Antonio Sabatini

Investigation of equilibria in solution. Determination of equilibrium constants with the HYPERQUAD suite of programs

A new suite of 10 programs concerned with equilibrium constants and solution equilibria is described. The suite includes data preparation programs, pretreatment programs, equilibrium constant refinement and post-run analysis. Data preparation is facilitated by a customized data editor. The pretreatment programs include manual trial and error data fitting, speciation diagrams, end-point determination, absorbance error determination, spectral baseline corrections, factor analysis and determination of molar absorbance spectra. Equilibrium constants can be determined from potentiometric data and/or spectrophotometric data. A new data structure is also described in which information on the model and on experimental measurements are kept in separate files.

Hyperquad simulation and speciation (hyss): a utility program for the investigation of equilibria involving soluble and partially soluble species

Abstract Hyperquad simulation and speciation (HySS) is a computer program written for the Windows operating system on personal computers which provides (a) a system for simulating titration curves and (b) a system for providing speciation diagrams. The calculations relate to equilibria in solution and also include the possibility of formation of a partially soluble precipitate. There are no restrictions as to the number of reagents that may be present or the number of complexes that may be formed.

Miniquad—A general computer programme for the computation of formation constants from potentiometric data

A new computer programme for the computation of formation constants of complex species in solution is presented. The programme can be applied to all kinds of potentiometric titration data, including multi-reactant and multi-electrode systems. A statistical analysis is made of the results in order to assess their validity, and to assist in hypothesis testing.

An improved computer program for the computation of formation constants from potentiometric data

Abstract An improved version of the computer program MINIQUAD is described. The new program, MINIQUAD 75, is faster by a factor of 2–3 and more reliable in extreme cases. The programs are compared on a benchmark consisting of eight chemical problems. Improvements in speed and reliability open the way to the development of a sound model selection procedure.

SUPERQUAD: an improved general program for computation of formation constants from potentiometric data

A new computer program has been developed in which formation constants are determined by minimisation of an error-square sum based on measured electrode potentials. The program also permits refinement of any reactant concentration or standard electrode potential. The refinement is incorporated into a new procedure which can be used for model selection.

Mathematical algorithms and computer programs for the determination of equilibrium constants from potentiometric and spectrophotometric measurements

A. Introduction B. The method of least-squares ........ (i) Concentrations of species in solution C. The programs LETAGROP and SCOGS D. The programs LEAST and MINIQUAD E. MINIQUAD F. The program BEST G. The program SUPERQUAD ....... H. The program HYPERQUAD ....... I. Conclusions References 389 390 393 394 394 397 399 399 402 404 405

In vivo assessment of free magnesium concentration in human brain by 31P MRS. A new calibration curve based on a mathematical algorithm.

Free cytosolic [Mg2+] can be assessed in vivo by 31P MRS from the chemical shift of β‐ATP which in turn depends on the fraction of total ATP complexed to Mg2+ ions. The reliability of these in vivo measurements depends on the availability of an appropriate in vitro calibration to determine the limits of chemical shifts of unbound ATP and Mg‐ATP complexes, using solutions that mimic the in vivo cytosolic conditions as far as possible. We used an algorithm and software to allow a quantitative definition of the Mg2+‐binding molecules to build a semi‐empirical equation that correlates the chemical shift of the β‐ATP signal to the [Mg2+] taking into account the amount of Mg2+ bound to all other constituents in solution. Our experiments resulted in a simple and reliable equation directly usable to assess in vivo the free cytosolic magnesium concentration of human brain by 31P MRS. Our method is also flexible enough to make it suitable for in vivo measurements of [Mg2+] in other organs and tissues.

