Mass Law Equations Research Articles

Sorption of rare earth elements onto basaluminite: The role of sulfate and pH

Abstract Scandium, yttrium and lanthanides (REE) are critical raw materials in increasing demand for modern technology, so identifying and developing new sources of REE has become a pressing need. REE concentrations in acid mine drainage (AMD) are several orders of magnitude higher than those in natural water, and their recovery is of economic interest. Passive remediation systems designed to minimize AMD impact on the ecosystem retain REE in solid waste, where basaluminite, Al4SO4(OH)10·5H2O, is the mineral responsible for the scavenge. However, no information about the retention mechanisms of REE is currently available in the literature. The objective of the present work is to study the adsorption of lanthanides, yttrium and scandium onto synthetic basaluminite over a pH range of 4–7 at room conditions. Since sulfate is ubiquitous in AMD, the adsorption has been investigated with variable sulfate concentrations. Experimental results show that sorption onto basaluminite is strongly dependent on pH, starting at pH 5 for lanthanides and yttrium and at pH 4 for scandium. At any given pH values, sorption increases with sulfate concentration. Distribution coefficients, defined as KD = [REEsorbed]/[REEsolution], are higher for Sc, and across the lanthanide series, the distribution coefficients increase from La to Lu according to decreasing ionic radius, where yttrium is considered close to Ho. Experimental results were modeled using a sorption model that considers mass law equations where the strong sulfate aqueous complex, MSO4+, is adsorbed by exchanging a proton with the mineral surface. The dependence of the experimental results on pH suggests the formation of monodentate binding for Y and lanthanides. The bidentate complex for Sc is deduced by the two proton exchange per mol of Sc extracted from the experiments. The thermodynamic constants for the surface complexation reactions were obtained from experiments with high sulfate concentration and were successfully applied to the experiment with low sulfate content and different solid-liquid ratios. Therefore, the model can be applied to interpret the REE geochemistry in natural systems with variable pH and sulfate concentrations.

Micellization of Pentanediyl-1,5-bis(hydroxyethylmethyl hexadecylammonium Bromide) as a Cationic Gemini Surfactant in Aqueous Solutions: Investigation Using Conductometry and Fluorescence Techniques

Pentanediyl-1,5-bis (hydroxyethylmethylhexadecylammonium bromide) was synthesized and characterized as a type of novel gemini cationic surfactant. Its solution properties were determined at various temperatures by conductivity measurements and the fluorescence quenching technique. The CMC increased in the range of 1.85 to 2.77 μmol⋅L−1 as the temperature increased. The aggregation number was determined at various concentrations of NaBr solutions by the fluorescence quenching of pyrene. The thermodynamic parameters of micellization were determined using the mass law equation and the values of ΔG °, ΔH °and ΔS ° were determined for the micellization process.

Solid Supports in Enzyme‐Linked Immunosorbent Assay and Other Solid‐Phase Immunoassays

AbstractFor Abstract see ChemInform Abstract in Full Text.

Solid supports in enzyme-linked immunosorbent assay and other solid-phase immunoassays.

Most modern immunoassays involve the use of synthetic solid phases to immobilize one of the reactants, often by simple adsorption. These solid-phase immunoassays (SPIs) involve ligand-receptor interactions that occur within a reaction volume close to the solution/solid-phase interface. As a consequence, the immunochemistry/biochemistry of these ligand-receptor interactions differ from their counterparts in solution. Nevertheless, mass law equations can be derived for measuring the antigen capture of solid-phase antibodies, for determining the affinity of solid phases for protein adsorption, and for estimating antibody affinity. Many proteins adsorbed on polystyrene or silicone suffer adsorption-induced conformational changes (ACC) and are partially or largely denatured. Alternative methods for immobilizing proteins and virus, while preserving antigenicity, may yield only a modest increase in functional reactant concentration. Peptides and small recombinant proteins appear to benefit especially from nonadsorptive immobilization. Not all solid phases commonly used in SPIs have the same properties, the same capacity for reactant immobilization, cause the same level of denaturation, or experience the same level of nonspecific binding. Empiricism, adherence to a few practical rules of thumb, and avoidance of certain "old wives tales" can be valuable in the successful development of SPIs.

