Altered cerebellar ganglioside pattern in rett syndrome

The membrane lipids were examined in the cerebellum from five patients who died with Rett syndrome (RS). The major lipids of cerebellar folia and white matter did not show any difference compared with age-matched controls. There were slightly low values for cerebrosides, a biochemical marker for myelin, in cerebellar folia but high values in white matter of corpus medullare. The ganglioside concentration was reduced in one case which had shown marked astrocytosis at histological examination. Astrocyte associated gangliosides were significantly increased in this case, but their proportion was also increased in the four other patients. Lacto series acidic glycosphingolipids, 3′-LM1 and LK1, closely associated with Purkinje cells were reduced in the Rett cases which fits well with neuropathological examination demonstrating the loss of Purkinje cells. The most prominent finding was a decreased proportion of gangliosides GD1a and GT1b in cerebellar folia and white matter. The decreased proportion of GD1a might reflect an abnormality of synaptogenesis in RS and would be compatible with the clinical profile of this disease.     

Pattern formation in the cerebellar cortex.

The cerebellar cortex is subdivided rostrocaudally and mediolaterally into a reproducible array of zones and stripes. This makes the cerebellum a valuable model for studying pattern formation in the vertebrate central nervous system. The structure of the adult mouse cerebellar cortex and the series of embryological events that generate the topography are reviewed.     

Time and tide in cerebellar memory formation

The notion that the olivocerebellar system is crucial for motor learning is well established. In recent years, it has become evident that there can be many forms of both synaptic and non-synaptic plasticity within this system and that each might have a different role in developing and maintaining motor learning across a wide range of tasks. There are several possible molecular and cellular mechanisms that could underlie adaptation of the vestibulo-ocular reflex and eyeblink conditioning. Although causal relationships between particular cellular processes and individual components of a learned behaviour have not been demonstrated unequivocally, an overall picture is emerging that the different types and sites of cellular plasticity relate importantly to the stage of learning and/or its temporal specifics.     

Dynamics of pattern formation

Experiments were designed to test the validity ofTuring's suggested pattern-forming mechanisms, which are initially capable of giving rise to only five to seven uniform structures.TheOregon-R (wild-type), mass-cultured strain ofDrosophila melanogaster was employed. Selection for the regular arrangement of microchaetac on the margin of the fourth abdominal sternite was practiced for twenty generations. In the L line, individuals with six uniformly spaced bristles were selected as parents of every generation. Due to the absence of nine bristles dividing the sternal margin uniformly, the progeny was raised in each generation in the H line from males and females with nine as equidistant bristles as possible. The whole experiment was performed at 25±0.50°C.Selection was effective in increasing the frequency of six regular bristles in the L line. But no progress in the desired direction was obtained in the H line, although the proportion of sternites with nine irregular structures was found to increase. The experimental results supportTuring's diffusion-reaction scheme of pattern formation in morphogenesis.Supported by grants GB-1388 and GB-3219 from the National Science Foundation.     

A model of activity-dependent formation of cerebellar microzones

According to modern views of the cerebellum in motor control, each cerebellar functional unit, or microzone, learns how to execute predictive and coordinative control, based on long-term depression of the granule cell-Purkinje cell synapses. In the present paper, in light of recent experimental and theoretical studies on synaptic elimination and cerebellar motor learning, a model of the formation of cerebellar microzones by climbing fiber synaptic elimination is proposed. It is shown that competition for an activity-dependent supply of neurotrophic factor can reproduce the spatio-temporal characteristics of climbing fiber synaptic elimination. It is further shown that when this elimination is accurate, motor coordination can be acquired in an arm reaching task. In view of the results of the present study, several predictions are proposed. Received: 19 January 1998 / Accepted in revised form: 22 April 1998     

Positional information and pattern formation

Spatial patterns of cellular differentiation may arise from cells first being assigned a position, as in a coordinate system, and then interpreting the positional value that they have acquired. This interpretation will depend on their genetic constitution and developmental history. Different patterns may thus arise from similar positional fields. The specification of positional value may involve a positional signal, such as the concentration of a diffusible morphogen, but can also depend on how long the cells remain in a particular region, such as a progress zone. Positional values may also be acquired by direct transfer from one cell layer to another, as in directed embryonic induction. Positional value, unlike a positional signal, involves long-term memory, and can be regarded as a type of cell determination. Cells of the same differentiation class may have different positional values and may thus be non-equivalent. Evidence is presented for a signal providing positional information along the antero-posterior axis during chick limb development. This signal has properties similar to those of a diffusible morphogen.     

Pigmentation pattern formation on snakes

We consider a cell-chemotaxis model mechanism for generating some of the common, simple and complex, patterns found on the skin of snakes. By investigating the pattern generation potential of the model we show that many of the more complex patterns might result from growth of the integument during the pattern formation process. We suggest that many of the diverse elaborate patterns on snakes, and other species, can be generated by a single mechanism if the time scale of the pattern process is commensurate with the time scale associated with significant embryonic growth.     

In silico zebrafish pattern formation

Mutations that affect pattern formation in the zebrafish have been widely studied over the past few decades, leading to speculations as to the mechanism by which stripes, spots and other skin patterns are formed. Recent in silico developments in modeling of cellular dynamics now permit explicit analysis of how cells migrate and interact, and we describe here an in silico simulation that appears to reproduce many of the surface patterns previously reported in zebrafish. We find that many observed zebrafish patterns are necessarily associated with expression of repulsive as well as attractive cellular ligands, and we make predictions for the detailed effects of changes in expression of these ligands.     

