Electrical transmission between nonsymmetrical neurons in the leech ganglion

The extent of the electrical transmission (ET) between different nonsymmetrical neurons in the segmental ganglion of the abdominal nerve chain of the leechHirudo medicinalis L. was investigated. ET was demonstrated by simultaneous recording of the intracellular potentials in two neurons when bursts of a polarizing current were passed alternately into each of them. At least 16 different pairs of nonsymmetrical identifiable neurons with ET which, as a rule, was symmetrical with a coefficient of attenuation of the order of 10 in the direction of greater effectiveness, were found. In different pairs of nonsymmetrical identifiable neurons, the ET of hyperpolarizing currents as a rule is more effective from neurons with a higher frequency of background activity. The presence of ET was also shown between many nonsymmetrical unidentifiable neurons of the ganglion. The assymetrical ET in some of the combinations of neurons investigated did not have rectifying properties. The direction of the ET was retained in them for any polarity of the polarizing current. In some experiments hyperpolarization of one of the neurons of a pair evoked depolarization and an increase in the frequency of the impulse activity of the other, while depolarization had the opposite effect ("negative" ET). It was concluded that the broad extent of the ET between nonsymmetrical neurons indicates its important role in the integrating activity of the central nervous system of the leech.Institute of Higher Nervous Activity and Neurophysiology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 3, No. 5, pp. 550–556, September–October, 1971.     

Synthesis of novel triplet drugs with 1,3,5-trioxazatriquinane skeletons and their pharmacologies. 1: Synthesis of triplet drugs with morphinan skeletons

We synthesized symmetrical and nonsymmetrical triplet drugs with 1,3,5-trioxazatriquinane skeletons. The isolation of key intermediates, oxazoline dimers, made it possible to effectively produce nonsymmetrical triplets. Among the synthesized triplets, KNT-93, composed of three identical opioid μ receptor agonists, showed dose-dependent antinociception via the μ receptor. The effect was 56-fold more potent than that of morphine, a representative μ agonist. The profound analgesic effect induced by KNT-93 might result from simultaneous occupation of three μ opioid receptors.     

Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?

The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention.     

Synthesis,antiviral activity and pharmacokinetics of P1/P1' substituted 3-aminoindazole cyclic urea HIV protease inhibitors

A series of P1/P1' substituted cyclic urea analogues were prepared in an attempt to increase the intra-cellular antiviral potency of the nonsymmetrical 3-aminoindazoles DMP 850 and DMP 851. The effect of alkyl substitution of the P1/P1' residues on cellular antiviral potency, protein binding, resistance profile and pharmacokinetics are described.     

A convenient procedure for the synthesis of nonsymmetrical bivalent selective serotonin reuptake inhibitors using polymer-supported reagents

A convenient synthesis of nonsymmetrical bivalent inhibitors of the serotonin transporter is described. The synthesis utilizes polymer-supported reagents that allow for rapid access to novel bivalent ligands without the need for isolation or purification of synthetic intermediates.     

Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models

When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifurcations, and homoclinic loop bifurcations. These may be important epidemiologically in that they demonstrate the possibility of infection outbreak and collapse, or autonomous periodic coexistence of disease and host. The possible mechanisms leading to nonlinear incidence rates are discussed. Finally, a modified general criterion for supercritical or subcritical Hopf bifurcation of 2-dimensional systems is presented.     

Arterial bifurcations in the human retina

The branching angles and relative diameters of blood vessels in 51 arterial bifurcations in the retina of a normal human eye were measured. In eight other bifurcations, only the total branching angles were measured. The results are compared with theoretical predictions in an attempt to understand the physiological principles governing branching in the cardiovascular system.     

Improved reduced-order modelling of cerebrovascular flow distribution by accounting for arterial bifurcation pressure drops