Solid Supports in Enzyme-Linked Immunosorbent Assay and Other Solid-Phase Immunoassays

A very large proportion of modern immunoassays involve the use of synthetic solid phases to immobilize one of the reactants. These solid-phase immunoassays (SPIs) therefore involve ligand–receptor interactions that occur within a reaction volume close to the solution/solid phase interface. As a consequence, the immunochemistry/biochemistry of these ligand–receptor interactions differs from that of their counterparts in solution. Furthermore, the immobilization process can significantly alter the biological activity of the reactant; most adsorbed proteins on polystyrene or silicone are partially or largely denatured. Therefore the use of alternative methods of immobilization is attractive but may result in little increase in the amount of total functional reactant. However, all commonly used solid phases do not have the same properties or the same capacity for reactant immobilization or experience the same level of nonspecific binding. Empiricism plays a major role in SPIs. Derivations of mass law equations for measuring the antigen capture of solid-phase antibodies, for determining the affinity of solid phase for protein adsorption, and for estimating antibody affinity are reviewed.

Fluorescence Analysis of the Labile Iron Pool of Mammalian Cells

The labile iron pool (LIP) of cells constitutes a cytosolic fraction of iron which is accessible to permeant chelators and contains the cells’ metabolically and catalytically reactive iron. LIP is maintained by a balanced movement of iron from extra- and intracellular sources. We describe here an approach for tracing LIP levels in living cells based on the fluorescent probe calcein (CA). This probe binds Fe(II) rapidly, stoichiometrically, and reversibly while forming fluorescence-quenched CA–Fe complexes. Cells are loaded with CA via its acetomethoxy precursor CA-AM, attaining 1–10 μmintracellular concentrations and retaining full viability. LIP is defined here operationally as the sum of “free” and CA-bound iron of the cell. The method for assessing LIP is based on the measurement of : (a) the total intracellular concentration of CA in CA-loaded cells ([CA]t), which is estimated from fluorimetric measurements of CA in a given suspension of cells, the number of cells, and the cell volume; (b) the intracellular [CA–Fe], the concentration of [CA] bound to metals (>95% iron), which is assessed from the relative rise in fluorescence (ΔF) elicited by addition of highly permeant and high-affinity binding chelators such as salicyladehyde-isonicotinoyl-hydrazone (SIH) and the value of [CA]t; and (c) the “free” cell iron concentration [Fe(II)], which is computed from the experimentally determined values of CA–Fe(II)'s dissociation constant (Kd) in various cell lines grown in suspension (Kd= 0.22 ± 0.01 μm). The value of cellular LIP is defined as the sum of [CA–Fe] and [Fe]. It is derived from the experimental determination of [CA]tand [CA–Fe] and from calculation of [Fe] by application of the mass law equation using theKdvalue of [CA–Fe]. The estimated values of LIP for resting erythroid and myeloid cells are in the range of 0.2–1.5 μm. The values varied commensurately with cell iron loads and iron chelator treatment. The method provides a simple, noninvasive tool for on-line monitoring of cytosolic iron under normal and abnormal conditions of cell iron supply and for assessing the dynamics of intracellular iron in living cells.

Sensitivity of Uranium Solubility to Variation of Ligand Concentrations in Groundwater.

Abstract The sensitivity of uranium solubility to variation of ligand concentrations in the groundwater was systematically evaluated. Predominant dissolution reactions between uranium solubility limiting solids and predominant aqueous species were obtained by means of calculating uranium solubility and speciation using the NEA Thermochemical Data Base of uranium and the geochemical code SOLGASWATER. Logarithm of the mass law equations for the predominant dissolution reactions allowed that logarithmic concentration of total dissolved uranium species, log[UO2+ 2]T, was a linear function of pH and logarithm of ligand concentration. The equation for the difference of log[UO2+ 2]T between the U-H2O system and U-ligand-H2O system was derived from the linear functions in the common pe-pH area of the two systems. Differential coefficients obtained from the difference of log[UO2+ 2]T allowed to judge which predominant dissolution reactions are sensitive to the variation of ligand concentrations as follows: (1) The...

