for "Human lipoproteins comprise at least 12 different classes that are lognormally distributed."
Konishi et al. 2021
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Fig. S1 The age of volunteers.
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Fig. S2 The need for class "TR".
This class was fairly minor and was lacking in rats.
It is unique in that it is smaller and very low in cholesterol.
However, fitting is difficult without this.
The fitting of triacylglycerol is shown.
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Fig. S3 Elution pattern of ApoB100, ApoB48, and Lp(a).
Bands of the silver-stained SAS-PAGEs were determined by densitometry.
The bands were identified by MALDI-TOF MS and western blotting using specific antibodies.
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Fig. S4 Elution pattern of ApoA1. Results of western blotting.
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Fig. S5 Elution pattern of LACs.
Bands of the silver-stained SAS-PAGEs were determined by densitometry.
The bands were identified by MALDI-TOF MS.
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Fig. S6 An alternative version of Fig. 1: record of a healthy volunteer.
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Fig. S7 QQ plots for logaritms of Cholesterol and TG raw data.
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Fig. S8 Correlation between classes.
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Fig. S9 A part of SDS-PAGE, fractions 15-32, with the elution pattern superimposed.
Immunoglobulins are marked. IgM formed a large molecule of ca 20 nm; the size was comparable to LDL1.
Also, IgG was 8 nm; some of those further bound to complement factor C3 as well as H, and the size became comparable with LDL2.
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Fig. S10 Total cholesterol compared with HDL and LDL measured by conventional methods.
The level of lipids in the serum was monitored and adjusted to an appropriate amount. Possible factors affecting the level of lipids were simulated using Dice.
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Fig. S11 Histograms of the simulated levels. A. additive and B. multiplicative models.
When factors act additively, lipid levels are normally distributed (A). This is because the sum of random numbers will take a normal distribution (central limit theorem). The 95% range is represented by a dotted line, and the median is represented by a straight line. The median is at the centre of the distribution, and the upper and lower bounds are symmetric. However, if the factors behave multiplicatively, the distribution is lognormal (B). The distribution was highly skewed. The upper and lower limits are not symmetrical.
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Fig. S12 Sums of randomly selected five samples.
Five numbers were randomly sampled from each of these two distributions, and the sum was obtained. In the additive model, the sum of the samples converges to a fixed point (A). The flicker of this value was small. Therefore, this sum is a good indicator of these levels. However, in the multiplicative model, the distribution of sums is biased (B). Owing to the chance of sampling, the obtained value changes significantly. According to the central limit theorem, if the number of samples is sufficient, the sum should have a normal distribution. In fact, the skewness of the distribution was less than that of the original distribution (Fig. S11B). However, the lognormality feature remained unchanged (B).
Therefore, the sum of the samples is not informative in the multiplicative model. Theoretically, the geometric mean is appropriate; however, this cannot be estimated experimentally. The levels of LDL and HDL measured by the conventional enzymatic method are not randomly selected; however, in the sense of instability, they will have a similar weakness.
Tables S1 and S2
The standard values and 95% intervals.
Class values of healthy volunteers for TG and cholesterol(mg/dL), tab separated text.