Calcium: amplitude, duration, or location?

Calcium plays a role in long-term plasticity by triggering postsynaptic signaling pathways for both the strengthening (LTP) and weakening (LTD) of synapses. Since these are opposing processes, several hypotheses have been developed to explain how calcium can trigger LTP in some situations and LTD in others. These hypotheses fall broadly into three categories, based on the amplitude of calcium concentration, the duration of the calcium elevation, and the location of the calcium influx. Here we review the experimental evidence for and against each of these hypotheses and the recent computational models utilizing each. We argue that with new experimental techniques for the precise visualization of calcium and new computational techniques for the modeling of calcium diffusion, it is time to take a new look at the location hypothesis.

Calcium-dependent inactivation of calcium channels in the medial striatum increases at eye opening.

Influx of calcium through voltage-gated calcium channels (VGCCs) is essential for striatal function and plasticity. VGCCs expressed in striatal neurons have varying kinetics, voltage dependences, and densities resulting in heterogeneous subcellular calcium dynamics. One factor that determines the calcium dynamics in striatal medium spiny neurons is inactivation of VGCCs. Aside from voltage-dependent inactivation, VGCCs undergo calcium-dependent inactivation (CDI): inactivating in response to an influx of calcium. CDI is a negative feedback control mechanism; however, its contribution to striatal neuron function is unknown. Furthermore, although the density of VGCC expression changes with development, it is unclear whether CDI changes with development. Because calcium influx through L-type calcium channels is required for striatal synaptic depression, a change in CDI could contribute to age-dependent changes in striatal synaptic plasticity. Here we use whole cell voltage clamp to characterize CDI over developmental stages and across striatal regions. We find that CDI increases at the age of eye opening in the medial striatum but not the lateral striatum. The developmental increase in CDI mostly involves L-type channels, although calcium influx through non-L-type channels contributes to the CDI in both age groups. Agents that enhance protein kinase A (PKA) phosphorylation of calcium channels reduce the magnitude of CDI after eye opening, suggesting that the developmental increase in CDI may be related to a reduction in the phosphorylation state of the L-type calcium channel. These results are the first to show that modifications in striatal neuron properties correlate with changes to sensory input.

Dynamic modulation of spike timing-dependent calcium influx during corticostriatal upstates.

The striatum of the basal ganglia demonstrates distinctive upstate and downstate membrane potential oscillations during slow-wave sleep and under anesthetic. The upstates generate calcium transients in the dendrites, and the amplitude of these calcium transients depends strongly on the timing of the action potential (AP) within the upstate. Calcium is essential for synaptic plasticity in the striatum, and these large calcium transients during the upstates may control which synapses undergo plastic changes. To investigate the mechanisms that underlie the relationship between calcium and AP timing, we have developed a realistic biophysical model of a medium spiny neuron (MSN). We have implemented sophisticated calcium dynamics including calcium diffusion, buffering, and pump extrusion, which accurately replicate published data. Using this model, we found that either the slow inactivation of dendritic sodium channels (NaSI) or the calcium inactivation of voltage-gated calcium channels (CDI) can cause high calcium corresponding to early APs and lower calcium corresponding to later APs. We found that only CDI can account for the experimental observation that sensitivity to AP timing is dependent on NMDA receptors. Additional simulations demonstrated a mechanism by which MSNs can dynamically modulate their sensitivity to AP timing and show that sensitivity to specifically timed pre- and postsynaptic pairings (as in spike timing-dependent plasticity protocols) is altered by the timing of the pairing within the upstate. These findings have implications for synaptic plasticity in vivo during sleep when the upstate-downstate pattern is prominent in the striatum.

Approaches and tools for modeling signaling pathways and calcium dynamics in neurons.

Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.

Ionic currents underlying difference in light response between type A and type B photoreceptors.

