Sources:

Hille: Ionic Channels of Excitable Membranes ---Chap 10

Robinson & Stokes - ‘Electrolyte Solutions’, Butterworth, 1958.

J Koryta: Ions Electrodes and Membranes, Wiley 2nd ed 1991

Tables of coefficients in eg CRC ‘Rubber Book’ and chemical ref books

Definitions:

Concentration scales mole - molecular weight in grammes

Molar - moles/litre of solution

Molal - moles/ kg solvent

Mole fraction moles solute/(moles solute + moles solvent)

Osmolality osmoles/kg solvent – quantifies

transmembrane water movement

Ionic strength For solutions of inorganic ions and small organic ions

I = 0.5*z2c z=valence, c= molar concn

Equilibrium constants, reaction rates and activity coefficients are specified

at particular ionic strengths. For mammalian physiological saline I = 0.150

ELECTROLYTE SOLUTIONS

Dissociation of salts into Ions:

AxBy xAy+ + yBx-

Strong electrolytes – at low concentration have complete dissociation in water into

independent ions e.g. NaCl, KCl, CaCl2 , strong acids, strong bases

Weak electrolytes - Partial dissociation even at low concentration

e.g. divalent metal phosphates, carbonates, sulphates, gluconate

pH buffers at pH near pK- H2PO4- , HCO3

-, HEPES- , proteins

Divalent cation buffers - MgATP, Ca-Calmodulin, EGTA, Ca Indicators

Endogenous binding proteins

Strong electrolytes- properties

Ions in free solution diffuse independently – current carried by each ion species

can be calculated from individual conductivities and concentrations.

Interactions between ions in solution are weak.

1 equivalent of ions of any species carries the same charge

- Faraday F = 96486 coulombs/equiv; 1 equiv is the atomic mass/valency

Hydration of Ions:

Free ions associate with water to form hydration shells- this is seen as :

(1) slowed diffusion compared with calculations based on atomic size,

(2) proton NMR spectra of water are modified by ions in solution,

association time for exchange of waters in hydration shell estimated as 1nsec.

(3) Hydration energy measured for NaCl in solution is similar to the energy

calculated for the spacing of Na+ Cl- ions in NaCl crystals, there is little energy

associated with dissolving salts in water - hydration favours aqueous solution.

Strong electrolytes

Water molecules have loose dipolar interactions with exchange times ~1ps

Interactions with ions are stronger – lifetimes in the hydration shell are 0.1-10 ns for

Na, K, Ca ions – Mg is longer 10 µs

Strong electrolytes

Interactions between ions in solution - ion activities:

Mean separation of Na+ ,Cl- ions in solutions of concn:

1mM -10 nm 10 mM - 4.4 nm 100 mM - 2 nm 1M - 0.9 nm

As concentration increases association between anions and cations increases.

Interactions are specified by using ‘Activities’ a rather than concentrations and by

‘Activity coefficients’ that multiply concentration a= .c

Activity coefficient depends on concentration - NaCl decreases from 1 at infinite

dilution to minimum 0.65 as NaCl concentration increases up to 1.2 M, then

increases to 0.98 as concentration increases further to 6 M.

Ionic conditions that affect interactions in a solution are specified by the ‘Ionic

Strength’

I = 0.5*z2.c z=valence, c= molar concn

Ion activities and activity coefficients

Activity a = .c is activity coeff c is concn

Activity a has same units as concn c - molar, molal, or mole fraction.

Activity difference for an ion between two solutions can be measured electrochemically

with an ion selective electrode

ERT

ZF

a

a2 1

2

1

ln

•Activity coeff depends on concn units used - often tabulated for molal concentrations.

Because of interactions between ions, depends on both ion concn and on the species

of counter-ions present -

•It is specified for ions of particular salts - Na is different for Na in salts with different

anions because of interaction between anions and Na.

•Activity coefficients of physiological ions are tabulated for most common salts.

Units: J/Coulomb = Volts

Exponential decay of potential away from a charge in solution depends on ionic strength

has characteristic Debye length of 0.78 nm in mammalian solution.

Osmotic effects - Interactions between solute and solvent

Osmotic properties - Solvent activity

The solute affects the activity of the solvent – solvent activity measured by osmotic

properties of the solution.

Both ionic and non-ionic solutes affect the activity of the solvent - solutions with low

solute activity have high solvent activity.

Solvent activity determines: osmotic pressure, vapour pressure, boiling and freezing

temperatures. Osmometers measure one of these, usually vapour pressure or freezing

point

At equilibrium water activities are equal on both sides of a cell membrane,

differences imposed by changing extracelluar ions are reduced quickly – in seconds- by

water movement and consequent change in cell volume,

more slowly – in minutes- by redistribution of ions across membrane.

