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Research Article | DOI: https://doi.org/10.31579/2637-8914/093
* Institute of Health and Society, Faculty of Medicine, University of Oslo, Norway, Box 1130 Blindern, 0318 Oslo, Norway, Telephone: +47 22844629/Fax: +47 22850590.
*Corresponding Author: Arne Torbjørn Høstmark, Institute of Health and Society, Faculty of Medicine, University of Oslo, Norway, Box 1130 Blindern, 0318 Oslo, Norway.
Citation: Arne T Høstmark. (2022). Studies to Explain Further, why Percentages of Eicosanoid Precursor Fatty Acids Associate Positively in Chicken Muscle. J Nutrition and Food Processing. 5(2); DOI: 10.31579/2637-8914/093
Copyright: © 2022 Arne Torbjørn Høstmark, this is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: 15 March 2022 | Accepted: 23 March 2022 | Published: 05 April 2022
Keywords: fatty acids; eicosanoid precursors; relative amounts; correlation rules; ranges; 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).
This work relates to body fatty acids, which are major diet constituents, and important factors in health and disease; polyunsaturated fatty acids with 20 or 22 carbon atoms are precursors of eicosanoids and docosanoids, which are significant regulatory molecules in cell physiology [1, 3]. AA, EPA, DPA, DHA, and DGLA are examples of such precursor fatty acids. Most organs and cell types produce eicosanoids, as catalyzed by cyclooxygenases, lipoxygenases, and epoxygenases [3].
EPA and AA represent two of the eicosanoid precursors, and these fatty acids seem to be metabolic antagonists [1 - 5]. EPA derived eicosanoids may decrease inflammatory diseases [6, 7], and may have a positive influence on coronary heart diseases [8, 9], and cancer [10]. However, a Cochrane Review of selected studies questioned the beneficial effects of long-chain n-3 fatty acids on all- cause and cardiovascular mortality [11].
We might expect positive effects of EPA if the fatty acid works to counteract effects of AA. LA, which is a major constituent in many plant oils, is the precursor of AA [1]. Under the catalysis of cyclooxygenase and lipoxygenase in tissues, AA may be transformed into various eicosanoids, i.e. prostacyclin, thromboxane, and leukotrienes [1, 4, 5]. Thromboxane A2 (TXA2) and leukotriene B4 (LTB4), synthesized from AA, have strong proinflammatory and prothrombotic properties [1, 2, 10], and may cause allergy [12]. Thus, an antagonism between EPA and AA could possibly explain positive health effects of EPA. In line with this reasoning, a decreased EPA/AA ratio in serum seems to be a risk factor for cancer death [10].
Also, docosanoids, originating from C22 fatty acids (DPA, DHA), have strong metabolic effects. Among these latter compounds are protectins, resolvins, and maresins, which may strongly counteract immune- and inflammatory reactions [3, 13]. Also, eicosatrienoic acid, i.e. 20:3 n6 (dihomo-gammalinolenic acid, DGLA) may give eicosanoids [3]. To our knowledge, there are less data on eicosanoids derived from three other C20 fatty acids: the two eicosatrienoic acids 20:3 n3 and 20:3 n9 (Mead acid), and eicosadienoic acid (20:2 n6).
We should accordingly expect regulatory mechanisms ensuring a proper balance between the relative amounts of EPA and AA, and possibly between other eicosanoid (docosanoid) precursor fatty acids. One such mechanism could be that increased (decreased) relative amount of one of the precursor fatty acid would be accompanied by increased (decreased) percentages of many other precursors as well. In line with this reasoning, we previously reported strong positive correlations (Spearman’s rho > 0.7) between relative amounts of many eicosanoid precursors, in breast muscle of chickens [14, 15].
Previously, we observed in muscle tissue of chickens that eicosanoid and docosanoid precursor fatty acids had narrow ranges (low variability) relative to ranges of the predominant fatty acids such as OA and ALA; the potential precursors were EPA, AA, DGLA, DPA, DHA, EDA, and ETA [20].
