- Email: [email protected]
Calibration of ion-selective microelectrodes: flow-system and analysis program for the IBM PC
Journal of Neurosczence Methods, 30 (1989) 263-266
263
Elsevier NSM
01016
Calibration of ion-selective microelectrodes: flow-system and analysis program for the IBM PC A l a n W . B a r o l e t 1, R o n A n d r e w s 2 a n d M a r y E. M o r r i s a I Department of Pharmacology and 2 The Playfaw Neurosclence Untt, Umversm' of Toronto, Toronto M5S 1A1 (Canada), and -~Departments of Medteme and Pharmacology, Unwerstty of Ottawa. Ottawa K I H 8M5 (Canada)
(Recexved 8 March 1989) (Revised 17 July 1989) (Accepted 20 July 1989)
Key words: lon-selecUve microelectrodes; C a l l b r a u o n ; S o l u t i o n flow control; I B M microprocessor, PC compatibles; A n a l y t i c a l / p l o t t i n g software; Selectivity coefficients A menu-driven program - written m C and Assembly language - has been developed for use with an IBM PC or compattble computer for cahbratxon of ton-selectwe nucroelectrodes Available features include (0 user-logical commands, (10 rapt& accurate construction and display of cahbratxon curves (fitted by least squares non-hnear regression), (m) analysts of data (stored etther on- or off-hne), with correction for draft and conversion from voltage or length to ion concentration or actiwty, 0v) calculation of selecnvlty coefficxents, (v) optional storage and use of actwlty coefficients, and (vl) output of data, calculatmns and graphics to prmter and plotter A s~mple chamber and valve-activated flow-system for rap~d change of solunons with etther manual selecuon or computer control ts also described.
Introduction The m e a s u r e m e n t of 1on levels in biological tissue with ion-selective microelectrodes produces large a m o u n t s of c o n t i n u o u s l y recorded D C voltage data, with p o t e n t i a l error from the c o n t r i b u tion of different runs at the site of m e a s u r e m e n t as well as voltage d n f t (Durst, 1975; A m m a n n , 1986). A l t h o u g h the ideal electrode shows absolute selectxvity a n d a pure N e r n s t m n response, the i n f l u e n c e of different interfering ions ts taken into a c c o u n t b y the extended Nicolsky-E~senman e q u a u o n (Nlcolsky, 1937a,b; E i s e n m a n , 1967):
E=Eo+s'log
.: pot :
a,+^,:
x z,,/z:
~a:)
]
]
(1)
Correspondence Dr Mary. E. Morns, Department of Pharmacology, Umvers~ty of Ottawa, 451 Smyth Road, Ottawa Ontario, Canada K1H 8M5
where E = electrochemical cell potential ( E M F ) , E 0 = c o n s t a n t reference potential, a, = activity of p r i m a r y i o n t, s = 2.303. R T / z , F ( R = gas constant: T = a b s o l u t e t e m p e r a t u r e ; F = F a r a d a y , :, = charge of i o n z), a: = actwlty of interfering ion j. K, p°t -- selectivity factor, z: = charge of interfering i o n j. The l o g a n t h m a c a n d generally n o n - i d e a l n a t u r e of the response of i o n - e x c h a n g e r a n d n e u t r a l carh e r m e m b r a n e s , especially when used with finetipped mxcroelectrodes, reqmres accurate fitting of curves to c a l i b r a t i o n data. A l t h o u g h these electrodes have b e e n widely used for more than a decade, there have b e e n few descriptions of p r a c n cal aspects of c a l i b r a t i o n m e t h o d s a n d the use of rmcroprocessors for d a t a storage a n d analysis ( B o e r n g t e r a n d Lehmenki~ler, 1984; E l l e r m a n n et al., 1985; Levy et al., 1985; A m m a n n , 1986; Barolet et al 1988). W e describe here a simple c h a m b e r a n d system to c o n t r o l flow a n d change solunons,
0165-0270/89/$03 50 © 1989 Elsevter Science Pubhshers B V Biomedical Division)
264
and a versatile computer program for calibrating electrodes. The analysis software is user-friendly and quickly learned, and provides a highly accurate, rapid fit of data (using least-squares, nonlinear regression analysis (Hartley. 1948. 1961, Draper and Smith, 1981)). Although developed for off-line storage and use, it can be easily adapted for on-line processing.
