed in the expression of some segmentation genes. It is suggested that a pattern formation mechanism based on such an RD system may exist in the embryo where it produces a sequence of prepatterns to regulate the expression of various segmentation genes leading ultimately to a segmented embryo. There is sufficient spatial information in the sequence of banded prepatterns for the segments to be unique.     

Morphogen prepatterns during mitosis and cytokinesis in flattened cells: three dimensional Turing structures of reaction-diffusion systems in cylindrical coordinates

Computer simulation of spontaneous morphogen prepattern formation (spatial dissipative structures, Turing structures) is studied during change from a spherical geometry to a flat cylinder (axis ratio 1:5), resembling compression of a spherical cell in metaphase to a flat disc. Abnormal forms of mitosis and cytokinesis have been reported experimentally during this process. The prepatterns obtained numerically account for several of these abnormalities, notably the occurrence of quadripartition in bipolar cells, or the arrest of cytokinesis. The prepatterns recorded may open a route for experimental testing of the prepattern model of mitosis and cytokinesis.     

Cell sociology and the problem of position effect: Pattern formation,origin and role of gradients

The control of pattern formation and the significance of gradients is reconsidered on the basis of the concept of cell sociology (which takes into account continuous exchange of information between cells and the possibility of autonomous progression in differentiation). Not all traits of a pattern are imposed by a single prepattern, which would be an organized molecular framework or a gradient. Patterns are unfolded in steps; these are readjustments of a cell population to intrinsic and extrinsic changes in cell activities. Prepatterns are the various components of the programme of every readjustment and are established by information of various origins, which can be dissociated experimentally: determination (elementary social prepattern), pre-existing organization (antecedent pp.), surrounding cell populations (environmental pp.), position among other tissues (positional pp.) and the organization of inducers (imprinting pp.). Every transitory pattern formed during a readjustment serves as antecedent pp. during the next readjustment. Covert graded patterns result from various aspects of the social behaviour of cells (growth, aggregation, induction, cell renewal) and may serve as antecedent or imprinting prepatterns. They appear as water marks in the final patterns, or generate overt graded patterns. They also manifest themselves in temporal patterns, particularly in gradients of relative growth.Dedicated to Professor P. D. Nieuwkoop on the occasion of his 60th birthday.     

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 yields 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.     

Bifurcations of nonlinear reaction-diffusion systems in oblate spheroids

Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing chemical reaction-diffusion systems. Bipolarity in mitosis and cleavage planes in cytokinesis may be related to this formation of prepatterns. Three dimensional prepatterns are investigated, as they emerge in flattened spheres (i.e. oblate spheroids). Pattern sequences and selection rules are established numerically. The results confirm previously recorded results of the spherical and prolate regions, upon which a prepattern theory of mitosis and cytokinesis is based. Especially, the phenomenon of 90 degree axis tilting and the formation of a highly symmetrical saddle shaped pattern, crucial for the prepattern theory of mitosis and cytokinesis, is examined. Present results show, that these phenomena are stabilized in oblate spheroids. The bipolar mitosis prepattern is found as well, although the polar axis may appear with an angle toward the axis of the oblate spheroid. These results are thus further support for the prepattern theory of mitosis and cytokinesis.     

Labyrinthine versus straight-striped patterns generated by two-dimensional Turing systems

Striped patterns are often observed on fish skin. Such patterns have been accounted for by reaction-diffusion (RD) Turing-type models, in which two substances can spontaneously form a spatially heterogeneous pattern in a homogeneous field. Among the striped patterns generated by Turing-type models, some are "straight-striped patterns," with many stripes running in parallel, while others are "labyrinthine patterns," in which the stripes often change direction, merge with each other, and frequently branch out. RD models differ in terms of their tendency to generate either labyrinthine or straight-striped patterns. Here, we studied the conditions under which either a labyrinthine or straight-striped pattern would emerge. First, we defined an index for stripe clearness, Sh. Straight-striped patterns (large Sh) are formed if only a narrow range of spatial periods corresponds to an unstable mode. Labyrinthine patterns (small Sh) are formed when a wide range of spatial periods is unstable. More specifically, labyrinthine patterns are formed when the maximum spatial period of unstable modes is more than twice that of the minimum spatial period of unstable modes; otherwise, straight-striped patterns are formed. We then examined RD models with nonlinear reaction terms, including both activator-inhibitor and substrate-depletion models, and we demonstrated that the same conclusions hold with respect to the conditions required for labyrinthine versus straight-striped patterns.     