In computer experiments, we here used random numbers in lieu of the fatty acids, as reported previously [14-20]. To mimic the situation with eicosanoids, we made two of the variables (A and B) with narrow ranges, and a third (C) with broad range. Thus, C would represent sum of the remaining fatty acids, when omitting A and B. We generated uniformly distributed random numbers with true ranges. The outcome was, however, qualitatively the same if using random numbers with normal distribution (results not shown). Thus, A + B + C = S, where S is sum of the variables. Furthermore, each of the variables, and accordingly S, would have particular ranges, i.e. varying S – values for each of e.g. 200 “cases”. We may express relative amounts of the variables as fractions, or percentages of S. The A-, B-, and C-fractions of S would be Af =A/S, Bf = B/S, and Cf = C/S. Hence, Af + Bf + Cf =1, or e.g. Bf = -Af + (1 - Cf). Alternatively, we may use percentages of S, i.e. %A = (A/S) ·100; %B = (B/S) ·100; and %C = (C/S) ·100. Thus, %A + %B + %C = 100, or e.g. %B = -%A + (100 - %C). These formulas show dependency between the fractions (percentages).
Previously, we reported correlation coefficients (Spearman’s rho), and scatterplots of e.g. %EPA (=”%A”) vs.
Associations between eicosanoid and docosanoid precursor fatty acids
We previously reported that relative amounts of EPA, AA, DGLA, DPA, DHA, EDA, and ETA correlated positively in chicken breast muscle [20]. Furthermore, we were able to reproduce the correlations, using random numbers in lieu of the true values, if the numbers had true ranges of the precursor fatty acids. Below, we try to clarify linearity and slope of associations between the precursor percentages.
Associations between A (B, C) ranges and A (B, C) fractions of S
If S = A + B + C, we previously [14 - 21] utilized the equation of a straight line (y = ax + b), to explain correlations between %A, %B, and %C. Additionally, we considered the relationship between S and A (B, C) fractions of S. Below, we extend these analyses, focusing upon how ranges of the variables relate to the A (B, C) fractions (percentages) of S.
We define S to be the sum of three positive scale variables (A, B, C), making %A + %B + %C = 100. With ranges of the variables included (in parentheses), the equation would be:%A(p-q) + %B(r-s) +%C(t-u) =100, or %B(r-s)= - %A(p-q) +(100 - %C(t-u)
For simplicity in the presentation, below we omit indication of ranges, and mostly use A (B, C) fractions instead of percentages. Thus, Af + Bf + Cf =1. The A-fraction of S is Af = A/(A + B + C) = 1/[1 + (B + C)/A]. Similarly, the B fractions of S is Bf = B/(A + B + C) = 1/[1 + (A + C)/B], and the C-fraction is Cf = C/(A + B + C) = 1/[1 + (A + B)/C]. We see that the three fractions of S have similar structures, and that three ratios govern the fractions, i.e. R1 = (B + C)/A; R2 = (A + C)/B, and R3 = (A + B)/C, respectively. Thus, sum of two of the variables makes the numerators of the three ratios, and the remaining one is the denominator.
Furthermore, each of the fractions Af = 1/[1 + (B + C)/A]; Bf = 1/[1 + (A + C)/B]; and Cf = 1/[1 + (A + B)/C] should decrease as the numerators of R1 (R2, R3) increase, and increase as the denominators increase.
Since these fractions are functions of three variables, each of which with particular ranges, it could in general be hard to predict the combined influence of A, B, and C upon each of the fractions. However, in some situations we might predict how the fractions should respond as A (B, C) goes from lowest to highest value within the range. Below, we present one of these conditions, presumably relating to ranges of eicosanoid (docosanoid) precursor fatty acids (vide infra). We previously reported that ranges of these fatty acids were narrow relative to the large-amount fatty acids, e.g. OA and ALA, as observed in chicken muscle [19,20].
When reasoning about associations between ranges and A (B, C) fractions, a crucial point would be to clarify whether there is a main variable, and how each of the fractions should relate to this variable. As discussed below, we suggest that the main variable should have broad range relative to ranges of the other variables. Furthermore, we would expect positive (negative) associations between fractions (percentages) of two of the three variables, if their relative amounts relate similarly (in opposite directions) to the main variable.
Mimicking ranges of eicosanoid precursors: Two of three variables (A, B) having narrow ranges relative to a third one (C)
We previously encountered variables in physiology with narrow ranges of some variables relative to others [14-26]. For example, in chicken breast muscle, the concentration of fatty acids that are precursors of eicosanoids (docosanoids) had narrow ranges as compared with other fatty acids [20]; the former ones had coefficients of variation about 10%, against 40 to 60% for other fatty acids.
