Negative feedback contributes to the stochastic expression of the interferon-β gene in virus-triggered type I interferon signaling pathways

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary reaction functions are derived by applying the quasi-steady-state approximation (QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems. In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA, developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation. To facilitate the framework, we provide a user-friendly open-source computational package, ASSISTER, that automatically performs the present framework.

Investigating Functional Roles for Positive Feedback and Cellular Heterogeneity in the Type I Interferon Response to Viral Infection

Secretion of type I interferons (IFN) by infected cells mediates protection against many viruses, but prolonged or excessive type I IFN secretion can lead to immune pathology. A proper type I IFN response must therefore maintain a balance between protection and excessive IFN secretion. It has been widely noted that the type I IFN response is driven by positive feedback and is heterogeneous, with only a fraction of infected cells upregulating IFN expression even in clonal cell lines, but the functional roles of feedback and heterogeneity in balancing protection and excessive IFN secretion are not clear. To investigate the functional roles for feedback and heterogeneity, we constructed a mathematical model coupling IFN and viral dynamics that extends existing mathematical models by accounting for feedback and heterogeneity. We fit our model to five existing datasets, reflecting different experimental systems. Fitting across datasets allowed us to compare the IFN response across the systems and suggested different signatures of feedback and heterogeneity in the different systems. Further, through numerical experiments, we generated hypotheses of functional roles for IFN feedback and heterogeneity consistent with our mathematical model. We hypothesize an inherent tradeoff in the IFN response: a positive feedback loop prevents excessive IFN secretion, but also makes the IFN response vulnerable to viral antagonism. We hypothesize that cellular heterogeneity of the IFN response functions to protect the feedback loop from viral antagonism. Verification of our hypotheses will require further experimental studies. Our work provides a basis for analyzing the type I IFN response across systems.

Integrated modeling and analysis of intracellular and intercellular mechanisms in shaping the interferon response to viral infection

The interferons (IFNs) responses to viral infection are heterogeneous, while the underlying mechanisms for variability among cells are still not clear. In this study, we developed a hybrid model to systematically identify the sources of IFN induction heterogeneity. The experiment-integrated simulation demonstrated that the viral dose/type, the diversity in transcriptional factors activation and the intercellular paracrine signaling could strikingly shape the heterogeneity of IFN expression. We further determined that the IFNβ and IFNλ1 induced diverse dynamics of IFN-stimulated genes (ISGs) production. Collectively, our findings revealed the intracellular and intercellular mechanisms contributing to cell-to-cell variation in IFN induction, and further demonstrated the significant effects of IFN heterogeneity on antagonizing viruses.

Several Indicators of Critical Transitions for Complex Diseases Based on Stochastic Analysis

Many complex diseases (chronic disease onset, development and differentiation, self-assembly, etc.) are reminiscent of phase transitions in a dynamical system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. Understanding such nonlinear behaviors is critical to dissect the multiple genetic/environmental factors that together shape the genetic and physiological landscape underlying basic biological functions and to identify the key driving molecules. Based on stochastic differential equation (SDE) model, we theoretically derive three statistical indicators, that is, coefficient of variation (CV), transformed Pearson's correlation coefficient (TPC), and transformed probability distribution (TPD), to identify critical transitions and detect the early-warning signals of the phase transition in complex diseases. To verify the effectiveness of these early-warning indexes, we use high-throughput data for three complex diseases, including influenza caused by either H3N2 or H1N1 and acute lung injury, to extract the dynamical network biomarkers (DNBs) responsible for catastrophic transition into the disease state from predisease state. The numerical results indicate that the derived indicators provide a data-based quantitative analysis for early-warning signals for critical transitions in complex diseases or other dynamical systems.

Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation

Biochemical reaction networks (BRNs) in a cell frequently consist of reactions with disparate timescales. The stochastic simulations of such multiscale BRNs are prohibitively slow due to high computational cost for the simulations of fast reactions. One way to resolve this problem uses the fact that fast species regulated by fast reactions quickly equilibrate to their stationary distribution while slow species are unlikely to be changed. Thus, on a slow timescale, fast species can be replaced by their quasi-steady state (QSS): their stationary conditional expectation values for given slow species. As the QSS are determined solely by the state of slow species, such replacement leads to a reduced model, where fast species are eliminated. However, it is challenging to derive the QSS in the presence of nonlinear reactions. While various approximation schemes for the QSS have been developed, they often lead to considerable errors. Here, we propose two classes of multiscale BRNs which can be reduced by deriving an exact QSS rather than approximations. Specifically, if fast species constitute either a feedforward network or a complex balanced network, the reduced model based on the exact QSS can be derived. Such BRNs are frequently observed in a cell as the feedforward network is one of fundamental motifs of gene or protein regulatory networks. Furthermore, complex balanced networks also include various types of fast reversible bindings such as bindings between transcriptional factors and gene regulatory sites. The reduced models based on exact QSS, which can be calculated by the computational packages provided in this work, accurately approximate the slow scale dynamics of the original full model with much lower computational cost.

Protein synthesis inhibition and GADD34 control IFN-β heterogeneous expression in response to dsRNA

In innate immune responses, induction of type-I interferons (IFNs) prevents virus spreading while viral replication is delayed by protein synthesis inhibition. We asked how cells perform these apparently contradictory activities. Using single fibroblast monitoring by flow cytometry and mathematical modeling, we demonstrate that type-I IFN production is linked to cell's ability to enter dsRNA-activated PKR-dependent translational arrest and then overcome this inhibition by decreasing eIF2α phosphorylation through phosphatase 1c cofactor GADD34 (Ppp1r15a) expression. GADD34 expression, shown here to be dependent on the IRF3 transcription factor, is responsible for a biochemical cycle permitting pulse of IFN synthesis to occur in cells undergoing protein synthesis inhibition. Translation arrest is further demonstrated to be key for anti-viral response by acting synergistically with MAVS activation to amplify TBK1 signaling and IFN-β mRNA transcription, while GADD34-dependent protein synthesis recovery contributes to the heterogeneous expression of IFN observed in dsRNA-activated cells.