Estimating the ${\mathrm{C}\mathrm{a}}^{2+}$ Permeability of NMDA Receptors with Whole-Cell Patch-Clamp Electrophysiology

Abstract

In the mammalian central nervous system (CNS), fast excitatory transmission relies primarily on the ionic fluxes generated by ionotropic glutamate receptors (iGluRs). Among iGluRs, NMDA receptors (NMDARs) are unique in their ability to pass large, ${\mathrm{C}\mathrm{a}}^{2+}$-rich currents. Importantly, their high ${\mathrm{C}\mathrm{a}}^{2+}$ permeability is essential for normal CNS function and is under physiological control. For this reason, the accurate measurement of NMDA receptor ${\mathrm{C}\mathrm{a}}^{2+}$ permeability represents a valuable experimental step in evaluating the mechanism by which these receptors contribute to a variety of physiological and pathological conditions. In this chapter, we provide a theoretical and practical overview of the common methods used to estimate the ${\mathrm{C}\mathrm{a}}^{2+}$ permeability of ion channels as they apply to NMDA receptors. Specifically, we describe the principles and methodology used to calculate relative permeability (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) and fractional permeability (P_f), along with the relationship between these two metrics. With increasing knowledge about the structural dynamics of ion channels and of the ongoing environmental fluctuations in which channels operate in vivo, the ability to quantify the ${\mathrm{C}\mathrm{a}}^{2+}$ entering cells through specific ion channels remains a tool essential to delineating the molecular mechanisms that support health and cause disease.

1. Introduction

Ion channels are transmembrane proteins that facilitate the diffusion of ions across an otherwise impermeable biological membrane. The physico-chemical properties of these ion-permeable pores control electrical and biochemical signal transduction through the exchange of matter between biological compartments. Broadly, the passing of ions across a membrane-embedded pore is described biophysically by the concepts of conductance and permeability. Conductance relates the magnitude of electrical current (I) passing across the membrane to a given membrane potential (V). This metric is independent of the ionic species that carry the current, and is expressed in units of siemens (S). Functionally, conductance is defined as the inverse-resistance of an electrically conductive space, and is determined experimentally by measuring the slope of the current-voltage (I-V) relationship (Fig. 1a). Permeability (also referred to as selectivity) quantifies the degree to which a barrier (a membrane or an ion channel protein) allows the preferential passage of certain ions over others. Therefore, permeability is specific to each ionic species. Because of the technical challenges of measuring the absolute permeability, it is more commonly measured as a ratio, relative to the current carried by a referent ionic species. Experimentally, it can be calculated by measuring the change in reversal potential (${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$) as a function of external ion concentration from the I-V relationship and using an established theoretical framework (Fig. 1b). In essence, channel conductance informs about how many ions pass through a pore, and permeability informs about which ions pass.

Figure 1: Measuring conductance and permeability from current-voltage (I-V) relationships.

In the absence of divalent cations, NMDA receptors exhibit an ohmic (linear) I-V relationship. (a) Hypothetical I-V curves each indicative of distinct channel conductances (λ) quantified by the slope at invariant permeability. (b) Hypothetical I-V curves each indicative of changes in permeability quantified by the reversal potential (E_rev) at constant conductance. In physiological conditions, the NMDA receptor E_rev is ~0 mV, indicating permeability to multiple cation species (e.g., ${\mathrm{N}\mathrm{a}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{C}\mathrm{a}}^{2+}$). In contrast, the E_rev of more stringently selective ion channels have values closer to the Nernst potential of the selective ion [37–39].

In this chapter, we describe approaches to estimate the ${\mathrm{C}\mathrm{a}}^{2+}$ permeability of N-Methyl-D-Aspartate receptors (NMDARs). NMDARs are ionotropic glutamate receptors (iGluRs) with critical roles in the normal development and function of the mammalian central nervous system (CNS). Upon binding glutamate, and in the presence of the obligatory co-agonist glycine, NMDA receptors experience dynamic structural changes, which include the opening of a transmembrane ion-channel. In physiologic conditions, NMDAR activation produces relatively large (40–60 pS) currents that reverse direction around 0 mV, indicative of nonselective cationic permeability (${\mathrm{N}\mathrm{a}}^{+}$, ${\mathrm{K}}^{+}$ & ${\mathrm{C}\mathrm{a}}^{2+}$) [1,2]. The total charge transfer through NMDA receptors during an activation episode, as well as the kinetics of this charge transfer contribute critically to neuronal excitability, and therefore to electrical transmission in the CNS. Additionally, the kinetics and degree of NMDAR-mediated ${\mathrm{C}\mathrm{a}}^{2+}$ current represents a powerful biochemical signal. This signal is essential for the normal development and physiology of excitatory synapses, enabling processes such as synapse formation, plasticity, and pruning [3,4]. Importantly, dysregulated NMDAR ${\mathrm{C}\mathrm{a}}^{2+}$ currents initiate pathological processes associated with numerous neurological conditions, including developmental disorders, acute and chronic neurodegeneration, and mood disorders [5–11]. Therefore, methods for the accurate quantification of NMDAR ${\mathrm{C}\mathrm{a}}^{2+}$ permeability across biological preparations and experimental conditions represent necessary tools in in neuroscience research.

To date, the magnitude of the NMDAR ${\mathrm{C}\mathrm{a}}^{2+}$ signal has been estimated with two related parameters: relative ${\mathrm{C}\mathrm{a}}^{2+}$ permeability and fractional ${\mathrm{C}\mathrm{a}}^{2+}$ permeability. Relative ${\mathrm{C}\mathrm{a}}^{2+}$ permeability, P_Ca/P_mono, measures the preference with which NMDARs allow ${\mathrm{C}\mathrm{a}}^{2+}$ passage relative to a referent, usually monovalent, cationic species. Fractional ${\mathrm{C}\mathrm{a}}^{2+}$ permeability, Pf, measures the charge carried by ${\mathrm{C}\mathrm{a}}^{2+}$ ions relative to the total charge transferred [12,13].

Relative permeability can be calculated from experimental measurements of shifts in reversal potential induced by one of two methods: the high monovalent or the bi-ionic method. In the high monovalent method, the experimenter supplements an exclusively monovalent external solution (${\mathrm{N}\mathrm{a}}^{+}$, ${\mathrm{K}}^{+}$, or ${\mathrm{Cs}}^{+}$) with increasing concentrations of ${\mathrm{C}\mathrm{a}}^{2+}$. In contrast, the bi-ionic method replaces an exclusively monovalent current with a ${\mathrm{C}\mathrm{a}}^{2+}$-exclusive current [14–16]. Regardless of the method, the calculation of P_Ca/P_mono relies on the Goldman-Hodgkin-Katz (GHK) equation, and therefore its accuracy depends on the same inherent assumptions [16,17,18,]. The present literature reports values for NMDAR P_Ca/P_mono ranging from 0.8 to 10.5 [12,19]. This broad range reflects largely three experimental variables: 1) the method used to calculate ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ (high monovalent vs. bi-ionic), 2) the NMDAR preparation examined (e.g., GluN2A vs. GluN3A, recombinant vs. endogenous), and 3) the composition of the external and internal solution used, particularly the extracellular pH. We present a comprehensive summary of this variability in Table 1.