Very narrow range of a variable would make this variable approaching a fixed number. Thus, with two of three variables approaching constants, we have one main variable only, implying that all fractions would depend mainly on this variable. To elucidate direction and strength of associations between fractions in this case, we start studying associations between fractions when two (A, B) of three variables are constants, and the third (C) has broad range. Below, we reason about linearity, slope, and equation concerning these associations.
LINEARITY and SLOPE of Af (abscissa) vs. Bf when ranges of A and B are very narrow relative to the C-range
To clarify the association between Af and Bf in this case, we consider Af = 1/(1 + B/A + C/A), and Bf = 1/( 1 + A/B + C/B). Since A and B are close to constants, we may simplify to Af = 1/(k + C/A), and Bf = 1/( t + C/B), where k = 1 + B/A, and t = 1 + A/B. Accordingly, both fractions should decrease as C increases, implying that Af should correlate positively with Bf. Since Af and Bf depend mainly on C, we make C the abscissa variable when plotting C vs. Af (Bf).
We next raise the question of whether the Af vs. Bf association is linear in this particular case. If so, we should find a constant slope estimate, i.e. ΔY/ΔX. When computing slope estimates of associations between e.g. Af and Bf, it is crucial to know which one is the abscissa and the ordinate. Below, we clarify by writing Af (abscissa) vs. Bf, Af (abscissa) vs. Cf, and Bf (abscissa) vs. Cf.
To investigate linearity (slope) of the Af (abscissa) vs. Bf association, we raise the question of what happens to Bf (= Y), as Af (= X) increases, realizing that X as well as Y are mainly functions of C. For simplicity, we first consider A and B to be constants. If there is a linear relationship between X and Y, the equation of a straight line (y = ax + b) should apply. Thus, we should expect ΔY/ΔX = (Y2 – Y1)/(X2 – X1) to be constant. Thus, we find the C value (C1) corresponding to X1 and Y1. X1 = A/(A + B + C1); i.e. C1 = (A – AX1 – BX1)/X1. We next compute C2 (corresponding to X2 and Y2) by adding ΔX to X1. To simplify the presentation, below we use ΔX = 1, however obtaining the same result if using just ΔX (not shown). Hence, X1 +1 = A/(A + B + C2), giving C2 = (- B – AX1 – BX1)/(X1 + 1).
To find ΔY, we use C1 and C2, and compute Y1 and Y2. Thus, Y1 = B/(A+B+C1); i.e.
Y1 = X1·B/A. Similarly, Y2 =B/(A + B + C2); i.e.Y2 = (X1 + 1)·B/A. Accordingly, ΔY = Y2 - Y1 = (X1 + 1)·B/A – X1·B/A = B/A, which is the change in Y per one-unit increase in X1, i.e. ΔY/ΔX = (B/A)/1= B/A. Thus, there should be a linear, positive association between Af (%A=abscissa) and Bf (%B), the slope being estimated by ΔY/ΔX = B/A.
LINEARITY and SLOPE of Af (abscissa) vs. Cf, when ranges of A and B are very narrow relative to the C- range
If there is a linear relationship between Af (=X) and Cf (=Y), the equation of a straight line (y = ax + b) should apply to the relationship. Thus, we should find a constant slope value equal to ΔY/ΔX = (Y2 – Y1) /(X2 –X1). We accordingly need to find what happens to ΔY when increasing X1 by ΔX, e.g. by one unit. Realizing that C governs both X and Y, we first find the C-values (C1,C2) that correspond to X1 and X2 = X1 +1. Below, we use A and B to denote the near to constant values of A and B.
Finding C1 and C2: By definition, X1 = A/(A + B + C1), i.e. C1 = ( A – AX1 – BX1)/X1. To find C2, we add one X-unit to X1. Thus, (X1 + 1) = X1/(A + B + C2), i.e. C2 = (- B – AX1 – BX1)/(X1 + 1).
Computing Y1 and Y2: We use the above expressions of C1 and C2 to find the Y- values (Y1 and Y2) corresponding to X1 and X2. Thus, Y1 = C1/(A + B + C1);i.e. Y1 = [(A – AX1 – BX1)/X1]/[A + B +(A – AX1 – BX1)/X1]. Simplifying this expression, we obtain
Y1 = (A – AX1 – BX1)/A.
