Integrative and Comparative Biology Advance Access originally published online on May 17, 2008
Integrative and Comparative Biology 2008 48(5):548-559; doi:10.1093/icb/icn039
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Emerging methodologies for the study of hypothalamic gonadotropin-releasing-hormone (GnRH) neurons
* Department of Biology, University of Texas at San Antonio, 1 UTSA Circle, San Antonio TX, 78249; Department of Electrical and Computer Engineering, Boston University, 8 Saint Mary's Street, Boston, MA 02215, USA
Correspondence: 1E-mail: kelly.suter{at}utsa.edu
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Synopsis
IntroductionGonadotropin-releasing-hormone (GnRH) neurons form part of a central neural oscillator that controls sexual reproduction through intermittent release of the GnRH peptide. Activity of GnRH neurons, and by extension release of GnRH, has been proposed to reflect intrinsic properties and synaptic input of GnRH neurons. To study GnRH neurons, we used traditional electrophysiology and computational methods. These emerging methodologies enhance the elucidation of processing in GnRH neurons. We used dynamic current-clamping to understand how living GnRH somata process input from glutamate and GABA, two key neurotransmitters in the neuroendocrine hypothalamus. In order to study the impact of synaptic integration in dendrites and neuronal morphology, we have developed full-morphology models of GnRH neurons. Using dynamic clamping, we have demonstrated that small-amplitude glutamatergic currents can drive repetitive firing in GnRH neurons. Furthermore, application of simulated GABAergic synapses with a depolarized reversal potential have revealed two functional subpopulations of GnRH neurons: one population in which GABA chronically depolarizes membrane potential (without inducing action potentials) and a second population in which GABAergic excitation results in slow spiking. Finally, when AMPA-type and GABA-type simulated inputs are applied together, action potentials occur when the AMPA-type conductance occurs during the descending phase of GABAergic excitation and at the nadir of GABAergic inhibition. Compartmental computer models have shown that excitatory synapses at >300 microns from somtata are unable to drive spiking with purely passive dendrites. In models with active dendrites, distal synapses are more efficient at driving spiking than somatic inputs. We then used our models to extend the results from dynamic current clamping at GnRH somata to distribute synaptic inputs along the dendrite. We show that propagation delays for dendritic synapses alter synaptic integration in GnRH neurons by widening the temporal window of interaction for the generation of action potentials. Finally, we have shown that changes in dendrite morphology can modulate the output of GnRH neurons by altering the efficacy of action potential generation in response to after-depolarization potentials (ADPs). Taken together, the methodologies of dynamic current clamping and multi-compartmental modeling can make major contributions to the study of synaptic integration and structure-function relationships in hypothalamic GnRH neurons. Use of these methodological approaches will continue to provide keen insights leading to conceptual advances in our understanding of reproductive hormone secretion in normal and pathological physiology and open the door to understanding whether the mechanisms of pulsatile GnRH release are conserved across species.
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Introduction |
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Geoffery Harris’ pioneering work demonstrated the importance of the hypophysial portal vessels for the control of anterior-pituitary function. His speculation with regard to the role of the central nervous system in the secretion of hormones fundamentally changed the view of his time with respect to the neural-humoral interface. Moreover, his hypothesis that neural substances liberated from the hypothalamus and carried in the portal vessels are the principal regulators of anterior hypophysiotropic function (Green and Harris 1947
) has been a key concept in modern neuroendocrinology.
Although his conceptual insights are widely lauded, Geoffery Harris was also a toolmaker. His development of new experimental approaches, as well as his extension of existing methodologies, moved him from hypothesis-making to hypothesis-testing. He fashioned a chronic indwelling electrode system that allowed him to deliver electrical stimulation to discreet regions of the brain. In doing so, he was able to provide definitive evidence that stimulation of the hypothalamus lead to ovulation (Harris 1948). His second methodological advancements reconciled disparate findings with respect to the role of the portal vasculature. Specifically, he demonstrated that the atrophy of the gonads in response to transection of the pituitary stalk was maintained when one prevented revascularization of the pituitary by placement of a wax barrier (Harris 1950). Thus, his seminal conceptual contributions were proffered in tandem with what, at that time, were heroic advancements in methodology.
