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1

Statistical Analysis of Dose-Response Data

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All raw, individual-level data are presented in data file S1. P values between groups were determined by two-tailed t test with Wilcoxon matched-pairing (Fig. 7, B and E) or two-tailed student’s unpaired t test (Fig. 7, C and F), using GraphPad Prism v9.2. All conducted statistical tests were two-tailed. P values of less than 0.05 were considered statistically significant. Data are presented as mean ± standard error of the mean (SEM) or standard deviation (SD) as described in the corresponding figure legends. Curve fitting was conducted by fitting a nonlinear five-parameter dose-response curve using GraphPad Prism v9.2.
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2

Anthropometry and Metabolic Profiles

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Descriptive statistics were used to analyze the data. Nonparametric paired Wilcoxon t-tests were used to compare anthropometry (weight, height and BMI), blood tyrosine and phenylalanine concentrations between the subjects. A p-value < 0.05 was considered statistically significant (analyzed using Prism GraphPad v 9.0).
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3

Statistical Analysis Methodology for Cell Cultures

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Statistical analysis was performed with Prism GraphPad V9.0.2 software (GraphPad by Dotmatics, San Diego, CA, 92108). Data were tested for normality via Shapiro-Wilks test. Data are presented as the mean ± SEM. Cell culture experiments were performed in technical triplicates, with three independent experimental replicates. Statistical significance was assessed via unpaired two-tailed Student’s t-test or ANOVA, with Tukey’s multiple comparisons test. Results were regarded as statistically significant for p < 0.05.
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4

Evaluation of Molecular Mechanisms

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Data are presented as mean ± standard deviation (SD) from at least 3 independent experiments carried out in triplicate except for flow cytometry data where nMFI was used. Differences between 2 groups were assessed using either Student’s t test or Mann-Whitney U test, while differences between group data were assessed using 1-way analysis of variance (ANOVA) followed by Tukey’s post hoc multiple comparison test for parametric or nonparametric data, respectively, following a normality test. Survival data were evaluated using the Kaplan-Meier method, and comparisons between individual curves were made using the log-rank test. Statistical analysis was performed using GraphPad Prism v8.4.0 (GraphPad Software), and statistical significance was assumed at P < 0.05.
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5

Flow Cytometry Analysis of Cell Subpopulations

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Unless otherwise stated, all experiments were repeated at least 3 times. Only representative data are shown. Statistical analyses were performed using GraphPad Prism v.6 (GraphPad Software, Inc, La Jolla, CA, USA) and Microsoft® Excel 2016 (Microsoft Corporation, Redmond, WA, USA).
Flow cytometry plots showed representative examples of the relative percentages of each population or subpopulation. To obtain the absolute or calculated percentage of a particular subpopulation, its relative percentage was multiplied by the relative percentage of its parent population and the product was divided by 100 and presented as an absolute percentage.
One‐way ANOVA or Student t tests were performed to determine whether treatment means differed significantly. The output was then subjected to Bonferroni multiple group comparisons or Fisher least significant difference (LSD) post‐test. Unless otherwise indicated, significance was as follows: ***P < .001, **P < .01, and *P < .05.
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6

Breast Milk Microbiota Analysis

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The following software was used for analysis: Calypso online platform (V8.84) [30 (link)], SPSS V.27 [31 ] (IBM Corp. Released 2020; IBM SPSS Statistics for Windows, Version 27.0. Armonk, NY: IBM Corp); and Graphpad Prism v. 5.04 (GraphPad Software, San Diego, CA, USA, www.graphpad.com accessed on 1 April 2021). Redundancy analysis (RDA) was applied to study the statistical effect of breastfeeding practices on breast milk microbiota. The differences between the groups were visualized by the discriminant of principal components analysis (DAPC) at the amplicon sequence variant (ASV) level and the Adonis test was achieved based on the Bray-Curtis distance.
T-test and Mann-Whitney analysis were used depending on data normality assessed by Kolmogorov-Smirnov and Shapiro-Wilk test (Graphpad Prism v5.04). Spearman correlations between relative abundances of bacterial and maternal age were using RStudio [32 ]. Multivariable Poisson regression models adjusted by covariables were run in SPSS V.27 to assess differential abundance at the genus levels (dependent variable), variable that consists of count data, according to pre-gestational BMI, weight gain, and breastfeeding practices (independent variable). The covariables that were used to adjust each model are specified in the description of their results.
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7

