Mathematical analysis of optimal multichannel filtering for nerve signals

This paper extends recent analyses (Roberts and Hartline, 1975; Ouztöreli and Stein, 1977) of optimal linear filters for separating neural signals from more than one electrode site. Roberts and Hartline's result, using a matched filter criterion, represents one of a class of optimal filters with different, but symmetrical, output waveforms derived by Ouztöreli and Stein (1977). Another narrow bandwidth filter of this class will give the optimal results according to an energy criterion, but may be less useful in practical situations.This work was partially supported by the Medical Research Council of Canada (Grant MRC-MT3307), the Technical Research Council of Denmark (Grant 516-6703 E406) and the National Research Council of Canada (Grant NRC A-4345)     

A kinetic study of muscular contractions

Summary In the present work the kinetics of muscular contractions are studied, based on a three-state model which is introduced in Section I. The general properties of this class of models for muscular contractions are derived in Sections II–VI. The kinetic equations are solved for four particular examples in Sections VII–X. These analytical results should be useful for comparison with experimental data to determine the functional dependence of the rate constants and on muscle length.This work was partly supported by the National Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MA-3307 through the University of Alberta.     

Analysis of a model for antagonistic muscles

In the present work a linear model for a pair of antogonistic muscles is analysed. Each constituent muscle in this model is identical to ones considered previously (Stein and Ouztöreli, 1976). Analytical properties of the antagonistic muscles and dynamics of the system are described and some numerical results are discussed. The natural modes of the system are determined by a fourth order polynomial, which most commonly has one pair of conjugate complex roots and two negative real roots. The filtering of neural inputs through the active state properties of the muscle increases the order of the system to fifth order for these inputs.This work was partly supported by the National Scientific and Engineering Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MT-3307 through the University of Alberta     

Optimal task performance of antagonistic muscles

Movements against a variety of loads are relatively invariant in form. These movements are controlled in general by antagonistic groups of muscles. In this paper optimal control strategies are computed for coupling antagonistic muscles so as to minimize deviations from a desired trajectory. Simulations are presented for linear and nonlinear decision functions linking control of the two muscles for a variety of movements in a way that may be compared with experimental observations.This work was partly supported by the Natural Sciences and Engineering Research Council of Canada Grant NSERC OGP-4345 and by the Medical Research Council of Canada Grant MRC PG-47 through the University of Alberta     

Predator-prey systems with group defence: The paradox of enrichment revisited

The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically). Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823. Research partially supported by a Natural Sciences and Engineering Research Council of Canada postdoctoral fellowship.     

Interactions between centrally and peripherally generated neuromuscular oscillations

Summary An experimentally based model of the mammalian neuromuscular system has been extended to include the interaction of sinusoidal inputs generated within the central nervous system and those produced peripherally by reflex pathways, together with muscle properties and external loads. Multiple reflex pathways and pathways having acceleration as well as velocity and length sensitivity are considered. The responses are analyzed for brief inputs (Dirac -functions), sinusoidal driving functions and mixtures of the two over ranges in which the model behaves either linearly or non-linearly. Approximate solutions are derived for the non-linear range, and exact numerical solutions are computed for a few examples within the linear range. The extent to which brief inputs can reset ongoing oscillations and the extent to which sinusoidal inputs can entrain these oscillations are of particular interest.This work was supported by grants from the Canadian National Research Council (to M. N. O.) and the Canadian Medical Research Council (to R. B. S.)     

Regulation of amylase activity in Drosophila melanogaster: Variation in the number of enzyme molecules produced by different amylase genotypes

Purified amylases from high- and low-activity variants of Drosophila melanogaster showed identical specific activities. Immunoelectrophoresis of crude larval homogenates showed severalfold differences between strains in the amounts of cross-reacting material. Control of amylase activity is trans-acting in heterozygotes between high- and low-activity variants. These results suggest the existence of polymorphic regulatory genes affecting the production levels of amylase protein in D. melanogaster.This work was supported by Grant GM-21279 from the Institute of General Medical Science of the NIH to R. C. Lewontin and by an Operating Grant from the Natural Sciences and Engineering Research Council Canada to D. A. Hickey.     