Table 1:

Reported Values for NMDAR ${\mathrm{C}\mathrm{a}}^{2+}$ Permeability

NMDAR Subtype	Method	pH 8.0	pH 7.2- pH 7.4	pH 6.8	Selected References
N1–1a/N2A	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	7.0–10.5 - - -	3.2–4.5 5.5–8.0 3.0–4.1 12.0–15.0	- - - 8.5	[14, 20, 31, 40, 41]
N1–1a/N2B	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	- - - -	2.3 10.4 - 9.1	- - - 8.1	[15, 31]
N1–1a/N2C	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	- - - -	2.2 2.7–5.0 - 8.2	- - - -	[20, 42]
N1–1a/N2D	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	- - - -	- 4.5 - -	- - - -	[42]
N1–1a/N3A	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	- - - -	0.8 - - -	- - - -	[19]
Hippocampal	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	- - - -	3.0–5.0 3.6–6.2 - 10.7–10.9	- - - -	[12, 43]
Forebrain	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	- - - -	- - - 6.8	- - - -	[13]
Astrocyte	High Monovalent (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Bi-ionic (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Converted from Pf(%) (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) Pf(%)	- - - -	3.1 - - -	- - - -	[44]

Fractional permeability can be calculated from experimental measurements of fluorescence intensity shifts using ${\mathrm{C}\mathrm{a}}^{2+}$-sensitive dyes. In contrast to relative permeability, fractional permeability relates the fluxed ${\mathrm{C}\mathrm{a}}^{2+}$ to the total ionic flux, irrespective of the identity of co-permeant cations. Therefore, it allows a more direct observation of the ${\mathrm{C}\mathrm{a}}^{2+}$ signal [20,21]. Notably, fractional permeability is independent of the assumptions inherent to the GHK equation. This is of particular importance for NMDARs, which deviate from GHK assumptions at extreme (high and low) ${\mathrm{C}\mathrm{a}}^{2+}$ concentrations [21]. For NMDARs, the reported values for ${\mathrm{C}\mathrm{a}}^{2+}$ fractional permeability measured under physiological conditions range from 12 to 15% and therefore, are more consistent across literature than those reported for relative permeability (Table 1). When using reported fractional permeability values to estimate relative permeability using the GHK equation, as will be discussed in section 3.2.6., the calculated values match more closely to those reported with the high monovalent method (Table 1) [14].

Below, we provide a comprehensive methodology for the quantification of ${\mathrm{C}\mathrm{a}}^{2+}$ permeability in NMDARs using whole-cell patch-clamp electrophysiology. This will include: 1) estimating relative permeability using the high monovalent method; 2) estimating fractional permeability using patch-clamp ${\mathrm{C}\mathrm{a}}^{2+}$ fluorometry; and 3) interconverting values for relative with fractional permeability. We focus on the high monovalent method for estimating relative permeability since it is more readily translatable to physiological conditions, and because it generally provides results that are more consistent across laboratories. Understanding the theory and advantages/limitations of each of these methods will provide investigators with the necessary information to choose the most appropriate approach for their specific aims.

2. Materials

2.1. Cell Culture and NMDAR Expression

High-quality NMDAR macroscopic current recordings can be acquired using several preparations. These include recombinant protein expression in cells lacking endogenous NMDARs (e.g., HEK293 cells) [22,23], or by isolating the NMDAR response from cells expressing endogenous NMDARs (e.g., CA1 neurons of the hippocampus) [24,25]. However, the selection of an appropriate system ultimately relies on the aims pursued and the availability of reagents and preparations. For the purpose of this chapter, all experimental protocols have been designed using HEK293 cells expressing recombinant GluN1–1a and GluN2A subunits, co-transfected with plasmids encoding fluorescent proteins (GFP or mCherry) (see Note 1), as described previously [23].

2.2. Electrophysiology and ${\mathrm{C}\mathrm{a}}^{2+}$ Fluorometry Setup

2.2.1. Electrophysiology Setup

For collecting macroscopic NMDAR responses, standard patch-clamp electrophysiology equipment is required; the setup and use of which has been previously covered [26].

2.2.2. ${\mathrm{C}\mathrm{a}}^{2+}$ Fluorometry Setup

1. Digital Microscopy Setup:

   1. Inverted Microscope.
   2. UV-transmitting, high magnification objective.
   3. Digital fluorescence imaging system.
   4. Fura-2 excitation filters (380 nm, 25 mm diameter).
   5. High speed controller.
   6. CMOS camera.
2. Recording Setup:

   1. 25 mm #1.5 glass coverslips.
   2. Coverslip imaging chamber.
   3. Immersion Oil.

3. Carboxylate Microspheres.

4. Objective Maintenance:

   1. Cotton swabs.
   2. Lens cleaning paper.
   3. 100% ethanol.
   4. Kimwipes.

2.3. Computer Hardware and Software

1. Electrophysiology acquisition software.

2. Electrophysiology processing software.

3. Fluorometry acquisition and processing software.

4. General Data Processing Software.

5. Computer specifications: due to the large size of fluorometry data files, a computer with sufficient processing power to collect, store and analyze multiple >2 GB files is required for ${\mathrm{C}\mathrm{a}}^{2+}$ imaging experiments. Each of the examples below were performed using a system with 8 GB RAM, 64-bit Intel Core i5 processor with Windows 11 operating system and an additional >1 TB external storage system.

2.4. Solutions

2.4.1. Relative ${\mathrm{C}\mathrm{a}}^{2+}$ Permeability

1. ${\mathrm{N}\mathrm{a}}^{+}$-wash extracellular solution (see Note 2): 150 mM NaCl, 2.5 mM KCl, 0.1 mM CaCl₂, 10 mM HEPES, 0.1 mM EDTA and 0.1 mM glycine. pH set to 7.2 using HCl and NaOH.

2. ${\mathrm{N}\mathrm{a}}^{+}$-agonist extracellular solution: ${\mathrm{N}\mathrm{a}}^{+}$-wash extracellular solution supplemented with 1 mM glutamate.

3. ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution: 150 mM NaCl, 2.5 mM KCl, 2 mM CaCl₂, 10 mM HEPES, 0.1 mM EDTA and 0.1 mM glycine. pH set to 7.2 using HCl and NaOH.

4. ${\mathrm{C}\mathrm{a}}^{2+}$-agonist extracellular solution: ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution supplemented with 1 mM glutamate.

5. Intracellular Solution 1: 135 mM CsCl, 33 mM CsOH, 2 mM MgCl₂, 10 mM HEPES and 10 mM EGTA. pH set to 7.4 using HCl or CsOH.

6. Bath Solution: Dulbecco’s Phosphate Buffered Saline (DPBS): 137.9 mM NaCl, 8.1 mM Na₂HPO₄, 2.7 mM KCl, 1.5 mM KH₂PO₄, 0.9 mM CaCl₂, and 0.5 mM MgCl₂.

2.4.2. Fractional ${\mathrm{C}\mathrm{a}}^{2+}$ Permeability

1. F/Q calibration extracellular wash solution: 150 mM N-Methyl-D-Glucamine (NMDG), 10 mM CaCl₂, 10 mM HEPBS, 0.1 mM EDTA and 0.1 glycine. pH set to 8.0 using HCl and NMDG.

2. F/Q calibration extracellular agonist solution: F/Q calibration extracellular wash solution supplemented with 1 mM glutamate.

3. Pf extracellular wash solution: 150 mM NaCl, 2 mM CaCl₂, 10 mM HEPES, 0.1 mM EDTA and 0.1 mM glycine. pH set to 7.2 using HCl or NaOH.

4. Pf extracellular agonist solution: Pf extracellular wash solution supplemented with 1 mM glutamate.

5. Intracellular solution 2: 140 mM CsCl, 10 mM HEPES, 1 mM Fura-2. pH set to 7.4 using HCl and CsOH.

6. Bath solution: Dulbecco’s Phosphate Buffered Saline (DPBS): 137.9 mM NaCl, 8.1 mM Na₂HPO₄, 2.7 mM KCl, 1.5 mM KH₂PO₄, 0.9 mM CaCl₂, and 0.5 mM MgCl₂.

2.5. Additional Materials

1. 0.25% trypsin/2.21 mM EDTA.

2. Tissue culture dishes (e.g., 35×10 mm polystyrene dishes).

3. 12 M nitric acid.

4. 70% ethanol.

5. PDL: 0.1 mg/mL poly-d-lysine diluted in DPBS.

6. Coverslip wash/dry rack.

7. 3D/Orbital Rocker.

8. Glass Pipettes.

9. Pipette Bulb.

3. Methods

3.1. Relative ${\mathrm{C}\mathrm{a}}^{2+}$ Permeability ($P_{Ca}/P_{Na}$)

3.1.1. Theoretical Considerations

The generalized Goldman-Hodgkin-Katz current equation from constant field theory is:

$$Ix=\frac{F^2{Z}^2{x}^P{x}^V}{RT}\frac{{\left[x\right]}_o-\left[X\right]i{e}^{Z_{x}FV/RT}}{1-e^{Z_{x}FV/RT}}$$ [Eq 1.1]

Where $\mathrm{F}$ is Faraday’s constant, $\mathrm{Z}$ is the ionic valence, $\mathrm{P}$ is the permeability coefficient, $\mathrm{V}$ is the membrane potential, $\mathrm{R}$ is the ideal gas constant, $\mathrm{T}$ is temperature in Kelvins and ${\mathrm{x}}_{\mathrm{o}}$ and ${\mathrm{x}}_{\mathrm{i}}$ are a given ion in extracellular or intracellular solution respectively. Solving for ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$ (i.e., where $I_{total}=I_{Na}+I_K+I_{Ca}=0$), as derived by Anne Lewis [16]:

$$Erev=\frac{RT}{F}\frac{\left[Na\right]o+\frac{PK}{PNa}\left[K\right]o+4\frac{P\mathrm{\text{'}}Ca}{PNa}\left[Ca\right]o}{\left[Na\right]i+\frac{PK}{PNa}\left[K\right]i+4\frac{P\mathrm{\text{'}}Ca}{PNa}\left[Ca\right]i}$$ [Eq 1.2]

Where, due to the divalence (i.e., $\mathrm{Z}=2$) of ${\mathrm{C}\mathrm{a}}^{2+}$:

$${P^{\prime }}_{Ca}=\frac{P_{Ca}}{1+e^{FV/RT}}$$

Assuming ${\mathrm{P}}_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{o}}={\mathrm{P}}_{\mathrm{K}}={\mathrm{P}}_{\mathrm{N}\mathrm{a}}={\mathrm{P}}_{\mathrm{C}\mathrm{s}}$ [27,19], ${\left[{\mathrm{C}\mathrm{a}}^{2+}\right]}_{\mathrm{i}}={\left[{\mathrm{N}\mathrm{a}}^{+}\right]}_{\mathrm{i}}={\left[{\mathrm{C}\mathrm{s}}^{+}\right]}_0\sim 0$ and $\mathrm{\alpha }=RT/F$, the Lewis equation takes the form of equation [Eq 1.3]. This equation and experimental setup are often referred to as the “high monovalent method” in literature.

$$\frac{P_{Ca}}{P_{Na}}=\frac{{\left[Na\right]}_o{(e}^{\frac{\Delta E_{rev}}{\alpha }}-1)(e^{\frac{E_{Ca}}{\alpha }}+1)}{4{\left[Ca\right]}_o}$$ [Eq 1.3]

Where ${\mathrm{E}}_{\mathrm{C}\mathrm{a}}$ is the reversal potential observed in ${\mathrm{C}\mathrm{a}}^{2+}$-containing solutions, ${\mathrm{E}}_{\mathrm{N}\mathrm{a}}$ is the reversal potential observed in ${\mathrm{C}\mathrm{a}}^{2+}$-free solutions and $\mathrm{\Delta }{\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}={\mathrm{E}}_{\mathrm{C}\mathrm{a}}-{\mathrm{E}}_{\mathrm{N}\mathrm{a}}$.

Additionally, one can derive ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ by fitting the Lewis equation to [${\mathrm{C}\mathrm{a}}^{2+}$]-dependent shifts in $\mathrm{\Delta }{\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$ [28,21]. Doing so requires the assumption that ${\mathrm{E}}_{\mathrm{N}\mathrm{a}}=0\mathrm{m}\mathrm{V}$ (i.e., ${\mathrm{E}}_{\mathrm{C}\mathrm{a}}=\mathrm{\Delta }{\mathrm{E}}_{\text{rev}}$), which only occurs under the condition $[\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{o}{]}_{\mathrm{i}}=[\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{o}{]}_{\mathrm{o}}$. This assumption yields the equation:

$$\Delta E_{rev}=\frac{a}{2}\ln \left(1+\frac{P_{Ca}}{P_{Na}}\frac{4{\left[Ca\right]}_o}{{\left[Na\right]}_o}\right)$$ [Eq 1.4]

3.1.2. High Monovalent Method

1. Transfer transfected cells from overnight cultures onto recording cell-culture dishes at a low density. Allow 1 – 2 hours for cells to adhere fully to dish.

