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Innovative Methodology
Department of Neurobiology and Center for the Neural Basis of Cognition, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania 15261
Submitted 10 June 2003; accepted in final form 22 September 2003
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ABSTRACT |
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43 kHz while simultaneously saving two channels of data with 16-bit precision. G-clamp also includes utilities for measuring current-voltage relations, synaptic strength, and synaptic gain. Taking an approach built on a commercially available software/hardware platform has resulted in a system that is easy to assemble and upgrade. In addition, the graphical programming structure of LabVIEW should make it relatively easy for others to adapt G-clamp for new experimental applications. |
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INTRODUCTION |
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Although the value of the dynamic-clamp technique has become widely appreciated (Dorval et al. 2001
), the lack of standardized tools for its implementation remains problematic. Early approaches employed hardware and software that are now obsolete. More recent solutions exist (Butera et al. 2001
; Dorval et al. 2001
; Jaeger and Bower 1999
) but adapting them to new experimental applications requires expertise in the DOS or real-time Linux operating systems coupled with programming skills in assembly languages and C. Our goal was to simplify dynamic-clamp experiments by developing a high-performance system that would be straightforward to put together and use. As part of the strategy, the application software was written in a high-level programming environment, thus making it easier to share and easier for others to modify. The result is G-clamp, a dynamic clamp solution based on Lab-VIEW-RT programming tools and associated hardware manufactured by National Instruments. The system runs under a standard Windows user-interface, and its performance can be upgraded as faster processors and data acquisition boards become available.
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METHODS |
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Because all currents through ion channels generally obey Ohm's law [I = g * (Vm - Erev)], creating a virtual conductance has three requirements: a description of the conductance (g) as a function of voltage and/or time, measurement of the membrane potential (Vm), and knowledge of the reversal potential (Erev) for current through the conductance. These values are then used to compute a signal that drives the current command input of a current-clamp amplifier. Because of the reciprocal interactions between injected current, changes in Vm and the gating of voltage-dependent conductances (Fig. 1A), the feedback loop in a dynamic clamp (Fig. 1B) must run faster than the gating kinetics of the conductances under study. In many cases, this can be achieved with loop speeds in the range of 2-20 kHz. In this way, a dynamic clamp functions as a conductance clamp that effectively introduces a population of virtual ion channels into a living cell.
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Commercially obtained components in G-clamp
The commercial components of G-clamp (Table 1) include an ordinary PC running Windows, a set of LabVIEW RT hardware and software components (National Instruments, Austin, TX), and an Axoclamp 2B intracellular recording amplifier (Axon Instruments, Foster City, CA). All of the National Instruments components cost approximately $10,000, which is similar to the cost of the recording amplifier.
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G-clamp has a hierarchical modular structure (Fig. 2) that facilitates sharing between users and is open to future development of new applications. The user interface (Fig. 3), residing at the top level on the host computer, serves to select and control the experiment and to display its results. On starting an experiment, the user-interface module calls the LabVIEW run-time engine on the embedded CPU and commands it to execute one of three experiment modules. Unlike the user-interface module, all of the other software modules (Fig. 2) reside on the hard disk of the embedded processor and are loaded into the embedded memory as needed. This arrangement enhances performance by circumventing the need for continual downloads over the Ethernet link from the host hard drive. Each of the experiment modules runs a specific experimental protocol the purpose of which reflects our particular research on synaptic integration, but the structure of which could be adapted to related applications.
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The second experiment module implements a virtual excitatory synapse and uses a binary search paradigm to scale the magnitude of the synaptic conductance until the excitatory postsynaptic potential (EPSP) reaches threshold for stimulating an action potential. By scaling a conductance waveform relative to this threshold, one can effectively normalize synaptic strength and more easily compare the behavior of different neurons.
