Computer Methods and Programs in Biomedicine 70 (2003) 61–69

Labview virtual instruments for calcium buffer calculations

Frederick B. Reitz *, Gerald H. PollackDepartment of Bioengineering, Uni�ersity of Washington, Box 357962, Seattle, WA 98195-7962, USA

Received 5 March 2001; received in revised form 28 August 2001; accepted 4 October 2001

Abstract

Labview VIs based upon the calculator programs of Fabiato and Fabiato (J. Physiol. Paris 75 (1979) 463) arepresented. The VIs comprise the necessary computations for the accurate preparation of multiple-metal buffers, forthe back-calculation of buffer composition given known free metal concentrations and stability constants used, for thedetermination of free concentrations from a given buffer composition, and for the determination of apparent stabilityconstants from absolute constants. As implemented, the VIs can concurrently account for up to three divalent metals,two monovalent metals and four ligands thereof, and the modular design of the VIs facilitates further extension oftheir capacity. As Labview VIs are inherently graphical, these VIs may serve as useful templates for those wishing toadapt this software to other platforms. © 2002 Elsevier Science Ireland Ltd. All rights reserved.

Keywords: Calcium buffer; EGTA; Labview VI; Multiple equilibria

www.elsevier.com/locate/cmpb

1. Introduction

The calculation of required calcium buffer com-ponents is made difficult by the large number ofinterdependent equilibria involved. For example,ethylene glycol-bis(�-aminoethyl ether)N,N,N �,N �-tetraacetic acid (EGTA) alone has five distinctstates of hydrogen binding, each with a differentaffinity for calcium, which also binds to adenosine5�-triphosphate (ATP), which in turn may alreadybe bound to hydrogen and/or magnesium, etc.

Typically, to begin to rein in this complexity,

apparent binding constants are computed. Anapparent binding constant of a metal for a ligandat a given pH represents a distillation into onenumber of the absolute binding constants of themetal with each hydrogen-bound state of the lig-and (cf. Ref. [1]).

Still, an analytical solution to the problem re-mains prohibitively difficult, requiring the use ofiterative computation to converge upon a self-consistent set of values. Accordingly, many pro-grams have been written for the computation ofcalcium buffer composition (e.g. Refs. [2–6]).

The programs described herein are adaptedfrom the calculator programs of Fabiato andFabiato [2]. They are intended to update thismethodology to a more contemporary platform aswell as to provide a graphical view of the complextask of calcium buffer analysis.

* Corresponding author. Tel.: +1-206-685-2733; fax: +1-206-685-3300.

E-mail addresses: freitz@u.washington.edu (F.B. Reitz),ghp@u.washington.edu (G.H. Pollack).

0169-2607/02/$ - see front matter © 2002 Elsevier Science Ireland Ltd. All rights reserved.

PII: S 0169 -2607 (01 )00196 -1

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2. Methods

The software was developed in Labview 4.1 ona PC with a 266 MHz Pentium II processor, 96Mb RAM and Windows NT. On this platform,program runs took at most several seconds(uncompiled).

3. Program description

As in Ref. [2], the software is divided intoseveral parts.

First, all valences and absolute stability con-stants to be used are specified as arrays in asimple VI that serves simply to store and formatthese data (the ‘fabiatoKs’ sub-vi in Fig. 1; sub-vidiagram not shown). The first output (counting‘fabiatoKs’ outputs from top to bottom) is a 4×8array containing the logarithms of the four hydro-gen-ligand absolute stability constants for each ofthe eight ligands (EGTA, ATP, creatine phos-phate (CP), hexamethylenediaminetetraacetic acid(HDTA), ethylenediaminetetraacetic acid(EDTA), adenosine 5�-diphosphate (ADP), ox-alate and phosphate). As per the convention ofFabiato and Fabiato [2], inapplicable constantsare assigned a logarithm of zero as a placeholder,with the understanding that the constants them-selves will be interpreted as zero.

The second output is a 2×8×6 array contain-ing the logarithms of the two metal– ligand abso-lute stability constants for each combination ofthe above eight ligands and six metals (Ca, Mg,Sr, K, Na and Li). Inapplicable constants arehandled as above. The third and fourth arrays aresimply vectors containing the eight valences of theligands and the six valences of the metals, respec-tively.

