(A-35) Ranking Computational Model Parameters by Information Gained from Data Facilitates Searching for Evidence of Alternative Biological Hypotheses

Introduction:: Biological hypotheses may be formalized via computational models; consequently, if a model fails to explain experimental data, an alternative hypothesis may exist[1]–[3]. Evidence of alternative hypotheses can manifest as discrepancies between model predictions and data. It can also manifest in the marginal Bayesian posterior distribution—that is, the plausible values of one parameter, given data—as a bimodality, or, as discrepancies between data subsets[4]–[7]. Searching marginals compliments comparing predictions to data; it associates evidence with a particular parameter, which may then serve as a valuable starting point for hypothesis refinement. However, existing approaches have limited applicability, as they are largely ungeneralizable and unsystematic. We hypothesize that ranking parameters by information gained from data will facilitate searching for alternative hypothesis evidence in marginals: rather than searching at random, one can search per the ranking.

Materials and Methods:: We use an established measure, the Kullback-Leibler (KL) divergence from the marginal Bayesian prior distribution to the marginal Bayesian posterior distribution, to quantify the information gained for each parameter [8], [9]. This measure quantifies the difference between what parameter values are plausible before and after experimental data—the more informative the data, the larger the difference. Once the KL divergence is estimated for each parameter, we examine the corresponding marginal posteriors in order of most to least informed. We expect to find alternative hypothesis evidence in highly ranked marginals. We test our approach on 2 models with such evidence: a 5-parameter model of protease self-digest kinetics with a marginal that is inconsistent with all the data and a 33-parameter model of pancreatic beta cell signaling with a marginal that is bimodal [5], [10]. In both cases, variables represent molecule concentrations and parameters represent reaction rate constants.

Results, Conclusions, and Discussions:: Ranking parameters by information gained highlights the evidence present in each test case. For test case 1, the marginal posterior inconsistent with all data is ranked 1st of the 5 parameters. For test case 2, the bimodal marginal is ranked 3rd of the 33 parameters (Figure 1). In this second case, we compare our approach to an applicable alternative: bimodality search. The bimodality search flags 12 of 33 parameters. Although this group includes the bimodal posterior, it also contains several false positives. Overall, our ranking systematically uncovers different manifestations of alternative hypothesis evidence. Further, it outperforms ungeneralizable alternatives, like bimodality search. Our approach facilitates model evaluation; by rigorously evaluating computational models, we better test and refine the hypotheses they characterize. Indeed, in a follow-up investigation, we used the evidence uncovered here to guide a novel investigation of pancreatic beta cell signaling [7].

Acknowledgements (Optional): : The authors acknowledge members of the Finley research group for constructive feedback and both Niklas Totsch and Robert Sorenson for their generous help in accessing the data presented in their respective papers.

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