The third experiment module simulates specific patterns of synaptic activity by reading long data files that contain templates describing appropriate conductance waveforms. In this experiment, the strength of synapses in the template file can be scaled using threshold results from the second experiment. At the end of the experiment, the program automatically calculates synaptic gain by counting the number of action potentials elicited by a given pattern of virtual EPSPs and dividing their frequency by the presynaptic firing rate associated with the template file. By sequentially testing a series of template files reflecting different rates of presynaptic activity, the system can automatically measure and display the relation between presynaptic firing rate and synaptic gain.
Serving as the heart of the G-clamp feedback loop, the RT module interacts with the experiment modules, the I/O hardware, and the virtual-conductance modules. The RT module executes each experimental protocol by using a hardware clock on the DAQ board to control A-D conversions and thereby drive iterations of the virtual-clamp loop (Fig. 1B). The loop module also makes the required calls to virtual conductance modules, generates analog output to the current-clamp command circuitry, and writes results to memory.
The virtual conductance modules work by evaluating kinetic equations and by reading files that contain predefined conductance waveforms. Equations describing a voltage-dependent Na+ conductance, a noninactivating delayed rectifier K+ conductance, an M-type K+ conductance, and a linear leak conductance are based on a Hodgkin-Huxley style model used previously to describe the amphibian sympathetic B-type neuron (Schobesberger et al. 2000
). The only difference from the previous model is that activation of the Na+ conductance was slowed by a factor of 5 so that it would run accurately at a clamp speed of 20 kHz. The excitatory synapse in G-clamp is modeled after the nicotinic synapse found on B neurons. This synapse mediates a fast EPSP whose underlying conductance waveform can be described as the sum of two exponentials; an activation time constant of 1 ms and a decay time constant of 5 ms (Schobesberger et al. 2000
). To illustrate the system's flexibility, we include in the results the implementation of a new conductance module for an A-type potassium conductance.
During each cycle of the dynamic feedback loop, G-clamp predicts the next value of every voltage-dependent conductance by solving the ordinary differential equations that describe them. The numerical integration is based on Euler's method, which involves a simple linear extrapolation of the appropriate gating variables. All of the calculations for evaluating equations are performed in RT, using the arithmetic operations and functions available in LabVIEW. Synaptic conductance is treated differently because we wanted to perform experiments that incorporated complicated patterns of synaptic activity. To accommodate this requirement, the system was designed to update the synaptic conductance during each cycle of the RT loop by reading the next value from a template file stored in memory. After determining an updated value for every conductance, the software then calculates the current that should flow through each virtual conductance, adds them, and sends out an appropriate signal to the constant-current command input. In this way, the system continually supplies the current needed to mimic one or more virtual conductances.
The synaptic conductance template files are prepared using NEUROSIM, a program that we have written in MATLAB (R12, The MathWorks, Natick, MA). Every file has a header that includes scaling information and parameters used to generate the template followed by a string of numbers that describe either a single synaptic event or complex patterns of synaptic events lasting several minutes.
The speed of the clamp is set in one of two ways. In experiments using conductance templates, the template controls the timing. Otherwise, clamp speed is set through the sampling rate control in the user interface (Fig. 3).
Distribution and installation of G-clamp software
G-clamp v1.1, as described in this paper, consists of two LabVIEW library files (LLBs), two dynamic link libraries (DLLs), and a read-me text file with additional instructions. This application software was developed with grant support from the National Institutes of Health, is freely available for research purposes, and can be obtained by contacting the authors. NEUROSIM, a MATLAB program for preparing synaptic template files and simulating synaptic activity in a conductance-based model neuron, is similarly available and will be described elsewhere in more detail. MATLAB simulations of action potentials used the ode15s equation solver.