To find Y2, we use C2, i.e. Y2 = C2/(A + B + C2). Inserting the expression above, in lieu of C2, we obtain: Y2 = [(- B – AX1 – BX1)/(X1 + 1)]/[ A + B + (- B – AX1 – BX1)/(X1 + 1)]. Simplifying this expression, we obtain Y2 = (-B –AX1 – BX1)/A.
Accordingly, ΔY = Y2 – Y1 = (-B – AX1 – BX1)/A – (A – AX1 – BX1)/A = (-B – A)/A, i.e. ΔY = – (1 + B/A), which is the change in Y corresponding to a one-unit increase in X, i.e. ΔY/ΔX = – (1 + B/A)/1 = – (1 + B/A). Thus, Af ( %A =(abscissa) should have a negative, linear relationship to CF (%C), with slope = ΔY/ΔX = – (1 + B/A).
LINEARITY and SLOPE of Bf (abscissa) vs. Cf when ranges of A and B are very narrow
Using the approach above, we find that Bf (abscissa) should have a negative, linear association with Cf, the slope being estimated by ΔY/ΔX = – (1 + A/B).
Thus, if A, as well as B have very narrow ranges relative to C, then we have three slope estimates for the linear associations between relative amounts of A (B, C). 1) B/A estimates slope of %A(abscissa) vs. %B; 2) – (1 + B/A) estimates slope of %A (abscissa) vs. %C; and 3) – (1 + A/B) estimates slope of %B (abscissa) vs. %C.
We suggest that the slope estimates found above should apply also to conditions where the ranges of A and B are somewhat broadened. However, since we then would violate the requirement of having near constant values of A and B (relative to C), the scatterplots – and correlation coefficients - should be poorer, and the slope estimates should not work well, especially if increasing the A and/or B ranges appreciably (vide infra).
Suggested general rule, pertaining unit systems consisting of three positive scale variables (A, B, C, with S = A + B + C), where A and B have very narrow ranges relative to C:
%A (abscissa) should have a positive, linear association with %B, with slope approaching B/A. Furthermore, %A (abscissa) should have a negative, linear association with %C, with slope approaching – (1 + B/A), and %B (abscissa) should relate linearly and negatively to %C, with slope approaching – (1 + A/B).
If using these formulas, we emphasize that A and B must be the two close-to-constant variables, and C the broad-range variable. The crucial point is to define the abscissa variable correctly.
Finding EQUATION of the positive, linear Af (abscissa) vs. Bf association when ranges of A and B are very narrow relative to the C-range
We next try to find the complete equation of the relationship between relative amounts of A and B, knowing that the formula of a straight line (y = ax + b) should apply. Above, we computed the slope value to approach B/A, if A and B have very narrow ranges relative to C. Thus, if Y = Bf and X = Af, we have Y = (B/A)·X + b. To find b, we use corresponding values of X and Y, e.g. their maximum or minimum values. Thus,
b = Ymin – (B/A) · Xmin, and b = Ymax – (B/A) · Xmax. Accordingly, equation of the linear, positive X (Af) vs. Y (Bf) association should be:
Y = (B/A)·X +Ymin – (B/A) · Xmin , or Y = (B/A)·X +Ymax – (B/A) · Xmax
Example: A = 1, B = 2, C 1-10. We first use minimum and maximum values of X (= Af) and Y (= Bf). Thus, Y = B/(A + B + C) = 1/[1 +(A + C)/B]; Ymin = 1/[1 +(A + Cmax)/B], i.e. Ymin = 1/[1 +(1 + 10)/2] =1/6.5 = 0.154 (15.4%).
Similarly, X (=Af) = A/(A + B + C) = 1/[1 +(B + C)/A]. Thus, Xmin = 1/[1 +(2 + 10)/1] = 0.077 (7.7%). Inserting the actual numbers into Y = (B/A)·X +Ymin – (B/A) · Xmin, we obtain Y = (2/1)·X + 0.154 – (2/1)·0.077 = 0, i.e. Y = 2X. Thus, Bf = 2Af, or %B = 2·%A
We obtain the same result if using maximum values of X and Y to compute b. Thus,
Ymax = 1/[1+ (A +Cmin)/B] = 1/[1 +(1+1)/2] = 0.5. Similarly, X =Af = A/(A + B + C) = 1/[1 +(B + Cmin)/A). Xmax = 1/[1 + (2 + 1)/1] = 0.25. Using the equation above, i.e.
