Background: The post-genomic era poses several challenges. The biggest is the identification of biochemical function for protein sequences and structures resulting from genomic initiatives. Most sequences lack a characterized function and are annotated as hypothetical or uncharacterized. While homology-based methods are useful, and work well for sequences with sequence identities above 50%, they fail for sequences in the twilight zone (<30%) of sequence identity. For cases where sequence methods fail, structural approaches are often used, based on the premise that structure preserves function for longer evolutionary time-frames than sequence alone. It is now clear that no single method can be used successfully for functional inference. Given the growing need for functional assignments, we describe here a systematic new approach, designated ligand-centric, which is primarily based on analysis of ligand-bound/unbound structures in the PDB. Results of applying our approach to S-adenosyl-L-methionine (SAM) binding proteins are presented. Results: Our analysis included 1,224 structures that belong to 172 unique families of the Protein Information Resource Superfamily system. Our ligand-centric approach was divided into four levels: residue, protein/domain, ligand, and family levels. The residue level included the identification of conserved binding site residues based on structure-guided sequence alignments of representative members of a family, and the identification of conserved structural motifs. The protein/domain level included structural classification of proteins, Pfam domains, domain architectures, and protein topologies. The ligand level included ligand conformations, ribose sugar puckering, and the identification of conserved ligand-atom interactions. The family level included phylogenetic analysis. Conclusion: We found that SAM bound to a total of 18 different fold types (I-XVIII). We identified 4 new fold types and 11 additional topological arrangements of strands within the well-studied Rossmann fold Methyltransferases (MTases). This extends the existing structural classification of SAM binding proteins. A striking correlation between fold type and the conformation of the bound SAM (classified as types) was found across the 18 fold types. Several site-specific rules were created for the assignment of functional residues to families and proteins that do not have a bound SAM or a solved structure.

A simulation study is done to compare Ridge Regression (RR) and the Lasso, under the assumption of a linear model, by calculating four metrics: the squared distance, from the true coefficients, of estimated coefficients that are both statistically significant and true; the proportion of true regressors discovered; the squared distance, from the true predictions, of the predictions made using the estimated coefficients that are only statistically significant (but not necessarily true); and the chance that no estimated coefficient is true. Results indicate that RR surpasses the Lasso in regard to all of these metrics. This indicates that RR can add value to model discovery, in Economics and the Sciences, by continuing to employ the key concept of statistical significance in the classical sense to find true regressors. This is important, because it allows the “manufacturer” of models to focus on the process generating the data, if indeed there is one. And, thus, provide important feedback on the outputs of other fashionable competitors, such as Machine Learning, with their pervasive “black-box” focus on prediction as an end in itself.

For the linear model $Y=Xb+error$, where the number of regressors ($p$) exceeds the number of observations ($n$), the Elastic Net (EN) was proposed, in 2005, to estimate $b$. The EN uses both the Lasso, proposed in 1996, and ordinary Ridge Regression (RR), proposed in 1970, to estimate $b$. However, when $p>n$, using only RR to estimate $b$ has not been considered in the literature thus far. Because RR is based on the least-squares framework, only using RR to estimate $b$ is computationally much simpler than using the EN. We propose a generalized ridge regression (GRR) algorithm, a superior alternative to the EN, for estimating $b$ as follows: partition $X$ from left to right so that every partition, but the last one, has 3 observations per regressor; for each partition, we estimate $Y$ with the regressors in that partition using ordinary RR; retain the regressors with statistically significant $t$-ratios and the corresponding RR tuning parameter $k$, by partition; use the retained regressors and $k$ values to re-estimate $Y$ by GRR across all partitions, which yields $b$. Algorithmic efficacy is compared using 4 metrics by simulation, because the algorithm is mathematically intractable. Three metrics, with their probabilities of RR’s superiority over EN in parentheses, are: the proportion of true regressors discovered (99%); the squared distance, from the true coefficients, of the significant coefficients (86%); and the squared distance, from the true coefficients, of estimated coefficients that are both significant and true (74%). The fourth metric is the probability that none of the regressors discovered are true, which for RR and EN is 4% and 25%, respectively. This indicates the additional advantage RR has over the EN in terms of discovering causal regressors.

To-date, no claim regarding finding a consensus sequon for O-glycosylation has been made. Thus, predicting the likelihood of O-glycosylation with sequence and structural information using classical regression analysis is quite difficult. In particular, if a binary response is used to distinguish between O-glycosylated and non-O-glycosylated sequences, an appropriate set of non-O-glycosylatable sequences is hard to find. Three sequences from similar post-translational modifications (PTMs) of proteins occurring at, or very near, the S/T-site are analyzed: N-glycosylation, O-mucin type (O-GalNAc) glycosylation, and phosphorylation. Results found include: 1) The consensus composite sequon for O-glycosylation is: ~(W–S/T–W), where “~” denotes the “not” operator. 2) The consensus sequon for phosphorylation is ~(W–S/T/Y/H–W); although W–S/T/Y/H–W is not an absolute inhibitor of phosphorylation. 3) For linear probability model (LPM) estimation, N-glycosylated sequences are good approximations to non-O-glycosylatable sequences; although N – ~P – S/T is not an absolute inhibitor of O-glycosylation. 4) The selective positioning of an amino acid along the sequence, differentiates the PTMs of proteins. 5) Some N-glycosylated sequences are also phosphorylated at the S/T-site in the N – ~P – S/T sequon. 6) ASA values for N-glycosylated sequences are stochastically larger than those for O-GlcNAc glycosylated sequences. 7) Structural attributes (beta turn II, II´, helix, beta bridges, beta hairpin, and the phi angle) are significant LPM predictors of O-GlcNAc glycosylation. The LPM with sequence and structural data as explanatory variables yields a Kolmogorov-Smirnov (KS) statistic of 99%. 8) With only sequence data, the KS statistic erodes to 80%, and 21% of out-of-sample O-GlcNAc glycosylated sequences are mispredicted as not being glycosylated. The 95% confidence interval around this mispredictions rate is 16% to 26%. The data indicates the existence of a consensus sequon for O-glycosylation; and underscores the germaneness of structural information for predicting the likelihood of O-glycosylation.

The classic approximation of the random present value (PV) of a life annuity is its expected PV (EPV) over its term. EPV minimizes mean squared error per expec

The lessons I (Gana 2014) have learned from the vivid contrast between the mean and median fair values (Hayden and Platt 2009) of the game (Bernoulli 1738) unde