Two independent positive feedbacks and bistability in the Bcl-2 apoptotic switch

Apoptotic signaling: Beyond cell death

Apoptosis is the best described form of regulated cell death, and was, until relatively recently, considered irreversible once particular biochemical points-of-no-return were activated. In this manuscript, we examine the mechanisms cells use to escape from a self-amplifying death signaling module. We discuss the role of feedback, dynamics, propagation, and noise in apoptotic signaling. We conclude with a revised model for the role of apoptosis in animal development, homeostasis, and disease.

Hsp70-Bim incoherent feedforward loop contributes to cell-fate heterogeneity and fractional killing

BACKGROUND AND PURPOSE

Although chemotherapeutics or molecular targeted drugs often elicit profound initial responses, fractional killing capable of driving acquired resistance can persist. Identifying stress-induced negative feedback or an incoherent feedforward loop (IFFL), which may contribute to fractional killing, is urgently needed.

EXPERIMENTAL APPROACH

Mathematical modelling was used to identify how and to what extent a recently reported Hsp70-Bim protein-protein interaction (PPI) contributes to the adaptation of the Bcl-2 network. Experimental validation was made by using a specific inhibitor of Hsp70-Bim PPI, S1g-2, as chemical tool. Bifurcation analysis and stochastic simulation were used for the theoretical study of the impact of Hsp70-Bim PPI on cell-fate heterogeneity and factional killing.

KEY RESULTS

The Hsp70-Bim-AKT circuit forms an IFFL that greatly contributes to the adaptation of the Bcl-2-regulated apoptosis network, thus leading to fractional killing. This adaptive programme enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario.

CONCLUSION AND IMPLICATIONS

Hsp70-Bim IFFL serves as a molecular pathway induced by DNA damaging drugs or tyrosine kinase inhibitors that enabled fractional killing, whereby acquired resistance emerges. A synergistic strategy is unveiled for overcoming fractional killing by suppressing Hsp70-Bim PPI.

Mitochondrial outer membrane permeabilization and inner membrane permeabilization in regulating apoptosis and inflammation

Recent studies delineate an intimate crosstalk between apoptosis and inflammation. However, the dynamic mechanism linking them by mitochondrial membrane permeabilization remains elusive. Here, we construct a mathematical model consisting of four functional modules. Bifurcation analysis reveals that bistability stems from Bcl-2 family member interaction and time series shows that the time difference between Cyt c and mtDNA release is around 30 min, which are consistent with previous works. The model predicts that Bax aggregation kinetic determines cells to undergo apoptosis or inflammation, and that modulating the inhibitory effect of caspase 3 on IFN-β production allows the concurrent occurrence of apoptosis and inflammation. This work provides a theoretical framework for exploring the mechanism of mitochondrial membrane permeabilization in controlling cell fate.

Computational modeling of DLBCL predicts response to BH3-mimetics

In healthy cells, pro- and anti-apoptotic BCL2 family and BH3-only proteins are expressed in a delicate equilibrium. In contrast, this homeostasis is frequently perturbed in cancer cells due to the overexpression of anti-apoptotic BCL2 family proteins. Variability in the expression and sequestration of these proteins in Diffuse Large B cell Lymphoma (DLBCL) likely contributes to variability in response to BH3-mimetics. Successful deployment of BH3-mimetics in DLBCL requires reliable predictions of which lymphoma cells will respond. Here we show that a computational systems biology approach enables accurate prediction of the sensitivity of DLBCL cells to BH3-mimetics. We found that fractional killing of DLBCL, can be explained by cell-to-cell variability in the molecular abundances of signaling proteins. Importantly, by combining protein interaction data with a knowledge of genetic lesions in DLBCL cells, our in silico models accurately predict in vitro response to BH3-mimetics. Furthermore, through virtual DLBCL cells we predict synergistic combinations of BH3-mimetics, which we then experimentally validated. These results show that computational systems biology models of apoptotic signaling, when constrained by experimental data, can facilitate the rational assignment of efficacious targeted inhibitors in B cell malignancies, paving the way for development of more personalized approaches to treatment.

