Slimphoria Keto UPDATE 2020 Impact On Protein-phenotype Interaction?

January 8 2020

Slimphoria Keto factor (TF) binding data analyzed in this work were collected from in vitro and in vivo studies. Specifically, CAP-SELEX and HT-SELEX sequencing reads were retrieved from the European Nucleotide Archive, under accession entries PRJEB7934, PRJEB7934, and PRJEB20112. Protein binding microarray (PBM) data were downloaded from the UniProbe database52. ChIP-seq peak datasets were collected from the ReMap2 database26.

The first step in the computational processing of SELEX data is the generation of count tables for k-mers (sequence patterns of length k), for each experiment where a TF or a TF pair was probed. CAP-SELEX sequencing data used to generate count tables always comes from a fixed selection round (positive) and is compared against an input library (background, or Slimphoria Keto round zero). For each TF pair, we select the positive round where a binding motif targeted by the two TFs is overrepresented in the reads for a given topology vs. All other possible topologies10. From this, the initial value of k is the length of the reported reference k-mers, trimming out ambiguous nucleotides in the flankings (IUPAC=N). For example, the reference k-mer GAAAACCGAANM has a length of 12, and thus k = 12. If more than one reference k-mer is enriched in one dataset, those are processed independently.

Once k-mer tables are defined, relative affinity estimates for each k-mer are obtained from the counts of each k-mer observed in the positive round, versus the amount estimated in the input data (round zero) using a fifth-order Markov Model. This correction takes into account sequencing biases18. Given this information, for a k-mer k in selection round r, its relative affinity S(k,r) is calculated as

$$S\left( {k,r} \right) = ^{1 + r}\sqrt {\frac{{P_{{\mathrm{obs}}}\left( {k,r} \right)}}{{P_{{\mathrm{exp}}}\left( {k,r}\right)}}},$$

where $P_{{\mathrm{obs}}}\left( {k,r} \right)$ is the fraction of counts for k in r, and $P_{{\mathrm{exp}}}\left( {k,r} \right)$ is the expected fraction of counts for k in round r. The derivation of the formula has been extensively described in previous work18.

From the k-mer tables and their relative affinity Slimphoria Keto estimates, we further subset this table for k-mers with high similarity between those and the reference k-mers indicated to be enriched, allowing up to m mismatches5. The m-value threshold is proportional to the consensus sequence length and the information content for each of its nucleotides, using the proposed formula by Yang et al.5:

$$m = \lfloor \frac{{L - 4}}{2} \rfloor + 1,$$

where L is the length of the consensus sequence, corrected by the ambiguity of each nucleotide. For example, GAGCA has an L-value of 5, but RRGCA has an L-value of 4, as R (purine) can represent either G or A. Datasets and reference k-mers used are listed in Supp. Data 1.

Tiled k-mer tables

There is an exponential decrease in the counts recovered per k-mer and the value of k, which prevents the calculation of robust k-mer tables and robust relative affinity estimates for high k values. To overcome this, we trimmed nucleotides from both flanking regions of each consensus sequence in the list derived from the CAP-SELEX data. We thereby obtain tiled k-mer tables with sufficient counts for further analyses. To avoid lower complexity of DNA sequences, tiled k-mer tables with a length lower than ten are not considered for further analyses. Our trimming approach was benchmarked through a comparison between the effect of shorter k-mers on the final performance metrics (see Trim-and-summarize coefficient of determination section and Supplementary Figs. 1a-b and 8). To avoid relative affinity estimates with low support, thresholds of counts per k-mer are defined5,18. In this work, k-mers derived from CAP-SELEX data are discarded if the number of counts supporting those are lower than 20 counts.

