In systems biology, qualitative data are often generated, but rarely used to parameterize models. We demonstrate an approach in which qualitative and quantitative data can be combined for parameter identification. In this approach, qualitative data are converted into inequality constraints imposed on the outputs of the model. These inequalities are used along with quantitative data points to construct a single scalar objective function that accounts for both datasets. To illustrate the approach, we estimate parameters for a simple model describing Raf activation. We then apply the technique to a more elaborate model characterizing cell cycle regulation in yeast. We incorporate both quantitative time courses (561 data points) and qualitative phenotypes of 119 mutant yeast strains (1647 inequalities) to perform automated identification of 153 model parameters. We quantify parameter uncertainty using a profile likelihood approach. Our results indicate the value of combining qualitative and quantitative data to parameterize systems biology models.

SummaryIn systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit, which in addition supports checking models against known system properties and solving design problems. PyBioNetFit introduces Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving various example problems, including the challenging problem of parameterizing a 153-parameter model of cell cycle control in yeast based on both quantitative and qualitative data. We demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of targeted drug interventions in autophagy signaling.

Mathematical models can provide quantitative insight into immunoreceptor signaling, but require parameterization and uncertainty quantification before making reliable predictions. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena. Highlights• Models of immunoreceptor signaling often contain parameters that must be fit to data.• New tools including PyBioNetFit and AMICI support automated parameter estimation.• Optimization algorithms can be used to obtain point estimates of parameter values.• Parameter estimation can incorporate both quantitative and qualitative data.• Uncertainty quantification assesses confidence in parameter values and model predictions.

The high-affinity receptor for IgE expressed on the surface of mast cells and basophils interacts with antigens, via bound IgE antibody, and triggers secretion of inflammatory mediators that contribute to allergic reactions. To understand how past inputs (memory) influence future inflammatory responses in mast cells, a microfluidic device was used to precisely control exposure of cells to alternating stimulatory and non-stimulatory inputs. We determined that the response to subsequent stimulation depends on the interval of signaling quiescence. For shorter intervals of signaling quiescence, the second response is blunted relative to the first response, whereas longer intervals of quiescence induce an enhanced second response. Through an iterative process of computational modeling and experimental tests, we found that these memory-like phenomena arise from a confluence of rapid, short-lived positive signals driven by the protein tyrosine kinase Syk; slow, long-lived negative signals driven by the lipid phosphatase Ship1; and slower degradation of Ship1 co-factors. This work advances our understanding of mast cell signaling and represents a generalizable approach for investigating the dynamics of signaling systems.

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Using a modified single-molecule pull-down (SiMPull) approach, the first direct detection of activation-dependent multisite phosphorylation on intact EGFR is provided. Integrating SiMPull data with rule-based modeling revealed roles for receptor dimerization dynamics and adaptor protein concentrations in directing EGFR signaling.

Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages. Here, we provide both a high-level description of the algorithms underlying the simulation engines, termed network-free simulation algorithms, and how they have been applied in systems biology research. We also define a generic rule-based modeling framework and describe a number of technical details required for adapting Gillespie's direct method for network-free simulation. Finally, we briefly discuss potential avenues for advancing network-free simulation and the role they continue to play in modeling dynamical systems in biology.

Motivation Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of a lack of a statistical interpretation of the objective functions used in optimization. Results We formulated likelihood functions suitable for performing Bayesian UQ using qualitative observations of underlying continuous variables or a combination of qualitative and quantitative data. To demonstrate the resulting UQ capabilities, we analyzed a published model for immunoglobulin E (IgE) receptor signaling using synthetic qualitative and quantitative datasets. Remarkably, estimates of parameter values derived from the qualitative data were nearly as consistent with the assumed ground-truth parameter values as estimates derived from the lower throughput quantitative data. These results provide further motivation for leveraging qualitative data in biological modeling. Availability and implementation The likelihood functions presented here are implemented in a new release of PyBioNetFit, an open-source application for analyzing Systems Biology Markup Language- and BioNetGen Language-formatted models, available online at www.github.com/lanl/PyBNF. Supplementary information Supplementary data are available at Bioinformatics online.