Spatial patterns produced by a reaction-diffusion system in primary hair follicles

This paper is the third in a series examining the role of a reaction-diffusion (RD) system as the principal mechanism providing spatial information for cell differentiation during hair follicle initiation and development and hair fibre formation. A theoretical mechanism is described by which the RD system supplies positional information during hair follicle development. Solutions of the RD system within the primordial follicle are described as well as the sequence of spatial patterns provides the follicle/epidermis boundary conditions required to account for the density and grouping of follicles during initiation. At the same time the spatial patterns are also shown to be capable of providing the positional information which determines various geometrical aspects of follicle development; in particular the development of follicles at an angle to the skin surface and the initiation and location of sweat glands and sebaceous glands on the follicle.     

``BACWAVE,' a Spatial–Temporal Model for Traveling Waves of Bacterial Populations in Response to a Moving Carbon Source in Soil

Abstract Previously, we discovered the phenomenon of wavelike spatial distributions of bacterial populations and total organic carbon (TOC) along wheat roots. We hypothesized that the principal mechanism underlying this phenomenon is a cycle of growth, death, autolysis, and regrowth of bacteria in response to a moving substrate source (root tip). The aims of this research were (i) to create a simulation model describing wavelike patterns of microbial populations in the rhizosphere, and (ii) to investigate by simulation the conditions leading to these patterns. After transformation of observed spatial data to presumed temporal data based on root growth rates, a simulation model was constructed with the Runge–Kutta integration method to simulate the dynamics of colony-forming bacterial biomass, with growth and death rates depending on substrate content so that the rate curves crossed over at a substrate concentration within the range of substrate availability in the model. This model was named ``BACWAVE,' standing for ``bacterial waves.' Cyclic dynamics of bacteria were generated by the model that were translated into traveling spatial waves along a moving nutrient source. Parameter values were estimated from calculated initial substrate concentrations and observed microbial distributions along wheat roots by an iterative optimization method. The kinetic parameter estimates fell in the range of values reported in the literature. Calculated microbial biomass values produced spatial fluctuations similar to those obtained for experimental biomass data derived from colony forming units. Concentrations of readily utilizable substrate calculated from biomass dynamics did not mimic measured concentrations of TOC, which consist not only of substrate but also various polymers and humic acids. In conclusion, a moving pulse of nutrients resulting in cycles of growth and death of microorganisms can indeed explain the observed phenomenon of moving microbial waves along roots. This is the first report of wavelike dynamics of microorganisms in soil along a root resulting from the interaction of a single organism group with its substrate. Received: 2 October 1999; Accepted: 9 March 2000; Online Publication: 28 August 2000     

Zebrafish leopard gene as a component of the putative reaction-diffusion system

It has been suggested, on a theoretical basis, that a reaction-diffusion (RD) mechanism underlies pigment pattern formation in animals, but as yet, there is no molecular evidence for the putative mechanism. Mutations in the zebrafish gene, leopard, change the pattern from stripes to spots. Interestingly each allele gives a characteristic pattern, which varies in spot size, density and connectivity. That mutations in a single gene can generate such a variety of patterns can be understood using a RD model. All the pattern variations of leopard mutants can be generated in a simulation by changing a parameter value that corresponds to the reaction kinetics in a putative RD system. Substituting an intermediate value of the parameter makes the patterns similar to the heterozygous fish. These results suggest that the leopard gene product is a component of the putative RD mechanism.     