In brief, installing G-clamp requires that one first create a folder named "G-clamp" anywhere on the host computer and a second folder named "G-clamp" in the NI-RT directory on the embedded PC. Copy the files "G-clamp Host.LLB" and "lvanlys.DLL" into the G-clamp folder on the host computer. Use FTP to transfer the files "Embedded.LLB" into the folder "c\NI-RT\G-clamp" and "nbfifo.DLL" into the folder "c\NI-RT\System" on the embedded PC. Enable the TCP/IP protocol for the VI server of the LabVIEW-RT run-time engine and allow TCP/IP access by the host computer. Finally, set the instruction "UseSleepingTimedNonBuffered" to FALSE in the file "NI-RT.INI" on the embedded PC and the system is ready for operation.
Recordings from bullfrog sympathetic neurons
Paravertebral ganglia 8-10 were isolated from bullfrogs (Rana catesbeiana, 3-5 in), dissociated by enzymatic digestion with Liberase Blendzyme 1 (Roche Diagnostics, Indianapolis, IN), and the cells plated onto coverslips coated with poly-D-lysine (BD Biosciences, Bedford, MA). All procedures followed a protocol approved by the University's Institutional Animal Care and Use Committee. Cultures were maintained at room temperature for
1 wk in a diluted L-15 medium (65%) supplemented with 5 mM dextrose, 2 mM L-glutamine, 1 mM CaCl2, 5% fetal bovine serum, 100 U/ml penicillin and 100 µg/ml streptomycin. Whole cell recordings were performed at room temperature with external solution containing (in mM) 115 NaCl, 2 KCl, 1.8 CaCl2, and 4 NaHEPES, adjusted to pH 7.3 with HCl. Patch pipettes had resistances of 2-5 M
when filled with internal solution consisting of (in mM) 110 KCl, 1 MgCl2, 0.4 CaCl2, 4.4 EGTA, 5 NaHEPES, 5 dextrose, and 2 Na2ATP, adjusted to pH 7.2 with KOH.
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RESULTS |
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G-clamp was developed through an iterative process of design, programming, and evaluation. Here we begin by describing version 1.0 in terms of test results, comparisons with numerical simulations, and program demonstrations. This version of the program has five conductance modules (Fig. 2) the properties of which reflect data describing sympathetic neurons. The results from tests of this system document performance of the dynamic clamp, define its limits, and identify potential sources of experimental error that can arise from improper settings of the recording amplifier. We then describe a minor upgrade of the software (version 1.1) to illustrate how the system can be extended to incorporate a new virtual conductance, which in this instance mimics the macroscopic behavior of A-type potassium channels.
Determinism of the RT loop
Each cycle through the RT loop in G-clamp, v1.0, (Fig. 1B) has a computational overhead that ranges from 2 to 113 arithmetic operations, depending on the type and number of virtual conductances being implemented (Table 3). Proper performance of the system requires that timing of this loop be reliable with minimal variation or jitter from cycle to cycle. Engineers describe these timing characteristics of a system as its determinism. To measure how fast G-clamp can run before determinism breaks down, a timer was incorporated into the RT loop. For this purpose we implemented the Read Time Stamp Counter (RDTSC) assembly instruction for Pentium-class processors, which can record from the processor the time of each iteration through the loop. After the loop has finished executing, the time stamps are analyzed and the results displayed in terms of mean cycle length and jitter, defined as the SD and maximum deviation. In addition to loop performance data, the user-interface (Fig. 3) also displays the A-D sampling rate of the multifunction board. By comparing these outputs, we found that loop timing was deterministic when the measured loop rate agreed with the sampling rate. For example, when all virtual conductances were being used, the system could run at speeds
32.7 kHz before the RT loop failed to keep up with A-D conversions. Table 3 summarizes the maximum loop speeds attainable for different combinations of virtual conductances. Over the entire range of usable speeds, the SD of mean cycle time was <0.5 µs and relatively constant, independent of the number of virtual conductances. These results identified the conditions where timing of the RT loop was reliable, but additional tests were needed to evaluate whether the dynamic clamp was correctly implementing virtual conductances.