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New methodology for studying hypothalamic GnRH neurons |
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Arguably, the least tractable population of neurons controlling anterior hypophysiotropic function has been the gonadotropin-releasing hormone (GnRH) neurons due to their limited number and their diffuse distribution (Silverman et al. 1994
). The development of transgenic rodent models with the reporter gene green fluorescent protein (GFP) specifically in GnRH neurons has allowed individual GnRH neurons to be visualized in hypothalamic slices prepared for electrophysiological experiments (Spergel et al. 1999; Suter et al. 2000; Kato et al. 2003). As originally demonstrated by Spergel et al. (1999), a 3.47 kB fragment of the GnRH gene promoter directs GFP to hypothalamic GnRH neurons. This results in GnRH neurons in which GFP is expressed specifically, conveying fluorescence to only these neurons and permitting their visualization.
The usefulness of such animals as a tool for studies of living GnRH neurons is predicated on the assumption of normal physiologic function(s) of GnRH neurons after incorporation of GFP. As shown in Fig. 1, males from the line of Spergel et al. (1999) exhibit robust intermittent hormone secretion following castration to eliminate steroid-dependent inhibition by gonadal steroids. All males exhibited at least two LH pulses during the 3 h of sampling (range: 2–6 pulses; Fig. 1). Transgenic males had an average of 2.8 (±0.7; n = 14) pulses per 3 h and control males had an average of 2.3 (±0.9; n = 7) pulses per 3 h. Mean LH levels and amplitude and frequency of pulses did not differ between transgenic and control males (Fig. 1). As such, these animals provide an important new tool for studies of living GnRH neurons.
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Pulsatile GnRH release likely reflects input to the GnRH cells and synaptic interactions between GnRH neurons and a secondary network (Kusano et al. 1995
). Anatomical studies have shown that alterations in synaptic input occur during reproductive transitions in several species ranging from rodents, to sheep and nonhuman primates (Witkin and Romero 1995; Perera and Plant 1997; Witkin et al. 1997; Xiong et al. 1997; Jansen et al. 2003). The most recent studies in mice indicate that the number of dendritic spines (the location of excitatory input) increases to GnRH somata and dendrites during sexual maturation (Cottrell et al. 2006). Thus, alterations in synaptic input may underlie changes in GnRH secretion between physiological states. In addition to synapses, GnRH neurons express a host of post-synaptic receptors (Todman et al. 2005) which allow them to integrate multiple signals relaying cues about internal homeostasis and the external environment (Herbison 2006).
Dynamic current-clamping
As recently demonstrated (Wintermantel et al. 2006; Campell and Herbison 2007), multiple hypothalamic regions and at least one extra-hypothalamic region provide afferent input to GnRH neurons. The innovative technique of dynamic current-clamping (Sharp et al. 1993; Prinz et al. 2004) is a powerful tool for investigating the influence of synaptic inputs or receptor activation on GnRH firing. The dynamic clamping approach allows one to develop controlled patterns of synaptic conductance from multiple inputs that are modeled on physiological data (e.g., specific types and number of synapses) and can provide key insights into the direct relationship between synaptic inputs and neuronal firing.
Dynamic current-clamp integrates measurements of membrane voltage with model equations of synaptic conductance to calculate and inject realistic synaptic current (Fig. 2). Total synaptic current (Isyn) is defined by the equation
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where Iexcitatory is the total excitatory synaptic current and Iinhibitory is the total inhibitory synaptic current. The magnitude of synaptic current is determined by the conductances for inputs mediating excitatory (gex) and inhibitory (gin) input and the electrochemical driving forces, calculated as the difference between membrane potential (Vm) and the reversal potential (E) for these currents:
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In dynamic current-clamping, Vm is used to calculate injected current and is updated online to reflect changes in membrane potential. This feedback alters the net driving force and therefore the magnitude of current injected. The size of the conductance is tailored to PSC amplitudes but amplitudes change based on Vm (just as in vivo) since changes in Vm alter the electrochemical driving force.