Adsorption of Inorganic Pollutants in Aquatic Systems

Adsorption often dictates the fate of trace inorganic pollutants in aquatic systems. In contrast to the nonspecific sorption mechanism proposed for hydrophobic organic compounds, adsorption of inorganic solutes is viewed as a site‐specific process in which ions bind (chemically) at functional groups on particle surfaces. This conceptual model is supported by the finding that adsorption of ions on model adsorbents with relatively well‐defined surface groups (e.g., hydrous metal oxides) can be described via mass law equations, a fact which forms the basis for all of the so‐called surface complexation models. Surface complexation reactions are distinguished from reactions among monomelic solutes in that the total energy of interaction includes long‐range electrostatic effects that vary with surface charge. Electrostatic effects are accounted for by applying a coulombic correction factor (activity coefficient) to intrinsic surface complexation constants. Formulations for the coulombic correction term differ a...

Surface ionization and complexation at the oxide/water interface. 3. Adsorption of anions

The site-binding model for the electrical double layer of hydrous oxides reported in a previous paper is applied to adsorption of anions from dilute solution. Generally, more than one stoichiometric surface reaction is needed to describe the adsorption behavior of divalent weak acid anions. If mass law equations for surface reactions are corrected for effects of the electrostatic field at the interface, the calculated adsorption density depends upon the type of surface species formed. It is shown that calculations which consider formation of surface complexes by protonated anionic forms, e.g., HCrO 4 −, HSeO 4 −, HSO 4 −, are more consistent with experimental adsorption data than complexation by bidentate surface sites. Modeling results predict that adsorbed anions are more easily protonated than those in bulk water, and a qualitative explanation for this phenomenon is presented. The model applies over a wide range of solute concentrations and accounts for effects of changes in composition of the supporting electrolyte. In addition calculated results for a shift in pH PZC upon specific adsorption of sulfate are in reasonable agreement with other experimental studies.

Surface ionization and complexation at the oxide/water interface II. Surface properties of amorphous iron oxyhydroxide and adsorption of metal ions

The site-binding model for the electrical double layer of hydrous oxides reported in a previous paper is applied to the adsorption of metal ions from dilute solution and to complex heterogeneous systems, i.e., amorphous iron oxyhydroxide. More than one stoichiometric surface reaction is usually needed to describe the adsorption behavior of dilute heavy metal ions. If mass law equations for surface reactions of metal ions are corrected for effects of the electrostatic field at the interface, the calculated adsorption density depends upon the type of surface species formed. It is shown that calculations with surface reactions involving hydrolytic complexes of metal ions, e.g., Pb(II), Cd(II), Cu(II), Ag(I), are more consistent with experimental adsorption data than complexation by bidentate surface sites. A table of intrinsic surface complexation constants for various metal ions and oxide substrates is presented. Similar to results reported earlier for major electrolyte ions, the stability constants of surface complexes of heavy metal ions with the silica surface are significantly less than for other oxide surfaces. Empirical surface parameters for model calculations with iron oxyhydroxide are derived and the results are compared with experimental adsorption data for Cu(II) and Ag(I).

An analysis of measured and calculated calcium quantities in serum.

Potentiometrically measured ionized calcium (Ca2+) was compared with total and albumin corrected S-Calcium and calculated Ca2+ in serum samples from blood donors and patients, for whom a request of S-Calcium has been made. Total S-Calcium, Ca2+ and S-Albumin in donors conformed with a simple mass law equation with a mean KCaAlb = 95 l/mol, whereas apparent albumin binding affinity rose with decreasing S-Albumin in patients (due to rise of other calcium binding proteins) with resulting overestimation of albumin corrected and particularly of calculated Ca2+. The frequency and severity of hypoalbuminaemia in patients make calculated Ca2+ unreliable and albumin corrected S-Calcium the clinically most satisfactory routinely practicable substitute for direct Ca2+ measurement.