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Dynamic-clamp performance was evaluated by examining the resting properties and excitability of an artificial neuron with four virtual conductances (Fig. 4A). The combination of conductances and their magnitudes was chosen to resemble a model sympathetic neuron the behavior of which is well known from numerical simulations (Schobesberger et al. 2000
). The system was tested by grounding the headstage of the current-clamp amplifier through an RC circuit (500 M
, 33 pF) in series with a 10 M
resistor (MCW-1U, Axon Instruments), a configuration that mimics a passive cell and recording electrode. After placing the amplifier into standard current-clamp mode, a current pulse was injected through the passive circuit so that the electrode resistance and stray capacitance could be nulled using the bridge balance and negative capacitance controls. The hybrid artificial neuron created by turning on the dynamic clamp consisted of the passive RC circuit in parallel with the virtual conductances (Fig. 4B).
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Although G-clamp action potentials and numerical simulations appeared similar, subtle differences between them became clear when the clamp's loop speed was varied and the results were viewed at sub-millisecond resolution (Fig. 5). Not surprisingly, the most challenging tasks for the dynamic clamp are to reproduce the upstroke and peak of the action potential because these events depend critically on the voltage-dependent Na+ conductance the kinetics of which are the fastest process in the entire system. Comparing virtual action potentials recorded at different loop rates (2.5-30 kHz) revealed two important features of dynamic-clamp performance (Fig. 5). First, as loop rate was lowered, the upstroke of the action potential shifted leftward by
200 µs and its peak amplitude increased by
9 mV. Below 2.5 kHz, the system was unstable with the spike going positive to ENa and the repolarization phase going into large oscillations. A less extreme version of this oscillation behavior appears as a notch in the 2.5-kHz response (Fig. 5). The effects of loop speed on spike shape arise in part from Euler's method, which G-clamp uses to integrate the conductance equations. The linear extrapolations employed by this method will give inaccurate results when the time steps between points are large relative to the rates of change in gating variables. Indeed similar problems will arise with other methods when the integration step size is too large. As a consequence of such errors, when the dynamic clamp runs too slowly, it overestimates gNa near threshold and near the peak of the action potential, thus leading to a shift in the time of spike initiation and to an artifactual increase in spike amplitude. The second insight obtained from comparing loop speeds was that action potentials recorded at 20 and 30 kHz were nearly identical, thus demonstrating that G-clamp can produce a generic voltage-dependent gNa at less than maximum speed. However, it is important to remember that the optimal loop speed for a given conductance will always depend on its particular kinetics.
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6 mV below the G-clamp spikes recorded at
20 kHz, but otherwise is very similar. To investigate this 6-mV difference, we conducted numerical simulations that were designed to mimic the Euler method, as implemented by G-clamp. In a simulation of the clamp running at a loop speed of 20 kHz, the output current was updated with a 30-µs lag behind each voltage measurement, and the cellular potential was allowed to change continuously (i.e., 1 MHz) in response to 20-kHz current updates. The resulting action potential amplitude agreed well with the MATLAB result, differing by only 1.5 mV (not shown). The remaining 4.5-mV difference could not be explained by the choice of integration method used in the MATLAB computations. When the MATLAB solvers for stiff equations (ode15s, ode23t, ode23tb, ode23s) were compared, they all yielded similar results. The remaining 4.5-mV disparity between the G-clamp's action potential and purely numerical solutions of the equations must therefore originate elsewhere. The most likely source is inadequate electrode compensation, a view supported by experimental tests described in the following section. Errors arising from improper compensation of electrode resistance and capacitance
Dynamic-clamp experiments often employ whole cell recordings with patch-clamp electrodes. The relatively low resistance and capacitance of such electrodes are generally easy to null out with a standard current-clamp amplifier. Nonetheless, it is quite likely that small errors in bridge balance or capacitance compensation will arise during real experiments. We therefore wanted to examine how such errors influence dynamic-clamp performance. In principle, one would expect bridge errors to be most problematic because they will lead to incorrect measurements of membrane potential across the entire frequency spectrum. By contrast, incorrect capacitance compensation should only influence high-frequency components of the voltage signal. Experimental tests confirmed this prediction. Overcompensating a 10-M
electrode by 4 M
can artifactually increase action potential amplitude and cause oscillations during repolarization (Fig. 6A). Overcompensating by as little as 1 M
is sufficient to increase action potential amplitude by 5 mV and account for the disparity between G-clamp recordings and MATLAB simulations. By contrast, undercompensating the bridge reduces the apparent size of the action potential but is stable and does not lead to ringing. As expected, improper capacitance compensation has smaller effects (Fig. 6B). Overcompensation generally causes the amplifier to ring, even without the dynamic clamp, and can be easily recognized and avoided. Capacitance undercompensation slows down the spike and increases its amplitude but produces little change in repolarization.