Mathematical Models of Death Signaling Networks

This review provides an overview of the progress made by computational and systems biologists in characterizing different cell death regulatory mechanisms that constitute the cell death network. We define the cell death network as a comprehensive decision-making mechanism that controls multiple death execution molecular circuits. This network involves multiple feedback and feed-forward loops and crosstalk among different cell death-regulating pathways. While substantial progress has been made in characterizing individual cell death execution pathways, the cell death decision network is poorly defined and understood. Certainly, understanding the dynamic behavior of such complex regulatory mechanisms can be only achieved by applying mathematical modeling and system-oriented approaches. Here, we provide an overview of mathematical models that have been developed to characterize different cell death mechanisms and intend to identify future research directions in this field.

An integrative systems biology approach to overcome venetoclax resistance in acute myeloid leukemia

The over-expression of the Bcl-2 protein is a common feature of many solid cancers and hematological malignancies, and it is typically associated with poor prognosis and resistance to chemotherapy. Bcl-2-specific inhibitors, such as venetoclax, have recently been approved for the treatment of chronic lymphocytic leukemia and small lymphocytic lymphoma, and they are showing promise in clinical trials as a targeted therapy for patients with relapsed or refractory acute myeloid leukemia (AML). However, successful treatment of AML with Bcl-2-specific inhibitors is often followed by the rapid development of drug resistance. An emerging paradigm for overcoming drug resistance in cancer treatment is through the targeting of mitochondrial energetics and metabolism. In AML in particular, it was recently observed that inhibition of mitochondrial translation via administration of the antibiotic tedizolid significantly affects mitochondrial bioenergetics, activating the integrated stress response (ISR) and subsequently sensitizing drug-resistant AML cells to venetoclax. Here we develop an integrative systems biology approach to acquire a deeper understanding of the molecular mechanisms behind this process, and in particular, of the specific role of the ISR in the commitment of cells to apoptosis. Our multi-scale mathematical model couples the ISR to the intrinsic apoptosis pathway in venetoclax-resistant AML cells, includes the metabolic effects of treatment, and integrates RNA, protein level, and cellular viability data. Using the mathematical model, we identify the dominant mechanisms by which ISR activation helps to overcome venetoclax resistance, and we study the temporal sequencing of combination treatment to determine the most efficient and robust combination treatment protocol.

In this work, we develop a multi-scale systems biology approach to study the mechanisms by which the integrated stress response (ISR) activation helps to overcome venetoclax resistance in acute myeloid leukemia (AML). The multi-scale model enables the integration of RNA-level, protein-level, and cellular viability and proliferation data. The model developed in this work can predict several important features of the resistant AML cell lines that are consistent with experimental data. Further, our integrative systems biology approach led to the determination of the optimal combination treatment protocol.

Effective description of bistability and irreversibility in apoptosis

Apoptosis is a mechanism of programmed cell death in which cells engage in a controlled demolition and prepare to be digested without damaging their environment. In normal conditions, apoptosis is repressed until it is irreversibly induced by an appropriate signal. In adult organisms, apoptosis is a natural way to dispose of damaged cells and its disruption or excess is associated with cancer and autoimmune diseases. Apoptosis is regulated by a complex signaling network controlled by caspases, specialized enzymes that digest essential cellular components and promote the degradation of genomic DNA. In this work, we propose an effective description of the signaling network focused on caspase-3 as a readout of cell fate. We integrate intermediate network interactions into a nonlinear feedback function acting on caspase-3 and introduce the effect of pro-apoptotic stimuli and regulatory elements as a saturating activation function. We show that activation dynamics in the theory is similar to previously reported experimental results. We compute bifurcation diagrams and obtain cell fate maps describing how stimulus intensity and feedback strength affect cell survival and death fates. These fates overlap within a bistable region that depends on total caspase concentration, regulatory elements, and feedback nonlinearity. We study a strongly nonlinear regime to obtain analytical expressions for bifurcation curves and fate map boundaries. For a broad range of parameters, strong stimuli can induce an irreversible switch to the death fate. We use the theory to explore dynamical stimulation conditions and determine how cell fate depends on stimulation temporal patterns. This analysis predicts a critical relation between transient stimuli intensity and duration to trigger irreversible apoptosis. We derive an analytical expression for this critical relation, valid for short stimuli. Our description provides distinct predictions and offers a framework to study how this signaling network processes different stimuli to make a cell fate decision.

