Spatial convergence and divergence between cutaneous afferent axons and dorsal horn cells are not constant.

We have proposed a quantitative model of the development of dorsal horn cell receptive fields (RFs) and somatotopic organization (Brown et al. [1997] Somatosens. Motor Res. 14:93-106). One component of that model is a hypothesis that convergence and divergence of connections between low-threshold primary afferent mechanoreceptive axons and dorsal horn cells are invariant over skin location and dorsal horn location. The more limited, and more easily tested, hypothesis that spatial convergence and divergence between cutaneous mechanoreceptors and dorsal horn cell are constant was examined. Spatial divergence is the number of dorsal horn cells whose RFs overlap the RF center of a primary afferent, and spatial convergence is the number of afferent RF centers that lie within the RF of a dorsal horn cell. Innervation density was determined as a function of location on the hindlimb by using peripheral nerve recording and axon counting. A descriptive model of dorsal horn cell receptive fields (Brown et al. [1998] J. Neurophysiol. 31:833-848) was used to simulate RFs of the entire dorsal horn cell population in order to estimate RF area and map scale as a function of location on the hindlimb. Previously reported correlations among innervation density, map scale, and RF size were confirmed. However, these correlations were not linear. The hypothesis that spatial convergence and divergence are constant was rejected. The previously proposed model of development of dorsal horn cell somatotopy and RF geometries must be revised to take variable spatial convergence and divergence into account.

Dorsal horn spatial representation of simple cutaneous stimuli.

A model of lamina III-IV dorsal horn cell receptive fields (RFs) has been developed to visualize the spatial patterns of cells activated by light touch stimuli. Low-threshold mechanoreceptive fields (RFs) of 551 dorsal horn neurons recorded in anesthetized cats were characterized by location of RF center in cylindrical coordinates, area, length/width ratio, and orientation of long axis. Best-fitting ellipses overlapped actual RFs by 90%. Exponentially smoothed mean and variance surfaces were estimated for these five variables, on a grid of 40 points mediolaterally by 20/segment rostrocaudally in dorsal horn segments L4-S1. The variations of model RF location, area, and length/width ratio with map location were all similar to previous observations. When elliptical RFs were simulated at the locations of the original cells, the RFs of real and simulated cells overlapped by 64%. The densities of cell representations of skin points on the hindlimb were represented as pseudocolor contour plots on dorsal view maps, and segmental representations were plotted on the standard views of the leg. Overlap of modeled and real segmental representations was at the 84% level. Simulated and observed RFs had similar relations between area and length/width ratio and location on the hindlimb: r(A) = 0.52; r(L/W) = 0.56. Although the representation of simple stimuli was orderly, and there was clearly only one somatotopic map of the skin, the representation of a single point often was not a single cluster of active neurons. When two-point stimuli were simulated, there usually was no fractionation of response zones or addition of new zones. Variation of stimulus size (area of skin contacted) produced less variation of representation size (number of cells responding) than movement of stimuli from one location to another. We conclude that stimulus features are preserved poorly in their dorsal horn spatial representation and that discrimination mechanisms that depend on detection of such features in the spatial representation would be unreliable.

Visualization of significant differences in somatotopic maps: a distributed t-test.

In order to test for differences in the properties of two populations of cells within a somatotopic map we need to be able to compare data sets in which sampled cells are randomly scattered throughout the map, and the variable being compared varies with location in the map. We can describe cell properties as exponentially smoothed surfaces fitted to data in the plane of the map, where all data contribute to the computation of the value of each grid point on the surface, with weights which decline exponentially with distance from the grid point. Means, variances and Student's t values can be computed at all grid points, keeping in mind the fact that grid points' t values are not independent of each other. We used Monte Carlo methods to demonstrate that two random samples of 500 values from two populations of 100,000 values at 4000 grid can provide a very useful picture of regions with significant differences. We recommended this procedure, or analogous approaches using other statistical tests, for any analysis where it is necessary to compare values of dependent variables when matched locations on the independent axis or plane cannot be sampled in the two populations.

Correlation of peripheral innervation density and dorsal horn map scale.