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Having created a hybrid artificial neuron with a realistic resting potential and action potential, we next added a virtual nicotinic synapse whose reversal potential was 0 mV. As with the voltage-dependent conductances, the synaptic response was designed to mimic data from sympathetic neurons (Schobesberger et al. 2000
). For these experiments, synaptic conductance waveforms were prepared in advance using a MATLAB program and stored as template files.
The conductance waveform required for a given experiment was selected from the templates menu (Fig. 7A). As would be expected, the time course of the conductance command signal differed from those of the synaptic current and EPSP that it produced (Fig. 7B). For purposes of illustration, the synaptic strength in this example was chosen to generate an EPSP with a subthreshold active component, which disappeared when the voltage-dependent gNa was turned off. When the numerical solution describing the EPSP was computed in a MATLAB simulation, it superimposed exactly on the G-clamp response. The EPSP undershoot seen in Fig. 7B arises from small changes in gK produced by the transient depolarization. By varying the loop speed, it was determined that G-clamp accurately implemented the nicotinic conductance at rates
5kHz (data not shown). This is consistent with the fact that the fastest component of gsyn, its rising phase, has a time constant of 1 ms.
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Measurement of synaptic strength
A central motivation for developing G-clamp was to study how virtual excitatory synapses interact on real neurons. This approach can be powerful because it permits synaptic events to be precisely defined in terms of their strength and timing. To define synaptic strength in a population of cells, it is useful to have a normalization method. For this reason, we have defined the threshold synaptic conductance (thresh-gsyn) as the conductance that is just barely strong enough to trigger an action potential (Schobesberger et al. 2000
). G-clamp incorporates an algorithm for measuring thresh-gsyn. To use the routine, one must first estimate an upper boundary greater than the expected answer and enter it into the template window (Fig. 7A; Gmax). The search range can be further limited by setting a lower boundary >0 with the Gmin control. The program then uses a binary search to find thresh-gsyn in just a few trials (Fig. 7D).
To further evaluate the performance of G-clamp, we measured how estimates of thresh-gsyn were influenced by loop rate and by electrode compensation. These tests revealed that over a fairly broad range of experimental conditions, the measurement of thresh-gsyn was relatively insensitive to loop rate (Fig. 7E) and to errors in bridge balance and capacitance compensation (Fig. 7F).