2. Backfill a borosilicate glass electrode (2 – 5 MΩ) with Intracellular solution 1. Remove any air bubbles from the electrode by gently tapping.

3. Lower the electrode onto a selected cell. Obtain a gigaseal, then apply additional negative pressure to rupture the membrane to move into a whole-cell configuration [29].

4. Obtain an I-V recording for ${\mathrm{N}\mathrm{a}}^{+}$ using the following protocol, summarized in Fig.2a:

   1. Baseline: with the holding potential at −100 mV, perfuse ${\mathrm{N}\mathrm{a}}^{+}$-wash extracellular solution onto the cell for 10 – 15 s, or until a stable baseline is reached.
   2. Ramp_leak: Continuously increase the holding potential to +60 mV across 3 s while continuing ${\mathrm{N}\mathrm{a}}^{+}$-wash extracellular solution perfusion. This step allows for the subtraction of leak current from the final I-V trace.
   3. Baseline: Return the holding potential to −100 mV, continue ${\mathrm{N}\mathrm{a}}^{+}$-wash extracellular solution perfusion for an additional 10 s.
   4. I_ss: With the holding potential at −100 mV, switch perfusion to ${\mathrm{N}\mathrm{a}}^{+}$-agonist extracellular solution for 7 s, or until the NMDAR-evoked current reaches a steady-state amplitude (I_ss).
   5. Ramp_Glu: Continuously increase the holding potential to +60 mV across 3 s while continuing ${\mathrm{N}\mathrm{a}}^{+}$-agonist extracellular solution perfusion.
   6. I_ss: Return the holding potential to −100 mV, continue ${\mathrm{N}\mathrm{a}}^{+}$-agonist extracellular solution perfusion for an additional 1 s to ensure I_ss has not been altered during the ramp step.
   7. Washout/Baseline: Continuing at −100 mV, switch perfusion back to ${\mathrm{N}\mathrm{a}}^{+}$-wash extracellular solution for 10 – 15 s to return to baseline.
5. To obtain an I-V recording for ${\mathrm{C}\mathrm{a}}^{2+}$, repeat the previous step with ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution and ${\mathrm{C}\mathrm{a}}^{2+}$-agonist extracellular solution on the same cell as the previous step:

   1. Baseline: With the holding potential at −100 mV, perfuse ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution onto the cell for 10 – 15 s, or until a stable baseline is reached.
   2. Ramp_leak: Continuously increase the holding potential to +60 mV across 3 s while continuing ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution perfusion.
   3. Baseline: Return the holding potential to −100 mV, continue ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution perfusion for an additional 10 s.
   4. I_ss: With the holding potential at −100 mV, switch perfusion to ${\mathrm{C}\mathrm{a}}^{2+}$-agonist extracellular solution n for 7 s, or until the NMDAR-evoked current reaches a steady-state amplitude (I_ss).
   5. Ramp_Glu: Continuously increase the holding potential to +60 mV across 3 s while continuing ${\mathrm{C}\mathrm{a}}^{2+}$-agonist extracellular solution perfusion.
   6. I_ss: Return the holding potential to −100 mV, continue ${\mathrm{C}\mathrm{a}}^{2+}$-agonist extracellular solution perfusion for an additional 1 s.
   7. Washout/Baseline: Continuing at −100 mV, switch perfusion back to ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution for 10 – 15 s to return to baseline.

6. Assess data quality (Fig. 2b). High-quality data will have the following: Ohmic I-V (see Note 2, Note 3); stable baseline (see Note 4); I_ss maintained after ramp_Glu (see Note 5).

7. Transfer wash (leak) and agonist (Glu) I-V data for ${\mathrm{N}\mathrm{a}}^{+}$ and ${\mathrm{C}\mathrm{a}}^{2+}$ to desired software for data analysis.

8. Normalize ${\mathrm{N}\mathrm{a}}^{+}$ I-V data by the following:

   1. To subtract leak current from Glu-elicited current, align leak-ramp and Glu-ramp currents by voltage. Subtract leak current from Glu current to get NMDAR current across the voltage range.
   2. Normalize NMDAR current at each voltage to that observed at +60 mV to calculate the final normalized ${\mathrm{N}\mathrm{a}}^{+}$ current.
9. Normalize ${\mathrm{C}\mathrm{a}}^{2+}$ I-V data by the following:

   1. To subtract leak current from Glu-elicited current, align leak-ramp and Glu-ramp currents by voltage. Subtract leak current from Glu-elicited current to get NMDAR current across the voltage range.
   2. Normalize NMDAR current at each voltage to that observed at +60 mV ${\mathrm{N}\mathrm{a}}^{+}$ NMDAR current to calculate the final normalized ${\mathrm{C}\mathrm{a}}^{2+}$ current. Normalizing ${\mathrm{C}\mathrm{a}}^{2+}$ current to ${\mathrm{N}\mathrm{a}}^{+}$ current also provides information regarding potential ${\mathrm{C}\mathrm{a}}^{2+}$ block. See [1].

10. Plot Normalized ${\mathrm{N}\mathrm{a}}^{+}$ current vs holding potential to get an I-V relationship for ${\mathrm{C}\mathrm{a}}^{2+}$-free conditions.

11. Superimpose Normalized ${\mathrm{C}\mathrm{a}}^{2+}$ current vs holding potential onto the same plot (Fig. 2c).

12. Calculate E_rev for ${\mathrm{C}\mathrm{a}}^{2+}$-free and ${\mathrm{C}\mathrm{a}}^{2+}$ conditions (see Note 6) as follows:

    1. Fit I-V data for each condition to a linear regression model restrained between [−20, +20 mV] (Fig. 2d). This range gives more robust measurements of ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$ and is less skewed by non-linearity at higher applied potentials.
    2. ${\mathrm{E}}_{\mathrm{N}\mathrm{a}}$ will be equal to the x-intercept of the ${\mathrm{N}\mathrm{a}}^{+}$ I-V relationship and should be ~0 mV, although variability will be observed. We observe a mean ${\mathrm{E}}_{\mathrm{N}\mathrm{a}}$ of −1 mV ± 5 mV (Fig. 3b).
    3. ${\mathrm{E}}_{\text{Ca}}$ will be equal to the x-intercept of the ${\mathrm{C}\mathrm{a}}^{2+}$ I-V relationship.
13. Calculate the observed shift in ${\mathrm{E}}_{\text{rev}}\left(\mathrm{\Delta }{\mathrm{E}}_{\text{rev}}\right)$ as:

    $$\Delta Erev=ECa-ENa$$

14. Calculate ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ (see Note 7): if deriving ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ from a ${\mathrm{C}\mathrm{a}}^{2+}$ titration of $\mathrm{\Delta }{\mathrm{E}}_{\text{rev}}$, fit equation [Eq 1.4] to data (Figs. 3c & d). For a single [${\mathrm{C}\mathrm{a}}^{2+}$], use equation [Eq 1.3] to calculate ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ (Fig. 3d).