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Dynamic clamping allows one to replicate temporal aspects of synaptic input or receptor activation that occur in vivo. Moreover, the magnitude of injected current is based on moment-to-moment voltage feedback from the recorded neuron. This allows the behavior of a simulated synapse to change during a dynamic clamp recording just as the electrochemical driving force on conductances changes in vivo with the dynamics of membrane potential. Accordingly, the approach integrates a living neuron into a "dynamic" synaptic network. Finally, one can apply defined patterns of synaptic stimulation and directly relate them to changes in firing. Thus, application of simulated conductances allows direct testing of hypotheses with regard to alterations in synaptic input and how these govern changes in neuronal firing.
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Using dynamic current-clamping to study synaptic input to GnRH neurons |
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A wealth of evidence supports the hypothesis that glutamate and GABA, dominant neurotransmitters in multiple hypothalamic regions (Decavel and van den Pol 1990
; van den Pol et al. 1990), participate in the regulation of pulsatile GnRH release. Electrophysiological studies employing the mouse models noted above have indicated that GnRH neurons express AMPA-type and NMDA-type glutamatergic receptors and A-type 
-aminobutyric acid (GABA-A) receptors (Spergel et al. 1999). Moreover, glutamatergic and GABAergic PSCs have been identified in hypothalamic GnRH neurons (Sullivan et al. 2003; Suter 2004). There is general agreement that glutamate excites GnRH neurons. AMPA-type glutamate receptors in GnRH neurons have a reversal potential of about 0 mV (Spergel et al. 1999). Pharmacological activation of AMPA-type receptors excites GnRH somata (Kuehl-Kovarik et al. 2002) and endogenous PSCs mediated by glutamate are excitatory (Suter 2004). However, most currents mediated by glutamate are relatively small (15–30 pA; Kuehl-Kovarik et al. 2002; Suter 2004). This observation raises the question as to whether these small glutamatergic currents could induce sufficient depolarization in GnRH neurons to induce action potentials. In order to ask this question, simulated AMPA-type glutamatergic inputs were constructed, based on the amplitude and time course of endogenous PSCs in GnRH neurons (Suter 2004) and then applied using dynamic current-clamping to the somata of GnRH neurons in slices. As shown in Fig. 3, activation of trains of small, simulated AMPA-type inputs (between arrowheads) elicits repetitive action potentials in GnRH neurons, the mode of neuronal firing that facilitates neuropeptide release (Legendre and Poulain 1992). In the top panel, simulated events were about 15 pA, the amplitude of a majority of synaptic currents induced by bath application of glutamate on GnRH somata. In the bottom panel, simulated events were about 30 pA, the average amplitude of synaptic currents induced by bath application of glutamate (Kuehl-Kovarik et al. 2002). Since endogenous PSCs mediated by AMPA-receptors are about 22 pA (Suter 2004), the findings with dynamic clamping support the hypothesis that despite their small amplitudes, glutamatergic input to GnRH neurons could make substantial contributions to action-potential firing.
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Using dynamic current-clamping to study synaptic integration in GnRH somata |
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In addition to glutamatergic inputs, GABAergic inputs have also been identified in hypothalamic GnRH neurons (Sullivan et al. 2003
). The effect of A-type -aminobutyric acid (GABA-A) receptor activation on adult GnRH neurons however, is unclear. Some studies indicate that GABA-A receptor-mediated events in adult GnRH neurons are hyperpolarizing (Han et al. 2002, 2004), whereas others indicate they are depolarizing (DeFazio et al. 2002). Since adult GnRH neurons have spike thresholds of about –33 mV (Spergel et al. 1999; Sim et al. 2001), the contribution of GABAergic excitation to action potential firing is uncertain. Additionally, GABA's actions may differ between individual hypothalamic GnRH neurons (Han et al. 2004; DeFazio and Moenter 2005) as a consequence of active chloride-handling mechanisms in some, but not all, GnRH neurons (Leupen et al. 2003).