Measurement of synaptic gain
Once thresh-gsyn has been measured experimentally, this information can be used to scale the strength of virtual synapses in a more complicated experiment. For our studies of synaptic integration in sympathetic ganglia, we wish to model two classes of nicotinic synapse (Karila and Horn 2000
). The strong inputs denoted as primary are expected to produce a postsynaptic conductance increase that is several times greater than thresh-gsyn. By contrast, the weak secondary synapses are associated with conductances that are less than thresh-gsyn. With G-clamp, one can take a template and easily scale the strength of synapses during an experiment. Figure 8 illustrates an example in which the primary synapse was 15 nS and the three secondary synapses were each 5 nS. The noisy pattern of primary and secondary EPSPs was generated by assuming that activity arises from Poisson processes in which intervals between events at each synapse are exponentially distributed. The conductance template then elicited a series of synaptic currents that produced EPSPs, some of which triggered postsynaptic action potentials. By counting the number of presynaptic events and the number of postsynaptic action potentials, G-clamp calculates the synaptic gain of the neuron. The embedded processor's memory can accommodate synaptic templates lasting 330 s at 20 kHz while recording two channels of data. These long templates become important if one needs to study large numbers of synaptic events for statistical purposes in the design of experiments. With the synaptic gain module in G-clamp, one can automatically call up the templates, record and analyze synaptic gain over a range of presynaptic firing rates, and display the resulting synaptic gain relation (Fig. 8). In G-clamp, gain has been defined as the average postsynaptic firing rate divided by the average firing rate of each presynaptic neuron. The justification for this calculation derives from the synaptic connectivity of sympathetic ganglia (Karila and Horn 2000
), but the analysis could be readily altered to reflect the organization of other neural circuits.
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After testing G-clamp by adding virtual conductances to a passive RC circuit, we next verified that the system would work on living cells by recording from dissociated sympathetic neurons with whole cell patch electrodes. In preliminary experiments using only the virtual nicotinic synapse, the system remained stable during physiological recordings and provided measures of threshold gsyn and synaptic gain that were consistent with theoretical predictions (Wheeler et al. 2002
). Figure 9 illustrates more challenging tests in which the voltage-dependent sodium conductance was added to or subtracted from two neurons. In a cell that was stimulated with a virtual suprathreshold EPSP, introducing increasing amounts of virtual gNa systematically shifted the action potential to the left, produced a small increase in its peak amplitude and increased the maximum upstroke velocity without causing any instability in the system (Fig. 9A). These effects on the action potential's threshold and waveform are consistent with an increase in the total voltage-dependent inward current. In the converse experiment, subtracting virtual gNa from an otherwise excitable neuron completely prevented the burst of action potentials generated by a prolonged depolarizing current pulse (Fig. 9B).
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A central goal in developing this system was flexibility. Prompted by a request from colleagues, we recently implemented a transient A-type potassium conductance (gKA) whose kinetics were modeled using voltage-clamp data from mammalian midbrain dopaminergic neurons (Hahn et al. 2003). To create the new conductance, an existing conductance was cloned and its equations were modified to reflect the properties of gKA (Fig. 10, A and B). The new gKA module was integrated into the RT loop by linking it with the resized input and output functions, following the exact same scheme used with the existing conductance modules (Fig. 10A). Recordings from a sympathetic neuron illustrate how the virtual gKA can be used to manipulate a cell's repetitive firing behavior (Fig. 10C). Adding increasing amounts of virtual gKA enhanced the adaptation of firing, ultimately reducing it to a single spike. Taken together, the experiments with living neurons show that G-clamp can effectively implement virtual conductances, even during the rapid voltage changes associated with action potentials.
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DISCUSSION |
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In developing G-clamp, the forward Euler method was chosen for numerical integration of differential equations because it is simple and therefore computationally efficient. Comparing the RT results obtained using a passive RC circuit with MATLAB simulations that employed more sophisticated integration methods revealed that the Euler method was both accurate and stable (Figs. 4, C and D, 5, and 6B). Further tests with sympathetic neurons confirmed that the system also performs well in biological experiments (Figs. 9 and 10C). However, it is conceivable that adding new virtual conductances will lead to problems. Because the forward Euler method can sometimes break down, it might become necessary to accept a higher computational load associated with a more stable integrator, such as the exponential Euler method (Bower and Beeman 1998
). Such a change can be done easily by editing the equations in the conductance modules (Fig. 10B). One feature of G-clamp that may surprise new users is the perceptible delay between the execution of an experiment and the appearance of data in the user-interface window. This behavior is different from that of many commonly used data-acquisition systems that can rapidly display data as they are digitized and stored. The reason for this disparity lies in the nature of the RT embedded processor. During execution of the RT feedback loop, the system writes the data to memory, but does not transfer it to disk or to the host computer over the Ethernet link. For brief experiments such as the threshold search (Fig. 7D), this problem is minimal. However, the delay does become noticeable when measuring synaptic gain with long template files (Fig. 8). Thus it takes
4 s to transfer the acquired traces of a 20-s recording to the host computer. It is therefore useful to monitor the progress of longer experiments with an oscilloscope or chart recorder. In future versions of the program, it should be possible to improve data transfers by including them in the RT loop when the system operates at lower computational loads. Data transfers will also improve as communication links become faster.