Electrode Calibration J u l y 11,1988 9O 8o-
Methods: hardware and software
TABLE 1 SUMMARY OF ELCAL PROGRAM MENUS AND FUNCTIONS Menu
Functmn
Mare menu
- uses 14 direct c o m m a n d s to enter, store a n d h a n d l e data, d i s p l a y and p n n t / p l o t c a l i b r a t i o n curves - ~s e x p a n d e d b y 4 c o m m a n d s to access a d d i t i o n a l m e n u s AXE, C A L , A C T a n d OLV - defines s e l e c u o n / d e f a u l t of p a r a m e t e r s for c o n s t r u c t i o n a n d l a b e h n g of g r a p h axes, a n d displays fitted c a h b r a t l o n curves - calculates a n d p n n t s slopes, curves, selectivity coefficients (using separate s o l u t i o n s or fixed interference m e t h o d s ~ ). a n d the m d w l d u a l ion levels for recorded voltage d a t a - installs a n d d i s p l a y s tables of a c t w l t y coefficients - enters c h a r t d i s p l a c e m e n t d a t a a n d selects voltage scales for length conversion
[4] O L V
G u d b a l t et al (1986)
(1976); A m m a n n
et al
.
....... i
, ....... )
10-1
. . . . . . . . i--, . . . . .,r)
100
101
102
[K+]o(mM)
Cahbratzon program ELCAL, a user-logical program for the analysis of electrode calibration data has been written m C and assembly language for use with the IBM PC or compatible rmcroprocessor. Requirements are 256K memory, either a colour or monochrome graphacs adaptor, a parallel IBM (or eqmvalent) graphics printer, and a serial Hewlett-Packard plotter (HP 747OA, Hewlett-Packard Ltd.) for high quality graphics. The command-driven program has 5 menus, as summarized in Table I. All commands are three-letter logical abbreviations.
[3] A C T
/
50-
1 0 0 0 0 - 10-2
[2] C A L
/
70-
0 -10
[1] A X E
/
(1979), A m m a n n
........................................................................ *draw
Fitting curve Curve htted
please stand by
Fig. 1 E x a m p l e of d i s p l a y of c a l i b r a t i o n curve tor K ~-sen~zt]ve m l c r o e l e c t r o d e F i t t e d w i t h e x t e n d e d N l c o l s k y - E a s e n m a n equation by n o n - h n e a r least-squares regression
with the exception of EXIT (to leave the program) and MAIN (to return to the MAIN menu from each of 4 submenus). Throughout the program the top segment of the screen is used for menu/graphics (20 text lines) and the bottom for communications (prompts, entries and commands; 4 text hnes). Fig. 1 demonstrates the graphic display of a typical single calibration curve, generated by the AXE menu setup, and accompanying text communications. The program allows data to be entered in integer, decimal or scaenUfic form from the console or obtained from disc storage. Graphs of calibration points and curves can be viewed and translated to hard copy. Offset correction for the Y axas zs available and multiple curves can be superimposed on the graph of a single plot or stored in memory for printer display. All descriptors, data points, calculations, equataons and statistical data can be recorded with the printer.
Cahbratlon flow-system Fig. 2 demonstrates the configuration of a simple system for manual or computer-controlled delivery of different solutions for the calibration of an lon-sensmve microelectrode. Voltage responses are differentially recorded from sensor and reference channels of double-barrelled rmcropipettes, with a high input Impedance electrometer amph-
265
12V Swltche~
Electrometer
~[~
Solutions for Cahbrahon
IonSelectwe Microelectrode
[ i-- WaterJacket Valves Ag/AgCI I ~ , Ground_J_ [ t,___
L r
W'ckT\
FIo~ '
Reservolr - - ~ '
Suction/Discard Fig 2 Dmgramof cahbrat~on apparatus. C1_6 reservoirs for cahbratmg solutions S1-6 sw~tchesfor 12 V actlvauon of VI_~ valves to allow flow of selected solution through 8-way connector to electrode measuring chamber.