Modeling the neuro-protection of theaflavic acid from black tea and its synergy with nimodipine via mitochondria apoptotic pathway

Ischemic stroke presents a leading cause of mortality and morbidity worldwide. Theaflavic acid (TFA) is a theaflavin isolated from black tea that exerts a potentially neuro-protective effect. However, the dynamic properties of TFA-mediated protection remain largely unknown. In the current study, we evaluated the function of TFA in the mitochondria apoptotic pathway using mathematical modeling. We found that TFA-enhanced B-cell lymphoma 2 (Bcl-2) overexpression can theoretically give rise to bistability. The bistability is highly robust against parametric stochasticity while also conferring considerable variability in survival threshold. Stochastic simulations faithfully match the TFA dose response pattern seen in experimental studies. In addition, we identified a dose- and time-dependent synergy between TFA and nimodipine, a clinically used neuro-protective drug. This synergistic effect was enhanced by bistability independent of temporal factors. Precise application of pulsed doses of TFA can also promote survival compared with sustained TFA treatment. These data collectively demonstrate that TFA treatment can give rise to bistability and that synergy between TFA and nimodipine may offer a promising strategy for developing therapeutic neuro-protection against ischemic stroke.

Joining and decomposing reaction networks

In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how cross-talk (coupling two or more pathways) or inhibiting molecular function (isolating one part of the pathway) affects systems-level behavior. However, the theory for tackling these larger systems in general has lagged behind. Here, we analyze how joining networks (e.g., cross-talk) or decomposing networks (e.g., inhibition or knock-outs) affects three properties that reaction networks may possess-identifiability (recoverability of parameter values from data), steady-state invariants (relationships among species concentrations at steady state, used in model selection), and multistationarity (capacity for multiple steady states, which correspond to multiple cell decisions). Specifically, we prove results that clarify, for a network obtained by joining two smaller networks, how properties of the smaller networks can be inferred from or can imply similar properties of the original network. Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.

Systems analysis of phosphorylation-regulated Bcl-2 interactions establishes a model to reconcile the controversy over the significance of Bcl-2 phosphorylation

BACKGROUND AND PURPOSE

The biological significance of the multi-site phosphorylation of Bcl-2 at its loop region (T69, S70 and S87) has remained controversial for decades. This is a major obstacle for understanding apoptosis and anti-tumour drug development.

EXPERIMENTAL APPROACH

We established a mathematical model into which a phosphorylation and de-phosphorylation process of Bcl-2 was integrated. Paclitaxel-treated breast cancer cells were used as experimental models. Changes in the kinetics of binding with its critical partners, induced by phosphorylation of Bcl-2 were experimentally obtained by surface plasmon resonance, using a phosphorylation-mimicking mutant EEE-Bcl-2 (T69E, S70E and S87E).

KEY RESULTS

Mathematical simulations combined with experimental validation showed that phosphorylation regulates Bcl-2 with different dynamics depending on the extent of Bcl-2 phosphorylation and the phosphorylated Bcl-2-induced changes in binding kinetics. In response to Bcl-2 homology 3 (BH3)-only protein Bmf stress, Bcl-2 phosphorylation switched from diminishing to enhancing the Bcl-2 anti-apoptotic ability with increased phosphorylation of Bcl-2, and the turning point was 50% Bcl-2 phosphorylation induced by 0.2 μM paclitaxel treatment. In contrast, Bcl-2 phosphorylation enhanced the anti-apoptotic ability of Bcl-2 towards other BH3-only proteins Bim, Bad and Puma, throughout the entire phosphorylation procedure.

CONCLUSIONS AND IMPLICATIONS

The model could accurately predict the effects of anti-tumour drugs that involve the Bcl-2 family pathway, as shown with ABT-199 or etoposide.