Dynamic clamping provides a mechanism to investigate how these two key hypothalamic neurotransmitters, glutamate and GABA, are integrated in GnRH neurons. Dynamic clamping is a particularly attractive approach in this regard since the reversal potential for chloride, which defines whether GABA would be inhibitory or excitatory, is defined in the computer simulation of GABAergic synaptic events. Thus, in a single GnRH neuron one can first test the impact of GABA in the classical inhibitory mode and then test the impact of GABA in the excitatory mode by simply changing the reversal potential of the simulated GABA synapse. This approach contrasts with traditional whole-cell recordings in which the reversal potential is fixed in any given GnRH neuron by the concentrations of chloride in the bath solution (external chloride in the Nernst equation used for calculating the reversal potential) and in the solution in the recording pipette (internal chloride concentration in the Nernst equation). Using this latter approach, GABAergic excitation has been studied by setting the reversal potential for GABAergic inputs to about 0 mV (Sullivan et al. 2003). In order to study synaptic integration of GABAergic input in both the excitatory and inhibitory modes in conjunction with AMPA-type inputs, AMPA-type synapses were constructed with a reversal potential of 0 mV (Spergel et al. 1999). For classical GABAergic inhibition, simulated GABA synapses were constructed with a chloride reversal potential of –70 mV. Simulated GABAergic excitation used a reversal potential of –36.5 mV (based on the findings of DeFazio et al. 2002).
The analysis of the results of these dynamic clamping experiments involves the technique of spike-triggered averaging. The theory behind this technique is that when a spike occurs, it is the result of inputs that preceded it. Thus, to understand the sort of inputs that will most likely lead to spikes, one must look at the inputs in a small temporal window before and after each spike. The first and simplest experiment is to apply simulated AMPA conductances alone to the cell, using the dynamic clamp. When the resulting voltage waveform is analyzed (Fig. 4A), the spike-triggered average shows a strong peak in the AMPA conductance at 2.8 ms before the spike. This indicates that a spike is most likely to occur about 2.8 ms after a peak in the AMPA conductance.
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When the experiment is repeated with excitatory GABA (with a –36.5 mV reversal potential, Fig. 4B) along with the same AMPA input profile, the spike-triggered average shows a peak in AMPA at 4.8 ms before the spike, and a peak in GABA conductance at 11 ms before the spike. This indicates that the AMPA and GABA inputs interact most efficiently to generate spikes when the maximum of the AMPA input occurs on the downward slope of the peak of the GABA input, with an optimal delay between AMPA and GABA of 6.2 ms.
With the dynamic-clamp inputs set to have the GABA reversal potential at an inhibitory value of –70 mV, the spike-triggered average shows that a spike is most likely to occur when the GABA conductance is at a minimum (Fig. 4C). In this case, the maximum of the GABA conductance occurs at –39.8 ms before the spike, while the maximum in the AMPA conductance occurs at 3.6 ms before the spike. Taken together, these experiments indicate that AMPA input is efficient at driving spikes in GnRH neurons, and that the resulting spikes are most likely to occur 2–5 ms after the peak in the AMPA conductance. Excitatory GABA, along with AMPA, can increase the spike rate, optimally with the GABA inputs preceding the AMPA inputs. Inhibitory GABA indeed inhibits spiking, and there is an inverse correlation between spikes and the amplitude of the GABA conductance. Thus, dynamic current-clamping allows one to analyze the interactions between conductances, and the dependence of the impact of synaptic reversal potentials on synaptic integration in a systematic and repeatable way not possible with more traditional electrophysiological techniques.
