Estimating the Ca²⁺ Block of NMDA Receptors with Single-Channel Electrophysiology

Abstract

In vertebrate central neurons, NMDA receptors are glutamate- and glycine-gated ion channels that allow the passage of Na⁺ and Ca²⁺ ions into the cell when these neurotransmitters are simultaneously present. The passage of Ca²⁺ is critical for initiating the cellular processes underlying various forms of synaptic plasticity. These Ca²⁺ ions can autoregulate the NMDA receptor signal through multiple distinct mechanisms to reduce the total flux of cations. One such mechanism is the ability of Ca²⁺ ions to exclude the passage of Na⁺ ions resulting in a reduced unitary current conductance. In contrast to the well characterized Mg²⁺-block, this “channel block” mechanism is voltage-independent. In this chapter, we discuss theoretical and experimental considerations for the study of channel block by Ca²⁺, using single-channel patch-clamp electrophysiology. We focus on two classic methodologies to quantify the dependence of unitary channel conductance on external concentrations of Ca²⁺, as the basis for quantifying Ca²⁺ block.

1. Introduction

Ion channels are membrane-embedded enzymes that catalyze the opening of an ion-permeable pore in the membrane. Once the pore opens, ions flow freely down their respective electrochemical gradients and generate a current that can be measured with patch clamp techniques. Which ions can pass through the pore and how fast they flow depend on intrinsic structural properties of each ion channel protein and on environmental conditions such as ionic concentrations, and membrane potential. The predilection of a channel protein to permit the flow of one ion over another determines which ion carries what fraction of the measured current. This property, termed “permeability,” is an important biophysical property of each channel protein and is discussed in another chapter of this volume (see Weaver and Popescu). By contrast, the biophysical property termed “unitary conductance” measures the ease with which ions traverse the pore. Often, the passage of one type of ion is hindered by the presence of another type, such that the conductance of the first type is reduced. It is said that the second ion “blocks” the channel. Given that physiological fluids represent always mixtures of ions, it is important to understand how ions interact with each other to produce the observed electrical signal.

Channel block is defined as the reduction in unitary conductance by physical impedance of ion diffusion through a given open pore. This simple idea serves as the mechanistic basis of innumerable therapeutic drugs and physiological regulatory processes for a multitude of ion channels. The molecular basis of this phenomenon, however, is far from simple and decades of research have revealed a diversity of mechanisms. The classic pharmacological model of channel block is the binding of a molecule to a site within the membrane-embedded pore which prevents ion flow. This type of interaction imparts sensitivity to fluctuations in membrane voltage which disrupt electrostatic interactions between the channel and the blocking molecule. Another mechanism is the binding of the molecule to a distant allosteric site which results in the pore to block itself in an unspecified manner (Hille 2001).

NMDA receptors have been a long sought-after pharmaceutical target given their essential role in neurophysiology, and channel block is an essential property that governs the physiological function of NMDA receptors. In response to binding glutamate and glycine, NMDA receptors open a cation-permeable pore that can generate prolonged excitatory currents. However, at resting hyperpolarized membrane potentials, no current is observed due to strong competition of permeant ions with Mg²⁺, which is impermeant (Burnashev et al. 1992; Sharma and Stevens 1996b). Only when the membrane depolarizes, the interaction between Mg²⁺ and the pore weakens, allowing Na⁺ and Ca²⁺ to flow into the cell. This voltage-dependent Mg²⁺ block ensures that substantial NMDA receptor fluxes occur only when neurotransmitters (Glu and Gly) occur simultaneously with membrane depolarization occur simultaneously, rendering NMDA receptors bona fide coincidence detectors (Nowak et al. 1984; Mayer et al. 1984). Much less understood is the NMDA receptor current block by Ca²⁺, which is a permeant ion.

The high permeability of NMDA receptor channels for calcium ions has been determined by direct measurements of calcium entry using calcium-sensitive dyes (MacDermott et al. 1986; Schneggenburger et al. 1993) and by the reversal potential method (Jahr and Stevens 1987; Mayer and Westbrook 1987; Ascher and Nowak 1988). Curiously, however, despite the substantially higher permeability of divalent Ca²⁺ compared with monovalent Na⁺, the amplitude of the unitary current in the presence of Ca²⁺ is significantly smaller compared to Na⁺-only currents (Ascher and Nowak 1988; Jahr and Stevens 1993; Maki and Popescu 2014). Thus, like Mg²⁺, Ca²⁺ ions reduce the conductance of the channel. Unlike Mg²⁺, the magnitude of the current reduction is independent of membrane voltage indicating that the binding site responsible for Ca²⁺ block resides outside the membrane field (Jahr and Stevens 1993; Mayer et al. 1989; Premkumar and Auerbach 1996). The location of the site by which Ca²⁺ ions exert this blocking effect remains poorly delineated. Initial competition experiments suggested that Ca²⁺ and Mg²⁺ share the same binding site (Mayer and Westbrook 1987). However, this does not explain the voltage insensitivity of the Ca block. Later work has revealed the presence of a highly negatively charged surface within the extracellular vestibule (Watanabe et al. 2002; Karakas and Furukawa 2014), suggesting a role for this electrostatic potential in increasing the local concentration of Ca²⁺, and possibly hindering Na⁺ from entering the pore. Clearly, the mechanism of Ca²⁺ block remains unresolved and its investigation requires precise methodology to study this process quantitatively. In this chapter we will discuss a single-molecule approach to probe Ca²⁺-block of NMDA receptor currents.