The optimal regulation mode of Bcl-2 apoptotic switch revealed by bistability analysis

In most cell types, apoptosis occurs by the mitochondrial outer membrane permeability (MOMP)-mediated pathway, which is controlled by Bcl-2 family proteins (often referred to as Bcl-2 apoptotic switch). These proteins, which display a range of bioactivities, can be divided into four types: effectors, inhibitors, activators and sensitizers. Although the complex interactions among Bcl-2 family members have been studied intensively, a unifying hypothesis for the mechanism they use to regulate MOMP remains elusive. The bistable behaviors are often used to explain the all-or-none decisions of apoptosis. Here, we attempt to reveal the optimal interaction mode by comparing the bistable performances of three different modes (direct activation, indirect activation, and unified mode) proposed by biologists. Using the method that combines mathematical analysis and numerical simulation, we discover that bistability can only emerge from the unified mode when proteins synthesis and degradation are considered, which is in favor of it as an optimal regulation mode of Bcl-2 apoptotic switch. The parameter sensitivity analysis for the unified mode further consolidates this view. Moreover, two-parameter bifurcation analysis suggests that the sensitizers lower the threshold of activation of Bax, but have a negative influence on the width of the bistability region. Our study may provide mechanistic insights into the heterogeneity of tumor cells and the efficiency of BH3 mimetic-mediated killing of cancer cells, and suggest that a combination treatment might be required to overcome apoptosis resistance in the Bcl-2 family targeted therapies.

Time to Decide? Dynamical Analysis Predicts Partial Tip/Stalk Patterning States Arise during Angiogenesis

Angiogenesis is a highly dynamic morphogenesis process; however, surprisingly little is known about the timing of the different molecular processes involved. Although the role of the VEGF-notch-DLL4 signaling pathway has been established as essential for tip/stalk cell competition during sprouting, the speed and dynamic properties of the underlying process at the individual cell level has not been fully elucidated. In this study, using mathematical modeling we investigate how specific, biologically meaningful, local conditions around and within an individual cell can influence their unique tip/stalk phenotype switching kinetics. To this end we constructed an ordinary differential equation model of VEGF-notch-DLL4 signaling in a system of two, coupled endothelial cells (EC). Our studies reveal that at any given point in an angiogenic vessel the time it takes a cell to decide to take on a tip or stalk phenotype may be drastically different, and this asynchrony of tip/stalk cell decisions along vessels itself acts to speed up later competitions. We unexpectedly uncover intermediate "partial" yet stable states lying between the tip and stalk cell fates, and identify that internal cellular factors, such as NAD-dependent deacetylase sirtuin-1 (Sirt1) and Lunatic fringe 1 (Lfng1), can specifically determine the length of time a cell spends in these newly identified partial tip/stalk states. Importantly, the model predicts that these partial EC states can arise during normal angiogenesis, in particular during cell rearrangement in sprouts, providing a novel two-stage mechanism for rapid adaptive behavior to the cells highly dynamic environment. Overall, this study demonstrates that different factors (both internal and external to EC) can be used to modulate the speed of tip/stalk decisions, opening up new opportunities and challenges for future biological experiments and therapeutic targeting to manipulate vascular network topology, and our basic understanding of developmental/pathological angiogenesis.

Mathematical models of the transitions between endocrine therapy responsive and resistant states in breast cancer

Endocrine therapy, targeting the oestrogen receptor pathway, is the most common treatment for oestrogen receptor-positive breast cancers. Unfortunately, these tumours frequently develop resistance to endocrine therapies. Among the strategies to treat resistant tumours are sequential treatment (in which second-line drugs are used to gain additional responses) and intermittent treatment (in which a 'drug holiday' is imposed between treatments). To gain a more rigorous understanding of the mechanisms underlying these strategies, we present a mathematical model that captures the transitions among three different, experimentally observed, oestrogen-sensitivity phenotypes in breast cancer (sensitive, hypersensitive and independent). To provide a global view of the transitions between these phenotypes, we compute the potential landscape associated with the model. We show how this oestrogen response landscape can be reshaped by population selection, which is a crucial force in promoting acquired resistance. Techniques from statistical physics are used to create a population-level state-transition model from the cellular-level model. We then illustrate how this population-level model can be used to analyse and optimize sequential and intermittent oestrogen-deprivation protocols for breast cancer. The approach used in this study is general and can also be applied to investigate treatment strategies for other types of cancer.

