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H Meinhardt

Publications and source records attributed to H Meinhardt.

At least 19 recordsLinked to original sources
PubMed2001

Pattern formation in Escherichia coli: a model for the pole-to-pole oscillations of Min proteins and the localization of the division site.

Proper cell division requires an accurate definition of the division plane. In bacteria, this plane is determined by a polymeric ring of the FtsZ protein. The site of Z ring assembly in turn is controlled by the Min system, which suppresses FtsZ polymerization at noncentral membrane sites. The Min proteins in Escherichia coli undergo a highly dynamic localization cycle, during which they oscillate between the membrane of both cell halves. By using computer simulations we show that Min protein dynamics can be described accurately by using the following assumptions: (i) the MinD ATPase self-assembles on the membrane and recruits both MinC, an inhibitor of Z ring formation, and MinE, a protein required for MinC/MinD oscillation, (ii) a local accumulation of MinE is generated by a pattern formation reaction that is based on local self-enhancement and a long range antagonistic effect, and (iii) it displaces MinD from the membrane causing its own local destabilization and shift toward higher MinD concentrations. This local destabilization results in a wave of high MinE concentration traveling from the cell center to a pole, where it disappears. MinD reassembles on the membrane of the other cell half and attracts a new accumulation of MinE, causing a wave-like disassembly of MinD again. The result is a pole-to-pole oscillation of MinC/D. On time average, MinC concentration is highest at the poles, forcing FtsZ assembly to the center. The mechanism is self-organizing and does not require any other hypothetical topological determinant.

Adenosine Triphosphatases↗
PubMed2001

Dynamic localization cycle of the cell division regulator MinE in Escherichia coli.

The MinC protein directs placement of the division septum to the middle of Escherichia coli cells by blocking assembly of the division apparatus at other sites. MinD and MinE regulate MinC activity by modulating its cellular location in a unique fashion. MinD recruits MinC to the membrane, and MinE induces MinC/MinD to oscillate rapidly between the membrane of opposite cell halves. Using fixed cells, we previously found that a MinE-green fluorescent protein fusion accumulated in an annular structure at or near the midcell, as well as along the membrane on only one side of the ring. Here we show that in living cells, MinE undergoes a rapid localization cycle that appears coupled to MinD oscillation. The results show that MinE is not a fixed marker for septal ring assembly. Rather, they support a model in which MinE stimulates the removal of MinD from the membrane in a wave-like fashion. These waves run from a midcell position towards the poles in an alternating sequence such that the time-averaged concentration of division inhibitor is lowest at midcell.

Adenosine Triphosphatases↗
PubMed2001

Organizer and axes formation as a self-organizing process.

It is a widely held view that axis formation is based essentially on pre-localized determinants. However, the robustness of early development, the pattern regulation observed after experimental interferences and the existence of systems that don't require maternal determinants suggest that self-regulating pattern forming systems are also involved. A model is proposed that allows axes formation by a chain of reactions based on local self-enhancement and long-range inhibition. Their appropriate linkage ensures that the intermediary patterns emerge in the correct sequence and have the correct spatial relation to each other. Specifically, the model comprises the following events: the generation of a pole by a pattern-forming process, the formation of a second organizer eccentric to the pole (e.g. the Nieuwkoop center), the ecto-meso-endo subdivision, the generation of the Spemann-Mangold organizer with its anterior-posterior subdivision under the influence of the Nieuwkoop center, the conversion of the Spemann-Mangold organizer (a hot spot) into the notochord (a hot stripe), and the marking of the left side of the organism by a patterning reaction influenced by the midline. The pattern forming reactions do not depend on but can make use of maternally pre-localized determinants or asymmetries. Comparison with known genes and molecules reveals that many of the expected ingredients are present. Computer simulations show that the model accounts for many regulatory features reported in the literature. The computer simulations are available in an animated form at.

Animals↗
PubMed2000

Pattern formation by local self-activation and lateral inhibition.

