Spread of discrete structural changes in synthetic polyanionic gel: a model of propagation of a nerve impulse

Thin fibers of cross-linked polyacrylate gel were prepared by inducing polymerization reaction inside long glass or Tygon tubings. By immersing these gel fibers in salt solutions containing both Ca(2+) and Na(+) at varying ratios, a discontinuous transition from the swollen state to the shrunken was demonstrated. A very sharp boundary was observed between the swollen and shrunken portions of the gel fiber. It was found possible to displace this sharp boundary continuously by application of a weak electric current. Based on the similarity in swelling behavior between nerve fibers and synthetic gel fibers, a non-myelinated nerve fiber carrying an impulse was treated as a cylindrical gel layer consisting of two distinct portions, a swollen (active) portion connected directly to the remaining shrunken (resting) portion. By applying the cable theory to this model of the nerve fiber, mathematical expressions describing the conduction velocity, the maximum rate of potential rise, etc. in terms of the electric parameters of the fiber were derived.     

The properties and propagation of a cardiac-like impulse in the skin of young tadpoles

Summary The contact relationships of skin cells in late embryos and young larvae of Xenopus laevis are described. Superficial cells are joined by tight or gap junctions at their outer periphery but elsewhere simple appositions are found. All-or-none impulses are evoked in the skin by electrical or mechanical stimuli (Fig. 3). Evidence is presented in favour of the view that these impulses are generated by the majority of skin cells and not by some neuronal element in the skin. The impulse propagates throughout the skin from any stimulated point (at average speed of 7.7 cm/sec) even when the animal is in distilled water. However, removal of Na⁺ from solutions bathing the inner skin surface or treatment with Tetrodotoxin abolishes the impulse indicating that it is Na⁺ dependent. Current injected into skin cells spreads to others so it is suggested that the impulse propagates by direct current flow from cell to cell. The neuroid conduction system in the skin of Xenopus tadpoles is compared to similar systems in coelenterates and to the propagation of the vertebrate cardiac impulse.Partly supported by an S.R.C. Fellowship.     

Wave propagation of a discrete SIR epidemic model with a saturated incidence rate

This paper is concerned with the traveling wave solutions for a discrete SIR epidemic model with a saturated incidence rate. We show that the existence and non-existence of the traveling wave solutions are determined by the basic reproduction number R0 of the corresponding ordinary differential system and the minimal wave speed c*. More specifically, we first prove the existence of the traveling wave solutions for R0>1 and c>c* via considering a truncated initial value problem and using the Schauder’s fixed point theorem. The existence of the traveling wave solutions with speed c=c? is then proved by using a limiting argument. The main difficulty is to show that the limit of a decreasing sequence of the traveling wave solutions with super-critical speeds is non-trivial. Finally, the non-existence of the traveling wave solutions for R0>1,00 is proved.     

Wave propagation of a discrete SIR epidemic model with a saturated incidence rate

This paper is concerned with the traveling wave solutions for a discrete SIR epidemic model with a saturated incidence rate. We show that the existence and non-existence of the traveling wave solutions are determined by the basic reproduction number R0 of the corresponding ordinary differential system and the minimal wave speed c*. More specifically, we first prove the existence of the traveling wave solutions for R0>1 and c>c* via considering a truncated initial value problem and using the Schauder’s fixed point theorem. The existence of the traveling wave solutions with speed c=c? is then proved by using a limiting argument. The main difficulty is to show that the limit of a decreasing sequence of the traveling wave solutions with super-critical speeds is non-trivial. Finally, the non-existence of the traveling wave solutions for R0>1,00 is proved.     

A perturbation method for the analysis of impulse propagation in a mathematical neuron model

A perturbation method is presented for the calculation of signal propagation velocities in a mathematical neuron model. Impulse frequencies and waveforms are also determined. The method uses a non-linear conduction model containing a small parameter, such that analytical solutions are possible, yet the inherently non-linear physiological phenomena involved, can be explained. A simple two-variable membrane equation is used, but the method is generally applicable to various more complete systems.     

Electrodiffusion model of a nerve impulse

Electrodiffusion equations are deduced which describe the formation of the action potential in the axone. It is suggested that the membrane dividing internal and external axone electrolytes after being stimulated with an electric impulse returns after some time to the initial "closed" state. It is shown that the overshut of the action potential takes place due to non-linear profile distortion of the shock wave of electrical field tension vector created by the movement of sodium and potassium ions through the membrane of the axone.     

Influence of dynamic gap junction resistance on impulse propagation in ventricular myocardium: a computer simulation study

The gap junction connecting cardiac myocytes is voltage and time dependent. This simulation study investigated the effects of dynamic gap junctions on both the shape and conduction velocity of a propagating action potential. The dynamic gap junction model is based on that described by Vogel and Weingart (J. Physiol. (Lond.). 1998, 510:177-189) for the voltage- and time-dependent conductance changes measured in cell pairs. The model assumes that the conductive gap junction channels have four conformational states. The gap junction model was used to couple 300 cells in a linear strand with membrane dynamics of the cells defined by the Luo-Rudy I model. The results show that, when the cells are tightly coupled (6700 channels), little change occurs in the gap junction resistance during propagation. Thus, for tight coupling, there are negligible differences in the waveshape and propagation velocity when comparing the dynamic and static gap junction representations. For poor coupling (85 channels), the gap junction resistance increases 33 MOmega during propagation. This transient change in resistance resulted in increased transjunctional conduction delays, changes in action potential upstroke, and block of conduction at a lower junction resting resistance relative to a static gap junction model. The results suggest that the dynamics of the gap junction enhance cellular decoupling as a possible protective mechanism of isolating injured cells from their neighbors.     