Consistent with the conceptual definition of channel block, the magnitude of the Ca²⁺-dependent reduction in conductance (i.e. block) can be quantified as (Sharma and Stevens 1996a; Maki and Popescu 2014):

$$Block=1-{\gamma }_{Ca}/{\gamma }_{Na}$$ (1)

where γ_Ca is the unitary conductance in the presence of external Ca²⁺ (and Na⁺), and γ_Na is the unitary conductance in the absence of external Ca²⁺ (i.e. Na⁺-only currents). Thus, precise quantification of block due to Ca²⁺ (or other molecule) is predicated upon the accurate measurement of channel conductance. In this chapter, we will discuss two classic methods for measuring channel conductance using single-channel currents: (1) voltage-ramps and (2) voltage-steps. We will discuss the advantages and limitations of each method and highlight several key technical considerations when designing experiments to limit common sources of error.

2. Equipment and Materials

2.1. Cell Culture and NMDA Receptor Expression

High-quality current recordings from one NMDA receptor can be acquired from several preparations including, but not limited to, recombinant expression systems (HEK293 cells, Xenopus oocytes, and others), in vitro cultured primary neurons, brain or spinal cord slices, and under minimal noise conditions, in vivo awake organisms. Each preparation has advantages and limitations and, thus, it is at the discretion of the experimenter to select the best approach for the specific question being addressed. For the purposes of this chapter, we describe the procedure we use with HEK293 cells given their lack of endogenous ionotropic glutamate receptors allowing recombinant expression of channels of interest using well-established protocols (Maki et al. 2014). All traces illustrated in this chapter represent currents recorded from recombinant expressed GluN1-2a/GluN2A receptors.

2.2. Electrophysiology Equipment

For collecting microscopic NMDA receptor responses, standard patch-clamp electrophysiology equipment is required. The setup and use of electrophysiology equipment has been covered extensively previously (Maki et al. 2014; Sakmann and Neher 1995).

2.3. Solutions

2.3.1. Extracellular Solution

All reagents must be ultra-pure (e.g. HPLC-grade) to minimize the effects of contaminating divalent and heavy metals on channel function.

1. “Ca²⁺-free” Pipette Solution, in mM: 150 NaCl, 2.5 KCl, 0.1 EDTA*, 10 HEPBS, 0.1 glycine, 1 glutamate, pH** set to 8 using HCl or NaOH

   *the choice of divalent buffer should be chosen to control concentrations effectively within the range of desired free Ca²⁺ concentrations (see Note 4.3, Figure 5b).

   **be mindful that all metal chelation/buffer agents are sensitive to solution pH to some degree. Ensure that your choice of pH does not significantly alter the buffer capacity of your chelation agent (Figure 5b).

2. Ca²⁺-containing Pipette solution(s)¸ in mM: to the “Ca²⁺-free” solution prepared as above, calculate the “total” CaCl₂ concentration that needs to be added* to achieve a desired free Ca²⁺ concentration. We recommend using the free online MaxChelator tool (somapp.ucdmc.ucdavis.edu/pharmacology/bers/maxchelator/index) which allows users to calculate free and total metal and chelator concentrations for a variety of common metals and chelation agents over a range of user-defined conditions (e.g. pH, temperature, and osmolarity). See Note 4.1.

   *be mindful that added CaCl₂ solution volume will impact your final volume, and therefore free concentration. This should be factored into your calculations.

Figure 5: Potential sources of experimental and statistical errors.

(a) Example of classic “J-shape” <i>/V relationship indicates the presence of contaminating voltage-dependent blockers (usually divalent metal ions, M²⁺), which can be eliminates with a metal-chelating buffer. (b) Top, fraction of free buffer available to capture contaminating metals in each total added Ca²⁺. Below, predicted free concentrations of contaminating metals, given predicted free concentrations of each indicated buffer at various total added Ca²⁺. (c) Leak-subtracted average unitary current in 2 mM Ca²⁺ (grey) overlaid with fits of the linear model (yellow) and the Jahr model (red) to account for nonlinearity of <i>/V relationship.

2.3.2. Bath Solution

1. Dulbecco’s Phosphate Buffered Saline (DPBS), in mM: 0.9 CaCl₂, 0.5 MgCl₂, 2.7 KCl, 1.5 KH₂PO₄, 137.9 NaCl, 8.1 Na₂HPO₄ (Gibco, Life Technologies, 21600-010)

2.4. Software

Several programs are available for the acquisition and analysis of single-channel data. The leading programs for single-channel analyses are HJCFIT, developed at the University College London by Dr. David Colquhoun and collaborators (Colquhoun et al. 2003; Hawkes et al. 1992); and QuB, developed at the University at Buffalo by Dr. Frederick Sachs and collaborators (Qin 2014; Qin et al. 2000a, b). In this chapter, we describe the steps for using QuB in the analysis of single-channel current amplitude using the program’s built-in segmental-k-means (SKM) algorithm (Qin 2004). This will be used to analyze data obtained from the voltage-step protocol. This software is freely available and can be obtained by contacting the authors.