tier (e.g., A X O P R O B E 1, Axon Instruments, Inc.). Grawty flow from a reservoir (C) to the electrode calibrating chamber can be selected manually from a controller circuit via switches (S), using 12 V d.c. (rechargable battery G C 1290, Electro Sonic Inc.) to actuate o p e n / c l o s e d positions of in-line valves (V) (Model No. 3-188-900, General Valve Corporation). Alternatively the valves can be controlled mdwidually or in sequence using a computer, digital i n p u t / o u t p u t interface (e.g., IBM PC data acquisition and control adaptor, Mendelson Electronics, Inc.) and electrical relays (Potter and Brumfield No. JWD-107-5, Electrosomc Inc.). Opening of a valve allows flow from a single reservoir through the corresponding open valve of an 8-way zero dead-space connector ( O M N I F I T No. N 1103, Omnifit Ltd.) to the outflow valve (set to limit the rate < 4 m l / m i n , as monitored by flowmeter (e.g., Gilmont No. F 2100-11, ColeParmer Instrument Company)). The controller
panel allows no flow, single solution flow (one of six), or simultaneous purge of all solutions. For calibraUons at room temperature, a s~mple chamber can be made with polyethylene tubing, smtered Ag/AgC1 wire ground (No. 5415, A-M Systems, Inc.), sihcon adhesive sealant (RTV-108, Canadian General Electric), cotton gauze wick and outer support of glass tubing. For temperature control, the addition of a thermostatted water jacket is needed. The speed of calibration will vary, depending on flow-rate, reservoir capacity and the dead-space between the 8-way valve and electrode.
Acknowledgments / information The authors gratefully acknowledge The Medical Research Council and Savoy Foundation for financial support, and thank A d a m Charlinskl and
266
Peter Pennefather for help m the design and construction of the flow-control system. The computer program was written by R.A., with assistance for the incorporation of curve-fitting routines from A.B. Copies of the ELCAL program, source codes and brief user manual can be obtained directly from the authors for recovery of disk and shipping costs. References Ammann, D (1986) Ion-selective Mlcroelectrodes, Pnnoples, Design and Apphcataon, Spnnger-Verlag Berlin, 346 pp Ammann, D., Meier, P.C and Simon, W. (1979) Design and use of calcium-selective macroelectrodes In: C C. Ashley and A.K Campbell (Eds), Detection and Measurement of Free Ca 2+ in Cells, Elsevier/North-Holland Blome&cal Press, Amsterdam/New York, pp. 117-129. Barolet, A.W, Andrews, R. and Morns, M.E (1988) Computer analys~s of ~on-selectlve rmcroelectrode responses cahbrauon and recording. Soc. Neurosct Abstr, 14 643 Boerngter, J.P C. and Lehmenkt~ler, A. (1984) Microprocessor aided correction of the Ca z+ error in the signal of a Na+-selecUve rmcroelectrode, Pflugers Arch Suppt, 400 R56 Draper, N.R. and Snuth. H. (1981) Apphed Regression Analysts 2nd edn., John Wiley & Sons, Toronto, pp 458-474
Durst R A (1975) lon-selectlve electrode response m biolog~ flmds In H Berman and N Hebert (Eds), Ion-selective Mlcroelectrodes, Adv E~p Med. Blol, 50, pp 13-21_ Ellermann, A , Hoper J , Brunner, M and Kessler, M (19851 Computer-assisted processing of lon-selectwe microelectrodes, In M Kessler, D K Harrison and J H6per (Eds.), Ion Measurements m Physiology and Me&clne, SprmgerVerlag. Berlin, pp 90-95 Elsenman, G (1967) Glass electrodes for hydrogen and other cations, pnnoples and practtce, Marcel Dekker, New York Gudbault, G , G , Durst, R,A, Frant, M S, Fret~er. H , Hansen, E H., Light, T.S, Pungor, E., Rechmtz, ( ; , Race, N M, Robin, T J , Simon, W and Thomas, J D R (1976) Recommendations for nomenclature of ton-selective m~croelectrodes, Pure Appl Chem, 48 127-14l Gmlbault, G.G. (1979) IUPAC Commlslon on Analyucal Nomenclature Recommendauons for pubhstung manuscripts on ~on-selectwe electrodes, Ion-Selecuve Electrode Rev. 1 139-162. Hartley, H O (1948) The estlmauon of non-hnear parameters by "internal least-squares", Bmmetnka, 35 32-45. Hartley, H O (1961) The too&fled Gauss-Newton method for the fittmg of non-hnear regression funcuons by least squares, Technometncs. 3 269-280 Levy, S. Tlllem, L and Tdlot~on, D L (1985) Ion-selective mtcroelectrodes computer-controlled cahbratlon, plotting, and data analysis, J Neuroso Methods, 15 253-261 Nlcolsky B P (1937a) Theory of the glass electrode, Zh Fls Kbam, 10. 495-501 Nlcolsky, B P (1937b) Theory of the glass electrode I, Acta Physlcochlm USSR, 7 597-610