Reduced-order modelling offers the possibility to study global flow features in cardiovascular networks. In order to validate these models, previous studies have been conducted in which they compared 3D computational fluid dynamics simulations with reduced-order simulations. Discrepancies have been reported between the two methods. The loss of energy at the bifurcations is usually neglected and has been pointed out as a possible explanation for these discrepancies. We present distributed lumped models of cerebrovasculatures created automatically from 70 cerebrovascular networks segmented from 3D angiograms. The outflow rate repartitions predicted with and without modelling the energy loss at the bifurcations are compared against 3D simulations. When neglecting the energy loss at the bifurcations, the flow rates though the anterior cerebral arteries are overestimated by 4.7±6.8% (error relative to the inlet flow rate, mean ± standard deviation), impacting the remaining volume of flow going to the other vessels. When the energy loss is modelled, this error is dropping to 0.1±3.2%. Overall, over the total of 337 outlet vessels, when the energy losses at the bifurcations are not modelled the 95% of agreement is in the range of ±13.5% and is down to ±6.5% when the energy losses are considered. With minimal input and computational resources, the presented method can estimate the outflow rates reliably. This study constitutes the largest validation of a reduced-order flow model against 3D simulations. The impact of the energy loss at the bifurcations is here demonstrated for cerebrovasculatures but can be applied to other physiological networks.     

Hopf bifurcations in multiple-parameter space of the Hodgkin-Huxley equations II. Singularity theoretic approach and highly degenerate bifurcations

In the Hodgkin-Huxley equations (HH), we have identified the parameter regions in which either two stable periodic solutions with different amplitudes and periods and an equilibrium point or two stable periodic solutions coexist. The global structure of bifurcations in the multiple-parameter space in the HH suggested that the bistabilities of the periodic solutions are associated with the degenerate Hopf bifurcation points by which several qualitatively different behaviors are organized. In this paper, we clarify this by analyzing the details of the degenerate Hopf bifurcations using the singularity theory approach which deals with local bifurcations near a highly degenerate fixed point. Received: 23 April 1999 / Accepted in revised form: 24 September 1999     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare-Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

Global bifurcations of a periodically forced nonlinear oscillator

The effects of periodic pulsatile stimulation on a simple mathematical model of biological oscillations, called the radial isochron clock (RIC), are investigated as a function of stimulus frequency and amplitude. This system can be reduced to a two parameter, one-dimensional circle map. Numerical and topological methods are used to give a very detailed picture of the observed bifurcations over the complete range of parameters. The bifurcations are generic for a class of models which generalize the RIC.     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

具有三时滞Lotka-Volterra互惠系统的Hopf分支

建立了具有三个时滞的Lotka-Volterra互惠系统;获得了正平衡点和Hopf分支存在的条件等;并对所获得的结果进行了数值模拟．     

Bifurcations and chaos in a time-discrete integral model of population dynamics.

The properties of a time-discrete integral model of population dynamics are studied. The model equations define a dynamic system in the cone of nonnegative functions in L2. The presence of dissipator caused by spatial interaction is detected. Several bifurcations of codimensions 1 and 2 are investigated. The model may go over to chaotic behavior through a sequence of period-doubling bifurcations. The Lyapunov exponents and dimension of an attractor are found. The higher dimension of an attractor is shown to be a common feature of chaotic behavior.     

Bifurcation analysis of the Nowak-Bangham model in CTL dynamics

This paper investigates the local bifurcations of a CTL response model published by Nowak and Bangham [M.A. Nowak, C.R.M. Bangham, Population dynamics of immune responses to persistent viruses, Science 272 (1996) 74]. The Nowak-Bangham model can have three equilibria depending on the basic reproduction number, and generates a Hopf bifurcation through two bifurcations of equilibria. The main result shows a sufficient condition for the interior equilibrium to have a unique bifurcation point at which a simple Hopf bifurcation occurs. For this proof, some new techniques are developed in order to apply the method established by Liu [W.M. Liu, Criterion of Hopf bifurcations without using eigenvalues, J. Math. Anal. Appl. 182 (1) (1994) 250]. In addition, to demonstrate the result obtained theoretically, some bifurcation diagrams are presented with numerical examples.     

High codimensional bifurcation analysis to a six-neuron BAM neural network

In this article, the high codimension bifurcations of a six-neuron BAM neural network system with multiple delays are addressed. We first deduce the existence conditions under which the origin of the system is a Bogdanov–Takens singularity with multiplicities two or three. By choosing the connection coefficients as bifurcation parameters and using the formula derived from the normal form theory and the center manifold, the normal forms of Bogdanov–Takens and triple zero bifurcations are presented. Some numerical examples are shown to support our main results.     

[K+] dependence of open-channel conductance in cloned inward rectifier potassium channels (IRK1, Kir2.1).

