Reticuloendothelial System

1. Molecular structure files: Protein-ligand complex files for re-docking experiments were obtained from the PDBbind database. To validate predictive models with less bias, native ligands of the co-crystallized complexes were first extracted and converted into 2D using Open Babel [43] (link). For the following docking simulation, 2D structures were then re-converted to 3D using a 3D structure generator called CORINA version 3.4 [44] .
2. Molecular docking simulation packages: Native ligands were docked to their corresponding target proteins using eHiTS, GOLD, and AutoDock VINA (Table S7). These docking tools are used to generate numerous binding modes of the test compound in a defined binding site, and the number of binding modes generated varies with the docking tools. For a docking simulation, eHiTS was set to output 1000 conformations for each docking study. Considering the computing speed of GOLD, we set the maximum as 300. The maximum binding mode of AutoDock VINA varies with an energy range of 10 (kcal/mol).
3. Application of machine learning systems: Binding modes generated by the three docking tools were re-scored by machine learning system A, and only the three top-score candidates in each set were retained. Subsequently, machine learning system B assessed the three top-score candidates and identified the most predictive one. Modeling exercises of the machine learning systems A and B were conducted using the R statistical package. The Random Forest algorithm was applied to build machine learning system A, which was implemented in “randomForest” (Breiman and Cutler's random forests for classification and regression) module. For machine learning system B, the multinomial logistic regression of “nnet” (Feed-forward Neural Networks and Multinomial Log-Linear Models) and “MASS” (Modern Applied Statistics with S. Fourth Edition) modules was utilized.
4. Re-docking result: The Pearson correlation coefficient between the predicted docking scores and the experimental binding affinities was calculated using R to determine the predictiveness of the screening approach.

The MRI data were visually inspected for obvious artifacts arising from subject motion and instrument malfunction. The high-resolution T₁WI was preprocessed and the cortical surface was extracted using automated procedures in Computational Anatomy Toolbox (CAT12)¹ within SPM12 while running MATLAB 8.4 (R2014b; MathWorks, Natick, MA, USA). Briefly, T1 images were bias-field corrected, skull-stripped, aligned to a Montreal Neurological Institute standard space (MNI-152 template), and classified as GM, WM, or cerebrospinal fluid, all within the same generative model (Kurth et al., 2015 (link)). To improve registration accuracy, the DARTEL algorithm was used to create a group-specific template and calculate the individual non-linear transformation to this template in SPM8.
In CAT12, a new fully automated method allows cortical thickness to be measured and the central surface to be reconstructed in a single step (Dahnke et al., 2013 (link)). The program uses tissue segmentation to estimate the WM distance and projects the local maxima (which is equal to the cortical thickness) to other GM voxels using a neighbor relationship that is described by the WM distance. This PBT allows partial volume information, sulcal blurring, and sulcal asymmetries to be managed without explicit sulcus reconstruction via skeleton or thinning methods. For inter-subject comparisons, local complexity maps were re-parameterized into a common coordinate system and smoothed using a 15-mm Gaussian heat kernel (Yotter et al., 2011a (link); Madan and Kensinger, 2016 (link)). For quality control, we excluded two WMH subjects and four healthy controls based on the poor quality of their cortical surface reconstructions.

The contrast agent used in the present study (Viscover™ ExiTron™ nano; Miltenyi Biotec, Bergisch-Gladbach, Germany) is an alkaline earth-based nanoparticulate contrast agent specifically formulated for pre-clinical computed tomography imaging. The nanoparticles are sterically stabilized by a polymer coating and have a mean hydrodynamic diameter of 110 nm. Upon i.v. injection, ExiTron nano circulates in the blood stream and is taken up by cells of the reticuloendothelial system (RES), including macrophages within the liver, the so-called Kupffer cells. Two different formulations of the contrast agent are available and both were used in the underlying study: ExiTron nano 6000 (optimized for liver/spleen imaging) and ExiTron nano 12000 (optimized for angiography) with densities of the undiluted contrast agents prior to injection of approx. 6000 HU and approx. 12000 HU, respectively. The injected volume of 100 µl ExiTron nano per mouse (25g) corresponds to a dose equivalent to 640 mg iodine/kg body weight or 1200 mg iodine/kg body weight for ExiTron nano 6000 and ExiTron nano 12000, respectively.