Y = Af = (B/A)·X + Ymax – (B/A) · Xmax, we obtain Y = (2/1) ·X + 0.5 – 2·0.25= 2X. Thus, Y = 2X, which may be written Bf =2Af, or %B = 2·%A.
Thus, in this particular case, Af vs. Bf shows a straight line with slope = 2. The extrapolated line should pass through (X, Y = 0, 0).
Finding EQUATION of the linear, negative Af (abscissa) vs. Cf association
As shown above, there should be a linear, negative association between Cf and Af (Bf). We define Cf = Y, and Af = X. Applying the equation of a straight line (y = ax + b), and the slope expression computed above, we have Y = - (1 + B/A)·X + b. We find b using corresponding values of X and Y, e.g. their maximum (minimum) values. Since there is an inverse relationship between X and Y, Ymax corresponds to Xmin,
Thus, Ymax = -(1 + B/A)·Xmin + b , and Ymin = -(1 + B/A)·Xmax + b. We compute
b = Ymax + (1 + B/A)·Xmin. Inserting this b-value into Y = - (1 + B/A)·X + b, we obtain
Y = - (1 + B/A)·X + Ymax + (1 + B/A)·Xmin
We next need to find Ymax and Xmin. By definition, Cf (i.e. Y) = C/(A+ B + C) = 1/[ 1 + (A + B)/C]. Using numbers of the example above, i.e. A = 1; B = 2.0; C 1- 10, we obtain Ymax = 1/[1 + (1 + 2)/10] = 1/1.3 = 0.77. Similarly, Af (i.e. X) = A/(A + B + C) = 1/[1 + (B + C)/A]. Thus, Xmin = 1/[1 + (2 + 10)/1] = 0.077. The equation of X vs. Y in this case should be Y = -(1 +2/1)·X + 0.77 + (1 + 2/1)·0.077 = 1, i.e. Y = -3X + 1.
Accordingly, the inverse, linear association between X (Af ) and Y (Cf) should be Y = -3X + 1.00 . Since Y = Cf, and X = Af , we may write Cf = -3Af + 1.00 , or %C = -3·%A + 100.
Alternatively, we could use Ymin = -(1 + B/A)·Xmax + b, i.e. b = Ymin +(1 + B/A)·Xmax Hence, the alternative, general formula would be
Y = - (1 + B/A)·X + Ymin + (1 + B/A)·Xmax
Finding Ymin and Xmax: Cf (i.e. Y) = C/(A+ B + C) = 1/[ 1 + (A + B)/C . Thus, Ymin= 1/[1 + (1 + 2)/1] = 0.25. Af (i.e. X) = A/(A + B + C) = 1/[1 + (B + C)/A], i.e. Xmax = 1/[1 + (2 + 1)/1] = 0.25. We insert the numbers into the general formula, i.e. Y = - (1 + 2/1)·X + 0.25 + (1 + 2/1)·0.25, i.e. Y = -3X + 1. Thus, the equation of the negative Af vs. Cf association should be Cf = -3·Af + 1.00 (or %C = -3·%A + 100).
Finding EQUATION of the linear, negative Bf (abscissa) vs. Cf association
The general equation is Y = - (1 + A/B)·X + b, where Y = Cf and X = Bf. We find b using corresponding values of X and Y, e.g. their maximum (minimum) values. Since there is an inverse relationship between X and Y, Ymax corresponds to Xmin.
Using the slope value found above, we have Ymax = -(1 + A/B)·Xmin + b , and Ymin = -(1 + A/B)·Xmax + b. We next compute b =Ymax + (1 + A/B)·Xmin = Ymax + (1 + A/B)·Xmin . Accordingly, the general formula would be
Y = - (1 + A/B)·X + Ymax + (1 + A/B)·Xmin
We may alternatively use Xmax and Ymin, giving the equation
Y = - (1 + A/B)·X + Ymin + (1 + A/B)·Xmax
With the example above, i.e. A = 1; B = 2.0; C 1- 10, we find max (min) value of Cf (=Y), and min (max) value of Bf (=X). Since Cf = C/(A + B + C) = 1/[1 + (A + B)/C], Cfmax = 1/[1 + (1 + 2)/10] =0.77, and Cfmin = 1/[1 + (1 + 2)/1] =0.25.