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Compartmental modeling in GnRH neurons |
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The earliest perspective on dendrites viewed them as passive linear elements whose role was largely limited to collecting current arising from synaptic inputs and conveying the resulting changes in voltage to somata. This view of dendrite function has changed in two important ways. First, the dendrites in at least some populations of neurons are not passive. Instead, it is now clear that in some types of neurons, dendrites possess a host of active conductances that can have a significant impact on synaptic integration and neuronal processing. In some neurons, activation by excitatory inputs of voltage-sensitive sodium channels expressed in dendrites results in local action potentials initiated in the dendrite. Active dendritic conductances allow for synaptic amplification, coincidence detection, generation of "plateau potentials", where the cell membrane remains depolarized for an extended period of time, bistability, and bursting. Such processes can fundamentally change the integrative function of neurons. While the same conductances in the soma can have similar functions, unique dendritic locations significantly change the amplitude, time course, and interaction with synaptic inputs of such mechanisms. Secondly, the passive aspects of dendrite morphology such as length and branching patterns can substantially influence the electrical properties of dendrites. Thus, in the past decade, dendrites have emerged as engaged participants in several aspects of neuronal processing (see Stuart et al. 1997
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Constructing compartmental models of GnRH neurons |
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GnRH neurons are generally described as possessing a simple bipolar morphology and assuming a vertical orientation in the hypothalamus (Silverman et al. 1994
). The dendrites of GnRH neurons are long (often in excess of 1 mm) and thin (many processes <1 µm in diameter). This makes direct electrical measurement and stimulation (as in dynamic clamping) difficult, if not impossible, in GnRH dendrites. In order to expand our studies of processing in GnRH neurons, we have constructed multi-compartmental, conductance-based models of these cells. Models were constructed, and simulations performed, using the GENESIS (General Neural Simulation System) modeling environment (www.genesis-sim.org/GENESIS/). The use of compartmental models has allowed us to incorporate aspects of dendritic function into our understanding of GnRH neurons.
The first step in constructing a morphologically realistic computer model of a living neuron is to measure its morphology. The advent of transgenic animal models in which the GnRH neurons express GFP has made it possible to fill hypothalamic GnRH neurons in brain slices with cellular markers such as biocytin (Spergel et al. 1999, Suter et al. 2000). This has increased our ability to obtain high-fidelity anatomical reconstructions since the biocytin may reach regions of neurons where the GnRH peptide may not be present. A direct comparison of the two approaches indicated that while GnRH somata were roughly comparable between immuno-detection and biocytin-detection methods, significantly longer dendrites were identified with biocytin-filling (Suter et al. 2000).
The above initial study with biocytin-filled GnRH neurons concluded that the primary dendrites of GnRH neurons were about 125 µm, and exhibited modest branching (Suter et al. 2000). Recent studies (Campell et al. 2005; Roberts et al. 2006) have provided additional insight regarding the morphology of GnRH neurons. Campbell et al. (2005) studied biocytin-filled GnRH neurons in coronal sections and found lengths of about 300 µm. In our recent study, we used hemisagittal slices and found the average dendrite length to be about 500 µm (Roberts et al. 2006). In both studies, some biocytin-filled dendrites had lengths that exceeded 1200 µm in length. Moreover, both studies noted that dendrites often exited the plane of slices (thereby preventing measurement of their total length) and suggesting that GnRH dendrites extend into hypothalamic regions that are quite distal from regions where the GnRH somata reside. Thus, it appears that dendrites of GnRH neurons are much longer than previously appreciated. The second important observation is that the GnRH dendrite often branches (Campell et al. 2005; Roberts et al. 2006). Moreover, some of these branches do not assume the classical vertical orientation in the hypothalamus. About half of branches arch and project back toward GnRH somata and closely follow the trajectory of the GnRH axon toward the median eminence (Roberts et al. 2006).
After recording active and passive electrophysiological activity in a cell in a hypothalamic slice, the slice is fixed and the biocytin-filled cell is stained. A three-dimensional tracing of the relocated cell from which the electrophysiological measures were obtained is performed using a camera lucida and computer, leading to a "morphology file". This file contains the geometrical coordinates of a series of cylindrical compartments that trace out the actual morphology of the living cell. In the development of our models, we identified two main morphology types, which we refer to as "bipolar" (with an un-branched dendrite), and "branching". We have studied models of both morphological types.
