Microtubule Dynamics may Embody a Stationary Bipolarity Forming Mechanism Related to the Prokaryotic Division Site Mechanism (Pole-to-Pole Oscillations).

Cell division mechanisms in eukaryotes and prokaryotes have until recently been seen as being widely different. However, pole-to-pole oscillations of proteins like MinE in prokaryotes are now known to determine the division plane. These protein waves arise through spontaneous pattern forming reaction-diffusion mechanisms, based on cooperative binding of the proteins to a quasistationary matrix (like the cell membrane or DNA). Rather than waves, stationary bipolar pattern formation may arise as well. Some of the involved proteins have eukaryotic homologs (e.g. FtsZ and tubulin), pointing to a possible ancient shared mechanism. Tubulin polymerizes to microtubules in the spindle. Mitotic microtubules are in a highly dynamical state, frequently undergoing rapid shortening (catastrophe), and fragments formed from the microtubule ends are inferred to enhance the destabilization. Here, we show that cooperative binding of such fragments to microtubules may set up a similar pattern forming mechanism as seen in prokaryotes. The result is a spontaneously formed, well controllable, bipolar state of microtubule dynamics in the cell, which may contribute to defining the bipolar spindle.

Chemical waves in open flows of active media: their relevance to axial segmentation in biology.

The boundary forcing of open flows of active media can lead to a variety of spatiotemporal structures, depending on the local kinetics of the medium and on the characteristics of the forcing. Here, we demonstrate that regardless of the local kinetics, the combination of flow and boundary forcing is a powerful method for replacing intrinsic modes with extrinsic ones. This entrainment of dynamics has important implications for biological morphogenesis. During early embryonic development it is frequently observed that stripes of gene expression and segments arise one after the other along a growth-axis. We show that axial growth can be viewed as an open flow of cells away from a growth zone. Based on this realisation, we demonstrate using three generic reaction-diffusion-advection schemes how a space-periodic structure is induced, one "segment" at a time along the growth/flow axis, by a segmental clock that is synchronised within the growth zone. The schemes are investigated in the context of an abrupt and a gradual change in the properties of the segmental clock. Experimental observations provide evidence that the latter is involved in the early development of many vertebrates.

A chemical flow system mimics waves of gene expression during segmentation.

The early vertebrate developmental process of somitogenesis involves bands of gene expression that form periodically at the posterior end of the presomitic mesoderm (PSM) and traverse it with decreasing width and velocity. We have constructed a chemical flow system that, based on the novel flow-distributed oscillator (FDO) mechanism of wave pattern formation, reproduces key physical features of the PSM and observe concentration waves having similar spatio-temporal behavior. This suggests that the gene expression waves can be understood qualitatively in terms of phase dynamics in an open flow of a self-oscillating medium and that chemical flow systems can be used to mimic and model biological pattern formation during axial growth. In fact, expressions for wavelength and wave velocity derived from phase dynamics are found to be in quantitative agreement with measurements from both the biological and the chemical systems. This indicates that they, despite their significant differences, have common dynamics.

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.

Self-organization and evolution in a simulated cross catalyzed network.

Motivated by an alternative to the concept of a prebiotic soup in the form of interacting crystal growth close to hot vents, we investigate a model system in which the growth rate of a particular entity is modified (enhanced or reduced) by other entities present, thus forming a web of cross catalysis. Initially random interactions are imposed, but the entities compete for a common source, and some entities may thus vanish 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 stiff ordinary differential equations. Entities with positive growth may create 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 no initial autocatalysis may eventually create highly stable self-organized systems. We find that an already established cross catalyzed system often wins over a selfreplicating invader (or mutant).

The effect of slow allosteric transitions in a coupled biochemical oscillator model.

The effect of slowed allosteric transitions in a coupled biochemical oscillator model showing complex dynamic behavior is investigated. When the allosteric transitions are sufficiently fast one can obtain a low-dimensional asymptotic approximation for the dynamics of the species that evolve on a slow time-scale. Such low-dimensional models are common in studies of biological control systems and little attention has, so far, been given to the dynamic effect of the large number of species usually eliminated from more biochemically detailed models. Here we investigate the dynamic effect of explicit inclusion of allosteric transitions having finite time-scales of equilibration. It is found that slowed allosteric transitions suppress complex dynamic modes such a bursting, quasi-periodicity and chaos. The effect arises as the enzyme of consideration becomes trapped in an active state where it is unable to respond to changes in effector concentration on the time-scale necessary to support the modes of complex dynamics. Slow allosteric transitions may be favourable in biological systems in which complex oscillations are not desirable but which, at the same time, may benefit from the presence of positive feedbacks. Our findings suggest that slow allosteric transitions and finite internal rates in general may contribute significantly to the dynamics of biological control mechanisms.

