A general saturation equation is derived which is shown to describe a wide variety of nutrient-response relationships in higher organisms. Iterative multiple linear regression analysis is used to obtain least squares estimates of the constants defining theoretical nutrient-response curves. Curves thus generated accurately predict experimentally observed responses. From this treatment, response parameters are developed which are analogous to Vi.. and Km of enzyme kinetics. It is proposed that this model be applied in evaluating nutritional requirements and in assessing the relative biological efficiency of nutrient sources.It is well established that bacterial growth rates obey saturation kinetics with respect to the concentration of limiting nutrient (1, 2). However, the nutritional responses of animals and humans have been less amenable to satisfactory mathematical analysis. Linear, semi-logarithmic, and quadratic equations have been developed to describe the nutrient-response curves of higher organisms (3-5). In general, these models have found utility only within narrow ranges of nutrient intake and possess little, if any, theoretical basis. In this communication, we report the derivation of a general saturation equation and its application to the nutritional responses of higher organisms. A preliminary report of these findings has recently been published (6, 7). DERIVATIONThe rationale for applying saturation kinetics to gross biological responses derives from the following considerations. Organisms absorb and utilize nutrients via sequences of translocations and transformations, and for any particular metabolic state one step of a sequence would be expected to be ratelimiting for the process as a whole. If the identity of the sequence-controlling reaction does not change with time or nutrient intake, then the overall response of the sequence to graded levels of nutrient will reflect the kinetics of the ratelimiting step. Since many translocations and transformations. of intermediary metabolism obey saturation kinetics individually, we have explored the possibility that data from feeding experiments might be treated mathematically as manifestations of saturable phenomena.Visual inspection of a number of nutrient-response curves from literature sources reveals basic similarities to saturation functions. In general, most nutrient-response curves tend to "plateau out," i.e., to approach an asymptotic or limiting response at high nutrient intake. We have observed that the curvature of nutrient-response functions in approaching this asymptote resembles either hyperbolic saturation curves of the Michaelis-Menten type or sigmoidal saturation curves described by the Hill equation (8, 9). However, direct application of either the Michaelis-Menten or Hill equation to nutrient-response curves is ordinarily precluded by the fact that experimental nutrient-response curves rarely pass through the origin of the coordinate axes as required by these equations. 4327From such considerations, two criteria evolved which...
L-lysine monohydrochloride (LMH) is widely available to the public as a nonprescription oral supplement. Most of the pharmaceutical-grade product is used as a suppressant of recurrent herpes simplex infections. Recent publications indicate the possibility of other therapeutic uses, e.g., in cardiovascular disease and osteoporosis. These and other potential applications are surveyed and evaluated in this review with suggestions for further study. Data on toxicity are reviewed and recommendations made regarding safety of chronic dosage levels.
Evidence is reviewed that dietary habits in industrially developed countries, especially an increased frequency of ingestion of foods of high energy density, may contribute to excessive hepatic cholesterol synthesis and to a preponderance of lipogenic versus lipolytic effects on the arterial intima, thereby favoring the formation and progression of atheroma. These effects are mediated by the rise and fall of circulating insulin levels. The evidence is suggestive of the possibility that frequent and prolonged exposure of the arterial wall to high circulating levels of insulin may favor the development of atherosclerotic lesions. Research on diet-atherosclerosis relationships should take into account not only overall diet composition but individual meal composition and size and their effects on serum insulin levels, as well as meal spacing and the relative durations of absorptive and postabsorptive periods during the 24-hour daily cycle.
The objective of this study is to propose new methods for the determination of biological efficiency (the ability of a nutrient to produce a response) and for comparison of the efficiencies of alternate nutrient sources. The proposed methods are based on a four-parameter kinetic model which describes response as a function of intake. The comparison of the abilities of two proteins (casein and soybean protein concentrate) to promote weight gain in weanling rats is presented as an example; however, the model is also useful for other nutrients (proteins, amino acids, vitamins, minerals, etc.) and other responses (blood enzyme or protein levels, tissue enzyme levels, etc.). Application of the method leads to useful comparisons of nutrient sources as well as information concerning the maximum efficiencies and rates of nutrient utilization from different sources.
The reaction between diborane and boron trimethyl leads to the formation of mono-, di-, tri-, and tetramethyl derivatives of diboranee2 But only one dimethyldiborane, namely, the unsymmetrical compound, is obtained by this reaction. I t therefore seemed desirable to seek for a method by which the symmetrical isomer, C H~B H~B H Z -CH3, could be prepared. The success of this search was a direct consequence of the hypothesis that the molecular group BH3 (borine) plays an important role in many of the reactions of diborane; the usefulness of this hypothesis is thus further demonstrated.Earlier work had shown that diborane reacts with substances such as trimethylamine, to form complex compounds of b~r i n e .~ As described below, the methyl derivatives of diborane react with trimethylamine in analogous fashion, producing methyl derivatives of borine trimethylammine-derivatives in which the complex bond is less stable than in borine trimethylammine itself. It therefore seemed feasible to search for a reagent which would form a complex compound of borine a t a temperature a t which this reagent could not form an analogous complex compound of methylborine. Such a reagent would be expected to react with methyldiborane (CH3BH2-BH3) to remove the borine group, leaving the methylborine free to form the desired symmetrical dimethyldiborane by direct association. The whole process thus would be represented by theTrimethylamine is not a suitable reagent for this purpose, because its complex compounds with the borines are too stable. But dimethyl ether reacts with diborane to form the compound BH3-(CH&O, whose decomposition pressure a t -80" is more than half as great as the vapor tension of the ether a t this ternperat~re.~ Since complex (1) This paper is taken from a dissertation presented by Nestor W. Flodin t o the Faculty of the Division of the physical Sciences of the University of Chicago, in partial fulfilment of the requirements for the degree of Doctor of Philosophy. Its contents were presented a t the Ninety-sixth meeting of the American Chemical Society, Milwaukee, September 7, 1938.(2) Schlesinger and Walker, THIS JOURNAL, 51, 621 (1935).Burg and Schlesinger, d i d . , 59, 780 (1937). (4) Schlesinger and Burg, ibid., 60, 296 (1938). compounds of methyl borines are, in general, less stable than those of borine, it seemed likely that the methyl ether compound of methylborine could not exist at this temperature. In agreement with this reasoning, monomethyldiborane was found to react with dimethyl ether according to the equation 2CHsBHzBHs + 2(CHs)zO 2BHs.(CHs)20 + CHsBHpBHzCHsThe conclusion that the stabilities of complex compounds of borine and its methyl derivatives decrease with increase in the number of methyl groups, is based upon evidence of the following type. Molecular weight determinations in the gas phase show that trimethylborine trimethylammine, (CH3)3B.N(CH3)3r is about 70% dissociated at 80" into its constituents, trimethylborine and trimethylamine. The compound ( C H~) Z B H . N ( C H~)~, on the other h...
During the period 1950-1975, protein and amino acid metabolism and its application to world nutrition problems constituted a major focus of nutrition research. A large part of this research was concerned with the potential benefits to be expected from lysine supplementation of cereal foods, stimulated by the availability, beginning in 1955, of commercial quantities of L-lysine monohydrochloride from industry. Events during this era and lessons learned are reviewed by the author, a participant in the commercialization of lysine.
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