Dorsal horn map scale and peripheral innervation density were compared to test a hypothesized linear relationship. In anesthetized cats, low-threshold mechanoreceptive peripheral nerve innervation fields (IFs) were measured by outlining areas of skin from which action potentials could be elicited in cutaneous nerves. The same nerves were processed histologically and used to count myelinated axons. Innervation density for each nerve was calculated as number of axons divided by IF area. Single units were recorded throughout the hindlimb representation, in laminae III and IV. These data, combined with single-unit data from other animals and with cell counts in laminae III and IV, permitted estimation of numbers of cells whose receptive field centers fell in contiguous 1-cm bands from tips of toes to proximal thigh. A similar estimate was performed with the use of the nerve innervation data, so that peripheral innervation densities and map scales for the different 1-cm bands of skin could be compared. Correlation between the two was quite high (r = 0.8), and highly significant (P = 2.5 x 10(-7)). These results are consistent with a proposed developmental model in which map scale, peripheral innervation density, and reciprocal of dorsal horn cell receptive field size are mutually proportional, as a result of developmental mechanisms that produce constant divergence and convergence between primary afferent axons and dorsal horn cells.

Assembly of the dorsal horn somatotopic map.

We hypothesize: (a) peripheral innervation densities determine map scales in dorsal horn, (b) dorsal horn cell (DHC) receptive field (RF) geometries are determined by map scales, and (c) morphologies of primary afferents (PAs) and DHCs reflect their developmental history. We suggest the following sequence: (A) PAs project in a somatotopic mediolateral sequence. (B) DHCs assemble prototype RFs by sampling presynaptic neuropil with their dendrites. (C) PAs then project to all levels where their RFs are contained within prototype RFs of DHCs. (D) A competitive mechanism produces the adult form of DHC RFs. (E) Adult distributions of PA terminals and DHC dendrites reflect this developmental history. (F) Mediolateral somatotopic gradients are determined by RF densities of axons entering at the same levels. (G) Map scales at different rostrocaudal levels are determined by somatotopic gradients. (H) Geometries of DHC RFs are determined by constant convergence and divergence of monosynaptic connections. (I) Secondary processes further modify geometries of DHC RFs. (J) Residual self-organizing capacity supports maintenance and plastic mechanisms. We adduce the following evidence: (1) agreement between monosynaptically coupled inputs and cells' excitatory low threshold mechanoreceptive fields; (2) the temporal sequence of events during penetration of the gray matter by PAs; (3)variation of PA terminal and DHC dendritic domains as a function of map scale; (4) somatotopic gradients and geometries of DHC RFs in adult dorsal horn; (5) calculations of peripheral innervation densities and dorsal horn map scales; and (6) constant divergence and convergence between PAs and DHCs.

Variation of dorsal horn cell dendritic spread with map scale.

Cells in laminae III, IV, and V of cat dorsal horn were injected with horseradish peroxidase or neurobiotin. Dorsal views of the dendritic domains were constructed in order to measure their lengths, widths, areas, and length/width ratios in the horizontal plane (the plane of the somatotopic map). Dendritic domain width and area in the horizontal plane were negatively correlated with fractional distance between the medial and lateral edges of the dorsal horn. These results are consistent with the hypothesis that dendritic domain width varies with map scale, which is maximal in the medial dorsal horn. This is similar to the variation in widths of primary afferent bouton distributions. The parallel variation of dorsal horn cell dendritic domain width and primary afferent bouton distribution width with map scale suggests that there is a causal relation between morphology and map scale in the dorsal horn representation of the hindlimb. This variation of adult morphology with map scale must reflect mechanisms responsible for the assembly of receptive fields.

Crossed receptive field components and crossed dendrites in cat sacrocaudal dorsal horn.