Osmotic pressure - pressure difference required on one side of a rigid semi-permeable

membrane - permeable to solvent but not solute- to prevent net water movement from

the other side.

Solutions of equal osmotic pressure (tension) are Iso-osmotic or Isotonic

Water activity is quantified by osmolality.

Osmolality = x molal concns of solutes; are osmotic coefficients

Units : osmols/kg solvent .

Measured usually from vapour pressure generated by the solution, or by the

depression of freezing point.

Mammalian solutions are approx 300 mosmol/kg

Sea water approx 1000 mosm/kg

Extracellular and intracellular solutions should have similar osmolality.

Isotonic substitution of ions can be made if osmotic coefficients are known and

appropriate concentration scales used. Osmotic coefficients are tabulated (usually

for molal concns) e.g. in Robinson and Stokes or chemical reference books.

Osmolality of internal and external solns should always be measured .

Amplifier reference potential

Grounding

point

Connecting electronics

to the solution and cell

Reversible AgCl

electrodes avoid

polarisation

Junction potentials,

‘Tip’ potentials

R D Purves 1981 ‘Microelectrode methods for Intracellular recording and Iontophoresis’

Academic Press

Mechanical

stability

Liquid junction potentials

Liquid Junction Potential (LJP) errors in patch recording

Due to differences of ion concentrations and mobilities across pipette tip

- give rise to an offset error in the membrane potential recorded.

Ion Mobilities are different : e.g. K+ > Na+, Cl- > Gluconate-

Before sealing

Pipette loses K+ faster than gaining

Na+ and gains Cl- faster than losing

Gluc-

At zero current :

net movement of charge prevented

by negative offset potential applied

to pipette (pipette – bath)

On sealing:

Junction potential disappears

- Offset potential remains

Membrane potential error :

Cell attached:

Transmembrane patch potential =

Resting Vm -’command Vm’ - offset

Whole cell recording:

Membrane pot =

‘command Vm’ + offset

Na+ Cl-

Offset

Potential

(hidden)

150 mM

150 mM

Na+ Cl-

150 mM

150 mM

‘Vm’

Offset

Potential

‘Vm’

Command

(displayed)

Command

3M KCl Pipette Soln

0 mV

3M KCl Pipette Soln

- LJP

External

solution

1. Set up 3M KCl pipette as reference

with pipette solution in pipette and bath.

Both junctions have zero LJP

Set pipette voltage to zero mV

in current clamp (zero current)

2. Change solution in bath for external.

Potential change pipette-bath is recorded in

current clamp, due to potential developed at

pipette/bath junction. Check reversibility.

LJP measurement: Neher 1992 Meth Enzy 207, 123 : Measurement of LJPs

Need an error-free reference-

Flowing 3M KCl junction has zero LJP against dilute 150 mM solutions of any ion

Potential change recorded on changing from pipette soln (0 mV) to external soln is the offset

potential due to LJP before sealing, polarity is pipette-bath. In whole cell recording this reading

adds to command set on the patch clamp. However---

Convention:

Definition of LJP polarity : LJP = Bath potential – Pipette potential

This is opposite in sign to the potential measured going from pipette to bath soln.

Cell attached: patch potential = cell membrane pot - Command + LJP

Whole cell: membrane pot = Command - LJP

How large are junction potentials?

Bath pipette

+ - Na+ Cl- 17 mV K+ Gluconate- LJP +17 mV

154 mM 154 mM

+ -

Na+ Cl- 9 mV Na+ Gluconate- LJP +9 mV

154 mM 154 mM

LJP also occur at reference electrode salt bridges on changing bath ion concentrations.

Important to correct for LJP in reversal potential measurements e.g. for calculating

relative permeabilities to ions from reversal potential measurements,

and for ion selective electrode measurements when bath composition is changed.

Barry & Lynch 1991 J Mem Biol 121, 101; Calculation of LJPs from mobilities

JPCalcW

Peter Barry has a written programmes to numerically calculate LJP for different solutions

and the effects of changing external solution on the ref electrode LJP- ‘JPCalcW’.

It has mobilities for almost all ion substitutions made in physiology

Distributed with some Axon software – Pclamp- or from webpage

www.med.unsw.edu.au/PHBSoft .

Workshop has a copy if you need it.