In Hermissenda crassicornis, the memory of light associated with turbulence is stored as changes in intrinsic and synaptic currents in both type A and type B photoreceptors. These photoreceptor types exhibit qualitatively different responses to light and current injection, and these differences shape the spatiotemporal firing patterns that control behavior. Thus the objective of the study was to identify the mechanisms underlying these differences. The approach was to develop a type B model that reproduced characteristics of type B photoreceptors recorded in vitro, and then to create a type A model by modifying a select number of ionic currents. Comparison of type A models with characteristics of type A photoreceptors recorded in vitro revealed that type A and type B photoreceptors have five main differences, three that have been characterized experimentally and two that constitute hypotheses to be tested with experiments in the future. The three differences between type A and type B photoreceptors previously characterized include the inward rectifier current, the fast sodium current, and conductance of calcium-dependent and transient potassium channels. Two additional changes were required to produce a type A photoreceptor model. The very fast firing frequency observed during the first second after light onset required a faster time constant of activation of the delayed rectifier. The fast spike adaptation required a fast, noninactivating calcium-dependent potassium current. Because these differences between type A and type B photoreceptors have not been confirmed in comparative experiments, they constitute hypotheses to be tested with future experiments.

Using potassium currents to solve signal-to-noise problems in inhibitory feedforward networks of the striatum.

Fast-spiking (FS) interneurons provide the main route of feedforward inhibition from cortex to spiny projection neurons in the striatum. A steep current-firing frequency curve and a dense local axonal arbor suggest that even small excitatory inputs could translate into powerful feedforward inhibition, although such an arrangement is also sensitive to amplification of spurious synaptic inputs. We show that a transient potassium (KA) current allows the FS interneuron to strike a balance between sensitivity to correlated input and robustness to noise, thereby increasing its signal-to-noise ratio (SNR). First, a compartmental FS neuron model was created to match experimental data from striatal FS interneurons in cortex-striatum-substantia nigra organotypic cultures. Densities of sodium, delayed rectifier, and KA channels were optimized to replicate responses to somatic current injection. Spontaneous alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and gamma-aminobutyric acid (GABA) synaptic currents were adjusted to the experimentally measured amplitude, rise time, and interevent interval histograms. Second, two additional adjustments were required to emulate the remaining experimental observations. GABA channels were localized closer to the soma than AMPA channels to match the synaptic population reversal potential. Correlation among inputs was required to produce the observed firing rate during up-states. In this final model, KA channels were essential for suppressing down-state spikes while allowing reliable spike generation during up-states. This mechanism was particularly important under conditions of high dopamine. Our results suggest that KA channels allow FS interneurons to operate without a decrease in SNR during conditions of increased dopamine, as occurs in response to reward or anticipated reward.

Calcium waves and closure of potassium channels in response to GABA stimulation in Hermissenda type B photoreceptors.

Classical conditioning of Hermissenda crassicornis requires the paired presentation of a conditioned stimulus (light) and an unconditioned stimulus (turbulence). Light stimulation of photoreceptors leads to production of diacylglycerol, an activator of protein kinase C, and inositol triphosphate (IP(3)), which releases calcium from intracellular stores. Turbulence causes hair cells to release GABA onto the terminal branches of the type B photoreceptor. One prior study has shown that GABA stimulation produces a wave of calcium that propagates from the terminal branches to the soma and raises the possibility that two sources of calcium are required for memory storage. GABA stimulation also causes an inhibitory postsynaptic potential (IPSP) followed by a late depolarization and increase in input resistance, whose cause has not been identified. A model was developed of the effect of GABA stimulation on the Hermissenda type B photoreceptor to evaluate the currents underlying the late depolarization and to evaluate whether a calcium wave could propagate from the terminal branches to the soma. The model included GABA(A), GABA(B), and calcium-sensitive potassium leak channels; calcium dynamics including release of calcium from intracellular stores; and the biochemical reactions leading from GABA(B) receptor activation to IP(3) production. Simulations show that it is possible for a wave of calcium to propagate from the terminal branches to the soma. The wave is initiated by IP(3)-induced calcium release but propagation requires release through the ryanodine receptor channel where IP(3) concentration is small. Wave speed is proportional to peak calcium concentration at the crest of the wave, with a minimum speed of 9 microM/s in the absence of IP(3). Propagation ceases when peak concentration drops below 1.2 microM; this occurs if the rate of calcium pumping into the endoplasmic reticulum is too large. Simulations also show that both a late depolarization and an increase in input resistance occur after GABA stimulation. The duration of the late depolarization corresponds to the duration of potassium leak channel closure. Neither the late depolarization nor the increase in input resistance are observed when a transient calcium current and a hyperpolarization-activated current are added to the model as replacement for closure of potassium leak channels. Thus the late depolarization and input resistance elevation can be explained by a closure of calcium-sensitive leak potassium currents but cannot be explained by a transient calcium current and a hyperpolarization-activated current.

