Proportions of macronutrients, including specific dietary fats, in prospective anti-Alzheimer’s diet

Here we present a novel life-long whole-population study, which enabled us to predict a diet that, in terms of macronutrient proportions, may be prophylactic against Alzheimer’s Disease (AD). The method is based on the existence of oscillations in the correlation between historical per capita personal income (PCPI) and age-adjusted death rates (AADR) for AD for each state of the USA in 2005. These oscillations can be explained by changing proportions of macronutrients in the average American diet between 1929 and 2005. We assumed that reducing future correlation of PCPI with AADR will reduce the population’s susceptibility to AD. Based on the results of fitting macronutrient availabilities to the variability of Roriginal, using Generalized Additive Models (GAM) analysis, we constructed four “Calculator” equations. The Calculator allowed for prediction of an optimal diet characterized by low correlation of PCPI with AADR (Rpredicted) and minimum energy difference from the historical average macronutrient consumption for each corresponding period of life. We predict that protein consumption should be reduced by half in early middle age and late middle age, whereas in late age it should increase. Our predictions are in line with results on humans and simpler organisms in the context of prolonging life.


Results and Discussion
Precedence periods and estimation of relative confidence levels of the precedence periods.
The consumed diet exerts its effects, either positive or negative, after a certain period of time, which we call precedence period. Using a global optimization procedure (see Methods) we determined the precedence periods of all nutrients studied for the four periods of life. The results are presented in Fig. 1. They vary significantly from 0 till 20 years, depending on the nutrient and the period of life. Some have tendency to increase during the life course, as in the case of protein, others to decrease like, for example, PUF. Still others, like carbohydrates, have a U-shaped dependence on time. This variability probably depends on the aging processes occurring during the life course and the differences in metabolic pathways for each nutrient. To determine confidence levels of the estimation of precedence periods we used the method of relative sequence of confidence described in Methods. Precedence periods determined for youth have, on average, the lowest confidence for all nutrients. Precedence periods determined for carbohydrates have the highest confidence level (marked with three stars in Fig. 1) in the three last periods of life and the lowest in youth. Precedence periods determined for proteins are characterized by low or high confidence of determination in the two first periods of life, respectively, whereas in the late middle age and late age by the highest confidence. Precedence periods for specific types of fat are determined with, on average, lower confidence levels than for protein and carbohydrates and that change throughout the periods of life.
prediction of the proportions of macronutrients. Table 1. presents the results of the "Calculator" output i.e. predicted proportions of macronutrients in percent of energy equivalent and in grams in the diet scaled to 2000 kcal. These data are compared with percent of energy equivalent of mean availabilities and mean availabilities in grams for a given period of life, scaled also to a 2000 kcal diet. This comparison points to the necessity of reducing the protein intake in early middle age and late middle age by half. These predictions are accompanied by high or the highest confidence levels of precedence periods determination. The change is compensated by a slight increase in all remaining nutrients. In the late age we predict higher than historical consumption of proteins whereas in youth the prediction is almost equal to the mean availability in this period of life. the optimal diet. The suboptimal diet has unexpectedly high influence on the development of non-communicable diseases 15 . Here we present a method of prediction of a life-long optimal diet in regard to macronutrient proportions. The diet human populations are consuming is a complex exposure to many and often synergistic factors. Thousands of bioactive components are present in the diet an individual is consuming 16 . Therefore, exact quantification information concerning the dietary intake is crucial for obtaining reliable results as to the effects of this diet on short term health, health-span and longevity. Nutritional epidemiology relies mainly on observational design of studies, which can be criticized for being dependent on food questionnaires based on the recall of food intake. However, they are usually performed on large cohorts, which reduces bias inevitably present in the food questionnaires. On the other hand, randomized trials are performed on much smaller cohorts and with shorter time of duration [16][17][18] . Despite all these problems, nutritional epidemiology, backed by short term interventional studies and translational research on animals, provides the background to propose dietary guidelines for the human populations to follow. Taking into consideration the high impact of dietary guidelines on public health, there is an urgent need to provide independent and novel methods of determination of the long term effects of diet on the prevention of AD and other diseases related to old age. Methods that would confirm and complement the results obtained with standard nutritional epidemiology studies. In our previous [12][13][14] and the current paper we provide such a new method for predicting the long term effects of a diet based on estimation of the optimal proportions of macronutrient content. Our method could be assigned to the discipline of so called life-course epidemiology 19 .
