Chemical excitation of Limulus photoreceptors. I. Phosphatase inhibitors induce discrete-wave production in the dark

Molybdate, tungstate, fluoride, vanadate, and GTP-gamma-S [guanosine-5'- 0-(3-thiotriphosphate)] were injected into Limulus ventral photoreceptors by ionophoresis from microelectrodes. All of these drugs induce discrete waves of depolarization similar in waveform to, but smaller in amplitude than, those normally elicited by dim light. As for light-evoked waves, the amplitude of drug-induced waves decreases with light adaptation. For the compounds examined so far (fluoride, vanadate, GTP-gamma-S), the drug-induced waves share a reversal potential with light-induced discrete waves at about +15 mV. The induction of discrete waves by fluoride, vanadate, and molybdate was found to be reversible, whereas the induction of waves by GTP-gamma-S was not. Unlike fluoride and vanadate, which induce waves when added to the bath, molybdate appears to be ineffective when applied extracellularly. Because of the similarity of the drug-induced waves to light-induced discrete waves, we conclude that the drug-induced waves arise from a process similar or perhaps identical to visual excitation of the photoreceptor. However, the smaller size of drug-induced waves suggests that they arise at a stage of phototransduction subsequent to the isomerization of rhodopsin. On the basis of the chemical properties and action of the drugs, we suggest that discrete waves may arise through the activation of a GTP-binding protein.     

Light Adaptation in the Ventral Photoreceptor of Limulus

Light adaptation in both the ventral photoreceptor and the lateral eye photoreceptor is a complex process consisting of at least two phases. One phase, which we call the rapid phase of adaptation, occurs whenever there is temporal overlap of the discrete waves that compose a light response. The recovery from the rapid phase of adaptation follows an exponential time-course with a time constant of approximately 75 ms at 21°C. The rapid phase of adaptation occurs at light intensities barely above discrete wave threshold as well as at substantially higher light intensities with the same recovery time-course at all intensities. It occurs in voltage-clamped and unclamped photoreceptors. The kinetics of the rapid phase of adaptation is closely correlated to the photocurrent which appears to initiate it after a short delay. The rapid phase of adaptation is probably identical to what is called the "adapting bump" process. At light intensities greater than about 10 times discrete wave threshold another phase of light adaptation occurs. It develops slowly over a period of ½ s or so, and decays even more slowly over a period of several seconds. It is graded with light intensity and occurs in both voltage-clamped and unclamped photoreceptors. We call this the slow phase of light adaptation.     

Stochastic Properties of Discrete Waves of the Limulus Photoreceptor

In the dark-adapted photoreceptor of the horseshoe crab, Limulus, transient discrete depolarizations of the cell membrane, discrete waves, occur in total darkness and their rate of occurrence is increased by illumination. The individual latencies of the discrete waves evoked by a light stimulus often cannot be resolved because the discrete waves overlap in time. The latency of the first discrete wave that follows a stimulus can be determined with reasonable accuracy. We propose a model which allows us to make an estimate of the distribution of the latencies of the individual light-evoked discrete waves, and to predict the latency distribution of the first discrete wave that follows a stimulus of arbitrary intensity-time course from the latency distribution of the first discrete wave that follows a brief flash of light. For low intensity stimuli, the predictions agree well with the observations. We define a response as the occurrence of one or more discrete waves following a stimulus. The distribution of the peak amplitudes of responses suggests that the peak amplitude of individual discrete waves sometimes has a bimodal distribution. The latencies of the two types of discrete waves, however, follow similar distributions. The area under the voltage-time curve of responses that follow equal energy long (1.25 sec) and short (10 msec) light stimuli follows similar distributions, and this suggests that discrete waves summate linearly.     

Unidirectional waves on rings: Models for chiral preference of circumnutating plants

Twining plants exhibit a striking oscillation of their stems in their quest for a support. The oscillations, called circumnutation, have periods generally of 1–5 hr, and virtually all species have a preferred direction of twining. I seek to explain these chiral asymmetries in plant behavior by hypothesizing a chiral asymmetry in plant anatomy. Such asymmetries already exist, for example, in phyllotaxis. I explore wave phenomena on asymmetric but isotropic rings, and seek systems which will only support (stable) waves in one direction around the ring, and not in the other. Simulations indicate that (1) oscillatory reaction-diffusion systems do not support unidirectional waves on rings; (2) excitable reaction-diffusion systems do support unidirectional waves on rings; and (3) unidirectional phase-locking (discrete unidirectional waves) occurs in rings of coupled oscillators. Thus, chiral asymmetries of circumnutating plants cannot be explained by continuum oscillator phenomena, but can be explained by general discrete oscillators, or excitable phenomena on the continuum.     