The indirect activation model of mitochondrial outer membrane permeabilisation (MOMP) initiation requires a trade-off between robustness in the absence of and sensitivity in the presence of stress

Mitochondrial outer membrane permeabilisation (MOMP) is a hallmark of apoptosis and is controlled by antagonising members of the BCL 2 protein family. However, whether the effector proteins for MOMP, BAX and BAK, require a separate activation step (direct activation model) or if the sole inhibition of otherwise active effectors by anti-apoptotic BCL 2 proteins suffices (indirect activation model) is controversial. To address this question, we recently identified that, in most cells, effector proteins were more abundant than their inhibitors. We now employ systems modelling to elucidate fundamental consequences of this imbalance for the indirect activation model by integrating its key features into the recently validated implementation of the direct activation model. First, by modelling constitutively active BAK, several cell lines were predicted to be unstable against MOMP even in the absence of stress. This instability could be rectified by assuming BAK pores to be subject to degradation, which however demanded BAK to underlie a high and biologically unreasonable protein turnover. Stability against MOMP in the absence of stress was similarly reconstituted by assuming BAK oligomerisation to be weak, but predicted some cells to be MOMP resistant even under high stress. Assuming also BAX to be constitutively active required highly effective BAX re-translocation to the cytosol along with weak BAX oligomerisation, which again rendered some cells insensitive to induce MOMP in the presence of stress. Our results suggest that an activation step of the two effectors is required to allow stability against MOMP in the absence of stress and execution of MOMP under stress.

The mathematical model of the Bcl-2 family mediated MOMP regulation can perform a non-trivial pattern recognition

Interactions between individual members of the B-cell lymphoma 2 (Bcl-2) family of proteins form a regulatory network governing mitochondrial outer membrane permeabilization (MOMP). Bcl-2 family initiated MOMP causes release of the inter-membrane pro-apoptotic proteins to cytosol and creates a cytosolic environment suitable for the executionary phase of apoptosis. We designed the mathematical model of this regulatory network where the synthesis rates of the Bcl-2 family members served as the independent inputs. Using computational simulations, we have then analyzed the response of the model to up-/downregulation of the Bcl-2 proteins. Under several assumptions, and using estimated reaction parameters, a non-linear stimulus-response emerged, whose characteristics are associated with bistability and switch-like behavior. Interestingly, using the principal component analysis (PCA) we have shown that the given model of the Bcl-2 family interactions classifies the random combinations of inputs into two distinct classes, and responds to these by one of the two qualitatively distinct outputs. As we showed, the emergence of this behavior requires specific organization of the interactions between particular Bcl-2 proteins.

Systems biology and the integration of mechanistic explanation and mathematical explanation

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models-which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation (as the analysis of a whole in terms of its structural parts and their qualitative interactions) have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena (rather than the explanation of quantitative details), where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism's ability to respond to perturbations (beyond its actual operation). I offer general conclusions for philosophical accounts of explanation.

Bayesian parameter inference by Markov chain Monte Carlo with hybrid fitness measures: theory and test in apoptosis signal transduction network

When exact values of model parameters in systems biology are not available from experiments, they need to be inferred so that the resulting simulation reproduces the experimentally known phenomena. For the purpose, Bayesian statistics with Markov chain Monte Carlo (MCMC) is a useful method. Biological experiments are often performed with cell population, and the results are represented by histograms. On another front, experiments sometimes indicate the existence of a specific bifurcation pattern. In this study, to deal with both type of such experimental results and information for parameter inference, we introduced functions to evaluate fitness to both type of experimental results, named quantitative and qualitative fitness measures respectively. We formulated Bayesian formula for those hybrid fitness measures (HFM), and implemented it to MCMC (MCMC-HFM). We tested MCMC-HFM first for a kinetic toy model with a positive feedback. Inferring kinetic parameters mainly related to the positive feedback, we found that MCMC-HFM reliably infer them with both qualitative and quantitative fitness measures. Then, we applied the MCMC-HFM to an apoptosis signal transduction network previously proposed. For kinetic parameters related to implicit positive feedbacks, which are important for bistability and irreversibility of the output, the MCMC-HFM reliably inferred these kinetic parameters. In particular, some kinetic parameters that have the experimental estimates were inferred without these data and the results were consistent with the experiments. Moreover, for some parameters, the mixed use of quantitative and qualitative fitness measures narrowed down the acceptable range of parameters. Taken together, our approach could reliably infer the kinetic parameters of the target systems.