Activity analysis of neural networks

In a series of articles (Leung et al., 1973, 1974; Ogztöreli, 1972, 1975, 1978, 1979; Stein et al., 1974) we have investigated some of the physiologically significant properties of a general neural model. In these papers the nature of the oscillations occuring in the model has been briefly analyzed by omitting the effects of the discrete time-lags in the interaction of neurons, although these time-lags were incoporated in the general model. In the present work we investigate the effects of the time-lags on the oscillations which are intrinsic to the neural model, depending on the structural parameters such as external inputs, interaction coefficients, self-inhibition, self-excitation and selfadaptation coefficients. The numerical solution of the neural model, the computation of the steady-state solutions and the natural modes of the oscillations around the steady-state solutions are described.This work was partly supported by the Natural Sciences and Engineering Research Council of Canada under Grant NRC-A-4345 through the University of Alberta     

Evolutionary games for spatially dispersed populations

An evolutionary game model is developed that incorporates both spatial dispersion and density effects in the evolutionary dynamic. It is shown that a stable equilibrium (e.g. an evolutionarily stable strategy) of the non-dispersed frequency dynamic becomes a stable equilibrium of the larger system if population density stabilizes at these fixed frequencies. It is also shown, by example, that other equilibria, whose frequencies change from one location to another, may appear when dispersal rates are relatively small.Research supported by Natural Sciences and Engineering Research Council of Canada Operating Grant A6187Research supported by Natural Sciences and Engineering Research Council of Canada Operating Grant A7822     

Global dynamics of a selection model for the growth of a population with genotypic fertility differences

A population growth model is considered for a one locus two allele problem with selection based entirely on fertility differences. A local stability analysis is carried out for the critical points — which include possible polymorphic states — of the resulting nonlinear differential equations. The methods of dynamical systems theory are applied to obtain limiting genotypic proportions for every initial state. Thus the results are global and there are no periodic solutions.Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-8130Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-4823Research supported by NSF Grant MCS 7901069. A portion of the work was carried out while the author was a Visiting Professor at the University of Utah, Salt Lake City, Utah     

Effect of cycloheximide on the fine structure of corpus luteum in intact and hypophysectomized rats

Summary In rats, one large intravenous dose of cycloheximide leads to extensive development of two types of membrane-formations in the cells of corpora lutea, within two hours. Both the laminated dense bodies (concentric layers of smooth membranes showing high electron density) and the tubular aggregates (tightly packed smooth tubules with diameter smaller than usual) exhibited obvious connections with endoplasmic reticulum membranes. The reorganization of tubular aggregates gave rise to crystalloids showing hexagonal symmetry. The crystalloids, being obviously unstable, were transformed into smooth fingerprints (concentric arrays of paired agranular membranes showing the same density as endoplasmic reticulum membranes). Hypophysectomy, performed 24 hours previously, moderated but did not totally abolish the development of membranous configurations. The described effect of cycloheximide is considered to represent cellular injury, probably due to membrane-denaturation.This work was supported in part by the Medical Research Council of Canada (Block Term Grant MT-1829), the Ministère des Affaires Sociales, Quebec, and Succession J.A. DeSève. The authors thank the Upjohn Company, Kalamazoo, Michigan, U.S.A., for the cycloheximide used in these experiments.Fellow of the Medical Research Council of Canada.     

Control mechanisms of a neural network

In this paper we consider some classical control theoretic properties of a nonlinear neural network proposed by Ouztöreli (1979) to represent the activities of constiuent neurones in terms of the input signals and coupling (associative) properties. By breaking the network into linear and nonlinear components we have been able to localize the nonlinearities in the individual neural response latencies through the system.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada by Grant NSERC-A 4345 to M.N.O. and Grant NSERC-A 2568 to T.M.C. through the University of Alberta     

Relationship between stimulus and intensity characteristics of a sensory receptor

In this work a bridge is built between a neural model studied in a series of papers (cf. Ouztöreli 1979; Ouztöreli et al. 1987) and certain experimental laws of psychophysics and neurophysiology (Hartline 1942; Fechner 1860; Stevens 1961).This project was patially supported by Grant A4345 from the Natural Sciences and Engineering Research Council of Canada     

On the identification of neural responses

The most common form of measuring electrical responses of nerve cells is the recording of a given cell's spike train profile to the parameters of a given input signal. In this paper we consider the conditions under which it is possible to relate such response measures to (a) the properties of the cell's underlying activity characteristics, (b) the neural network, and (c) the input signal.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 to M.N.O. and under Grant A-4395 to T.M.C. through the University of Alberta     

On the ultrastructure of the abdominal sense organ of the giant scallop,Placopecten magellanicus (Gmelin)

Summary The abdominal sense organ of the giant scallop, Placopecten magellanicus, is composed of two cell types. The presumed receptor cells bear a single cilium 60 to 70 m in length. The microvilli at the apices of these cells may also be modified into microvillous whorls. From eight to twelve ciliated cells are associated with a single mucous cell. The mucous cells have a much greater diameter than the ciliated cells and contain many electron-dense mucous granules. No function has yet been determined for the ciliated cells, although a number of theories are presented.This research was supported by National Research Council of Canada Operating Grant No. A-6444 to Dr. V.C. Barber. Additional support came from the Department of Biology and the School of Graduate Studies, Memorial University. Contribution no. 250 from the Marine Sciences Research Laboratory, Memorial University of Newfoundland     

