Liquid Junction Potential (LJP) Theory and Correction
This page contains notes about the analytical methods LJPcalc uses to calculate LJP from ion tables as well as notes for experimenters about what causes LJP and how to compensate for it in electrophysiology experiments.
Table of Contents
LJP Calculation Notes
LJPcalc Calculation Method
LJPcalc calculates the liquid junction potential according to the stationary NernstPlanck equation which is typically regarded as superior to the simpler Henderson equation used by most commercial LJP calculators. Both equations produce nearly identical LJPs, but the Henderson equation becomes inaccurate as ion concentrations increase, and also when calculating LJP for solutions containing polyvalent ions.
LJPcalc Ion Mobility Library
LJPcalc uses an extensive ion mobility library
The ion mobility table is stored in Markdown format. Not only does Markdown make it easy to display the table nicely in a browser,
but it also makes the table easy to edit in any text editor. Users desiring to use their own ion mobilities or add new ions to the table
can do so by editing the IonTable.md
file adjacent to LJPcalc.exe
as needed.
Influence of Ion Sequence on Calculated LJP
💡 LJPcalc automatically sorts the ion table into an ideal sequence prior to solving for LJP. Attention only needs to be paid to the ion sequence if automatic sorting is disabled.
When calculating LJP for a set of ions it is important to consider the sequence in which they are listed. Additional information can be found in Marino et al., 2014 which describes the exact computational methods employed by LJPcalc.

The last ion's c0 may be overridden to achieve electroneutrality on the c0 side. This will not occur if the sum of charge on the c0 side is zero.

cL for most ions will be slightly adjusted to achieve electroneutrality on the cL side. The secondtolast ion's cL (which cannot equal its c0) will remain fixed, while the last cL will be adjusted to achieve electroneutrality. During the solving process all cL values (but the secondfromlast) will be slightly adjusted. The adjustments are likely negligible experimentally, but this is why cL values in the output table slightly differ from those given for inputs.
Effect of Temperature on LJP
The LJP is temperature dependent. There are two sources of temperaturedependent variation: the Einstein relation and the conductivity table. The former can be easily defined at calculation time, while the latter requires modifying conductances in the ion mobility table. These modifications typically have a small effect on the LJP, so standard temperature (25C) can be assumed for most applications.
The Einstein relation defines diffusion as D = µ * k * T
where:
D
is the diffusion coefficientµ
(mu) is ionic mobilityk
is the Boltzmann constant (1.380649e23 J / K)T
is temperature (K)
The ion conductivity table is temperaturespecific. Ion conductivity was measured experimentally and varies with temperature. The ion conductivity table here assumes standard temperature (25C), but ion conductivity values can be found for many ions at nonstandard temperatures. LJPcalc users desiring to perform LJP calculations at nonstandard temperatures are encouraged to build their own temperaturespecific ion tables.
Calculating Ionic Mobility from Charge and Conductivity
Ionic mobility is µ = Λ / (N * e² * z)
where:
µ
(mu) is ionic mobility (m² / V / sec)Λ
(Lambda) is molar conductivity (S * cm²/ mol)N
is the Avogadro constant (6.02214076e23 particles / mol)e
is the elementary charge (1.602176634e19 Coulombs)z
is the absolute value of the elementary charge of the ion
How to Correct for LJP in Electrophysiology Experiments
Patchclamp electrophysiologists impale cells with glass microelectrodes to measure or clamp their voltage. Amplifier offset voltage is adjusted to achieve a reading of zero volts when the pipette is in opentip configuration with the bath, but this voltage includes offset for a liquid junction potential (LJP) caused by the free exchange of ions with different mobilities between the pipette and bath solutions. Wholecell patchclamp experiments typically fill the pipette with large anions like gluconate, aspartate, or methanesulfonate, and their low mobility (relative to ions like K, Na, and Cl) causes them to accumulate in the pipette and produce a LJP (where the bath is more positive than then pipette). After establishment of wholecell configuration, ions no longer freely move between pipette and bath solutions (they are separated by the cell membrane), so there is effectively no LJP but the offset voltage is still offsetting as if LJP were present. By knowing the LJP, the scientist can adjust offset voltage to compensate for it, resulting in more accurate measured and clamped voltages.
V_{meter} = V_{cell} + LJP
To correct for LJP, the electrophysiologist must calculate LJP mathematically (using software like LJPcalc) or estimate it experimentally (see the section on this topic below). Once the LJP is known it can be compensated for experimentally to improve accuracy of recorded and clamped voltages.
V_{cell} = V_{meter}  LJP
⚠️ This method assumes that the amplifier voltage was zeroed at the start of the experiment when the pipette was in opentip configuration with the bath, and that concentration of chloride (if using Ag/AgCl electrodes) in the internal and bath solutions are stable throughout experiments.
Example PatchClamp LJP Calculation & Correction
This ion set came from in Figl et al., 2003 Page 8. They have been loaded into LJPcalc such that the pipette solution is c0 and the bath solution is cL. Note that the order of ions has been adjusted to place the most abundant two ions at the bottom. This is ideal for LJPcalc's analytical method.
Name  Charge  pipette (mM)  bath (mM) 