Programming biological models in Python using PySB

PySB is a framework for creating biological models as Python programs using a high-level, action-oriented vocabulary that promotes transparency, extensibility and reusability. PySB interoperates with many existing modeling tools and supports distributed model development.

PySB models are programs and leverage existing programming tools for documentation, testing, and collaborative development.

Reusable functions can encode common low-level biochemical processes as well as high-level modules, making models transparent and concise.

Modeling workflow is accelerated through close integration with Python numerical tools and interoperability with existing modeling software.

We demonstrate the use of PySB to encode 15 alternative hypotheses for the mitochondrial regulation of apoptosis, including a new ‘Embedded Together' model based on recent biochemical findings.

Mathematical equations are fundamental to modeling biological networks, but as networks get large and revisions frequent, it becomes difficult to manage equations directly or to combine previously developed models. Multiple simultaneous efforts to create graphical standards, rule-based languages, and integrated software workbenches aim to simplify biological modeling but none fully meets the need for transparent, extensible, and reusable models. In this paper we describe PySB, an approach in which models are not only created using programs, they are programs. PySB draws on programmatic modeling concepts from little b and ProMot, the rule-based languages BioNetGen and Kappa and the growing library of Python numerical tools. Central to PySB is a library of macros encoding familiar biochemical actions such as binding, catalysis, and polymerization, making it possible to use a high-level, action-oriented vocabulary to construct detailed models. As Python programs, PySB models leverage tools and practices from the open-source software community, substantially advancing our ability to distribute and manage the work of testing biochemical hypotheses. We illustrate these ideas using new and previously published models of apoptosis.

Boolean network-based model of the Bcl-2 family mediated MOMP regulation

Background

Mitochondrial outer membrane permeabilization (MOMP) is one of the most important points in the majority of apoptotic signaling cascades and it is controlled by a network of interactions between the members of the Bcl-2 family.

Methods

To understand the role of individual members of this family within the MOMP regulation, we have constructed a Boolean network-based model of interactions between the Bcl-2 proteins.

Results

Computational simulations have revealed the existence of trapping states which, independently from the incoming stimuli, block the occurrence of MOMP. Our results emphasize the role of the antiapoptotic protein Mcl-1 in the majority of these configurations. We demonstrate here the importance of the Bid and Bim for activation of effectors Bax and Bak, and the irreversibility of this activation. The model further points to the antiapoptotic protein Bcl-w as a key factor preventing Bax activation.

Conclusions

In spite of relative simplicity, the Boolean network-based model provides useful insight into main functioning logic of the Bcl-2 switch, consistent with experimental findings.

Data-driven modeling of SRC control on the mitochondrial pathway of apoptosis: implication for anticancer therapy optimization

Src tyrosine kinases are deregulated in numerous cancers and may favor tumorigenesis and tumor progression. We previously described that Src activation in NIH-3T3 mouse fibroblasts promoted cell resistance to apoptosis. Indeed, Src was found to accelerate the degradation of the pro-apoptotic BH3-only protein Bik and compromised Bax activation as well as subsequent mitochondrial outer membrane permeabilization. The present study undertook a systems biomedicine approach to design optimal anticancer therapeutic strategies using Src-transformed and parental fibroblasts as a biological model. First, a mathematical model of Bik kinetics was designed and fitted to biological data. It guided further experimental investigation that showed that Bik total amount remained constant during staurosporine exposure, and suggested that Bik protein might undergo activation to induce apoptosis. Then, a mathematical model of the mitochondrial pathway of apoptosis was designed and fitted to experimental results. It showed that Src inhibitors could circumvent resistance to apoptosis in Src-transformed cells but gave no specific advantage to parental cells. In addition, it predicted that inhibitors of Bcl-2 antiapoptotic proteins such as ABT-737 should not be used in this biological system in which apoptosis resistance relied on the deficiency of an apoptosis accelerator but not on the overexpression of an apoptosis inhibitor, which was experimentally verified. Finally, we designed theoretically optimal therapeutic strategies using the data-calibrated model. All of them relied on the observed Bax overexpression in Src-transformed cells compared to parental fibroblasts. Indeed, they all involved Bax downregulation such that Bax levels would still be high enough to induce apoptosis in Src-transformed cells but not in parental ones. Efficacy of this counterintuitive therapeutic strategy was further experimentally validated. Thus, the use of Bax inhibitors might be an unexpected way to specifically target cancer cells with deregulated Src tyrosine kinase activity.