Once the cell morphology has been determined, the next step in building the computer model is to assign electrical properties to each of the compartments that make up the morphology. These electrical properties are of two types, active and passive. The passive properties are membrane capacitance, membrane leakage conductance, and axial resistance along the lengths of the compartments. In our models, all compartments are set to have the same densities of passive parameters, so a larger compartment will have a larger capacitance and membrane leak conductance, but a lower axial resistance. In this way, the morphology directly affects the passive electrical properties of the model. Active electrical parameters include voltage-gated conductances, such as the sodium and potassium conductances involved in spiking, and ligand-gated conductances such as glutamatergic and GABAergic synaptic inputs. All these active electrical properties are modeled with mathematical formulae that represent the evolution of these conductances with voltage and time.
The compartments that make up the models are divided into three types, soma, axon, and dendrite. With the exception of synaptic inputs, all compartments of a given type will have identical densities of active conductances, though the densities differ between compartment types. The actual values of the active and passive electrical parameters for the different compartments are determined by an iterative computer search, which attempts to minimize the difference between the voltage response of the model cell and the measured electrophysiological voltage response in the same neuron when it was alive in the hypothalamic slice. In practice, the passive responses are matched first, and then the passive parameters are held fixed while the active parameters are varied to match spiking responses.
In a computer model of an electrically active cell, the magnitude of the membrane potential is calculated for each compartment at discrete points in time. Based on the calculated membrane potential, and the instantaneous values of all conductances, the computer calculates the magnitudes of all the currents that would flow in the model cell. The amount of current that flows during a single time step (typically a small fraction of a millisecond) is then calculated.
In addition to the ionic currents that flow through the cell membranes, living neurons have flows of ions from place to place within the cell. The voltage of each compartment is calculated as described above, and then the currents that would flow from one region of the cell to the next are approximated at each time step. In this way, currents that flow between parts of the cells can be modeled simultaneously with those that flow across the membrane.
Using the mathematics of electrical circuits, changes in membrane potential due to these brief flows of current can be calculated, and the new membrane potential used to calculate the currents that will flow in the next time step. In this way, the computer model can step through time and approximate the way in which the membrane potential of every part of a living cell would vary with time.
To address questions of synaptic integration, a mathematical model of a conductance that rises and falls with time is used to simulate the postsynaptic response to the firing of a presynaptic cell. The effects of the activity of multiple presynaptic cells is modeled by generating random trains of activation times, at set average frequencies. These trains of activation times are stored, so that multiple simulations can be run with the same patterns of input. This method of simulating trains of synaptic inputs is identical to that used in the dynamic clamping experiments.
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Using compartmental models to enhance an understanding of GnRH neuronal function |
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Our initial models of GnRH dendrites were constructed with passive dendrites, including active conductances only in model somata and axons. The effectiveness of simulated AMPA-type glutamatergic conductances at driving firing was examined at varying distances along the passive dendrite. It was found that trains of AMPA input which could drive firing at rates of 10–20 Hz when applied at the soma became progressively less effective as the inputs were moved out along the dendrite. At passive dendrite lengths of >300 µm, attenuation of the postsynaptic potentials rendered them insufficient to cause any spiking at all, despite the fact that total lengths of dendrites averaged 510 µm, with some longer than 1000 µm (Roberts et al. 2006
). The finding that distal dendritic synapses do not alter firing called into question the physiological significance of changes in input to the dendrite. As noted above, however, our initial model made the assumption that the dendrite of the GnRH neuron is passive. The above findings in compartmental models led to the conclusion that purely passive integration was unlikely to be a suitable mechanism for the processing of synaptic input over much of the length of the dendrite. Therefore, these results from the models led us to investigate the possibility that the dendrites of GnRH neurons might express active electrical properties. To begin to address this, a new set of models was constructed, with the same morphologies (bipolar and branching) but with active voltage-gated sodium and potassium conductances in the dendrites. The conductance densities in these models were tuned to match the measured electrophysiology and to be capable of initiating spikes in response to injection of current to the distal tip of the dendrite.
