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.     

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 mechanism for ParB-dependent waves of ParA,a protein related to DNA segregation during cell division in prokaryotes

Prokaryotic plasmids encode partitioning (par) loci involved in segregation of DNA to daughter cells at cell division. A functional fusion protein consisting of Walker-type ParA ATPase and green fluorescent protein (Gfp) oscillates back and forth within nucleoid regions with a wave period of about 20 minutes. A model is discussed which is based on cooperative non-specific binding of ParA to the nucleoid, and local ParB initiated generation of ParA oligomer degradation products, which act autocatalytically on the degradation reaction. The model yields self-initiated spontaneous pattern formation, based on Turing's mechanism, and these patterns are destroyed by the degradation products, only to initiate a new pattern at the opposite nucleoid region. A recurrent wave thus emerges. This may be a particular example of a more general class of pattern forming mechanisms, based on protein oligomerization upon a template (membranes, DNA a.o.) with resulting enhanced NTPase function in the oligomer state, which may bring the oligomer into an unstable internal state. An effector initializes destabilization of the oligomer to yield degradation products, which act as seeds for further degradation in an autocatalytic process. We discuss this mechanism in relation to recent models for MinDE oscillations in E.coli and to microtubule degradation in mitosis. The study points to an ancestral role for the presented pattern types in generating bipolarity in prokaryotes and eukaryotes.     

Simulation of waves in calcium models with 3D spherical geometry

Waves of calcium ions are present in fertilized eggs of many species. Models for pulse and tidal wave propagation have usually been studied in one or two spatial coordinates only. We examine in three spatial coordinates some established models, based on Ca(2+)-induced Ca(2+)-release from both (assumed) continuously or heterogeneously distributed stores of endoplasmic reticulum (ER) through channels activated by inositol triphosphate (IP(3)). With continuous IP(3) distribution decreasing radially towards the interior, we obtain concave pulse shapes for waves penetrating the interior. Concave waves are also recorded in systems with ER confined to distributions of small spheres (microdomains) inside the cell, which we simulate for front waves (tides) in bistable systems.     

Segmentation and somitogenesis derived from phase dynamics in growing oscillatory media

The formation of spatially repetitive structures along the growth axis of a developing embryo is a common theme in developmental biology. Here we apply the novel flow-distributed oscillator (FDO) mechanism of wave pattern formation to the problem of axial segmentation in general and to somitogenesis in particular. We argue that the conditions for formation of FDO waves are satisfied during somitogenesis in the chick and mouse and that the waves of gene expression observed in these species arise from phase dynamics in a growing oscillatory medium. We substantiate this claim by showing that the FDO mechanism allows the waves to be mimicked by an inorganic experiment and that it predicts a wavelength that coincides with that observed experimentally. To see whether the FDO mechanism is compatible with other aspects of somitogenesis, we construct an FDO-based model of somitogenesis and successfully test it against a number of experimental observations, including the effect of heat shock. Our analysis provides a rigorous physical basis for the hypothesis that the phase dynamics of a segmental clock controls important stages of segmentation during somitogenesis in the chick and mouse as well as in other organisms that undergo segmentation during their axial growth.     

Question 7: The First Units of Life Were Not Simple Cells

Five common assumptions about the first cells are challenged by the pre-biotic ecology model and are replaced by the following propositions: firstly, early cells were more complex, more varied and had a greater diversity of constituents than modern cells; secondly, the complexity of a cell is not related to the number of genes it contains, indeed, modern bacteria are as complex as eukaryotes; thirdly, the unit of early life was an ‘ecosystem’ rather than a ‘cell’; fourthly, the early cell needed no genes at all; fifthly, early life depended on non-covalent associations and on catalysts that were not confined to specific reactions. We present here the outlines of a theory that connects findings about modern bacteria with speculations about their origins. Presented at the International School of Complexity – 4th Course: Basic Questions on the Origins of Life; “Ettore Majorana” Foundation and Centre for Scientific Culture, Erice, Italy, 1–6 October 2006.     

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.     

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.     

Self-Organization and Evolutionin a Simulated Cross Catalyzed Network

Motivated by an alternative to the concept of a prebiotic soup inthe form of interacting crystal growth close to hot vents, we investigatea model system in which the growth rate of a particular entity is modified (enhanced or reduced) by other entities present, thus forming aweb of cross catalysis. Initially random interactions are imposed, butthe entities compete for a common source, and some entities may thusvanish in the competition. New entities, or mutations (error copies),with randomly selected interactions to the web are then introduced,and the concentrations of the entities are followed as solutions to stiffordinary differential equations. Entities with positive growth maycreate new related entities with slightly randomly modified interactions to the web. Extinctions, wild-type survival and replacement,and self-organization to sustain periodic external variations, are studied. It is shown that even systems with mostly cross-inhibition and noinitial autocatalysis may eventually create highly stable self-organizedsystems. We find that an already established cross catalyzed systemoften wins over a selfreplicating invader (or mutant).     

High mortality by natural and unnatural causes: a 10 year follow up study of patients admitted to a poisoning treatment centre after suicide attempts.

OBJECTIVE--To describe mortality by suicide and other causes of death in a group of patients who attempted suicide, and to identify predictive factors. DESIGN--10 year follow up study based on records of suicide attempters in 1980. SETTING--Poisoning treatment centre at a general hospital. SUBJECTS--974 patients aged 15 and over referred to the poisoning treatment centre after deliberate self poisoning. MAIN OUTCOME MEASURES--Death by different causes registered in the Danish death cause register. RESULTS--In 10 years of follow up 306 patients died: 103 by suicide, 131 from natural causes, and 31 by accident; five were murdered, and in 36 cases the cause of death was uncertain. The standard mortality ratio was 550. Cause specific standardised mortality rates were 2960 for suicide, 236 for natural causes, 1256 for accidents, and 5459 for uncertain causes. In a Cox regression analysis, high risk factors for subsequent suicide were: more than one previous suicide attempt (relative risk 2.25), living alone (2.28), and age (1.03 per year). Predictors of death by natural causes were receiving a pension (1.69), drug misuse (2.72), more than one previous suicide attempt (2.25), age (1.06 per year), and male sex (2.49). The group of patients fulfilling at least one high risk criterion for later suicide differed significantly from the rest of the patient group in incidence of suicide, but both sensitivity and specificity were low. CONCLUSIONS--Most patients who attempted suicide were at high risk of succeeding because the risk factors, though significant, are not very specific. A strategy to prevent suicide must be directed toward the majority of those who attempt suicide.