The main finding of this work is that lower consumption of protein in the mid-life and higher for the period of late age, compared with what was eaten in the USA, may benefit our health and longevity. We propose that these potentially prophylactic proportions of protein to other macronutrients maintained throughout life will reduce the burden of AD and other age related degenerative diseases as well as will extend the health-span and longevity. Our proposal is substantiated by the research on simple organisms and mammals reviewed in 1,2 , as well as on humans 20 . This research has shown, across all the species studied, that protein reduction extends health-span and longevity. In the last period of life -late age, we propose to increase protein consumption above the observed levels. This is consistent with the observations that the overall synthesis of proteins in human organism is compromised at this age 21,22 (and references therein) due to "anabolic resistance". Higher protein consumption and subsequent essential amino acids availability from intestines will activate the signaling pathways stimulating protein synthesis, which in turn will improve muscle and overall health. This reasoning is endorsed by the results of Senior et al. 23 who found that at old age mice need higher protein intake than in the early and mid-life. It is interesting to compare the protein/carbohydrates ratio optimal for the lowest mortality and risk of death from AD, for old age mice in 23 and our results for humans of old age. It is approximately 1:1 for mice and 1:2.5 for humans. In mid-life this ratio is equal to 1:2 for mice and to approximately 1:8 for humans. We predict a ratio of 1:5 as optimal for humans at youth. We predict also that the intake of carbohydrates is in the range of their percentage share in energy, which is consistent with the U-shaped dependence of all-cause mortality and cause-specific mortality on carbohydrates consumption 24 . Our results correspond to the optimum for the lowest mortality 24 .
Wang et al. 25 reported associations between specific types of fat intake and total mortality. They found positive associations of increased intake of saturated fat with total mortality, whereas increase in the intake of monounsaturated and polyunsaturated fats was negatively associated with mortality. Our predictions rank within the highest quintiles in Wang et al. or slightly above for all types of fats. We think that the potential influence on mortality of increased saturated fat intake we predict is counterbalanced by increased intake of unsaturated fats.
In the present paper we used de novo global optimization of five macronutrients whereas in the previous paper 13 the global optimization was performed on three macronutrients (total fat instead of specific types of fats). It is interesting that comparison of the results for predicted carbohydrates and protein content are similar, which strengthens the reliability of our results.
Limitations of our studies. The crucial assumption we made is that the oscillations of Roriginal in time can be explained by the variability of macronutrient consumption by the population of the USA. The only proof of this concept are the rational results obtained as the output of the "Calculator" e.g. reasonable predictions of prophylactic diet supported by the results of other studies 1,2,6,7,20,23,24,26,27 . Besides that, the main limitation of our studies are the input data of macronutrient availabilities. The possible bias related to the values we have used (SI Dataset S1) is difficult to judge. For most of the macronutrients we used a 5 g step in our calculator, which seems to be a reasonable estimation of the errors of data presented in Table 1. We have assumed that the consumption within the population follows the normal Gaussian distribution and the average consumption per-capita covers the majority of population and all age groups and both sexes. We did not consider the medical conditions of the population since, it would be extremely difficult, if not impossible, to do it for the whole population data for the USA. We assume that our predictions are valid for the healthy part of the population. We also did not differentiate the source of protein i.e. animal or plant due to lack of such data available to the public. This may influence

Proportions of macronutrients [%]
Grams per day the results as consumption of plant protein instead of animal protein is considered as more healthy 28 . Due to the nature of our analysis it is not possible to introduce exact age ranges for the four periods of life. This is because in the 2005 the population of people dying from AD was of different age. We do not have data about their average age. In this case we think that it is better to leave age limits as they are generally thought to be and not to assign strict boundaries. Youth poses a special problem with assigning boundaries since it is not clear from our studies when it begins. It might be even childhood. The other source of bias is the relation between availability per capita and average consumption per capita, which is unknown. We assumed that the availability is proportional to average per-capita consumption. Since we have obtained a reasonable diet content in regard to consumption of macronutrients, which is backed up by studies done by others 1,2,6,7,20,23,24,26,27 , these assumptions are most probably valid. The message described in this paper is important for Public Health and we hope it will prompt new research by standard epidemiological methods to confirm it. Appropriate measures should be then applied to deliver this message to the general public.