Characterization of rebound depolarization in hippocampal neurons

Rebound depolarization (RD) following hyperpolarizing pulses is found in several neuronal cell types where it takes part in the regulation of neuronal firing behavior. During whole-cell current and voltage clamp recordings in slice preparations, we investigated the modulation of RD by different stimulation patterns and its underlying ionic currents in rat CA1 pyramidal cells. RD was mainly carried by the hyperpolarization-activated cation current I(h) (about two-third) and T-type calcium currents (about one-third), respectively. RD increased with increasing hyperpolarizing amplitude and stimulation frequency, whereas RD substantially decreased with longer pulse duration and, less pronounced, with increasing pulse number. The pulse duration-related decrease of RD was due to a decrease of the driving force of I(h). In conclusion, we showed that RD is differentially modulated by precedent hyperpolarization. Since RD amplitude was high enough to generate action potentials, RD may serve, even under physiologic conditions, as an inhibition-excitation converter.     

Self-organization in biological systems with multiple cellular contacts

The self-organizing properties of an ensemble of interconnected units are studied by linear stability analyses. Small perturbations of a uniform steady-state may result in bifurcations to other solutions that exhibit spatial or temporal order. We show that increasing the number of connections that a unit makes with its neighbors changes the nature of these solutions and tends to destroy spatiotemporal patterns. If an unconnected system is orginally stable, the formation of multiple interconnections can never induce temporal periodicity but may, under certain circumstances, allow the emergence of stationary spatial patterns. We have verified the predictions of the linear stability analysis on a model system and comment on the implications of these results for multicellular ensembles.     

Spatial patterning in Polysphondylium: monoclonal antibodies specific for whorl prepatterns

In this report we describe three monoclonal antibodies which detect prepatterning events preceding the appearance of visible tips in Polysphondylium pallidum whorls. A spatial and temporal analysis of the antigens against which these antibodies are directed reveals that the radial distribution of arms within whorls has its origins in an initial global amplification of tip-specific antigens over the surface of very early whorl masses. This two-dimensional distribution becomes restricted with time to a single dimension, a smooth distribution of antigen in a band about the equator of the whorl mass. This equatorial distribution breaks up into patches which eventually become visible tips. These results reveal that a spatial pattern can arise from a smooth prepattern, and grow through a series of intermediates characteristic of the symmetry breaking model first described by A. Turing (1952).     

Temporal control of self‐organized pattern formation without morphogen gradients in bacteria

Diverse mechanisms have been proposed to explain biological pattern formation. Regardless of their specific molecular interactions, the majority of these mechanisms require morphogen gradients as the spatial cue, which are either predefined or generated as a part of the patterning process. However, using Escherichia coli programmed by a synthetic gene circuit, we demonstrate here the generation of robust, self‐organized ring patterns of gene expression in the absence of an apparent morphogen gradient. Instead of being a spatial cue, the morphogen serves as a timing cue to trigger the formation and maintenance of the ring patterns. The timing mechanism enables the system to sense the domain size of the environment and generate patterns that scale accordingly. Our work defines a novel mechanism of pattern formation that has implications for understanding natural developmental processes.     

Rapid ligand-regulated gating kinetics of single inositol 1,4,5-trisphosphate receptor Ca2+ release channels

The ubiquitous inositol 1,4,5-trisphosphate receptor (InsP(3)R) intracellular Ca(2+) release channel is engaged by thousands of plasma membrane receptors to generate Ca(2+) signals in all cells. Understanding how complex Ca(2+) signals are generated has been hindered by a lack of information on the kinetic responses of the channel to its primary ligands, InsP(3) and Ca(2+), which activate and inhibit channel gating. Here, we describe the kinetic responses of single InsP(3)R channels in native endoplasmic reticulum membrane to rapid ligand concentration changes with millisecond resolution, using a new patch-clamp configuration. The kinetics of channel activation and deactivation showed novel Ca(2+) regulation and unexpected ligand cooperativity. The kinetics of Ca(2+)-mediated channel inhibition showed the single-channel bases for fundamental Ca(2+) release events and Ca(2+) release refractory periods. These results provide new insights into the channel regulatory mechanisms that contribute to complex spatial and temporal features of intracellular Ca(2+) signals.     

