Full system bifurcation analysis of endocrine bursting models

Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.     

Heteroclinic bifurcation in a ratio-dependent predator-prey system

In this paper we study the heteroclinic bifurcation in a general ratio-dependent predator-prey system. Based on the results of heteroclinic loop obtained in [J. Math. Biol. 43(2001): 221–246], we give parametric conditions of the existence of the heteroclinic loop analytically and describe the heteroclinic bifurcation surface in the parameter space, so as to answer further the open problem raised in [J. Math. Biol. 42(2001): 489–506].Supported by NNSFC(China) # 10171071, TRAPOYT and China MOE Research Grant # 2002061003     

Quantitative analysis of the Hopf bifurcation in the Goodwin n-dimensional metabolic control system

We study, from a quantitative point of view, the Hopf bifurcation in an ODE model of feedback control type introduced by Goodwin (1963) to describe the dynamics of end-product inhibition of gene activity. We formally prove that the exchange of linear stability of the positive equilibrium in the n-dimensional Goodwin system with equal reaction constants coexists with a Hopf bifurcation of nontrivial periodic solutions emanating from this equilibrium, without any further restriction on the dimension n 3 or on the Hill coefficient . The direction of the bifurcation, and the stability and the period of the bifurcating orbits are estimated by means of the algorithm proposed by Hassard et al. (1981).Supported by MURST 40/60%     

Maintenance of polygenic variation through mutation-selection balance: bifurcation analysis of a biallelic model

Biallelic models which ignore linkage disequilibrium have been used to study variability maintained by mutation in the presence of Gaussian stabilizing selection. Recent work of Barton (1986) showed that these models have stable equilibria at which the mean phenotype differed from the optimum, and that the variability maintained at such equilibria would be higher than at the symmetric equilibria calculated by Bulmer (1980) and others. Here I determine the bifurcation structure of this model, and confirm and extend Barton's results. The form of the bifurcations gives information about the domains of attraction of various equilibria, and shows why the nonsymmetric equilibria may not be observed. The techniques may prove useful in the analysis of other population genetic models.     

Bifurcation analysis of periodic SEIR and SIR epidemic models

The bifurcations of the periodic solutions of SEIR and SIR epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.     

A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

Stabilization of inhomogeneous patterns in a diffusion-reaction system under structural and parametric uncertainties

Many phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction-diffusion mechanisms. The FitzHugh-Nagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion-reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feedback controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feedback logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments.     

Modeling the joint epidemics of TB and HIV in a South African township

We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control measures might change the course of these epidemics. Condom promotion, increased TB detection and TB preventive therapy have a clear positive effect. The impact of antiretroviral therapy on the incidence of HIV is unclear and depends on the extent to which it reduces sexual transmission. However, our analysis suggests that it will greatly reduce the TB notification rate.     

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

 We study the existence and stability of traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons with synaptic coupling. This provides a simple model of excitable neural tissue. We first derive a self-consistency condition for the existence of traveling waves, which generates a dispersion relation between velocity and wavelength. We use this to investigate how wave-propagation depends on various parameters that characterize neuronal interactions such as synaptic and axonal delays, and the passive membrane properties of dendritic cables. We also establish that excitable networks support the propagation of solitary pulses in the long-wavelength limit. We then derive a general condition for the (local) asymptotic stability of traveling waves in terms of the characteristic equation of the linearized firing time map, which takes the form of an integro-difference equation of infinite order. We use this to analyze the stability of solitary pulses in the long-wavelength limit. Solitary wave solutions are shown to come in pairs with the faster (slower) solution stable (unstable) in the case of zero axonal delays; for non-zero delays and fast synapses the stable wave can itself destabilize via a Hopf bifurcation. Received: 27 October 1998     

Retrieval of a Micra transcatheter pacing system in a heart with a preexisting lead

We report the case of a 74-year-old man with a previously implanted pacemaker lead. He had undergone Medtronic? Micra Transcatheter Pacing System (TPS, Medtronic plc, MN, USA) implantation because of lead fracture. We implanted a new TPS and retrieved the dislodged one. We used a multiple-loop snare (EN snare^®) and an 8.5F steerable sheath (Agilis NXT; St. Jude Medical, St Paul, MN, USA). The TPS was obstructed by the chordae tendineae of the tricuspid valve and the pacemaker lead. We pushed the TPS to the apex site; this enabled us to move the TPS away from the chordae tendineae and pacemaker lead. The TPS body was caught in the inferior vena cava and was successfully retrieved. To our knowledge, this is the first case reporting TPS retrieval in a heart with preexisting lead.     

Bifurcational and dynamical analysis of a continuous biofilm reactor

A dynamical model of a continuous biofilm reactor is presented. The reactor consists of a three-phase internal loop airlift operated continuously with respect to the liquid and gaseous phases, and batchwise with respect to the immobilized cells. The model has been applied to the conversion of phenol by means of immobilized cells of Pseudomonas sp. OX1 whose metabolic activity was previously characterized (Viggiani, A., Olivieri, G., Siani, L., Di Donato, A., Marzocchella, A., Salatino, P., Barbieri, P., Galli, E., 2006. An airlift biofilm reactor for the biodegradation of phenol by Pseudomonas stutzeri OX1. Journal of Biotechnology 123, 464-477). The model embodies the key processes relevant to the reactor performance, with a particular emphasis on the role of biofilm detachment promoted by the fluidized state. Results indicate that a finite loading of free cells establishes even under operating conditions that would promote wash out of the suspended biophase. The co-operative/competitive effects of free cells and immobilized biofilm result in rich bifurcational patterns of the steady state solutions of the governing equations, which have been investigated in the phase plane of the process parameters. Direct simulation under selected operating conditions confirms the importance of the dynamical equilibrium establishing between the immobilized and the suspended biophase and highlights the effect of the initial value of the biofilm loading on the dynamical pattern.     

