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Despite significant progress in vaccine research, the level of protection provided by vaccination can vary significantly across individuals. As a result, understanding immunologic variation across individuals in response to vaccination is important for developing next-generation efficacious vaccines. Accurate outcome prediction and identification of predictive biomarkers would represent a significant step towards this goal. Moreover, in early phase vaccine clinical trials, small datasets are prevalent, raising the need and challenge of building a robust and explainable prediction model that can reveal heterogeneity in small datasets. We propose a new model named Generative Mixture of Logistic Regression (GeM-LR), which combines characteristics of both a generative and a discriminative model. In addition, we propose a set of model selection strategies to enhance the robustness and interpretability of the model. GeM-LR extends a linear classifier to a non-linear classifier without losing interpretability and empowers the notion of predictive clustering for characterizing data heterogeneity in connection with the outcome variable. We demonstrate the strengths and utility of GeM-LR by applying it to data from several studies. GeM-LR achieves better prediction results than other popular methods while providing interpretations at different levels. 

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data forE. coliand mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise. 

Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection in Drosophila , a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches. 

A full understanding of cell signaling processes requires knowledge of protein structure–function relationships, protein–protein interactions, and the abilities of pathways to control phenotypes. Computational models offer a valuable framework for integrating that knowledge to predict the effects of system perturbations and interventions in health and disease. Whereas mechanistic models are well suited for understanding the biophysical basis for signal transduction and principles of therapeutic design, data-driven models are particularly suited to distill complex signaling relationships among samples and between multivariate signaling changes and phenotypes. Both approaches have limitations and provide incomplete representations of signaling biology, but their careful implementation and integration can provide new understanding for how manipulating system variables impacts cellular decisions.