Probability distributions of Markovian sodium channel states during propagating axonal impulses with or without recovery supernormality.

This study addressed a macroscopic neurophysiological phenomenon - supernormality during the recovery phase of propagating axonal impulses - in explicit chemical terms. Excitation was reconstructed numerically using the kinetic scheme of multiple-state probabilistic transitions within a population of voltage-dependent sodium channels (NaCh) derived by Vandenberg and Bezanilla ("PC" scheme). Each NaCh transition was characterized as a reversible Markov process with voltage-dependent rate constants associated with each respective directional transition. While recovery reconstructed with the Hodgkin-Huxley formalism included a supernormal period, the PC scheme did not. The present analysis showed that the occurrence and degree of supernormality with the PC scheme was determined by the relative speed of the transitions within the closed loop of the kinetic scheme; supernormality was promoted by speeding these kinetics. The analysis also showed that concurrent with supernormality, the faster loop kinetics caused (1) an elevation in the C(1) --> C(2) transitions, and (2) a reduction in the I(4) --> I(5) transitions. Thus, macroscopic functionality in information processing could be expressed in terms of probabilistic interstate transitions among a population of NaCh molecules.

Rallian "equivalent" cylinders reconsidered: comparisons with literal compartments.

In Rall's "equivalent" cylinder morphological-to-electrical transformation, neuronal arborizations are reduced to single unbranched core-conductors. The conventional assumption that such an "equivalent" reconstructs the electrical properties of the fibers it represents was tested directly; electrical properties and responses of "equivalent" cylinders were compared with those of their literal branch constituents for fibers with a single symmetrical bifurcation. The numerical solution methods were validated independently by their accurate reconstruction of the responses of an analog circuit configured with compartmental architecture to solve the cable equation for passive fibers with a symmetrical bifurcation. In passive fibers, "equivalent" cylinders misestimated the spatial distribution of voltage amplitudes and steady-state input resistance, partly due to the lack of axial current bifurcation. In active fibers with a single propagating action potential, the spatial distributions of point-to-point conduction velocity values (measured in meters/second) for a literal branch point differed significantly from those of their "equivalent" cylinders. "Equivalent" cylinders also underestimated the diameter-dependent delay in propagation through the branch point and branches, due to the larger "equivalent" diameter. Corrections to the "equivalent" cylinder did not reconcile differences between "equivalent" and literal models. However, "equivalent" and literal branch fibers had the same (a) steady-state resistance "looking into" an isolated symmetrical branch point and (b) geometry-independent point-to-point propagation velocity when measured in space constants per millisecond except within +/-1 space constant from the geometrical inhomogeneity. In summary, Rall's "equivalent" cylinders did not accurately reconstruct all passive or active electrophysiological properties and responses of their literal compartments. For the modeling of individual neurons, the requirement of single-branch resolution is discussed.

Computation of high safety factor impulse propagation at axonal branch points.

The propagation of single impulses at axonal branch points and widenings was computed numerically. Previous computational studies have held that an action potential propagates across an unmyelinated axonal branch point with diameter-dependent lowered likelihood, such that increasingly complex arborizations could eliminate propagating information. This result is counter-intuitive to the principle of information divergence within neuronal circuits. The present study re-examined this result. The boundary conditions at a branch point were extracted from a physical analog circuit with actual branches. The main results were that impulse propagation was reliable past branch points and widenings, and that conduction velocity changed spatially as a function of fiber geometrical inhomogeneity.

Computation of long-distance propagation of impulses elicited by Poisson-process stimulation.