Bilaterally propagating waves of spontaneous activity arising from discrete pacemakers in the neonatal mouse cerebral cortex

Spontaneous electrical activity that moves in synchronized waves across large populations of neurons plays widespread and important roles in nervous system development. The propagation patterns of such waves can encode the spatial location of neurons to their downstream targets and strengthen synaptic connections in coherent spatial patterns. Such waves can arise as an emergent property of mutually excitatory neural networks, or can be driven by a discrete pacemaker. In the mouse cerebral cortex, spontaneous synchronized activity occurs for approximately 72 h of development centered on the day of birth. It is not known whether this activity is driven by a discrete pacemaker or occurs as an emergent network property. Here we show that this activity propagates as a wave that is initiated at either of two homologous pacemakers in the temporal region, and then propagates rapidly across both sides of the brain. When these regions of origin are surgically isolated, waves do not occur. Therefore, this cortical spontaneous activity is a bilateral wave that originates from a discrete subset of pacemaker neurons. © 2009 Wiley Periodicals, Inc. Develop Neurobiol, 2009     

Chemical excitation of Limulus photoreceptors. II. Vanadate, GTP-gamma- S, and fluoride prolong excitation evoked by dim flashes of light

We treated Limulus ventral photoreceptors with the phosphatase inhibitors fluoride, vanadate, and GTP-gamma-S [guanosine-5'0-(3-thiotriphosphate)] under various conditions of illumination and external calcium concentrations. In the dark in low-calcium (1 mM) artificial seawater (ASW), fluoride-induced discrete waves cluster together in time. Under these conditions, the intervals between waves were found to be correlated, and there were excess short intervals beyond the number expected from an exponential interval distribution. To assess the effects of the inhibitors on the light response, we stimulated ventral receptors with a series of dim flashes and averaged the current response under voltage clamp. In ASW, vanadate and GTP-gamma-S prolong the decay of the averaged response to dim test flashes, but prolongation does not always accompany the induction of discrete waves in the dark. Prolongation induced by vanadate in normal-calcium (10 mM) ASW was enhanced in low-calcium (1 mM Ca2+) ASW. Many individual response records suggest that prolongation results from extra discrete waves late in the light response, whereas others reveal long-lasting complex waveforms that cannot easily be resolved into discrete waves. The apparent effect of the inhibitors on the light response is to allow a single photoactivated rhodopsin molecule to produce multiple discrete waves and complex long-lasting events. We suggest that both prolongation of the light response and clustering of waves in the dark result from inhibition of a step in the pathway of visual transduction, in which GTP hydrolysis normally helps to turn off the production of both light-evoked and spontaneous waves.     

Discrete Waves and Phototransduction in Voltage-damped Ventral Photoreceptors

Discrete waves in the voltage-clamped photoreceptor of Limulus are remarkably similar in all essential properties to those found in an unclamped cell. The latency distribution of discrete waves is not affected by considerable changes in the holding potential in a voltage-clamped cell. Both large and small waves occur in voltage-clamped and unclamped cells and in approximately the same proportion. Large and small waves also share the same latency distributions and spectral sensitivity. We suggest that small waves may result from the activation of damaged membrane areas. Large waves have an average amplitude of approximately 5 nA in voltage-clamped photoreceptors. It probably requires several square microns of cell membrane to support this much photo-current. Thus the amplification inherent in the discrete wave process may involve spatial spread of activation from unimolecular dimensions to several square microns of cell membrane surface. Neither local current flow, nor pre-packaging of any transmitter substance appears to be involved in the amplification process. The possible mechanisms of the amplification are evaluated with relationship to the properties of discrete waves.     