Figure 2: Protocol for recording macroscopic voltage-ramp waveforms.

(a) To generate I-V curves, follow the protocol described in section 3.1.2: (1) obtain a high-quality seal in the whole-cell configuration; (2) ramp the clamping voltage from −100 to +60 mV over 5 s, in the absence of agonist, to record the baseline leak current; (3) apply agonist (Glu, 1 mM) for 7 s to activate NMDA receptors and reach steady-state current amplitude; (4) repeat the initial voltage ramp and record the changing current amplitude. (b) Example traces illustrating common sources of error. Top, rectification (likely due to due to Mg²⁺ contamination) (red box); middle, poor seal integrity; bottom, failure to return to initial current level after the voltage ramp. (c) Leak-subtracted I-V curves recorded in zero ${\mathrm{C}\mathrm{a}}^{2+}$ (black) as in panel (a), and in 2 mM ${\mathrm{C}\mathrm{a}}^{2+}$ (blue) illustrate ${\mathrm{C}\mathrm{a}}^{2+}$-dependent reduction in conductance and increase in E_rev. Estimate values for E_rev as the intercepts of linear regressions fitted onto the linear region of each I-V relationship (box). (d) Regression model fits for the I-V curves recorded in (c) on an expanded scale, with corresponding E_Na, E_Ca and ΔE_rev estimations.

Figure 3: Effect of [${\mathrm{C}\mathrm{a}}^{2+}$] on E_rev for estimating ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$.

(a) In the presence of 150mM ${\mathrm{N}\mathrm{a}}^{+}$, 2mM ${\mathrm{C}\mathrm{a}}^{2+}$ (blue) reduces I_pk and I_ss of the macroscopic NMDAR response, and the E_rev is right-shifted relative to the ${\mathrm{C}\mathrm{a}}^{2+}$-free response (black). (b) The theoretical E_rev of the ${\mathrm{C}\mathrm{a}}^{2+}$-free response (E_Na) for NMDARs is 0 mV. Variance in measured E_Na values (black histogram, E_Na = −1.46 ± 5.36 mV, n = 306) conform to a normal distribution (E_Na = 0.00 ± 5.00 mV. W = 0.98, p < 0.01, Shapiro-Wilk test). (c) The shift in E_rev (ΔE_rev) increases with [${\mathrm{C}\mathrm{a}}^{2+}$], predicted by equation 1.4, where ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ = 3.91. Data points represent mean ± SE. (d) Contour plot of equation 1.4 illustrates the estimation of ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ from a single [${\mathrm{C}\mathrm{a}}^{2+}$] (“X”, data from (a), ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ = 3.99) using equation 1.3, or by a [${\mathrm{C}\mathrm{a}}^{2+}$] titration (dashed line, data from (c), ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ = 3.91) using equation 1.4.

3.2. Fractional ${\mathit{C}\mathit{a}}^{2+}$ Permeability (Pf)

3.2.1. Theoretical Considerations

Here, we provide a brief overview of the theoretical background of patch-clamp fluorometry. For a comprehensive background of the equations used for calculating Pf, see [30,21].

Fractional permeability can only be calculated under “Fura-overload” conditions, meaning that the Fura-2 buffering capacity is vastly greater than the endogenous buffering capacity. This ensures that all incoming ${\mathrm{C}\mathrm{a}}^{2+}$ is captured by Fura-2 and converted into a change in fluorescence intensity (i.e., $\mathrm{\Delta }{\mathrm{F}}_{380}={\mathrm{\Delta }\mathrm{F}}_{\mathrm{M}\mathrm{a}\mathrm{x}}$). This can be accomplished with 1 mM Fura-2 in the patch-pipette as demonstrated in [14,31]. The use of Fura-2 and other ratiometric ${\mathrm{C}\mathrm{a}}^{2+}$dyes are unique in their ability to directly measure ionic permeation. This contrasts other ${\mathrm{C}\mathrm{a}}^{2+}$imaging systems, such as genetically encoded ${\mathrm{C}\mathrm{a}}^{2+}$ indicators, which cannot precisely capture the biophysical mechanisms surrounding ion permeation (see Note 8).

$$\Delta F380=\Delta FMax\frac{KB}{1+KE+KB}$$

$$\therefore KB\gg KE⟹\Delta F380=\Delta FMax$$

Where $\mathrm{K}\mathrm{B}$ is the Fura-2 buffering capacity, $\mathrm{K}\mathrm{E}$ is the endogenous buffering capacity, $\mathrm{\Delta }\mathrm{F}380$ is the observed change in fluorescence intensity from 380 nm light stimulation and ${\mathrm{\Delta }\mathrm{F}}_{\mathrm{M}\mathrm{a}\mathrm{x}}$ is the shift in fluorescence that is attributable to ${\mathrm{C}\mathrm{a}}^{2+}$ binding to the Fura-2 molecule. Note that 380 nm of light is used, as this is the wavelength that corresponds to the maximum absorbance of the ${\mathrm{C}\mathrm{a}}^{2+}$-unbound state of the Fura molecule.

Equation [Eq 1.1] can also be used to interconvert relative permeability (${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$) and fractional permeability (Pf).

$$Pf(\mathrm{\%})=\frac{ICa}{INa+IK+ICa}$$ [Eq 2.1]

Inserting equation [Eq 1.1] into equation [Eq 2.1] yields the equation:

$$Pf(\mathrm{\%})=\frac{1}{1+\frac{P_{Na}}{P\prime Ca}\frac{1}{4\left[Ca\right]}(\left[Na\right]e^{\frac{V}{\alpha }})}$$ [Eq 2.2]

Where $\mathrm{V}={\mathrm{V}}_{\mathrm{m}}-{\mathrm{E}}_{\text{rev}}$ and where:

$$P^{\prime }Ca=\frac{PCa}{1+e^{FV/RT}}$$

3.2.2. Fura-2 Loading

Exercise extreme caution for preparation of acid-treated coverslips when handling nitric acid and perform all steps under a chemical fume hood with protective equipment. Handle all solutions containing Fura-2 in darkness to avoid photobleaching.