K  +1  145  2.8 
Na  +1  13  145 
Mg  +2  1  2 
Ca  +2  0  1 
HEPES  1  5  5 
Gluconate  1  145  0 
Cl  1  10  148.8 
Loading this table into LJPcalc produces the following output:
Values for cL were adjusted to achieve electroneutrality:
Name  Charge  Conductivity (E4)  C0 (mM)  CL (mM)

K  +1  73.5  145  2.8098265
Na  +1  50.11  13  144.9794365
Mg  +2  53.06  1  1.9998212
Ca  +2  59.5  0  0.9999109
HEPES  1  22.05  5  4.9990023
Gluconate  1  24.255  145  0
Cl  1  76.31  10  148.789725
Equations were solved in 88.91 ms
LJP at 20 C (293.15 K) = 16.052319631180264 mV
💡 Figl et al., 2003 Page 8 calculated a LJP of 15.6 mV for this ion set (720 µV lesser magnitude than our calculated LJP). As discussed above, differences in ion mobility table values and use of the NernstPlanck vs. Henderson equation can cause commercial software to report values slightly different than LJPcalc. Experimentally these small differences are negligible, but values produced by LJPcalc are assumed to be more accurate. See Marino et al., 2014 for discussion.
If we have patchclamp data that indicates a neuron rests at 48.13 mV, what is its true resting potential? Now that we know the LJP, we can subtract it from our measurement:
V_{cell} = V_{measured}  LJP
V_{cell} = 48.13  16.05 mV
V_{cell} = 64.18 mV
We now know our cell rests at 64.18 mV.
Zeroed Voltage = LJP + Two Electrode HalfCell Potentials
The patchclamp amplifier is typically zeroed at the start of every experiment when the patch pipette is in opentip configuration with the bath solution. An offset voltage (V_{offset}) is applied such that the V_{measured} is zero. This process incorporates 3 potentials into the offset voltage:
 liquid junction potential (LJP) between the pipette solution and the bath solution (mostly from small mobile ions)
 halfcell potential (HCP) between the reference electrode and the bath solution (mostly from Cl)
 halfcell potential (HCP) between the recording electrode and the pipette solution (mostly from Cl)
When the amplifier is zeroed before to experiments, all 3 voltages are incorporated into the offset voltage. Since the LJP is the only one that changes after forming wholecell configuration with a patched cell (it is eliminated), it is the only one that needs to be known and compensated for to achieve a true zero offset (the rest remain constant).
However, if the [Cl] of the internal or bath solutions change during the course of an experiment (most likely to occur when an Ag/AgCl pellet is immersed in a flowing bath solution), the halfcell potentials become significant and affect V_{measured} as they change. This is why agar bridge references are preferred over Ag/AgCl pellets. See Figl et al., 2003 for more information about LJPs as they relate to electrophysiological experiments.
Measuring LJP Experimentally
It is possible to measure LJP experimentally, but this technique is often discouraged because issues with KCl reference electrodes make it difficult to accurately measure (Barry and Diamond, 1970). However, experimental measurement may be the only option to calculate LJP for solutions containing ions with unknown mobilities.
To measure LJP Experimentally:
• Step 1: Zero the amplifier with intracellular solution in the bath and in your pipette
• Step 2: Replace the bath with extracellular solution
• Step 3: The measured voltage is the negative LJP (invert its sign to get LJP)
✔️ Confirm no drift is present by replacing the bath with intracellular solution after step 3 to verify the reading is 0. If it is not 0, some type of drift is occurring and the measured LJP is not accurate.
❓ Why invert the sign of the LJP? The LJP measured in step 2 is the LJP of the pipette relative to the bath, but in electrophysiology experiments convention is to refer to LJP as that of the bath relative to the pipette. LJPs for experiments using typical ACSF bath and physiological Kgluconate pipette solutions are usually near +15 mV.
⚠️ Do not measure LJP using a Ag/AgCl reference electrode! because mobility will be low when the bath is filled with intracellular solution (physiological intracellular solutions have low [Cl]). Use a 3M KCl reference electrode instead, allowing high [K] mobility in intracellular solution and high [Cl] mobility in extracellular solution.
References