Pulsation and stabilization: Contractile forces that underlie morphogenesis

Embryonic development involves global changes in tissue shape and architecture that are driven by cell shape changes and rearrangements within cohesive cell sheets. Morphogenetic changes at the cell and tissue level require that cells generate forces and that these forces are transmitted between the cells of a coherent tissue. Contractile forces generated by the actin-myosin cytoskeleton are critical for morphogenesis, but the cellular and molecular mechanisms of contraction have been elusive for many cell shape changes and movements. Recent studies that have combined live imaging with computational and biophysical approaches have provided new insights into how contractile forces are generated and coordinated between cells and tissues. In this review, we discuss our current understanding of the mechanical forces that shape cells, tissues, and embryos, emphasizing the different modes of actomyosin contraction that generate various temporal and spatial patterns of force generation.     

On the function of cell systems in area 18. Part II

In addition to the asymmetry of the spatial coupling and of the specific temporal combination of excitation and inhibition, the non-linearity is very pronounced in area 18. Taking the sequence of a linear operation and a stationary nonlinear characteristic as a model, the experimental findings can be systematized and a cell classification specified which departs from the customary ones. The hypercomplex cell system probably originates in recurrent inhibition and leads to differentiation of the patterns along their contour line. Problems of cell classification and of the type of parallelism in the visual cortex are discussed.This research was supported by DFG Grants Se 251/14 and Se 251/16     

An olfactory recognition model based on spatio-temporal encoding of odor quality in the olfactory bulb

In order to study the problem how the olfactory neural system processes the odorant molecular information for constructing the olfactory image of each object, we present a dynamic model of the olfactory bulb constructed on the basis of well-established experimental and theoretical results. The information relevant to a single odor, i.e. its constituent odorant molecules and their mixing ratios, are encoded into a spatio-temporal pattern of neural activity in the olfactory bulb, where the activity pattern corresponds to a limit cycle attractor in the mitral cell network. The spatio-temporal pattern consists of a temporal sequence of spatial firing patterns: each constituent molecule is encoded into a single spatial pattern, and the order of magnitude of the mixing ratio is encoded into the temporal sequence. The formation of a limit cycle attractor under the application of a novel odor is carried out based on the intensity-to-time-delay encoding scheme. The dynamic state of the olfactory bulb, which has learned many odors, becomes a randomly itinerant state in which the current firing state of the bulb itinerates randomly among limit cycle attractors corresponding to the learned odors. The recognition of an odor is generated by the dynamic transition in the network from the randomly itinerant state to a limit cycle attractor state relevant to the odor, where the transition is induced by the short-term synaptic changes made according to the Hebbian rule under the application of the odor stimulus. Received: 28 July 1997 / Accepted in revised form: 6 May 1998     

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 cellular oscillator model for periodic pattern formation

In this paper, we present a model for pattern formation in developing organisms that is based on cellular oscillators (CO). An oscillatory process within cells serves as a developmental clock whose period is tightly regulated by cell autonomous or non-autonomous mechanisms. A spatial pattern is generated as a result of an initial temporal ordering of the cell oscillators freezing into spatial order as the clocks slow down and stop at different times or phases in their cycles. We apply a CO model to vertebrate somitogenesis and show that we can reproduce the dynamics of periodic gene expression patterns observed in the pre-somitic mesoderm. We also show how varying somite lengths can be generated with the CO model. We then discuss the model in view of experimental evidence and its relevance to other instances of biological pattern formation, showing its versatility as a pattern generator.     

Identification and expression analysis of MinD gene involved in plastid division in cassava

Cassava is a tropical crop known for its starchy root and excellent properties. Considering that starch biosynthesis in the amyloplast is affected by its division, it appears conceivable that the regulation of plastid division plays an important role in starch accumulation. As a member of the Min system genes, MinD participated in the spatial regulation of the position of the plastid division site.In our studies, sequence analysis and phylogenetic analysis showed that MeMinD has been highly conserved during the evolutionary process. Subcellular localisation indicated that MeMinD carries a chloroplast transit peptide and was localised in the chloroplast. Overexpression of MeMinD resulted in division site misplacement and filamentous formation in E. coli, indicating that MeMinD protein was functional across species. MeMinD exhibited different spatial and temporal expression patterns which was highly expressed in the source compared to that in the sink organ.