Studies With Ion Exchange Calcium Electrodes

Ion exchange calcium electrodes provide the first practical means for direct study of calcium-protein interaction in biologic fluids. Since cirrhotic patients frequently have hypocalcemia, hypoalbuminemia, hyperglobulinemia, and alkalosis, they are of particular interest for study of calcium binding and other physicochemical factors influencing serum calcium in man. Previous studies in normal subjects 2, 3 have shown that variation in serum total calcium [Ca] is almost entirely accounted for by variation in protein-bound calcium [CaProt]; serum-ionized calcium [Ca ++ ] remained within rather narrow limits. About 80% of [CaProt] was bound to albumin and 20% to globulin(s). Serum [Ca] was therefore an indirect measure of serum albumin. Binding appeared to obey the mass law equation and a nomogram was constructed for estimation of [CaProt] without ultrafiltration. In the present paper, these same normal subjects are compared with 42 patients with advanced cirrhosis. In both groups, there was no apparent relationship between serum-ionized and total calcium concentrations. Serum [Ca ++ ] was more variable in cirrhotic patients and, on the average, was reduced about 5%. Serum [Ca], [CaProt], and [Alb] were also significantly reduced; total ultrafiltrable calcium and diffusible calcium complexes [CaR] were significantly increased. The increase in [CaR] was not due to citrate or phosphate; the complexing ligand(s) remain unidentified. As in normal subjects, variation in [Ca] was almost entirely accounted for by variation in [CaProt]; the latter was linearly related to serum [Alb]. Serum [Ca] was therefore an indirect measure of [Alb]. In contrast to normal subjects, there was no detectable binding to globulins in patients with cirrhosis, despite significantly elevated globulin levels, an observation which strongly suggests deficiency of a normal globulin. A model is presented for the relation between total calcium and each of the three calcium fractions of serum as a function of serum albumin, and an equation is presented for estimating [CaProt] without ultrafiltration. A subsequent paper will consider the calcium-binding properties of serum proteins in cirrhosis in relation to the mass law equation. While the calcium electrode has not been perfected to the extent of current p H electrodes, we believe that it provides an important new tool for studies of calcium-protein interaction in biologic systems.

Some quantitative aspects of the labelling of proteins with 125 I by the iodine monochloride method.

The labelling of proteins by the iodine monochloride method was studied by using a mathematical model. The equations used were primarily derived from the mass law equation of the isotopic exchange reaction between [(125)I]iodide and iodine monochloride. For convenient application, all equations were programmed into a computing desk-top calculator. To support the validity of the theoretical model, a series of iodinations of insulin were performed under various labelling conditions. The results of these experiments compare well with the theoretically derived values. Deviations from the theoretical values occurring at molar ratios of [(125)I]iodide to iodine monochloride < 0.1 and > 4.0 are explained and suggestions made about how to prevent them. The mathematical model was used to simulate the isotopic exchange, and the iodination reaction under various conditions, to study (a) the influence of the amount of [(125)I]iodide on the amount of [(125)I]iodine monochloride formed, (b) the influence of the specific radioactivity of [(125)I]iodide on the amount of [(125)I]iodine monochloride formed, and (c) the influence of the specific radioactivity of [(125)I]iodide on the number of millicuries needed for labelling to a desired extent.

Ionized calcium in normal serum, ultrafiltrates, and whole blood determined by ion-exchange electrodes.

