Single-channel analysis of glutamate receptors.

Single-Channel Analysis of Glutamate Receptors

UNIT 11.17

Chris Shelley1,2 1

Department of Neuroscience, Physiology, and Pharmacology, University College London, London, United Kingdom 2 Present address: Department of Biology, Franklin and Marshall College, Lancaster, Pennsylvania

This is a companion to UNIT 11.16: Single-Channel Recording of Glutamate Receptors. Described here are techniques for analyzing single-channel currents recorded from glutamate receptors to characterize their properties. In addition, issues that need to be taken into account when analyzing glutamate receptor C 2015 by John Wiley & Sons, single-channel recording results are discussed. Inc. Keywords: single channel r glutamate receptor r ion channel

How to cite this article: Shelley, C. 2015. Single-Channel Analysis of Glutamate Receptors. Curr. Protoc. Pharmacol. 68:11.17.1-11.17.23. doi: 10.1002/0471141755.ph1117s68

INTRODUCTION Single-channel analysis is employed for studying recordings taken from biological membranes. Although many of the analytical techniques appear complex, the format of the raw data is simple, consisting of a large number of data points, each with an amplitude and a time value. Important information on ion channels can be obtained from such results, including insights into the molecular functioning of these channels. Given their properties, glutamate receptors present unique challenges for obtaining single-channel recording. Both AMPA and kainate receptors have low single-channel conductances, and many types of glutamate receptors exhibit subconductance levels, in which a single channel adopts different states with different conductances. Heterogeneity in the number and amplitude of the subconductance states is also a problem, particularly for AMPA receptors (Smith et al., 2000a; Gebhardt and Cull-Candy, 2006; Shelley et al., 2012). The presence of sublevels not only increases the difficulty in obtaining recordings, but also complicates the data analysis. Many types of glutamate receptors also undergo rapid desensitization, during which channels enter relatively long-lived closed states in the presence of agonist. Finally, many glutamate receptors display complex kinetics, with multiple modes of activity having been observed (Popescu, 2012). Detailed in this unit are some of the different types of analyses that can be performed on glutamate receptor ion channels in an attempt to elucidate their function at a molecular level.

DATA FORMATS Data generated from glutamate receptor channel analysis consists of a series of points with values for amplitude and time, with the latter indicating when during the recording the data point was obtained. Data are in the form of either a single continuous sequence of points or a series of sweeps of a defined length. Continuous data is the preferred Current Protocols in Pharmacology 11.17.1-11.17.23, March 2015 Published online March 2015 in Wiley Online Library (wileyonlinelibrary.com). doi: 10.1002/0471141755.ph1117s68 C 2015 John Wiley & Sons, Inc. Copyright

Electrophysiological Techniques

11.17.1 Supplement 68

Table 11.17.1 Software Available for the Analysis of Single-Channel Data

Name

Available from

Web site (as of September 2014)

Synaptosoft

http://www.synaptosoft.com/Channelab/

IonChannelLab

Universidad Michoacana de San Nicholás de Hidalgo

http://www.jadesantiago.com/Electrophysiology/ IonChannelLab/Default.aspx

pClamp

Molecular Devices

http://www.moleculardevices.com/products/ software/pclamp.html

DCProgs

University College London

http://www.onemol.org.uk/?page_id=8

QUB

University at Buffalo

http://www.qub.buffalo.edu/

Strathclyde Electrophysiology Software

University of Strathclyde

http://spider.science.strath.ac.uk/sipbs/software_ ses.htm

ChanneLab a

a Although

not for the direct analysis of single-channel data, this user-friendly program allows the simulation of singlechannel and macroscopic currents from kinetic models.

format as it allows prolonged, uninterrupted sequences of channel events to be recorded, although it is critical to note the exact position in a recording of condition changes, such as a change in the agonist concentration or an adjustment of the holding potential. In some situations data sweeps simplify the analysis, such as when channel activation is achieved by rapid switches into agonist solution. However, this approach is limited by the fact that the duration of the first and last event in each sweep will not be known.

SINGLE-CHANNEL ANALYSIS There are several software packages available for analysis of single-channel data. These have varying degrees of automation, with several developed specifically for singlechannel studies (Table 11.17.1). In some cases, more general numerical analysis software, such as IGOR Pro (Wavemetrics), Scilab (Scilab Enterprises), and even Excel (Microsoft) can be used to analyze these results. Listed in Basic Protocol 1 are the steps for determining whether the acquired singlechannel data are suitable for analysis, and ways to prepare the raw data for further analysis. Outlined in Basic Protocol 2 is the analysis used to characterize the basic properties of single-ion channel events. Provided in the Alternate Protocol is a description of the use of noise analysis to obtain single-channel parameters from records with a low signal-tonoise ratio, making it impossible to obtain single-channel parameters directly from the idealized channel events. The analysis of sublevels is covered in Basic Protocol 3. These sub-maximal single channel currents are seen with many different types of glutamate receptor channels. Described in Basic Protocol 4 are the steps taken to fit single-channel data to a kinetic model. BASIC PROTOCOL 1


FIRST PASS ANALYSIS OF GLUTAMATE RECEPTOR SINGLE-CHANNEL RECORDINGS Once data are acquired, it is imperative their quality be assessed prior to in-depth analysis. The chief aim of this step is to remove artifacts that will compromise the analysis. Considerations include the baseline noise level, the duration of the recording, the presence of electrical interference (“artifacts”), and the density of single channel events. Prior to this assessment, it is often useful to filter the data further to reduce background noise, although this maneuver distorts the single-channel events, as described below. Judgments


Current Protocols in Pharmacology

5 kHz

2 pA 25 msec

1 kHz

0.5 kHz

Figure 11.17.1 The effect of filtering on single-channel currents. The same data has been filtered at the indicated bandwidths. Note that with increased filtering, the amplitude of the brief openings is decreased (a), and the current amplitude of the brief closing within bursts of openings, increases in amplitude. Thus, with the filter set to 0.5 kHz and using a 50% threshold level to define openings, the first burst would be interpreted as a single opening with a duration of approximately 30 msec, rather than a burst of four or five openings.

concerning the quality of the data can be made once they are filtered to their final bandwidth.

