Phenotypic differences often occur even in clonal cell populations. Many potential sources of such variation have been identified, from biophysical rate variance intrinsic to all chemical processes to asymmetric division of molecular components extrinsic to any particular signaling pathway. Identifying the sources of phenotypic variation and quantifying their contributions to cell fate variation is not possible without accurate single cell data. By combining such data with mathematical models of potential noise sources it is possible to characterize the impact of varying levels of each noise source and identify which sources of variation best explain the experimental observations. The mathematical framework of information theory provides metrics of the impact of noise on the reliability of a cell to sense its environment. While the presence of noise in a single cellular system reduces the reliability of signal transduction its impact on a population of varied single cells remains unclear.

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose-response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis-Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context.

The nuclear factor kappa B (NFκB) family of transcription factors is a key regulator of immune development, immune responses, inflammation, and cancer. The NFκB signaling system (defined by the interactions between NFκB dimers, IκB regulators, and IKK complexes) is responsive to a number of stimuli, and upon ligand-receptor engagement, distinct cellular outcomes, appropriate to the specific signal received, are set into motion. After almost three decades of study, many signaling mechanisms are well understood, rendering them amenable to mathematical modeling, which can reveal deeper insights about the regulatory design principles. While other reviews have focused on upstream, receptor proximal signaling (Hayden MS, Ghosh S. Signaling to NF-κB. Genes Dev 2004, 18:2195-2224; Verstrepen L, Bekaert T, Chau TL, Tavernier J, Chariot A, Beyaert R. TLR-4, IL-1R and TNF-R signaling to NF-κB: variations on a common theme. Cell Mol Life Sci 2008, 65:2964-2978), and advances through computational modeling (Basak S, Behar M, Hoffmann A. Lessons from mathematically modeling the NF-κB pathway. Immunol Rev 2012, 246:221-238; Williams R, Timmis J, Qwarnstrom E. Computational models of the NF-KB signalling pathway. Computation 2014, 2:131), in this review we aim to summarize the current understanding of the NFκB signaling system itself, the molecular mechanisms, and systems properties that are key to its diverse biological functions, and we discuss remaining questions in the field. WIREs Syst Biol Med 2016, 8:227-241. doi: 10.1002/wsbm.1331 For further resources related to this article, please visit the WIREs website.

Immunology, along with other fields of biology, is undergoing a revolution. Here we discuss the challenges and opportunities presented by considering the dynamical systems properties of the immune system, and harnessing the power of data-rich technologies. We present specific recommendations for changing graduate programs to incorporate training that will enable students to actively participate in the analyses of complex data and their biological system, and urge that we move from viewing quantitative and computational biology as interdisciplinary, to recognizing these as intrinsic to the discipline of immunology going forward.

Rapid antibody production in response to invading pathogens requires the dramatic expansion of pathogen-derived antigen-specific B lymphocyte populations. Whether B cell population dynamics are based on stochastic competition between competing cell fates, as in the development of competence by the bacterium Bacillus subtilis, or on deterministic cell fate decisions that execute a predictable program, as during the development of the worm Caenorhabditis elegans, remains unclear. Here, we developed long-term live-cell microscopy of B cell population expansion and multiscale mechanistic computational modeling to characterize the role of molecular noise in determining phenotype heterogeneity. We show that the cell lineage trees underlying B cell population dynamics are mediated by a largely predictable decision-making process where the heterogeneity of cell proliferation and death decisions at any given timepoint largely derives from nongenetic heterogeneity in the founder cells. This means that contrary to previous models, only a minority of genetically identical founder cells contribute the majority to the population response. We computationally predict and experimentally confirm nongenetic molecular determinants that are predictive of founder cells' proliferative capacity. While founder cell heterogeneity may arise from different exposure histories, we show that it may also be due to the gradual accumulation of small amounts of intrinsic noise during the lineage differentiation process of hematopoietic stem cells to mature B cells. Our finding of the largely deterministic nature of B lymphocyte responses may provide opportunities for diagnostic and therapeutic development.

The dye-dilution assay is a powerful tool to study lymphocyte expansion dynamics. By combining time course dye-dilution experiments with computational analysis, quantitative information about cell biological parameters, such as percentage of cells dividing, time of division, and time of death, can be produced. Here, we describe the method to generate quantitative cell biological insights from dye-dilution experiments. We describe experimental methods for generating dye-dilution data with murine lymphocytes and then describe the computational data analysis workflow using a recently developed software package called FlowMax. The aim is to interpret the dye-dilution data quantitatively and objectively, such that cell biological parameters can be reported with an appropriate measure of confidence, which in turn depends on the quality and quantity of available data.