Under the framework of equilibrium statistical mechanics, the concept of entropy for a macroscopic variable could be interpreted as measuring the extent to which the probability of the system is spread out over different possible microstates. In this study, the (RE^I_0.25RE^II_0.25RE^III_0.25RE^IV_0.25)₂Si₂O₇ solid solution with random occupations of RE³⁺ cations on its sublattice sites could be understood as the macrostate; while the possible metastable configurations could be understood as the microstates. The thermodynamics of the macrostate could be derived from the partition function, which encodes how the probabilities are partitioned among different microstates based on their individual configurational energies. The partition function could be written in the formula for the canonical ensemble^{38 (link),50} : $Z=\sum _{i=1}^N\exp \left(-\frac{E_i}{k_{\mathrm{B}}T}\right)$ Herein, i is the index for the microstates of the system; N is the total number of the microstates; k_B is the Boltzmann constant; and T is the absolute temperature. E_i is the energy for the ith microstate, derived from the standard DFT total energy calculations (at temperature of T = 0 K): $E_i=E_{4\mathrm{mix}}-\frac{1}{4}{E}_{{\mathrm{RE}}^{\mathrm{I}}}-\frac{1}{4}{E}_{{\mathrm{RE}}^{\mathrm{II}}}-\frac{1}{4}{E}_{{\mathrm{RE}}^{\mathrm{III}}}-\frac{1}{4}{E}_{{\mathrm{RE}}^{\mathrm{IV}}}$ where E_4mix is the total energy of the (RE^I_0.25RE^II_0.25RE^III_0.25RE^IV_0.25)₂Si₂O₇ unit cell; E_RE (with superscript I−IV) is the total energy of the corresponding single-RE-principal-component RE₂Si₂O₇, in the same polymorphic structure as the multicomponent material. Herein, the calculated E_i could be understood as the energy of mixing, which interprets the procedure of several single-RE-principal-component RE₂Si₂O₇ mixed into a multi-RE-principal-component system through random assignment of the RE atoms onto the RE lattice sites. Then, the configurational energy for the macrostate could be written as the ensemble average of E_i, which is the sum of energies for the microstates weighted by their probabilities: $⟨E⟩=\frac{1}{Z}\sum _{i=1}^N{E}_i\exp \left(-\frac{E_i}{k_{\mathrm{B}}T}\right)$ And, the free energy raised from configurational disorders is given by: $F=-k_{\mathrm{B}}T\ln Z$
In practice, it is computationally challenging to model the ensemble of all possible configurations for the multicomponent materials. Instead, the ensemble average could be performed over a representative subset of the whole microstate populations, provided that the subset extensively samples the energy landscape of all the microstates, and thus lead to statistically converged thermodynamic properties with respect to those of the whole population. This restriction is expressed by: $\frac{Z}{N}=\frac{Z^{\prime }}{N^{\prime }}$ Herein, N’ is the total number of the sampled microstates; and Z′ is their partition function. Imposing the Eq. (5) into the Eq. (4) gives: $F=-k_{\mathrm{B}}T\ln \left(N\cdot \frac{Z^{\prime }}{N^{\prime }}\right)=-k_{\mathrm{B}}T\ln N-k_{\mathrm{B}}T\ln \frac{{\sum }_{i=1}^{N^{\prime }}\exp \left(-\frac{E_i}{k_{\mathrm{B}}T}\right)}{N^{\prime }}$
Finally, the configurational entropy is derived from: $S_{\mathrm{config}}=\left(⟨E⟩-F\right)/T$
It should be noticed that, in general, the entropy of materials comprises contributions from configuration, vibration, electronic excitation, magnetism, etc. This model mainly deals with the configurational entropy of mixing, as it is expected to have significant effect on the formation of multicomponent ceramics. Such theoretical framework has been successfully adopted in Anand et al.’s work to interpret the thermodynamics of high-entropy oxides.^{38 (link)} Alternatively, one could also examine the energy spread of a system by calculating the formation energy for every metastable configuration in the ensemble, such as using the RE₂O₃ and SiO₂ as reference states in the Eq. (2). Results are discussed in the Supplementary Note 5 and Supplementary Fig. 9. Such modification will not change the calculated S_config, as it is derived from the dispersive features of the energy spread.
The available configurations for the multicomponent solid solution are generated by employing the special quasirandom structures (SQS) generation code implemented in the Alloy Theoretic Automated Toolkit (ATAT) package^{51 (link)}, which allows for the simulation of disordered crystallines by sampling on supercells with varied shapes and randomized occupations on the RE cationic sites (Supplementary Fig. 6a). Supercells with 88 lattice sites are used to construct the β-type and γ-type (RE^I_0.25RE^II_0.25RE^III_0.25RE^IV_0.25)₂Si₂O₇ systems, corresponding to four times of the minimum cell size necessary to reproduce the required stoichiometry. The configuration ensembles are constructed to include 558 unique configurations for the β-type (RE^I_0.25RE^II_0.25RE^III_0.25RE^IV_0.25)₂Si₂O₇, and 319 for the γ-type structures. Details on the stochastic generation of configuration ensembles, as well as the convergence test on the size of configuration ensembles, are presented in the Supplementary Note 6 and Supplementary Fig. 10.