With the active-dendrite models, we again examined the efficacy of AMPA synaptic inputs at varying locations along the dendrite. For each dendritic compartment, a series of simulations was run to determine the minimum strength of a single AMPA synapse that would initiate an action potential at the soma. For the passive-dendrite models, the threshold conductance increased exponentially with distance (Fig. 5A). For the active-dendrite models, the magnitude of an AMPA synapse required to generate a spike initially increased with distance from the soma, then fell precipitously after about 200 µm, to a value about half that at the soma (Fig. 5B). For distances from the soma >400 µm, the synaptic threshold was relatively constant. This rise and fall of synaptic threshold led us to look more closely at the mechanisms of spike generation in the models. Again, in the model it is possible to keep track of the voltage in every compartment, and we were able to look at the data from the whole model to determine where the action potentials were actually initiated. This examination showed that, for inputs proximal to the soma, action potentials were initiated at the soma, while beyond some critical distance on the order of 200 µm, the mechanism switched to local initiation of a dendritic spike. Thus, our models indicated to us that passive dendrites were not likely to be effective at integrating synaptic input, but that if the dendrites were active, we should find that some fraction of action potentials should be initiated in the dendrites themselves.
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Two pieces of evidence from the model are that (1) with passive dendrites, distal synaptic inputs would be ineffective and that (2) spikes could be initiated both in the soma and in the dendrites, led us to look for direct evidence of properties of active spiking in dendrites. Dual electrophysiological recordings, with whole-cell patch on the soma, and tight-seal attached extracellular recording from dendrites, have shown clear back-propagation of somatically-induced action potentials. In addition, examination of the time courses of spontaneous action potentials observed in both the soma and dendrite have shown that the majority of the action potentials that were detected were observed first in the dendrite, although some clearly originated in the soma. These experimental results directly confirmed the predictions from studies using compartmental models that the dendrites of GnRH neurons were likely not passive, and that there could be both local and global integration of synaptic input leading to spiking.
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Synaptic integration |
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One of the limitations of dynamic current-clamping is that, by necessity, the current injecting electrode is located in the soma. While this is an accurate way of simulating somatic synaptic inputs, there is no way to examine spatial integration of synaptic input using dynamic clamping. However, with the compartmental models, trains of synaptic input can be applied at the soma, or in any distribution among the somatic and dendritic compartments. Thus, using compartmental models, the effects of spatial distribution of synaptic inputs can be systematically examined.
We have conducted simulations that replicate the experimental conditions of our dynamic clamping experiments involving the interactions between AMPA and excitatory GABA conductances. Comparisons between responses of the model and living cells are possible because the pattern of input applied with the dynamic-current clamp to living neurons can be identical to the input patterns applied to model neurons. Thus, the results from simulations with model neurons with all synaptic input located at the soma were similar to those found with dynamic clamping, indicating that results from simulations of spatial distribution, while not experimentally tractable, do have predictive value. In simulations in which the excitatory GABA input remains at the soma, but the AMPA inputs are distributed along progressively longer sections of the dendrite, the temporal interaction between AMPA and GABA requires less precision than in either dynamic clamping or simulations with inputs located only on the soma. Thus, the developmental changes in excitatory synaptic input to GnRH dendrites (Cottrell et al. 2006) probably increase firing rates not only due to an increase in overall excitatory drive but also due to alterations in temporal interactions between types of input that further facilitate spiking.
Studying dynamic changes in lengths of dendrites using compartmental models
A recent observation indicates that the GnRH dendrite undergoes structural remodeling during the early postnatal period (Cottrell et al. 2006) but the physiological significance of these structural changes is unclear. Our modeling studies indicate that changes in structure of the GnRH dendrite can profoundly alter neuronal output in conjunction with one key mode of activity, the after-depolarization potential (ADP; Kuehl-Kovarik et al. 2005; Chu and Moentor 2006). In magnocellular neurosecretory neurons, a brief pulse of injected depolarizing current initiates protracted periods of repetitive firing due to the generation of ADPs (Andrew and Dudek 1983). Moreover, there are decreases in total lengths of dendrites, and increases in firing rate of oxcytocin neurons associated with lactation (Stern and Armstrong 1998). These changes may be due in part to changes in ADPs since the incidence of ADPs in oxytocin neurons is increased during lactation when dendrites are shorter (Stern and Armstrong, 1996; Teruyama and Armstrong, 2002). Therefore, we have used our compartmental models to explore the effects of truncating the dendrites of model GnRH neurons on ADPs and repetitive firing.
