Axel Hunding | University of Copenhagen (original) (raw)
Papers by Axel Hunding
The Journal of Chemical Physics, 1978
The steady state spatial patterns arising in open nonlinear reaction–diffusion systems beyond an ... more The steady state spatial patterns arising in open nonlinear reaction–diffusion systems beyond an instability point of the thermodynamic branch are studied for a simple kinetic scheme derived from glycolysis. Bifurcation theory is used to derive analytic expressions for patterns within a sphere. The results indicate that a gradient of substance may arise spontaneously from a homogeneous distribution within a cell or a blastula, thus establishing a prepattern. Finally, the derived solution scheme is shown to simplify considerably if rotation matrices are introduced into the formalism.
Physica D: Nonlinear Phenomena, 1990
ABSTRACT
Journal of immunoassay, 1995
The association constant Ka for mouse monoclonal antibody raised against human angiotensinogen wa... more 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.
Acta Medica Scandinavica, 1981
Systemic iron deficiency was found in 63 (56%) of 113 joggers and competition runners (33 women a... more Systemic iron deficiency was found in 63 (56%) of 113 joggers and competition runners (33 women and 80 men). Thirteen women and ten men had latent anemia. A majority of the women were fertile with iron loss from menstruation; the men were runners training long distances. The average transferrin iron-binding capacity was 80 mu mol/l serum in the women and 77 (iron-binding groups) in the men. The haptoglobin and iron concentrations in serum were remarkably low (most often below 10 and 20 mu mol/l, respectively). Three of the long-distance runners ran 25 km daily. They returned with so much free hemoglobin in their plasma that an accompanying iron loss (integrated over months), if not balanced by diet, would lead to iron deficiency and anemia. Oral iron therapy (200 mg ferrous sulphate per day) normalized the hemoglobin concentration and improved the transferrin saturation fraction in 61 persons. The competition runners reported personal records.
Biochemical Education, 1998
A recently proposed function fl)r optimization of anaerobic glycolysis is analysed. The maximum v... more A recently proposed function fl)r optimization of anaerobic glycolysis is analysed. The maximum value of this optimization function is shown in general to lead to a conserved energy yield of 50% fi)r any coupled reactkm. Maximization of the optimization function is shown to correspond to maximizing the product of two variables, the sum of which is constant. The maximum wdue of the product is always obtained when the two variables have the same size.
Journal of Mathematical Biology, 1987
Spontaneous pattern formation (emergence of Turing structures) may take place in biological syste... more 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.
Journal of Mathematical Biology, 1983
Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcatio... more 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.
Origins of Life and Evolution of Biospheres, 2007
Five common assumptions about the first cells are challenged by the pre-biotic ecology model and ... more 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.
Mathematical Biosciences, 2003
Waves of calcium ions are present in fertilized eggs of many species. Models for pulse and tidal ... more 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.
Journal of Theoretical Biology, 1998
The quasi-steady state approximation (QSSA) has an important role in models of biological control... more The quasi-steady state approximation (QSSA) has an important role in models of biological control systems. Often internal dynamics is assumed to be sufficiently fast to allow relative simple polynomial functions, e.g. Hill-type kinetics, to be used in a description of minimal dimensionality. Here we investigate the effect of a finite rate alosteric transition, or finite rates for substrate or product
Journal of Theoretical Biology, 1998
The autonomous cell divisions during the early development of Xenopus laevis believed to comprise... more 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.
Journal of Theoretical Biology, 1999
The effect of slowed allosteric transitions in a coupled biochemical oscillator model showing com... more 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 as 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.
Journal of Theoretical Biology, 2000
The formation of spatially repetitive structures along the growth axis of a developing embryo is ... more 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 #ow-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 satis"ed 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 e!ect 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.
Journal of Mathematical Biology, 1988
Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcatio... more 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/R 2 (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/R 2 is varied as well. We show, that actual biochemical control systems may vary Dapp/R 2, where Dapp(k ) 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.
Faraday Discussions, 2002
The boundary forcing of open Ñows of active media can lead to a variety of spatiotemporal structu... more The boundary forcing of open Ñows 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 Ñow 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 Ñow of cells away from a growth zone. Based on this realisation, we demonstrate using three generic reactionÈdi †usionÈadvection schemes how a space-periodic structure is induced, one "" segment ÏÏ at a time along the growth/Ñow 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.