Concentrations of DON and ZEN in corn were determined using the commercially available ELISA kits RIDASCREEN™ DON and RIDASCREEN™ ZEN (R-Biopharm GmbH, Darmstadt, Germany). The clinical chemical analyses of serum samples (AST and ALT activity, concentrations of glucose, cholesterol, triglyceride, creatinine, and uric acid) were performed by Vet-Med-Labor Ltd. using colorimetric assay kits (Diagnosticum Co., Budapest, Hungary) based on spectrophotometric methods. Histopathological examinations were performed by Autopsy KKT (Budapest, Hungary). The liver, spleen, and bursa of Fabricius samples in formaldehyde solution were embedded in paraffin and 5 μm thick sections were stained with hematoxylin and eosin. Tissue morphology was observed under a light microscope. The mean histological score was derived from the grade and stage of histological lesions seen in the investigated organs of the affected animals. The listed lesions were characterized per animal (1 point = mild, 2 points = medium, 3 points = high-grade alterations) and then mean score values were calculated in the group. The extent of vacuolar degeneration of hepatocytes, solitary hepatocyte necrosis, individual cell deaths of the mononuclear phagocyte system (MPS), focal lymphocytic and histiocytic interstitial infiltrates and interstitial fibrosis in liver samples, as well as lymphocyte counts in spleen and bursa of Fabricius samples, were evaluated.

DNA extraction was performed using the Epicentre MasterPure™ DNA Purification Kit (Epicenter, Middleton, WI, USA), according to the manufacturer’s recommendations. The quality and quantity of the extracted DNA was checked using a NanoDrop (Colibri Microvolume Spectrometer; Titertek-Berthold, Germany). Amplification of the entire (~1500 bp) 16S rRNA gene was performed using the 16S Barcoding Kit (SQK-RAB204; Oxford Nanopore Technologies, Oxford, UK) and LongAmp™ Taq 2 × Master Mix (New England Biolabs, UK) with 1 µg of input DNA per sample. Purification of the PCR products was performed using AMPure XP (Beckman Coulter, CA, USA) followed by quantification using a Qubit 4 fluorometer (Thermo Fisher Scientific, Waltham, MA, USA). Equimolar amounts of the amplification products were pooled together, then a total of 100 ng DNA of the pooled sample was used for library preparation. The microbiota was analyzed using third-generation sequencing with Nanopore technology on a MinION device (Oxford Nanopore Technologies, UK). MinION™ sequencing was performed using R9.4 flow cells (Oxford Nanopore Technologies, UK) according to the manufacturer’s instructions. MinKNOW version 2.0 (Oxford Nanopore Technologies, UK) was used for live base calling and data acquisition. The raw data were converted into FASTQ format using Guppy v3.4.4, followed by demultiplexing and removal of nanopore and adaptor sequences. The FASTQ files were analyzed on the Nanopore EPI2ME platform with a default minimum Q score of 7. Preliminary bacterial identification was performed via the ‘What’s in my Pot?’ (WIMP) workflow provided by Oxford Nanopore Technologies (UK). Reads assigned to all targets were re-analyzed by the Kraken taxonomic sequence classification system using Partek^® Genomics Suite^® software (Copyright^© 2022; Partek Inc., St. Louis, MO, USA). The numbers of reads assigned per taxon were counted and the relative abundance of reads per taxon were used for separate downstream analysis, as described in our previous publications [27 (link),28 (link)].