Since the morphology of the models consists of a series of connected cylindrical compartments, it is possible to shorten the dendrite in the model by removing compartments one by one. If a simulation is run on several models, with all the same parameters except for the morphology, then differences in the outputs can be correlated directly with differences in morphology. To test the hypothesis that there is a relationship between length of dendrite and amplitude of ADP, we studied the response in simulations in which compartments were removed, one by one, starting from the tip of the dendrite, until the entire dendrite had been removed. The same protocol of current injection was employed for each model and the maximum of the voltage after the spike was recorded. This series of simulations showed, in both morphological types, that the magnitude of the ADP increases with decreasing length of dendrite, and that for sufficiently short dendrite lengths, the models would repetitively fire after a short burst of inputs.
In response to bursts of input that induced repetitive firing, the full models stopped firing after the cessation of the input, but the reduced-morphology models continued to fire after the stimulus was removed, and the rate of repetitive firing increased as the lengths of dendrites decreased. Thus, we were able, by manipulating the morphology of our model, to show an enhancement of an important mode of activity in neurosecretory neurons based on the length of dendrites.
The most obvious properties of the models that depend on dendrite length are the passive parameters input resistance and membrane capacitance. As the length of the dendrite decreases, the total surface area of the cell also decreases, resulting in an increase in resistance of the membrane and a reduction in capacitance. Since the input resistance depends on the surface resistance, the smaller models will have larger input resistances, and smaller capacitances than will larger ones.
In the full-morphology model, the conductances were tuned to duplicate the resting membrane potential of the living cell. Since the larger full-morphology model has a proportionately larger leakage resistance, the soma of the model (or living) cell must supply a compensating depolarizing current to maintain a resting membrane potential above the leak-reversal potential. As the dendrite with its associated leak is removed, this compensating current is no longer balanced by the leak, and thus the cell begins to depolarize. In conjunction with this, the smaller models have lower capacitance, and therefore the same amount of injected charge will lead to a larger change in voltage. It is mainly these two passive effects that lead to the ADPs seen in truncated models.
The models offer a prediction about activity in living cells, specifically that the magnitude of the ADP would depend on the length of the dendrite. To test this prediction experimentally, cells were specifically selected for especially long or short dendrites, and their response was measured to a current injection protocol that had been shown to elicit ADPs (from Chu and Moenter 2006). The results, as shown in Fig. 6, confirm the predictions of the model. For a cell with a relatively short dendrite (400 µm), average ADPs of about 3 mV were observed, while for a longer cell with a branching dendrite of >1000 µm, the average ADP was <1 mV.
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The computational methods of dynamic clamping and compartmental modeling can be valuable additions to standard electrophysiological techniques, both in testing hypotheses intractable by traditional methods, and in generating predictions that are testable through experimentation. A continuing interaction between simulation and experimentation enhances progress, with new experimental results informing improvements in the simulations, and with results from simulations providing predictions and new directions for experiments. Thus, these emerging tools for the study of reproductive endocrinology will allow the field to continue in the tradition of Harris: conceptual advances driven by methodological innovation.
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Acknowledgments |
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This work was supported by HD-45436 to KJS. Analysis and modeling facilities were provided by the Computational Biology Initiative (http://www.cbi.utsa.edu) at the University of Texas San Antonio and the University of Texas Health Sciences Center at San Antonio which is funded by a partnership between National Institutes of Health (RR013646) and the Vice Chancellor for Medical Affairs of the University of Texas.
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Footnotes |
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From the symposium, "Advances in Neurobiology" presented at the annual meeting of the Society for Integrative and Comparative Biology, January 2–6, 2008, at San Antonio, Texas.
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