1. The purpose of this work was to determine whether computed temporally coded axonal information generated by Poisson process stimulation were modified during long-distance propagation, as originally suggested by S. A. George. Propagated impulses were computed with the use of the Hodgkin-Huxley equations and cable theory to simulate excitation and current spread in 100-microns-diam unmyelinated axons, whose total length was 8.1 cm (25 lambda) or 101.4 cm (312.5 lambda). Differential equations were solved numerically, with the use of trapezoidal integration over small, constant electrotonic and temporal steps (0.125 lambda and 1.0 microsecond, respectively). 2. Using dual-pulse stimulation, we confirmed that for interstimulus intervals between 5 and 11 ms, the conduction velocity of the second of a short-interval pair of impulses was slower than that of the first impulse. Further, with sufficiently long propagation distance, the second impulse's conduction velocity increased steadily and eventually approached that of the first impulse. This effect caused a spatially varying interspike interval: as propagation proceeded, the interspike interval increased and eventually approached stabilization. 3. With Poisson stimulation, the peak amplitude of propagating action potentials varied with interspike interval durations between 5 and 11 ms. Such amplitude attenuation was caused by the incomplete relaxation of parameters n (macroscopic K-conductance activation) and h (macroscopic Na-conductance inactivation) during the interspike period. 4. The stochastic properties of the impulse train became less Poisson-like with propagation distance. In cases of propagation over 99.4 cm, the impulse trains developed marked periodicities in Interevent Interval Distribution and Expectation Density function because of the axially modulated transformation of interspike intervals. 5. Despite these changes in impulse train parameters, the arithmetic value of the mean interspike interval did not change as a function of propagation distance. This work showed that in theory, whereas the pattern of Poisson-like impulse codes was modified during long-distance propagation, their mean rate was conserved.

Poisson-process electrical stimulation: circuit and axonal responses.

This work describes a simple circuit which generated a highly Poisson-like sequence of pulses. Resistor noise was amplified in three series stages followed by rectification through a relatively large shunt resistance. This yielded a sequence of variable-amplitude transients, which were inverted, amplified with DC adjustment, and fed into a Schmitt trigger/multivibrator chip for pulse generation. The pulse generation frequency was modulated by the amplification of the rectified transients. The stochastic characteristics of the output pulse train were Poisson-like over a wide frequency range, as assessed using the intervent interval distribution and expectation density as steady-state and real-time estimators, respectively. In separate tests, the output pulse train was applied to forelimb cutaneous axons of the anesthetized cat; trains of elicited propagating action potentials were recorded extracellularly from individual G1 axons in the cuneate fasciculus. The stochastic properties of the action potential train differed from those of the stimulus, with longer deadtime, lower mean rate, and an early expectation density peak. These physiological responses to circuit output were similar to those elicited by other generators of Poisson-like stimulation.

Evidence for amino acid concentration gradients between CSF and extracellular fluid.

A small volume in the extracellular space of the medulla in the anesthetized cat was perfused with cisternal cerebrospinal fluid (CSF) using a push-pull technique. The recovered perfusate was a mixture of pushed CSF and the extracellular fluid. HPLC-EC analysis showed that the concentration of some primary amino acids in recovered perfusate often differed from their concentrations in CSF. These results suggested that amino acid gradients existed between CSF and the extracellular space.

Theoretical studies of impulse propagation in serotonergic axons.

Impulse propagation in small-diameter (1-3 microns) axons with inhomogeneous geometry was simulated. The fibres were represented by a series of 3 microns-long compartments. The cable equation was solved for each compartment by a finite-difference approximation (Cooley and Dodge 1966). First-order differential equations governing temporal changes in membrane potential or Hodgkin-Huxley (1952) conductance parameters were solved by numerical integration. It was assumed that varicosity and intervaricosity segments had the same specific cable constants and excitability properties, and differed only in length and diameter. A single long varicosity or a 'clump' of 3 microns-long varicosities changed the point-to-point (axial) conduction velocity within as well as to either side of the geometrically inhomogeneous regions. When 2 microns-diameter, 3 microns-long varicosities were distributed over the 1 micron-diameter fiber length as observed in serotonergic axons, mean axial conduction velocity was between that of uniform-diameter 1 and 2 microns fibers, and changed predictably with different cable parameters. Fibers with inexcitable varicosity membranes also supported impulse propagation. These simulations provided a general theoretical basis for the slow (less than 1 M/s) conduction velocity attributed to small-diameter unmyelinated varicose axons.

HPLC-EC determination of free primary amino acid concentrations in cat cisternal cerebrospinal fluid.

This paper describes an HPLC-EC method for measuring the concentrations of 9 free primary amino acids in cerebrospinal fluid (CSF) withdrawn from the cisterna magna of Nembutal-anesthetized adult cats. Amino acid derivatives were formed with o-phthalaldehyde and beta-mercaptoethanol; subsequently, excess thiol reagent was removed with iodoacetamide. During elution through a C18 5-micron column, the electrochemical detector's sensitivity was switched to accommodate the wide ranges of CSF amino acid concentrations. The analysis was acceptably precise and linear at and above the CSF levels and did not require CSF deproteinization. During the 23 min elution, the concentrations of 8 CSF amino acids were determined: alanine, asparagine, glutamate, glutamine, glycine, serine, taurine, and tyrosine; measurable concentrations were between 1 and 800 microM. The concentration of GABA was below its detection limit (0.5 microM). To assess the ability to detect small concentration increases which might occur due to experimental manipulations, the minimum detectable increments in CSF amino acid concentrations above endogenous levels were determined.