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus. The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles. In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.     

Preparation and optimization of tablets containing a self-nano-emulsifying drug delivery system loaded with rosuvastatin

Background: Rosuvastatin (ROS) calcium is the latest synthetic drug in the statin group that has an anti-hyperlipidemic activity. It is available as tablets, and its poor aqueous solubility, slow dissolution rate and low-absorption extent result in less than 20% bioavailability and about 80% being excreted unchanged in the feces without absorption.

Objective: To utilize nanotechnology to reformulate ROS as a self-nano-emulsifying drug delivery system (SNEDDS), and utilizing design optimization to fabricate the SNEDDS as a tablet.

Methods: The solubility of ROS in different oils, surfactants and co-surfactants was tested. Pseudo-ternary phase diagrams were developed and various SNEDDS formulations were prepared and evaluated regarding globule size, self-emulsification, viscosity and transmittance. The optimized system was examined using transmission electron microscopy. The self-nano-emulsifying tablets were prepared using two types of nano-silica and different percentages of Avicel as a binder and Ac-Di-Sol as a disintegrant. The prepared tablets were evaluated for their physicochemical properties. Bioavailability in human volunteers was assessed.

Results: A SNEDDS system was successfully developed with a droplet size range of 15?nm and a composition of 10% Labrafac, 80% Cremophore RH40 and 10% Propylene glycol. The optimized tablet formula contained: hydrophilic nano-silica, 3% Ac-Di-Sol and 30% Avicel. The pharmacokinetic study revealed that the bioavailability was enhanced by more than 2.4-fold compared with the commercially available tablet.

Conclusions: Tablets containing SNEDDS loaded with ROS represent a promising novel formula that has higher gastrointestinal absorption and enhanced systemic bioavailability.     

Use of the glucose oxidase system for estimation of oxygen transfer rate in a solid-state bioreactor

The glucose oxidase system was adapted for estimation of the overall oxygen transfer rate in a periodic pressure oscillating, solid-state bioreactor. Enzyme concentration of 40 ml enzyme preparation L⁻¹ was found adequate to give linear gluconic acid production and attain maximal oxygen absorption rates. At 4 atm and 30°C, the oxygen transfer rate reached 892 mmol kg⁻¹ initial dry matter h⁻¹ in this system, while only 121 mmol kg⁻¹ initial dry matter h⁻¹ was obtained in a conventional static tray bioreactor.     

The dynamics of a Lotka–Volterra predator–prey model with state dependent impulsive harvest for predator

According to the economic and biological aspects of renewable resources management, we propose a Lotka–Volterra predator–prey model with state dependent impulsive harvest. By using the Poincaré map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three under some conditions. Numerical results are carried out to illustrate the feasibility of our main results. The bifurcation diagrams of periodic solutions are obtained by using the numerical simulations, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex.     

Coupling of the Deformation of a Model Endothelial Cell and a Steady Laminar Flow

Abstract

Mechanical forces influence endothelial cell's (EC) morphology and functions. In this work it was proposed a numerical analysis of steady laminar flows near a modelled monolayer of elastic ECs in order to determine the local distributions of mechanical forces on the surface and inside the cell.

Numerical results showed that the flow induced non uniform mechanical stresses on cell surface and led to a cell deformation. These numerical results were compared with experimental measurements of the deformation of cultured human aortic endothelial cells under flow. It will be interesting to study eventual correlations between the distributions of biological receptors (cytoskeleton, adhesion molecules, etc.) and that of the non-uniform mechanical forces.     

Efficient expansion of mesenchymal stromal cells in a disposable fixed bed culture system

The need for efficient and reliable technologies for clinical‐scale expansion of mesenchymal stromal cells (MSC) has led to the use of disposable bioreactors and culture systems. Here, we evaluate the expansion of cord blood‐derived MSC in a disposable fixed bed culture system. Starting from an initial cell density of 6.0 × 10⁷ cells, after 7 days of culture, it was possible to produce of 4.2(±0.8) × 10⁸ cells, which represents a fold increase of 7.0 (±1.4). After enzymatic retrieval from Fibra‐Cell disks, the cells were able to maintain their potential for differentiation into adipocytes and osteocytes and were positive for many markers common to MSC (CD73, CD90, and CD105). The results obtained in this study demonstrate that MSC can be efficiently expanded in the culture system. This novel approach presents several advantages over the current expansion systems, based on culture flasks or microcarrier‐based spinner flasks and represents a key element for MSC cellular therapy according to GMP compliant clinical‐scale production system. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 568–572, 2013     

Bifurcation analysis of a predator-prey model with predators using hawk and dove tactics

Most classical prey-predator models do not take into account the behavioural structure of the population. Usually, the predator and the prey populations are assumed to be homogeneous, i.e. all individuals behave in the same way. In this work, we shall take into account different tactics that predators can use for exploiting a common self-reproducing resource, the prey population. Predators fight together in order to keep or to have access to captured prey individuals. Individual predators can use two behavioural tactics when they encounter to dispute a prey, the classical hawk and dove tactics. We assume two different time scales. The fast time scale corresponds to the inter-specific searching and handling for the prey by the predators and the intra-specific fighting between the predators. The slow time scale corresponds to the (logistic) growth of the prey population and mortality of the predator. We take advantage of the two time scales to reduce the dimension of the model and to obtain an aggregated model that describes the dynamics of the total predator and prey densities at the slow time scale. We present the bifurcation analysis of the model and the effects of the different predator tactics on persistence and stability of the prey-predator community are discussed.