Developmental Dynamics, 2006
Blowflies are the primary facultative agent in causing myiasis of domestic sheep in the whole wor... more Blowflies are the primary facultative agent in causing myiasis of domestic sheep in the whole world and, at the same time, it is an important tool for forensic medicine. Surprisingly, and in contrast to its importance, almost no data regarding the embryology and molecular markers are known for this insect. In this report, we present a detailed description of the blowfly Lucilia sericata embryogenesis and of imaginal disc development. The embryogenesis of Lucilia strongly resembles that of Drosophila, despite their apparent size difference. Moreover, imaginal disc development appears to be equally well conserved. Through cloning, expression, and functional studies, we show that the Lucilia Wingless (Wg) protein is highly conserved between the two species. We further show that parasegments are established in Lucilia, however, engrailed expression shows a more dynamic expression pattern than expected in comparison to Drosophila.
BMJ, 1993
Objective-To describe mortality by suicide and other causes of death in a group of patients who a... more Objective-To describe mortality by suicide and other causes of death in a group of patients who attempted suicide, and to identify predictive factors.
Biophysical Chemistry, 2000
The early vertebrate developmental process of somitogenesis involves bands of gene expression tha... more 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.
BioEssays, 2006
We hypothesize that life began not with the first selfreproducing molecule or metabolic network, ... more We hypothesize that life began not with the first selfreproducing molecule or metabolic network, but as a prebiotic ecology of co-evolving populations of macromolecular aggregates (composomes). Each composome species had a particular molecular composition resulting from molecular complementarity among environmentally available prebiotic compounds. Natural selection acted on composomal species that varied in properties and functions such as stability, catalysis, fission, fusion and selective accumulation of molecules from solution. Fission permitted molecular replication based on composition rather than linear structure, while fusion created composomal variability. Catalytic functions provided additional chemical novelty resulting eventually in autocatalytic and mutually catalytic networks within composomal species. Composomal autocatalysis and interdependence allowed the Darwinian co-evolution of content and control (metabolism). The existence of chemical interfaces within complex composomes created linear templates upon which self-reproducing molecules (such as RNA) could be synthesized, permitting the evolution of informational replication by molecular templating. Mathematical and experimental tests are proposed.
The Journal of Chemical Physics, 1978
The steady state spatial patterns arising in open nonlinear reaction–diffusion systems beyond an ... more The steady state spatial patterns arising in open nonlinear reaction–diffusion systems beyond an instability point of the thermodynamic branch are studied for a simple kinetic scheme derived from glycolysis. Bifurcation theory is used to derive analytic expressions for patterns within a sphere. The results indicate that a gradient of substance may arise spontaneously from a homogeneous distribution within a cell or a blastula, thus establishing a prepattern. Finally, the derived solution scheme is shown to simplify considerably if rotation matrices are introduced into the formalism.
Physica D: Nonlinear Phenomena, 1990
ABSTRACT
Journal of immunoassay, 1995
The association constant Ka for mouse monoclonal antibody raised against human angiotensinogen wa... more 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.
Acta Medica Scandinavica, 1981
Systemic iron deficiency was found in 63 (56%) of 113 joggers and competition runners (33 women a... more Systemic iron deficiency was found in 63 (56%) of 113 joggers and competition runners (33 women and 80 men). Thirteen women and ten men had latent anemia. A majority of the women were fertile with iron loss from menstruation; the men were runners training long distances. The average transferrin iron-binding capacity was 80 mu mol/l serum in the women and 77 (iron-binding groups) in the men. The haptoglobin and iron concentrations in serum were remarkably low (most often below 10 and 20 mu mol/l, respectively). Three of the long-distance runners ran 25 km daily. They returned with so much free hemoglobin in their plasma that an accompanying iron loss (integrated over months), if not balanced by diet, would lead to iron deficiency and anemia. Oral iron therapy (200 mg ferrous sulphate per day) normalized the hemoglobin concentration and improved the transferrin saturation fraction in 61 persons. The competition runners reported personal records.
Biochemical Education, 1998
A recently proposed function fl)r optimization of anaerobic glycolysis is analysed. The maximum v... more A recently proposed function fl)r optimization of anaerobic glycolysis is analysed. The maximum value of this optimization function is shown in general to lead to a conserved energy yield of 50% fi)r any coupled reactkm. Maximization of the optimization function is shown to correspond to maximizing the product of two variables, the sum of which is constant. The maximum wdue of the product is always obtained when the two variables have the same size.