Analogue pattern matching in a dendritic spine model based on phosphorylation of potassium channels.

Modification of potassium channels by protein phosphorylation has been shown to play a role in learning and memory. If such memory storage machinery were part of dendritic spines, then a set of spines could act as an 'analogue pattern matching' device by learning a repeatedly presented pattern of synaptic activation. In this study, the plausibility of such analogue pattern matching is investigated in a detailed circuit model of a set of spines attached to a dendritic branch. Each spine head contains an AMPA synaptic channel in parallel with a calcium-dependent potassium channel whose sensitivity depends on its phosphorylation state. Repeated presentation of synaptic activity results in calcium activation of protein kinases and subsequent channel phosphorylation. Simulations demonstrate that signal strength is greatest when the synaptic input pattern is equal to the previously learned pattern, and smaller when components of the synaptic input pattern are either smaller or larger than corresponding components of the previously learned pattern. Therefore, our results indicate that dendritic spines may act as an analogue pattern matching device, and suggest that modulation of potassium channels by protein kinases may mediate neuronal pattern recognition.

Evidence for a distinct light-induced calcium-dependent potassium current in Hermissenda crassicornis.

A model of phototransduction is developed as a first step toward a model for investigating the critical interaction of light and turbulence stimuli within the type B photoreceptor of Hermissenda crassicronis. The model includes equations describing phototransduction, release of calcium from intracellular stores, and other calcium regulatory mechanisms, as well as equations describing ligand-gating of a rhabdomeric sodium current. The model is used to determine the sources of calcium in the soma, whether calcium or IP3 is a plausible ligand of the light-induced sodium current, and whether the light-induced potassium current is equivalent to the calcium-dependent potassium current activated by light-induced calcium release. Simulations show that the early light-induced calcium elevation is due to influx through voltage-dependent channels, whereas the later calcium elevation is due to release from intracellular stores. Simulations suggest that the ligand of the fast, light-induced sodium current is IP3 but that there is a smaller, prolonged component of the light-induced sodium current that is activated by calcium. In the model, the calcium-dependent potassium current, located in the soma, is activated only slightly by light-induced calcium elevation, leading to the prediction that a calcium-dependent potassium current, active at resting potential, is located in the rhabdomere and is responsible for the light-induced potassium current.

Ryanodine receptor modulation of in vitro associative learning in Hermissenda crassicornis.

Classical conditioning of the mollusc, Hermissenda crassicornis, is a model system used to study cellular correlates of associative learning. Paired presentation of light and turbulence, but not unpaired presentations, causes Hermissenda to contract its foot in response to light alone. Intracellular recordings from the type B photoreceptors of the Hermissenda eye reveal a learning specific increase of input resistance, and a reduction of voltage-dependent potassium currents, both of which depend on an elevation of intracellular calcium. Two previously demonstrated sources of calcium are influx through voltage-dependent channels, and release of calcium from intracellular stores through the IP3 receptor channel. Both modeling studies and identification of memory-related genes using RNA fingerprinting suggest that a third source of calcium, release from intracellular stores through the ryanodine receptor, may be involved in classical conditioning. We describe here an experiment suggesting that this third source of calcium is necessary for the cellular changes underlying associative memory storage. Paired presentations of a light stimulus with a turbulence stimulus resulted in a significant increase in input resistance. Unpaired presentations of light and turbulence did not produce a significant increase in input resistance. A third group of nervous systems first was incubated in dantrolene to block release of calcium through the ryanodine receptor, and then received paired training. There was no change in input resistance for this group. The effect of dantrolene on light adaptation of the photoreceptor was assessed by measuring the generator potential of a second light pulse presented some number of seconds after a first light pulse. The results show that at interpulse intervals of 5 s, 10 s and 20 s, the generator potential of the dantrolene group is significantly greater than that of the control group. These results suggest a role for the ryanodine receptor in both a cellular correlate of classical conditioning and light adaptation.