Materials Single-channel data Computer Analysis software (See Table 11.17.1) 1. Decide whether to low-pass-filter the data. During acquisition, the data are filtered by the intrinsic bandwidth of the recording apparatus, and may be filtered further prior to acquisition. If multiple rounds of filtering are employed, the effective cutoff frequency is lower than that of the lowest filter (f), as illustrated by (Eq. 1):

f 1 = f2 f n2 n

i=1

Equation 1

Although low-pass filtering increases the signal-to-noise ratio of full amplitude events, it also distorts the shape of the single-channel events and reduces the amplitude of brief events (Fig. 11.17.1). Thus, because of filtering, the essentially square current pulses of the single channel events do not appear as square pulses but instead have measurable rise-times. If an event has a duration similar or less than that of the rise-time, then full observed amplitude will be less than the true full amplitude. Therefore, the magnitude of short duration events are underestimated. Using a 10% to 90% definition of rise-time


11.17.3 Current Protocols in Pharmacology

Supplement 68

and a Bessel filter, the rise-time can be approximated (Eq. 2), where fc is the filtering level in kHz, and the rise-time (Tr ) is obtained in msec:

Tr =

0.3321 fc

Equation 2

For example, if the final filtering of the signal is 5 kHz, then an event must be at least 66 μsec in duration for the full amplitude to be observed. In practice, it is usual to err on the side of caution such that a value like 2 × Tr can be used to unambiguously assign a full amplitude to an event. Further details regarding the effects of filtering single channel data can be found in Chapter 19 of Sakmann and Neher, 1995. 2. Divide the data record into sections that consist of a single condition (e.g., one glutamate concentration at one voltage). Sections should be analyzed individually at this stage. 3. Measure the baseline noise of the recording. This is measured as peak-to-peak noise or as root mean squared (r.m.s.) noise. A consistent cut-off value across data sets should be decided upon beforehand. Recordings that exceed this value should be discarded. The cut-off value should be chosen to facilitate the identification of the single-channel events while minimizing the interference from noise. The cut-off value chosen for a data set will vary as a function of the amplitude of the single-channel currents being analyzed and the underlying noise of the recording system. 4. Eliminate regions of seal breakdown and artifacts from the data. Eventual breakdown of the high resistance seal is inevitable, with breakdowns sometimes occurring temporarily during recordings. A breakdown is usually evidenced by the appearance of dramatic, often saturating levels of current overlaid onto a shifting baseline. Electrical artifacts are most often apparent as very brief, high amplitude spikes within the recording. They can occur for any number of reasons, with the two most common being the results of intermittent suction from the perfusion apparatus and call activity on mobile phones. While these regions of noise can be digitally excised from recordings, consideration should be given as to how the events on either side of the excised region are treated (Fig. 11.17.2). 5. Attempt to remove alternating current (AC) noise, if present. An AC noise interference is visible as a low-amplitude noise with a frequency of either 60 Hz (in the Americas) or 50 Hz (most of the rest of the world). Ideally, visible AC noise is eliminated prior to recording by adequate grounding of the electrophysiological apparatus. However, if appreciable AC noise is recorded it can, in theory at least, be removed digitally with some software packages. The removal works best on short stretches with well-defined 50/60 Hz cycle noise. This is accomplished by selecting a region of the recording with well-defined AC noise but no channel openings. This region is used as a template for the software to define the AC noise for subtraction from the rest of the recording.


6. Ensure the amount of channel activity recorded is neither too high nor low. For example, if the recording conditions are such that the open probability is very low and there are very few channels in the patch, it may be difficult to obtain recordings that are long enough to contain sufficient openings for meaningful conclusions. Conversely, if many channels are present in the patch there can be too much channel activity, which is also problematic. Thus, if multiple channels remain open at the



A

*

2 pA 100 msec

B 2 pA *

20 msec

Figure 11.17.2 Excision of “bad” events. (A) Noise due to temporary patch breakdown, marked with an asterisk, has occurred during a long closed interval between two bursts of openings. The region indicated by the dotted line should be excised from the record as it is not known whether a true opening occurred within the noisy region, and thus the true duration of the shut times either side are unknown. In the idealized sequence of events, this would then place two bursts of openings adjacent to each other, and thus a flag must be inserted here to indicate an excision occurred. (B) A second channel opening has occurred while one channel was already open. The entire region marked with the dotted line should be excised as the durations of the individual openings are unknown. At the point marked by the asterisk it is not known whether this corresponds to closure of the first activated channel or the second activated channel. This excision would place two shut intervals adjacent to each other and so a flag should be inserted to indicate that they are separate shut times.

same time, the durations of the individual, overlapping, events will be unknown. These multiple, open-channel events should be excluded from the analysis and, as with the excision of brief artifacts, consideration given as to how to treat the events immediately adjacent to the excised region (Fig. 11.17.2). The entire record should be discarded if a large amount of data needs to be excised because of multiple concurrent openings. A cut-off, either in terms of the proportion of events or the proportion of time, should be applied to determine whether a recording is suitable for further analysis. Data with too many of these types of excisions should be discarded because the true burst length duration (or open time duration, if openings occur singly) will be underestimated because excised events are more likely to be “long” events. This leads to a final event distribution that contains a disproportionate number of brief events. 7. Examine patch stability. Unless stimulating conditions are varying, channel activity should remain stable over time. Stability is visualized with stability plots, in which a single-channel parameter is plotted against time or event number. Examples of parameters to be plotted include channel amplitude, dwell-time duration, and open probability. Changes that occur in activity over time may be intrinsic to the channel or due to artifacts in recording conditions. For example, a rearrangement of the patch architecture within the pipet may affect the number of channels being isolated in the gigaohm seal. This can have the appearance of altering the frequency of opening. Changes in intrinsic channel properties might include rundown of currents that can occur because of a loss of intracellular constituents (in the case of pulled patches), or slow changes in the desensitization of channels. More abrupt changes in activity may be the result of channel mode switching in which a channel adopts a different set of states under continuous conditions. This has been observed with several types of glutamate receptors (Popescu, 2012), and, in some cases, may be related to the presence of auxiliary subunits (Zhang et al., 2014).



Supplement 68

BASIC PROTOCOL 2

ANALYSIS OF GLUTAMATE RECEPTOR SINGLE-CHANNEL RECORDINGS The analysis of channel events of interest can commence after the first pass data analysis or “clean up.” The aim of the data analysis is to characterize the amplitudes and the durations of single-channel events.

Materials Single-channel data Computer Analysis software (See Table 11.17.1) 1. Determine a resolution for the analysis. During analysis, a decision must be made about when to ignore current fluctuations that are deemed to be the result of random electrical noise and when to consider them as genuine channel events. Conversely, the amplitude of brief channel events is attenuated by filtering. These, along with events that have a full current amplitude that is comparable to the baseline noise, will be interpreted as noise rather than channel events. These so-called ‘missed events’ can complicate the analysis and interpretation of single-channel data. To deal with missed events and occasional threshold-crossing noise, a method implemented in many programs is to pick a time duration as a resolution or dead time, below which potential events are ignored. The duration should be chosen taking into account the filtering characteristics of the recording and the mean duration of obviously ‘true’ full amplitude events. A second approach, implemented in the DCProgs idealization software, is to deliberately “over fit” potential events during idealization and then to calculate a theoretical false event rate which depends on the baseline noise and the filter cut off (Chapter 19, Sakmann and Neher, 1995). A resolution is then chosen that yields an acceptable false event rate, which is the frequency at which random noise is interpreted as a true event. A value of 1 × 10−4 would, for example, be expected to have a minimal effect on the overall idealization. Missed events distort the true dwell times. Thus, a missed brief shutting between two open times indicates that a single observed open time is twice as long (on average) as the true open dwell time. Conversely, a missed brief opening concatenates two shut times, distorting the final shut time distribution.