Solubility measured by Solubility product - product of ion concns in a saturated solution

S = [Cation]*[Anion]

AgCl S= 1.5x10-10 eg [Cl-] = 150 mM, [Ag+] = 1 nM

CaPO4 S= 5x10-6

CaCO3 S= 1x10-8 eg [Ca2+] = 1 mM, [CO32-] = 10 mM

BaCO3 S= 8x10-9

MgCO3 S= 2.6x10-5

CaSO4 S= 6x10-5 eg [Ca2+] = 1 mM , [SO42-] = 60 mM

NB: Ion concentrations can be reduced without forming a visible precipitate.

Normal bicarbonate buffered ACSF has free Ca reduced to ~1.8 mM at pH 7.4

Weak electrolytes

divalent metal phosphates, carbonates, sulphates, gluconate

Weak electrolytes – pH buffers

pH buffers at pH near pK- : HEPES- , H2PO4- , HCO3

-

H+ + A- ↔ HA At equilibrium Ka = k-/k+= [H+][A-]

[HA]

pH = pKa + log10 ([A-]/[HA]) Henderson-Hasselbach Equ

pH-pKa

[A-]

[HA]Tot

Useful buffering range is pKa ± 1

pK’s are affected by ionic strength

Bicarbonate-CO2 buffers

- buffering by solution of CO2 in water H2O + CO2 ↔ H+ + HCO3-

2 advantages- Large reservoir of CO2 gas replenishes buffer

CO2 equilibrates across plasma membrane to control internal pH

At 37o HA term replaced by solubility 0.03 partial pressure pCO2

At pH 7.4 5% CO2 equilibrates with 26 mM HCO3-

Solubility of CO2 increases greatly at low temperature

Reaction is slow – carbonic anhydrase increases rate in erythrocytes and some

neurons.

Weak electrolytes – bicarbonate buffer

pH = pKa + log10 ([A-]/[HA]) pH = 6.1 + log([HCO3

-]/0.03*pCO2)

CO2 ↔ CO2 + H2O ↔ H+ + HCO3-

Weak electrolytes - pH indicators

Fluorescent pH indicators – the acid form HA is quenched by protonation

Examples with pKa near 7.0

Carboxy fluorescein pK 6.8

Pyranine (HPTS) pK=7.25, ratiometric

BCECF “ “ AM-ester available

SNARF “ “ “

eGFP pK = 5.9

Synaptophluorin VAMP-GFP

Alkalinisation of secretory vesicles/granules during secretion

can be shown by fluorescence changes in eGFP or synaptoflurin.

Buffer capacity of cells and organelles can be determined by NH4Cl titration of

indicator or eGFP fluorescence expressed in the organelle

NH4+Cl- ↔ NH3 + HCl NH3 crosses cell membranes

typically ≈ 10-50 mM/pH unit

Weak electrolytes - Ca - buffering

Ca2+ + D ↔ CaD

At equilibrium KCa = k-/k+= [Ca2+][D]

[CaD]

pCa = pKCa + log10 ([D]/[CaD])

pKCa-pCa

[CaD] [D]tot

Steady state buffering determined by

KCa Total buffer conc

Buffering kinetics is determined by rate

of Ca binding - k+Total buffer concn

Ca-buffering

Ca2+ + EGTA ↔ Ca.EGTA + 2H+ - Slow, pH dependent binding 2x106 M-1s-1

Ca2+ + BAPTA ↔ Ca.BAPTA Fast binding pH independent 2x108 M-1s-1

Spatial range of Ca depends on relative rates of diffusion and Ca binding

Fast binding reduces range of Ca diffusion from release sites – √(2.DiffCa./k+.[D])

The relative concentrations of BAPTA or EGTA needed to inhibit show the spatial

proximity of Ca sources and sensors

Endogenous buffers: Endogenous buffering capacity (free/bound Ca ions) has

physiological variation from 50-100 for pyramidal neurons up to 2000 for PV –

parvalbumin- positive interneurons.

Parvalbumen K = 0.15 μM k+ = 6x106 M-1s-1 Mg and Ca compete

Calbindin 0.45 μM 8x107 M-1s- Ca selective

ATP Ca- 90 μM, Mg- 45 μM Mg and Ca compete

Buffering calculator –steady state - Maxchelator at http://maxchelator.stanford.edu/

Fluorescent Ca-indicators

Ca2+ + D ↔ CaD At equilibrium

KCa = k-/k+= [Ca2+][D]

[CaD]

At high [Ca] - Fluorescence = F(max)

At 0 [Ca] - Fluorescence = F(min)

Free Ca : [Ca]/ KCa = F-F(min)/F(max)-F

However – it is difficult to determine Fmin at 0 Ca and Fmax at high Ca

BAPTA Ca chelator coupled with Fluorescein or other

fluorophore – Fura, Indo, Rhodamine

Fluorescence of Ca-bound Fluo3 is 50-200 Ca-free Fluo3

-dynamic range 50-200- depends on batch

Fluorescent Ca-indicators- F/F

KCa [Ca]/K

F

Fmax

Fmin

F0

F

↓

Free Ca : [Ca]/ KCa = F-F(min)/F(max)-F

Because of problems determining Fmin at 0 Ca and Fmax at high Ca

Ratio of Fluorescence change divided by resting Fluorescence - F/ F0 - often used,