Genetic Association Analysis Pipeline

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Compliance with the Hardy-Weinberg equilibrium for each SNP was tested by a chi-square test. Standard and allelic case/control association analysis with disease phenotype were performed using a chi-square test and Fisher’s exact test. Significant associations between phenotype/genotype and bacterial counts were established by the two-stage step-up adaptive method [59 (link)]. Briefly, in the first stage, the genotype (represented as a binary variable by allele-carrying) was sequentially tested against the counts for each bacterial species, obtaining a series of p-values. The distribution of these p-values was used to estimate the fraction of null hypothesis that were actually true. In the second stage, a reductive iterative process determined which p-values were low enough to be considered discoveries. A Q value of 5% was accepted as the maximum false positive rate. This adaptive procedure greatly diminishes the probability of false positives in repetitive testing.
A p-value < 0.05 was considered significant. Analyses were performed in GraphPad Prism v7.02 (GraphPad software, La Jolla, CA, USA), Stata14 (Stata Corp, College Station, TX, USA) and PLINK v1.07 [60 (link)].
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8

Analyzing Conditioned Place Preference and Locomotion

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For analysis of CPP and locomotion, 2-way repeated measures ANOVAs were performed using time and training as factors. Post-hoc comparisons were performed using Holm-Sidak corrections for multiple comparisons. For analysis of reinstatement data in Experiment 2, a 1-way ANOVA was performed with Holm-Sidak post-hoc comparisons among the groups. For correlations between training performance and CPP levels, the slope coefficient of a linear regression curve fitted to CPP from days 1–14 (the time period in which we observed a difference between trained and yoked animals) was used as a measure of CPP for each mouse. Pearson correlations were performed between training performance and CPP slope coefficients; a non-parametric Spearman correlation was used for one dataset determined to have a non-normal distribution by a D’Agostino-Pearson omnibus test. Analysis and graphing were performed using GraphPad Prism v6.05.
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9

Quantifying Neuronal Projection Patterns

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To distinguish the axons of passage vs. terminal innervations, we take the ended axons as terminal axons while others as passage axons. For terminals quantification, the reconstructed neurons carried spatial information of all nodes that we could calculate the ended nodes based on registered single neurons to obtain the terminals in different regions. In addition, we employed the Amira software to quantify the length of dendrites and axons of individual neurons. Statistical graphs were generated using GraphPad Prism v.8.02 and Microsoft Excel (Office 2020). We employed GraphPad Prism v. 8.02 for the significance test, Neurolucida360 software for the polar histogram, and MATLAB (2017a) for the Sholl Analysis. We conducted one-way ANOVA followed by Tukey’s post hoc tests to compare the difference among four projections patterns of same nuclei while two-tailed t-tests to compare the difference between the PPN and LDT. The confidence level was set to 0.05 (P value) and all results were presented as mean ± SEM.
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10

Comparison of Automated and Manual AVC Measurements

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All statistical and graphical analyses were performed using standard computer software (Microsoft Office Excel 2003, Microsoft Corporation, Redmond, WA; SigmaStat v3.5, SPSS Inc, Chicago, IL; GraphPad Prism v5.00 for Windows, GraphPad Software, San Diego California USA). The agreement between tAVCa and tAVCm was compared by paired t test and Bland-Altman statistics. The corresponding heart rates (HRAVCm and HRAVCa) were compared by paired t test. For segmental 2DST indices, 2-way repeated-measures analysis of variance was used to detect differences between segments and treatment (i.e., awake vs. anesthetized). When the F test indicated significant differences, all pairwise multiple comparisons were performed using the Holm-Sidak post hoc test. The effect of general anesthesia on averaged 2DST indices and on STIε was assessed by paired t tests, reporting the 95% confidence intervals for the difference of means. Validity of the normality assumption was confirmed by assessment of normal probability plots of the residuals. The level of significance was set at P=0.05.
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