1. Transfer coverslips to a coverslip wash/dry rack and wash 3x with double distilled H2O (ddH2O).

2. Place coverslips in a glass beaker with enough 70% ethanol (EtOH) to cover the top of the slips

3. Incubate at room temperature (RT) for 15 min, shaking frequently.

4. Follow the EtOH wash with a 3x ddH2O wash.

5. Place washed coverslips in a glass beaker with enough 12 M nitric acid to cover the top of the slips

6. Incubate at RT for 20 min, shaking frequently.

7. Following incubation, wash coverslips 8x with ddH2O.

8. Rinse coverslips 1x with EtOH.

9. Remove coverslips from EtOH and place in a running tissue culture hood. Allow 1 – 3 h for coverslips to dry completely.

10. Once dried, transfer coverslips to a beaker or other autoclaving container, separating slips with pieces of aluminum foil to prevent sticking.

11. Autoclave coverslips and allow them to cool to RT. Store at RT in container used to autoclave.

12. Transfer coverslips to 1.5 cm dishes and pipette 1 – 2 mL of RT PDL onto each coverslip.

13. Set dishes on an orbital shaker and incubate at RT for a minimum of 30 min (see Note 9).

14. Aspirate PDL and wash coverslips 3x with DPBS.

15. Transfer transfected cells onto acid-washed, PDL-coated glass coverslips at a low density.

16. Allow 2 – 4 h for cells to adhere fully to the coverslips.

17. Transfer a coverslip to imaging chamber and wash 3x with DPBS.

18. Pipette enough DPBS onto cells to cover and transfer to microscope stage.

19. Backfill a borosilicate glass electrode (2 – 5 MΩ) with Intracellular solution 2.

20. Lower the recording electrode onto an isolated, transfected cell. Obtain a gigaseal, then apply additional negative pressure to rupture the membrane to move into a whole-cell configuration.

21. Switch microscope filter to the 380 nm filter and the objective to the 40x immersion objective and focus on cell of interest.

22. Allow 5 – 10 min for Fura-2 to load into the cell cytosol. During the loading process, the 380 nm signal intensity will progressively increase as more Intracellular solution 2 is exchanged with the cytosol.

23. Adjust camera acquisition settings (e.g., laser intensity, exposure time, and gain) such that the Fura-2-loaded cell’s emission intensity is bright, but not saturating.

3.2.3. Calibration: F/Q

Once the cell is fully loaded with Fura-2, and optics have been adjusted to maximize the brightness of the signal (see 3.2.2), the system must first be calibrated as described below. Also see [21,31].

1. Begin imaging recording.

2. While imaging recording is running, begin patch-clamp recording using the following protocol. For each step, clamp cells at ${\mathrm{V}}_{\mathrm{m}}=-60\mathrm{m}\mathrm{V}$:

   1. Perfuse F/Q calibration extracellular wash solution onto cell for 10 – 15 s, or until a stable electrical baseline is reached.
   2. Perfuse F/Q calibration extracellular agonist solution onto cell for 0.1 – 2.0 s to obtain the NMDAR macroscopic response. During this time, a noticeable decrease in the fluorescence signal will be observed.
   3. Perfuse F/Q calibration extracellular wash solution onto cell for 10 – 15 s, or until current returns to baseline.
3. Once recording has ended, measure ΔF as follows (Fig. 4a):

   1. Define ROI_Ca: ROI_Ca should be set as the perimeter of the cell to capture any fluorescence changes across the entire cell. Measure this both prior to glutamate (ROI_Ca,Base) and after glutamate (ROI_Ca,Glu) perfusion.
   2. Define ROI_Bkg: Once ROI_Ca is defined for baseline and glutamate conditions, copy/paste the region into a surrounding region to account for changes in background fluorescence. Measure both prior to glutamate (ROI_Bkg,Base) and after glutamate (ROI_Bkg,Glu) perfusion.
4. Measure ΔF of the ROIs using the following equation:

   $$\Delta F380=(\stackrel{-}{F}Ca,Glu-\stackrel{-}{F}Bkg,Glu)-(\stackrel{-}{F}Ca,Base-\stackrel{-}{F}Bkg,Base)$$ [Eq 3.1]
5. Calculate charge transfer ($\mathrm{Q}\mathrm{T}$) (Fig. 4b): $\mathrm{Q}\mathrm{T}$ is defined as the time-integral of the current waveform across the NMDAR-response:

   $$QT={\int }_{t1}^{t2}I\left(t\right)dt$$ [Eq 3.2]

   Where ${\mathrm{t}}_1$ is the time of the glutamate application and ${\mathrm{t}}_2$ is the time following glutamate withdrawal.

6. Repeat steps 1 – 10 on multiple cells using different F/Q calibration extracellular agonist solution perfusion times to generate an F/Q calibration curve (Fig. 4c).

7. Assess data quality. High-quality data will have appreciable ΔF (see Note 10); stable baseline (see Note 11); ΔF:QT Linearity (see Note 12).

8. Between recordings, wipe oil off lens using an ethanol-soaked cotton swab. If oil falls elsewhere on the objective, use an ethanol soaked Kimwipe. Additionally, clean lens with lens-cleaning paper at the end of each experimental day.

Figure 4: Relating fluorescence intensity with ${\mathrm{C}\mathrm{a}}^{2+}$ flux.

(a) Representative fluorometry images used to calculate the difference in fluorescence intensity (ΔF) between baseline (left) and 1mM Glu-evoked ${\mathrm{C}\mathrm{a}}^{2+}$ influx (right) with equation 3.1 at 380 nm light stimulation. (b) Representative NMDA receptor current carried by ${\mathrm{C}\mathrm{a}}^{2+}$ used to calculate charge transfer (Q_T, shaded) with equation 3.2 (c) Correlation between fluorescence intensity shift and charge transfer from data represented in (a) and (b) (n = 5), serves to calibrate experimental conditions where ${\mathrm{C}\mathrm{a}}^{2+}$ is not the only permeant ion (Pf). The slope of a linear regression fitted to the data represents f_max used for Pf(%) estimation in equation 3.4. (d) Representative fluorescent beads imaged at 10x (left) and 40x (right) magnification for calculating 1 BU using equation 3.3.

3.2.4. Bead Unit (BU) Normalization

To account for day-to-day variability in environmental light contamination, as well as hardware wear-and-tear over time, one can also normalize the fluorescence signal to carboxylate microspheres (bead units) using the following protocol.