Pattern matching in a model of dendritic spines.

Pattern matching, the ability to recognize and maximally respond to an input pattern that is similar to a previously learned pattern, is an essential step in any learning process. To investigate the properties of pattern matching in biological neurons, and in particular the role of a calcium-dependent potassium conductance, a circuit model of a small area of dendritic membrane with a number of dendritic spines is developed. Circuit model simulations show that dendritic membrane depolarization is greater in response to a previously learned pattern of synaptic inputs than in response to a novel pattern of synaptic inputs. These simulations, in combination with an analysis of the circuit model equations, reveal that when a synaptic input pattern is similar to the learned pattern of synaptic inputs, the total dendritic depolarization is a linear combination of dendritic depolarization contributed by individual spines. When at least one synaptic input differs markedly from the learned value, dendritic depolarization is a nonlinear combination of individual spine depolarizations. These principles of spine interactions are captured in a computationally simple set of 'similarity measure' equations which are shown to reproduce the response surface of the circuit model output. Thus, these similarity measure equations not only describe a biologically plausible model of pattern matching, they also satisfy computational requirements for use in artificial neural networks.

The effect of white and filtered noise on contrast detection thresholds.

Models of the dipper effect seen in contrast discrimination experiments predict that small amounts of noise should facilitate detection of a subthreshold sinusoidal grating. Although facilitation of chromatic sine waves has been measured with chromatic or luminance noise, a facilitory effect of luminance sinusoidal gratings has not been measured, most likely because the stimulus characteristics were not tuned for revealing facilitation. The present study measures contrast detection thresholds (CDTs) of sinusoidal gratings in two-dimensional, static, band-limited white noise and low-pass and high-pass filtered noise using a two-interval forced-choice paradigm. The results show facilitation in near threshold white noise of middle frequency sinusoidal gratings, and facilitation in filtered noise of sinusoidal gratings whose frequency is far outside the pass band of the noise. Based on these results, a model of contrast detection thresholds is modified such that the facilitation is attributed to reduced observer uncertainty caused by small amounts of noise.

Utility of a Wisconsin Card Sorting Test short form in persons with Alzheimer's and Parkinson's disease.

The utility of administering only the first deck of 64 cards from the Wisconsin Card Sorting Test (WCST-64) in persons with Alzheimer's (AD) and Parkinson's disease (PD) was evaluated. There were 35 elderly subjects matched for gender, age, and education in each of four groups: controls, PD without dementia (PDN), PD with dementia (PDD), and AD. Additionally, the control and PDN subjects were matched for level of cognitive functioning as were the PDD and AD groups. Results revealed that demented persons performed significantly worse than nondemented subjects. The WCST-64 was also sensitive to the subtle executive deficits demonstrated by persons with PD without dementia. The findings support the use of the WCST-64 in elderly persons with AD and PD.

Orange juice classification with a biologically based neural network.

Dystal, an artificial neural network, was used to classify orange juice products. Nine varieties of oranges collected from six geographical regions were processed into single-strength, reconstituted or frozen concentrated orange juice. The data set represented 240 authentic and 173 adulterated samples of juices; 16 variables [8 flavone and flavanone glycoside concentrations measured by high-performance liquid chromatography (HPLC) and 8 trace element concentrations measured by inductively coupled plasma spectroscopy] were selected to characterize each juice and were used as input to Dystal. Dystal correctly classified 89.8% of the juices as authentic or adulterated. Classification performance increased monotonically as the percentage of pulpwash in the sample increased. Dystal correctly identified 92.5% of the juices by variety (Valencia vs non-Valencia).

Associative learning in a network model of Hermissenda crassicornis. II. Experiments.

A companion paper in a previous issue of this journal presented a resistance-capacitance circuit computer model of the four-neuron visual-vestibular network of the invertebrate marine mollusk Hermissenda crassicornis. In the present paper, we demonstrate that changes in the model's output in response to simulated associative training is quantitatively similar to behavioral and electrophysiological changes in response to associative training of Hermissenda crassicornis. Specifically, the model demonstrates many characteristics of conditioning: sensitivity to stimulus contingency, stimulus specificity, extinction, and savings. The model's learning features also are shown to be devoid of non-associative components. Thus, this computational model is an excellent tool for examining the information flow and dynamics of biological associative learning and for uncovering insights concerning associative learning, memory, and recall that can be applied to the development of artificial neural networks.