Excitation of waves in an inhomogeneous plasma

The evolution of initial perturbations in a spatially inhomogeneous cold electron plasma in the absence of an external magnetic field is considered. The excitation of both continuous-spectrum bulk plasma waves and surface plasma waves with a discrete frequency spectrum is investigated. Analytic solutions are obtained in the long-wavelength limit, and the excitation of waves of arbitrary length is analyzed numerically. The local, integral, and spatial spectra are calculated, as well as the field structures and dispersion properties of waves in waveguides filled nonuniformly with a plasma. It is shown that, in a plasma with a smooth boundary, there also exist surface waves with a discrete spectrum (although with somewhat different properties as compared to those in a plasma with a sharp boundary), which are excited together with continuous-spectrum bulk waves during the evolution of the initial perturbation.     

Spiralizations and tropisms in Arabidopsis roots.

When Arabidopsis seedlings are grown on a hard-agar plate, their primary roots show characteristic spiralling movements, apparent as waves, coils and torsions, together with a slanting toward the right-hand side. All these movements are believed to be the result of three different processes acting on the roots: circumnutation, positive gravitropism and negative thigmotropism. The basic movement of the roots is described as that of a growing right-handed helix, which, because of the root tip hitting the agar plate, is continuously switched from the right-hand to the left-hand of the growth direction, and vice versa. This movement also produces a slanting root-growth direction toward the right-hand because of the incomplete waves made by the right-handed root to the left-hand. By contrast, the torsions seen in the coils and waves are interpreted as artefacts that form as an adaptation of the three-dimensional root helix to the flat two-dimensional agar surface.     

Adaptation as process: the future of Darwinism and the legacy of Theodosius Dobzhansky

Conceptions of adaptation have varied in the history of genetic Darwinism depending on whether what is taken to be focal is the process of adaptation, adapted states of populations, or discrete adaptations in individual organisms. I argue that Theodosius Dobzhansky's view of adaptation as a dynamical process contrasts with so-called "adaptationist" views of natural selection figured as "design-without-a-designer" of relatively discrete, enumerable adaptations. Correlated with these respectively process and product oriented approaches to adaptive natural selection are divergent pictures of organisms themselves as developmental wholes or as "bundles" of adaptations. While even process versions of genetical Darwinism are insufficiently sensitive to the fact much of the variation on which adaptive selection works consists of changes in the timing, rate, or location of ontogenetic events, I argue that articulations of the Modern Synthesis influenced by Dobzhansky are more easily reconciled with the recent shift to evolutionary developmentalism than are versions that make discrete adaptations central.     

Structural correlates of mechanosensory transduction and adaptation in identified neurons of spider slit sensilla

We used isolated but functionally intact preparations of the lyriform slit-sense organ VS-3 from the leg of the spider, Cupiennius salei Keys, to examine the role of prominent fine-structural elements for mechanosensory transduction and adaptation. Slit sensilla act as strain sensors in the cuticular exoskeleton; each slit is innervated by two mechanosensitive neurons. Punctate mechanical deformation at four points along the dendrites demonstrated that mechanical excitability is confined to membrane sites at the extreme dendrite tips that are enclosed by cuticular slit structures. Depletion of microtubules in VS-3 neurons by prolonged mechanical stimulation and application of 5 mmol l(-1) colchicine did not disrupt the generation of a receptor potential. Hence, putative gating mechanisms of the mechanically activated membrane channels at the dendrite tips appear to be largely independent of microtubular structures. The discrete adaptation pattern in each of the two partner neurons, rapidly adapting versus slowly adapting, did not depend on the distinct mode of dendrite attachment to cuticular slit structures, and even persisted in isolated neurons after their dendrite tips and auxiliary structures were lost. We suggest that the two discrete adaptation patterns are based on intrinsic differences in the action potential encoding process rather than differences in stimulus transformation or mechanotransduction.     

Oscillations of Potential in the Electroretinogram of the Lobster

The electroretinogram (ERG) evoked in the lobster by a short flash of light consists of a highly damped, slow oscillation of potential, triggered apparently by a single excitatory process. Near the threshold, only one wave may be evident; but as the intensity of stimulus rises, a prior wave appears, and grows so much more rapidly as to become dominant. Simultaneously third and later waves appear, so that at high intensities the response may include five to seven waves. Dark adaptation favors the second and later waves relative to the first; light adaptation tends to suppress them. On turning on a steady light the oscillations are superimposed on the early stages of development of a maintained, steady-state potential (on-response). Turning off the light causes a rapid fluctuation of potential followed by a similarly damped slow oscillation (off-response). These phenomena resemble in part oscillations recently observed in the b wave of the ERG of many vertebrates including man.     