For analysis of single-channel voltage-ramp data, we describe acquisition and data pre-processing in ClampFit (Molecular Devices), which can then be exported to another statistical analysis software of your choice for custom curve fitting (e.g. RStudio, MATLAB, Origin, etc.).

2.5. Data Analysis

A computer processor with sufficient power is necessary for fast handling of the large data files that store a channel’s activity over long periods of time. Linux, MacOS, and Windows operating systems (both 32-bit and 64-bit) can run the software described below. We routinely use computers with Intel^® Core^™ i5 CPU and 8 GB of installed memory, with 64 bit Windows 10 operating system.

3. Methods

3.1. General Theoretical Considerations

Measurement of Ca²⁺ block requires accurate measurement of channel conductance (γ_channel). Classically, the description of the time-evolution of the macroscopic current I(t) measured using whole-cell patch clamp can be described as:

$$I\left(t\right)=N\cdot i\cdot P_o\left(t\right)$$ (2)

Where N is the number of channels present on the membrane capable of conducting current, i is the unitary current amplitude of the single-channel, and P_o(t) is the time-dependent open probability of the single-channel. According to Ohm’s law, a change in the applied voltage, dV, to a circuit is directly proportional to the resulting change in current, dI. In ligand-gated channels where the gating reaction is not voltage-dependent, the voltage-dependent change in the macroscopic current, dI(t), reflects a change in the single-channel current, di. Thus, the experimentally observed conductance is related to the single-channel conductance by:

$$\begin{gathered} {\gamma }_{obs}\cdot dV=N\cdot di\cdot P_o \\ {\gamma }_{obs}\cdot dV=N\cdot {\gamma }_{channel}\cdot dV\cdot P_o \\ {\gamma }_{channel}=\frac{{\gamma }_{obs}}{N\cdot P_o} \end{gathered}$$ (3)

Where γ_obs is the experimentally observed conductance defined as 1/R of the cell and channel is the conductance of the single channel. In a typical whole-cell patch clamp experiment, the value of N is unknown and cannot be determined unambiguously. Thus, because the observed conductance in this set up is proportional to N and P_o, and we cannot control the number of channels expressed in each membrane, it is not possible to determine the channel conductance reliably using whole-cell methodology (Figure 1a).

Figure 1: Macroscopic and unitary conductance measurement.

(a) Top, schematic of applied voltage (red), glutamate (Glu, 1 mM, black), and glycine (Gly, 0.1 mM, grey). Bottom, Macroscopic current elicited with the protocol above from a HEK293 cell expressing GluN1/GluN2A recombinant receptors using whole-cell patch clamp. Upon Glu-application, the current rises from a zero-level to a peak level (I_pk), reflecting receptor activation (yellow), after which the current declines gradually, indicative of desensitization (green), to a steady-state level (I_ss) (green). At steady-state, when the P_o is constant, the applied voltage is ramped from −100 mV to +60 mV and then returned to −100 mV. Upon Glu withdrawal, the current declines rapidly to the initial zero level, indicative of deactivation (blue). (b) Unitary current trace recorded in the continuous presence of Glu (1 mM) and Gly (0.1 mM) using cell-attached path-clamp reflects the steady-state phase of the macroscopic current, when channels maintain constant Po by cycling stochastically through periods of activation, deactivation, and desensitization. (c) Current trace recorded form a cell-attached membrane patch illustrates three characteristic current levels indicative of zero, one, and two simultaneously open channels. (d) The probability that a recording with openings to only one level originates from a patch with more than one active channel decreases with the number of consecutive openings observed (n_o) and with the P_o of the channels observed.

To overcome these limitations, single-channel electrophysiology allows direct measurement of P_o and channel unitary amplitude, i, for a known number of channels, N = 1. Therefore, it is essential to ascertain that the patch under analyses contains a single ion channel. The probability that a patch contains a single ion channel can be easily calculated given a certain a priori knowledge about the channel’s activity (i.e. Po) and given a sufficiently large number of gating events (Figure 1b, see Note 4.2). In this chapter, we discuss two methods to measure conductance: (1) interpolation from discrete voltage steps and (2) continuous voltage ramps. We first discuss theoretical considerations for each method which informs our understanding of the strengths and limitations for each.

3.2. Continuous Voltage Ramps

3.1.1. Theoretical Considerations and Limitations

In the analysis of single-channel voltage ramps, it is necessary to obtain several traces of steady-state, single-channel gating currents measured while the applied voltage is gradually ramped across a specified range (Figure 2a). Post-hoc, these traces are averaged together at each sample point to generate an average observed current. After appropriate leak current and artifact subtraction (Figure 2b), the resulting signal represents the averaged unitary current, <i>, at each sample point, t, across k repeated measurements (sweeps) from the same patch, which can be approximated by:

$$\langle i\rangle \left(t\right)=\frac{1}{k}\sum _1^k{i}_k\left(t\right)\approx i\left(t\right)\cdot P_o\left(t\right)$$ (4)

Figure 2: Recording unitary current during a voltage ramp.

(a) Top, voltage ramp protocol used to elicit unitary currents from receptors residing in a cell-attached patch. Bottom, current traces recorded from a cell-attached patch subjected to consecutive sweeps of the protocol above (grey). Sweeps 2 and n elicit no openings, indicative of a desensitized period (red). (b) Left, observed current (<i_obs>) represents the average of all sweeps (black). Right, observed leak current <i_leakî represents the average of all sweeps with no openings.

