The synthesis-diffusion-degradation model explains Bicoid gradient formation in unfertilized eggs.

Precise formation of morphogen gradients is essential to the establishment of reproducible pattern in development. Mechanisms proposed for obtaining the requisite precision range from simple models with few parameters to more complex models involving many regulated quantities. The synthesis-diffusion-degradation (SDD) model is a relatively simple model explaining the formation of the Bicoid gradient in Drosophila melanogaster, in which the steady-state characteristic length of the gradient is determined solely by the rates of diffusion and degradation of the morphogen. In this work, we test the SDD model in unfertilized D. melanogaster eggs, which contain a single female pronucleus and lack the nuclear division cycles and other zygotic regulatory processes seen in fertilized eggs. Using two-photon live imaging as well as a novel method for quantitative imaging based on decorrelation of photoswitching waveforms, we find that the Bicoid gradient is longer and shallower in unfertilized eggs as compared to the gradient at the same time points in fertilized eggs. Using a means of measuring the Bicoid lifetime by conjugation to a photoconvertible fluorophore, we find that the lifetime is correspondingly longer in unfertilized eggs, providing qualitative and quantitative agreement with the predictions of the SDD model.

Spontaneous eye movements in goldfish: oculomotor integrator performance, plasticity, and dependence on visual feedback.

To quantify performance of the goldfish oculomotor neural integrator and determine its dependence on visual feedback, we measured the relationship between eye drift-velocity and position during spontaneous gaze fixations in the light and in the dark. In the light, drift-velocities were typically less than 1 deg/s, similar to those observed in humans. During brief periods in darkness, drift-velocities were only slightly larger, but showed greater variance. One hour in darkness degraded fixation-holding performance. These findings suggest that while visual feedback is not essential for online fixation stability, it may be used to tune the mechanism of persistent neural activity in the oculomotor integrator.

A miniature head-mounted two-photon microscope. high-resolution brain imaging in freely moving animals.

Two-photon microscopy has enabled anatomical and functional fluorescence imaging in the intact brain of rats. Here, we extend two-photon imaging from anesthetized, head-stabilized to awake, freely moving animals by using a miniaturized head-mounted microscope. Excitation light is conducted to the microscope in a single-mode optical fiber, and images are scanned using vibrations of the fiber tip. Microscope performance was first characterized in the neocortex of anesthetized rats. We readily obtained images of vasculature filled with fluorescently labeled blood and of layer 2/3 pyramidal neurons filled with a calcium indicator. Capillary blood flow and dendritic calcium transients were measured with high time resolution using line scans. In awake, freely moving rats, stable imaging was possible except during sudden head movements.

In vivo intracellular recording and perturbation of persistent activity in a neural integrator.

To investigate the mechanisms of persistent neural activity, we obtained in vivo intracellular recordings from neurons in an oculomotor neural integrator of the goldfish during spontaneous saccades and fixations. Persistent changes in firing rate following saccades were associated with step changes in interspike membrane potential that were correlated with changes in eye position. Perturbation of persistent activity with brief intracellular current pulses designed to mimic saccadic input only induced transient changes of firing rate and membrane potential. When neurons were hyperpolarized below action potential threshold, position-correlated step changes in membrane potential remained. Membrane potential fluctuations were greater during more depolarized steps. These results suggest that sustained changes in firing rate are supported not by either membrane multistability or changes in pacemaker currents, but rather by persistent changes in the rate or amplitude of synaptic inputs.

The autapse: a simple illustration of short-term analog memory storage by tuned synaptic feedback.

According to a popular hypothesis, short-term memories are stored as persistent neural activity maintained by synaptic feedback loops. This hypothesis has been formulated mathematically in a number of recurrent network models. Here we study an abstraction of these models, a single neuron with a synapse onto itself, or autapse. This abstraction cannot simulate the way in which persistent activity patterns are distributed over neural populations in the brain. However, with proper tuning of parameters, it does reproduce the continuously graded, or analog, nature of many examples of persistent activity. The conditions for tuning are derived for the dynamics of a conductance-based model neuron with a slow excitatory autapse. The derivation uses the method of averaging to approximate the spiking model with a nonspiking, reduced model. Short-term analog memory storage is possible if the reduced model is approximately linear and if its feedforward bias and autapse strength are precisely tuned.

Action potentials reliably invade axonal arbors of rat neocortical neurons.