The hypothesis that sacrocaudal dorsal horn neurons with crossed receptive field components on the tail have dendrites which cross to the contralateral dorsal horn was tested in a combined electrophysiological and morphological study. Dorsal horn cells in the sacrocaudal spinal cord of anesthetized cats were penetrated with horseradish peroxidase-filled microelectrodes. After mapping their low threshold mechanoreceptive fields, cells were iontophoretically injected with horseradish peroxidase. A sample of 16 well-stained cells was obtained in laminae III and IV. Cells with receptive fields crossing the dorsal midline of the tail (n = 8) had somata in the lateral ipsilateral dorsal horn, and some of these cells (5/8) had dendrites which crossed to the lateral contralateral dorsal horn. Cells with receptive fields spanning the ventral midline (n = 2) were located near the center of the fused dorsal horn, and one of these had bilateral dendrites in this region. Cells with receptive fields on the lateral tail, crossing neither the dorsal nor the ventral midline (n = 6), had cell bodies in the middle of the ipsilateral dorsal horn; half had only ipsilateral dendrites, and half had crossed dendritic branches. Although the relationship between cell receptive field (RF) location (RF center, expressed as distance from tips of toes) and mediolateral location of the cell body was statistically significant, the correlation between crossed RF components and crossed dendritic branches was not significant.

Using the Gompertz-Strehler model of aging and mortality to explain mortality trends in industrialized countries.

Mortality trends in industrialized countries are characterized by declines in vascular disease (ischemic heart disease and stroke) and rises in cancers and degenerative diseases. These trends are typically analyzed by examining each disorder in isolation using the perspective of genetic and environmental influences. However, longitudinal Gompertzian analysis and the Gompertz-Strehler model of aging and mortality as modified by Lestienne suggest that age-specific mortality rates, for both general and disease-specific mortality, are an interrelated deterministic function of aggregate genetic, environmental and competitive influences. Consequently, evolving mortality trends and patterns appear to be influenced by three factors (with deterministic competition being the third factor), rather than just two factors (genetic and environmental) as commonly depicted.

Mortality among the elderly in the U.S., 1956-1987: demonstration of the upper boundary to Gompertzian mortality.

Mortality in the United States among individuals aged 85 years and older between the years 1956 and 1987 was analyzed using a cumulative summation technique. This analysis demonstrates that general mortality conforms to Gompertzian dynamics through age 96 years for both men and women. Of the 33 320 985 deaths in men in the U.S. between 1956 and 1987, only 123,643 (0.37%) occurred in men aged 97 years and older. Of the corresponding 26,946,599 deaths in women, only 327,291 (1.21%) occurred in women aged 97 years and older. These results suggest that the competitive and deterministic features of the Gompertzian model of human aging and mortality remain valid through age 96 years and cover the vast majority of human mortality.

Influence of map scale on primary afferent terminal field geometry in cat dorsal horn.

1. Thirty-one physiologically identified primary afferent fibers were labeled intracellularly with horseradish peroxidase (HRP). 2. A computer analysis was used to determine whether the distribution of cutaneous mechanoreceptive afferent terminals varies as a function of location within the dorsal horn somatotopic map. 3. An analysis of the geometry of the projections of these afferents has shown that 1) terminal arbors have a greater mediolateral width within the region of the foot representation than lateral to it, 2) terminal arbors have larger length-to-width ratios outside the foot representation than within it, and 3) the orientation of terminal arbors near the boundary of the foot representation reflects the angle of the boundary. Previous attribution of mediolateral width variations to primary afferent type are probably in error, although there appear to be genuine variations of longitudinal extent as a function of primary afferent type. 4. Nonuniform terminal distributions represent the first of a three-component process underlying assembly of the monosynaptic portions of cell receptive fields (RFs) and the somatotopic map. The other two components consist of the elaboration of cell dendritic trees and the establishment of selective connections. 5. The variation of primary afferent terminal distributions with map location is not an absolute requirement for development of the map; for example, the RFs of postsynaptic cells could be assembled with the use of a uniform terminal distribution for all afferents, everywhere in the map, as long as cell dendrites penetrate the appropriate portions of the presynaptic neuropil and receive connections only from afferent axons contributing to their RFs.(ABSTRACT TRUNCATED AT 250 WORDS)

Somatotopic organization of single primary afferent axon projections to cat spinal cord dorsal horn.