263
Elsevier NSM
01016
Calibration of ion-selective microelectrodes: flow-system and analysis program for the IBM PC A l a n W . B a r o l e t 1, R o n A n d r e w s 2 a n d M a r y E. M o r r i s a I Department of Pharmacology and 2 The Playfaw Neurosclence Untt, Umversm' of Toronto, Toronto M5S 1A1 (Canada), and -~Departments of Medteme and Pharmacology, Unwerstty of Ottawa. Ottawa K I H 8M5 (Canada)
(Recexved 8 March 1989) (Revised 17 July 1989) (Accepted 20 July 1989)
Key words: lon-selecUve microelectrodes; C a l l b r a u o n ; S o l u t i o n flow control; I B M microprocessor, PC compatibles; A n a l y t i c a l / p l o t t i n g software; Selectivity coefficients A menu-driven program - written m C and Assembly language - has been developed for use with an IBM PC or compattble computer for cahbratxon of ton-selectwe nucroelectrodes Available features include (0 user-logical commands, (10 rapt& accurate construction and display of cahbratxon curves (fitted by least squares non-hnear regression), (m) analysts of data (stored etther on- or off-hne), with correction for draft and conversion from voltage or length to ion concentration or actiwty, 0v) calculation of selecnvlty coefficxents, (v) optional storage and use of actwlty coefficients, and (vl) output of data, calculatmns and graphics to prmter and plotter A s~mple chamber and valve-activated flow-system for rap~d change of solunons with etther manual selecuon or computer control ts also described.
Introduction The m e a s u r e m e n t of 1on levels in biological tissue with ion-selective microelectrodes produces large a m o u n t s of c o n t i n u o u s l y recorded D C voltage data, with p o t e n t i a l error from the c o n t r i b u tion of different runs at the site of m e a s u r e m e n t as well as voltage d n f t (Durst, 1975; A m m a n n , 1986). A l t h o u g h the ideal electrode shows absolute selectxvity a n d a pure N e r n s t m n response, the i n f l u e n c e of different interfering ions ts taken into a c c o u n t b y the extended Nicolsky-E~senman e q u a u o n (Nlcolsky, 1937a,b; E i s e n m a n , 1967):
E=Eo+s'log
.: pot :
a,+^,:
x z,,/z:
~a:)
]
]
(1)
Correspondence Dr Mary. E. Morns, Department of Pharmacology, Umvers~ty of Ottawa, 451 Smyth Road, Ottawa Ontario, Canada K1H 8M5
where E = electrochemical cell potential ( E M F ) , E 0 = c o n s t a n t reference potential, a, = activity of p r i m a r y i o n t, s = 2.303. R T / z , F ( R = gas constant: T = a b s o l u t e t e m p e r a t u r e ; F = F a r a d a y , :, = charge of i o n z), a: = actwlty of interfering ion j. K, p°t -- selectivity factor, z: = charge of interfering i o n j. The l o g a n t h m a c a n d generally n o n - i d e a l n a t u r e of the response of i o n - e x c h a n g e r a n d n e u t r a l carh e r m e m b r a n e s , especially when used with finetipped mxcroelectrodes, reqmres accurate fitting of curves to c a l i b r a t i o n data. A l t h o u g h these electrodes have b e e n widely used for more than a decade, there have b e e n few descriptions of p r a c n cal aspects of c a l i b r a t i o n m e t h o d s a n d the use of rmcroprocessors for d a t a storage a n d analysis ( B o e r n g t e r a n d Lehmenki~ler, 1984; E l l e r m a n n et al., 1985; Levy et al., 1985; A m m a n n , 1986; Barolet et al 1988). W e describe here a simple c h a m b e r a n d system to c o n t r o l flow a n d change solunons,
0165-0270/89/$03 50 © 1989 Elsevter Science Pubhshers B V Biomedical Division)
264
and a versatile computer program for calibrating electrodes. The analysis software is user-friendly and quickly learned, and provides a highly accurate, rapid fit of data (using least-squares, nonlinear regression analysis (Hartley. 1948. 1961, Draper and Smith, 1981)). Although developed for off-line storage and use, it can be easily adapted for on-line processing.