2. Construct an all points amplitude histogram. This procedure bins the picoamp current value of each of the sampled data points (Fig. 11.17.3B). The resulting histogram is then fitted with a multi-component Gaussian equation to obtain the amplitude distribution, yielding the mean and standard deviations of the event amplitudes. For a single channel with a single conductance level, two well-separated peaks are obtained, giving the amplitude of the closed and open events. The relative area of the nonzero current component(s) provides the open probability of the channel. In the vast majority of cases, the all points histogram should not be used for calculating the single-channel current, as longer events contribute disproportionately to the histograms as compared to the shorter events. However, these types of histograms are fast and easy to construct and give a measure of the frequency of multiple channel openings. The presence of more than two peaks indicates either the presence of channel sublevels, or multiple channel openings occurring simultaneously (or both). Such information can guide the decision as to whether further analysis is needed. If multiple, identical, channels that lack sublevels are present then the amplitude distribution will consist of multiple peaks of increasing amplitude but decreasing area. This is because it is less likely for many channels to be open simultaneously than for only a few. 3. Idealize the single-channel record. Idealization consists of assigning an amplitude and a duration to every sequential event in the single-channel record. While this may



A

2 pA 50 msec C

Idealization

Count

Non-idealization

Count

B

Current (pA)

Current (pA)

Figure 11.17.3 (A) Section of a 100-sec record of simulated single-channel data that had a mean single-channel current of −5 pA and an open probability of 0.373. (B) All-points amplitude histogram in which the amplitude of each sample point is binned. A double Gaussian fit (red line) gave mean parameters of 0.0 ± 0.10 pA and 5.0 ± 0.10 pA, and an open probability estimate of 0.366. (C) Histogram of idealized (example shown in inset) single-channel events. A double Gaussian fit (red line) gave the mean parameters of 0.0 ± 0.10 pA and 5.0 ± 0.05 pA.

seem a simple task as an opening clearly occurs when there is a rapid change in current amplitude, the effect of filtering and noise must be taken into account. Idealization is achieved by a variety of methods that differ as a function of the analysis software. A common approach is the 50% threshold method. From visual examination of the raw data (or from an all-points histogram), a rough estimate is made of the mean single-channel amplitude, with the threshold level set at 50% of this value. Thus, an open event is considered to have begun whenever the current amplitude passes this threshold from baseline. This method is unsuited to the idealization of data having multiple current levels, as occurs in the presence of sublevels. In this case is may be necessary to assign multiple “50% levels” for each event to a particular subconductance class. An alternative method that allows for the detection of more events is the direct fitting of current time courses, as implemented in the DCProgs suite of programs (Chapter 19, Sakmann and Neher, 1995). With this approach a least squares fit of a set of sampled points is performed, taking into account the distortion of truly square channel events that occurs as a result of the recording conditions. A third approach, which is utilized in the QUB program (Qin, 2004), is based on hidden Markov modeling. The recorded data is modeled as a Markov process with added Gaussian noise. While the Markov model employed need not represent the “true” channel model, it must contain a sufficient number of states to account for all genuine conductance levels (i.e., closed, open and subconductance open states). The parameters of this model are then obtained using an algorithm. From this algorithm the sequential idealized single-channel current is obtained using a likelihood function. 4. Construct a single-channel amplitude histogram. Single-channel amplitudes are investigated using amplitude histograms, from which single-channel conductance is



Supplement 68

calculated using Ohm’s law. This method bins the amplitudes of individual events, as opposed to individual sampled points (Fig. 11.17.3). These histograms are fitted with multicomponent Gaussians of the form (Eq. 3):

f (y) =

k

ai f i (y)

i

Equation 3

where ai is the relative area of each component and fi (y) a standard Gaussian function with a mean of ui and a standard deviation of σi (Eq. 4): f i (y) =

1 2 e−u i /2 1/2 σi (2π)

Equation 4

The component means of the distribution yield the mean current levels of the open channels, and of the closed channels (baseline). If there is any minor baseline drift, the true single-channel amplitudes can be obtained by shifting the data by the appropriate amount to ensure the mean baseline current is zero. It is frequently found that the histogram data have a sharper peak than the fitted Gaussian distributions. This occurs because the binned amplitude values are not actually a homogeneous population as a result of the differing event durations. It is easier to determine accurately the amplitudes of longer events, with their greater number of sample points, than shorter events, which may only contain a few sampling points. Once an amplitude histogram is constructed, the events are then classified into closed and open. If there is little overlap in the components, the cut-off amplitude separating different classes of events (e.g., closed and open) are often chosen as the midpoint between the means of the individual Gaussian components. However, if there is considerable overlap in the individual Gaussian components then, regardless of the selected cut-off value, there will be a misclassification of some low-amplitude open events as closed events, and some high-amplitude closed events as open events. In this case it is desirable to use a standardized mathematical procedure across data sets to define the open and closed state current amplitudes. One approach is to minimize the total number of misclassified events (Howe et al., 1991). This minimum is reached when:

−u2 −u2 a2 a1 1 2 e 2 − e 2 σ1 σ2 Equation 5

where a is the component area, σ is the component standard deviation, μ is the component mean, and the subscripts refer to the component numbers. Such a procedure can be repeated to classify events into many different subconductance classes. Single-Channel Analysis of Glutamate Receptors

5. Construct open and closed dwell-time histograms. The duration of single-channel open events, and the closed times separating them, are exponentially distributed. Inasmuch as virtually all channels can exist in multiple open and closed states, the dwell time distributions consist of multiple exponential components. Displayed



A

B

Count

Count

tcrit

Shut time (msec)

Shut time (msec) D

Count

Count

C

Open time (msec)

Burst length (msec)

Figure 11.17.4 Distributions of single-channel events. (A) Histogram and overlaid double exponential fit to the dwell times, shown on linear scale. The inset shows a scaled up section of the briefest events highlighting that there are two components. (B) Plotting the same data as in (A) using log-binning and the Sigworth-Sine transform highlights the existence of two components. The peaks of the distributions correspond to the two means of the exponential components. In this case the mean shut times were 0.05 msec and 6.68 msec. The tcrit value, calculated so that an equal number of short and long intervals are misclassified, is shown by the dotted line. (C) Opentime histogram overlaid with a single exponential plotted using log-binning and the Sigworth-Sine transform. (D) Burst-length histogram plotted using log-binning and the Sigworth-Sine transform using the tcrit value of 0.23 msec derived from the data in (B).

on Figure 11.17.4 are histograms of dwell times from a simulated channel with two distinct shut states having different mean lifetimes, and a single open state. It is useful to visualize the histograms and fitted distributions using log-binning (McManus et al., 1987) and the Sigworth-Sine transform (Sigworth and Sine, 1987). This simplifies the identification of overlapping components as the peak of each equals its mean value (Fig. 11.17.4B). Often the y axis is plotted as a square root scale as this normalizes errors across the logarithmic x axis (Sigworth and Sine, 1987). Although the dwell-times are visualized in the dwell-time histogram, the actual fitting of the data with exponential functions is best accomplished using the raw dwell-times rather than the binned values to ensure the fit parameters do not depend on the bin widths employed. The bin width value is usually selected solely for presentation purposes. The dwell times are fitted with a mixture of exponentials of the form:

f (t) = a1 τ1−1 e(−t/τ1 ) + a2 τ2−1 e(−t/τ2 ) + · · · an τn−1 e(−t/τn ) Equation 6



