*3.1. Study Population*

The present investigation included 66 F-T2DM older adults and 30 age and sex-matched robust, non-diabetic controls. The main characteristics of the two groups are reported in Table 1. F-T2DM and control participants were comparable for age, sex distribution, and number of diseases. F-T2DM older adults showed higher body mass index relative to controls. As expected, a significant di fference was found in physical functional between groups, as indicated by the scores on the short physical performance battery (SPPB).



§ Includes hypertension, coronary artery disease, prior stroke, peripheral vascular disease, diabetes, chronic obstructive pulmonary disease, and osteoarthritis; Abbreviations: BMI, body mass index; F-T2DM, frail/pre-frail older adults with type 2 diabetes mellitus; SD, standard deviation; SPPB, short physical performance battery.

#### *3.2. Identification of Circulating Amino Acid Profiles*

In the present study, we aimed at identifying profiles of circulating amino acids that discriminate older persons with F-T2DM from functionally intact non-diabetic peers. Among the available statistical options, we selected a PLS-DA-based strategy for its ability to handle multiple interdependent variables. The best PLS-DA model was built using two LVs. As indicated by the stringent DCV applied, the classification performance of the model was almost perfect. Indeed, the proportion of correct classification of participants was 96.6 ± 1.5% over the calibration sets (95.0 ± 2.2% for cases and 100.0 ± 0.0% for controls), 96.6 ± 1.5% (95.0 ± 2.2% for cases and 100.0 ± 0.0% for controls) in the internal DCV loop (i.e., the one used for model selection), and 95.9 ± 1.3% (94.1 ± 1.9% for cases and 100.0 ± 0.0% for controls) in the outer DCV loop, which accounts for the results of repeated external validation.

The remarkable classification performance of the PLS-DA model can be appreciated by inspecting the projection of study participants over the space spanned by the two LVs (Figure 1).

A sharp separation between F-T2DM participants and controls is evident. To ensure the reliability of our findings against the possibility of chance correlations, DCV results of the PLS-DA model were compared with the distributions of specific figures of merit under the null hypothesis. As depicted in Figure 2, for all of the figures considered (i.e., NMC, AUROC, and DQ2), values obtained from the unpermuted dataset fell outside the corresponding null hypothesis distribution, indicating a *p* value <0.05.

**Figure 1.** Scores plot showing the separation of frail/pre-frail older adults with type 2 diabetes mellitus (F-T2DM) from control participants according to the serum concentrations of amino acids and derivatives in the space spanned by the two latent variables (LV1 and LV2), as determined by partial least squares-discriminant analysis.

**Figure 2.** Distribution of values of number of misclassifications (NMC), area under the receiver operating characteristic curve (AUROC), and discriminant Q2 (DQ2) under their respective null hypothesis as estimated by permutation tests (blue histograms) and the corresponding values obtained by the partial least squares-discriminant analysis model on unpermuted data (red circles). Values obtained on the real dataset (red circles) fall outside of the corresponding null hypothesis distribution (blue histograms), corresponding to a *p* < 0.05.

The identification of the metabolites with the greatest discriminating power was accomplished by inspecting variable importance in projection (VIP) indices. Table 2 reports variables with a VIP value higher than 1.


**Table 2.** Serum concentrations of discriminant biomolecules as resulted from partial least squares-discriminant analysis.

Data are shown as mean ± standard deviation. Concentrations are expressed in μmol/L.

F-T2DM participants showed higher serum levels of 3-methyl histidine, alanine, arginine, ethanolamine, glutamic acid, sarcosine, and tryptophan. Instead, controls were characterized by higher circulating levels of ornithine and taurine. Serum concentrations of non-discriminant analytes in the two participant groups are listed in Table S1.