Given that, for NMDA receptors in the absence of voltage-dependent modulators, channel open probability does not vary with voltage, and can be assumed to be constant across the experiment, the unitary current amplitude can be reconstituted according to:

$$i\left(t\right)=\frac{\langle i\rangle \left(t\right)}{P_o}$$ (5)

In the case of ligand-gated ion channels where the experiment is carried out in the continuous presence of ligand, the observed activity at each timepoint, P_o(t), reflect stationary, steady-state gating kinetics which remain constant throughout the duration of the experiment. By measuring the voltage-dependence of <i>, we can determine the effective conductance, γ_obs. Returning to Equation 3, and assuming N = 1 for these experiments, we see that:

$${\gamma }_{obs}=\frac{d\langle i\rangle }{dV}=\frac{{\gamma }_{channel}}{P_o}$$ (6)

Where the channel conductance can be calculated from the measured conductance corrected by the steady-state channel P_o. The P_o can be measured in a separate set of experiments in which channel gating is measured at a constant applied voltage. Importantly, the steady-state P_o is also impacted by the presence of Ca²⁺. Therefore, additional measurements of Po at a constant applied voltage in the presence of the Ca²⁺ concentration used in the voltage ramp experiments are required to determine the γ_channel for each [Ca²⁺] tested (Figure 3b, d).

Figure 3: Correcting voltage-ramp currents for channel kinetics.

(a) In physiologic conditions, single-channel recordings illustrate reduced global open probability (P_o), reduced principal current level (O_p), and a prominent sub-conductance level (O_s) relative to 0 Ca²⁺ conditions. (b) Unitary currents recorded in the presence of increasing extracellular Ca²⁺ concentrations. (c) Top, Leak-subtracted, average unitary current (see Figure 2). Below, resultant leak-subtracted unitary current <i> corrected for channel open probability which varies with Ca²⁺. (d) Leak-subtracted, P_o-corrected unitary currents recorded during voltage-ramp at several extracellular Ca²⁺ concentrations.

Note that, as with other modulators, Ca²⁺ can induce multiple conductance levels. Therefore the open probability (P_o) will represent the sum of a principal- (P_p) and a sub-conductance (P_s) levels such that P_o = P_p + P_s. This cannot be explicitly accounted for in analysis of voltage ramp data as all conductance levels are averaged together.

3.1.2. Method

There are numerous resources available that describe, in detail, the required hardware, pipette fabrication, and steps to use cell-attached patch clamp to obtain high-quality single-channel recordings (Maki et al. 2014; Sakmann and Neher 1995). In this chapter, we focus on the steps to create the acquisition protocol in Clampex software once a single-channel is captured in a cell-attached patch.

1. Open Clampex (pClamp, Molecular Devices).

2. Create a voltage ramp protocol. At the top of the Clampex window, select “Acquire” to open the drop down menu and select “New Protocol.” This will open the Edit Protocol dialog box to create the protocol. To create the protocol we utilized to create the data in this chapter, we used the following settings:

   1. In the Waveform tab, select “Analog Waveform” and set to “Epochs.”
   2. Set Intersweep holding level to “Use Last Epoch.”
   3. In the table to specify protocol epochs, you will need four epochs. For epochs A, B, and D, left-click in the Type row and select “Step.” For epoch C, select “Ramp.”
   4. For epoch A and D:

      1. Set “First level (mV) to 0
      2. Set “Delta level (mV) to 0
      3. Set “First Duration (ms)” to 1000
      4. Set “Delta Duration (ms)” to 0
   5. For epoch B:

      1. Set “First level (mV) to −100
      2. Set “Delta level (mV) to 0
      3. Set “First Duration (ms)” to 1
      4. Set “Delta Duration (ms)” to 0
   6. For epoch D:

      1. Set “First level (mV) to 60
      2. Set “Delta level (mV) to 0
      3. Set “First Duration (ms)” to 4000 (Note: this is the duration of the ramp. We select 4 seconds to ensure it is short enough to capture enough sweeps of no activity while the channel is desensitized to use for leak current subtraction while being long enough to not destabilize the patch. For channels with differing gating/de-sensitization kinetics, adjust this value accordingly to suit your needs).
      4. Set “Delta Duration (ms)” to 0
   7. In the Mode/Rate tab, set Acquisition Mode to “Episodic stimulation.”
   8. Under Trial Hierarchy:

      1. Set Trial delay to 0
      2. Set Runs/Trial to 1
      3. Set Sweeps/run to 100 (The more the better here; keep in mind that you will likely need to delete some sweeps from analysis for noise artifacts).
      4. Set Sweep duration to a value equal to or slightly larger than the total protocol time when constructing the protocol in the waveform tab. For our protocol above, we use 6.2 sec.
   9. Set Sampling Rate to 40000 Hz (Note, according to Nyquist-Shannon sampling theory, the chosen sampling rate should be at least twice the fastest cycle length possible in the data to reliably capture all signals. Because in our experimental set up we employ a 10 kHz low-pass Bessel filter, the fastest cycle length possible is 10 kHz; therefore, we require at least 20 kHz sampling rate to capture this signal. We use 40 kHz to ensure high-quality resolution).
   10. The settings in other tabs of the Edit Protocol window depend on your specific hardware configuration and experimental requirements.
   11. Press OK to create the protocol file. Save this APF protocol file by select “Acquire” and “Save Protocol As.”