Amino acid content of rat cerebral astrocytes adapted to hyperosmotic medium in vitro.

Rat cerebral astrocytes from confluent primary cultures were grown for two weeks in medium made hyperosmotic with additional NaCl. At the time the cells were harvested (four weeks in culture), the medium osmolality of experimental cultures was approximately 600 mOsm. Amino acid, protein, and potassium contents and the cell volume were measured. Compared to cells maintained in control medium (approximately 300 mOsm), cells grown in hyperosmotic conditions had over two times the content of taurine and five times the content of glutamine. Alanine, aspartate, glutamate, glycine, and tyrosine contents also were elevated in these hyperosmotic-treated cells, while asparagine contents were unchanged relative to control cells. Cell volume and potassium content were decreased to approximately 50% of control levels by the hyperosmotic treatment while total protein content per cell was unchanged relative to cells from control cultures. Seven min after hyperosmotic-exposed cells were rapidly diluted into PBS with osmolality equal to about 330 mOsm, cell contents of alanine, asparagine, glutamine, glutamate, glycine, taurine, and tyrosine fell toward control levels. The data indicate that significant alterations in intracellular osmolytes occur in astrocytes adapted to hyperosmotic conditions. We suggest that a loss of intracellular potassium is at least partially compensated by accumulation of taurine, glutamine, and perhaps other amino acids acting as intracellular osmolytes.

Random-sequence stimulation of the G1 hair afferent unit.

Impulse trains were recorded from the parent axon of the cat G1 hair afferent unit. Separate random (Poisson-like) trains of mechanical stimuli were applied to two coinnervated receptive field hairs individually or concurrently. The objective was to determine whether the parent axonal impulse train elicited by dual-hair stimulation was due to a temporal combining ("mixing"; Fukami, 1980) of the impulse trains elicited in the parent axons by the same stimulation to each hair alone. Both impulse rates and patterns were assessed. During single-hair random stimulation, impulse trains differed from stimulus trains, having lower mean rates and short-interval doublets. During dual-hair random stimulation, mean impulse frequencies were on average 36% less than those predicted for mixing. There were no correlations between stimulus amplitude and departures from mixing. As a further test of the mixing hypothesis, the two single-hair-elicited impulse trains were temporally merged (i.e., superimposed to form one impulse train). Such merged impulse trains were compared with the corresponding dual-hair-elicited impulse train. Dual-hair-elicited frequencies were typically less than those of the merged trains, despite the use of an absolute-refractory-period criterion during merging. The impulse patterns elicited by dual-hair stimulation usually differed from the merged-train patterns. Temporal coupling between stimuli and impulses was either variable or absent during single-hair random stimulation; such coupling was altered during dual-hair random stimulation. In summary, this work showed that the dual-hair responses could not be predicted from the single-hair responses. Limitations of the mixing hypothesis and possible biophysical mechanisms in the axonal arborization are discussed. The results are consistent with a general hypothesis of analog processing within the arborization of the parent axon.

Identification of gamma-aminobutyric acid-like immunoreactive neurons in the rat cuneate nucleus.

Neurons in the cuneate nucleus of the rat were examined for gamma-aminobutyric acid-like immunoreactivity (GABA-LI) using antiserum raised against GABA-glutaraldehyde-keyhole limpet hemocyanin. GABA-LI neurons were analyzed for size, shape, and distribution and compared to Nissl-stained neurons. GABA-LI cell bodies were located at all rostral-caudal levels and were distributed randomly throughout the nucleus except at the level of the obex, where they were limited to the peripheral region of the cuneate nucleus. GABA-LI cell bodies had a significantly smaller mean cross-sectional area than the total cuneate neuronal population and comprised 21.5% of the total neuronal population as assessed with Nissl-staining. These results are consistent with the hypothesis that GABA is involved in processing somatosensory information in the rat dorsal column nuclei.

The morphology and distribution of serotonin-like immunoreactive fibers in the cat dorsal column nuclei.