Electrode Calibration J u l y 11,1988 9O 8o-
Methods: hardware and software
TABLE 1 SUMMARY OF ELCAL PROGRAM MENUS AND FUNCTIONS Menu
Functmn
Mare menu
- uses 14 direct c o m m a n d s to enter, store a n d h a n d l e data, d i s p l a y and p n n t / p l o t c a l i b r a t i o n curves - ~s e x p a n d e d b y 4 c o m m a n d s to access a d d i t i o n a l m e n u s AXE, C A L , A C T a n d OLV - defines s e l e c u o n / d e f a u l t of p a r a m e t e r s for c o n s t r u c t i o n a n d l a b e h n g of g r a p h axes, a n d displays fitted c a h b r a t l o n curves - calculates a n d p n n t s slopes, curves, selectivity coefficients (using separate s o l u t i o n s or fixed interference m e t h o d s ~ ). a n d the m d w l d u a l ion levels for recorded voltage d a t a - installs a n d d i s p l a y s tables of a c t w l t y coefficients - enters c h a r t d i s p l a c e m e n t d a t a a n d selects voltage scales for length conversion
[4] O L V
G u d b a l t et al (1986)
(1976); A m m a n n
et al
.
....... i
, ....... )
10-1
. . . . . . . . i--, . . . . .,r)
100
101
102
[K+]o(mM)
Cahbratzon program ELCAL, a user-logical program for the analysis of electrode calibration data has been written m C and assembly language for use with the IBM PC or compatible rmcroprocessor. Requirements are 256K memory, either a colour or monochrome graphacs adaptor, a parallel IBM (or eqmvalent) graphics printer, and a serial Hewlett-Packard plotter (HP 747OA, Hewlett-Packard Ltd.) for high quality graphics. The command-driven program has 5 menus, as summarized in Table I. All commands are three-letter logical abbreviations.
[3] A C T
/
50-
1 0 0 0 0 - 10-2
[2] C A L
/
70-
0 -10
[1] A X E
/
(1979), A m m a n n
........................................................................ *draw
Fitting curve Curve htted
please stand by
Fig. 1 E x a m p l e of d i s p l a y of c a l i b r a t i o n curve tor K ~-sen~zt]ve m l c r o e l e c t r o d e F i t t e d w i t h e x t e n d e d N l c o l s k y - E a s e n m a n equation by n o n - h n e a r least-squares regression
with the exception of EXIT (to leave the program) and MAIN (to return to the MAIN menu from each of 4 submenus). Throughout the program the top segment of the screen is used for menu/graphics (20 text lines) and the bottom for communications (prompts, entries and commands; 4 text hnes). Fig. 1 demonstrates the graphic display of a typical single calibration curve, generated by the AXE menu setup, and accompanying text communications. The program allows data to be entered in integer, decimal or scaenUfic form from the console or obtained from disc storage. Graphs of calibration points and curves can be viewed and translated to hard copy. Offset correction for the Y axas zs available and multiple curves can be superimposed on the graph of a single plot or stored in memory for printer display. All descriptors, data points, calculations, equataons and statistical data can be recorded with the printer.
Cahbratlon flow-system Fig. 2 demonstrates the configuration of a simple system for manual or computer-controlled delivery of different solutions for the calibration of an lon-sensmve microelectrode. Voltage responses are differentially recorded from sensor and reference channels of double-barrelled rmcropipettes, with a high input Impedance electrometer amph-
265
12V Swltche~
Electrometer
~[~
Solutions for Cahbrahon
IonSelectwe Microelectrode
[ i-- WaterJacket Valves Ag/AgCI I ~ , Ground_J_ [ t,___
L r
W'ckT\
FIo~ '
Reservolr - - ~ '
Suction/Discard Fig 2 Dmgramof cahbrat~on apparatus. C1_6 reservoirs for cahbratmg solutions S1-6 sw~tchesfor 12 V actlvauon of VI_~ valves to allow flow of selected solution through 8-way connector to electrode measuring chamber.