Neocortical pyramidal neurons have extensive axonal arborizations that make thousands of synapses. Action potentials can invade these arbors and cause calcium influx that is required for neurotransmitter release and excitation of postsynaptic targets. Thus, the regulation of action potential invasion in axonal branches might shape the spread of excitation in cortical neural networks. To measure the reliability and extent of action potential invasion into axonal arbors, we have used two-photon excitation laser scanning microscopy to directly image action-potential-mediated calcium influx in single varicosities of layer 2/3 pyramidal neurons in acute brain slices. Our data show that single action potentials or bursts of action potentials reliably invade axonal arbors over a range of developmental ages (postnatal 10-24 days) and temperatures (24 degrees C-30 degrees C). Hyperpolarizing current steps preceding action potential initiation, protocols that had previously been observed to produce failures of action potential propagation in cultured preparations, were ineffective in modulating the spread of action potentials in acute slices. Our data show that action potentials reliably invade the axonal arbors of neocortical pyramidal neurons. Failures in synaptic transmission must therefore originate downstream of action potential invasion. We also explored the function of modulators that inhibit presynaptic calcium influx. Consistent with previous studies, we find that adenosine reduces action-potential-mediated calcium influx in presynaptic terminals. This reduction was observed in all terminals tested, suggesting that some modulatory systems are expressed homogeneously in most terminals of the same neuron.

Anatomy and discharge properties of pre-motor neurons in the goldfish medulla that have eye-position signals during fixations.

Previous work in goldfish has suggested that the oculomotor velocity-to-position neural integrator for horizontal eye movements may be confined bilaterally to a distinct group of medullary neurons that show an eye-position signal. To establish this localization, the anatomy and discharge properties of these position neurons were characterized with single-cell Neurobiotin labeling and extracellular recording in awake goldfish while monitoring eye movements with the scleral search-coil method. All labeled somata (n = 9) were identified within a region of a medially located column of the inferior reticular formation that was approximately 350 microm in length, approximately 250 microm in depth, and approximately 125 microm in width. The dendrites of position neurons arborized over a wide extent of the ventral half of the medulla with especially heavy ramification in the initial 500 microm rostral of cell somata (n = 9). The axons either followed a well-defined ventral pathway toward the ipsilateral abducens (n = 4) or crossed the midline (n = 2) and projected toward the contralateral group of position neurons and the contralateral abducens. A mapping of the somatic region using extracellular single unit recording revealed that position neurons (n > 120) were the dominant eye-movement-related cell type in this area. Position neurons did not discharge below a threshold value of horizontal fixation position of the ipsilateral eye. Above this threshold, firing rates increased linearly with increasing temporal position [mean position sensitivity = 2.8 (spikes/s)/ degrees, n = 44]. For a given fixation position, average rates of firing were higher after a temporal saccade than a nasal one (n = 19/19); the magnitude of this hysteresis increased with increasing position sensitivity. Transitions in firing rate accompanying temporal saccades were overshooting (n = 43/44), beginning, on average, 17.2 ms before saccade onset (n = 17). Peak firing rate change accompanying temporal saccades was correlated with eye velocity (n = 36/41). The anatomical findings demonstrate that goldfish medullary position neurons have somata that are isolated from other parts of the oculomotor system, have dendritic fields overlapping with axonal terminations of neurons with velocity signals, and have axons that are capable of relaying commands to the abducens. The physiological findings demonstrate that the signals carried by position neurons could be used by motoneurons to set the fixation position of the eye. These results are consistent with a role for position neurons as elements of the velocity-to-position neural integrator for horizontal eye movements.

Stability of the memory of eye position in a recurrent network of conductance-based model neurons.

Studies of the neural correlates of short-term memory in a wide variety of brain areas have found that transient inputs can cause persistent changes in rates of action potential firing, through a mechanism that remains unknown. In a premotor area that is responsible for holding the eyes still during fixation, persistent neural firing encodes the angular position of the eyes in a characteristic manner: below a threshold position the neuron is silent, and above it the firing rate is linearly related to position. Both the threshold and linear slope vary from neuron to neuron. We have reproduced this behavior in a biophysically plausible network model. Persistence depends on precise tuning of the strength of synaptic feedback, and a relatively long synaptic time constant improves the robustness to mistuning.

In vivo dendritic calcium dynamics in deep-layer cortical pyramidal neurons.