Similarly, Bf = B/(A + B + C) = 1/[1 + (A + C)/B]; Bfmin = 1/[1 + (1 + 10)/2] = 1/6.5 = 0.154, and Bfmax =1/[1 + (1 + 1)/2] = 0.5.
Thus, Cf = - (1 + A/B)·Bf + Cfmax + (1 + A/B)·Bfmin = -1.5·Bf + 0.77 + 1.5·0.154, i.e. Cf = -1.5Bf + 1.00, or %C = -1.5·%B + 100.
Alternatively, we may compute Cf = -1.5·Bf + 0.25 + 1.5·0.5, i.e. Cf = -1.5Bf + 1.00.
Computer Test: With A = 1; B = 2.0; C 1- 10, the A (B, C) - fractions of S are Af = 1/(3 + C); Bf = 2/(3 +C); and Cf =C/(3 + C)= 1/(1 +3/C). Thus, C is the only variable; Af and Bf should decrease as C runs from lowest to highest value, whereas Cf should increase (Fig. 1, upper panels). Accordingly, we should expect a strong positive association The outcome was as expected (Fig. 1, lower panels). There was a perfect positive association (rho = 1.000, p<0 n =200), xss=removed xss=removed n =200.>%C = -3·%A + 100, and %C = -1.5·%B + 100. We previously explained the curvilinear associations, shown in the top panels [21].
This work deals with computer experiments. To evaluate the suggested concepts of Intended Ranges and Distribution Dependent Correlations, we need diet trials in various species, including man.
The present study explains in more detail the strong correlations between eicosanoid (docosanoid) precursor fatty acid percentages in chicken muscle. In particular, our results explain why the associations should be positive and linear. Thus, if A, as well as B represent two of the precursor fatty acids, and C the remaining ones, we have A + B + C = S. Then, slope of %A (abscissa) vs. %B would approach B/A. Furthermore, slope of %A (abscissa) vs. %C would be near –(1+B/A), and slope of %B (abscissa) vs. %C would be close to –(1+A/B).
The study supports the idea that Intended Ranges could make Distribution Dependent Correlations, mathematically. We suggest that such ranges might have arisen through evolutionary selection. Possibly, eicosanoid and docosanoid precursor fatty acids in chicken breast muscle are examples of intended ranges, which would make their relative amounts correlate positively.
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Thank you most sincerely, with regard to the support you have given in relation to the reviewing process and the processing of my article entitled "Large Cell Neuroendocrine Carcinoma of The Prostate Gland: A Review and Update" for publication in your esteemed Journal, Journal of Cancer Research and Cellular Therapeutics". The editorial team has been very supportive.
Testimony of Journal of Clinical Otorhinolaryngology: work with your Reviews has been a educational and constructive experience. The editorial office were very helpful and supportive. It was a pleasure to contribute to your Journal.
Dr. Bernard Terkimbi Utoo, I am happy to publish my scientific work in Journal of Women Health Care and Issues (JWHCI). The manuscript submission was seamless and peer review process was top notch. I was amazed that 4 reviewers worked on the manuscript which made it a highly technical, standard and excellent quality paper. I appreciate the format and consideration for the APC as well as the speed of publication. It is my pleasure to continue with this scientific relationship with the esteem JWHCI.
This is an acknowledgment for peer reviewers, editorial board of Journal of Clinical Research and Reports. They show a lot of consideration for us as publishers for our research article “Evaluation of the different factors associated with side effects of COVID-19 vaccination on medical students, Mutah university, Al-Karak, Jordan”, in a very professional and easy way. This journal is one of outstanding medical journal.
Dear Hao Jiang, to Journal of Nutrition and Food Processing We greatly appreciate the efficient, professional and rapid processing of our paper by your team. If there is anything else we should do, please do not hesitate to let us know. On behalf of my co-authors, we would like to express our great appreciation to editor and reviewers.