Horseradish peroxidase injection of identified low threshold cutaneous mechanoreceptor (LTCM) primary afferent axons was used to assess the somatotopic organization of hindlimb projections to laminae III and IV of cat dorsal horn. Multiple injections in the same animals were used to assess bilateral symmetry and precision. Thirty-one axons were injected, with more than 1 axon injected in each of 8 animals (25 axons). Somatotopic relations between their receptive field (RF) centers and the centers of their dorsal horn projections were similar to the somatotopic relations between dorsal horn cell RF centers and cell locations. Very few reversals of mediolateral somatotopic gradients (proximodistal RF location as a function of mediolateral projection center) were observed. Two afferents with nearly identical RFs in 1 animal had nearly identical projections. These observations held for many different combinations of receptor types. A simple mathematical model was used to demonstrate that assembly of dorsal horn cell RFs via passive sampling of the presynaptic neuropil by dorsal horn cell dendrites cannot account for the sizes of dorsal horn cell LTCM RFs. Hypothesized mechanisms for assembly of dorsal horn cell RFs must take into account the functional selectivity of connections required to produce RFs smaller than those predicted by the passive assembly model.

Cellular potentials, electrogenic sodium pumping and sensitivity in guinea-pig atria.

Intracellular recording techniques in guinea-pig atrial pacemaker and nonpacemaker cells were used to investigate 1) the role of membrane potential changes in postjunctional supersensitivity, 2) the electrogenicity of the Na+,K+ pump and 3) the role of electrogenic pumping in sensitivity of the atria to agonists. In nonpacemaker cells, ouabain (10(-6) M) had no effect on resting membrane potential (left atria) or maximum diastolic potential (right atria). However, ouabain effectively suppressed the transient hyperpolarization that followed cessation of electrical stimulation. In pacemaker cells, ouabain and chronic treatment with reserpine (0.1 mg/kg/day) produced quite different patterns of changes in intracellular potentials. Chronic treatment with reserpine induced chronotropic supersensitivity to isoproterenol but not to histamine. Ouabain did not alter the chronotropic sensitivity to either agonist. The effects of isoproterenol and histamine on intracellular potentials in pacemaker cells were investigated in the presence and absence of ouabain and in control atria vs. atria from guinea pigs chronically pretreated with reserpine. Analysis of the data indicated that 1) electrophysiological measurements do not provide a discernible explanation for chronotropic supersensitivity, 2) the Na+ pump has the capacity for electrogenic pumping under conditions of Na+ loading, but demonstrates little indication of electrogenicity under basal conditions and 3) chronic treatment with reserpine does suppress the Na+,K+ pump in some areas of the right atrium, but this activity probably does not contribute to chronotropic supersensitivity. Other possible mechanisms of postjunctional supersensitivity in atria are discussed.

Photoreception in a barnacle: electrophysiology of the shadow reflex pathway in Balanus cariosus.

The photoreceptors in the median ocellus of the rock barnacle depolarize when illuminated. This depolarization spreads passively to the axon terminals in the supraesophageal ganglion. A small number of cells in the supraesophageal ganglion hyperpolarize when the median ocellus is illuminated and depolarize when it is shadowed. Nerve impulses are superimposed on the slow depolarization of the ganglion cells. Impulse activity in response to shadowing the median ocellus is recorded in a few fibers of the circumesophageal connectives. Picrotoxin blocks this shadow-induced activity. A model of the shadow reflex pathway is presented.

The ventral photoreceptor cells of Limulus. I. The microanatomy.