Dynamics of the cell cycle engine: Cdk2-kinase and the transition into mitosis.

The autonomous cell divisions during the early development of Xenopus laevis believed to comprise a universal cell cycle engine. Recent experimental data indicates that the Cdk2-cyclin E kinase is required for the rapid divisions during Xenopus embryogenesis and that the complex is crucial for the transition into mitosis. In the present paper, the activity of Cdk2-cyclin E is incorporated into an existing comprehensive model of the cell cycle engine as an activity operating in parallel with the mitosis promotion factor (MPF) on the phosphatase Cdc25. This introduces interesting regulatory and dynamic properties for the transition into mitosis that reveals new insight into the mechanisms of the cell division process. It is shown that the Cdk2-cyclin E complex can act as an effective modulator of the threshold MPF activity needed to initiate mitosis. When the Cdk2-cyclin E activity is below a critical value, the cell cycle arrests in a well-defined state of low MPF activity corresponding to G2 arrest. In agreement with experiments a single mitotic event occurs following injection of free cyclin B. Above a critical activity, the presence of Cdk2-cyclin E allows for sustained oscillations corresponding to repeated cell divisions and the Cdk2-cyclin E may be the cause for the suppressed G2 checkpoint in the early embryonic cell cycles. A detailed bifurcation analysis reveals that the transition from steady to oscillatory behavior involves a homoclinic orbit of infinite period through an omega explosion. The general properties of the omega explosion explain the bifurcation as a dynamic mechanism well-suited for the G2 checkpoint and suggest a plausible explanation for the elongation of the cell cycle as observed at the mid-blastula transition. The proposed mechanism also suggests a plausible explanation of G2 checkpoint failure following DNA damage in human cells overexpressing Cdk2 and we suggest that the onset of mitosis in the mammalian cell occurs as the result of a slow passage through a critical point.

A reliable method to estimate the association constant for a monoclonal antibody and a protein antigen by enzyme linked immunosorbent assay, ELISA.

The association constant Ka for mouse monoclonal antibody raised against human angiotensinogen was calculated using a mathematical model, SAM I. K1 represents the equilibrium constant for the binding of antibody to the solid phase with antigen previously absorbed. K2 represents the interaction between antibody and antigen in solution (Ag + Ab = AgAb). K3 represents binding to the antigen absorbed on the solid phase by an antigen-antibody complex. K4 represents the second binding of the antigen to the antigen-antibody complex (AgAb + AgAb = (Ag)2Ab). The model unveils cooperativity for the first (K1 and K2) and second (K3 and K4) binding of antigen to antibody. The model gives the association constant in a high affinity interaction between antigen and antibody.

[High mortality from both natural and unnatural causes. A 10-year follow-up of patients admitted to a center for poisoning treatment after attempted suicide]. / Høj dødelighed af naturlige og unaturlige årsager. En tiårs-opfølgningsundersøgelse af patienter indlagt på en forgiftningscentral efter selvmordsforsøg.

While it is well known that suicide rates for suicide attempters are high, mortality rates for all causes needed to be more thoroughly investigated. A Danish 10-year follow-up study of patients who in 1980 were admitted to a poisoning treatment centre after attempted suicide was carried out with the purpose of describing mortality by suicide and other causes of death, and to identify predictive factors. A total of 974 patients aged 15 and over referred to a poisoning treatment centre after deliberate self-poisoning were included in the study. Death by different causes registered in the Danish Death Cause Register was the outcome measure. Over a 10-year follow-up period 306 patients had died; 103 by suicide, 131 from natural causes, 31 by accidents, five were murdered and in 36 cases the cause of death was uncertain. The Standard Mortality Rate (SMR) was 550. The cause-specific SMRs were for suicide 2960, for natural causes 236, for accidents 1256 and for uncertain causes 5459. In Cox-regression analysis high-risk factors for later suicide were more than one previous suicide attempt (relative risk (RR) 2.25), living alone (RR 2.28) and age (RR 1.03 per year). Predictors of death by natural causes were pension (RR 1.69), drug abuse (RR 2.72), more than one previous suicide attempt (RR 2.25), age (RR 1.06 per year) and male sex (RR 2.49). The group of patients fulfilling at least one high-risk criteria for later suicide differed significantly from the rest of the patient group regarding frequency of suicide, but both sensitivity and specificity remain low.(ABSTRACT TRUNCATED AT 250 WORDS)

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.