3. To start acquisition, press the “Membrane Test” icon at the top of the Clampex window. This will open the Membrane Test window. Press the play icon to start the test pulse oscilloscope function.

4. In the Membrane Test window, select “Bath.”

5. Ensure the AgCl ground wire is attached to the headstage and is placed in the bath solution. Secure the wire on a small block of clay or similar apparatus to ensure the wire is not in contact with the dish as this can cause the dish to move.

6. Fill the recording pipette with the extracellular solution containing the Ca²⁺ concentration you are testing. The pipette needs to only be filled to allow the tip of the AgCl wire is submerged. If the pipette is overfilled, spillage of solution into the headstage can result in noise. Secure the pipette on the headstage and apply a positive pressure through your suction device. Lower the pipette into the bath solution. You should see the square test pulse waveform appear on the Clampex Membrane Test oscilloscope function. Continue to lower the pipette onto a cell of interest until you observe a slight decrease in the amplitude of the test pulse indicating contact with the cell. Release the positive pressure and apply slight negative pressure to form a tight gigaseal between the pipette and the cell membrane.

7. Press the “Record” icon at the top of the Clampex window to begin recording data using the voltage ramp protocol (Figure 2a).

3.1.3. Data Analysis

Here we describe the steps for preprocessing voltage ramp raw data using Clampfit 10.7 software from the pClamp software suite (Molecular Devices).

1. Open Clampfit software on your local computer.

2. Open ABF data file containing your voltage ramp experiment.

3. Obtain leak current waveform for the patch by discarding all sweeps in the file that contain channel openings (Figure 2a, grey traces):

   1. Press “shift” + “>” or “<” keys to quickly cycle through sweeps in the file. Alternatively, you can manually select a sweep by clicking it with your mouse.
   2. As you cycle through sweeps, the ‘active’ sweep will be highlighted in red. If you observe any single-channel openings in the active sweep, delete that sweep by pressing the “Delete” key.
   3. As you cycle through sweeps, if you observe a sweep with any large noise spike, delete that sweep by pressing the “Delete” key.
   4. As you cycle through sweeps, if you encounter a sweep with no activity (Figure 2a, red traces), keep that sweep and continue cycling.

4. Save the file of the average leak current as a separate file (take care not to overwrite your original raw data; recommended to use File >> Save As).

5. Re-open the original ABF data file containing all voltage ramp data

6. If necessary, remove any sweeps that contain large noise spikes or patch instability.

7. Obtain the average single-channel current waveform of all remaining sweeps:

   1. Press “Average Traces” icon in the file window. A dialog box will appear, ensure it is set to “All visible signals.” Press OK.

8. Save the file of the average single-channel current as a separate file (take care not to overwrite your original raw data; recommend using File >> Save As).

9. To begin data extraction, in the average leak current file, place Cursor 1 at the start of the ramp. Place Cursor 2 at the end of the ramp. Double-click Cursor 1 to open a dialog box and take note of the exact timepoint of the cursor. Repeat for Cursor 2.

10. Extract the numeric data by selecting Edit >> Transfer Traces. This will open a dialog window to specify transfer settings. Under “Destination Window” select “Results Window.” Under “Region to Transfer” select “Cursors 1.2.” Under “Trace Selection” Select “All visible signals” and “All visible traces.” Select “OK.” This will output a list of numeric current values and timepoints at each sample point between Cursors 1 and 2 into the Results window.

11. In the average single-channel current file, double click Cursor 1 to open the dialog box and enter the timepoint value for Cursor 1 in the leak current file. Repeat for Cursor 2. This will ensure you extract data within the exact same time frame between the two files.

12. Display the stimulus waveform (i.e. applied voltage waveform) on the single-channel current file by selecting Edit >> Create Stimulus Waveform Signal… This will open a dialog box. Select OK.

13. In the same file, repeat step 10. This will output numeric values of the current, timepoints, and applied voltage at each sample point between Cursors 1 and 2 in the Results window.

14. Navigate to the Results window. Select the “Column Arithmetic” icon. This will open a dialog box. In the “Expression” field, enter a formula such that for each sample point (row) the average leak current column is subtracted from the average single-channel current. If you followed the order of steps outlined above, the expression will have form: “cF = cD – cB” where each row in column F is the value in column D (average current amplitude) minus value in column B (average leak current amplitude).

15. In the Results window, you now have for each sample point within your voltage ramp, the leak-subtracted, average single-channel current and the corresponding applied voltage. You can export these to a statistical software for curve fitting and analysis (see Note 4.4).

16. Because the stochastic gating is not resolved upon averaging many traces together (Figure 3a), to correct the resultant average unitary current for channel activity, applying Equation 5 (Figure 3c). The channel activity (P_o) will be dependent on external Ca²⁺ concentrations, determine the P_o at each concentration tested using voltage-ramp (Figure 3b). A comprehensive guide on acquiring and analyzing single-channel kinetics can be found elsewhere (Cummings et al. 2016; Maki et al. 2014; Sakmann and Neher 1995).