As an author who has recently published in the journal "Brain and Neurological Disorders". I am delighted to provide a testimonial on the peer review process, editorial office support, and the overall quality of the journal. The peer review process at Brain and Neurological Disorders is rigorous and meticulous, ensuring that only high-quality, evidence-based research is published. The reviewers are experts in their fields, and their comments and suggestions were constructive and helped improve the quality of my manuscript. The review process was timely and efficient, with clear communication from the editorial office at each stage. The support from the editorial office was exceptional throughout the entire process. The editorial staff was responsive, professional, and always willing to help. They provided valuable guidance on formatting, structure, and ethical considerations, making the submission process seamless. Moreover, they kept me informed about the status of my manuscript and provided timely updates, which made the process less stressful. The journal Brain and Neurological Disorders is of the highest quality, with a strong focus on publishing cutting-edge research in the field of neurology. The articles published in this journal are well-researched, rigorously peer-reviewed, and written by experts in the field. The journal maintains high standards, ensuring that readers are provided with the most up-to-date and reliable information on brain and neurological disorders. In conclusion, I had a wonderful experience publishing in Brain and Neurological Disorders. The peer review process was thorough, the editorial office provided exceptional support, and the journal's quality is second to none. I would highly recommend this journal to any researcher working in the field of neurology and brain disorders.
Dear Agrippa Hilda, Journal of Neuroscience and Neurological Surgery, Editorial Coordinator, I trust this message finds you well. I want to extend my appreciation for considering my article for publication in your esteemed journal. I am pleased to provide a testimonial regarding the peer review process and the support received from your editorial office. The peer review process for my paper was carried out in a highly professional and thorough manner. The feedback and comments provided by the authors were constructive and very useful in improving the quality of the manuscript. This rigorous assessment process undoubtedly contributes to the high standards maintained by your journal.
International Journal of Clinical Case Reports and Reviews. I strongly recommend to consider submitting your work to this high-quality journal. The support and availability of the Editorial staff is outstanding and the review process was both efficient and rigorous.
Thank you very much for publishing my Research Article titled “Comparing Treatment Outcome Of Allergic Rhinitis Patients After Using Fluticasone Nasal Spray And Nasal Douching" in the Journal of Clinical Otorhinolaryngology. As Medical Professionals we are immensely benefited from study of various informative Articles and Papers published in this high quality Journal. I look forward to enriching my knowledge by regular study of the Journal and contribute my future work in the field of ENT through the Journal for use by the medical fraternity. The support from the Editorial office was excellent and very prompt. I also welcome the comments received from the readers of my Research Article.
Dear Erica Kelsey, Editorial Coordinator of Cancer Research and Cellular Therapeutics Our team is very satisfied with the processing of our paper by your journal. That was fast, efficient, rigorous, but without unnecessary complications. We appreciated the very short time between the submission of the paper and its publication on line on your site.
I am very glad to say that the peer review process is very successful and fast and support from the Editorial Office. Therefore, I would like to continue our scientific relationship for a long time. And I especially thank you for your kindly attention towards my article. Have a good day!
"We recently published an article entitled “Influence of beta-Cyclodextrins upon the Degradation of Carbofuran Derivatives under Alkaline Conditions" in the Journal of “Pesticides and Biofertilizers” to show that the cyclodextrins protect the carbamates increasing their half-life time in the presence of basic conditions This will be very helpful to understand carbofuran behaviour in the analytical, agro-environmental and food areas. We greatly appreciated the interaction with the editor and the editorial team; we were particularly well accompanied during the course of the revision process, since all various steps towards publication were short and without delay".
I would like to express my gratitude towards you process of article review and submission. I found this to be very fair and expedient. Your follow up has been excellent. I have many publications in national and international journal and your process has been one of the best so far. Keep up the great work.
We are grateful for this opportunity to provide a glowing recommendation to the Journal of Psychiatry and Psychotherapy. We found that the editorial team were very supportive, helpful, kept us abreast of timelines and over all very professional in nature. The peer review process was rigorous, efficient and constructive that really enhanced our article submission. The experience with this journal remains one of our best ever and we look forward to providing future submissions in the near future.
I am very pleased to serve as EBM of the journal, I hope many years of my experience in stem cells can help the journal from one way or another. As we know, stem cells hold great potential for regenerative medicine, which are mostly used to promote the repair response of diseased, dysfunctional or injured tissue using stem cells or their derivatives. I think Stem Cell Research and Therapeutics International is a great platform to publish and share the understanding towards the biology and translational or clinical application of stem cells.