Fabiato1.VI (Fig. 1) corresponds to Program 1of Ref. [2]. This program can compute: (a) anapparent stability constant at a given pH usingthe corresponding absolute stability constants; (b)an absolute stability constant from an apparentconstant at a given pH; (c) the mean squarecharges of a metal– ligand complex and the freeligand; and (d) the contribution of a given pHbuffer to the ionic strength of the solution.

For buffer ionic strength calculation, the re-quired inputs of Fabiato1.VI are buffer concen-tration, buffer pKa, whether the buffer is cationicor anionic, and the pH. For the determination ofan absolute stability constant from an apparentconstant, the required inputs are pH and theapparent constant. To compute the root meansquare charge of the metal– ligand complex and/or that of free ligand, or to compute an apparentstability constant for the complex, the requiredinputs are the metal, the ligand, and the pH.Optionally, a specified apparent stability constantmay be used in lieu of the constant determinedfrom the program’s default absolute constants forroot mean square charge calculation.

To simplify the subsequent VIs which make useof Fabiato1.VI for the determination of manyapparent stability constants, an intermediate VIwas written (FabiatoK.VI; see Fig. 2). Given apH, FabiatoK.VI simply runs Fabiato1.VI repeat-edly for all metal– ligand combinations to beused. As implemented, four ligands and fivemetals (three divalent and two monovalent) arespecified, producing a 4×5 array of apparentstability constants for use by Fabiato2.VI andFabiato3.VI.

Fabiato2.VI (Fig. 3) corresponds to Program 2of Ref. [2]. This VI calculates the buffer composi-tion necessary to achieve the desired free ionconcentrations and ionic strength. The inputs arethe buffer concentration and whether it is cationicor anionic, its pKa, pH, and the amount of addedbase required to achieve this pH (these are neededfor ionic strength determination); the four ligands,three divalent metals and the two monovalentmetals to be used and the amounts thereof desired(which may be zero, if fewer metals and ligandsare to be used), and a convergence criterion speci-fying a maximum amount of concentrationchange per program iteration allowable before theprogram will terminate.

Several assumptions are made regarding themethod of buffer production, as per Ref. [2]. Mgis assumed to be added as MgA2, where A is amonovalent anion. The divalent cation labeled‘M2+ ’ is considered to be added using this sameanion. ‘M2+E’ is considered to be added withEGTA as the anion, and with two cations of the

F.B. Reitz, G.H. Pollack / Computer Methods and Programs in Biomedicine 70 (2003) 61–69 63

major monovalent metal. If two monovalentmetals are used, the second one is considered tobe that added as an ATP and CP salt.

The concentrations of the divalent metals arespecified as pM2+ , pMg, and pM2+E. Theconcentrations of the ligands are specified explic-

Fig. 1. Fabiato1.VI, for preliminary stability constant and ionic strength calculations (cf. Ref. [2], Program 1).

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Fig. 2. Fabiatok.VI, which calls Fabiato 1.VI repeatedly to generate the array of all metal-ligand apparent stability constants to beused in later VIs.

itly, except for the second ligand, presumablyATP, which is specified indirectly, through thepMg and pMgATP.

Given all of these inputs, Fabiato2.VI producesthe free amounts of all ligands and monovalentmetals and the total amounts of ATP and all themetals to be used.

Program modifications necessary to achieve apredesignated amount of the major monovalentcation, discussed separately by Fabiato and Fabi-ato [2], are not implemented herein.

Fabiato3.VI (Fig. 4) corresponds to Program 3of Ref. [2], performing the reverse operation ofFabiato2.VI; i.e. Fabiato3.VI calculates free ionconcentrations from a specified buffer composi-tion. Again, ‘M2+E’ is considered to be thedivalent cation associated with EGTA, ‘M+ ’ isthe major monovalent cation, and ‘M+1’ is themonovalent cation added with ATP and CP, if asecond monovalent cation is used. Given specifi-cation of the ligands and metals to be used, thetotal amounts thereof, the pH, and a convergencecriterion as per Fabiato2.VI, the free amounts ofall ligands and metals are calculated.