3.3. Discrete Voltage Steps

3.2.1. Theoretical Considerations

The voltage-ramp method discussed above allows high resolution of voltage-dependent current. This method falls short for channels that have multiple conductance levels (especially, if the block differentially affects these conductance levels) or have extremely low P_o. To circumvent these challenges, unitary current fluctuations can be directly measured at specified voltages. By applying a constant voltage to the membrane patch for an extended duration of time, individual gating events can be clearly resolved such that the unitary current amplitude can be directly measured for a given applied voltage (Figure 4a). We can extend the stochasticity of channel opening to the theoretical foundations already outlined above by:

$${\gamma }_{channel}=\frac{{\gamma }_{obs}}{N\cdot P_o}\{\begin{array}{c}{P}_o=1whenchannelopen\\ P_o=0whenchannelclosed\end{array}$$ (7)

Figure 4: Voltage-step method for measuring unitary conductance.

(a) Unitary currents recorded using cell-attached patch clamp at various applied voltages in the absence (left) and presence (right) of extracellular Ca²⁺. Dashed lines indicate zero-current amplitudes for closed channels (C), and two levels of non-zero current for the principal (O_p) and the sub-conductance (O_s) level. (b) Unfiltered, raw unitary current traces recorded at several applied voltages with corresponding amplitude histograms. Curves represent conductance-level class prediction using segmental-k-means algorithm. (c) Current-voltage relationships recorded in zero and 2 mM Ca²⁺.

Thus, the conductance of the channel is directly proportional to the conductance observed and requires no correction for channel kinetics.

This method encounters challenges when attempting to accurately measure unitary amplitudes at applied voltages near the channel’s reversal potential (Figure 4b). Because it may be difficult to accurately measure the amplitude above the intrinsic thermal noise of the system, there is a limited range of voltages within which one can interpolate current-voltage trends (Figure 4c). Extrapolation beyond this data range (e.g. to estimate reversal potential) can be subject to error.

3.1.2. Method

As in the voltage-ramp analysis described above, transfected HEK293 cells expressing GluN1/GluN2A NMDA receptors are washed and bathed in PBS. The process for forming a gigaseal between pipette and cell membrane is described in detail elsewhere (Maki et al. 2014; Sakmann and Neher 1995). To use QuB for data acquisition, the appropriate analog/digital converter hardware is required to interface QuB software with the amplifier (e.g. National Instrument SCB-68 I/O Connector Blocks and the corresponding NIDAQ card, PCI-6229). For this chapter, we will start the protocol from the point of having already formed a cell-attached gigaseal and you are ready to record single-channel activity.

1. Open QuB software (Note: access to QuB is free and can be requested by contacting the authors of this chapter).

2. Navigate to QuB “Acq” acquisition interface on the left of the QuB window. You will only need the “Data” and “Acquisition Input” panels.

3. Create a new QDF file on which to write acquired data. Name the file according to your record keeping protocols.

4. Under the Acquisition Input panel, press the “Data” drop-down menu and select the data file you just created.

5. Right-click the Data panel to open a drop-down menu and select “Properties.” This opens a dialog box to set parameters of the data file. Navigate to the “Data” tab and input the appropriate values for “Scaling [V/Units],” “Sampling,” and “A/D Scaling.” These will be specific to your acquisition hardware which you must determine. When finished, select OK. (Note, if you perform Step 5 before Step 4, then the properties will be reset to default settings).

6. Select the “Play” icon.

7. If you have not already, apply a constant positive voltage using the amplifier to ensure an equivalent negative voltage is applied to the inner membrane leaflet.

8. Select the “Record” icon to begin data acquisition.

9. Record continuous single-channel data for predefined amount of time to record sufficient gating events to measure amplitude of each conductance class.

10. Press the “Stop” icon.

11. Adjust the applied potential to a new value using the voltage dial on the amplifier.

12. Press the “Record” icon. The data will begin acquiring on a new segment of the file and will not append directly to the previously recorded data. This is advantageous for subsequent record keeping to know each segment in the file corresponds to a different applied voltage.

13. Repeat Step 10 – 12 with new applied potentials until the full range of desired potentials has been sampled (Figure 4a).

14. We recommend utilizing the QuB “Notes” function to record critical information about the data file (e.g. the applied potential used for each data segment). To open this function, select “View” at the top of the QuB window and select “Data Notes” to open the Notes panel where you can record free text information.

15. When you have finished acquisition, select the “Stop” icon to stop recording and save the file.

3.1.3. Data Analysis

We have described the acquisition of single-channel stationary gating data at constant applied voltages using QuB software. To analyze these files using QuB software, the data must first be preprocessed and cleaned to remove noise spikes and baseline drift as described in detail previously (Cummings et al. 2016). This analysis requires an accurate measurement of channel unitary amplitude, therefore, removal of noise spikes and drift are critical to avoid skewed results. For this chapter, we will assume you have completed these steps and will focus on the analysis of these files.

1. Open the QDF file containing your preprocessed voltage step single-channel gating data in QuB software (Note: for analysis of files, you can install QuB on any local machine; you do not need to use the same installation and computer that you used for data acquisition). For this analysis, we recommend using the “Mod” interface which is predefined to display a “Data” panel, a “Model” panel, a “Report” panel, and a “Results” panel. You can select this interface by clicking the “Mod” icon at the left of the QuB window. Your version of QuB may default to display less or additional panels. You can customize your display to your preferences. To remove a panel, simply click the ‘x’ icon at the top right corner of the panel you wish to remove. To add a panel, select “View” and, in the drop-down menu, select the panel you wish to display.