Ion-exchange calcium electrodes represent the first practical method for the direct measurement of ionized calcium [Ca(++)] in biologic fluids. Using both "static" and "flow-through" electrodes, serum [Ca(++)] was within a rather narrow range: 0.94-1.33 mmoles/liter (mean, 1.14 mmoles/liter). Within a given individual, [Ca(++)] varied only about 6% over a several month period. Consistent pH effects on [Ca(++)] were observed in serum and whole blood, [Ca(++)] varying inversely with pH. Less consistent pH effects were also noted in ultrafiltrates, believed to largely represent precipitation of certain calcium complexes from a supersaturated solution. Heparinized whole blood [Ca(++)] was significantly less than in corresponding serum at normal blood pH, related to the formation of a calcium-heparin complex. [Ca(++)] in ultrafiltrates represented a variable fraction (66.7-90.2%) of total diffusible calcium. There was no apparent correlation between serum ionized and total calcium concentrations. Thus, neither serum total calcium nor total ultrafiltrable calcium provided a reliable index of serum [Ca(++)]. Change in serum total calcium was almost totally accounted for by corresponding change in protein-bound calcium [CaProt]. About 81% of [CaProt] was estimated to be bound to albumin and about 19% to globulins. From observed pH, serum protein, and [CaProt] data, a nomogram was developed for estimating [CaProt] without ultrafiltration. Data presented elsewhere indicate that calcium binding by serum proteins obeys the mass-law equation for a monoligand association. This was indicated in the present studies by a close correspondence of observed serum [Ca(++)] values with those predicted by the McLean-Hastings nomogram. While these electrodes allow study of numerous problems not possible previously, they have not been perfected to the same degree of reliability obtainable with current pH electrodes. The commercial (Orion flow-through) electrode is: (a) expensive. (b) requires periodic replacement of membranes, and (c) has not yet been thermostated. As with blood pH measurements. (d) electrode response is logarithmic, i.e. small potential errors generate rather large [Ca(++)] errors. (e) loss of CO(2) should be prevented, and (f) errors due to other cations must be considered under certain conditions. Despite these limitations, we believe the electrode represents a major advance in calcium metabolism.

Cation-binding capacity of membranes isolated from Micrococcus lysodeikticus.

A study was made of H(+), Na(+), K(+), Ca(++), and Mg(++) binding and ion-exchange properties of the plasma-mesosome membrane system isolated from Micrococcus lysodeikticus strain NCTC 2665. Titration curves were obtained on membranes prepared according to the method of M. R. J. Salton and further exposed to pH 4 for 4 hr (membranes-H). The dissociation coefficients and binding capacities were obtained by applying the mass law equation and the plot of G. Schatchard to the data. The membranes-H possess four kinds of dissociable groups with pK 4.96, 4.18, 3.60, and 3.09, respectively, and a total binding capacity of 0.65 meq/g (dry weight). Potentiometric titrations of cations in the presence and in the absence of membranes-H show that cations (Na(+), K(+), Ca(++), and Mg(++)) are bound by the dissociated groups of the membrane. The fall in pH value for bivalent cations is greater than that for monovalent cations. Cations of the same valency produce equal diminutions on pH. Furthermore, ion-exchange tests carried out on membranes saturated with Mg(++) or Na(+) and suspended in a medium containing (45)Ca show that the cations are reversibly bound.

Circulation of the Blood—Men and Ideas Edited by Alfred P. Fishman and Dickinson W. Richards (review)