A new approach to the determination of ethanol elimination rate in vivo: an extension of Widmark's equation.

In order to provide more experimental data about a single ethanol elimination sequence, tracer amounts of 14C-labelled ethanol were given intravenously in fed and fasted rats into a preexisting pool of unlabelled ethanol. The profiles of the elimination curves of 14C-labelled ethanol were distinctly different from those of unlabelled ethanol. This necessitated the elaboration of a mathematical model based on a two-compartment system, which by using the early distribution phase of the 14C-labelled ethanol and the linear part of the elimination curve of unlabelled ethanol enables the determination of the time-rate constants for distribution of ethanol, K12 and K21 and ethanol elimination rate Q. It is shown that the ratio K21'/(K21' + K12') is "r", the distribution volume of ethanol in the sense of Widmark, K12' is K12 divided with Va (initial distribution space of ethanol) and K21' is K21 divided with Vb (the peripheral compartment). The mean value +/- S.E.M. is 0.57 +/- 0.05 for fed rats and 0.49 +/- 0.03 for fasted. The slope of the time-concentration curve of ethanol, Widmark's beta, is shown to be K12'/(K12' x K21') x Q where Q is ethanol elimination rate. The mean elimination rate is 0.303 +/- 0.036 mmol x l-1 x min-1 in fed rats and 0.219 +/- 0.015 mmol x l-1 x min.-1 in fasted (P less than 0.05). It is concluded that we are now able to extend Widmark's equation by an independent determination of the distribution factor "r".

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.

Alternative routes for angiotensin-I conversion: kinetics of the renin-angiotensin system in mouse plasma.

Angiotensin-I in plasma may be converted to angiotensin-II or alternatively metabolized through other routes. The aim of the present work has been to quantitate the role of the alternative routes in mouse plasma. A kinetic model for metabolism of the angiotensins through the renin-angiotensin system is proposed, the model allows for alternative routes and for simultaneous reactions to occur. Exogenously added angiotensin-I and angiotensin-II, or endogenously formed angiotensin-I and angiotensin-II from the action of exogenously added renin, were measured in plasma with time. The concentrations of angiotensin-I and angiotensin-II were measured by radioimmunoassay after separation by Dowex cation exchange and HPLC reverse-phase chromatography. The rate constants for the enzymatic reactions were experimentally determined and fitted to the kinetic model. The data were incompatible with a quantitative conversion of angiotensin-I to angiotensin-II, and indicate that about half of the angiotensin-I formed in plasma is metabolized in plasma through alternative routes.

Size adaptation of Turing prepatterns.

Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing chemical reaction-diffusion systems. Such Turing prepatterns have a specified geometry as long as D/R2 (the diffusion coefficient of the morphogen D divided by the square of a characteristic length) is confined to a (usually) limited interval. As real biochemical systems like cleaving eggs or early embryos vary considerably in size, Turing prepatterns are unable to maintain a specified prepattern-geometry, unless D/R2 is varied as well. We show, that actual biochemical control systems may vary Dapp/R2, where Dapp (kappa) is an apparent diffusion constant, dependent on enzyme regulated rate constants, and that such simple control systems allow Turing structures to adapt to size variations of at least a factor 10(3) (linearly), not only in large connected cell systems, but in single cells as well.

Pathways of reducing equivalents in hepatocytes from rats. Estimation of cytosolic fluxes by means of 3H-labelled substrates for either A- or B-specific dehydrogenases.

The metabolism of [2-3H]lactate and [2-3H]glycerol was studied in isolated hepatocytes from fed rats. In order to estimate the rate of equilibrium between the 4A and 4B hydrogen atoms of NADH, we compared the flow of 3H from [2-3H]lactate and [2-3H]glycerol, the oxidations of which are catalysed by A- and B-type dehydrogenases, respectively. Hepatocytes were incubated with lactate, glycerol and ethanol and tracer amounts of [2-3H]lactate or [2-3H]glycerol and the labelling rates of lactate, ethanol, glucose and glycerol phosphate were determined. The data were used to calculate the oxidation rate of NADH catalysed by lactate dehydrogenase, alcohol dehydrogenase, triosephosphate dehydrogenase and glycerol phosphate dehydrogenase. The rates were calculated by obtaining the best fit of a model to the experimental data by using a least-squares procedure. The results support our model and suggest that the fluxes through various dehydrogenases are sufficient to equilibrate the 4A and 4B hydrogen atoms of cytosolic NADH. The validity of the metabolic models used was evaluated by comparison of rates of NADH oxidation catalysed by cytosolic dehydrogenases as calculated by two different models.

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.

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.