I would like to give my testimony in the support I have got by the peer review process and to support the editorial office where they were of asset to support young author like me to be encouraged to publish their work in your respected journal and globalize and share knowledge across the globe. I really give my great gratitude to your journal and the peer review including the editorial office.
I am delighted to publish our manuscript entitled "A Perspective on Cocaine Induced Stroke - Its Mechanisms and Management" in the Journal of Neuroscience and Neurological Surgery. The peer review process, support from the editorial office, and quality of the journal are excellent. The manuscripts published are of high quality and of excellent scientific value. I recommend this journal very much to colleagues.
Dr.Tania Muñoz, My experience as researcher and author of a review article in The Journal Clinical Cardiology and Interventions has been very enriching and stimulating. The editorial team is excellent, performs its work with absolute responsibility and delivery. They are proactive, dynamic and receptive to all proposals. Supporting at all times the vast universe of authors who choose them as an option for publication. The team of review specialists, members of the editorial board, are brilliant professionals, with remarkable performance in medical research and scientific methodology. Together they form a frontline team that consolidates the JCCI as a magnificent option for the publication and review of high-level medical articles and broad collective interest. I am honored to be able to share my review article and open to receive all your comments.
“The peer review process of JPMHC is quick and effective. Authors are benefited by good and professional reviewers with huge experience in the field of psychology and mental health. The support from the editorial office is very professional. People to contact to are friendly and happy to help and assist any query authors might have. Quality of the Journal is scientific and publishes ground-breaking research on mental health that is useful for other professionals in the field”.
Dear editorial department: On behalf of our team, I hereby certify the reliability and superiority of the International Journal of Clinical Case Reports and Reviews in the peer review process, editorial support, and journal quality. Firstly, the peer review process of the International Journal of Clinical Case Reports and Reviews is rigorous, fair, transparent, fast, and of high quality. The editorial department invites experts from relevant fields as anonymous reviewers to review all submitted manuscripts. These experts have rich academic backgrounds and experience, and can accurately evaluate the academic quality, originality, and suitability of manuscripts. The editorial department is committed to ensuring the rigor of the peer review process, while also making every effort to ensure a fast review cycle to meet the needs of authors and the academic community. Secondly, the editorial team of the International Journal of Clinical Case Reports and Reviews is composed of a group of senior scholars and professionals with rich experience and professional knowledge in related fields. The editorial department is committed to assisting authors in improving their manuscripts, ensuring their academic accuracy, clarity, and completeness. Editors actively collaborate with authors, providing useful suggestions and feedback to promote the improvement and development of the manuscript. We believe that the support of the editorial department is one of the key factors in ensuring the quality of the journal. Finally, the International Journal of Clinical Case Reports and Reviews is renowned for its high- quality articles and strict academic standards. The editorial department is committed to publishing innovative and academically valuable research results to promote the development and progress of related fields. The International Journal of Clinical Case Reports and Reviews is reasonably priced and ensures excellent service and quality ratio, allowing authors to obtain high-level academic publishing opportunities in an affordable manner. I hereby solemnly declare that the International Journal of Clinical Case Reports and Reviews has a high level of credibility and superiority in terms of peer review process, editorial support, reasonable fees, and journal quality. Sincerely, Rui Tao.
Clinical Cardiology and Cardiovascular Interventions I testity the covering of the peer review process, support from the editorial office, and quality of the journal.
Clinical Cardiology and Cardiovascular Interventions, we deeply appreciate the interest shown in our work and its publication. It has been a true pleasure to collaborate with you. The peer review process, as well as the support provided by the editorial office, have been exceptional, and the quality of the journal is very high, which was a determining factor in our decision to publish with you.
The peer reviewers process is quick and effective, the supports from editorial office is excellent, the quality of journal is high. I would like to collabroate with Internatioanl journal of Clinical Case Reports and Reviews journal clinically in the future time.
Clinical Cardiology and Cardiovascular Interventions, I would like to express my sincerest gratitude for the trust placed in our team for the publication in your journal. It has been a true pleasure to collaborate with you on this project. I am pleased to inform you that both the peer review process and the attention from the editorial coordination have been excellent. Your team has worked with dedication and professionalism to ensure that your publication meets the highest standards of quality. We are confident that this collaboration will result in mutual success, and we are eager to see the fruits of this shared effort.
