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M Kaern

Publications and source records attributed to M Kaern.

9 recordsLinked to original sources
PubMed2001

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.

Algorithms↗
PubMed2000

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.

Animals↗
PubMed2000

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.

Animals↗
PubMed2000

Pulsating wave propagation in reactive flows: flow-distributed oscillations

Stationary waves in a reactive flow with equal transport coefficients were recently generated by passing the oscillating Belousov-Zhabotinsky reaction medium through a tubular packed bed reactor while keeping the concentrations constant at the inflow boundary [M. Kaern and M. Menzinger, Phys. Rev. E 60, 3471 (1999)]. Here we study the effects of oscillatory boundary conditions, and observe traveling wave fronts that propagate in either a pulsating or a steady manner. The present experiment is isothermal and conditions are such that all species have identical transport properties. This excludes rapid thermal or activator diffusion and the wave pulsation appears to be induced by an essentially kinematic mechanism. Our experimental findings are supported by numerical simulations of the full reaction-diffusion-advection system using a realistic kinetic model. Finally, the kinematic essence of the mechanism inducing wave pulsation is captured in an iterative one-variable map.

Journal Article↗
PubMed2000

Reply to "Comment on 'Flow-distributed oscillations: stationary chemical waves in a reacting flow' "

Stationary waves (wavelength lambda) are the necessary result of spatial recurrence of phase in the open flow (rate v) of an oscillating medium with fixed inflow boundary conditions. Any nonlinear dependence lambda(v) on flow is the result of dispersion that is implicit in lambda=v/omega(v), where omega(v) is the oscillation frequency in a reference frame moving with the flow. The flow-distributed oscillator mechanism extends thus from the purely kinematic limit omega=const to the case where a nonlinear dependence lambda(v) is subsumed by the dispersion relationship omega(v).

Journal Article↗
PubMed1999

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.

Allosteric Regulation↗
PubMed1999

Flow-distributed oscillations: stationary chemical waves in a reacting flow.

A recent prediction of stationary waves in open, reacting flows is experimentally verified. We show that stationary waves are generated by a mechanism whereby the flow carries a time-oscillating subelement, behaving like a batch reactor, through space while a fixed boundary condition at the inflow locks the phase of the oscillation. This mechanism can generate stationary patterns when all diffusion coefficients are equal. The experimental system is the ferroin-catalyzed Belousov-Zhabotinsky reaction in a tubular reactor, fed by the outflow of a continuous flow stirred tank reactor (CSTR). Parameter conditions are such that the concentrations are constant in the CSTR while they oscillate in the flow tube.

Journal Article↗
PubMed1998

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.

Animals↗