A powerful application of dynamic clamping involves the creation of virtual synapses between pairs of neurons or even small networks of cells (Bartos et al. 1999
; Manor and Nadim 2001
; Pinto et al. 2001
; Sharp et al. 1996
; Wilson et al. 2001
). Performing such experiments with G-clamp will require additional channels for measurement of Vm and output of Im command signals. Fourteen unused input channels and one additional output are available on the system's present I/O board. As the need arises, it will be possible to extend the G-clamp program to utilize these system resources. More output channels can also be added to the system by plugging another board with D-A channels into the unused slot in the backplane of the embedded computer.
Despite its virtues, dynamic clamping has been limited by its inability to mimic the electrotonic structure of neurons. More specifically, G-clamp incorporates the means for implementing multiple synapses but not for placing them at different sites on a dendrite. In the future, it may be possible to solve this problem, at least partially, by designing virtual synapses on virtual dendrites (Dorval et al. 2001
).
These and other ideas for further development of G-clamp will ultimately depend on the availability of computational speed and system memory. Fortunately, this is a generic problem that will benefit from general progress in hardware and software design. In the 2 yrs since this project began, a new generation of embedded processors with faster CPUs, and more memory has already become available. Although these recent enhancements in hardware performance are modest, the trend will likely continue. By transferring the current software and its successors to updated hardware, it should be possible to upgrade dynamic clamp performance with minimal effort. For these reasons, G-clamp may prove useful to other investigators and applicable to other dynamic-clamp experiments for at least several years to come.
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ACKNOWLEDGMENTS |
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Present address of J. Beacom: Keck School of Medicine, University of Southern California, Los Angeles, CA 90089 (E-mail: beacom{at}usc.edu.).
GRANTS
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-21065 to J. P. Horn and by a postdoctoral fellowship from the American Heart Association, Pennsylvania/Delaware Affiliate, to D. W. Wheeler.
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FOOTNOTES |
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Address for reprint requests and other correspondence: P.H.M. Kullmann, Dept. of Neurobiology, E 1440 Biomedical Science Tower, University of Pittsburgh School of Medicine, Pittsburgh, PA 15261 (E-mail: pkullman{at}pitt.edu).
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REFERENCES |
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W. Akemann and T. Knopfel Interaction of Kv3 potassium channels and resurgent sodium current influences the rate of spontaneous firing of Purkinje neurons. J. Neurosci., April 26, 2006; 26(17): 4602 - 4612. [Abstract] [Full Text] [PDF] |
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D. F. Kutz, N. Marzocchi, P. Fattori, S. Cavalcanti, and C. Galletti Real-Time Supervisor System Based on Trinary Logic to Control Experiments With Behaving Animals and Humans J Neurophysiol, June 1, 2005; 93(6): 3674 - 3686. [Abstract] [Full Text] [PDF] |
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D. W. Wheeler, P. H. M. Kullmann, and J. P. Horn Estimating Use-Dependent Synaptic Gain in Autonomic Ganglia by Computational Simulation and Dynamic-Clamp Analysis J Neurophysiol, November 1, 2004; 92(5): 2659 - 2671. [Abstract] [Full Text] [PDF] |
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