Periodic calcium waves cross ascidian eggs after fertilization

Ascidian eggs respond to fertilization with one to two dozen periodic calcium pulses (J.E. Speksnijder, D.W. Corson, C. Sardet, and L.F. Jaffe, 1989a, Dev. Biol. 135, 182-190). We examined the spatial pattern of these pulses and found that they are initiated in discrete regions from which they propagate as waves. The first few pulses start in the animal hemisphere, whereas the later ones are mostly initiated near the vegetal pole. Such vegetal waves are often followed by a contraction of the egg surface. Since these waves are attenuated as they spread, they repeatedly expose the vegetal pole region to more calcium. The mechanism of these repetitive calcium waves and their possible role in establishing pattern or completing meiosis is discussed.     

Traveling waves in the discrete fast buffered bistable system

We study the existence and uniqueness of traveling wave solutions of the discrete buffered bistable equation. Buffered excitable systems are used to model, among other things, the propagation of waves of increased calcium concentration, and discrete models are often used to describe the propagation of such waves across multiple cells. We derive necessary conditions for the existence of waves, and, under some restrictive technical assumptions, we derive sufficient conditions. When the wave exists it is unique and stable.      

On reverberatory processes in homogeneous neuronal spaces

Reverberating neural activity is strictly defined and examined in continuous and discrete neuronal spaces with homogeneous structure. Reverberations start with a specific population of firing neurons called the initial excitation and spread out in waves of firing and refractory bands of neurons toward the periphery. The necessary and sufficient conditions for having reverberations are obtained for continuous space and discrete one-dimensional space. The excitation fronts of reverberating waves have stable shapes which depend only upon the structure of the neuronal space. The reverberatory processes in high-threshold discrete neuronal spaces show strongly nonlinear properties. Relation between reverberations and nervous functions is discussed.     

Ca<Superscript>2+</Superscript> spiral waves in a spatially discrete and random medium

It is well known that the spatial distribution of the calcium ion channels in the endoplasmic reticulum is discrete. We study the Ca²⁺ spiral pattern formation based on a model in which ion channels are discretely and randomly distributed. Numerical simulations are performed on different types of media with the Ca²⁺ release sites uniformly distributed, discretely and uniformly arranged, or discretely and randomly arranged. The comparisons among the different media show that random distribution is necessary for spontaneous initiation of Ca²⁺ spiral waves, and the discrete and random distribution is of significance for spiral waves under physiologically reasonable conditions. The period and velocity of spiral waves are also calculated, and they are not prominently changed by varying the type of medium.     

A dynamic theory of coordination of discrete movement

The concepts of pattern dynamics and their adaptation through behavioral information, developed in the context of rhythmic movement coordination, are generalized to describe discrete movements of single components and the coordination of multiple components in discrete movement. In a first step we consider only one spatial component and study the temporal order inherent in discrete movement in terms of stable, reproducible space-time relationships. The coordination of discrete movement is captured in terms of relative timing. Using an exactly solvable nonlinear oscillator as a mathematical model, we show how the timing properties of discrete movement can be described by these pattern dynamics and discuss the relation of the pattern variables to observable end-effector movement. By coupling several such component dynamics in a fashion analogous to models of rhythmic movement coordination we capture the coordination of discrete movements of two components. We find the tendency to synchronize the component movements as the discrete analogon of in-phase locking and study its breakdown when the components become too different in their dynamic properties. The concept of temporal stability leads to the prediction that remote compensatory responses occur such as the restore synchronization when one component is perturbed. This prediction can be used to test the theory. We find that the discrete analogon to antiphase locking in rhythmic movement is a tendency to move sequentially, a finding that can also be subjected to empirical test.     

Independence of Location of Light Absorption and Discrete Wave Latency Distribution in Limulus Ventral Nerve Photoreceptors

Discrete waves of depolarization evoked by dim pulses of light in dark-adapted ventral nerve photoreceptors in Limulus show fluctuation in their latency. To a resolution of 5–10 µm the latency distribution function appears to be independent of where in the receptor light is absorbed. Also, there is apparent local adaptation to bright light pulses.