1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

A new conceptual framework and a minimization principle together provide an understanding of computation in model neural circuits. The circuits consist of nonlinear graded-response model neurons organized into networks with effectively symmetric synaptic connections. The neurons represent an approximation to biological neurons in which a simplified set of important computational properties is retained. Complex circuits solving problems similar to those essential in biology can be analyzed and understood without the need to follow the circuit dynamics in detail. Implementation of the model with electronic devices will provide a class of electronic circuits of novel form and function.

https://science.sciencemag.org/content/sci/233/4764/625.full.pdf

Computing with neural circuits: a model

We describe a modification to our recent model of the action potential which introduces two additional equilibrium points. By using stability analysis we show that one of these equilibrium points is a saddle point from which there are two separatrices which divide the phase plane into two regions. In one region all phase paths approach a limit cycle and in the other all phase paths approach a stable equilibrium point. A consequence of this is that a short depolarizing current pulse will change an initially silent model neuron into one that fires repetitively. Addition of a third equation limits this firing to either an isolated burst or a depolarizing afterpotential. When steady depolarizing current was applied to this model it resulted in periodic bursting. The equations, which were initially developed to explain isolated triggered bursts, therefore provide one of the simplest models of the more general phenomenon of oscillatory burst discharge.

/pdf/a-model-of-neuronal-bursting-using-three-coupled-first-order-56eke0sz43.pdf

A model of neuronal bursting using three coupled first order differential equations.

Experimental Neurology By Prof Paul Glees Pp xii + 532 (Oxford: Clarendon Press; London: Oxford University Press, 1961) 75s net

The Nervous System

The detection of neural spike activity is a technical challenge that is a prerequisite for studying many types of brain function. Measuring the activity of individual neurons accurately can be difficult due to large amounts of background noise and the difficulty in distinguishing the action potentials of one neuron from those of others in the local area. This article reviews algorithms and methods for detecting and classifying action potentials, a problem commonly referred to as spike sorting. The article first discusses the challenges of measuring neural activity and the basic issues of signal detection and classification. It reviews and illustrates algorithms and techniques that have been applied to many of the problems in spike sorting and discusses the advantages and limitations of each and the applicability of these methods for different types of experimental demands. The article is written both for the physiologist wanting to use simple methods that will improve experimental yield and minimize the selection biases of traditional techniques and for those who want to apply or extend more sophisticated algorithms to meet new experimental challenges.

A review of methods for spike sorting: the detection and classification of neural action potentials.

Rapid conduction and the evolution of giant axons and myelinated fibers.

Many of the motor neurons in the lobster (Panulirus interruptus) stomatogastric ganglion exhibit plateau potentials; that is, prolonged regenerative depolarizations resulting from active membrane properties, that drive the neurons to fire impulses during bursts. Plateaus are latent in isolated ganglia but are unmasked by central input. These findings emphasize the role of cellular properties as compared to synaptic wiring in the production of cyclic motor patterns by ensembles of neurons.

http://science.sciencemag.org/content/sci/200/4340/453.full.pdf

Bursting Neural Networks: A Reexamination

Mechanoreception in marine copepods: electrophysiological studies on the first antennae

Planktonic copepods exhibit rapid escape behavior in response to hydrodynamic distur- bances. Small disturbances of brief duration were produced by a piezoelectric transducer moving a small cylinder. The escape responses of free-swimming adult males and females of the copepods Acartia tonsa and A. lilljeborgii were recorded using high-speed video and quantified using comput- erized motion analysis techniques. Response latency, swimming speed, acceleration and turning rate during escape behavior were measured. Acartia spp. typically respond within 4 ms to a hydro- dynamic disturbance with multiple power strokes of the swimming legs. Each stroke and recovery is of ca. 7 ms duration with maximum speeds often exceeding 500 mm s -1 and minimum speeds be- tween strokes rarely falling below 100 mm s -1 . Acceleration during initial escape usually exceeds 100 m s -2 . Escapes often begin with rapid reorientation away from the source of the disturbance, with maximum turning rates of about 30° ms -1 . Significant differences were found between the kinetics of escape responses of adult male and female copepods of each species, with males having greater maximum speeds and accelerations, and females having longer duration jumps. Significant differ- ences were also found between males and females of the 2 species, with A. lilljeborgii exhibiting greater speeds and more rapid acceleration than the smaller A. tonsa.

/pdf/escape-behavior-of-planktonic-copepods-in-response-to-4zsxn9bkjy.pdf

Escape behavior of planktonic copepods in response to hydrodynamic disturbances: high speed video analysis

1. Results from the companion paper were incorporated into a physiologically realistic computer model of the three principal cell types (PD/AB, LP, PY) of the pyloric network in the stomatogastric ganglion. Parameters for the model were mostly calculated (sometimes estimated) from experimental data rather than fitting the model to observed output patterns. 2. The initial run was successful in predicting several features of the pyloric pattern: the observed gap between PD and LP bursts, the appropriate sequence of the activity periods (PD, LP, PY), and a substantial PY burst not properly simulated by an earlier model. 3. The major discrepancy between model and observed patterns was the too-early occurrence of the PY burst, which resulted in a much shortened LP burst. Motivated by this discrepancy, additional investigations were made of PY properties. A hyperpolarization-enabled depolorization-activated hyperpolarizing conductance change was discovered which may make an important contribution to the late phase of PY activity in the normal burst cycle. Addition of this effect to the model brought its predictions more in line with observed patterns. 4. Other discrepancies between model and observation were instructive and are discussed. The findings force a substantial revision in previously held ideas on pattern production in the pyloric system. More weight must be given to functional properties of individual neurons and less to properties arising purely from network interactions. This shift in emphasis may be necessary in more complicated systems as well. 5. An example has been provided of the value quantitative modeling can be to network physiology. Only through rigorous quantitative testing can qualitative theories of how the nervous system operates be substantiated.

Daniel K. Hartline

Papers

Rapid conduction and the evolution of giant axons and myelinated fibers.

Bursting Neural Networks: A Reexamination

Mechanoreception in marine copepods: electrophysiological studies on the first antennae

Escape behavior of planktonic copepods in response to hydrodynamic disturbances: high speed video analysis

Pattern generation in the lobster (Panulirus) stomatogastric ganglion