Charles M. Brown

EQUIL 93: a tool for experimental and clinical urolithiasis

An extensively updated version of the EQUIL software is described. The former version, designated EQUIL2, is widely used to study urolithiasis and related areas of biomineralization. In this report, we discuss recent enhancements which give EQUIL93 an expanded scope of application. This program has been frequently used in studies of the physicochemical processes underlying stone salt crystallization, especially crystal growth and nucleation, but it has also been employed as an aid for in vivo research and as an evaluator of therapeutic measures. We illustrate several new applications, including some outside the urologic realm, and we discuss how the enhanced software can be helpful in stone risk assessments.

Nucleation of calcium oxalate monohydrate: use of turbidity measurements and computer-assisted simulations in characterizing early events in crystal formation☆

Abstract To examine the nucleation of calcium oxalate monohydrate (COM) crystallization, we have determined the time interval from initial formation of a supersaturated COM solution to the first appearance of turbidity or crystals. The turbidity measurements were conducted with the unaided eye, whereas crystal formation was analyzed using an inverted and an image analysis system. The lag time kinetics were compared with previous nucleation studies using computer simulations with the Gibbs-Thomson nucleation equation and the parabolic growth rate law. The nucleation behavior can be described as homogeneous or heterogeneous depending on the range of initial relative supersaturation. The calculated interfacial energies for homogeneous and heterogeneous nucleation agreed rather well with earlier investigations. Moreover, this investigation provided the opportunity to verify the utility of our particle size distribution program for simulating precipitating systems, and the experimentally determined surface energy was obtained from simulations of the nucleation kinetics.

Calcium oxalate monohydrate crystallization: citrate inhibition of nucleation and growth steps

Abstract The inhibitory action of citrate on calcium oxalate monohydrate (COM) crystallization has been examined in terms of nucleation and crystal growth kinetic properties. Lag-time data for the appearance of crystals and [14C] oxalate incorporation under crystal growth conditions allowed us to investigate the influence of citrate at physiological levels (3.5mM). Moreover, through the use of the EQUIL software, we formulated our solutions based on calculations of solute composition such that free calcium concentrations were the same in the absence and presence of this tricarboxylic acid. The presence of citrate had little effect on the apparent interfacial free energy as determined by nucleation kinetic studies, but total particle production was greater in the absence of citrate; this was evident from electron microscopy and was also indicated by corresponding values of pre-exponential terms of the Gibbs-Thomson equation. Crystal growth rates were lowered in the presence of citrate to 30% of the uninhibited value, and distinctive morphological habit modifications were also observed by scanning electron microscopy. Together, these findings suggest that citrate may influence COM crystallization at several stages, and we present a model for face-specific growth inhibition by citrate acting on the (010) COM crystal face.

Use of the computer program EQUIL to estimate pH in model solutions and human urine.

SummaryThe computer program EQUIL was designed to calculate relative supersaturations of solute components of common urinary stones. In an extended software version, quantitative consideration of charge balance for a priori or a posteriori pH estimation was added. The reliability of this computation was tested with hydrogen ion titration of buffer solutions containing HEPES [N-(2-hydroxyethyl)piperaizine-N′-ethanesulfonic acid] as well as samples of normal human urine. In the model solutions with HEPES, the difference between calculated pH values and the measured pH was smaller than 1.2% for any titration step within the buffer zone (pH 8.5-6.8). The pH values calculated for whole urine differed from the measured pH by 7% to 53%, and the calculated charge inbalance ranged from 2.6 to 9.6 mM. This net cation inbalance indicates that there is a need to account for other anionic components, including hippurate, amino acids, and isocitrate. In experimental solutions, charge balance calculations with EQUIL can be of great utility because they permit a priori estimation of pH or computation of the composition at a desired pH.

Calcium oxalate crystal morphology: influence of phospholipid micelles with compositions based on each leaflet of the erythrocyte membrane☆

Abstract Because phospolipids appear to be involved in kidney stone formation, we investigated in vitro calcium oxalate crystal formation in the presence of micelles corresponding to the phospholipid content in the cytoplasmic and exoplasmic leaflets of the plasma membrane. For these studies, we used values for phospholipid composition in human red blood cells as a model system. Distinct morphological and particle number concentrations were observed with these and phosphatidylcholine micelles as well. The relationship of these observations to mechanisms of crystal-membrane interactions and possible early steps in kidney stone formation are discussed.

Suitability of three kinetic models for whewellite crystallization

SummaryModels commonly used to interpret seeded crystal growth data were examined numerically: the parabolic model, the Burton-Cabrera-Frank (BCF) model, and three variations of a surface nucleation model. The choice of the time-dependent variable in the parabolic model had no important effect on the goodness of fit to experimental data. In the integral representation of all the models, curve-fitting of parameters gave such excellent fits of a common data set that useful distinctions between the models could not be made. In the differential representation, curve-fitting showed small differences that might be used with very precise data to choose the most appropriate model when the assumption of constant surface area is valid. In the differential representation, the parabolic growth law is clearly distinguished from the BCF model. We conclude that even with high-quality constant-composition growth data on seeded crystals with monitoring of changes in accessible surface, it would be difficult to identify the most appropriate model(s) to use in the relative supersaturation range of 1–11.

Inhibitory Action of Citrate on Calcium Oxalate Monohydrate Crystal Nucleation and Growth

Because calcium oxalate monohydrate is an important urinary stone salt, considerable attention has been devoted to the analysis of COM crystallization in an attempt to understand the associated processes of nucleation, crystal growth, aggregation, and breakup. Considering the paracrystalline dendritic nature of oxalate stones, many urinary agents may bind to and thereby alter crystal growth and/or adhesion to other components in the stone lamina. In addition to calcium oxalate hydrates, other carboxylic ligands that may interact with COM crystals include citrate1, phosphocitrate2, the aspartate-rich uropontin3, γ-carboxyglutamate-containing nephrocalcin4, and the cytoplasmic membrane component phosphatidylserine (F Novin, CM Brown, and DL Purich, unpublished findings). These agents each contain one or more carboxyl groups which potentially could substitute for oxalate carboxyls within the crystal lattice. Recently, our laboratory conducted crystal growth and nucleation rate measurements to investigate how agents might promote or inhibit COM crystallization5. Our work has centered on the inhibitory action of citrate, a prominent urinary metabolite that can sequester calcium ions and thereby reduce the relative supersaturation of urine with respect to calcium oxalate monohydrate1. In the present study we describe nucleation and growth kinetics in experiments for which we used the EQUIL speciation software to maintain the free, uncomplexed calcium ion concentration and hence avoid effects of changes in relative supersaturation. We also explored the relationship of these kinetic data to crystal morphology changes arising in the presence of citrate, and we have rationalized structural changes in terms of crystal face-specific interactions with citrate and/or calcium citrate complex. This has required the application of molecular recognition theory6, 7 to calculate the electrostatic surface potential of stable calcium oxalate monohydrate crystal surfaces and to characterize stereochemical interactions of carboxylic ligands with COM crystal faces. Our work supports the conclusion that citrate binds selectively to the (010) face, thereby blocking further crystal growth on that face.

Use of EQUIL to Estimate pH of Well-Defined Solutions

The software EQUIL (1, 2) allows calculations of ion activities, relative supersaturations and charge balance, when concentrations and pH are entered. In a well-defined solution, charge balance is expected to be zero at any measured pH and, therefore, calculations of pH should be possible. This concept was examined with titrations of HEPES buffer (3).