Bayesian data integration for quantifying the contribution of diverse measurements to parameter estimates

Prediction of transcript structure and concentration using RNA-Seq data

Alternative splicing (AS) is a key post-transcriptional modification that helps in increasing protein diversity. Almost 90% of the protein-coding genes in humans are known to undergo AS and code for different transcripts. Some transcripts are associated with diseases such as breast cancer, lung cancer and glioblastoma. Hence, these transcripts can serve as novel therapeutic and prognostic targets for drug discovery. Herein, we have developed a pipeline, Finding Alternative Splicing Events (FASE), as the R package that includes modules to determine the structure and concentration of transcripts using differential AS. To predict the correct structure of expressed transcripts in given conditions, FASE combines the AS events with the information of exons, introns and junctions using graph theory. The estimated concentration of predicted transcripts is reported as the relative expression in terms of log2CPM. Using FASE, we were able to identify several unique transcripts of EMILIN1 and SLK genes in the TCGA-BRCA data, which were validated using RT-PCR. The experimental study demonstrated consistent results, which signify the high accuracy and precision of the developed methods. In conclusion, the developed pipeline, FASE, can efficiently predict novel transcripts that are missed in general transcript-level differential expression analysis. It can be applied selectively from a single gene to simple or complex genome even in multiple experimental conditions for the identification of differential AS-based biomarkers, prognostic targets and novel therapeutics.

Systematic Bayesian posterior analysis guided by Kullback-Leibler divergence facilitates hypothesis formation

Bayesian inference produces a posterior distribution for the parameters of a mathematical model that can be used to guide the formation of hypotheses; specifically, the posterior may be searched for evidence of alternative model hypotheses, which serves as a starting point for hypothesis formation and model refinement. Previous approaches to search for this evidence are largely qualitative and unsystematic; further, demonstrations of these approaches typically stop at hypothesis formation, leaving the questions they raise unanswered. Here, we introduce a Kullback-Leibler (KL) divergence-based ranking to expedite Bayesian hypothesis formation and investigate the hypotheses it generates, ultimately generating novel, biologically significant insights. Our approach uses KL divergence to rank parameters by how much information they gain from experimental data. Subsequently, rather than searching all model parameters at random, we use this ranking to prioritize examining the posteriors of the parameters that gained the most information from the data for evidence of alternative model hypotheses. We test our approach with two examples, which showcase the ability of our approach to systematically uncover different types of alternative hypothesis evidence. First, we test our KL divergence ranking on an established example of Bayesian hypothesis formation. Our top-ranked parameter matches the one previously identified to produce alternative hypotheses. In the second example, we apply our ranking in a novel study of a computational model of prolactin-induced JAK2-STAT5 signaling, a pathway that mediates beta cell proliferation. Within the top 3 ranked parameters (out of 33), we find a bimodal posterior revealing two possible ranges for the prolactin receptor degradation rate. We go on to refine the model, incorporating new data and determining which degradation rate is most plausible. Overall, while the effectiveness of our approach depends on having a properly formulated prior and on the form of the posterior distribution, we demonstrate that our approach offers a novel and generalizable quantitative framework for Bayesian hypothesis formation and use it to produce a novel, biologically-significant insight into beta cell signaling.

Bayesian uncertainty quantification for data-driven equation learning

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with relatively small amounts of noise, the relationship between observation noise and uncertainty in the learned differential equation models remains unexplored. We demonstrate that for noisy datasets there exists great variation in both the structure of the learned differential equation models and their parameter values. We explore how to exploit multiple datasets to quantify uncertainty in the learned models, and at the same time draw mechanistic conclusions about the target differential equations. We showcase our results using simulation data from a relatively straightforward agent-based model (ABM) which has a well-characterized partial differential equation description that provides highly accurate predictions of averaged ABM behaviours in relevant regions of parameter space. Our approach combines equation learning methods with Bayesian inference approaches so that a quantification of uncertainty can be given by the posterior parameter distribution of the learned model.

Bayesian Data Integration Questions Classic Study on Protease Self-Digest Kinetics

We combine Bayesian data integration with kinetic modeling to rigorously identify reaction mechanisms. This approach forces models to be consistent not only with kinetic measurements but with all available information. We revisit a classic study on trypsin self-digest acceleration by colloidal silica. Bayesian data integration reveals that the mechanism suggested in that study is inconsistent with its presented data. We propose an improved hypothesis. However, the detailed mechanism of the surface reaction cannot be inferred from the available data.