A cellular stress-directed bistable switch controls the crosstalk between autophagy and apoptosis

Decision-making between life and death is one of the most important tasks of cells to maintain their genetic integrity. While the surviving mechanism is driven by Beclin1-dependent autophagy, the suicide processes are controlled by caspases-mediated apoptosis. Interestingly, both these processes share regulators such as Bcl2 and influence each other through feedback loops. The physiological relevance of the crosstalk between autophagy and apoptosis is still unclear. To gain system level insights, we have developed a mathematical model of the autophagy-apoptosis crosstalk. Our analysis reveals that a combination of Bcl2-dependent regulation and feedback loops between Beclin1 and caspases robustly enforces a sequential activation of cellular responses depending upon the intensity and duration of stress levels. The amplifying loops for caspases activation involving Beclin1-dependent inhibition of caspases and cleavage of Beclin1 by caspases (Beclin1 ┤ caspases ┤ Beclin1; caspases → cleaved Beclin1 → caspases) not only make the system bistable but also help to switch off autophagy at high stress levels. The presence of an additional positive feedback loop between Bcl2 and caspases helps to maintain the caspases activation by making the switch irreversible. Our results provide a framework for further experiments and modelling.

Dynamical behaviors of Rb-E2F pathway including negative feedback loops involving miR449

MiRNAs, which are a family of small non-coding RNAs, regulate a broad array of physiological and developmental processes. However, their regulatory roles have remained largely mysterious. E2F is a positive regulator of cell cycle progression and also a potent inducer of apoptosis. Positive feedback loops in the regulation of Rb-E2F pathway are predicted and shown experimentally. Recently, it has been discovered that E2F induce a cluster of miRNAs called miR449. In turn, E2F is inhibited by miR449 through regulating different transcripts, thus forming negative feedback loops in the interaction network. Here, based on the integration of experimental evidence and quantitative data, we studied Rb-E2F pathway coupling the positive feedback loops and negative feedback loops mediated by miR449. Therefore, a mathematical model is constructed based in part on the model proposed in Yao-Lee et al. (2008) and nonlinear dynamical behaviors including the stability and bifurcations of the model are discussed. A comparison is given to reveal the implication of the fundamental differences of Rb-E2F pathway between regulation and deregulation of miR449. Coherent with the experiments it predicts that miR449 plays a critical role in regulating the cell cycle progression and provides a twofold safety mechanism to avoid excessive E2F-induced proliferation by cell cycle arrest and apoptosis. Moreover, numerical simulation and bifurcation analysis shows that the mechanisms of the negative regulation of miR449 to three different transcripts are quite distinctive which needs to be verified experimentally. This study may help us to analyze the whole cell cycle process mediated by other miRNAs more easily. A better knowledge of the dynamical behaviors of miRNAs mediated networks is also of interest for bio-engineering and artificial control.

Plasmin triggers a switch-like decrease in thrombospondin-dependent activation of TGF-β1

