Dental Alloys

The purpose of this study is to apply PCA to a previously published study by Pereira et al. [10 (link)] (Table 1) in order to better understand the differences in the functioning of multiple metal oxide nanoparticle (MONP)-based hydrogels based on their adsorption properties. PCA is regarded as a technique for identifying patterns among variables. The bi-dimensional statistical approach failed to reveal these patterns. It presents an unsupervised machine-learning method because, once applied, no prior knowledge of the data or the investigated phenomena is assumed. A unit-weighting vector (W_j) and the original data matrix M with m × n dimensions (m: number of variables, n: number of datasets) are used to express the jth PC matrix (Pj) [31 (link),54 (link),55 (link)].
$$Pj=WM={{\displaystyle \sum }}_{}^{i=0}{W}_{ji}{M}_i$$
where W is the loading coefficient and M is the n-dimensional data vector. M(Var(M)), which is obtained by projecting M to W, should be maximized as follows: $$Var\left(M\right)=\frac{1}{n}\left(W^{T}M\right){\left(WM\right)}^T=\frac{1}{n}{W}^{T}M{M}^{T}W$$
$$MaxVar\left(M\right)=Max\left(\left(\frac{1}{n}\right) W^{T}M{M}^{T}W\right)$$
Since $\frac{1}{n}M{M}^T$ is the same as the covariance matrix of M(cov(M)), Var(M) can be expressed as follows: $$Var\left(M\right)=W^{T}cov\left(M\right)W$$
The Lagrangian function can be defined using the Lagrange multiplier method, which is as follows: $$L=W^T$$
$$L=W^{T}cov\left(M\right)W-\delta \left(W^{T}W-1\right)$$
Because the weighting vector is a unit vector, “W^TW − 1” is assumed to be equal to zero in Equation (6). As a result, the maximum value of Var(M) can be calculated by equating the derivative of the Lagrangian function (L) with respect to W, as follows: $$\frac{dL}{dW}=0$$
$$cov\left(M\right)\mathrm{W}-\delta W=\left(cov\left(M\right)-\delta I\right)\mathrm{W}=0$$
where, δ: eigenvalue of cov(M), W: eigenvector of cov(M).

In vivo imaging of L4 DRG in awake mice was performed > 4 days after surgery. To minimize motion artifacts during imaging, the animal was vertebrae restrained. In addition, mice were placed in a 2.9-cm-diameter transparent plastic cylinder to further attenuate motion artifacts. The cylinder had a custom-made window that exposed the DRG window for imaging, and the arm of vertebral mount for fixation to metal base. This cylinder could minimize intense struggle, but had less effect on the movements of limbs (Supplementary Fig. 4). Thereafter, the mouse together with the cylinder was mounted onto a heavy metal base. Mice were habituated for at least three trials (10 min per trial) before imaging.
The genetically encoded Ca²⁺ indicator GCaMP6 slow (GCaMP6s) was used for Ca²⁺ imaging of sensory neurons in the DRG. The in vivo imaging experiments were performed using a Bruker Investigator two-photon system equipped with a DeepSee Ti:sapphire laser (Spectra Physics) tuned to 920 nm. The average laser power on the sample was ~20–30 mW. L4 DRG is 180–250 µm in depth. For Ca²⁺ imaging, images were collected 30–200 µm below the DRG surface at frame rates of 1.3–1.7 Hz at a resolution of 512 × 512 pixels using a ×25 objective (NA = 1.05) immersed in artificial cerebrospinal fluid and with a 1 × digital zoom. There was no marked difference in image quality at different depths of DRG. Image acquisition was performed using Bruker PrairieView software. The imaging parameters were chosen to allow repeated imaging of the same cells without causing damage to cells and surrounding tissues. To evaluate the imaging quality of DRG window over time (Fig. 3a–b), the experimental conditions were kept exactly the same throughout all the imaging sessions to ensure proper calculation of image contrast.

Activity rates were measured by a C18-HPLC method [13] (link), [37] (link), based on measurement of the product formed by the NMNAT-catalyzed reaction, i.e. NAD or its analogs (respectively, nicotinamide hypoxanthine dinucleotide from ITP and nicotinamide guanine dinucleotide from GTP). Rates were calculated as tangent lines in the linear region of plots of product accumulation versus time. Kinetic parameters were measured as described [13] (link) under 15% maximum consumption of both substrates concentration. One unit (U) of NMNAT activity refers to the enzyme amount catalysing 1 µmol/min product formation at 37°C.
The assays discriminating for individual isozyme activity (discrimination assays) are based on isozyme-selective metal ion dependence. The reference assay mixture (0.4 mL final volume) contained 30 mM HEPES/KOH, pH 7.5, 0.6 mg/mL BSA, 25 mM MgCl₂, 20 mM NaF, 1 mM DDT, 1 mM both NMN and ATP, and either ∼1 mg/mL protein tissue extract or 0.15–2.5 µg/mL each pure recombinant isozyme. The above assay, referred as “A”, was used to measure total NMNAT activity, i.e. the “reference” activity value for all different mNMNAT isoforms. For isozyme discrimination, the additional mixtures “B”, “C”, and “D” were set replacing 25 mM MgCl₂ with either 50 µM MgCl₂ (B) or 1.5 mM ZnCl₂ (C) or 4 mM CoCl₂ (D). The assays under condition “D” were carried out in the absence of DTT. Suitable parameters for subsequent calculation were obtained by parallel assaying of each recombinant isozyme under the four conditions above. Then, reaction rates obtained from “B”, “C”, and “D” were divided each by the reference activity value obtained from “A”. The resulting reaction rate ratios, i.e. the coefficients b1, b2, b3; c1, c2, c3; d1, d2, d3, were substituted in the following system of three linear equations:
Tissue NMNAT activity (condition assay “B”) = (b1·X)+(b2·Y)+(b3·Z).
Tissue NMNAT activity (condition assay “C”) = (c1·X)+(c2·Y)+(c3·Z).
Tissue NMNAT activity (condition assay “D”) = (d1·X)+(d2·Y)+(d3·Z).
where X, Y, and Z represent the true enzymatic activities of mNMNAT1, mNMNAT2, and mNMNAT3, respectively, in the complex mixture. Solution of the matrix based on the Cramer’s rule [38] yields the actual activity values X, Y, and Z as if they were measured under reference condition “A”. Matrix calculation was carried out by Microsoft Excel and, specifically, by using the functions MDETERM(array), MINVERSE(array) and MMULT(array-1,array2), were “array” is the matrix of coefficients b1, b2, b3; c1, c2, c3; d1, d2, d3; “array-1“ is the transposed matrix of “array” obtained by the function MINVERSE(array), and “array2” is the vector obtained from tissue NMNAT activity values under conditions “B”, “C”, and “D”. The whole procedure including a numerical example of the matrix substitution calculation is detailed in Supporting Information files: Methods S1, Table S2, and Methods S2.