Marino et al. (2014)  describes a computational method to calculate LJP according to the stationary NernstPlanck equation. The JAVA software described in this manuscript is opensource and now on GitHub (JLJP). Figure 1 directly compares LJP calculated by the NernstPlanck vs. Henderson equation.

Perram and Stiles (2006)  A review of several methods used to calculate liquid junction potential. This manuscript provides excellent context for the history of LJP calculations and describes the advantages and limitations of each.

Shinagawa (1980) "Invalidity of the Henderson diffusion equation shown by the exact solution of the NernstPlanck equations"  a manuscript which argues that the Henderson equation is inferior to solved NernstPlanckPoisson equations due to how it accounts for ion flux in the charged diffusion zone.

Lin (2011) "The Poisson The PoissonNernstPlanck (PNP) system for ion transport (PNP) system for ion transport"  a PowerPoint presentation which reviews mathematical methods to calculate LJP with notes related to its application in measuring voltage across cell membranes.

NernstPlanck equation (Wikipedia)

Goldman Equation (Wikipedia)

EGTA charge and pH  Empirical determination of EGTA charge state distribution as a function of pH.

LJPCalcWin  A Program for Calculating Liquid Junction Potentials

LJP Corrections (Axon Instruments Application Note) describes how to calculate LJP using ClampEx and LJPCalcWin and also summarizes how to measure LJP experimentally