Fibers showing serotonin-like immunoreactivity (5-HT-LI) are demonstrated in the gracile, cuneate and external cuneate nuclei of the cat using avidin-biotinylated horseradish peroxidase and indirect fluorescence immunohistochemical methods. 5-HT-LI fibers are located in all cytoarchitectural subdivisions of the gracile and cuneate nuclei but are restricted to the medial half of the external cuneate nucleus. In all nuclei, 5-HT-LI fibers consist of long, varicose strands showing a wide range in the diameters of both varicosities and intervaricose segments. Results support the concept that serotonergic systems may be involved in the processing of non-noxious somatosensory submodalities.

Poisson process stimulation of an excitable membrane cable model.

The convergence of multiple inputs within a single-neuronal substrate is a common design feature of both peripheral and central nervous systems. Typically, the result of such convergence impinges upon an intracellularly contiguous axon, where it is encoded into a train of action potentials. The simplest representation of the result of convergence of multiple inputs is a Poisson process; a general representation of axonal excitability is the Hodgkin-Huxley/cable theory formalism. The present work addressed multiple input convergence upon an axon by applying Poisson process stimulation to the Hodgkin-Huxley axonal cable. The results showed that both absolute and relative refractory periods yielded in the axonal output a random but non-Poisson process. While smaller amplitude stimuli elicited a type of short-interval conditioning, larger amplitude stimuli elicited impulse trains approaching Poisson criteria except for the effects of refractoriness. These results were obtained for stimulus trains consisting of pulses of constant amplitude and constant or variable durations. By contrast, with or without stimulus pulse shape variability, the post-impulse conditional probability for impulse initiation in the steady-state was a Poisson-like process. For stimulus variability consisting of randomly smaller amplitudes or randomly longer durations, mean impulse frequency was attenuated or potentiated, respectively. Limitations and implications of these computations are discussed.

Detection by HPLC-EC of primary amines recovered in aqueous push-pull perfusates from cat cuneate nucleus.

A method is described for the quantitative detection of primary amines - particularly free amino acids - recovered in aqueous push-pull perfusates obtained from the cat cuneate nucleus. Isoindole derivatives of primary amine groups are formed by precolumn reaction with o-phthalaldehyde and mercaptoethanol. Derivatized sample components are separated and detected using HPLC with electrochemical detection. Of 22 amino acids standards studied individually, 12 were detectable under the conditions described. Variability of elution times and detector output peak heights were less than 2% and less than 10%, respectively. Concentration curves were linear to the 10 picomole order of magnitude. For cuneate nucleus perfusates, samples recovered during continuous peripheral somatosensory stimulation contained detectable derivative levels elevated above those of control samples. Sources of error in data interpretation are discussed.

Recovery by push-pull perfusion of neurochemicals released within the cuneate nucleus of the cat by somatosensory stimulation.

The present work describes a combination of techniques for the identification of neurochemicals released within the cuneate nucleus. During electrical stimulation of the superficial radial nerve, the extracellular fluid of the nucleus is continuously sampled by push-pull perfusion. In addition, the population electrical activity of peripheral nerve as well as the activity of cuneate neurons are recorded. Subsequently, the neurochemical content of the sampled fluid is assessed by HPLC analysis. The comparison of sampled fluid content during control (no stimulation) versus stimulation runs indicates that somatosensory stimulation elicits the release of specific neurochemicals within the cuneate nucleus. The possible sources of released neurochemicals are discussed.

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.

Chiriquitoxin, a new tool for mapping ionic channels.

Chiriquitoxin is a new natural analog of tetrodotoxin in which the -CH2OH group on C6 has been replaced with a yet unidentified group consisting of 104 mass units. It is unique in being the only known stable analog to be equally potent as tetrodotoxin in blocking the sodium channel. It additionally interferes with the delayed rectifier (potassium) channel. In frog skeletal muscle, it significantly reduced the outward current while abolishing the inward current. It also slows the fast repolarization of the action potential and obliterates the voltage response characteristic of delayed rectification to large outward currents. It completes the tetrodotoxin for the same membrane binding site, thereby suggesting that the same molecule interferes with both the sodium and the potassium channels. A new working hypothesis is proposed in which tetrodotoxin and chiriquitoxin are postulated to bind to a membrane receptor located in the outside surface of the muscle fiber membrane. From the structure of tetrodotoxin and a presumed structure of chiriquitoxin, the Na+ and K+ channels have been estimated to be separated from each other by not less than 5 A nor much more than 15 A.