Nonlinear population dynamics: complication in the age structure influences transition-to-chaos scenarios

The work continues a series of studies on the evolution of a natural population of explicitly seasonal organisms. Model analyses have revealed relationships between the duration of ontogenesis and the pattern of temporal dynamics in size of an isolated population (i.e., the structure and dimensionality of the chaotic attractors). For nonlinear models of age-structured population dynamics (under long-lasting ontogenesis), increase in the reproductive potential is shown to result in the chaotic attractors whose structure and dimensionality changes in response to variations in the model parameters. When the ontogenesis becomes longer and more complicated, it does not, "on the average", augment the level of chaos in the attractors observed. There are wide enough regions in the space of the birth and death parameter values that provide for windows in the chaotic dynamics where the total or partial regularization occurs.     

A Cayley tree immune network model with antibody dynamics

A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analysed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percolation and chaotic attractors. Stable limit cycles, which are frequent in the two-clone antibody B cell (AB) model, are only observed in highly connected networks. Also found in highly connected networks are localized chaotic attractors. As in experiments by Lundkvistet al. (1989.Proc. natn. Acad. Sci. U.S.A. 86, 5074–5078), injection ofAb ₁ antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations ofAb ₁ andAb ₂ antibodies, a phenomenon already observed in the two-clone AB model. Interestingly, chaotic fluctuations continue at higher levels of the tree, a phenomenon observed by Lundkvistet al. but not accounted for previously.     

Growth of cranial synchondroses and sutures requires polycystin-1

In vertebrates, coordinated embryonic and postnatal growth of the craniofacial bones and the skull base is essential during the expansion of the rostrum and the brain. Identification of molecules that regulate skull growth is important for understanding the nature of craniofacial defects and for development of non-invasive biologically based diagnostics and therapies.Here we report on spatially restricted growth defects at the skull base and in craniofacial sutures of mice deficient for polycystin-1 (Pkd1). Mutant animals reveal a premature closure of both presphenoid and sphenooccipital synchondroses at the cranial base. Furthermore, knockout mice lacking Pkd1 in neural crest cells are characterized by impaired postnatal growth at the osteogenic fronts in craniofacial sutures that are subjected to tensile forces. Our data suggest that polycystin-1 is required for proliferation of subpopulations of cranial osteochondroprogenitor cells of both mesodermal and neural crest origin during skull growth. However, the Erk1/2 signalling pathway is up-regulated in the Pkd1-deficient skeletal tissue, similarly to that previously reported for polycystic kidney.     

Cancer attractors: A systems view of tumors from a gene network dynamics and developmental perspective

Cell lineage commitment and differentiation are governed by a complex gene regulatory network. Disruption of these processes by inappropriate regulatory signals and by mutational rewiring of the network can lead to tumorigenesis. Cancer cells often exhibit immature or embryonic traits and dysregulated developmental genes can act as oncogenes. However, the prevailing paradigm of somatic evolution and multi-step tumorigenesis, while useful in many instances, offers no logically coherent reason for why oncogenesis recapitulates ontogenesis. The formal concept of “cancer attractors”, derived from an integrative, complex systems approach to gene regulatory network may provide a natural explanation. Here we present the theory of attractors in gene network dynamics and review the concept of cell types as attractors. We argue that cancer cells are trapped in abnormal attractors and discuss this concept in the light of recent ideas in cancer biology, including cancer genomics and cancer stem cells, as well as the implications for differentiation therapy.     

Stochastic Sensitivity Analysis of Noise-Induced Extinction in the Ricker Model with Delay and Allee Effect

A susceptibility of population systems to the random noise is studied on the base of the conceptual Ricker-type model taking into account the delay and Allee effect. This two-dimensional discrete model exhibits the persistence in the form of equilibria, discrete cycles, closed invariant curves, and chaotic attractors. It is shown how the Allee effect constrains the persistence zones with borders defined by crisis bifurcations. We study the role of random noise on the contraction and destruction of these zones. This phenomenon of the noise-induced extinction is investigated with the help of direct numerical simulations and semi-analytical approach based on the stochastic sensitivity functions. Stochastic transitions from the persistence regimes to the extinction are studied by the analysis of the mutual arrangement of the basins of attraction and confidence domains.     

Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics.

We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.     

Complex asparagine-linked oligosaccharides are required for morphogenic events during post-implantation development.

Complex asparagine (N)-linked oligosaccharides appear late in phylogeny and are highly regulated in vertebrates. Variations in these structures are found on the majority of cell-surface and secreted proteins. Complex N-linked oligosaccharide biosynthesis is initiated in the Golgi apparatus by the action of Mgat-1-encoded UDP-N-acetylglucosamine:alpha-3-D- mannoside beta-1,2-N-acetylglucosaminyltransferase I (GlcNAc-TI). To determine if these structures govern ontogenic processes in mammals, mouse embryos were generated that lacked a functional Mgat-1 gene. Inactivation of both Mgat-1 alleles produced deficiencies in GlcNAc-TI activity and complex N-linked oligosaccharides. Embryonic lethality occurred by day 10.5, thus establishing that complex N-linked oligosaccharides are required during post-implantation development. Remarkably, embryonic development proceeded into day 9 with the differentiation of multiple cell types. Complex N-linked oligosaccharides are important for morphogenic processes as neural tube formation, vascularization and the determination of left-right body plan asymmetry were impaired in the absence of a functional Mgat-1 gene.     

Craniofacial shortening by contraction osteogenesis: an experimental model

Application of gradual external forces to correct craniofacial deformities challenges many procedures in conventional craniomaxillofacial surgery. Distraction osteogenesis is replacing traditional osteotomies for correction of patients with craniomaxillofacial deficiencies. However, the reverse concept, contraction osteogenesis, has yet to be established for patients with craniomaxillofacial excesses. The purpose of this investigation is to demonstrate the contraction osteogenesis phenomenon applied in a controlled animal model during the craniofacial growth period. Twenty-six 26-day-old rabbits were assigned to one of four groups: 0, control; 1, pin control (pin insertion); 2, no contraction (pins and contraction device application, without active contraction); and 3, contraction (pin insertion, contraction device application, and active contraction). An external fixator was placed across the incisive-maxillary suture, and the effects after 4.5 weeks of contraction at a rate of 0.5 mm twice a week were compared with control groups. The results were assessed by craniometric and cephalometric measurements and by histologic examination. Gross alterations were evident in the contraction group, characterized by midface anteroposterior shortening, maxillary regression, snout deviation, and anterior crossbite. Histologic examination of the contraction group demonstrated a significant increase in osteoblastic activity. Contraction osteogenesis is a new treatment concept in craniofacial development and may offer therapeutic opportunities for shortening skeletal structures without the need of osteotomies, thus taking advantage of the potential of craniofacial growth and remodeling.     

Severe nasal clefting and abnormal embryonic apoptosis in Alx3/Alx4 double mutant mice

A group of mouse aristaless-related genes has been implicated in functions in the development of the craniofacial skeleton. We have generated an Alx3 mutant allele in which the lacZ coding sequence is inserted in-frame in the Alx3 gene and the sequences encoding the conserved protein domains are deleted. Mice homozygous for this null allele are indistinguishable from wild-type mice. Compound mutants of Alx3 and Alx4, however, show severe craniofacial abnormalities that are absent in Alx4 single mutants. Alx3/Alx4 double mutant newborn mice have cleft nasal regions. Most facial bones and many other neural crest derived skull elements are malformed, truncated or even absent. The craniofacial defects in Alx3/Alx4 double mutant embryos become anatomically manifest around embryonic day 10.5, when the nasal processes appear to be abnormally positioned. This most probably leads to a failure of the medial nasal processes to fuse in the facial midline and subsequently to the split face phenotype. We detected a significant increase in apoptosis localised in the outgrowing frontonasal process in embryonic day 10.0 double mutant embryos, which we propose to be the underlying cause of the subsequent malformations.     