Potassium conduction through unblocked inwardly rectifying (IRK1, Kir2.1) potassium channels was measured in inside-out-patches from Xenopus oocytes, after removal of polyamine-induced strong inward rectification. Unblocked IRK1 channel current-voltage (I-V) relations show very mild inward rectification in symmetrical solutions, are linearized in nonsymmetrical solutions that bring the K+ reversal potential to extreme negative values, and follow Goldman-Hodgkin-Katz constant field equation at extreme positive E alpha. When intracellular K+ concentration (KIN) was varied, at constant extracellular K+ concentration (KOUT) the conductance at the reversal potential (GREV) followed closely the predictions of the Goldman-Hodgkin-Katz constant field equation at low concentrations and saturated sharply at concentrations of > 150 mM. Similarly, when KOUT was varied, at constant KIN, GREV saturated at concentrations of > 150 mM. A square-root dependence of conductance on KOUT is a well-known property of inward rectifier potassium channels and is a property of the open channel. A nonsymmetrical two-site three-barrier model can qualitatively explain both the I-V relations and the [K+] dependence of conductance of open IRK1 (Kir2.1) channels.     

Effects of curved inlet tubes on air flow and particle deposition in bifurcating lung models

In vivo bifurcating airways are complex and the airway segments leading to the bifurcations are not always straight, but curved to various degrees. How do such curved inlet tubes influence the motion as well as local deposition and hence the biological responses of inhaled particulate matter in lung airways? In this paper steady laminar dilute suspension flows of micron-particles are simulated in realistic double bifurcations with curved inlet tubes, i.e., 0 degrees < or =theta< or =90 degrees, using a commercial finite-volume code with user-enhanced programs. The resulting air-flow patterns as well as particle transport and wall depositions were analyzed for different flow inlet conditions, i.e., uniform and parabolic velocity profiles, and geometric configurations. The curved inlet segments have quite pronounced effects on air-flow, particle motion and wall deposition in the downstream bifurcating airways. In contrast to straight double bifurcations, those with bent parent tubes also exhibit irregular variations in particle deposition efficiencies as a function of Stokes number and Reynolds number. There are fewer particles deposited at mildly curved inlet segments, but the particle deposition efficiencies at the downstream sequential bifurcations vary much when compared to those with straight inlets. Under certain flow conditions in sharply curved lung airways, relatively high, localized particle depositions may take place. The findings provide necessary information for toxicologic or therapeutic impact assessments and for global lung dosimetry models of inhaled particulate matter.     

Discontinuity induced bifurcations in a model of Saccharomyces cerevisiae

We perform a bifurcation analysis of the mathematical model of Jones and Kompala [K.D. Jones, D.S. Kompala, Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotechnol. 71 (1999) 105-131]. Stable oscillations arise via Andronov-Hopf bifurcations and exist for intermediate values of the dilution rate as has been noted from experiments previously. A variety of discontinuity induced bifurcations arise from a lack of global differentiability. We identify and classify discontinuous bifurcations including several codimension-two scenarios. Bifurcation diagrams are explained by a general unfolding of these singularities.     

Observance of period-doubling bifurcation and chaos in an autonomous ODE model for malaria with vector demography

We illustrate that an autonomous ordinary differential equation model for malaria transmission can exhibit period-doubling bifurcations leading to chaos when ecological aspects of malaria transmission are incorporated into the model. In particular, when demography, feeding, and reproductive patterns of the mosquitoes that transmit the malaria-causing parasite are explicitly accounted for, the resulting model exhibits subcritical bifurcations, period-doubling bifurcations, and chaos. Vectorial and disease reproduction numbers that regulate the size of the vector population at equilibrium and the endemicity of the malaria disease, respectively, are identified and used to simulate the model to show the different bifurcations and chaotic dynamics. A subcritical bifurcation is observed when the disease reproduction number is less than unity. This highlights the fact that malaria control efforts need to be long lasting and sustained to drive the infectious populations to levels below the associated saddle-node bifurcation point at which control is feasible. As the disease reproduction number increases beyond unity, period-doubling cascades that develop into chaos closely followed by period-halving sequences are observed. The appearance of chaos suggests that characterization of the physiological status of disease vectors can provide a pathway toward understanding the complex phenomena that are known to characterize the dynamics of malaria and other indirectly transmitted infections of humans. To the best of our knowledge, there is no known unforced continuous time deterministic host-vector transmission malaria model that has been shown to exhibit chaotic dynamics. Our results suggest that malaria data may need to be critically examined for complex dynamics.