William R. Holmes

Cytosolic zinc buffering and muffling: Their role in intracellular zinc homeostasis

Our knowledge of the molecular mechanisms of intracellular homeostatic control of zinc ions is now firmly grounded on experimental findings gleaned from the study of zinc proteomes and metallomes, zinc transporters, and insights from the use of computational approaches. A cells repertoire of zinc homeostatic molecules includes cytosolic zinc-binding proteins, transporters localized to cytoplasmic and organellar membranes, and sensors of cytoplasmic free zinc ions. Under steady state conditions, a primary function of cytosolic zinc-binding proteins is to buffer the relatively large zinc content found in most cells to a cytosolic zinc(ii) ion concentration in the picomolar range. Under non-steady state conditions, zinc-binding proteins and transporters act in concert to modulate transient changes in cytosolic zinc ion concentration in a process that is called zinc muffling. For example, if a cell is challenged by an influx of zinc ions, muffling reactions will dampen the resulting rise in cytosolic zinc ion concentration and eventually restore the cytosolic zinc ion concentration to its original value by shuttling zinc ions into subcellular stores or by removing zinc ions from the cell. In addition, muffling reactions provide a potential means to control changes in cytosolic zinc ion concentrations for purposes of cell signalling in what would otherwise be considered a buffered environment not conducive for signalling. Such intracellular zinc ion signals are known to derive from redox modifications of zinc-thiolate coordination environments, release from subcellular zinc stores, and zinc ion influx via channels. Recently, it has been discovered that metallothionein binds its seven zinc ions with different affinities. This property makes metallothionein particularly well positioned to participate in zinc buffering and muffling reactions. In addition, it is well established that metallothionein is a source of zinc ions under conditions of redox signalling. We suggest that the biological functions of transient changes in cytosolic zinc ion concentrations (presumptive zinc signals) complement those of calcium ions in both spatial and temporal dimensions.

Models of Calmodulin Trapping and CaM Kinase II Activation in a Dendritic Spine

Activation of calcium/calmodulin-dependent protein kinase II (CaMKII) by calmodulin following calcium entry into the cell is important for long-term potentiation (LTP). Here a model of calmodulin binding and trapping by CaMKII in a dendritic spine was used to estimate levels and durations of CaMKII activation following LTP-inducing tetani. The calcium signal was calcium influx through NMDA receptor channels computed in a highly detailed dentate granule cell model. Calcium could bind to calmodulin and calmodulin to CaMKII. CaMKII subunits were either free, bound with calmodulin, trapped, autonomous, or capped. Strong low-frequency tetanic input produced little calmodulin trapping or CaMKII activation. Strong high-frequency tetanic input caused large numbers of CaMKII subunits to become trapped, and CaMKII was strongly activated. Calmodulin trapping and CaMKII activation were highly dependent on tetanus frequency (particularly between 10 and 100 Hz) and were highly sensitive to relatively small changes in the calcium signal. Repetition of a short high-frequency tetanus was necessary to achieve high levels of CaMKII activation. Three stages of CaMKII activation were found in the model: a short, highly activated stage; an intermediate, moderately active stage; and a long-lasting third stage, whose duration depended on dephosphorylation rates but whose decay rate was faster at low CaMKII activation levels than at high levels. It is not clear which of these three stages is most important for LTP.

Role of multiple calcium and calcium-dependent conductances in regulation of hippocampal dentate granule cell excitability.

We have constructed a detailed model of a hippocampal dentate granule (DG) cell that includes nine different channel types. Channel densities and distributions were chosen to reproduce reported physiological responses observed in normal solution and when blockers were applied. The model was used to explore the contribution of each channel type to spiking behavior with particular emphasis on the mechanisms underlying postspike events. T-type calcium current in more distal dendrites contributed prominently to the appearance of the depolarizing after-potential, and its effect was controlled by activation of BK-type calcium-dependent potassium channels. Co-activation and interaction of N-, and/or L-type calcium and AHP currents present in somatic and proximal dendritic regions contributed to the adaptive properties of the model DG cell in response to long-lasting current injection. The model was used to predict changes in channel densities that could lead to epileptogenic burst discharges and to predict the effect of altered buffering capacity on firing behavior. We conclude that the clustered spatial distributions of calcium related channels, the presence of slow delayed rectifier potassium currents in dendrites, and calcium buffering properties, together, might explain the resistance of DG cells to the development of epileptogenic burst discharges.