Supplement 68

where a is the component area, τ is the component time constant and t is the duration of each event. For most software developed for single-channel analysis, this is achieved using likelihood methods, in which the likelihood of the multi-exponential distribution generating the observed dwell times is maximized. The likelihood expression takes the form:

ln L (τ ) = ln f (t1 ) + ln f (t2 ) + · · · ln f (tn ) Equation 7

The number of components fitted to the data should be the minimum that satisfactorily describes the data. This is accomplished by beginning with a single component and overlaying the probability density function (pdf) of the resulting fit onto the histogram data. Additional components are then added one by one and the resulting pdfs examined visually to decide whether the fit has been noticeably improved. The likelihood ratio test is a more rigorous method for determining the number of components to be fitted. This type of test is employed to determine if the addition of another component significantly increases the quality of the fit (McManus and Magleby, 1988). An alternative approach is to start with a large number of different components and then, using an algorithm to gradually reduce their number to the minimum needed to describe the data (Landowne et al., 2013). In theory, the number of states that the channel can adopt should equal the number of exponential components of the dwell-time distribution. In practice, however, the number of components only provides a lower limit on the number of states. For this reason, limited information regarding kinetic models is obtained by examining only dwell time components. In addition, in all but the very simplest of cases (i.e., physiologically unrealistic) the time constants derived from the dwell-time histograms do not correspond to the mean lifetimes of the different states even though the two are related, although in non-intuitive ways (Shelley and Magleby, 2008). 6. Construct histograms of burst properties. Channel openings often occur in groups, with a series of openings interspersed with brief closings. This is referred to as a “burst” of openings. These bursts provide a great deal of valuable information regarding channel properties. Intuitively, a burst is a series of openings in which the intraburst shut times are much shorter than the interburst shut times. Mathematically they are defined in much the same way as the classification of intervals. Thus, they can be considered as being open, closed, or, as a sublevel, with a critical shut time value (tcrit ) chosen as a cutoff point, in which shut times that are briefer than tcrit are deemed to be within bursts, while those longer than tcrit occur between bursts (Fig. 11.17.4B). Because shut time components often overlap, there are unavoidable misclassifications of some events. There are three conventional ways to determine tcrit (Chapter 19, Sakmann and Neher, 1995). Each defines tcrit slightly differently depending on how the procedure deals with misclassified events. However, all of these approaches involve solving the relevant equation by numerical bisection methods. Equal numbers of brief and long shut times misclassified (see Eq. 8):

a1 e Single-Channel Analysis of Glutamate Receptors

−tcrit τ1

−tcrit τ2 = a2 1 − e Equation 8



Equal proportions of brief and long shut times misclassified (see Eq. 9):

e

−tcrit τ1

=1−e

−tcrit τ2

Equation 9

Minimizes the total number of misclassified intervals (see Eq. 10):

−t −t crit crit a2 a1 e τ1 = e τ2 τ1 τ2 Equation 10

Once a tcrit is calculated, bursts can be identified and their properties analyzed in much the same way as open and closed dwell times. Burst analysis is often more informative than open time analysis as burst duration is less sensitive than open times to the effects of the imposed resolution. Multi-exponential fits to burst length, mean open time per burst, and mean closed time per burst are obtained and overlaid onto histograms of the appropriate data. Although the number of openings per burst can also be plotted and fitted, this takes the form of discrete rather than continuous data, a mixture of geometric distributions rather than exponential distributions can be used. Because shut time distributions of ion channels usually have more than two shut time components, a judgment must be made as to which two components the tcrit value is to separate. One criterion is to choose a tcrit value such that it identifies bursts of activity that can be assumed to arise from the same physical channel. Alternatively, several different tcrit values can be selected, that define not only ‘bursts of activity’ but also longer “clusters of bursts.” 7. Identify different potential gating modes. Modal gating refers to a rapid change in channel behavior under constant conditions that persists for an extended period of time. The phenomenon has been observed with several different types of glutamate receptors, including AMPA (Poon et al., 2011) and NMDA sites (Popescu and Auerbach, 2003). It can manifest as an abrupt and sustained change in open probability or mean open times, between modes. A method for distinguishing modes is to measure the open probability of each burst of openings and to determine whether the values cluster into distinct populations. Alternatively, closed probability is used to simplify matters when multiple conductance levels are present (Poon et al., 2011). Single-channel analysis can then be performed on each mode separately, and the results compared across modes. 8. Examine correlations between channel events. Often the duration of adjacent dwell times is correlated. That is, the longer open dwell times occur adjacent to shorter closed dwell times, and shorter openings occur adjacent to longer openings. These correlations suggest that there must be multiple closed and multiple open states, and that there are multiple pathways within a kinetic model connecting these closed and open states (Colquhoun and Hawkes, 1987; Blatz and Magleby, 1989). Correlations are investigated by examining two-dimensional histograms that bin adjacent open and closed events. The histogram data are fitted with two-dimensional exponential functions in which an open dwell time and the subsequent closed dwell time are treated as a single “paired” event. Along with dependency plots (Magleby and Song, 1992), they aid in the determination of correlations between open and closed dwelltimes, and are used in the fitting of kinetic models to single-channel data. Correlations



Supplement 68

can also be examined by plotting the mean shut time within discrete ranges against the mean adjacent open time (Gibb and Colquhoun, 1992). The measurement of correlations is particularly sensitive to missed events as these events distort the true dwell time and concatenate several adjacent events. Shown in Figure 11.17.5 are some typical single-channel analyses of two different glutamate receptor complexes. ALTERNATE PROTOCOL

ANALYSIS OF GLUTAMATE RECEPTOR SINGLE-CHANNEL RECORDINGS USING NOISE ANALYSIS A noise analysis, either on single-channel data or macroscopic data, can be performed to extract single-channel parameters. This procedure is particularly amenable to single channel data that contains sublevels that cannot be clearly resolved. Even if full amplitude single-channel events cannot be resolved, macroscopic current noise analysis can be performed to extract single-channel parameters.