tier (e.g., A X O P R O B E 1, Axon Instruments, Inc.). Grawty flow from a reservoir (C) to the electrode calibrating chamber can be selected manually from a controller circuit via switches (S), using 12 V d.c. (rechargable battery G C 1290, Electro Sonic Inc.) to actuate o p e n / c l o s e d positions of in-line valves (V) (Model No. 3-188-900, General Valve Corporation). Alternatively the valves can be controlled mdwidually or in sequence using a computer, digital i n p u t / o u t p u t interface (e.g., IBM PC data acquisition and control adaptor, Mendelson Electronics, Inc.) and electrical relays (Potter and Brumfield No. JWD-107-5, Electrosomc Inc.). Opening of a valve allows flow from a single reservoir through the corresponding open valve of an 8-way zero dead-space connector ( O M N I F I T No. N 1103, Omnifit Ltd.) to the outflow valve (set to limit the rate < 4 m l / m i n , as monitored by flowmeter (e.g., Gilmont No. F 2100-11, ColeParmer Instrument Company)). The controller
panel allows no flow, single solution flow (one of six), or simultaneous purge of all solutions. For calibraUons at room temperature, a s~mple chamber can be made with polyethylene tubing, smtered Ag/AgC1 wire ground (No. 5415, A-M Systems, Inc.), sihcon adhesive sealant (RTV-108, Canadian General Electric), cotton gauze wick and outer support of glass tubing. For temperature control, the addition of a thermostatted water jacket is needed. The speed of calibration will vary, depending on flow-rate, reservoir capacity and the dead-space between the 8-way valve and electrode.
Acknowledgments / information The authors gratefully acknowledge The Medical Research Council and Savoy Foundation for financial support, and thank A d a m Charlinskl and
266
Peter Pennefather for help m the design and construction of the flow-control system. The computer program was written by R.A., with assistance for the incorporation of curve-fitting routines from A.B. Copies of the ELCAL program, source codes and brief user manual can be obtained directly from the authors for recovery of disk and shipping costs. References Ammann, D (1986) Ion-selective Mlcroelectrodes, Pnnoples, Design and Apphcataon, Spnnger-Verlag Berlin, 346 pp Ammann, D., Meier, P.C and Simon, W. (1979) Design and use of calcium-selective macroelectrodes In: C C. Ashley and A.K Campbell (Eds), Detection and Measurement of Free Ca 2+ in Cells, Elsevier/North-Holland Blome&cal Press, Amsterdam/New York, pp. 117-129. Barolet, A.W, Andrews, R. and Morns, M.E (1988) Computer analys~s of ~on-selectlve rmcroelectrode responses cahbrauon and recording. Soc. Neurosct Abstr, 14 643 Boerngter, J.P C. and Lehmenkt~ler, A. (1984) Microprocessor aided correction of the Ca z+ error in the signal of a Na+-selecUve rmcroelectrode, Pflugers Arch Suppt, 400 R56 Draper, N.R. and Snuth. H. (1981) Apphed Regression Analysts 2nd edn., John Wiley & Sons, Toronto, pp 458-474
Durst R A (1975) lon-selectlve electrode response m biolog~ flmds In H Berman and N Hebert (Eds), Ion-selective Mlcroelectrodes, Adv E~p Med. Blol, 50, pp 13-21_ Ellermann, A , Hoper J , Brunner, M and Kessler, M (19851 Computer-assisted processing of lon-selectwe microelectrodes, In M Kessler, D K Harrison and J H6per (Eds.), Ion Measurements m Physiology and Me&clne, SprmgerVerlag. Berlin, pp 90-95 Elsenman, G (1967) Glass electrodes for hydrogen and other cations, pnnoples and practtce, Marcel Dekker, New York Gudbault, G , G , Durst, R,A, Frant, M S, Fret~er. H , Hansen, E H., Light, T.S, Pungor, E., Rechmtz, ( ; , Race, N M, Robin, T J , Simon, W and Thomas, J D R (1976) Recommendations for nomenclature of ton-selective m~croelectrodes, Pure Appl Chem, 48 127-14l Gmlbault, G.G. (1979) IUPAC Commlslon on Analyucal Nomenclature Recommendauons for pubhstung manuscripts on ~on-selectwe electrodes, Ion-Selecuve Electrode Rev. 1 139-162. Hartley, H O (1948) The estlmauon of non-hnear parameters by "internal least-squares", Bmmetnka, 35 32-45. Hartley, H O (1961) The too&fled Gauss-Newton method for the fittmg of non-hnear regression funcuons by least squares, Technometncs. 3 269-280 Levy, S. Tlllem, L and Tdlot~on, D L (1985) Ion-selective mtcroelectrodes computer-controlled cahbratlon, plotting, and data analysis, J Neuroso Methods, 15 253-261 Nlcolsky B P (1937a) Theory of the glass electrode, Zh Fls Kbam, 10. 495-501 Nlcolsky, B P (1937b) Theory of the glass electrode I, Acta Physlcochlm USSR, 7 597-610