LJP Corrections (Figl et al., AxoBits 39) summarizes LJP and discusses measurement and calculation with ClampEx
 title: LJPcalc  Liquid Junction Potential Theory and Correction description: What causes LJPs and how to correct for them in patchclamp experiments  # Liquid Junction Potential (LJP) Theory and Correction This page contains notes about the analytical methods LJPcalc uses to calculate LJP from ion tables as well as notes for experimenters about what causes LJP and how to compensate for it in electrophysiology experiments. ## Table of Contents ![](TOC) ## LJP Calculation Notes ### LJPcalc Calculation Method LJPcalc calculates the liquid junction potential according to the stationary NernstPlanck equation which is typically regarded as superior to the simpler Henderson equation used by most commercial LJP calculators. Both equations produce nearly identical LJPs, but the Henderson equation becomes inaccurate as ion concentrations increase, and also when calculating LJP for solutions containing polyvalent ions. ### LJPcalc Ion Mobility Library LJPcalc uses an extensive [ion mobility library](../iontable) The ion mobility table is stored in Markdown format. Not only does Markdown make it easy to display the table nicely in a browser, but it also makes the table easy to edit in any text editor. Users desiring to use their own ion mobilities or add new ions to the table can do so by editing the `IonTable.md` file adjacent to `LJPcalc.exe` as needed. ### Influence of Ion Sequence on Calculated LJP > 💡 LJPcalc automatically sorts the ion table into an ideal sequence prior to solving for LJP. Attention only needs to be paid to the ion sequence if automatic sorting is disabled. When calculating LJP for a set of ions it is important to consider the sequence in which they are listed. Additional information can be found in [Marino et al., 2014](https://arxiv.org/abs/1403.3640) which describes the exact computational methods employed by LJPcalc. * **The last ion's c0 may be overridden** to achieve electroneutrality on the c0 side. This will not occur if the sum of charge on the c0 side is zero. * **cL for most ions will be slightly adjusted** to achieve electroneutrality on the cL side. The secondtolast ion's cL (which cannot equal its c0) will remain fixed, while the last cL will be adjusted to achieve electroneutrality. During the solving process all cL values (but the secondfromlast) will be slightly adjusted. The adjustments are likely negligible experimentally, but this is why cL values in the output table slightly differ from those given for inputs. ### Effect of Temperature on LJP **The LJP is temperature dependent.** There are two sources of temperaturedependent variation: the Einstein relation and the conductivity table. The former can be easily defined at calculation time, while the latter requires modifying conductances in the ion mobility table. These modifications typically have a small effect on the LJP, so standard temperature (25C) can be assumed for most applications. **The [Einstein relation](https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory))** defines diffusion as **`D = µ * k * T`** where: * **`D`** is the diffusion coefficient * **`µ`** (mu) is [ionic mobility](https://en.wikipedia.org/wiki/Electrical_mobility) * **`k`** is the [Boltzmann constant](https://en.wikipedia.org/wiki/Boltzmann_constant) (1.380649e23 J / K) * **`T`** is temperature (K) **The ion conductivity table is temperaturespecific.** Ion conductivity was measured experimentally and varies with temperature. The ion conductivity table here assumes standard temperature (25C), but ion conductivity values can be found for many ions at nonstandard temperatures. LJPcalc users desiring to perform LJP calculations at nonstandard temperatures are encouraged to build their own temperaturespecific ion tables. ### Calculating Ionic Mobility from Charge and Conductivity Ionic mobility is **`µ = Λ / (N * e² * z)`** where: * **`µ`** (mu) is [ionic mobility](https://en.wikipedia.org/wiki/Electrical_mobility) (m² / V / sec) * **`Λ`** (Lambda) is [molar conductivity](https://en.wikipedia.org/wiki/Molar_conductivity) (S * cm²/ mol) * **`N`** is the [Avogadro constant](https://en.wikipedia.org/wiki/Avogadro_constant) (6.02214076e23 particles / mol) * **`e`** is the [elementary charge](https://en.wikipedia.org/wiki/Elementary_charge) (1.602176634e19 Coulombs) * **`z`** is the absolute value of the [elementary charge](https://en.wikipedia.org/wiki/Elementary_charge) of the ion ## How to Correct for LJP in Electrophysiology Experiments Patchclamp electrophysiologists impale cells with glass microelectrodes to measure or clamp their voltage. Amplifier offset voltage is adjusted to