Dendritic Ca2+ action potentials in neocortical pyramidal neurons have been characterized in brain slices, but their presence and role in the intact neocortex remain unclear. Here we used two-photon microscopy to demonstrate Ca2+ electrogenesis in apical dendrites of deep-layer pyramidal neurons of rat barrel cortex in vivo. During whisker stimulation, complex spikes recorded intracellularly from distal dendrites and sharp waves in the electrocorticogram were accompanied by large dendritic [Ca2+ ] transients; these also occurred during bursts of action potentials recorded from somata of identified layer 5 neurons. The amplitude of the [Ca 2+] transients was largest proximal to the main bifurcation, where sodium action potentials produced little Ca2+ influx. In some cases, synaptic stimulation evoked [Ca2+] transients without a concomitant action potential burst, suggesting variable coupling between dendrite and soma.

Spread of dendritic excitation in layer 2/3 pyramidal neurons in rat barrel cortex in vivo.

In layer 2/3 pyramidal neurons of barrel cortex in vivo, calcium ion concentration ([Ca2+]) transients in apical dendrites evoked by sodium action potentials are limited to regions close to the soma. To study the mechanisms underlying this restricted pattern of calcium influx, we combined two-photon imaging of dendritic [Ca2+] dynamics with dendritic membrane potential measurements. We found that sodium action potentials attenuated and broadened rapidly with distance from the soma. However, dendrites of layer 2/3 cells were electrically excitable, and direct current injections could evoke large [Ca2+] transients. The restricted pattern of dendritic [Ca2+] transients is therefore due to a failure of sodium action-potential propagation into dendrites. Also, stimulating subcortical activating systems by tail pinch can enhance dendritic [Ca2+] influx induced by a sensory stimulus by increasing cellular excitability, consistent with the importance of these systems in plasticity and learning.

Human primary visual cortex and lateral geniculate nucleus activation during visual imagery.

The functional magnetic resonance (fMRI) technique can be robustly used to map functional activation of the visual pathway including the primary visual cortex (V1), the lateral geniculate nucleus (LGN), and other nuclei of humans during visual perception stimulation. One of the major controversies in visual neuroscience is whether lower-order visual areas involve the visual imagery process. This issue was examined using fMRI at high magnetic field. It was demonstrated for the first time that the LGN was activated during visual imagery process in the human brain together with V1 and other activation. There was a tight coupling of the activation between V1 and the LGN during visual imagery.

Functional study of the rat cortical microcircuitry with voltage-sensitive dye imaging of neocortical slices.

The computations performed within cortex are likely to be determined by its internal dynamics in addition to its pattern of afferent input. As a step toward characterizing these dynamics, we have imaged electrical activity in slices from rat primary visual cortex stained with the voltage-sensitive dye di-4-ANEPPS. In response to electrical stimulation two fluorescence signals of similar maximum amplitude are elicited, (i) A fast signal that peaks in a few milliseconds, is dependent on membrane voltage, and has a significant presynaptic component. This signal can be used to image electrical activity ratiometrically. (ii) A slow signal that peaks a few seconds after stimulation, does not reflect voltage changes, and may originate from changes in scattering properties of the slice and from interactions of the dye with the cells. The spatial pattern of fast signals obtained in response to focal stimulation of coronal slices is consistent with known interlaminar projection patterns. In tangential slices, imaging of fast signals reveals clustered horizontal responses. Finally, imaging of fast signals during epileptiform activation of the disinhibited circuit reveals propagating responses, without evidence for modular activation.

In vivo dendritic calcium dynamics in neocortical pyramidal neurons.

The dendrites of mammalian pyramidal neurons contain a rich collection of active conductances that can support Na+ and Ca2+ action potentials (for a review see ref. 1). The presence, site of initiation, and direction of propagation of Na+ and Ca2+ action potentials are, however, controversial, and seem to be sensitive to resting membrane potential, ionic composition, and degree of channel inactivation, and depend on the intensity and pattern of synaptic stimulation. This makes it difficult to extrapolate from in vitro experiments to the situation in the intact brain. Here we show that two-photon excitation laser scanning microscopy can penetrate the highly scattering tissue of the intact brain. We used this property to measure sensory stimulus-induced dendritic [Ca2+] dynamics of layer 2/3 pyramidal neurons of the rat primary vibrissa (Sm1) cortex in vivo. Simultaneous recordings of intracellular voltage and dendritic [Ca2+] dynamics during whisker stimulation or current injection showed increases in [Ca2+] only in coincidence with Na+ action potentials. The amplitude of these [Ca2+] transients at a given location was approximately proportional to the number of Na+ action potentials in a short burst. The amplitude for a given number of action potentials was greatest in the proximal apical dendrite and declined steeply with increasing distance from the soma, with little Ca2+ accumulation in the most distal branches, in layer 1. This suggests that widespread Ca2+ action potentials were not generated, and any significant [Ca2+] increase depends on somatically triggered Na+ action potentials.