However- F/F0 is not a linear of [Ca] except when Ca<KCa

Fluorescent Ca-indicators - interference

•Equilibrium buffering due to indicator affects the free Ca :

Exogenous buffering added by indicator ≈ [Dtot]/KCa

• Indicator buffering kinetics compete with Ca binding to e.g. Calmodulin-

determined by k+ [D]tot

•Indicator response time – imaging time resolution - are limited by Ca-dissociation rate k-

- high affinity K=0.3 µM - rate 20 s-1 , low affinity K=50 µM rate 5000 s-1

•Spatial integration of microdomain [Ca] requires linear F:Ca relation – Ca2+<<KCa

KCa [Ca]/K

F

Fmax

Fmin

F0

F

↓

References for Ca-Indicator Methods:

•Yasuda et al 2004 Imaging calcium concentration dynamics in small neuronal

compartments. Sci. STKE 2004, pl5 (2004)

•Maravall et al 2000 Estimating Intracellular Calcium Concentrations and

Buffering without Wavelength Ratioing Biophysical Journal 78 2655

•Naraghi 1997 T-jump study of calcium binding kinetics. Cell Calcium 22 255

•Baylor and Hollingworth 2011 Calcium indicators and calcium signaling– Prog

Biophys Mol Biol 105 162-179

•Mol Probes Handbook Chap 19 – lifescience.com

Properties of some Ca indicators

Fura 2 KCa= 0.25 μM k+= 4x108 k-= 100 s-1

Fluo 3 0.5 7x108 370

Oregon Green Bapta1 0.32 4x108 140

Low affinity for fast kinetics:

OGB5N 37.0 3x108 11000

Furaptra (Magfura2) 44 7x108 30000

Ion Substitutions - Extracellular

Comments Na Li Not pumped/transported

Choline Cholinergic, deliquescent, generates trimethylamine

N-methyl D-glucamine Commonly used impermeant cation

Tris Blocks channels

Na/Ca exchanger require Na – internal Ca is increased by Na-free solutions.

K TEA

Rb

Cs Block K channels

Ca Ba low solubility of salts SO4 HCO3 PO4; blocks K channels

Ca ions required for Ca –selectivity of Ca channels.

Ba activates Ca-activated Cl channels internally

Cl Gluconate Chelates Ca -1mM free at 5 mM Ca

Glucuronate

SO4 ditto

MeSO4

MeSO3 ditto

HEPES

Acetate weak acids/bases modify internal pH

HCO3 HEPES etc CO2/HCO3 buffers intracell. pH by CO2 permeation

CO3 binds Ca and other polyvalents - Ba, Co, La, Gd

Free Ca is reduced in bicarbonate solutions → CaCO3

HCO3 exchanges with Cl

Hepes blocks GABA-A

Glucose Young rodents may use ketone bodies as energy source

3-hydroxybutyrate 4 mM :-Vm, ECl → -80 mV

Pyruvate 5 mM

Temperature Warm slicing improves neuronal survival

K NMDG

Cs Interferes with Ca release from stores

Anions

Cl Affects secretion, e-c coupling

gluconate Contains heavy metals. Fast Ca buffer

Acetate

aspartate affects mitochondrial electron transport

glutamate affects glutamate transporters, required for

neurotransmitter uptake into vesicles

HEPES

Fl Seals leaky membranes, stable recordings

but binds Ca

AlFl4 activates G-proteins

Blocks Cl permeation in GABA/gly channels

ATP, Creatine Phosphate ATP, GTP are labile, bind Mg, Ca

GTP

EGTA/EDTA Chelate heavy metals, slow Ca buffer

BAPTA Fast localised Ca buffer

Pyruvate To maintain mitochondrial potential-

Transmitters glu/GABA/gly To maintain vesicular concns

Intracellular

Glucose- ketone bodies in development Rheims et al (2009) J. Neurochem. 110, 1330

Calcium-buffering effects of gluconate and nucleotides, as determined by a novel fluorimetric titration method.

Woehler A, Lin KH, Neher E. 2014 J Physiol.;592(Pt 22):4863-75. Sep 5.

Slice it hot: acute adult brain slicing in physiological temperature.

Ankri L, Yarom Y, Uusisaari MY 2014 J Vis Exp. Oct 30;(92):e52068.