Elementary granules,small vesicles and exocytosis in the rat neurohypophysis after acute haemorrhage

Summary Neural lobes of rats subjected to severe acute haemorrhage under sodium pentobarbitone anaesthesia were examined electron microscopically and the ultrastructure compared with that in anaesthetised and unanaesthetised controls. Changes in the localisation and numerical distribution of elementary granules and small vesicles in the neurohypophysial nerve endings of bled rats were consistent with the occurrence of exocytosis. The occurrence of exocytotic profiles was observed more frequently in freeze-etched tissue samples as compared with the material fixed for conventional electron microscopy. The ratio of small vesicles: elementary granules was shown to be significantly increased (P<0.005) in the nerve endings of neural lobes from bled rats. Equally, the numbers of exocytotic profiles related to 1000 m² of neurohypophysial tissue area were significantly greater (P<0.005) in bled rats.The study was supported by Medical Research Council of Canada. The authors are grateful to Dr. W. Costerton, Biology Department, The University of Calgary, for use of facilities for freeze-etching, and to Miss Y. Carter for technical assistance.Research Associate, Consejo Nacional de Investigationes Cientificas y Tecnicas, Argentina.Associate, Medical Research Council of Canada.     

Response analysis of vertebrate retina

In a recent work (Ouztöreli, 1980) a mathematical model for studying the neural activities in a vertebrate retina has been investigated, where the basic network contains five interconnected neurons: a receptor cell, a bipolar cell, a horizontal cell, an amacrine cell, and a retinal ganglion cell. More recently, in (Ouztöreli and O'Mara, 1980) the basic network has been extended to a larger network containing twelve neurons. In both of these works, the performances of the basic and extended models were discussed under different structural and processing conditions with constant inputs by using the results of one of our earlier work (Ouztöreli, 1979). In the present paper we investigate by simulations the responses of the basic retinal network to piecewise constant and periodic inputs. The step and frequency responses of the extended retinal network will be discussed in a forthcoming paper.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 through the University of alberta     

Regeneration in Phaseolus vulgaris L.: High-frequency induction of direct shoot formation in intact seedlings by N6-benzylaminopurine and thidiazuron

Induction of prolific shoot formation in Phaseolus vulgaris L. cv. Kinghorn Wax was achieved by germinating mature seeds and growing seedlings on a medium supplemented with 10 M thidiazuron (TDZ), a substituted phenylurea, or 80 M N⁶-benzylaminopurine (BAP). Culture for 7 d in the presence of 10 M TDZ was sufficient to induce maximal shoot formation, whereas a continuous presence of BAP was required for the induction and development of shoots. The differentiation of adventitious shoots occurred within four weeks of seed culture, from tissues in the regions of axillary buds on the cotyledonary node and also areas surrounding the shoot apex of the intact seedling. The number of shoots regenerated from intact seedlings was significantly higher than that obtained with expiants. Regenerated shoots developed into flowering plants. Similar results were obtained in six other bean cultivars.Abbreviations BAP N⁶-benzylaminopurine - MS Murashige and Skoog (1962) medium - TDZ N-phenyl-N 1-(1,2,3 thiadiazol-yl)urea (thidiazuron) To whom correspondence should be addressedThis research was supported by operating grants from the Natural Sciences and Engineering Research Council of Canada and the University Research Board Grant Programs of the University of Guelph to P.K.S. We thank Drs. Jean Gerrath and R. Rastogi for helpful discussions. Technical assistance from Sangeeta Saxena is gratefully acknowledged.     

Ultrastructural localization of glutamic oxalacetic transaminase activity in cardiac muscle fiber and cardiac mitochondrial fraction of the rat

Summary The ventricular heart muscle of the rat was fixed in glutaraldehyde-formaldehyde mixture. The tissue blocks were incubated in a medium containing 20 mM 1-aspartic acid, 2 mM -ketoglutaric acid and 6 mM lead nitrate as major ingredients. The enzymatic reaction product due to glutamic oxalacetic transaminase (GOT) activity was found to be localized in the cristae and at the surface of the mitochondria, in the cisternae of the nuclear envelope and in the sarcoplasmic reticulum. Isolation of the mitochondrial fraction from the homogenate of the fixed heart muscle was performed, and GOT activity in this fraction was demonstrated both histochemically and biochemically.This Work was Supported by a Research Grant from the Medical Research Council of Canada (MA-3340).     

The purification of cellulase and exo-laminaranase and their role in the formation ofPythium sp. “protoplasts”

A cellulase and a laminaranase have been purified from a Streptomyces lytic enzyme complex. Lipase and protease were separated from glucanases. A combination of the purified glucanases produced protoplasts fromPythium sp. PRL 2142. Lipase was shown to act as an adjuvant in this process.National Research Council of Canada Postdoctorate Fellow 1965–67.