BOOK REVIEWS Circulation ofthe Blood—Men and Ideas. Edited by Alfred P. Fishman and Dickinson W. Richards. New York: Oxford University Press, 1964. Pp. xiv+859. $18.00. "Magnificent" is the word for this beautifully illustrated, finely printed volume on the men and women who since ancient times have made circulatory physiology! The majority ofthe fourteen distinguished authors have gone back to antiquity, to the headwaters of our knowledge, and, following the ever-widening stream, bring us near or up to the present. Servetus walks out ofCournand's chapter "Air and Blood" to discover the pulmonary circulation, later to die at the stake for his unitarian beliefs. William F. Hamilton in his chapter on cardiac output takes us to the laboratory ofthe kind and generous Carl Ludwig , his newly developed kymograph at hand, to hear "the shout ofdelight with which he would greet some new finding." Vesalius' insistence on verifying anatomical fact at the dissecting table, rather than accepting Galen's precept, is documented in Richard Bing's chapter "Coronary Circulation." Physiology comes alive as we hear of the struggles, the successes, and the failures of these and dozens of other pioneers. W. H. Mommaerts presents a scholarly, essentially modern review ofheart muscle. Drs. Louis Katz and Hellerstein begin their discussion of electrocardiography with the early history ofelectricity and end with the micro-electrode in the cardiac muscle fiber. E. M. Landis brings us the perspective ofnearly forty years studying the capillaries, with August and Marie Krogh justifiably looming large. Drs. Heymans and Folkow tell us of Claude Bernard, Brown-Séquard, Cannon, Loewi, and Dale in their "Vasomotor Regulation." Stephen Hales measures the blood pressure of a horse in Sir George Pickering's article on hypertension, from one page ofwhich the keen eyes ofRichard Bright stare out. The story ofhow E. K. Marshall and the late Homer Smith got involved in studying the aglomerular kidney of the goosefish is told by the latter, to whom, most fittingly, this volume is dedicated. Dr. S. E. Bradley writes on the splanchnic circulation, with emphasis on the development of knowledge of the hepatic circulation. Seymour Kety takes us from the Egyptian concepts ofthe brain up to his own development ofthe nitrous oxide method for measuring the cerebral blood flow. Geoffrey Dawes's chapter on the fetal circulation combines historical background with his latest views on this ever-controversial subject. By pointing out where a given topic appears elsewhere in the text, the editors have 134 Book Reviews Perspectives in Biology and Medicine · Autumn ic, knit together the wealth ofmaterial. Here is a unique volume, rigorous in its scholarship yet delightful reading for medical students, physicians, and physiologists alike. It is both a modern review ofthe circulation and a history ofits great discoveries. John F. Perkins, Jr. University ofChicago Radiation, Isotopes and Bone. By F. C. McLean and A. M. Budy. New York and London: Academic Press, 1964. This monograph is one in a current series developed through the cooperative efforts of the American Institute ofBiological Sciences and the United States Atomic Energy Commission 's Division ofTechnical Information. The goal ofthis series is specifically to direct attention to biologists' increasing utilization ofradiation and radioisotopes and in general to represent "the new, closer association between the physical and biological sciences" (foreworded by John N. Olive of the AIBS). To a biologist like McLean (who is a physician), this association probablyseems neither new nor closer than it has always been: in 1914 he became one ofthe first to measure the concentration ofblood glucose in man; in 1935 he applied the mass-law equation to interpret the results offrog-heart determinations of the state of calcium in serum; he was one of the first in this country to apply ECG; he worked with Van Slyke in 1915 on the mathematics ofkidney clearance; and recently he has applied such cybernetic terms as "feed-back" in his interpretation of calcium homeostasis. In spite ofhis preoccupation for halfa century with the application of exact measurements to biological problems, it seems rather clear from this book that McLean hardly cares to present physics and biology as closely related fields: it is a matter ofdefinition whether physics and biology are different...

The relationship of the cell surface to metabolism. XIII. The cation-binding properties of the yeast cell surface

The binding of exogenous bivalent and univalent cations by the yeast cell is rapid and reversible, obeying a simple mass-law equation. Bivalent cations, especially UO 2++, are bound more firmly than are univalent cations. There are at least two species of binding sites, tentatively identified as phosphoryl and carboxyl groups. These are located at the periphery of the cell, isolated from endogenous cations by a permeability barrier.

Reaction Between Antiseptics and Proteins and Antiseptic Activity of the Adsorbed Portion.