Materials Single-channel or macroscopic current data Computer Analysis software (See Table 11.17.1) 1. If using single-channel data, construct mean-variance histograms (Patlak, 1993). The mean and variance of the current amplitudes from a small window of consecutive sampling points are calculated. The process is repeated by shifting the window of sampling points along the entire data record, with the resultant values used to construct a scatter plot or binned in a three-dimensional histogram because of the large number of data points. Regions of low variance indicate the amplitudes of the closed, open, and sublevel states (if present). In addition, the volumes of the low-variance regions in the three-dimensional plots contain information that makes possible the extraction of the dwell-times of states. 2. When using macroscopic current data, perform a noise analysis to obtain singlechannel parameters (Sigworth, 1980; Traynelis and Jaramillo, 1998). This procedure is particularly appropriate when the single channel conductance is very low and cannot readily be discerned from single-channel records. Because a macroscopic current (I) is composed of the sum of currents flowing through individual channels it depends on the number of channels (N), their unitary single-channel current (i), and their open probability (Po): I = i × N × Po Equation 11

Under conditions in which most of the channels are closed, there is minimal macroscopic current variance. Likewise, there is minimal macroscopic current variance when most of the channels are open. However, the macroscopic variance in the current is maximal when half of the channels are open and half are closed. This relationship between channel activity and variance shown in Equation 12: Single-Channel Analysis of Glutamate Receptors

σ = iI − 2

I2 N

+ σb2

Equation 12



GluA1 + γ-5

GluA1 + γ-4

A B

9 pS (32 %) 21 pS (59 %) 21

13 pS (40 %) 24 pS (44 %)

100 75

14

49 pS (15 %)

50

47 pS (9 %)

7

25

0

0 0

1

2 3 4 5 6 Amplitude (-pA)

0

7

1

Frequency

36

57 msec (6 %)

64

25 16

36

9

16

4

4

1

0.1

Frequency

D

1 10 100 Open time (msec)

1000

1.1 msec 57 msec (41 %) 4.9 msec (24 %) (23 %) 250 msec 64 (13 %) 36

0.1

16 9 4 1

10 100 1000 10000 Shut time (msec)

0.1

36

1.8 msec (27 %)

25

89 msec (14 %)

16

100

1000

2.3 msec (20 %) 33 msec (9 %)

1

10 100 1000 10000 Shut time (msec)

0.9 msec (64 %)

19 msec (59 %)

E

10

1700 msec (71 %)

4 1

1

Open time (msec)

16

0.1

Frequency

7

1.0 msec (68 %) 4.5 msec (32 %)

12 msec 1.8 msec (64 %) (31 %)

C

2 3 4 5 6 Amplitude (-pA)

25

6.5 msec (36 %)

16 9

9 4

4

1

1 0.1

1

10 100 1000 Burst length (msec)

0.1

1 10 100 Burst length (msec)

1000

Figure 11.17.5 Representative data recorded from outside-out patches containing the homomeric GluA1 AMPA receptor in combination with the auxiliary subunits γ-4 or γ-5 to compare the effects of the different subunits on the single-channel properties of GluA1. Reproduced with permission (Shelley et al., 2012). The patches were held at −80 mV with 10 mM glutamate in the extracellular solution. (A) Single-channel records filtered at 1 kHz. Although the different auxiliary subunits produce openings of different durations, the openings are clearly discernible above the baseline noise and are therefore suitable for single-channel analysis. (B) Amplitude histograms of idealized openings. In both cases the amplitude histograms were fitted with a three-component Gaussian function. The mean conductances (calculated from Ohm’s law) and component proportions are shown. The conductance levels and their relative proportions are similar between γ-4 and γ-5. (C) Open-time histograms fitted with multi-component exponential functions. In the case of γ-4, three components were needed to adequately describe the histogram, whereas only two components were needed to adequately describe the open time histogram of γ-5. The means of the individual components and their proportions are indicated. (D) Shut-time histograms fitted with multiple exponential components. (E) Burst-length histograms fitted with multi-component exponential functions. The bursts were defined by calculating a tcrit value between the second and third (γ-4) and the first and second (γ-5) shut time components. This approach gave tcrit values of 7.1 msec for γ-4, and 8.0 msec for γ-5. The γ-4 distribution contains a long-lived burst length component (mean = 89 msec), that is absent from the γ-5 distribution.



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where σ2 is the signal variance and σ2 b is the background variance. By fitting a plot of macroscopic current against macroscopic variance, it is possible to determine the parameters giving the single-channel current and number of channels. The open probability at a given macroscopic current value is determined by: I peak i/N

Po =

Equation 13

If sublevels are present the value of i given in Eq. 13 is a weighted mean, comprised of the relative current and open probabilities of all of the single-channel current levels. In this case the macroscopic current is represented by: I =N

Pok i k

k

Equation 14

where k is the number of different open states (Sigworth, 1980). The variance is shown in Equation 15: ⎡ σ2 = N ⎣

Pok i k2 −

k

2 ⎤ Pok i k ⎦

k

Equation 15

BASIC PROTOCOL 3

ANALYSIS OF GLUTAMATE RECEPTOR SUBLEVELS At the single-channel level many glutamate receptors exhibit multiple currents. For brevity, these are referred to as sublevels with the understanding that this term includes the highest unitary current level. These can complicate analysis, as they are necessarily of lower amplitude than the largest conducting open state, and they indicate that a single receptor can adopt many different conducting states. The presence of subconductance states further complicates the interpretation of data from patches containing more than one channel, as it can be difficult to discern whether a conductance level is truly from a single channel or is the sum of several subconductance states from several channels. However, sublevels provide insights into channel mechanisms as they increase the number of directly observable states. In characterizing sublevels the aim should be to determine the current amplitudes, frequencies, and durations of each of them.

Materials Single-channel data Computer Analysis software (See Table 11.17.1)


1. Construct an amplitude histogram (see Basic Protocol 2, step 4). Ideally, multiple, well-separated peaks will be obtained from multiple Gaussian fits to the binned current amplitude values. This histogram will show the number of sublevels present and their mean current amplitudes. It may be necessary to use define multiple Acrit parameters to characterize each sublevel. For AMPARs, it has been found that an increase in the



agonist concentration correlates positively with the prevalence of higher conductance states (Smith and Howe, 2000b; Gebhardt and Cull-Candy, 2006), leading to the hypothesis that the gating of individual subunits are responsible for the different current sublevels (Rosenmund et al., 1998). 2. Determine the frequency of transitions between the levels and the open probability of individual sublevels. A scatter plot of event n amplitude against event n + 1 amplitude highlights the frequency of transitions between particular conductance levels. Alternatively, as there are often a large number of data points on such scatter plots, the data can be binned and plotted as a three-dimensional histogram. In this case the volume of the peaks describes the transition frequency. The frequencies of conductance state transitions are of particular interest with NMDARs containing the 2D subunit as they show an unusual temporal asymmetry in which transitions from the high- to the low-conductance level occur more frequently than those from low to high (Wyllie et al., 1996). 3. Construct dwell time histograms for events with specified amplitudes. This procedure involves constructing open dwell time histograms as outlined previously, except that the events included in each histogram are limited to those within a particular amplitude range. Once these are constructed, it is possible to calculate the proportion of time the channel spends in each of the subconductance states. From these data it is possible to determine whether the subunits gate independently of one another. That is, for independent subunit gating the sublevel open probability should match the open probability predicted for a binomial process. This is generally the case for AMPARs (Jin et al., 2003; Prieto and Wollmuth, 2010; Shelley et al., 2012). If subunit gating is independent, then the subunit coupling efficiency can be calculated. Coupling efficiency is defined as the probability that each agonist-bound subunit can open the channel to a subconductance state.