Presynaptic calcium dynamics at the frog retinotectal synapse.

1. We characterized the kinetics of presynaptic Ca2+ ion concentration in optic nerve fibers and terminals of the optic tectum in Rana pipiens with the use of microfluorimetry. Isolated frog brains were incubated with the membrane-permeant tetraacetoxymethyl ester (AM) of the Ca2+ indicator fura-2. An optic nerve shock caused a transient decrease in the 380-nm excited fluorescence in the optic tectum with a rise time of <15 ms and a recovery to prestimulus levels on a time scale of seconds. 2. In normal saline, the amplitude of the fluorescence transients was dependent on stimulus intensity and at all levels it was directly correlated with the amplitude of postsynaptic field potentials produced by activation of unmyelinated optic nerve fibers. In the presence of the non-N-methyl-D-aspartate glutamate receptor antagonist 6-cyano-7-nitroquinoxaline-2,3-dione, the amplitude and time course of fluorescence transients remained essentially unchanged while postsynaptic field potential amplitude was greatly reduced. Replacing extracellular Ca2+ with Ba2+ blocked unfacilitated postsynaptic field potentials while fluorescence transients remained significant. In reduced-Ca2+ salines (<1 mM), the amplitude of fluorescence transients increased approximately linearly with extracellular [Ca2+], whereas the amplitude the corresponding field potential was nonlinearly related to the fluorescent transient amplitude (approximately 2.5 power). In thin sections of labeled tecta, fluorescence labeling was localized to 1-micron puncta in the termination zone of optic nerve fibers in the superficial layers. Taken together, these results provide strong evidence that the fluorescence transients correspond to an increase in Ca2+ in presynaptic terminals of unmyelinated optic nerve fibers. 3. During trains of optic nerve stimulation, the amplitude of fluorescence transients to succeeding action potentials became smaller. The decrement of the amplitudes was not observed in mag-fura-5-labeled tecta, when the intracellular Ca2+ buffering capacity of fura-2-labeled terminals was increased by incubation with bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid (BAPTA)-AM or ethylene glycol-bis (beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid (EGTA)-AM, or in low-Ca2+ saline. We conclude that the Ca2+ influx per action potential is constant during the train and that the reduced response was produced by saturation of the fura-2. We provide a mathematical analysis of this saturation effect and use it to estimate the Ca2+ change per action potential. 4. Both BAPTA-AM and EGTA-AM reduced the overall amplitude of fura-2-measured Ca2+ transients and reduced the saturation effect in action potential trains. However, there was a qualitative difference in their effects on the shape of the transient. Incubation with the fast buffer BAPTA prolonged the decay to baseline. In contrast, the slow buffer EGTA (or EDTA) produced an initial decay faster than the control condition while also producing the slower subsequent phase observed with BAPTA. We demonstrate that these results are consistent with numerical simulations of Ca2+ dynamics in a single-compartment model where the fast initial decay is produced by the forward rate of Ca2+ binding to EGTA. 5. Ca2+ influx into tectal presynaptic structures, and also into unmyelinated axons in the isolated optic nerve, was diminished (60-70%) in the presence of the voltage-activated Ca2+ channel blocker omega-conotoxin GVIA, but was only weakly affected (approximately 10%) by omega-agatoxin IVA. 6. After 10- to 50-Hz stimulus trains, synaptic enhancement of unmyelinated fibers decayed with a characteristic time similar to fura-2 fluorescence decays. Incubation with EDTA-AM or EGTA-AM produced little effect on evoked release but reduced both the amplitude of the fura-2-measured Ca2+ transient and the amplitude of short-term synaptic enhancement.

Imaging calcium dynamics in dendritic spines.

Recent advances in optical imaging technology have enabled the measurement of Ca2+ dynamics in individual synaptic spines with high time resolution. Results from work using this new technology have confirmed the view that individual synaptic spines can act as functional chemical compartments with independent dynamics of second-messenger concentration. In particular, the ability of Ca2+ to directly mediate Hebbian coincidence detection has been confirmed.

Direct measurement of coupling between dendritic spines and shafts.