Quantitative models of developmental pattern formation

Pattern formation in developing organisms can be regulated at a variety of levels, from gene sequence to anatomy. At this level of complexity, mechanistic models of development become essential for integrating data, guiding future experiments, and predicting the effects of genetic and physical perturbations. However, the formulation and analysis of quantitative models of development are limited by high levels of uncertainty in experimental measurements, a large number of both known and unknown system components, and the multiscale nature of development. At the same time, an expanding arsenal of experimental tools can constrain models and directly test their predictions, making the modeling efforts not only necessary, but feasible. Using a number of problems in fruit fly development, we discuss how models can be used to test the feasibility of proposed patterning mechanisms and characterize their systems-level properties.     

Modeling plant growth and pattern formation

Plants continue to grow and generate new organs in symmetric patterns throughout their lives. This development requires an interconnected regulation of genes, hormones, and anisotropic growth, which in part is guided by environmental cues. Recently, several studies have used a combination of experiments and mathematical modeling to elucidate the mechanisms behind different growth and molecular patterns in plants. The computational models were used to investigate the often non-intuitive consequences of different hypotheses, and the in silico simulations of the models inspired further experimentation.     

Retinoids and vertebrate limb pattern formation

It has long been suggested that pattern formation depends in part on signalling molecules known as 'morphogens', diffusible substances that determine cell fate in a concentration-dependent way. Retinoic acid, a small hydrophobic molecule that binds to nuclear receptors, is a candidate morphogen for specifying the anteroposterior pattern of vertebrate limbs.     

Regular pattern formation in real ecosystems

Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer-resource interactions, localized disturbance-recovery processes and scale-dependent feedback. Despite abundant theoretical literature, studies revealing spatial self-organization in real ecosystems are limited. Recently, however, many examples of regular pattern formation have been discovered, supporting the importance of scale-dependent feedback. Here, we review these studies, showing regular pattern formation to be a general phenomenon rather than a peculiarity. We provide a conceptual framework explaining how scale-dependent feedback determines regular pattern formation in ecosystems. More empirical studies are needed to better understand regular pattern formation in ecosystems, and how this affects the response of ecosystems to global environmental change.     

Cortical pattern formation during visual hallucinations

We theoretically investigate pattern formation during simple visual hallucinations caused by epileptic activity. To this end we analyze the activator-inhibitor model of Ermentrout and Cowan [1]. In contrast to these authors we focus on a different disease mechanism: According to experimental findings (cf. [2]) we decrease the influence of the inhibitor on the activator. This causes spontaneous pattern formation due to a bifurcation. The model parameters determine whether one or two or four modes become unstable. By means of the center manifold theorem, in all cases the order parameter equation is derived, the stability of the solution is proofed, and the bifurcating activity pattern is calculated explicitely in lowest order. Taking into account terms up to third order in all cases the order parameter equation has a potential. For the two-modes and the four-modes instability this potential causes a winner-takes all dynamics. We integrate the order parameter equation numerically and plot the visual hallucinations which result from the bifurcating cortical activity. The theoretically derived hallucinations correspond to clinically observed visual hallucinations (cf. [3, 4]), which are, for instance, well-known from petit mal epilepsy [5].Finally we investigate the influence of noise on the activity patterns as well as the visual hallucinations.     

A theory of biological pattern formation

One of the elementary processes in morphogenesis is the formation of a spatial pattern of tissue structures, starting from almost homogeneous tissue. It will be shown that relatively simple molecular mechanisms based on auto- and cross catalysis can account for a primary pattern of morphogens to determine pattern formation of the tissue. The theory is based on short range activation, long range inhibition, and a distinction between activator and inhibitor concentrations on one hand, and the densities of their sources on the other. While source density is expected to change slowly, e.g. as an effect of cell differentiation, the concentration of activators and inhibitors can change rapidly to establish the primary pattern; this results from auto- and cross catalytic effects on the sources, spreading by diffusion or other mechanisms, and degradation.Employing an approximative equation, a criterium is derived for models, which lead to a striking pattern, starting from an even distribution of morphogens, and assuming a shallow source gradient. The polarity of the pattern depends on the direction of the source gradient, but can be rather independent of other features of source distribution. Models are proposed which explain size regulation (constant proportion of the parts of the pattern irrespective of total size). Depending on the choice of constants, aperiodic patterns, implying a one-to-one correlation between morphogen concentration and position in the tissue, or nearly periodic patterns can be obtained. The theory can be applied not only to multicellular tissues, but also to intracellular differentiation, e.g. of polar cells.The theory permits various molecular interpretations. One of the simplest models involves bimolecular activation and monomolecular inhibition. Source gradients may be substituted by, or added to, sink gradients, e.g. of degrading enzymes. Inhibitors can be substituted by substances required for, and depleted by activation.Sources may be either synthesizing systems or particulate structures releasing activators and inhibitors.Calculations by computer are presented to exemplify the main features of the theory proposed. The theory is applied to quantitative data on hydra — a suitable one-dimensional model for pattern formation — and is shown to account for activation and inhibition of secondary head formation.