LTP in hippocampal area CA1 is induced by burst stimulation over a broad frequency range centered around delta

Long-term potentiation (LTP) is typically studied using either continuous high-frequency stimulation or theta burst stimulation. Previous studies emphasized the physiological relevance of theta frequency; however, synchronized hippocampal activity occurs over a broader frequency range. We therefore tested burst stimulation at intervals from 100 msec to 20 sec (10 Hz to 0.05 Hz). LTP at Schaffer collateral-CA1 synapses was obtained at intervals from 100 msec to 5 sec, with maximal LTP at 350-500 msec (2-3 Hz, delta frequency). In addition, a short-duration potentiation was present over the entire range of burst intervals. We found that N-methyl-d-aspartic acid (NMDA) receptors were more important for LTP induction by burst stimulation, but L-type calcium channels were more important for LTP induction by continuous high-frequency stimulation. NMDA receptors were even more critical for short-duration potentiation than they were for LTP. We also compared repeated burst stimulation with a single primed burst. In contrast to results from repeated burst stimulation, primed burst potentiation was greater when a 200-msec interval (theta frequency) was used, and a 500-msec interval was ineffective. Whole-cell recordings of postsynaptic membrane potential during burst stimulation revealed two factors that may determine the interval dependence of LTP. First, excitatory postsynaptic potentials facilitated across bursts at 500-msec intervals but not 200-msec or 1-sec intervals. Second, synaptic inhibition was suppressed by burst stimulation at intervals between 200 msec and 1 sec. Our data show that CA1 synapses are more broadly tuned for potentiation than previously appreciated.

Decreased afferent excitability contributes to synaptic depression during high-frequency stimulation in hippocampal area CA1.

Long-term potentiation (LTP) is often induced experimentally by continuous high-frequency afferent stimulation (HFS), typically at 100 Hz for 1 s. Induction of LTP requires postsynaptic depolarization and voltage-dependent calcium influx. Induction is more effective if the same number of stimuli are given as a series of short bursts rather than as continuous HFS, in part because excitatory postsynaptic potentials (EPSPs) become strongly depressed during HFS, reducing postsynaptic depolarization. In this study, we examined mechanisms of EPSP depression during HFS in area CA1 of rat hippocampal brain slices. We tested for presynaptic terminal vesicle depletion by examining minimal stimulation-evoked excitatory postsynaptic currents (EPSCs) during 100-Hz HFS. While transmission failures increased, consistent with vesicle depletion, EPSC latencies also increased during HFS, suggesting a decrease in afferent excitability. Extracellular recordings of Schaffer collateral fiber volleys confirmed a decrease in afferent excitability, with decreased fiber volley amplitudes and increased latencies during HFS. To determine the mechanism responsible for fiber volley changes, we recorded antidromic action potentials in single CA3 pyramidal neurons evoked by stimulating Schaffer collateral axons. During HFS, individual action potentials decreased in amplitude and increased in latency, and these changes were accompanied by a large increase in the probability of action potential failure. Time derivative and phase-plane analyses indicated decreases in both axon initial segment and somato-dendritic components of CA3 neuron action potentials. Our results indicate that decreased presynaptic axon excitability contributes to depression of excitatory synaptic transmission during HFS at synapses between Schaffer collaterals and CA1 pyramidal neurons.

Electrotonic models of neuronal dendrites and single neuron computation

Publisher Summary This chapter focuses on different electrotonic models of neuronal dendrites and single neuron computation to reduce the number degrees of freedom. The areas that help in reducing the degrees of freedom include the importance for modeling studies of having good estimates of the electrotonic structure of a cell, the dynamic range of computational possibilities available to a neuron, by considering its possible resting states, assuming that a real neuron ever can be considered to be at rest, and variables that may be important for producing modification in dendritic spines. Dendritic models concerned with computation must make assumptions about the morphological and electrotonic structure of the neuronal dendrites. The dynamic range of computational possibilities for a neuron is immense.