In Program 3 of Ref. [2], to speed computation,calculations for individual buffer species wereceased upon achieving a convergence criterion. Asprocessor economy was less of an issue on the

platform used herein, and to simplify programarchitecture, this technique was not used in Fabi-ato3.VI; instead, all calculations continued untilall buffer species achieved convergence.

4. Test run results

Fabiato and Fabiato [2] demonstrated the firstof their three programs by calculating an absolutestability constant for CaEGTA from an apparentconstant, by using the resulting absolute constantto calculate an apparent constant at a differentpH values, and by computing the ionic strengthcontributions of the CaEGTA complex, of theEGTA, and of a specified buffer (30 mM TES).Fabiato1.VI gave identical results for the sameinput parameters.

The second of the three programs of Ref. [2]was demonstrated by calculating the buffer com-position required to obtain a desired pCa, pSr,pMg, pMgATP and ionic strength. In all thecases, Fabiato2.VI gave similar results using theinput parameters specified, with identical resultsin the case of total ATP, total Mg, and total Na.The results of Fabiato2.VI for total Sr, total Ca,total KCl and total K+ deviated from the pro-gram of Fabiato and Fabiato [2] by 0.006, 0.02,

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Fig. 3. Fabiato2.VI, for the calculation of buffer composition required to achieve a given free ion concentration (cf. Ref. [2],Program 2).

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Fig. 3. (Continued)

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0.2 and 0.1%, respectively. Possible sources of thisdiscrepancy include the difference between apocket calculator and a PC in the number ofsignificant figures retained and the criteria forconvergence used by the respective implementa-tions of the program.

Fabiato3.VI was tested via the reverse of theabove operation, i.e. calculating the pSr, pCa andpMg of a buffer of a given composition. Theresults were found to correspond to those in Ref.[2] using either their input parameters or thosegenerated by Fabiato2.VI.

Fig. 4. Fabiato3.VI, for the calculation of free ion concentrations given a buffer composition (cf. Ref. [2], Program 3).

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Fig. 4. (Continued)

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5. Availability

The program is available at http://students.washington.edu/freitz/calcium.html, athttp://faculty.washington.edu/ghp/freitz/calcium.html, or by contacting the authors attheir respective email addresses.

References

[1] J.A.S. McGuigan, D. Luthi, A. Buri, Calcium buffer solu-tions and how to make them: a do it yourself guide, Can.J. Physiol. Pharmacol. 69 (1991) 1733–1749.

[2] A. Fabiato, F. Fabiato, Calculator programs for computingthe composition of the solutions containing multiple metalsand ligands used for experiments in skinned muscle cells, J.Physiol. Paris 75 (1979) 463–505.

[3] D. Chang, P.S. Hsieh, D.C. Dawson, Calcium: a programin basic for calculating the composition of solutions withspecified free concentrations of calcium, magnesium andother divalent cations, Comput. Biol. Med. 18 (1988) 351–366.

[4] A. Fabiato, Computer programs for calculating total fromspecified free or free from specified total ionic concentrationsin aqueous solutions containing multiple metals and ligands,Methods Enzymol. 157 (1988) 379–417.

[5] R.B. Taylor, C. Trimble, J.J. Valdes, M.J. Wayner, J.P.Chambers, Determination of free calcium, Brain Res. Bull.29 (1992) 499–501.

[6] S.P.J. Brooks, K.B. Storey, Bound and Determined: acomputer program for making buffers of defined ion concen-trations, Anal. Biochem. 201 (1992) 119–126.

Biographies

Frederick B. Reitz received his BS degree inElectrical Engineering in 1991 and his PhD inBioengineering in 2001, both from the Universityof Washington, Seattle. His research interests in-clude near-field scanning optical microscopy andthe application thereof to steady-state fluores-cence anisotropy.

Gerald H. Pollack received the PhD degree inBiomedical Engineering from the University ofPennsylvania, Philadelphia. He is the Professor ofBioengineering at the University of Washington,Seattle. He has focused on the molecular mecha-nism of contraction and more recently on thegel-like properties of cytoplasm.