Analysis of a mathematical model of apoptosis: individual differences and malfunction in programmed cell death

Efficient parameter generation for constrained models using MCMC

Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. We propose a Markov Chain Monte Carlo (MCMC) approach for the problem of constrained model parameter generation by designing a Markov chain that efficiently explores a model's parameter space. We demonstrate the use of our proposed methodology to analyze responses of a newly constructed bistability-constrained model of protein phosphorylation to perturbations in the underlying protein network. Our results suggest that parameter generation for constrained models using MCMC provides powerful tools for modeling-aided analysis of complex natural processes.

Signaling mechanisms of SARS-CoV-2 Nucleocapsid protein in viral infection, cell death and inflammation

COVID-19 which is caused by severe acute respiratory syndrome coronavirus (SARS-CoV-2) has posed a worldwide pandemic and a major global public health threat. SARS-CoV-2 Nucleocapsid (N) protein plays a critical role in multiple steps of the viral life cycle and participates in viral replication, transcription, and assembly. The primary roles of N protein are to assemble with genomic RNA into the viral RNA-protein (vRNP) complex and to localize to the replication transcription complexes (RTCs) to enhance viral replication and transcription. N protein can also undergo liquid-liquid phase separation (LLPS) with viral genome RNA and inhibit stress granules to facilitate viral replication and assembly. Besides the function in viral life cycle, N protein can bind GSDMD to antagonize pyroptosis but promotes cell death via the Smad3-dependent G1 cell cycle arrest mechanism. In innate immune system, N protein inhibits IFN-β production and RNAi pathway for virus survival. However, it can induce expression of proinflammatory cytokines by activating NF-κB signaling and NLRP3 inflammasome, resulting in cytokine storms. In this review article, we are focusing on the signaling mechanisms of SARS-CoV-2 N protein in viral replication, cell death and inflammation.

SARS-CoV-2 Membrane Glycoprotein M Triggers Apoptosis With the Assistance of Nucleocapsid Protein N in Cells

The pandemic of COVID-19 by SARS-CoV-2 has become a global disaster. However, we still don’t know how specific SARS-CoV-2-encoded proteins contribute to viral pathogenicity. We found that SARS-CoV-2-encoded membrane glycoprotein M could induce caspase-dependent apoptosis via interacting with PDK1 and inhibiting the activation of PDK1-PKB/Akt signaling. Our investigation further revealed that SARS-CoV-2-encoded nucleocapsid protein N could specifically enhance the M-induced apoptosis via interacting with both M and PDK1, therefore strengthening M-mediated attenuation of PDK1-PKB/Akt interaction. Furthermore, when the M-N interaction was disrupted via certain rationally designed peptides, the PDK1-PKB/Akt signaling was restored, and the boosting activity of N on the M-triggered apoptosis was abolished. Overall, our findings uncovered a novel mechanism by which SARS-CoV-2-encoded M triggers apoptosis with the assistance of N, which expands our understanding of the two key proteins of SARS-CoV-2 and sheds light on the pathogenicity of this life-threatening virus.

BAX and SMAC regulate bistable properties of the apoptotic caspase system

The initiation of apoptosis is a core mechanism in cellular biology by which organisms control the removal of damaged or unnecessary cells. The irreversible activation of caspases is essential for apoptosis, and mathematical models have demonstrated that the process is tightly regulated by positive feedback and a bistable switch. BAX and SMAC are often dysregulated in diseases such as cancer or neurodegeneration and are two key regulators that interact with the caspase system generating the apoptotic switch. Here we present a mathematical model of how BAX and SMAC control the apoptotic switch. Formulated as a system of ordinary differential equations, the model summarises experimental and computational evidence from the literature and incorporates the biochemical mechanisms of how BAX and SMAC interact with the components of the caspase system. Using simulations and bifurcation analysis, we find that both BAX and SMAC regulate the time-delay and activation threshold of the apoptotic switch. Interestingly, the model predicted that BAX (not SMAC) controls the amplitude of the apoptotic switch. Cell culture experiments using siRNA mediated BAX and SMAC knockdowns validated this model prediction. We further validated the model using data of the NCI-60 cell line panel using BAX protein expression as a cell-line specific parameter and show that model simulations correlated with the cellular response to DNA damaging drugs and established a defined threshold for caspase activation that could distinguish between sensitive and resistant melanoma cells. In summary, we present an experimentally validated dynamic model that summarises our current knowledge of how BAX and SMAC regulate the bistable properties of irreversible caspase activation during apoptosis.