It is a well know fact that the action of antiseptics upon bacteria is greatly diminished by the presence of proteins, blood serum, tissue juices and pus, but whether this is due to a chemical combination with the protein or to adsorption of the antiseptic on the surface of the protein, is not so certain. Mathews, Heidenhain, and Chapman, Greenberg and Schmidt, who advocated the theory of chemical combination, dealt with denatured lyophobic protein and not with protein in the natural lyophillic state; this has given rise to serious misconceptions. Ashley Cooper has advanced some evidence that proteins adsorb phenols and do not enter into true chemical combination with them. The experiments of Grollmann on the binding of phenol red indicate that the dyes are adsorbed, but the values (i. e., 1/N approximating 1) obtained lay too close to agreement with the mass law equation also to make fine distinctions possible. Rosenthal also obtained an adsorption curve for the binding of rose bengal on a variety of proteins in acid solution. If the reaction with protein is one of chemical combination, it should proceed in direct proportion to the reacting masses, while if it is an adsorption, it should follow the Freundlich adsorption isotherm (X/N = KCl/n) and give a logarithmic curve. In order to study the reaction with proteins in their natural state, the protein (purified egg albumin) and dye were placed in a small wide-mouthed bottle containing, as a dialyzer, a segment of viscose sausage skin filled with water. The free crystalloid dye passes through the dialyzer until its concentration in the outside chamber is equal to that within, while any portion that is in colloidal form does not do so.

Quantitative Studies on the Action of Compound Hemolysins

Summary A quantitative study of the characteristic curves defined in preceding papers (1, 2 and 3) led to the conclusion that the complexities of these curves as they are experimentally obtained can be removed and the curves so simplified that they assume forms which are in harmony with the views proposed by Svante Arrhenius on the reaction between hemolytic amboceptor and complement by introducing the assumption into the calculation that neither heat inactivated hemolytic amboceptor serum is free from complement nor complement serum from natural amboceptor. Geometrical methods for introducing suitable corrections were developed for this purpose. The application of such methods permits the quantitative estimation of the contaminations. Heat inactivated hemolytic amboceptor serum may, when undiluted, contain complement in quantities not much lower in order of magnitude than the complement serum. Its effect may nevertheless not be noticeable on the Wassermann reaction as long as potent amboceptor serum is used which permits a correspondingly high dilution. Application of the law of chemical mass action makes the construction of theoretical systems of characteristic curves possible. Only the exponents of the mass law equations determine the shape of these curves. Such curve systems were calculated under various assumptions regarding the chemical combination between amboceptor and complement and found to present typical pictures characteristic of each reaction. It was shown that when the corrections above referred to are applied to the curves derived from the law of chemical mass action in the opposite direction complex curves result which agree with those experimentally obtained within the limits of experimental errors except in the region of complement deviation which the theory is not designed to cover. Rational systems for expressing strength of amboceptor and complement were proposed. Conclusions were drawn regarding the relative molar concentrations of amboceptor and complement. The assumption of a stoichiometric chemical reaction between amboceptor and complement explains all observations. The stipulation of an enzymatic nature of one or both does not seem justified. Summing up the results of all four papers on this subject, we might state that while Manwaring rightfully pointed out that Arrhenius' mathematical representation of the reaction between hemolytic amboceptor, complement and red blood cells is not in agreement with the experimental facts, we find it in agreement with them so far as only the reaction between amboceptor and complement is concerned. The constants which Arrhenius used in his equations are as all constants obtained by experiment subject to revision by later investigators.

THE AUTODESTRUCTION OF PEPSIN IN RELATION TO ITS IONIZATION

1. Evidence is presented that pepsin is a univalent acid with a value for pK of 6.85 (or a base, with pK 7.39). 2. The autodestruction of the pepsin is shown to be dependent in part upon an instantaneous irreversible change occurring in the ionized form of the enzyme (if it be an acid) or in the unionized form (if it be a base). 3. A further progressive autodestruction of pepsin at any given hydrogen ion concentration and temperature is defined by the mass law equation for a monomolecular reaction 4. The velocity of autodestruction of pepsin is directly proportional to the hydroxyl ion concentration. It is much less in the range of hydroxyl ion concentration from pOH 9.89-7.7, than in the range greater than pOH 7.7. In both of these ranges variations in pK with pOH may be represented by straight lines.