achieve a reading of zero volts when the pipette is in opentip configuration with the bath, but this voltage includes offset for a _liquid junction potential_ (LJP) caused by the free exchange of ions with different mobilities between the pipette and bath solutions. Wholecell patchclamp experiments typically fill the pipette with large anions like gluconate, aspartate, or methanesulfonate, and their low mobility (relative to ions like K, Na, and Cl) causes them to accumulate in the pipette and produce a LJP (where the bath is more positive than then pipette). After establishment of wholecell configuration, ions no longer freely move between pipette and bath solutions (they are separated by the cell membrane), so there is effectively no LJP but the offset voltage is still offsetting as if LJP were present. By knowing the LJP, the scientist can adjust offset voltage to compensate for it, resulting in more accurate measured and clamped voltages. <p align="center">V<sub>meter</sub> = V<sub>cell</sub> + LJP</p> **To correct for LJP,** the electrophysiologist must calculate LJP mathematically (using software like LJPcalc) or estimate it experimentally (see the section on this topic below). Once the LJP is known it can be compensated for experimentally to improve accuracy of recorded and clamped voltages. <p align="center">V<sub>cell</sub> = V<sub>meter</sub>  LJP</p> > ⚠️ This method assumes that the amplifier voltage was zeroed at the start of the experiment when the pipette was in opentip configuration with the bath, and that concentration of chloride (if using Ag/AgCl electrodes) in the internal and bath solutions are stable throughout experiments. <div align="center"> ![](../graphics/ljp.png) </div> ### Example PatchClamp LJP Calculation & Correction This ion set came from in [Figl et al., 2003](https://medicalsciences.med.unsw.edu.au/sites/default/files/soms/page/ElectroPhysSW/AxoBits39New.pdf) Page 8. They have been loaded into LJPcalc such that the pipette solution is c0 and the bath solution is cL. Note that the order of ions has been adjusted to place the most abundant two ions at the bottom. This is ideal for LJPcalc's analytical method. Name  Charge  pipette (mM)  bath (mM)  K  +1  145  2.8 Na  +1  13  145 Mg  +2  1  2 Ca  +2  0  1 HEPES  1  5  5 Gluconate  1  145  0 Cl  1  10  148.8 Loading this table into LJPcalc produces the following output: ``` Values for cL were adjusted to achieve electroneutrality: Name  Charge  Conductivity (E4)  C0 (mM)  CL (mM)  K  +1  73.5  145  2.8098265 Na  +1  50.11  13  144.9794365 Mg  +2  53.06  1  1.9998212 Ca  +2  59.5  0  0.9999109 HEPES  1  22.05  5  4.9990023 Gluconate  1  24.255  145  0 Cl  1  76.31  10  148.789725 Equations were solved in 88.91 ms LJP at 20 C (293.15 K) = 16.052319631180264 mV ``` > 💡 _[Figl et al., 2003](https://medicalsciences.med.unsw.edu.au/sites/default/files/soms/page/ElectroPhysSW/AxoBits39New.pdf) Page 8 calculated a LJP of 15.6 mV for this ion set (720 µV lesser magnitude than our calculated LJP). As discussed above, differences in ion mobility table values and use of the NernstPlanck vs. Henderson equation can cause commercial software to report values slightly different than LJPcalc. Experimentally these small differences are negligible, but values produced by LJPcalc are assumed to be more accurate. See [Marino et al., 2014](https://arxiv.org/abs/1403.3640) for discussion._ If we have patchclamp data that indicates a neuron rests at 48.13 mV, what is its true resting potential? Now that we know the LJP, we can subtract it from our measurement: <p align="center">V<sub>cell</sub> = V<sub>measured</sub>  LJP</p> <p align="center">V<sub>cell</sub> = 48.13  16.05 mV</p> <p align="center">V<sub>cell</sub> = 64.18 mV</p> We now know our cell rests at 64.18 mV. ### Zeroed Voltage = LJP + Two Electrode HalfCell Potentials The patchclamp amplifier is typically zeroed at the start of every experiment when the patch pipette is in opentip configuration with the bath solution. An offset voltage (V<sub>offset</sub>) is applied such that the V<sub>measured</sub> is zero. This process incorporates 3 potentials into the offset voltage: * **liquid junction potential (LJP)** between the **pipette** solution and the **bath** solution (mostly from small mobile ions) * **halfcell potential (HCP)** between the **reference electrode** and the **bath** solution (mostly from Cl) * **halfcell potential (HCP)** between the **recording electrode** and the **pipette** solution (mostly from Cl) When the amplifier is zeroed before to experiments, all 3 voltages are incorporated into the offset voltage. Since the LJP is the only one that changes after forming wholecell configuration with a patched cell (it is