Search for: All records

Abstract Four statistical selection methods for inferring transcription factor (TF)–target gene (TG) pairs were developed by coupling mean squared error (MSE) or Huber loss function, with elastic net (ENET) or least absolute shrinkage and selection operator (Lasso) penalty. Two methods were also developed for inferring pathway gene regulatory networks (GRNs) by combining Huber or MSE loss function with a network (Net)-based penalty. To solve these regressions, we ameliorated an accelerated proximal gradient descent (APGD) algorithm to optimize parameter selection processes, resulting in an equally effective but much faster algorithm than the commonly used convex optimization solver. The synthetic data generated in a general setting was used to test four TF–TG identification methods, ENET-based methods performed better than Lasso-based methods. Synthetic data generated from two network settings was used to test Huber-Net and MSE-Net, which outperformed all other methods. The TF–TG identification methods were also tested with SND1 and gl3 overexpression transcriptomic data, Huber-ENET and MSE-ENET outperformed all other methods when genome-wide predictions were performed. The TF–TG identification methods fill the gap of lacking a method for genome-wide TG prediction of a TF, and potential for validating ChIP/DAP-seq results, while the two Net-based methods are instrumental for predicting pathway GRNs. 

Partition density functional theory is a density embedding method that partitions a molecule into fragments by minimizing the sum of fragment energies subject to a local density constraint and a global electron-number constraint. To perform this minimization, we study a two-stage procedure in which the sum of fragment energies is lowered when electrons flow from fragments of lower electronegativity to fragments of higher electronegativity. The global minimum is reached when all electronegativities are equal. The non-integer fragment populations are dealt with in two different ways: (1) An ensemble approach (ENS) that involves averaging over calculations with different numbers of electrons (always integers) and (2) a simpler approach that involves fractionally occupying orbitals (FOO). We compare and contrast these two approaches and examine their performance in some of the simplest systems where one can transparently apply both, including simple models of heteronuclear diatomic molecules and actual diatomic molecules with two and four electrons. We find that, although both ENS and FOO methods lead to the same total energy and density, the ENS fragment densities are less distorted than those of FOO when compared to their isolated counterparts, and they tend to retain integer numbers of electrons. We establish the conditions under which the ENS populations can become fractional and observe that, even in those cases, the total charge transferred is always lower in ENS than in FOO. Similarly, the FOO fragment dipole moments provide an upper bound to the ENS dipoles. We explain why and discuss the implications.