Intracellular dynamics of Smad-mediated TGFbeta signaling

The transforming growth factor-beta (TGFbeta) family represents a class of signaling molecules that plays a central role in morphogenesis, growth, and cell differentiation during normal embryonic development. Members of this growth factor family are particularly vital to development of the mammalian secondary palate where they regulate palate mesenchymal cell proliferation and extracellular matrix synthesis. Such regulation is particularly critical since perturbation of either cellular process results in a cleft of the palate. While the cellular and phenotypic effects of TGFbeta on embryonic craniofacial tissue have been extensively catalogued, the specific genes that function as downstream mediators of TGFbeta action in the embryo during palatal ontogenesis are poorly defined. Embryonic palatal tissue in vivo and murine embryonic palate mesenchymal (MEPM) cells in vitro secrete and respond to TGFbeta. In the current study, elements of the Smad component of the TGFbeta intracellular signaling system were identified and characterized in cells of the embryonic palate and functional activation of the Smad pathway by TGFbeta1, TGFbeta2, and TGFbeta3 was demonstrated. TGFbeta-initiated Smad signaling in cells of the embryonic palate was found to result in: (1) phosphorylation of Smad 2; (2) nuclear translocation of the Smads 2, 3, and 4 protein complex; (3) binding of Smads 3 and 4 to a consensus Smad binding element (SBE) oligonucleotide; (4) transactivation of transfected reporter constructs, containing TGFbeta-inducible Smad response elements; and (4) increased expression of gelatinases A and B (endogenous genes containing Smad response elements) whose expression is critical to matrix remodeling during palatal ontogenesis. Collectively, these data point to the presence of a functional Smad-mediated TGFbeta signaling system in cells of the developing murine palate.     

Evolution of specificity in an immune network

A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of specificity of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that specific and non-specific responses emerge as a function of antigen amounts. A specific response is observed with a fixed-point attractor, and a non-specific response is observed with a chaotic attractor for the lymphocyte population dynamics. The network topology also changes between fixed-point and chaotic attractors. For some antigen amounts, chaotic attractors will vanish or become long-lived super-transient states. A dynamic bell-shaped response function will thus emerge. The relevance of long-lived chaotic transient states embedded in fixed-point attractors is discussed with respect to immune functions.     

Neural crest cell deficiency of c-myc causes skull and hearing defects

The proto-oncogene c-myc has a central role in multiple processes important for embryonic development, including cell proliferation, growth, apoptosis, and differentiation. We have investigated the role of c-myc in neural crest by using Wnt1-Cre-mediated deletion of a conditional mutation of the c-myc gene. c-myc deficiency in neural crest resulted in viable adult mice that have defects in coat color, skull frontal bone, and middle ear ossicle development. Physiological hearing studies demonstrated a significant hearing deficit in the mutant mice. In this report, we focus on the craniofacial and hearing defects. To further examine neural crest cells affected by c-myc deficiency, we fate mapped Wnt1-Cre expressing neural crest cells using the ROSA26 Cre reporter transgene. The phenotype obtained demonstrates the critical role that c-myc has in neural crest during craniofacial development as well as in providing a model for examining human congenital skull defects and deafness.     

Genetic and environmental factors in the longitudinal growth of rats: II. Ventrodorsal craniofacial size

By means of roentgenographic cephalometry and quantitative genetic analysis, the relative contribution of the genetic and environmental components to the ontogenic change of the ventrodorsal view of the craniofacial complex was shown to vary with age. The genetic component of variance significantly increased until the 80th day. Inversely, the maternal component of variance showed a large value during the early stage of postnatal growth and gradually decreased thereafter to a very small amount by the 80th day. In general, it appeared that the genetic effect became larger with the age of the rat and the maternal effects tended to diminish. The environmental component of variance did not change much over the course of the experiment. We thus concluded that the genetic effect contributed to the change of the ontogenic variation of the craniofacial complex through all experimental periods and the maternal effect contributed to the change at the early growth stage of the craniofacial complex.     

Research on cascading high-dimensional isomorphic chaotic maps

In order to overcome the security weakness of the discrete chaotic sequence caused by small Lyapunov exponent and keyspace, a general chaotic construction method by cascading multiple high-dimensional isomorphic maps is presented in this paper. Compared with the original map, the parameter space of the resulting chaotic map is enlarged many times. Moreover, the cascaded system has larger chaotic domain and bigger Lyapunov exponents with proper parameters. In order to evaluate the effectiveness of the presented method, the generalized 3-D Hénon map is utilized as an example to analyze the dynamical behaviors under various cascade modes. Diverse maps are obtained by cascading 3-D Hénon maps with different parameters or different permutations. It is worth noting that some new dynamical behaviors, such as coexisting attractors and hyperchaotic attractors are also discovered in cascaded systems. Finally, an application of image encryption is delivered to demonstrate the excellent performance of the obtained chaotic sequences.     

Relationships between peroxidases and in vitro bulbification in garlic (Allium sativum L.)

Summary The relationship between in vitro bulbification and peroxidase activities of garlic (Allium sativum L.) was studied. Two stages could be distinguished during in vitro bulb formation characterized by the peroxidase activity, isoenzymatic patterns especially of the soluble fractions, dry weight, and bulbification index (BI). The first stage, called the morphogenic stage, started after planting until 30d of culture with a maximum soluble peroxidase activity, BI=1–0.5 and low dry weight. At that time axillary buds preformed at the base of the leaves grew and the in vitro bulb was generated. The second stage (filling in and bulb maturation) started when the BI reached 0.5 at 30 d of the ontogenic cycle, as a result of the bulb assimilate accumulation phenomenon. During the morphogenic stage the soluble peroxidase activity was maximum and the zymograms showed higher intensity bands. The second stage presented anodic ionic peroxidases and substantial increase in staining of the anodic covalent peroxidase fraction. The putative role of the different isoforms of peroxidases in relation to the bulbification process is discussed.     

Different stresses, similar morphogenic responses: integrating a plethora of pathways

Exposure of plants to mild chronic stress can cause induction of specific, stress-induced morphogenic responses (SIMRs). These responses are characterized by a blockage of cell division in the main meristematic tissues, an inhibition of elongation and a redirected outgrowth of lateral organs. Key elements in the ontogenesis of this phenotype appear to be stress-affected gradients of reactive oxygen species (ROS), antioxidants, auxin and ethylene. These gradients are present at the the organismal level, but are integrated on the cellular level, affecting cell division, cell elongation and/or cell differentiation. Our analysis of the literature indicates that stress-induced modulation of plant growth is mediated by a plethora of molecular interactions, whereby different environmental signals can trigger similar morphogenic responses. At least some of the molecular interactions that underlie morphogenic responses appear to be interchangeable. We speculate that this complexity can be viewed in terms of a thermodynamic model, in which not the specific pathway, but the achieved metabolic state is biologically conserved.     

The role of serotonin in the immune system development and functioning during ontogenesis

In this study, we investigated the influence of serotonin on the development and functioning of T- and B-cell-mediated immunity during ontogenesis using the pharmacological model of serotonin depletion in rat fetuses. It has been demonstrated that prenatal serotonin deficiency resulted in a decrease in thymus and spleen weights, changes in their cellular composition, and long-lasting disturbances in cell-mediated and humoral immunity in postnatal ontogenesis. The data obtained suggest that serotonin may be considered a morphogenic factor in development of the immune system.