In 1972, we proposed a theory of biological pattern formation in which concentration maxima of pattern forming substances are generated through local self-enhancement in conjunction with long range inhibition. Since then, much evidence in various developmental systems has confirmed the importance of autocatalytic feedback loops combined with inhibitory interaction. Examples are found in the formation of embryonal organizing regions, in segmentation, in the polarization of individual cells, and in gene activation. By computer simulations, we have shown that the theory accounts for much of the regulatory phenomena observed, including signalling to regenerate removed parts. These self-regulatory features contribute to making development robust and error-tolerant. Furthermore, the resulting pattern is, to a large extent, independent of the details provided by initial conditions and inducing signals.

Animals↗
PubMed2000

Olson EN, williams RS. Remodeling muscles with calcineurin. Bioessays 2000;22:510-519

The following sentence was omitted from the legend to Figure 3 in the above-mentioned article: The schematic depiction of intracellular calcium waveforms in skeletal muscle myofibers was based on primary data acquired by E.R. Chin and D.G.Allen ((62)). The authors and the BioEssays editorial office would like to express their regrets to Drs. Chin and Allen for this omission.

Journal Article↗
PubMed2000

Models for organizer and notochord formation.

In the development of higher organisms, small groups of cells can play an important role by directing the fate of the surrounding cells. Models are discussed that account for the generation of such organizing regions. The generation of local high concentrations of signalling substances was proposed to depend on local self-enhancement combined with a long-range inhibition. The model accounts for pattern regulation, for instance, for the formation of multiple embryos after fragmentation of the early blastodisc in chickens or for head regeneration in the fresh water polyp Hydra. The model has found support from more recently discovered interactions involved in organizer formation. The mutual down-regulation of noggin/chordin and BMP-4 is proposed to function as an indirect self-enhancement, establishing in this way an essential prerequisite for primary pattern formation. Self-enhancement and long-range inhibition is also crucial for the generation of substructures such as bristles or tracheae. A poisoning of an organizing region by a second antagonistic reaction of a short range but a long time constant can lead to its displacement. Long extended structures can be formed as a trace behind the moving organizer. The notochord and the tracheae of insects are discussed as examples.

Animals↗
PubMed1999

Orientation of chemotactic cells and growth cones: models and mechanisms.

A model is proposed for an amplification step in chemotactically sensitive cells or growth cones that accounts for their extraordinary directional sensitivity. It is assumed that cells have an intrinsic pattern forming system that generates the signals for extension of filopods and lamellipods. An external signal such as a graded cue is assumed to impose some directional preference onto the pattern formed. According to the model, a saturating, self-enhancing reaction is coupled with two antagonistic reactions. One antagonist equilibrates rapidly over the whole cell, causing competition between different surface elements of the cell cortex for activation. It will be won by those cortical regions of the cell that are exposed to the highest concentrations of the external graded cues. The second antagonistic reaction is assumed to act more locally and has a longer time constant. It causes a destabilization of peaks after they have formed. While the total activated area on the cell surface is maintained, the disappearance of some hot spots allows the formation of new ones, preferentially at positions specified by the actual external guiding signal. Computer simulations show that the model accounts for the highly dynamic behaviour of chemotactic cells and growth cones. In the absence of external signals, maxima of the internal signals emerge at random positions and disappear after some time. Travelling waves or oscillations in counter phase can emerge on the cell cortex, in agreement with observations reported in the literature. In other ranges of parameters, the model accounts for the generation of a stable cell polarity.

Animals↗
PubMed1996

Models of biological pattern formation: common mechanism in plant and animal development.

Earlier proposed models for primary pattern formation, for gene activation and for segmentation are summarized and compared with recent molecular-genetic observations. A model for head, foot, tentacle and bud formation in Hydra illustrates that complex patterns can be reliably generated. Stable cell determination requires autocatalytic (autoregulatory) genes. Segmentation in insects has been proposed to result from a reiteration of (at least three) cell states. Their patterning is achieved by a mutual activation of cell states that locally exclude each other. A model for accretion of new segments by proliferation at the posterior pole is proposed that accounts for the generation of a periodic and a sequential pattern in register with each other. The assumption of a process analogous to segmentation in plants can account for the initiation of leaves with an intrinsic polarity that eventually leads to the upper and lower leaf surfaces. The model accounts also for the formation of axillary buds in correct relation to a leaf and for the much smaller spacing of leaves within a whorl when compared with the spacing between two successive whorls along the shoot. It is concluded that the generation of complex structures in distantly related organisms may be based on similar mechanisms.