FITTING SINGLE-CHANNEL DATA TO KINETIC MODELS It is useful to develop a kinetic model that defines channel activity in which the states the channel adopts, the lifetimes of these states, and the frequencies of transitions between them may be determined. Such models allow channel activity to be simulated in response to any voltage or agonist waveform. In addition, even “incomplete” models, which is currently the status of virtually all ion channel models, that do not manage to describe every aspect of ion channel function can assist in visualizing the mechanics of channel operation. The simplest potential kinetic model for an ion channel consists of a single closed and a single open state that are connected to each other (Fig. 11.17.6).

BASIC PROTOCOL 4

The parameters defining this model are the conductance of each of the states (zero in the case of the closed state), the rate of channel opening (β), the rate of channel closing (α), and the relative occupancies of the closed state (pC ) and of the open state (pO ). The transitions between the closed and open states are reversible and are assumed to be in equilibrium. Thus, according to the Law of Mass Action, the rate of a reaction is proportional to the concentration of the reactants (Equation 16):

pc β = po α Equation 16 Electrophysiological Techniques


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Model I

C

II

R

III

β α

O

k+a

2k+a k-a

AR

Bk-a

AR

AR k+a a k IV

R

V

AR

AR k+a a Bk R

k+b Bk -b

2k-a

A2R

k+b k-b AR

k+b k-b

A2R

Ak+a

2k+a R

2k-a

k+a k-a

Ak +b k-b +a

AR

Ak k-a

AR

Figure 11.17.6 Simple kinetic models. Agonist binding sites are indicated with lower case letters, A indicates a single agonist. Model I shows the simplest possible mode, in which β is the (frequency) of channel opening, and α is the rate of channel closing. Models II is a linear model in which the binding sites are identical as the order of agonist binding cannot be specified. The first binding step rate constant is multiplied by two as agonist could bind to one of the two binding sites in the first step. Model III is a linear model with identical binding sites that have a cooperative interaction. Thus the binding of agonist to the first site alters the association rate at the second site by a factor of A. Model IV allows for two different binding sites, a and b. Model V is as Model IV but with cooperativity added between the binding sites.

The term proportion (p) or occupancy is used instead of reactant concentration as the receptors are unable to freely diffuse in three dimensions. As the receptor must be in some state (Equation 17):

pc + po = 1 Equation 17

By rearrangement and substitution it follows that the occupancy of the open state can be expressed in terms of the transition rate constants (Equation 18):


1 po = α β +1 Equation 18



Using probability theory (Chapter 18, Sakmann and Neher, 1995), it can also be shown that the mean duration of sojourns to specific states is equal to the inverse of the sum of the rates exiting that state (Equation 19): mean open duration =

1 α

Equation 19

From this, is it clear that a two-state model is inadequate for describing any glutamate receptor, or indeed virtually any ion channel. Nonetheless, the principles of analysis remain the same, in which the rates of transitions between discrete states are sought. As the number of states increases the equations describing the occupancy and dwell-time durations become increasingly unwieldy because of the large number of parameters. Due to this complexity, the use of transition rate matrices was adopted for estimating transition rate constants. This allows general equations to be derived for various channel properties that are applicable for any model (Chapter 18, Sakmann and Neher, 1995). Missed events must be taken into account when fitting single-channel data to kinetic models, as they can influence the results. Several methods of incorporating a missed event correction have been developed, (Magleby and Weiss, 1990; Colquhoun et al., 1996; Qin et al., 1996).

Materials Single-channel or macroscopic current data Computer Analysis software (see Table 11.17.1) 1. Select a kinetic model that will quantitatively describe the molecular events that occur during channel activity. Multiple kinetic models have been examined in an attempt to describe glutamate receptor function. While it is impossible to mention all of these, the data derived from such studies has generated general principles that should be considered when selecting the most appropriate model. Kinetic modeling should not be performed in isolation, but rather in combination with a priori knowledge of channel structure and function. This makes it possible to relate states and transitions between states to actual physical processes. Any complete kinetic model of glutamate receptor activity will include multiple agonist-binding steps, multiple open states, multiple desensitized states, while at the same time reflecting the tetrameric nature of receptor complexes. Progress in achieving this goal has been hampered by the multiple conductance levels of many receptor subtypes, the low conductance states of AMPARs and kainate receptors, the multiple kinetic modes for some glutamate receptors (Popescu, 2012), and the large number of states a tetrameric complex can potentially adopt. With all ion channels agonist binding and pore opening are separate events. For this reason, a complete model should include agonist-bound open and agonist-bound closed and open states. As all glutamate receptors are tetramers with a single agonist (or co-agonist) binding site per subunit, any complete model should account for the four glutamate sites in the case of AMPARs and kainate receptors, and the two glutamate and two glycine sites in the case of NMDARs. In addition, all of the glutamate receptors undergo desensitization. This is characterized by a decay in the macroscopic agonist-evoked current in the continued presence of agonist or a reduction in open probability when examined at the single-channel level. Therefore, various agonist-bound closed states representing desensitized receptors should be incorporated in the model. If agonist binding is to be included in the kinetic model, then thought must be given to the nature of the binding sites and potential interactions between them. It is possible that in heterodimeric NMDARs, and in the heterodimeric forms of AMPA and kainate receptors,



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the binding sites of the two different subunits differ in their agonist-binding properties. It may also be assumed that the binding sites of the two identical subunits in NMDAR, and of the four subunits in homomeric forms of AMPAR and kainate receptors, are identical. However, this may not be the case, as the crystal structure of unliganded homomeric GluA2 shows identical subunits in two different conformations (Sobolevsky et al., 2009). It is also possible that agonist binding is cooperative, with the binding of agonist at one site influences agonist binding at other sites. Displayed on Figure 11.17.6 are ways to incorporate these different possibilities into a kinetic model. For the sake of simplicity, only two binding sites are shown, although the principles hold for any number of binding sites. In the linear models (II and III) all binding sites are necessarily identical, whereas the branched models (IV and V) allow for different initial binding sites. Cooperativity is introduced by adding a cooperativity factors (A and B) to the binding and dissociation of the second agonist. A value greater than 1 indicates positive cooperativity, while a value less than 1 suggests negative cooperativity. If a model contains loops, such as models IV and V (Fig. 11.17.6), it is imperative to ensure that microscopic reversibility or detailed balance is obeyed. This relates to the fact that as the system is assumed to be at equilibrium, the number of transitions in each direction around the loop should be equal in the absence of an external energy source. This can be tested as the product of the rate constants should be identical no matter the direction the loop is followed. It is challenging, however, to impose this test on complex reaction mechanisms with multiple loops and many rate constants (Colquhoun et al., 2004). Finally, the number, and connections between them, of observable open-channel current levels should be taken into consideration. Thus, a model for an AMPAR that accounts for subconductance states may have three or four different open states, each with different conductances.