conclusions
We predict that the proportions of macronutrients in the diet in four periods of life (youth, early middle age, late middle age, late age) should differ, especially in regard to protein intake. Specifically, we postulate that protein intake in early middle age and late middle age should be reduced by half by comparison to historical consumption in the USA. Conversely, in the late age, the protein intake should be increased above the historical consumption. We postulate that applying these changes in the consumption of protein throughout the whole life of an individual will act prophylactically against development of AD and possibly will extend health-span and the duration of life

Methods
The graphical representation of input data variability in time is presented in Fig. 2 The flow charts of the "Calculator" Flow chart 1. General procedure. www.nature.com/scientificreports www.nature.com/scientificreports/ Flow chart 2. Global optimization procedure.
Flow chart 3. Procedure of calculation of optimal diet in regard to macronutrients proportions.
The calculator from our previous papers 12,13 was modified and optimized to obtain precedence periods for carbohydrates, protein, saturated, monounsaturated, and polyunsaturated fat. We used global de novo optimization for all 5 nutrients within GAM analysis procedure instead of multiple regression. This resulted in 4084101 variants of sets of precedence periods when using back steps up to −20 years. From them the one variant with the highest R was chosen as the optimal one (Roptimal). The results from GAM analysis with Roptimal for each period studied were chosen as calculator equations and are presented in SI Dataset S2. We obtained four equations corresponding to four periods of life: youth, early middle age, late middle age and late age. These equations were then used to generate a set of tables with new proportions of macronutrients to minimize Rpredicted and optimal proportions (optimal diet) were chosen as in our previous papers 12,13 except that the corresponding mean availability was calculated without back shift by precedence periods. The codes in R program for optimization, calculation of Rpredicted and minimum energy difference together with the manual are available in a public repositories at https://bitbucket.org/seventm/fsproj_alzheimeroptimaldiet and https://github.com/seventm/ fsproj_alzheimeroptimaldiet/releases/tag/v1.0, https://doi.org/10.5281/zenodo.3574598. The computations were performed on the computer cluster with 96 cores and 1TB of RAM. Parallel computing approaches based on snow packages are implemented in our R codes. The approximate time used for calculating results of optimization for one period was around 10 minutes. GAM analysis. Calculation of the optimal diet was based on a linear relationship between Roriginal (as predicted variable) and macronutrients (in grams of daily availabilities per capita) with separate types of fats (as predictor variable) modelled using Generalized Additive Models (GAM). In contrast to multiple regression model the GAMs are not assuming the linearity and normality of the error distribution. The GAMs are employed by modeling the expected value of Roriginal as follows: where: α is an intercept; f 1 ,f 2 ,f 3 ,f 4 and f 5 are unknown smooth nonparametric functions. In order to obtain an inference on and composition of a new diet more easily, we used linearized smooth functions described in 29 . The GAM was fitted using the function gam from package mgcv in the R environment (version 3.5.1; R Development Core Team, 2019) 30 .

Determination of confidence levels of precedence periods estimated from global optimization.
Global optimization was performed to find a set of optimal precedence periods corresponding to maximal R (Roptimal) for all five nutrients. Roptimal was calculated from regression procedure, implementing Generalized Additive Models as described above, using back shift of nutrients availability up to −20 years with a step equal to one year. For each shift for a given nutrient (starting from 0 to −20 years) R coefficients corresponding to all combinations of shifts for other nutrients were calculated. For each nutrient we obtained 21 sets of R. Subsequently Rmean and standard deviation (SD) of Rmean for each set were determined. Precedence periods corresponding to Roptimal, maximum Rmean and minimum SD of R mean, respectively, were used to calculate the mean precedence period and SD of the mean precedence period. The optimal precedence periods and SD of the mean precedence periods applied to them are presented in Fig. 1 www.nature.com/scientificreports www.nature.com/scientificreports/ divided into ranges corresponding to the highest confidence (from 0 to 2; ***), high confidence (from 2 to 5; **), lower confidence (from 5 to 8; *), and the lowest confidence (above 8;). The ranges are determined arbitrarily to give a relative sequence of confidence levels of the determined precedence periods. The procedure described above assumes that all three criteria of determination of the precedence periods: maximum R (Roptimal),  13 . Filled squares -Roriginal, empty rhombi -specific types of fat.