The nuclear factor κB (NF-κB) system is critical for various biological functions in numerous cell types, including the inflammatory response, cell proliferation, survival, differentiation, and pathogenic responses. Each cell type is characterized by a subset of 15 NF-κB dimers whose activity is regulated in a stimulus-responsive manner. Numerous studies have produced different mathematical models that account for cell type-specific NF-κB activities. However, whereas the concentrations or abundances of NF-κB subunits may differ between cell types, the biochemical interactions that constitute the NF-κB signaling system do not. Here, we synthesized a consensus mathematical model of the NF-κB multidimer system, which could account for the cell type-specific repertoires of NF-κB dimers and their cell type-specific activation and cross-talk. Our review demonstrates that these distinct cell type-specific properties of NF-κB signaling can be explained largely as emergent effects of the cell type-specific expression of NF-κB monomers. The consensus systems model represents a knowledge base that may be used to gain insights into the control and function of NF-κB in diverse physiological and pathological scenarios and that describes a path for generating similar regulatory knowledge bases for other pleiotropic signaling systems.

Balancing cell death is essential to maintain healthy tissue homeostasis and prevent disease. Tumor necrosis factor (TNF) not only activates nuclear factor κB (NFκB), which coordinates the cellular response to inflammation, but may also trigger necroptosis, a pro-inflammatory form of cell death. Whether TNF-induced NFκB affects the fate decision to undergo TNF-induced necroptosis is unclear. Live-cell microscopy and model-aided analysis of death kinetics identified a molecular circuit that interprets TNF-induced NFκB/RelA dynamics to control necroptosis decisions. Inducible expression of TNFAIP3/A20 forms an incoherent feedforward loop to interfere with the RIPK3-containing necrosome complex and protect a fraction of cells from transient, but not long-term TNF exposure. Furthermore, dysregulated NFκB dynamics often associated with disease diminish TNF-induced necroptosis. Our results suggest that TNF's dual roles in either coordinating cellular responses to inflammation, or further amplifying inflammation are determined by a dynamic NFκB-A20-RIPK3 circuit, that could be targeted to treat inflammation and cancer.

Nuclear factor kappa B (NFκB) is a transcription factor that controls inflammation and cell survival. In clinical histology, elevated NFκB activity is a hallmark of poor prognosis in inflammatory disease and cancer, and may be the result of a combination of diverse micro-environmental constituents. While previous quantitative studies of NFκB focused on its signaling dynamics in single cells, we address here how multiple stimuli may combine to control tissue level NFκB activity. We present a novel, simplified model of NFκB (SiMoN) that functions as an NFκB activity calculator. We demonstrate its utility by exploring how type I and type II interferons modulate NFκB activity in macrophages. Whereas, type I IFNs potentiate NFκB activity by inhibiting translation of IκBα and by elevating viral RNA sensor (RIG-I) expression, type II IFN amplifies NFκB activity by increasing the degradation of free IκB through transcriptional induction of proteasomal cap components (PA28). Both cross-regulatory mechanisms amplify NFκB activation in response to weaker (viral) inducers, while responses to stronger (bacterial or cytokine) inducers remain largely unaffected. Our work demonstrates how the NFκB calculator can reveal distinct mechanisms of crosstalk on NFκB activity in interferon-containing microenvironments.

Humoral immunity depends on efficient activation of B cells and their subsequent differentiation into antibody-secreting cells (ASCs). The transcription factor NFκB cRel is critical for B cell proliferation, but incorporating its known regulatory interactions into a mathematical model of the ASC differentiation circuit prevented ASC generation in simulations. Indeed, experimental ectopic cRel expression blocked ASC differentiation by inhibiting the transcription factor Blimp1, and in wild-type (WT) cells cRel was dynamically repressed during ASC differentiation by Blimp1 binding the Rel locus. Including this bi-stable circuit of mutual cRel-Blimp1 antagonism into a multi-scale model revealed that dynamic repression of cRel controls the switch from B cell proliferation to ASC generation phases and hence the respective cell population dynamics. Our studies provide a mechanistic explanation of how dysregulation of this bi-stable circuit might result in pathologic B cell population phenotypes and thus offer new avenues for diagnostic stratification and treatment.