Associative learning in a network model of Hermissenda crassicornis. I. Theory.

A time-varying Resistance-Capacitance (RC) circuit computer model was constructed based on known membrane and synaptic properties of the visual-vestibular network of the marine snail Hermissenda crassicornis. Specific biophysical properties and synaptic connections of identified neurons are represented as lumped parameters (circuit elements) in the model; in the computer simulation, differential equations are approximated by difference equations. The model's output, membrane potential, an indirect measure of firing frequency, closely parallels the behavioral and electrophysiologic outputs of Hermissenda in response to the same input stimuli presented during and after associative learning. The parallelism of the computer modeled and the biologic outputs suggests that the model captures the features necessary and sufficient for associative learning.

Performance comparison of a neural network with human observers on a visual target detection task.

An experiment is described which compares the performance of a neural network to human performance on a visual task which consists of detecting a target in a background image of correlated noise. A three-layer, feed-forward, multi-layer perceptron is trained to indicate the presence or absence of a target in images also presented to human observers. The basis for the comparison between the network and the human observers is the receiver operating characteristic (ROC) curve. Network performance is comparable to human performance for this particular task.

Pattern-recognition by an artificial network derived from biologic neuronal systems.

A novel artificial neural network, derived from neurobiological observations, is described and examples of its performance are presented. This DYnamically STable Associative Learning (DYSTAL) network associatively learns both correlations and anticorrelations, and can be configured to classify or restore patterns with only a change in the number of output units. DYSTAL exhibits some particularly desirable properties: computational effort scales linearly with the number of connections, i.e., it is O(N) in complexity; performance of the network is stable with respect to network parameters over wide ranges of their values and over the size of the input field; storage of a very large number of patterns is possible; patterns need not be orthogonal; network connections are not restricted to multi-layer feed-forward or any other specific structure; and, for a known set of deterministic input patterns, the network weights can be computed, a priori, in closed form. The network has been associatively trained to perform the XOR function as well as other classification tasks. The network has also been trained to restore patterns obscured by binary or analog noise. Neither global nor local feedback connections are required during learning; hence the network is particularly suitable for hardware (VLSI) implementation.

Quantitative studies of color constancy.

In order to study color constancy, the color appearance of the center of a center-surround paradigm was measured by using multiple-alternative forced-response matching. The center was presented with (1) no surround, (2) an adjacent chromatic surround, or (3) a chromatic surround separated from the center by an achromatic gap. The center and the surrounds were presented under various simulated illuminants ranging from illuminant A to illuminant D75. We found that when no surround is present, color constancy fails; however, when surrounds are present, some degree of color constancy is displayed. We also found that color constancy is poor when chromatic induction is minimal. In addition, it was determined that, if the ratios of R, G, and B of the center to R, G, and B of the surround remain constant as the illuminant changes, color constancy results. (R, G, and B correspond to the outputs of the retinal color mechanisms).

Measurement of empathy toward rape victims and rapists.

The purpose of the present study was the construction of the Rape Empathy Scale (RES), designed to measure subjects' empathy toward the rape victim and the rapist in a heterosexual rape situation. The results of psychometric analyses of reliability for both a student and juror sample are presented, in addition to evidence of cross-validation on separate student and juror samples. Significant differences between male and female subjects' RES scores were found, as well as differences between scores of women who had experienced a rape situation (rape victims and rape resisters) and women with no previous exposure to rape. RES scores were predictive of both students' and jurors' ratings of defendant guilt, as well as their recommended sentences for the defendant and their attributions of responsibility for the crime. Furthermore, subjects' RES scores were predictive of their social perceptions of the rape victim and defendant, and male jurors' RES scores were negatively correlated with their reported desire to rape a woman. The results are discussed in relation to the low conviction rate for sexual assault cases and the importance of juror selection as a vehicle for increasing the number of just convictions in rape cases.