A dynamical framework for complex fractional killing

When chemotherapy drugs are applied to tumor cells with the same or similar genotypes, some cells are killed, while others survive. This fractional killing contributes to drug resistance in cancer. Through an incoherent feedforward loop, chemotherapy drugs not only activate p53 to induce cell death, but also promote the expression of apoptosis inhibitors which inhibit cell death. Consequently, cells in which p53 is activated early undergo apoptosis while cells in which p53 is activated late survive. The incoherent feedforward loop and the essential role of p53 activation timing makes fractional killing a complex dynamical challenge, which is hard to understand with intuition alone. To better understand this process, we have constructed a representative model by integrating the control of apoptosis with the relevant signaling pathways. After the model was trained to recapture the observed properties of fractional killing, it was analyzed with nonlinear dynamical tools. The analysis suggested a simple dynamical framework for fractional killing, which predicts that cell fate can be altered in three possible ways: alteration of bifurcation geometry, alteration of cell trajectories, or both. These predicted categories can explain existing strategies known to combat fractional killing and facilitate the design of novel strategies.

Brachyantheraoside A8, a new natural nor-oleanane triterpenoid as a kidney-type glutaminase inhibitor fromStauntonia brachyanthera

With the aim of finding a better kidney-type glutaminase (KGA) inhibitor with potential anti-cancer properties, 18 nor-oleanane triterpenoids fromStauntonia brachyanthera, including 2 new ones, were screened against KGA.

Modeling heterogeneous responsiveness of intrinsic apoptosis pathway

BACKGROUND

Apoptosis is a cell suicide mechanism that enables multicellular organisms to maintain homeostasis and to eliminate individual cells that threaten the organism's survival. Dependent on the type of stimulus, apoptosis can be propagated by extrinsic pathway or intrinsic pathway. The comprehensive understanding of the molecular mechanism of apoptotic signaling allows for development of mathematical models, aiming to elucidate dynamical and systems properties of apoptotic signaling networks. There have been extensive efforts in modeling deterministic apoptosis network accounting for average behavior of a population of cells. Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level.

RESULTS

To address the inevitable randomness in the intrinsic apoptosis mechanism, we develop a theoretical and computational modeling framework of intrinsic apoptosis pathway at single-cell level, accounting for both deterministic and stochastic behavior. Our deterministic model, adapted from the well-accepted Fussenegger model, shows that an additional positive feedback between the executioner caspase and the initiator caspase plays a fundamental role in yielding the desired property of bistability. We then examine the impact of intrinsic fluctuations of biochemical reactions, viewed as intrinsic noise, and natural variation of protein concentrations, viewed as extrinsic noise, on behavior of the intrinsic apoptosis network. Histograms of the steady-state output at varying input levels show that the intrinsic noise could elicit a wider region of bistability over that of the deterministic model. However, the system stochasticity due to intrinsic fluctuations, such as the noise of steady-state response and the randomness of response delay, shows that the intrinsic noise in general is insufficient to produce significant cell-to-cell variations at physiologically relevant level of molecular numbers. Furthermore, the extrinsic noise represented by random variations of two key apoptotic proteins, namely Cytochrome C and inhibitor of apoptosis proteins (IAP), is modeled separately or in combination with intrinsic noise. The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments. Finally, simulations illustrate that the mean abundance of fluctuating IAP protein is positively correlated with the degree of cellular stochasticity of the intrinsic apoptosis pathway.

CONCLUSIONS

Our theoretical and computational study shows that the pronounced non-genetic heterogeneity in intrinsic apoptosis responses among individual cells plausibly arises from extrinsic rather than intrinsic origin of fluctuations. In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness.