Lyapunov function and the basin of attraction for a single-joint muscle-skeletal model

This paper provides an explicit Lyapunov function for a general single-joint muscle-skeletal model. Using this Lyapunov function one can determine analytically large subsets of the basin of attraction of an asymptotically stable equilibrium. Besides providing an analytical tool for the analysis of such a system we consider an elbow model and show that the theoretical predictions are in agreement with experimental results. Moreover, we can thus distinguish between regions where the self-stabilizing properties of the muscle-skeletal system guarantee stability and regions where nerval control and reflexes are necessary.      

Ciliary neurotrophic factor upregulates ubiquitin-proteasome components in a rat model of neuronal injury

Neuronal injury triggers the release of ciliary neurotrophic factor (CNTF), promoting local neuronal repair but producing systemic effects of anorexia and lean body weight loss. Due to the rapid rate of systemic protein loss stimulated by CNTF, we hypothesized involvement of the hepatic ubiquitin-proteasome proteolytic (UPP) pathway in CNTF-induced proteolysis. To assess the role of central CNTF in systemic UPP regulation, we measured hepatic UPP mRNA and proteasome activity in a rat model of neuronal injury and determined alterations induced by intracerebroventricular (ICV) administration of CNTF-neutralizing antibody or additional exogenous CNTF. We also assessed proteolytic parameters and nutritional status by measuring caloric intake, body weight, and protein levels. We produced neuronal injury by implanting a lateral ventricle cannula and giving daily ICV saline bolus injections, which increased hepatic 20S proteasome mRNA and enzymatic activity while reducing caloric intake, body weight, and protein levels compared to controls. Administration of ICV anti-CNTF antibodies (but not control antibodies) prevented these effects. Addition of exogenous CNTF augmented the weight loss along with the increases in 20S proteasome mRNA and proteolytic activity induced by neuronal injury. We conclude that CNTF decreases lean body weight through a combination of appetite inhibition and UPP pathway activation.     

Lyapunov functions for a generalized Gause-type model

Lyapunov functions are given to prove the global asymptotic stability of a large class of predator-prey models, including the ones in which the intrinsic growth rate of the prey follows the Ricker-law or the Odell generalization of the logistic law, and the functional predator response is of Holling type.Work supported by M.U.R.S.T., 60%.     

Dissociating ocular dominance column development and ocular dominance plasticity: a neurotrophic model

 Recent experimental data indicate that both neurotrophic factors (NTFs) and intracortical inhibitory circuitry are implicated in the development and plasticity of ocular dominance columns. We extend a neurotrophic model of developmental synaptic plasticity, which previously failed to account correctly for the differences between monocular deprivation and binocular deprivation, and show that the inclusion of lateral cortical inhibition is indeed necessary in understanding the effects of visual deprivation in the model. In particular, we argue that monocular deprivation causes a differential shift in the balance between inhibition and excitation in cortical columns, down-regulating NTFs in deprived-eye columns and up-regulating NTFs in undeprived-eye columns; during binocular deprivation, however, no such shift occurs. We thus postulate that the response to visual deprivation is at the level of the cortical circuit, while the mechanisms of afferent segregation are at the molecular or cellular level. Such a dissociation is supported by recent experimental work challenging the assumption that columnar organisation develops in an activity-dependent, competitive fashion. Our extended model also questions recent attempts to distinguish between heterosynaptic and homosynaptic models of synaptic plasticity. Received: 17 April 2001 / Accepted in revised form: 7 November 2001     

Aberrant adhesion impacts early development in a Dictyostelium model for juvenile neuronal ceroid lipofuscinosis

Neuronal ceroid lipofuscinosis (NCL), also known as Batten disease, refers to a group of severe neurodegenerative disorders that primarily affect children. The most common subtype of the disease is caused by loss-of-function mutations in CLN3, which is conserved across model species from yeast to human. The precise function of the CLN3 protein is not known, which has made targeted therapy development challenging. In the social amoeba Dictyostelium discoideum, loss of Cln3 causes aberrant mid-to-late stage multicellular development. In this study, we show that Cln3-deficiency causes aberrant adhesion and aggregation during the early stages of Dictyostelium development. cln3^? cells form ～30% more multicellular aggregates that are comparatively smaller than those formed by wild-type cells. Loss of Cln3 delays aggregation, but has no significant effect on cell speed or cAMP-mediated chemotaxis. The aberrant aggregation of cln3^? cells cannot be corrected by manually pulsing cells with cAMP. Moreover, there are no significant differences between wild-type and cln3^? cells in the expression of genes linked to cAMP chemotaxis (e.g., adenylyl cyclase, acaA; the cAMP receptor, carA; cAMP phosphodiesterase, pdsA; g-protein α 9 subunit, gpaI). However, during this time in development, cln3^? cells show reduced cell-substrate and cell-cell adhesion, which correlate with changes in the levels of the cell adhesion proteins CadA and CsaA. Specifically, loss of Cln3 decreases the intracellular level of CsaA and increases the amount of soluble CadA in conditioned media. Together, these results suggest that the aberrant aggregation of cln3^? cells is due to reduced adhesion during the early stages of development. Revealing the molecular basis underlying this phenotype may provide fresh new insight into CLN3 function.     

Prefoldin 5 is required for normal sensory and neuronal development in a murine model

Molecular chaperones and co-chaperones are crucial for cellular development and maintenance as they assist in protein folding and stabilization of unfolded or misfolded proteins. Prefoldin (PFDN), a ubiquitously expressed heterohexameric co-chaperone, is necessary for proper folding of nascent proteins, in particular, tubulin and actin. Here we show that a genetic disruption in the murine Pfdn5 gene, a subunit of prefoldin, causes a syndrome characterized by photoreceptor degeneration, central nervous system abnormalities, and male infertility. Our data indicate that a missense mutation in Pfdn5, may cause these phenotypes through a reduction in formation of microtubules and microfilaments, which are necessary for the development of cilia and cytoskeletal structures, respectively. The diversity of phenotypes demonstrated by models carrying mutations in different PFDN subunits suggests that each PFDN subunit must confer a distinct substrate specificity to the prefoldin holocomplex.     

Dissection of a model for neuronal parabolic bursting

We have obtained new insight into the mechanisms for bursting in a class of theoretical models. We study Plant's model [24] for Aplysia R-15 to illustrate our view of these so-called parabolic bursters, which are characterized by low spike frequency at the beginning and end of a burst. By identifying and analyzing the fast and slow processes we show how they interact mutually to generate spike activity and the slow wave which underlies the burst pattern. Our treatment is essentially the first step of a singular perturbation approach presented from a geometrical viewpoint and carried out numerically with AUTO [12]. We determine the solution sets (steady state and oscillatory) of the fast subsystem with the slow variables treated as parameters. These solutions form the slow manifold over which the slow dynamics then define a burst trajectory. During the silent phase of a burst, the solution trajectory lies approximately on the steady state branch of the slow manifold and during the active phase of spiking, the trajectory sweeps through the oscillation branch. The parabolic nature of bursting arises from the (degenerate) homoclinic transition between the oscillatory branch and the steady state branch. We show that, for some parameter values, the trajectory remains strictly on the steady state branch (to produce a resting steady state or a pure slow wave without spike activity) or strictly in the oscillatory branch (continuous spike activity without silent phases). Plant's model has two slow variables: a calcium conductance and the intracellular free calcium concentration, which activates a potassium conductance. We also show how bursting arises from an alternative mechanism in which calcium inactivates the calcium current and the potassium conductance is insensitive to calcium. These and other biophysical interpretations are discussed.     

Docosahexaenoic acid promotes hippocampal neuronal development and synaptic function

Docosahexaenoic acid (DHA, 22:6 n -3), the major polyunsaturated fatty acid accumulated in the brain during development, has been implicated in learning and memory, but underlying cellular mechanisms are not clearly understood. Here, we demonstrate that DHA significantly affects hippocampal neuronal development and synaptic function in developing hippocampi. In embryonic neuronal cultures, DHA supplementation uniquely promoted neurite growth, synapsin puncta formation and synaptic protein expression, particularly synapsins and glutamate receptors. In DHA-supplemented neurons, spontaneous synaptic activity was significantly increased, mostly because of enhanced glutamatergic synaptic activity. Conversely, hippocampal neurons from DHA-depleted fetuses showed inhibited neurite growth and synaptogenesis. Furthermore, n -3 fatty acid deprivation during development resulted in marked decreases of synapsins and glutamate receptor subunits in the hippocampi of 18-day-old pups with concomitant impairment of long-term potentiation, a cellular mechanism underlying learning and memory. While levels of synapsins and NMDA receptor subunit NR2A were decreased in most hippocampal regions, NR2A expression was particularly reduced in CA3, suggesting possible role of DHA in CA3-NMDA receptor-dependent learning and memory processes. The DHA-induced neurite growth, synaptogenesis, synapsin, and glutamate receptor expression, and glutamatergic synaptic function may represent important cellular aspects supporting the hippocampus-related cognitive function improved by DHA.     

A transient role for ciliary neurotrophic factor in chick photoreceptor development

Previous studies suggest that ciliary neurotrophic factor (CNTF) may represent one of the extrinsic signals controlling the development of vertebrate retinal photoreceptors. In dissociated cultures from embryonic chick retina, exogenously applied CNTF has been shown to act on postmitotic rod precursor cells, resulting in an two- to fourfold increase in the number of cells acquiring an opsin-positive phenotype. We now demonstrate that the responsiveness of photoreceptor precursors to CNTF is confined to a brief phase between their final mitosis and their terminal differentiation owing to the temporally restricted expression of the CNTF receptor (CNTFRα). As shown immunocytochemically, CNTFRα expression in the presumptive photoreceptor layer of the chick retina starts at embryonic day 8 (E8) and is rapidly down-regulated a few days later prior to the differentiation of opsin-positive photoreceptors, both in vivo and in dissociated cultures from E8. We further show that the CNTF-dependent in vitro differentiation of rods is followed by a phase of photoreceptor-specific apoptotic cell death. The loss of differentiated rods during this apoptotic phase can be prevented by micromolar concentrations of retinol. Our results provide evidence that photoreceptor development depends on the sequential action of different extrinsic signals. The time course of CNTFRα expression and the in vitro effects suggest that CNTF or a related molecule is required during early stages of rod differentiation, while differentiated rods depend on additional protective factors for survival. © 1998 John Wiley & Sons, Inc. J Neurobiol 37: 672–683, 1998     

A model for evoked activity of hippocampal neuronal population

A system of equations governing the activity of hippocampal neuron populations is proposed. This continual firing-rate model is aimed to simulate evoked potentials and synchronous wave activity of the neural tissue. The populations of excitatory and inhibitory neurons and the types of synaptic receptors are distinguished. The model is based on the idea of control and averaging of Hodgkin-Huxley equations, a simple model of a threshold elicitation of population action potential bursts, approximations of synaptic currents by the second-order differential equations, and hyperbolic partial derivative equation of axonal excitation propagation. The model was fitted to intracellular cordings of postsynaptic potentials and postsynaptic currents in CA1 of rat hippocampal slices.     

Long-term culture of mouse cortical neurons as a model for neuronal development, aging, and death

A long-term cell culture system was used to study maturation, aging, and death of cortical neurons. Mouse cortical neurons were maintained in culture in serum-free medium (Neurobasal supplemented with B27) for 60 days in vitro (DIV). The levels of several proteins were evaluated by immunoblotting to demonstrate that these neurons matured by developing dendrites and synapses and remained continuously healthy for 60 DIV. During their maturation, cortical neurons showed increased or stable protein expression of glycolytic enzyme, synaptophysin, synapsin IIa, alpha and beta synucleins, and glutamate receptors. Synaptogenesis was prominent during the first 15 days and then synaptic markers remained stable through DIV60. Very early during dendritic development at DIV3, beta-synuclein (but not alpha-synuclein) was localized at the base of dendritic growth cones identified by MAP2 and alpha-amino-3-hydroxy-5-methyl-4-isoxazole (AMPA) receptor GluR1. In mature neurons, alpha and beta synucleins colocalized in presynaptic axon terminals. Expression of N-methyl-D-aspartate (NMDA) and AMPA receptors preceded the formation of synapses. Glutamate receptors continued to be expressed strongly through DIV60. Cortical neurons aging in vitro displayed a complex profile of protein damage as identified by protein nitration. During cortical neuron aging, some proteins showed increased nitration, while other proteins showed decreased nitration. After exposure to DNA damaging agent, young (DIV5) and old (DIV60) cortical neurons activated apoptosis mechanisms, including caspase-3 cleavage and poly(ADP)-ribose polymerase inactivation. We show that cultured mouse cortical neurons can be maintained for long term. Cortical neurons display compartmental changes in the localization of synucleins during maturation in vitro. These neurons sustain protein nitration during aging and exhibit age-related variations in the biochemistry of neuronal apoptosis.     

Effect of neurotrophic factors on neuronal stem cell death

Neural cell survival is an essential concern in the aging brain and many diseases of the central nervous system. Neural transplantation of the stem cells are already applied to clinical trials for many degenerative neurological diseases, including Huntington\'s disease, Parkinson\'s disease, and strokes. A critical problem of the neural transplantation is how to reduce their apoptosis and improve cell survival. Neurotrophic factors generally contribute as extrinsic cues to promote cell survival of specific neurons in the developing mammalian brains, but the survival factor for neural stem cell is poorly defined. To understand the mechanism controlling stem cell death and improve cell survival of the transplanted stem cells, we investigated the effect of plausible neurotrophic factors on stem cell survival. The neural stem cell, HiB5, when treated with PDGF prior to transplantation, survived better than cells without PDGF. The resulting survival rate was two fold for four weeks and up to three fold for twelve weeks. When transplanted into dorsal hippocampus, they migrated along hippocampal alveus and integrated into pyramidal cell layers and dentate granule cell layers in an inside out sequence, which is perhaps the endogenous pathway that is similar to that in embryonic neurogenesis. Promotion of the long term-survival and differentiation of the transplanted neural precursors by PDGF may facilitate regeneration in the aging adult brain and probably in the injury sites of the brain.     

A human neuronal tissue culture model for Lesch-Nyhan disease

Mutations in the gene encoding the purine salvage enzyme, hypoxanthine-guanine phosphoribosyltransferase (HPRT) cause Lesch-Nyhan disease, a neurodevelopmental disorder characterized by cognitive, neurological, and behavioral abnormalities. Despite detailed knowledge of the enzyme's function, the key pathophysiological changes that accompany loss of purine recycling are unclear. To facilitate delineating the consequences of HPRT deficiency, four independent HPRT-deficient sublines of the human dopaminergic neuroblastoma, SK-N-BE(2) M17, were isolated by targeted mutagenesis with triple helix-forming oligonucleotides. As a group, these HPRT-deficient cells showed several significant abnormalities: (i) impaired purine recycling with accumulation of hypoxanthine, guanine, and xanthine, (ii) reduced guanylate energy charge and GTP:GDP ratio, but normal adenylate energy charge and no changes in any adenine nucleotide ratios, (iii) increased levels of UTP and NADP+, (iv) reduced DOPA decarboxylase, but normal monoamines, and (v) reduction in cell soma size. These cells combine the analytical power of multiple lines and a human, neuronal origin to provide an important tool to investigate the pathophysiology of HPRT deficiency.