2. In the Model panel, a new QMF model file is automatically created for you. It should contain two states (labeled “1” and “2”) connected by an equilibrium reaction arrow. If this does not display, you can create a new QMF file by selecting the “Create a new model file” icon at the top of the QuB window (Note: regarding the display of models in QuB, there is an important distinction between ‘states’ and ‘classes.’ Within a model, QuB uses numbers to signify different states of the model and uses colors to signify different classes of the model. For analysis, model classes are used to designate different channel conductance levels, [e.g. open, closed, subconductances] and states are used to designate different energetically distinct functional conformations that exist within each class.).

3. At the top of the QuB window, set dead time “td (samples)” to 1. This allows the analysis algorithm to utilize each sample point in the analysis.

4. If your data has more conductance levels beyond open and closed, you will need to add additional states/classes to your QMF model file. The number of states/classes in your model should equal the number of conductance levels in your data that you tend to model. If you do not define multiple conductance levels in your model, the resulting amplitude you measure will be skewed closer to the weighted-average of all conductance levels. To add additional states, double click anywhere within the Model panel field to create a new state (any new added state defaults to being within Class 1, color black). Connect this state to your model by right clicking and holding on your new state to create an equilibrium arrow and drag your cursor to another state within your model to connect the model to your new state. To change the class of this new state, double left click the new state until the state changes to a new color not already used in your model. Alternatively, right-click the state and select “Properties.” This opens a dialog window; under “Class,” simply enter the numeric value of class to which you wish to assign this state.

5. Once your model is complete, you must pre-define the current amplitudes corresponding to each conductance level in your data to a unique class within your model. Using the first data file segment corresponding to data acquired at the first applied voltage, use your cursor to highlight a small (few hundred milliseconds) portion of a conductance level within the Data panel. Once this is highlighted, hover your cursor over the state/class in your model you want to assign this conductance level to. Right-click that state/class to open a menu and select “Grab.” (Note: if your model has multiple states within a given class, the “Grab” function will assign the highlighted current amplitude to all states within that class).

6. Repeat Step 5 for each conductance level within the data segment.

7. Once all conductance levels have been defined to a unique class within your model, measure the amplitudes of the data for the entire data file segment corresponding to a single applied voltage using the segmental-k-means (SKM) function. Use your cursor to highlight the entire data file segment that corresponds to a single applied voltage that you want to analyze. On the right side of the QuB window, a list of functions are displayed. Right-click the “Idealize” function. (Note: If you do not see this function, you can customize what functions you want to display by hovering your cursor over the “Modeling” label and right-click to open a drop-down menu of available functions. A check mark indicates functions that are set to display. Find the “Idealize” function and select it to display. You may also have too many functions select to display than there is space on your QuB window. It is recommended to only select the necessary functions you need to run your analysis workflow).

8. After right-clicking the “Idealize” function, a dialog window will appear to specify the idealization settings. We recommend the following settings:

   1. Ensure that you uncheck the box corresponding to “Clear existing idealization.” If you run the Idealize function with this checked, all prior idealizations within the entire file will be deleted.
   2. Set “Data Source” to “Selection.” This will limit the idealization analysis to the portion of the data you have highlighted.
   3. Set “Pre-process data” to “None – use original data.” This will apply the idealization to the raw data without applying digital filtering. This will maximize the number of detectable events (Figure 4b).
   4. Set “Client/Server” to 1. This is likely the default setting.
   5. Set “Hist bin count” to 50. This applies a fixed-width number of bins to your data. If your data has any large noise spikes, the idealization algorithm will apply that outlier data point into its appropriate bin often resulting in fewer bins available to properly classify the true data resulting in inaccurate results. Ensure your data is cleaned prior to analysis.
   6. Set “Idealization method” to “SKM.”
   7. Set “LL conv” to 0.01.
   8. Set “Max iter” to 10.
   9. Optional: check or uncheck “Drop First/Last Event.” This is more relevant to kinetic analysis which is not covered in this chapter.
   10. Check “Re-estimate”
   11. There is a table where you can specify, for each model class (ie. conductance level) whether you want the SKM algorithm to update its estimate of the class/conductance mean amplitude (Amp) and/or standard deviation (Std) from the initial values it calculated from the data you specified using the “Grab” function in Step 5 and 6. It is recommended that you leave these boxes unchecked since the goal is to accurately measure the amplitude of each class. If you do not allow the algorithm to iteratively update its measurement as it classifies each data point then the final output will be no different than the initial values you manually specified.
   12. Check “Apply dead time to statistics”

9. Select “Run” to apply the SKM algorithm. This may take a few minutes depending on the amount of data you are analyzing. When complete, an “SKM” results file will appear in the “Results” section of the “Data” panel.

10. After you run the analysis, the idealized results should display in red over your raw data file. If the idealized results does not display, ensure that “Idl show” is selected at the top of the QuB window.

11. You can view the numeric results of the analysis by selecting the “Summary” and “Segments” tabs of the SKM results file viewed in the “Results” panel. In these tabs you can find the mean and standard deviation of amplitude for each class in your model. These are labeled ‘Amp1,’ ‘Amp2,’…’AmpX’ for X classes in the model, for example.