The effect of noise on CaMKII activation in a dendritic spine during LTP induction.

Activation of calcium-calmodulin dependent protein kinase II (CaMKII) during induction of long-term potentiation (LTP) is a series of complicated stochastic processes that are affected by noise. There are two main sources of noise affecting CaMKII activation within a dendritic spine. One is the noise associated with stochastic opening of N-methyl-d-aspartate (NMDA) receptor channels and the other is the noise associated with the stochastic reaction-diffusion kinetics leading to CaMKII activation. Many models have been developed to simulate CaMKII activation, but there is no fully stochastic model that studies the effect of noise on CaMKII activation. Here we construct a fully stochastic model to study these effects. Our results show that noise has important effects on CaMKII activation variability, with the effect from stochastic opening of NMDA receptor channels being 5-10 times more significant than that from stochastic reactions involving CaMKII. In addition, CaMKII activation levels and the variability of activation are greatly affected by small changes in NMDA receptor channel number at the synapse. One reason LTP induction protocols may require tetanic or repeated burst stimulation is that there is a need to overcome inherent variability to provide sufficiently large calcium signals through NMDA receptor channels; with meaningful physiological stimuli, noise may allow the calcium signal to exceed threshold for CaMKII activation when it might not do so otherwise.

Fitting experimental data to models that use morphological data from public databases

Ideally detailed neuron models should make use of morphological and electrophysiological data from the same cell. However, this rarely happens. Typically a modeler will choose a cell morphology from a public database, assign standard values for Ra, Cm, and other parameters and then do the modeling study. The assumption is that the model will produce results representative of what might be obtained experimentally. To test this assumption we developed models of CA1 hippocampal pyramidal neurons using 4 different morphologies obtained from 3 public databases. The multiple run fitter in NEURON was used to fit parameter values in each of the 4 morphological models to match experimental data recorded from 19 CA1 pyramidal cells. Fits with fixed standard parameter values produced results that were generally not representative of our experimental data. However, when parameter values were allowed to vary, excellent fits were obtained in almost all cases, but the fitted parameter values were very different among the 4 reconstructions and did not match standard values. The differences in fitted values can be explained by very different diameters, total lengths, membrane areas and volumes among the reconstructed cells, reflecting either cell heterogeneity or issues with the reconstruction data. The fitted values compensated for these differences to make the database cells and experimental cells more similar electrotonically. We conclude that models using fully reconstructed morphologies need to be calibrated with experimental data (even when morphological and electrophysiological data come from the same cell), model results should be generated with multiple reconstructions, morphological and experimental cells should come from the same strain of animal at the same age, and blind use of standard parameter values in models that use reconstruction data may not produce representative experimental results.

Active dendrites regulate spatio-temporal synaptic integration in hippocampal dentate granule cells

Abstract Compartmental modeling experiments were carried out to compare spatio-temporal synaptic integration in a model of a fully reconstructed hippocampal dentate granule (DG) cell containing either passive dendrites or dendrites with voltage-dependent conductances. The presence of active channels in dendrites increased the elastic properties of dendritic membrane, increased the sensitivity of the response to synapse clustering (up to an optimal degree of clustering), decreased the input location dependent variability of the response at the soma, and facilitated coincidence detection in the dendritic arbor. We conclude that active channels in dendrites may alter significantly both spatial and temporal integrative processes.

Comparison of CaMKinase II activation in a dendritic spine computed with deterministic and stochastic models of the NMDA synaptic conductance

Abstract In models of long-term potentiation the NMDA conductance is usually computed deterministically. However, the actual number of open NMDA receptor channels at a synapse is small, so a deterministic representation may not be valid. Here NMDA synaptic conductances computed stochastically with MCell were used in a dentate granule cell model that computed calcium influx and subsequent CaMKinase II activation in a dendritic spine following LTP induction conditions. Spine head calcium concentration and levels of CaMKinase II activation were highly variable with different stochastic simulations of NMDA channel openings. This variability in CaMKinase II activity levels due to stochastic NMDA channel openings may play an important role in LTP induction in individual spines.