Journal of Mathematical Biology, 1987
Spontaneous pattern formation (emergence of Turing structures) may take place in biological syste... more 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.
Journal of Mathematical Biology, 1983
Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcatio... more 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.
Origins of Life and Evolution of Biospheres, 2007
Five common assumptions about the first cells are challenged by the pre-biotic ecology model and ... more 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.
Mathematical Biosciences, 2003
Waves of calcium ions are present in fertilized eggs of many species. Models for pulse and tidal ... more 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.
Journal of Theoretical Biology, 1998
The quasi-steady state approximation (QSSA) has an important role in models of biological control... more The quasi-steady state approximation (QSSA) has an important role in models of biological control systems. Often internal dynamics is assumed to be sufficiently fast to allow relative simple polynomial functions, e.g. Hill-type kinetics, to be used in a description of minimal dimensionality. Here we investigate the effect of a finite rate alosteric transition, or finite rates for substrate or product
Journal of Theoretical Biology, 1998
The autonomous cell divisions during the early development of Xenopus laevis believed to comprise... more 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.
Journal of Theoretical Biology, 1999
The effect of slowed allosteric transitions in a coupled biochemical oscillator model showing com... more 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 as 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.
Journal of Theoretical Biology, 2000
The formation of spatially repetitive structures along the growth axis of a developing embryo is ... more 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 #ow-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 satis"ed 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 e!ect 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.
Journal of Mathematical Biology, 1988
Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcatio... more 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/R 2 (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/R 2 is varied as well. We show, that actual biochemical control systems may vary Dapp/R 2, where Dapp(k ) 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.
Faraday Discussions, 2002
The boundary forcing of open Ñows of active media can lead to a variety of spatiotemporal structu... more The boundary forcing of open Ñows 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 Ñow 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 Ñow of cells away from a growth zone. Based on this realisation, we demonstrate using three generic reactionÈdi †usionÈadvection schemes how a space-periodic structure is induced, one "" segment ÏÏ at a time along the growth/Ñow 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.
Developmental Dynamics, 2006
Blowflies are the primary facultative agent in causing myiasis of domestic sheep in the whole wor... more Blowflies are the primary facultative agent in causing myiasis of domestic sheep in the whole world and, at the same time, it is an important tool for forensic medicine. Surprisingly, and in contrast to its importance, almost no data regarding the embryology and molecular markers are known for this insect. In this report, we present a detailed description of the blowfly Lucilia sericata embryogenesis and of imaginal disc development. The embryogenesis of Lucilia strongly resembles that of Drosophila, despite their apparent size difference. Moreover, imaginal disc development appears to be equally well conserved. Through cloning, expression, and functional studies, we show that the Lucilia Wingless (Wg) protein is highly conserved between the two species. We further show that parasegments are established in Lucilia, however, engrailed expression shows a more dynamic expression pattern than expected in comparison to Drosophila.
BMJ, 1993
Objective-To describe mortality by suicide and other causes of death in a group of patients who a... more Objective-To describe mortality by suicide and other causes of death in a group of patients who attempted suicide, and to identify predictive factors.
Biophysical Chemistry, 2000
The early vertebrate developmental process of somitogenesis involves bands of gene expression tha... more 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.
BioEssays, 2006
We hypothesize that life began not with the first selfreproducing molecule or metabolic network, ... more We hypothesize that life began not with the first selfreproducing molecule or metabolic network, but as a prebiotic ecology of co-evolving populations of macromolecular aggregates (composomes). Each composome species had a particular molecular composition resulting from molecular complementarity among environmentally available prebiotic compounds. Natural selection acted on composomal species that varied in properties and functions such as stability, catalysis, fission, fusion and selective accumulation of molecules from solution. Fission permitted molecular replication based on composition rather than linear structure, while fusion created composomal variability. Catalytic functions provided additional chemical novelty resulting eventually in autocatalytic and mutually catalytic networks within composomal species. Composomal autocatalysis and interdependence allowed the Darwinian co-evolution of content and control (metabolism). The existence of chemical interfaces within complex composomes created linear templates upon which self-reproducing molecules (such as RNA) could be synthesized, permitting the evolution of informational replication by molecular templating. Mathematical and experimental tests are proposed.