Regression models to model k-mer relative affinities

To relate binding affinities with sequence and/or shape features, we used L2-regularized multiple linear regression (L2-MLR), with the following formula:

where y is the vector of relative affinities for each k-mer in the k-mer table, X (i = 1,…,n) represent a concatenated set of features that encode their respective DNA sequences, βi (i = 1,…,n) represent the regression coefficients, and β0 represents the intercept. To prevent overfitting, L2-regularization employs an additional penalty term on the coefficients in the loss function L(β), i.E., coefficients are obtained by minimizing.

For regression models based on DNA sequence features, the baseline models are named 1mer and are defined by mononucleotide representations of each k-mer. At any k-mer position i, four features 4i to 4i + j with j < 4 are defined based on the nucleotide identity of ki:

In total, 1mer models require 4k features for each sequence of length k to fully encode its sequence in numbers. For 2mer or 3mer models, dinucleotide or trinucleotides are also converted into coefficients, thus requiring more features per position. For 2mer model features, 16 coefficients between 16i to 16i + j with j < 15 features are necessary to describe the dinucleotide identity of each k-mer position and its immediate right-nucleotide.

Similarly, for 3mer models 64 features representing all the possibilities for trinucleotides are required. In general, for an N-mer model where N∈Z+, 4N would be required per k-mer position. Combinations of these models require the sum of features for each individual model, per position. For example, 1mer + 2mer models require 41 + 42 = 20 coefficients per position. Equivalences between some of these models are further described by Yang et al.5

Models that include DNA-shape features are labeled with the keyword shape (e.G., 1mer + shape), and consider DNA structure estimated for each tested DNA-sequence in all datasets, defined as descriptors of the overall DNA structure for that sequence. These values are listed in a DNA pentamer table, and are obtained from the DNAShapeR package53 centering each feature value on the middle nucleotide of the pentamer. In this work, we considered the four main features provided in the original version of this table: Propeller twist (ProT), roll, helical twist (HelT), and minor groove width (MGW). In Slimphoria Keto addition to these values, second order shape values are obtained by calculating the product of features in two consecutive positions, as a way to describe longer structure features. For that reason, four main shape and 4 second order shape features are required per position, allowing for eight features per position to be described in shape models. Additively, 1mer + shape models require 4 + 8 = 12 features per position where a centered DNA pentamer exists.

Flanking positions cannot be described by shape features, as these miss one or two nucleotides to successfully map a DNA pentamer. Solutions such as describing the flanks as 3mer features have been proposed (1mer + 3merE2, where E2 represents 3mer features on the two end positions)5. In this work, we extended the shape model features to include flanking regions as well by including the average feature value of all pentamers that contain a common tetramer or trimer as found in the flanking region. Briefly, whenever a shape feature in the flanking regions is required, we average pentamer shape features that contain a fixed trimer (16 options) or tetramer (4 options). This is done with similar rules and upstream or downstream of the k-mer flank, according to the 5′ to 3′ directionality (left flank = upstream trimming, right flank = downstream trimming), respectively. We calculated errors for each DNA-pentamer to estimate the amount of uncertainty for each calculation using all trimers and tetramers available in the dataset in comparison with all DNA-pentamers (Supplementary Data 2). Shape features based on averaging across trimers and tetramers are closer to real pentamer DNA-shape features than the global mean generated by using all 1024 DNA pentamers or scrambled versions. In this work, we refer to shape features as models that include these flanking features.

For each tiled k-mer table in each dataset, we use a 10-fold cross validation scheme to randomly separate the table into 10 fixed groups of equal size, iteratively Slimphoria Keto fitting L2-MLR models with nine out of ten groups, and then assessing coefficient of determination (R²) in the held-out group. This is done using scikit-learn54. As a summary statistic for each tiled k-mer table, we report the median R² of all held-out groups (Supplementary Data 1 and 4). As a quality control and to remove datasets with low variability and enrichment for mapped k-mers, at this stage we filter out datasets whose minimum testing R² value across all models for all tiled k-mer tables is lower than zero (i.E., model is worse than using the mean of all values as a single feature).

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