Studies to Explain Further, Why Percentages of Eicosanoid Precursor Fatty Acids Associate Positively in Chicken Muscle

Background: Polyunsaturated fatty acids with 20 or 22 carbon atoms are precursors of eicosanoids and docosanoids, which are important regulatory molecules in cell physiology. In breast muscle of chickens, we recently reported that percentages of these precursors were positively associated. Subsequently, we observed that the concentration ranges of the fatty acids seemed to cause the positive associations, e.g. between %EPA (eicosapentaenoic acid, 20:5: n3) and %AA (arachidonic acid, 20:4 n6). Aim: To explain further correlations between relative amounts of eicosanoid and docosanoid precursors. Methods: Typically, the precursors had low numbers and low variability, as compared with the predominant fatty acids, such as oleic acid (18:1 c9). We first present considerations concerning associations in general between relative amounts of three positive scale variables, two of which (A, B) having narrow ranges relative to the third one (C). Next, we show results of computer experiments to test the reasoning. Results and Discussions: We made S = A + B + C, i.e. %A + %B + %C = 100. %A correlated positively with %B, whereas %A (%B) related negatively to %C. The particular ranges of A, B, and C seemed to explain these associations. We found that slope of %A (abscissa) vs. %B approached B/A. Furthermore, slope of %A (abscissa) vs. %C approached –(1 +B/A), and that of %B (abscissa) vs. %C was near –(1+ A/B). We also show equations of regression lines concerning associations between A (B, C) percentages of S, when ranges of A and B are narrow relative to C. Finally, we compare slope values obtained by the formulas, and by linear regression. Conclusions: We suggest that Intended Ranges of eicosanoid precursor fatty acids might have arisen through evolutionary selection, thereby causing Distribution Dependent Correlations, mathematically. Possibly, this selection could improve the balance between eicosanoids (docosanoids). Definitions and Abbreviations: Variability: the width or spread of a distribution, measured e.g. by the range and standard deviation. Distribution: graph showing the frequency distribution of a variable within a particular range. In this article, we also use distribution when referring to a particular range, a – b, on the scale. Uniform distribution: every value within the range is equally likely. In this article, we may write “Distributions of A, B, and C were a - b, c - d, and e - f, respectively”. OA = Oleic Acid (18:1 c9); LA = Linoleic Acid (18:2 n6); ALA = Alpha Linolenic Acid (18:3 n3); AA = Arachidonic Acid (20:4 n6); EPA = EicosaPentaenoic Acid (20:5 n3); DPA = DocosaPentaenoic Acid (22:5 n3); DHA = Docosa Hexaenoic Acid (22:6 n3); DGLA= Dihomo Gamma Linolenic Acid (20:3 n6); EDA = Eicosa Dienoic Acid (20:2 n6); ETA = Eicosa Trienoic acid (20:3 n3).