Animals↗
PubMed1993

A model for pattern formation of hypostome, tentacles, and foot in hydra: how to form structures close to each other, how to form them at a distance.

A model for head, tentacle, and foot formation in Hydra is proposed. The model shows that systems which suggest a positional information scheme may be realized by a set of hierarchically coupled pattern forming systems: a structure generates the precondition for a second structure but excludes this structure locally. In this way, a well-regulated neighborhood of structures is enforced. According to the model, head, tentacle, and foot formation are under the control of separate activator-inhibitor systems. These systems are coupled via the source density. The head activator increases the source density and the activation takes place preferentially in regions of highest source density. The foot activation has the opposite behavior. It appears at the lowest source density and lowers the effective source density further. Therefore, head and foot activation appear preferentially at opposite positions of the field. Tentacle activation occurs in the region of highest source density that is not occupied by a primary head activation. Tentacle activation requires a certain threshold level of the source density. As shown by computer simulations, the model accounts for many so far unexplained observations, such as during regeneration the tissue obtains tentacle-like properties until the newly formed hypostome displaces the tentacles into a subhypostomal region. Since no direct inhibition between head and foot is involved, both structures can appear close to each other in experimental situations. The dramatic effects of treatment with diacylglycerol, such as the formation of new tentacles preceding the formation of additional hypostomes, become understandable under the simple assumption that the agent increases the source density. Budding is regarded as a trigger of a second head activator maximum. Budding can occur only beyond a minimum distance from the head due to the head inhibitor and beyond a minimum distance from the foot since the source density would be too low there. The model accounts for the periodic spacing of secondary structures around a primary organizing region such as that found in the arrangement of leaves and flower elements in plants around the primary meristem. Similarities to the vulva development of Caenorhabditis elegans and to the segmentation of insects are discussed.

Animals↗
PubMed1989

Models for positional signalling with application to the dorsoventral patterning of insects and segregation into different cell types.

Models of pattern formation and possible molecular realizations are discussed and compared with recent experimental observations. In application to the dorsoventral patterning of insects, it is shown that a superposition of two pattern-forming reactions is required. The first system generates the overall dorsoventral polarity of the oocyte, the second generates the positional information proper with a stripe-like region of high concentration along the ventral side of the embryo. A single reaction would be insufficient since the two reactions require different parameters. The model accounts for the orientation of the DV axes of the oocytes in the ovary of Musca domestica and Sarcophaga, independent of the DV axis of the mother, for the formation of several ventral furrows in the absence of the primary gurken/torpedo system in Drosophila, as well as for the good size regulation of the dorsoventral axis as observed in some insect species. Segregation of a homogeneous cell population into different cell types requires autocatalytic processes that saturate at relatively low concentrations and nondiffusible substances responsible for the autocatalytic feed-back loops. Thus, these loops can be realized directly on the gene level via their gene products, for instance, by the mutual repression of two genes. A balance of the two cell types is achieved by a long-ranging substance interfering with the self-enhancing process. This substance is expected to have a more or less homogeneous distribution. This model accounts for the reestablishment of the correct proportion after an experimental interference and the change of determination after transplantation. Applications to the segregation of pre-stalk and prespore cells in Dictyostelium and of neuroblast cells from the ventral ectoderm in Drosophila are provided.

Animals↗
PubMed1984

Models for positional signalling, the threefold subdivision of segments and the pigmentation pattern of molluscs.

Models of biological pattern formation are discussed. The regulatory features expected from the models are compared to those observed experimentally. It will be shown that: (i) Stable gradients appropriate to supply positional information can be produced by local autocatalysis and long-range inhibition. (ii) Spatially ordered sequences of differentiated cell states can emerge if these cell states mutually activate each other on long range but exclude each other locally. Segmentation results from the repetition of three such cell states, S, A and P (and not of only two, as is usually assumed). With a repetition of three states, each segment has a defined polarity. The confrontation of P cells and S cells lead to the formation of a segment border (...P/SAP/SAP/S...) while the A-P confrontation is a prerequisite for appendage formation. Mutations of Drosophila affecting larval segmentation are discussed in terms of this model. (iii) The two models for the generation of sequences of structures in space (positional information including interpretation versus mutual activation) lead to different predictions with respect to intercalary regeneration. This allows a distinction between the two models on the basis of experiments. (iv) The pigmentation patterns of certain molluscs emerge from a coupled oscillation of cells (that is, a lateral inhibition in time, instead of space). The oblique lines result from a chain of triggering events.