1. Transfer a coverslip to a coverslip imaging chamber and add 1 – 3 drops of fluorescence beads.

2. Remove excess liquid using a Kimwipe.

3. Switch the objective to the 40x immersion objective and isolate a region where 5 – 10 individual beads are scattered through the field of view.

4. Adjust camera acquisition settings (e.g., laser intensity, exposure time, and gain) such that bead emission intensity is bright, but not saturating.

5. Run imaging recording.

6. Once recording has ended, measure BU as follows (Fig. 4d):

   1. Define ROI_Bead,n: Each ROI should be measured as the perimeter of each bead. Generally, 5 – 8 beads should be averaged to define 1 BU.
   2. Define ROI_Bkg: Once ROI_Bead,n is defined, copy/paste the region into a surrounding background region to account for background fluorescence.
7. Calculate the bead unit as the average of the bead fluorescence minus the background fluorescence:

   $$1BU=\frac{{\sum }_{i=1}^n({\stackrel{-}{F}}_{bead,n}-{\stackrel{-}{F}}_{bkg})}{n}$$ [Eq 3.3]

3.2.5. Measuring Pf

Once the F/Q calibration and BU normalization are complete, fractional permeation experiments can be conducted. These steps essentially mirror those of 3.2.3 but replace F/Q calibration extracellular solutions with Pf extracellular solutions.

1. Prepare cells according to the protocol described in 3.2.2.

2. Begin imaging recording.

3. While imaging recording is running, begin patch-clamp recording using the following protocol:

   1. Perfuse Pf extracellular wash solution onto cell for 10 – 15 s, or until a stable electrical baseline is reached.
   2. Perfuse Pf extracellular agonist solution onto cell for 2 s to obtain the NMDAR macroscopic response. During this time, a noticeable decrease in the fluorescence signal will occur.
   3. Perfuse Pf extracellular wash solution onto cell for 10 – 15 s, or until current returns to baseline.

4. Once recording has ended, measure ΔF using equation [Eq 3.1].

5. Calculate QT using equation [Eq 3.2].

6. Calculate Pf from the following equation:

   $$Pf\left(\mathrm{\%}\right)=100\frac{\Delta F380}{QTfmax}\frac{1}{BU}$$ [Eq 3.4]

   Where ${\mathrm{f}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the slope of the calibration curve generated in 3.2.3 and $\mathrm{B}\mathrm{U}$ is the normalization from 3.2.4.

3.2.6. Converting Pf to ${\mathit{P}}_{\mathit{C}\mathit{a}}/{\mathit{P}}_{\mathit{N}\mathit{a}}$

The fractional permeability method has the key advantage over relative permeability methods of being independent of GHK assumptions. However, it is important to keep in mind that Pf is ultimately a measure of the total ${\mathrm{C}\mathrm{a}}^{2+}$ current (see equation [Eq 2.2]), which depends on both permeability and conductance. For this reason, it is important to convert Pf to ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ when seeking information about permeability properties of the receptor. This can be done with the following protocol:

1. Calculate Pf using the methods outlined in 3.2.5.

2. Additionally, following the patch-fluorometry protocol, measure ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$ by observing the I-V relationship on the same cell using the protocol described in step 5 of 3.1.2. Replace ${\mathrm{C}\mathrm{a}}^{2+}$-wash extracellular solution and ${\mathrm{C}\mathrm{a}}^{2+}$-agonist extracellular solution (2.4.1) with Pf extracellular wash solution and Pf extracellular agonist solution respectively (2.4.2).

3. Calculate ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$ using the protocol in steps 9 – 12 of 3.1.2.

4. Once Pf and ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$ have been obtained, Pf can be converted to ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ using equation [Eq 2.2].

4. Notes

1. In selecting a fluorophore to co-express with the NMDAR, it is important to consider the absorbance-emission properties of the fluorophore against those of the ${\mathrm{C}\mathrm{a}}^{2+}$ dye. For Fura-2, the absorbance spectrum peaks at 340 and 380 nm of light for the ${\mathrm{C}\mathrm{a}}^{2+}$-bound and ${\mathrm{C}\mathrm{a}}^{2+}$-free states respectively (Fig. 5a). However, common fluorophores such as GFP produce contaminating photon emission in this range due to overlap in the absorbance spectrums with Fura-2 (Fig. 5b). For this reason, it is convenient to replace GFP with mCherry, which has no overlapping absorbance with Fura-2 (Fig. 5c).

2. Rectification observed during the glu-ramp step indicates Mg²⁺ contamination. While it is reported that Mg²⁺ does not alter ${\mathrm{C}\mathrm{a}}^{2+}$ permeability [32,33], it can interfere with the accurate calculation of ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$. For more information on deriving reversal potentials from non-Ohmic I-V datasets (see Fig. 5 of Chapter 10 in this edition). This issue can be solved by increasing the concentration of EDTA in solution, or by selecting a NaCl stock of higher purity (>99.9%).

3. Keep in mind that changing the buffer concentration will also impact the free ${\mathrm{C}\mathrm{a}}^{2+}$ concentration. ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$ calculated from shifts in ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}\mathbf{i}\mathbf{s}\mathbf{p}\mathbf{r}\mathbf{o}\mathbf{p}\mathbf{o}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{a}\mathbf{l}\mathbf{t}\mathbf{o}\frac{\left[Na\right]}{4\left[Ca\right]}$ (see equation [Eq 1.3]). Accordingly, it is important to accurately measure the final concentration of free ${\mathrm{N}\mathrm{a}}^{+}$ and ${\mathrm{C}\mathrm{a}}^{2+}$ in the extracellular solutions. For ${\mathrm{N}\mathrm{a}}^{+}$, the final concentration, [${\mathrm{N}\mathrm{a}}^{+}$], will increase when adjusting the pH of solution with NaOH. To account for this, keep record of the exact volume (and concentration) of NaOH added to solution.

4. Total free ${\mathrm{C}\mathrm{a}}^{2+}$ will be dependent on the concentration of CaCl₂ and the buffering capacity of divalent buffers (EGTA, EDTA, BAPTA, etc.) in solution. For accurate estimations of total free ${\mathrm{C}\mathrm{a}}^{2+}$, we use the software MaxChelator (https://somapp.ucdmc.ucdavis.edu/pharmacology/bers/maxchelator/webmaxc/webmaxcS.htm).

5. Baseline instability will cause non-linearity during the voltage ramps and/or inaccurate leak-subtraction; both can ultimately skew the final ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$ calculation. This issue can be solved by allowing additional time between the formation of the whole-cell configuration and the beginning of the recording to allow stabilization of the gigaseal.

6. I_ss maintained after ramp_Glu: I_ss amplitudes differing before and after the voltage ramp indicates issues in baseline/seal stability, and/or that the NMDAR response prior to the ramp_Glu step had not reached a steady-state amplitude. This issue can be solved by ensuring I_ss has been reached prior to the ramp step.

