The study investigated the variability of genes coding for apolipoprotein A1 (APOA1), apolipoprotein C3 (APOC3), and apolipoprotein A4 (APOA4) in a healthy ageing population ranging from 18 to 109 years. The study aimed to describe possible modifications of the APOA1, APOC3, and APOA4 genes in healthy ageing people. The sample group consisted of 327 males and 473 females who were free of clinically manifested disease and had emato-chemical parameters within the norm. The APOA1-MspI-RFLP (75 nt from the transcription starting site), APOC3-SstI-RFLP (3 UTR, nt), and APOA4-HincII-RFLP (Asp/Ser) were analyzed according to age and sex. The study found a significant age variation of the APOA1 gene pool in males. An analysis of the allele average effect exerted by A/P alleles (Absence/Presence of the restriction site) on lipidemic parameters in 46-80-year-olds showed that allele A decreased while allele P significantly increased serum LDL-cholesterol. Unexpectedly, the P allele was over-represented in the group of oldest old subjects, thus giving evidence of another genetic paradox. Although epidemiological and clinical evidence has shown the significance of these genes in lipid metabolism and cardiovascular diseases, the importance of the variability of other APO genes, particularly APOA1, APOC3, and APOA4, on healthy ageing and mortality has yet to be assessed.Years (median age 29 years), 267 subjects aged DNA analyses. DNA was extracted from blood buffy coats following standard procedures. APOA1-MspI-RFLP (75 nt from S. Garasto et al., the transcription starting site), APOC3-SstI-RFLP 31 (3' UTR, 3238 nt), and APOA4-HincII-RFLP (Asp/127 Ser) were analyzed by restriction analysis after PCR amplification of the DNA regions containing the restriction sites. Regions, primers, and PCR experimental conditions are available on request from the email address of the corresponding author (g.debenedictis@unical.it). The effects of the locus on the lipidemic parameters were estimated according to Christiansen & Feldman (1986). The 95% confidence intervals of and were calculated by bootstrap (10,000 replications, MATLAB Statistics toolbox).

Results
Genotypic and allelic data of APOA1-MspI-RFLP, APOC3-SstI-RFLP, and APOA4-HincII-RFLP were analyzed in three age classes (18-45 years; 46-80 years; 81-109 years) for each sex. All the sample groups were in Hardy-Weinberg equilibrium (p>0.05).

Statistical analyses
For single markers, allele frequencies were obtained by counting genes from the observed genotypes. Chi-squared tests were applied to verify Hardy-Weinberg equilibrium (HWE) in each sample. Homogeneity of genotypic and allelic frequency distributions among the groups of different age (18-45 years; 46-80 years; 109 years) in each sex was tested by a chi-squared test.

In males (Table 1a), there was a significant difference among the age-related genotypic counts (χ2 = 9.63 with 4 df., p = 0.045 with Yates correction). Accordingly, allele counts were different among the three age-groups (χ2 = 8.29 with 2 df., p = 0.016). On inspecting the data, the P allele frequency showed a minimum (and the A allele frequency a maximum) in the intermediate age-class. To investigate this finding and outline the age-related frequency trajectory of the P (or A) allele, the group of 327 males was subdivided into five age-classes (18-25 years; 26-45 years; 46-65 years; 66-80 years; 81-109 years), and P allele frequency was estimated in each class. A concave frequency trajectory was observed, the significance of which was tested as described in the methods. The estimated value of the leading coefficient b = 0.217 was significantly larger than zero, because the central 95% empirical confidence interval of was 0.112-0.495. Out of the 10,000 trajectories simulated by bootstrap, 9,987 were concave, only one was convex, ten were monotone increasing, and two were monotone decreasing. By assuming that a trend in the data is significant if more than 95% of the simulated trajectories show that trend, the concave pattern of the P allele frequency fully satisfied this requirement. Denoting age as x and letting f(x) be the age-related frequency trajectory of the allele P, the age-related frequency trajectory of the A allele (absence of the restriction site) was given by f(x) = A - f(x), because only two alleles are present in the population. Fig.1 shows the relative frequency of the P allele in the five age-groups, the fitting curve, and the lower and upper envelopes of the 10,000 simulated trajectories.

The age-related frequency trajectory of the APOA1 allele P (Presence of the MspI restriction site) was analyzed by least squares method. The MATLAB function polyfit was used to fit a 2nd degree polynomial y = b0 + b1x/x + b2x2/x2 to the frequencies of allele P observed in five classes of age (18-25 years; 26-45 years; 46-65 years; 66-80 years; 81-109 years), thus obtaining estimates b0, b1, b2. The mean of the ages of individuals belonging to each age-class was taken as the x value for that class. Ten thousand replicates of b0, b1, b2 were then generated by the bootstrap method (MATLAB Statistics toolbox), from which the empirical distribution of b0, b1 was obtained and confidence limits were calculated for the age-related frequency trajectory.

To assess linkage disequilibrium D between pairs of markers at the three loci and to test the null hypothesis, D = 0, in the whole sample. Maximum LikelihoodThe text contains scientific data and tables, which are difficult to understand without proper context and background information. Therefore, it is not possible to provide a meaningful summary or interpretation of the content. However, I can assist in proofreading and improving the text as per the given instructions.