In vivo 31P-MRS assessment of cytosolic [Mg2+] in the human skeletal muscle in different metabolic conditions

Cytosolic free [Mg(2+)] can be assessed in vivo by (31)P-MRS from the chemical shift of beta-ATP. The reliability of in vivo measurements depends on the availability of appropriate in vitro calibration curves obtained by using solutions that mimic the in vivo cytosolic conditions as far as possible. We build a semi-empiric equation that correlates the chemical shift of beta-ATP to free [Mg(2+)] taking into account the amount of Mg(2+) bound to all other ligands in solution. Our experiments resulted in a reliable ten-parameters equation directly usable to assess the cytosolic free [Mg(2+)] of human skeletal muscle at rest, during work and recovery. Our experiments also resulted in a new equation that allows the assessment of cytosolic pH from the chemical shift of Pi taking into account the measured free [Mg(2+)]. To perform simultaneous calculation of free [Mg(2+)] and pH in the skeletal muscle in different metabolic conditions we developed a specific software package available on Internet (http://www.unibo.it/bioclin) together with another program based on the equation previously obtained to calculate cytosolic free [Mg(2+)] in the human brain. The reliability and effectiveness of our equations and software were tested on the calf muscles of healthy volunteers at rest, during work and recovery.

Complex formation equilibria between 2-amino-2(hydroxymethyl)-1,3,-propanediol (tris, tham) and nickel(II), copper(II), zinc(II) and hydrogen ions in aqueous solutions

Abstract The reactions of 2-amino-2(hydroxymethyl)-1,3-propanediol (TRIS, THAM) with H+, Ni2+, Cu2+, and Zn2+ ions have been studied at 298 K in aqueous solutions (0.15 mol dm−3 NaCl) using ptentiometric techniques. The protonation constant of the ligand and the formation constants of several metal complexes have been calculated with the aid of the program MIQUV. The equilibrium models are selected on the basis of a critical evaluation of the least squares results and of a statistical analysis of the wieghted residuals.

Superquad - a new computer program for determination of stability constants of complexes by potentiometric titration

Abstract We have developed, separately and together, a sequence of computer programs for the determination of stability constants from potentiometric titration data: LEAST [1], MINIQUAD [2], MINIQUAD75 [3], MINIQUAD76A [4] and MIQUV [5]. The objective of this research is to develop robust, reliable and fast programs which will enable the solution chemist to specify the composition of any given solution. The last-mentioned program MIQUV was developed to put the model selection process on a sounder statistical basis. Our new program SUPERQUAD is a development of MIQUV designed to be both more efficient and more flexible. The following is a summary of the most important features of the new program. 1. It uses the method of ‘rigorous least squares’ in which both e.m.f. (E) and tire values (vol.) are assumed to be subject to experimental error. The data is weighted by a statistically sound weighting scheme. This makes it easier to deal with whole titration curves which include end-points, where measured e.m.f. is very sensitive to variations in volume of titrant added. 2. The minimization is based on the measured e.m.f. values Ek and all requisite derivatives ∂Ek/∂Xj are obtained analytically in two stages. This approach was first presented by Nagypal [6]. Xj is the jth parameter; it may be a formation constant, a reactant or titrant concentration or a standard electrode potential. Certain parameters may be constrained to be equal. For example the concentration of added alkali can be refined, but constrained to be the same for a set of titration curves. Fk is the kth concentration of free reactant; for example it may be H+. Ti is the total concentration of the ith reactant. 3. The statistical information concerning the distribution of weighted residuals on e.m.f. is expected to be most valuable in the process of model selection. Early trials show that the statistical information supplied by SUPERQUAD is more satisfactory than that of MINIQUAD, and leads more convincingly to selection of the best model. In addition to the errors in e.m.f., the errors in volume can also be back-calculated. Thus, the original titration curve can be totally reconstructed, including calculated errors on all measurements. 4. Flexibility. There may be 1 or 2 electrodes reading either e.m.f. of −log Fk, 2, 3 or 4 reactants and up to 18 information constants. The case of 2 reactants and 2 electrodes is included. The computer coding (FORTRAN) has been thoroughly checked for portability onto the widest possible range of computers. Input and output have been oriented towards users having 80 characters video display terminals as the principal input/output device. 5. Details concerning availability of machine-readable copies of SUPERQUAD and associated text data are available from P.G.