2. Fit the single-channel data to the actual model. Once a model and the connections between states are established it must be fitted to the experimental data. The two main software programs employed for this analysis are HJCFIT (Colquhoun et al., 2003) and QUB (Qin et al., 1996, 1997). To begin, a set of starting guesses for the transition rate constants are supplied, after which the likelihood of the observations occurring given the model and rate constant values is calculated. The rate constants are then altered iteratively until the likelihood of the observations being produced by the model and rates is maximized. The form of the observations can be either a sequence of open and closed events or, in some cases, the two-dimensional dwell time histogram. In both cases the correlations between dwell-times are taken into consideration for the analysis. To increase the effectiveness of the fitting algorithm, several data sets can be analyzed simultaneously within the same likelihood calculation. This is especially useful as long as the agonist concentration for each data set is specified. That is, the distribution of steady state occupancies will differ for each agonist, and therefore a greater range of state transitions will be sampled by the channel than if a single agonist concentration were used.

3. Evaluate the quality of the fitting results. Once a model and a set of rate constants are derived it is imperative to determine whether they accurately describe the data. They should because they were calculated using maximum likelihood techniques. However, often they do not achieve this goal. There is no biological reason why several different set of rate constants could not describe the data equally well. Indeed, this has been found to be the case under certain circumstances (Colquhoun et al., 2003). Single-Channel Analysis of Glutamate Receptors

The easiest comparison, but by no mean the only one that should be performed, is to use the derived model to simulate single-channel data, and to determine whether it differs grossly from what was recorded. Matrix notation can also be used to simulate macroscopic data from the model parameters (Chapter 18, Sakmann and Neher, 1995). This makes it



possible to compare simulated macroscopic data in response to various agonist application protocols to recorded macroscopic data. The calculated probability density function for different types of dwell times from the model can also be compared to the recorded data histograms. For example, the predicted distributions for open times, closed times, burst durations (given the appropriate tcrit value), and first latency to opening can all be overlaid onto the relevant data histograms for comparisons. The ability of the model to predict correlations can also be examined by overlaying predicted open-shut dwell time correlations onto the appropriate data and comparing them to the predicted two-dimensional probability distribution and to the recorded two-dimensional histogram. A more robust measure of the suitability of the model and calculated rates is to consider the likelihood values that are obtained. For datasets with the same number of events that are fitted to models with the same number of free parameters (transition rates), the better model is indicated by a higher log-likelihood. However, adding further free parameters to a model, or performing the analysis on larger datasets, typically increases the loglikelihood, regardless of the quality of the model. A log-likelihood ratio (LLR) test is used to compare models with different numbers of free parameters. This discriminates between models based on the logarithm of the ratio of the maximum log-likelihoods of the two models (Equation (20)):

L L Rk = L L k − L L k−n Equation 20

where k is the number of free parameters, and n is the difference in the number of free parameters between the models. Twice the value of the log-likelihood ratio is distributed as X2 (Horn and Lange, 1983), where the number of free parameters represents the number of degrees of freedom to be applied. Other methods of ranking models include the use of the Akaike criteria and the Schwarz criteria. These methods, along with the log-likelihood ratio test, have been evaluated carefully for their ability to determine correct models (Csanády, 2006).

COMMENTARY Background Information The development of assays to directly visualize and measure ion flux through individual channel molecules was a major breakthrough in the history of ion channel physiology. From these first recordings, which were reported in the 1970s, it was apparent that the channel openings occurred as discrete events, with similar amplitudes over a large range of durations. The distribution of amplitudes approximates the familiar Gaussian distribution, whereas the distribution for event durations is distributed exponentially. Due to the exponential nature of event durations, a large number of individual event durations must be measured to obtain meaningful conclusions. At a minimum, hundreds of events should be analyzed, although the most robust parameter estimates are obtained if thousands of events are analyzed. The exponential nature of the event durations also means that, given sufficient resolution, there are always many more brief than long events,

something that is not always obvious by inspection when the dwell time distributions are displayed with the Sigworth-Sine transform (compare Fig. 11.17.4A to Fig. 11.17.4B of the same data). The use of single-channel recording and analysis allows not only the characterization of single-channel properties, such as conductance, dwell times, and sublevel frequency, but also, with the use of a suitable kinetic model, the quantification of both the binding (defining affinity) and gating parameters (defining efficacy) (Colquhoun, 1998). Deriving these microscopic parameters from macroscopic data, such as data obtained from radioligand binding studies or macroscopic concentrationresponse curves, is more challenging because of the difficulties associated with identifying unique parameter estimates that yield excellent fits to the data (Hines et al., 2014). In addition to quantitatively describing receptor-channel function, the use of kinetic models enables the



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Table 11.17.2 Estimation of Mean Open Time Varies with the Number of Events Measureda

Number of open times measured

Calculated mean open time (msec)

Deviation from true mean (%)

10

0.888

26.0

100

1.115

7.1

1000

1.163

3.1

10000

1.209

0.8

a Ten

to ten thousand random numbers were drawn from a single-component exponential distribution with a mean of 1.2 msec.

Table 11.17.3 Estimation of Mean Current Amplitude Varies with the Number of Events Measureda

Number of current amplitudes measured

Calculated mean current (pA)

Deviation from true mean (%)

10

5.035

0.70

100

4.975

0.50

1000

4.988

0.24

10000

4.999

0.02

a Ten to ten thousand random numbers were drawn from a single-component normal distribution with a mean of 5 pA and

a standard deviation of 0.2 pA.

prediction of synaptic currents, and provides a physical basis for the many molecular rearrangements that occur during receptor activity.

Critical Parameters


The higher the quality of the data acquired, the easier and faster the single-channel analysis becomes and the more robust the parameter estimates. High-quality data are described as data that have: a sufficient signal-to-noise ratio to clearly discern all open-channel current levels’ minimal regions of seal breakdown and electrical artifacts; sufficient resolution to capture all or a high proportion of the briefest events; and that contains many thousands of transitions between the closed and open channels. The number of events measured is particularly important due to the exponential nature of the dwell-time distributions. In other words, a large number of dwell times are needed to obtain accurate estimates of the mean dwell times. Shown on Tables 11.17.2 and 11.17.3 are examples of the errors that may arise when the number of channel events measured is insufficient. As illustrated, many more events must be measured to obtain accurate estimations of the exponentially distributed parameters than is the case for normally distributed parameters. It is important to keep in mind that the errors when the open time distribution is multiexponential, a more realistic situation, are much greater and will vary depending on

the separation of the time constants and the relative areas of the components.