Animals↗
PubMed1983

Cell determination boundaries as organizing regions for secondary embryonic fields.

A model is proposed for pattern formation in secondary embryonic fields. It is stipulated that the boundaries, resulting from the primary embryonic organization of a developing organism, act as organizing regions for secondary embryonic fields, e.g., imaginal discs in insects. This boundary mechanism would allow very reliable pattern formation in the course of development: Primary positional information leads to cells of different determination, separated by sharp borders. At these borders, in turn, positional information would be generated for the next finer subdivision, and so on. This occurs if two or more differently determined cell types (e.g., compartments) cooperate for the production of a morphogenetic substance. A high concentration of the morphogen would appear at the common boundary of the cell types involved. Many experiments reported in the literature, for instance, the formation of duplicated and triplicated insect legs and the regeneration-duplication phenomenon of imaginal disc fragments can be explained under this assumption. The proposed boundary mechanism provides a molecularly feasible basis for the polar coordinate model.

Animals↗
PubMed1983

A model for the prestalk/prespore patterning in the slug of the slime mold Dictyostelium discoideum.

We propose that the prestalk/prespore pattern in Dictyostelium is generated in two steps: In a first process, an intermingled, non-position dependent prestalk/prespore pattern is generated by a cell-restricted autocatalysis and the antagonistic action of a long-ranging substrate which becomes depleted during this autocatalysis. By computer simulations we show that the assumed interaction accounts for several experimentally observed features of the prestalk/prespore pattern: The size-independent ratio of both cell types, the pattern regulation after removal of one cell type, the development towards one or the other pathway before the slug obtains its final shape or even before aggregation is completed. Our hypothetical substrate may be identical with an experimentally found differentiation-inducing factor (DIF). Alternative molecular realizations of the basic mechanism are discussed. A second process leads to the aggregation of the prestalk cells in a particular region of the aggregate, the future tip region. Interactions which enable tip formation and the coupling between the prestalk/prespore and the tip-forming system are discussed. Our model shows that the formation of a single large patch of differentiated cells and its size regulation requires conflicting parameters. By a separation into a mechanism which determines the position and a second one which determines the size of a structure, each mechanism can be optimized individually without requiring compromises for the other. Such a separation also seems to occur in other developmental systems.

Catalysis↗
PubMed1983

A boundary model for pattern formation in vertebrate limbs.

We postulate that positional information for secondary embryonic fields is generated by a cooperative interaction between two pairs of differently determined cell types. Positional information is thus generated at the boundaries between cells of different determination. The latter are assumed to result from the primary pattern formation in the embryo. The application of this model to vertebrate limbs accounts for the pairwise determination of limbs at a particular location, with a particular handedness and alignment to the main body axes of the embryo. It accounts further for the gross difference in the regeneration of double anterior and double posterior amphibian limbs as well as for the formation of supernumerary limbs after certain graft experiments including supernumeraries in which the dorsoventral polarity changes or which consist of two anterior or two posterior halves. Our model provides a feasible molecular basis for the polar coordinate model and successfully handles recently found violations, for instance formation of supernumerary limbs after ipsilateral grafting with 90 degrees rotation. The most frequent types of developmental malformations become explicable. The models allow specific predictions which are fully supported by recent experiments (see the accompanying paper of M. Maden).

Animals↗
PubMed1983

A bootstrap model for the proximodistal pattern formation in vertebrate limbs.

For the sequential determination of proximodistal structures during the outgrowth of vertebrate limbs, a 'bootstrap'-mechanism is proposed: by increasing feedback of more distally determined cells onto the production of a morphogen at the apical ectodermal ridge a successive increase of the morphogen concentration is achieved during outgrowth. The model accounts for the formation of a progress-zone at the limb tip, for the correct regeneration after truncation, for the presence and absence of proximodistal intercalation after certain graft experiments in amphibian limbs, for the tendency with which distal structures form in proximal position after certain experimental manipulations and for the intimate coupling of the anteroposterior and the proximodistal axes.

Amphibians↗