The ventral photoreceptor cells of Limulus polyphemus resemble the retinular cells of the lateral eyes both in electrical behavior and in morphology. Because of the great size of the ventral photoreceptor cells they are easy to impale with glass capillary micropipettes. Their location along the length of the ventral eye nerve makes them easy to dissect out and fix for electron microscopy. Each cell has a large, ellipsoidal soma that tapers into an axon whose length depends upon the distance of the cell from the brain. The cell body contains a rich variety of cytoplasmic organelles with an especially abundant endoplasmic reticulum. The most prominent structural feature is the microvillous rhabdomere, a highly modified infolding of the plasmalemma. The microvilli are tightly packed together within the rhabdomere, and quintuple-layered junctions are encountered wherever microvillar membranes touch each other. Glial cells cover the surface of the photoreceptor cell and send long, sheet-like projections of their cytoplasm into the cell body of the photoreceptor cell. Some of these projections penetrate the rhabdomere deep within the cell and form quintuple-layered junctions with the microvilli. Junctions between glial cells and the photoreceptor cell and between adjacent glial cells are rarely encountered elsewhere, indicating that there is an open pathway between the intermicrovillous space and the extracellular medium. The axon has a normal morphology but it is electrically inexcitable.

The ventral photoreceptor cells of Limulus. 3. A voltage-clamp study.

In the dark, the ventral photoreceptor of Limulus exhibits time-variant currents under voltage-clamp conditions; that is, if the membrane potential of the cell is clamped to a depolarized value there is an initial large outward current which slowly declines to a steady level. The current-voltage relation of the cell in the dark is nonlinear. The only ion tested which has any effect on the current-voltage relation is potassium; high potassium shifts the reversal potential towards zero and introduces a negative slope-conductance region. When the cell is illuminated under voltage-clamp conditions, an additional current, the light-induced current, flows across the cell membrane. The time course of this current mimics the time course of the light response (receptor potential) in the unclamped cell; namely, an initial transient phase is followed by a steady-state phase. The amplitude of the peak transient current can be as large as 60 times the amplitude of the steady-state current, while in the unclamped cell the amplitude of the peak transient voltage never exceeds 4 times the amplitude of the steady-state voltage. The current-voltage relations of the additional light-induced current obtained for different instants of time are also nonlinear, but differ from the current-voltage relations of the dark current. The ions tested which have the greatest effect on the light-induced current are sodium and calcium; low sodium decreases the current, while low calcium increases the current. The data strongly support the hypothesis that two systems of electric current exist in the membrane. Thus the total ionic current which flows in the membrane is accounted for as the sum of a dark current and a light-induced current.

The ventral photoreceptor cells of Limulus. II. The basic photoresponse.

The ventral photoreceptors of Limulus polyphemus are unipolar cells with large, ellipsoidal somas located long both "lateral olfactory nerves." As a consequence of their size and location, the cells are easily impaled with microelectrodes. The cells have an average resting potential of -48 mv. The resting potential is a function of the external concentration of K. When the cell is illuminated, it gives rise to the typical "receptor potential" seen in most invertebrate photoreceptors which consists of a transient phase followed by a maintained phase of depolarization. The amplitude of the transient phase depends on both the state of adaptation of the cell and the intensity of the illumination, while the amplitude of the maintained phase depends only on the intensity of the illumination. The over-all size of the receptor potential depends on the external concentration of Na, e.g. in sodium-free seawater the receptor potential is markedly reduced, but not abolished. On the other hand lowering the Ca concentration produces a marked enhancement of both components of the response, but predominantly of the steady-state component. Slow potential fluctuations are seen in the dark-adapted cell when it is illuminated with a low intensity light. A spike-like regenerative process can be evoked by either the receptor potential or a current applied via a microelectrode. No evidence of impulse activity has been found in the axons of these cells. The ventral photoreceptor cell has many properties in common with a variety of retinular cells and therefore should serve as a convenient model of the primary receptor cell in many invertebrate eyes.

Simple photoreceptors in Limulus polyphemus.

The "olfactory nerve," the endoparietal eye, and the rudimentary lateral eyes of Limulus (polyphemus) contain simple photoreceptor cells that duplicate many of the electrical responses of the retinular cells of the lateral eye; the responses are a receptor potential consisting of aninitial transient phase and a subsequent steady phase,low-amplitude fluctuations, and a small locally regenerative response to pulses of both light and current. Photic stimulation does not induce conducted action potentials, but does increase the membrane conductance. The receptor potentialrequires the presence of sodium ions in the external medium. Measurements of action and absorption spectra indicate a photopigment whose maximum absorption is of light with wavelength of 535 nanometers. The functional significance of these cells has not been ascertained.