Troubleshooting Considerations for patches containing more than one channel While single channels are the target sites for these assays, usually the patch contains more than one channel. It could be argued that a more accurate description of the assay is “analysis of channels that are activated singly.” Despite the presence of multiple channels in a patch the data can be analyzed by considering open and burst events that are thought to have arisen from the same physical channel, and by assuming that all activations in a data set come from identical channels. Thus, for the data shown on Figure 11.17.4A, it is apparent that only a single, although not necessarily the same, channel is open during each burst of activity. A consequence of different bursts of openings potentially arising from distinct, although identical, channels is that the “true” interburst shut time is unknown. If the number of channels in the patch is known, then the true mean interburst shut time is the measured interburst mean shut time multiplied by the number of channels. There are several methods employed to estimate the number of channels within each patch. The most straightforward is use of a



maximal stimulus to activate all channels, with the peak current observed divided by the unitary current of a single channel. Because glutamate receptors undergo desensitization in the presence of agonists a fraction of the receptors will be in desensitized states. For this reason, the peak current will be less than the product of the number of channels and the unitary channel current. An approach more suited to glutamate receptors is to calculate the probability of different numbers of channels being present in the patch (Horn, 1991). The number of simultaneously open channels should follow a binomial distribution if the channels are identical and independent (see Eq. 21): N! Pok (1− Po) N−k p (k|N , Po) = k! (N −k)!

Equation 21

where k is the number of simultaneously open channels, N is the number of channels in the patch, and Po is the open probability of an individual channel. Alternatively, a number of repeated trials or sweeps can be performed and an estimate of N calculated directly (Horn, 1991). The sample mean and sample variance are calculated from a number (m) of repeated trials (or sweeps) (Eqs. 22 and 23): x¯ =

ki i m

Equation 22

σ2 =

(ki − x) ¯ 2 i m

Equation 23

For a binomially distributed process, the mean (μ) and the variance (s2 ) are given as (Eqs. 24 and 25): μ = N Po Equation 24

s 2 = N Po (1 − Po) Equation 25

which can be rearranged to: N=

μ2 μ − s2

Equation 26

using the sample mean and variance as estimates of the population mean and variance respectively, making it possible to estimate N. Tips for fitting kinetic mechanisms It is often difficult to obtain well-defined rate constants for every transition in the model being examined. One solution to this problem is to manipulate the experimental system such that only a subset of the states in the complete model is visited. For example, agonist is applied at a saturating concentration to minimize the amount of time that the receptor spends in the unstimulated states. Site-directed mutagenesis can also be used to limit the states the channel can adopt, to dramatically alter receptor activity to highlight gating facets, or to modulate the rates within a model by abolishing modulatory mechanisms, such as phosphorylation, that affect gating. Pharmacological agents can also be used to limit the number of accessible states. For example, cyclothiazide is used to block the desensitization of AMPA receptors. Alternatively, the number of transition rates to be determined can be reduced. This can be accomplished by, for example, assuming that the four binding sites are identical and independent, thereby reducing the number of agonist association and dissociation rates to two from eight, for four different, independent binding sites. The validity of this assumption should be investigated by examining the mechanism predicted to the actual dwell time distributions. Conversely, cooperativity between the binding sites will increase the number of rates even further. Specific rates can be fixed at predetermined values to reduce the number of free parameters. This could be done if it is found that the rate to be fixed cannot be determined or if there is information from other experiments to suggest a particular value. A range of fixed values in different fits should be examined to ensure that the value of the fixed rate does not affect the estimation of the other rate constants. Rather than reducing the number of free parameters, constraints can be applied to the model. This could involve constraining a specific rate to a range of physiologically relevant values, or constraining the whole set of rates to a range of macroscopic parameters, such as the EC50 value or the time constant of current decay following agonist application. The values obtained for the rate constants should be examined to identify potential problems in the fitting process. Some common issues include: (1) Rate is the same value as the initial guess given.



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(2) Rate is implausibly high for a physiological process, e.g., over 1 × 1010 sec−1 . (3) Rate is implausible low (or negative) for the time scale of the experiment, e.g., less than 1 × 100 sec−1 . Very low rates may indicate that this particular transition does not occur. In this case the model should be redesigned with this transition, the reverse transition removed and the fitting repeated. (4) Concentration-dependence of rates. If multiple data sets under different concentrations are analyzed, the rates should show no dependence on concentration, as agonist concentration is taken into account in this type of fitting. (5) Two or more rates are correlated with each other. (6) There is a large standard error or coefficient of variation across data sets.

Anticipated Results It is anticipated that a complete singlechannel characterization of a particular glutamate receptor channel will include descriptive data regarding the number, proportion, and amplitude of single-channel openings and sublevels, and distributions of channel dwell times in the open and closed states, and channel burst properties, such as burst length and the number of openings per burst. Kinetic modeling should attempt to produce a model that contains defined states with molecular correlates, and well as defined transition rates identifying the frequency of transitions between the states.

Time Considerations


For single-channel studies, the data analysis is usually more time consuming than the actual experiments. The amount of time needed for analysis varies greatly depending on the degree of automation employed. For example, semi-automated idealization using the direct fitting of current time courses can take from several hours to several days, depending on the duration of recordings obtained. In contrast, a completely automated idealization process may require only a minute or so. Firstpass analysis can take a few minutes to several hours, depending on the quality and quantity of data. Following idealization, histogram construction and fitting can be completed within a few minutes for each dataset. The time needed to fit single-channel data to kinetic models varies widely, depending on factors such as the number of single-channel events, the complexity of the model, the number of free parameters in the model, and the computer hardware. Completion of fits can take from a minute to

many days. Once initiated, the fitting process is an automated algorithm and therefore can be left to run without further user input.

Acknowledgements The author would like to thank Ian Coombs, Stuart Cull-Candy, and Mark Farrant for their helpful comments during the writing of this manuscript. The author was supported by Wellcome Trust (086185/Z/08/Z) and MRC Programme grants (MR/J002976/1) to Stuart Cull-Candy and Mark Farrant during part of this work.

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Supplement 68

Molecular neurobiology of glutamate receptors.

Glutamate receptors in the kidney.

Single-channel recording of glutamate receptors.

Regulation of glutamate receptors by cations.

Molecular diversity of the glutamate receptors.

Dynamics and modulation of metabotropic glutamate receptors.

Molecular biology of the glutamate receptors.

A family of AMPA-selective glutamate receptors.

A family of metabotropic glutamate receptors.

Glutamate and its receptors in cancer.

Multiple metabotropic glutamate receptors regulate hippocampal function.

Metabotropic glutamate receptors in the rat hippocampus.

Pharmacology and Structural Analysis of Ligand Binding to the Orthosteric Site of Glutamate-Like GluD2 Receptors.

Receptor changes and LTP: an analysis using aniracetam, a drug that reversibly modifies glutamate (AMPA) receptors.

Activation of glutamate receptors and glutamate uptake in identified macroglial cells in rat cerebellar cultures.

Different pools of glutamate receptors mediate sensitivity to ambient glutamate in the cochlear nucleus.

Development of PET and SPECT probes for glutamate receptors.

Vertebrate galectins: endogenous regulators of ionotropic glutamate receptors?

Structure and symmetry inform gating principles of ionotropic glutamate receptors.

Mechanism of partial agonism in AMPA-type glutamate receptors.

The role of glutamate and its receptors in multiple sclerosis.

Glutamate excitatory effects on ampullar receptors of the frog.

Photoinactivation of glutamate receptors by genetically encoded unnatural amino acids.

Molecular diversity of glutamate receptors and implications for brain function.