7. For additional accuracy in measuring ${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{v}}$, the liquid junction potential (LJP) should be monitored using the amplifier pipette-offset across the exchange of solutions relative to a high-${\mathrm{K}}^{+}$ reference. The LJP will increase linearly with increasing [${\mathrm{C}\mathrm{a}}^{2+}$], assuming extracellular monovalent concentrations are held constant between conditions (i.e., the high monovalent method). For the protocol described in this chapter, the LJP difference between ${\mathrm{C}\mathrm{a}}^{2+}$-free and ${\mathrm{C}\mathrm{a}}^{2+}$-containing solutions is estimated to be < 1 mV so long as [${\mathrm{C}\mathrm{a}}^{2+}$] < 10 mM. It is worth noting that the solution exchange of the bi-ionic protocol generates a substantially higher (> 10 mV) LJP [15]. For this reason, it is critical to account for LJP if using the bi-ionic method.

8. One can also calculate ${\mathrm{C}\mathrm{a}}^{2+}$ permeability from the activity (γ_X) of permeant ions rather than the concentration ([X]). The GHK and Lewis equations were originally derived from ionic concentrations, however accounting for ionic activity provides additional accuracy in permeability calculations. For a comprehensive review of ionic activity, see [34].

   The Davies equation ([Eq 4.1]) can be used to calculate γ_X for solutions of an ionic strength up to 0.5, making it appropriate for both physiological and non-physiological solutions.

   $$\log \left(\gamma \pm \right)=-A{z}^2\left(\frac{\sqrt{I}}{1+\sqrt{I}}-0.3I\right)$$ [Eq 4.1]
   Where $\mathrm{A}=0.51$ for water at 25°C, $\mathrm{z}$ is the ionic valence, and I is the total ionic strength of the solution. Due to the divalence of ${\mathrm{C}\mathrm{a}}^{2+}$, the mean activity coefficient for CaCl₂ is:

   $$\gamma \text{CaCl2}=\sqrt[3]{\gamma \text{Ca}{\gamma \text{Cl}}^2}$$ [Eq 4.2]
   The ionic activity of ${\mathrm{C}\mathrm{a}}^{2+}$ can then be calculated from equation [Eq 4.2] using either the Shatkay (4.3) or Guggenheim convention (4.4)

   $$\gamma \text{Ca}\text{=}\gamma \text{CaCl2}$$ [Eq 4.3]

   $$\gamma \text{Ca}\text{=}{\gamma \text{CaCl2}}^2$$ [Eq 4.4]

   Under physiological conditions, we calculate ${\mathrm{\gamma }}_{\mathrm{N}\mathrm{a}}=0.76$ and ${\mathrm{\gamma }}_{\mathrm{C}\mathrm{a}}=0.58$ with equation [Eq 4.3] or ${\mathrm{\gamma }}_{\mathrm{C}\mathrm{a}}=0.32$ with equation [Eq 4.4]. To apply activity coefficients to the calculation of ${\mathrm{P}}_{\mathrm{C}\mathrm{a}}/{\mathrm{P}}_{\mathrm{N}\mathrm{a}}$, multiply [${\mathrm{N}\mathrm{a}}^{+}$] and [${\mathrm{C}\mathrm{a}}^{2+}$] of equation [Eq 1.3] or [Eq 1.4] by ${\mathrm{\gamma }}_{\mathrm{N}\mathrm{a}}$ and ${\mathrm{\gamma }}_{\mathrm{C}\mathrm{a}}$ respectively.

9. Another powerful method for assessing the ${\mathrm{C}\mathrm{a}}^{2+}$ flux through NMDARs is through the use of genetically encoded ${\mathrm{C}\mathrm{a}}^{2+}$ indicators (GECIs). While this approach cannot provide direct quantitative information on receptor permeability, GECIs have the benefit of assaying NMDAR-expressing cells on a population level rather than having to rely on single-cell recordings. Förster Resonance Energy Transfer (FRET) based GECIs have the additional advantage of being able to quantify the absolute change in cytosolic free ${\mathrm{C}\mathrm{a}}^{2+}$ upon NMDAR stimulation. For additional information on GECIs, we direct the reader to [35,36].

10. The incubation step can also be done overnight.

11. Lack of a fluorescence change can be due to several factors: improper loading of Fura-2, low ${\mathrm{C}\mathrm{a}}^{2+}$ influx due to small current density and/or photobleaching of the internal solution to name a few. This should only cause concern if the issue persists across multiple cells. This issue can be solved in a number of ways. First, ensure that Fura-2 is fully loaded into the cell and that the acquisition settings are not saturated. If using a recombinant system, increasing the DNA concentration in the transfection mix to increase NMDAR expression can increase the overall current density. If these do not solve the issue, increase the driving force for ${\mathrm{C}\mathrm{a}}^{2+}$ influx by decreasing the holding potential (e.g., −100 mV) and/or by increasing the concentration of ${\mathrm{C}\mathrm{a}}^{2+}$ in the extracellular solution.

12. Baseline instability can be caused by poor seal stability, ${\mathrm{C}\mathrm{a}}^{2+}$ leak, or photobleaching of Fura-2. For both electrophysiological and fluorometry data, a stable baseline preceding the application of glutamate ensures that QT and ΔF are accurately estimated. This issue can be solved by allowing additional time between the formation of the whole-cell configuration and the beginning of the recording to allow stabilization of the gigaseal.

13. The relationship between QT and ΔF is linear (Fig. 4c) [21]. Therefore, if there is a nonlinear relationship between measured QT and ΔF, all calculations of Pf in subsequent experiments will be incorrect. This is most commonly due to issues in measuring ΔF. This issue can be solved with the same troubleshooting as in Note 10.

Figure 5: Fluorophore selection for minimal background fluorescence.

(a) Absorbance-emission spectra of Fura-2 in the ${\mathrm{C}\mathrm{a}}^{2+}$-free and ${\mathrm{C}\mathrm{a}}^{2+}$-bound state. (b) Absorbance-emission spectra of GFP and EGFP partially overlap with the Fura-2 spectrum. The filled green curve represents the averaged emission spectrum of GFP and EGFP (c) Absorbance-emission spectra of mCherry and RFP are distinct from the Fura-2 spectrum. Dashed lines represent absorbance range; filled areas represent emission range. Red lines mark excitation wavelengths commonly used during ${\mathrm{C}\mathrm{a}}^{2+}$ fluorometry recordings, 340 nm and 380 nm. Data reproduced from https://www.aatbio.com/fluorescence-excitation-emission-spectrum-graph-viewer