12. Inspect the idealization results to assess the quality of the output. It is common, especially in noisy data, for there to be misclassifications where amplitudes are placed in the wrong/undesired class. If this occurs, you can manually clean the idealize results by highlighting the misclassified event and pressing “J” key. This will reclassify every highlighted/selected data point into the class of the first event within your selection.

13. If you had to manually reclassify a substantial number of events and are concerned the statistical results are affected by this misclassification, you can re-estimate the SKM statistics on your re-classified data by running the “Stat” function. Use your cursor to highlight the data file segment you want to reanalyze. Find the “Stat” function on the right side list of functions on the QuB window. Right click this function to open a dialog box to specify the function settings. We recommend the following settings:

    1. Set “Data Source” to “Selection.”
    2. In the table, set “DeadTime” value to the duration (in milliseconds) between individual sample points in your data. For example, if you acquired your data at a rate of 40 kHz, this value is 0.025 msec.
    3. Set “Pre-process data” to “None – use original data.”
    4. Under “Parameters” set “Hist bin count” to 50.

14. Select “Run.” This will take a few minutes. When complete, a “Stat” results file will appear under “Results” in the “Data” panel which you can view in the “Results” panel.

15. Repeat Steps 7 – 14 for each data file segment corresponding to a different applied voltage. For each voltage, record the mean current amplitude for each conductance level in your data/model. This will be the data you use for model fitting (Figure 4c, see Note 4.4).

16. If your numeric results from SKM idealization appear to be significantly deviated (e.g. order of magnitude) from what is expected for your channel, your scaling settings may be off (especially if these were not set correctly when you acquired the file). To set these, hover your cursor over your data and right-click to open a drop-down menu and select “Properties.” This opens a dialog window. Navigate to the “Data” tab of this window and set the “Scaling [V/Units],” “Sampling,” and “A/D Scaling.” This will be unique to your acquisition hardware that you must determine.

4. Notes

4.1. Solution Preparation and Storage

4.1.1. Testing multiple Ca²⁺ concentrations

When testing multiple Ca²⁺ concentrations, depending on the choice of buffer used, small pipetting errors and stray Ca²⁺ ions from the experimental setting could amount to large fluctuations of free [Ca²⁺]_free in the pipette. To minimize technical variability between solution preparations, we recommend preparing serial dilutions from single stock concentrations. To do this, prepare a stock of “Ca²⁺-free” pipette solution (see section 2.3.1a) and a stock of patch solution with the highest Ca²⁺ concentration you intend on testing.

4.2. Channel counting

The determination of channel number in a patch is typically established by visual inspection. For a given run of continuous single channel openings in a patch, no, the probability that the observed record is generated by N = 2 channels can be determined by the following equation derived from binomial assumptions of independence of activity between the two channels (Colquhoun and Hawkes 1990, 1981):

$$P\left(n_o|N\right)={\left(\frac{1-P_o}{1-P_o/N}\right)}^{n_o-1}$$ (8)

4.3. Divalent buffers

Not all buffers/chelators are created equal. They differ substantially in their specificity for metals, affinity for metals, and sensitivity to conditions (e.g. pH, ionic strength, temperature, etc.). In addition, some buffers may exert undesired functional effects on the channel (Chen et al. 2000). Depending on your experimental question and the range of Ca²⁺ you are studying, selection of the appropriate buffer is critical (Figure 5b).

4.4. Fitting models

Several models can be useful to determine the conductance. Under Goldman-Hodgkin-Katz (GHK) assumptions in the absence of voltage dependent inhibitors, the current amplitude is expected to vary linearly with the applied voltage:

$$\langle i\rangle ={\gamma }_{obs}\left(V_{app}-V_{rev}\right)$$ (9)

Where V_app is the applied voltage, V_rev is the channel reversal potential. Several studies have utilized this model (Maki and Popescu 2014; Belin et al. 2022; Aman et al. 2014; Maki et al. 2012). However, NMDA receptors often deviate from GHK assumptions (Legendre et al. 1993; Wollmuth and Sakmann 1998) and the resulting current-voltage relationship is not perfectly linear (Figure 5c). Thus, results from linear fits to data may be inaccurate. Jahr and Stevens developed an alternative model for fitting nonlinear current-voltage relationships (Jahr and Stevens 1993):

$$\langle i\rangle =\left(V_{app}-V_{rev}\right)\left({\gamma }_{obs}\cdot \frac{1}{1+e^{p\left(V_{app}-V_{rev}\right)}}\right)$$ (10)

Where V_app is the applied voltage, V_rev is the channel reversal potential, p is a free parameter that defines the extent of curvature. Several studies have employed this model for conductance analysis (Iacobucci and Popescu 2017; Jahr and Stevens 1993; Sharma and Stevens 1996a).

Table:

Impurities present in sodium chloride

Metal	% in HPLC grade NaCl*	Potential [Metal] (μM) in a 150 mM NaCl solution
Ba2+	≤0.0005	0.32
Fe2+	≤0.0001	0.16
Mg2+	≤0.0005	1.81
Zn2+	≤0.0005	0.67
Co2+	≤0.0005	0.75
Mn2+	≤0.0005	0.80
Cd2+	≤0.0005	0.39

^*from Sigma-Aldrich product 71376 Specification Sheet