The universal properties of stem cells as pinpointed by a simple discrete model

The ability of a few stem-cells to repopulate a severely damaged bone marrow (BM) guarantees the stability of our physical existence, and facilitates successful BM transplantations. What are the basic properties of stem cells that enable the maintenance of the system's homeostasis? In the present work we attempt to answer this question by investigating a discrete (in time and phase-space) dynamical system. The model we present is shown to retrieve the essential properties of homeostasis, as reflected in BM functioning, namely, (a) to produce a constant amount of mature cells, and (b) to be capable of returning to this production after very large perturbations. The mechanism guaranteeing the fulfillment of these properties is extrinsic--negative feedback control in the micro-environment--and does not need additional stochastic assumptions. Nevertheless, the existence of a simple intrinsic control mechanism, a clock which determines the switch to differentiation, ascertains that the system does not admit non-trivial extinction states. This result may help clarifying some of the controversy about extrinsic versus intrinsic control over stem cell fate. It should be stressed that all conclusions are valid for any system containing progenitor and maturing cells.     

Effect of a DC external electric field on the properties of a nonuniform microwave discharge in hydrogen at reduced pressures

The effect of a dc external electrical field on the properties of a highly nonuniform electrode microwave discharge in hydrogen at a pressure of 1 Torr was studied using optical emission spectroscopy and selfconsistent two-dimensional simulations. It is shown that the negative voltage applied to the antenna electrode with respect to the grounded chamber increases the discharge radiation intensity, while the positive voltage does not affect the discharge properties. The simulation results agree well with the experimental data.     

Effect of space flight conditions on properties of hydrocarbon-oxidizing bacteria

Results of experiments on the Mir space station (EO-25 and EO-26) demonstrated that the conditions of orbital flight, primarily the cosmic radiation, was a mutagenic factor affecting both the genotype and phenotype of an oil-oxidizing bacterial strain, Mycobacterium flavescens EX-91. The emerging mutants differed from original culture by the rate of colony growth and the ability to ferment certain carbohydrates or synthesize beta-galactosidase. Changes in the rate of utilization of raw oil and individual hydrocarbon types (constituting model mixtures) suggest that cosmic radiation may serve as a means of obtaining mutant clones of microorganisms with new properties.     

Transport of a fluid in the lung interstitial space. A model of porous medium with distributed parameters

Velocity and behaviour of the fluid stream into lung interstitium was experimentally evaluated during and after hydrodynamic loading. A mathematical model of unsteady fluid movement in interstitium able to relaxation was proposed.     

Effects of Q-switched Nd:YAG laser irradiation on neural impulse propagation: I. Spinal cord.

We studied the effect of irradiation with Q-switched Nd:YAG laser light (1064 nm) on spinal cord dorsal column and dorsolateral white matter in anesthetized rats. To evoke a synchronous sensory input, the sciatic nerve was stimulated electrically and the resulting evoked spinal cord potential (SCP) recorded from the dorsal columns of the ipsilateral side. The waveshape of the SCP showed three components: an early positive peak (P1), representing the responses of the most rapidly conducting fibers, followed by two negative peaks (N1 and N2), which are mainly due to synaptic effects of the volley on dorsal horn cells located in dorsal grey matter. Laser irradiation at 50 mJ/pulse and above resulted in severe reduction in the amplitudes of N1 and N2. In contrast, there was either no reduction at all or only a slight decrease in the amplitude of P1. The selective loss of the synaptic field might be mediated by impairment of synaptic transmission or by loss of high threshold fiber input to dorsal horn neurones. In either event it is likely that the mechanism of the differential effects of laser irradiation on the components of the electrically evoked SCP is at least in part photothermally mediated, since intracord temperatures during laser application greatly exceeded the physiological range.     

The effects of discrete gap junction coupling on propagation in myocardium

A modified cable theory for a bi-domain model of myocardium that incorporates the effect of gap junctions as discrete objects coupling cardiac cells is derived. The theory is shown to be in agreement with a number of experiments that cannot be explained using standard continuous cable theory, and resolves some apparent contradictions on failure of propagation in two-dimensional anisotropic tissue. In addition, some as yet untested predictions of the theory are mentioned.     

Superposition of impulse activity in a rapidly-adapting afferent unit model

Mechanosensory afferent units consist of a parent axon, the peripheral axonal arborization, and the branch terminal mechanoreceptors. The present work uses a mathematical model to describe the contribution of a given number of rapidly-adapting mechanoreceptors to the impulse pattern of their parent axon. In the model impulses initiated by any driven mechanoreceptor instantaneously propagate orthodromically and antidromically. The model also incorporates the axonal absolute refractory period as well as ortho-and antidromically elicited recovery cycles. In separate computations, periodic or random (Poisson process) trains of short-duration stimuli at constant amplitude are delivered to a given number (N=2–30) of co-innervated mechanoreceptors. The superposition of component impulse trains always departs from the theoretical ideal (Poisson process). Such departures are attributable to: (i) the number of driven mechanoreceptors, when N is small, (ii) axonal absolute refractory period, during maximal amplitude stimulation, and (iii) antidromic recovery cycles as well as absolute refractoriness, during submaximal-amplitude stimulation. Computations reveal that this instantaneous reset model results in the elimination of information extracted by driven mechanoreceptors. Model predictions with Poisson stimulation at varied amplitudes are compared to G-hair afferent unit responses to analogous stimulation. Qualitatively opposite results with respect to parent axonal impulse patterns imply that the axonal arborization is not simply a substrate for impulse propagation from branch terminals to parent axon.