eliminated), it is the only one that needs to be known and compensated for to achieve a true zero offset (the rest remain constant). However, if the [Cl] of the internal or bath solutions change during the course of an experiment (most likely to occur when an Ag/AgCl pellet is immersed in a flowing bath solution), the halfcell potentials become significant and affect V<sub>measured</sub> as they change. This is why agar bridge references are preferred over Ag/AgCl pellets. See [Figl et al., 2003](https://medicalsciences.med.unsw.edu.au/sites/default/files/soms/page/ElectroPhysSW/AxoBits39New.pdf) for more information about LJPs as they relate to electrophysiological experiments. ### Measuring LJP Experimentally It is possible to measure LJP experimentally, but this technique is often discouraged because issues with KCl reference electrodes make it difficult to accurately measure ([Barry and Diamond, 1970](https://link.springer.com/article/10.1007/BF01868010)). However, experimental measurement may be the only option to calculate LJP for solutions containing ions with unknown mobilities. **To measure LJP Experimentally:**<br> • **Step 1:** Zero the amplifier with intracellular solution in the bath and in your pipette<br> • **Step 2:** Replace the bath with extracellular solution<br> • **Step 3:** The measured voltage is the negative LJP (invert its sign to get LJP) > **✔️ Confirm no drift is present** by replacing the bath with intracellular solution after step 3 to verify the reading is 0. If it is not 0, some type of drift is occurring and the measured LJP is not accurate. > **❓ Why invert the sign of the LJP?** The LJP measured in step 2 is the LJP of the _pipette_ relative to the _bath_, but in electrophysiology experiments convention is to refer to LJP as that of the _bath_ relative to the _pipette_. LJPs for experiments using typical ACSF bath and physiological Kgluconate pipette solutions are usually near +15 mV. > **⚠️ Do not measure LJP using a Ag/AgCl reference electrode!** because mobility will be low when the bath is filled with intracellular solution (physiological intracellular solutions have low [Cl]). Use a 3M KCl reference electrode instead, allowing high [K] mobility in intracellular solution and high [Cl] mobility in extracellular solution. ## References * **[Marino et al. (2014)](https://arxiv.org/abs/1403.3640)**  describes a computational method to calculate LJP according to the stationary NernstPlanck equation. The JAVA software described in this manuscript is opensource and now on GitHub ([JLJP](https://github.com/swharden/jljp)). Figure 1 directly compares LJP calculated by the NernstPlanck vs. Henderson equation. * **[Perram and Stiles (2006)](https://pubs.rsc.org/en/content/articlelanding/2006/cp/b601668e)**  A review of several methods used to calculate liquid junction potential. This manuscript provides excellent context for the history of LJP calculations and describes the advantages and limitations of each. * **[Shinagawa (1980)](https://www.ncbi.nlm.nih.gov/pubmed/7401663)** _"Invalidity of the Henderson diffusion equation shown by the exact solution of the NernstPlanck equations"_  a manuscript which argues that the Henderson equation is inferior to solved NernstPlanckPoisson equations due to how it accounts for ion flux in the charged diffusion zone. * **[Lin (2011)](http://www.sci.osakacu.ac.jp/~ohnita/2010/TCLin.pdf)** _"The Poisson The PoissonNernstPlanck (PNP) system for ion transport (PNP) system for ion transport"_  a PowerPoint presentation which reviews mathematical methods to calculate LJP with notes related to its application in measuring voltage across cell membranes. * **[NernstPlanck equation](https://en.wikipedia.org/wiki/Nernst%E2%80%93Planck_equation)** (Wikipedia) * **[Goldman Equation](https://en.wikipedia.org/wiki/Goldman_equation)** (Wikipedia) * **[EGTA charge and pH](https://www.sciencedirect.com/science/article/pii/S0165027099000369?via%3Dihub#FIG1)**  Empirical determination of EGTA charge state distribution as a function of pH. * **[LJPCalcWin](https://medicalsciences.med.unsw.edu.au/sites/default/files/soms/page/ElectroPhysSW/JPCalcWinDemo%20Manual.pdf)**  A Program for Calculating Liquid Junction Potentials * **[LJP Corrections](http://beenhakkerlab.org/lablinks/ephys/Guides/Theory/LiquidJunctionPotentialCorrectionsAxon.pdf)** (Axon Instruments Application Note) describes how to calculate LJP using ClampEx and LJPCalcWin and also summarizes how to measure LJP experimentally * **[LJP Corrections](https://medicalsciences.med.unsw.edu.au/sites/default/files/soms/page/ElectroPhysSW/AxoBits39New.pdf)** (Figl et al., AxoBits 39) summarizes LJP and discusses measurement and calculation with ClampEx