Characterization of the diffusional and electrotonic coupling of spines to the dendritic shaft is crucial to understanding neuronal integration and synaptic plasticity. Two-photon photobleaching and photorelease of fluorescein dextran were used to generate concentration gradients between spines and shafts in rat CA1 pyramidal neurons. Diffusional reequilibration was monitored with two-photon fluorescence imaging. The time course of reequilibration was exponential, with time constants in the range of 20 to 100 milliseconds, demonstrating chemical compartmentalization on such time scales. These values imply that electrical spine neck resistances are unlikely to exceed 150 megohms and more likely range from 4 to 50 megohms.

A quantitative analysis of presynaptic calcium dynamics that contribute to short-term enhancement.

Augmentation and posttetanic potentiation--two forms of short-term synaptic enhancement produced by repetitive presynaptic action potentials--are dependent on the buildup and decay of nerve terminal residual calcium that occurs on the seconds to minutes time scale. With the goal of providing a quantitative understanding of these kinetics, we measured the buildup and decay of calcium ions in nerve terminals at the crayfish neuromuscular junction under a variety of intracellular buffer conditions and stimulation paradigms. The calcium extrusion process in the terminals was characterized by analysis of calcium levels reached during long stimulus trains as a function of action potential frequency. The extrusion was linearly dependent on the free calcium ion concentration. Using this result, we developed a mathematical model and computer simulation of the residual calcium kinetics. The model demonstrates the experimentally observed dependence of decay rate on exogenous calcium buffer concentration, and can be explicitly solved to provide an expression for the limiting exponential time course of calcium decay following trains in terms of calcium buffer and extrusion characteristics. Methods to determine the calcium influx per action potential, characteristics of endogenous buffer, and the rate of calcium extrusion are suggested by our analysis and demonstrated experimentally.

Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy.

Light scattering by brain tissue and phototoxicity are major obstacles to the use of high-resolution optical imaging and photo-activation ('uncaging') of bioactive compounds from inactive ('caged') precursors in intact and semi-intact nervous systems. Optical methods based on 2-photon excitation promise to reduce these obstacles (Denk, 1994; Denk et al., 1990, 1994). Here we show a range of imaging modes based on 2-photon laser scanning microscopy (TPLSM) as applicable to problems in neuroscience. Fluorescence images were taken of neurons labeled with ion-sensitive and voltage-sensitive dyes in invertebrate ganglia, mammalian brain slices, and from the intact mammalian brain. Scanning photochemical images with whole-cell current detection (Denk, 1994) show how the distribution of neurotransmitter receptors on the surface of specific cells can be mapped. All images show strong optical sectioning and usable images can be obtained at depths greater than 100 microns below the surface of the preparation.

A quantitative measurement of the dependence of short-term synaptic enhancement on presynaptic residual calcium.

We simultaneously measured presynaptic free calcium ion concentration ([Ca2+]i) and synaptic strength at the crayfish claw opener neuromuscular junction (nmj) under a variety of experimental conditions. Our experiments were designed both to test the hypothesis that elevated [Ca2+]i is necessary and sufficient for the induction of a form of synaptic enhancement that persists for several seconds after tetanic stimulation--augmentation--and to determine the quantitative relationship between elevated [Ca2+]i and this enhancement. Action potential trains increased [Ca2+]i and enhanced transmission. During the decay phase of synaptic enhancement known as augmentation (time constant of decay approximately 7 sec at 20 degrees C with < 200 microM fura-2 in terminals), [Ca2+]i was elevated 700 nM or less above rest and an essentially linear relationship between [Ca2+]i and enhancement was observed. Introduction of exogenous Ca2+ buffers into the presynaptic terminal slowed the buildup and recovery kinetics of both [Ca2+]i and the component of synaptic enhancement corresponding to augmentation. The slope of the relationship relating delta [Ca2+]i to augmentation was not changed. The time course of augmentation and recovery of [Ca2+]i remained correlated as the temperature of the preparation was changed from about 10 degrees C to 20 degrees C, but the quantitative relationship of enhancement to [Ca2+]i was increased more than two- to threefold. During moderate frequency trains of action potentials, a slowly developing component of the total synaptic enhancement was approximately linearly related to residual [Ca2+]i measured with fura-2. The quantitative relationship between [Ca2+]i and this component of synaptic enhancement during trains was the same as that during synaptic augmentation after trains.(ABSTRACT TRUNCATED AT 250 WORDS)