Transforming growth factor-β1 (TGF-β1) is a potent regulator of extracellular matrix production, wound healing, differentiation, and immune response, and is implicated in the progression of fibrotic diseases and cancer. Extracellular activation of TGF-β1 from its latent form provides spatiotemporal control over TGF-β1 signaling, but the current understanding of TGF-β1 activation does not emphasize cross talk between activators. Plasmin (PLS) and thrombospondin-1 (TSP1) have been studied individually as activators of TGF-β1, and in this work we used a systems-level approach with mathematical modeling and in vitro experiments to study the interplay between PLS and TSP1 in TGF-β1 activation. Simulations and steady-state analysis predicted a switch-like bistable transition between two levels of active TGF-β1, with an inverse correlation between PLS and TSP1. In particular, the model predicted that increasing PLS breaks a TSP1-TGF-β1 positive feedback loop and causes an unexpected net decrease in TGF-β1 activation. To test these predictions in vitro, we treated rat hepatocytes and hepatic stellate cells with PLS, which caused proteolytic cleavage of TSP1 and decreased activation of TGF-β1. The TGF-β1 activation levels showed a cooperative dose response, and a test of hysteresis in the cocultured cells validated that TGF-β1 activation is bistable. We conclude that switch-like behavior arises from natural competition between two distinct modes of TGF-β1 activation: a TSP1-mediated mode of high activation and a PLS-mediated mode of low activation. This switch suggests an explanation for the unexpected effects of the plasminogen activation system on TGF-β1 in fibrotic diseases in vivo, as well as novel prognostic and therapeutic approaches for diseases with TGF-β dysregulation.

The molecular mechanism of apoptosis upon caspase-8 activation: quantitative experimental validation of a mathematical model

Caspase-8 (CASP8) is a cysteine protease that plays a pivotal role in the extrinsic apoptotic signaling pathway via death receptors. The kinetics, dynamics, and selectivity with which the pathway transmits apoptotic signals to downstream molecules upon CASP8 activation are not fully understood. We have developed a system for using high-sensitivity FRET-based biosensors to monitor the protease activity of CASP8 and its downstream effector, caspase-3, in living single cells. Using this system, we systematically investigated the caspase cascade by regulating the magnitude of extrinsic signals received by the cell. Furthermore, we determined the molar concentration of five caspases and Bid required for hierarchical transmission of apoptotic signals in a HeLa cell. Based on these quantitative experimental data, we validated a mathematical model suitable for estimation of the kinetics and dynamics of caspases, which predicts the minimal concentration of CASP8 required to act as an initiator. Consequently, we found that less than 1% of the total CASP8 proteins are sufficient to set the apoptotic program in motion if activated. Taken together, our findings demonstrate the precise cascade of CASP8-mediated apoptotic signals through the extrinsic pathway.

Rigor of cell fate decision by variable p53 pulses and roles of cooperative gene expression by p53

Upon DNA damage, the cell fate decision between survival and apoptosis is largely regulated by p53-related networks. Recent experiments found a series of discrete p53 pulses in individual cells, which led to the hypothesis that the cell fate decision upon DNA damage is controlled by counting the number of p53 pulses. Under this hypothesis, Sun et al. (2009) modeled the Bax activation switch in the apoptosis signal transduction pathway that can rigorously "count" the number of uniform p53 pulses. Based on experimental evidence, here we use variable p53 pulses with Sun et al.'s model to investigate how the variability in p53 pulses affects the rigor of the cell fate decision by the pulse number. Our calculations showed that the experimentally anticipated variability in the pulse sizes reduces the rigor of the cell fate decision. In addition, we tested the roles of the cooperativity in PUMA expression by p53, finding that lower cooperativity is plausible for more rigorous cell fate decision. This is because the variability in the p53 pulse height is more amplified in PUMA expressions with more cooperative cases.

Steady states and dynamics of urokinase-mediated plasmin activation in silico and in vitro

Plasmin (PLS) and urokinase-type plasminogen activator (UPA) are ubiquitous proteases that regulate the extracellular environment. Although they are secreted in inactive forms, they can activate each other through proteolytic cleavage. This mutual interplay creates the potential for complex dynamics, which we investigated using mathematical modeling and in vitro experiments. We constructed ordinary differential equations to model the conversion of precursor plasminogen into active PLS, and precursor urokinase (scUPA) into active urokinase (tcUPA). Although neither PLS nor UPA exhibits allosteric cooperativity, modeling showed that cooperativity occurred at the system level because of substrate competition. Computational simulations and bifurcation analysis predicted that the system would be bistable over a range of parameters for cooperativity and positive feedback. Cell-free experiments with recombinant proteins tested key predictions of the model. PLS activation in response to scUPA stimulus was found to be cooperative in vitro. Finally, bistability was demonstrated in vitro by the presence of two significantly different steady-state levels of PLS activation for the same levels of stimulus. We conclude that ultrasensitive, bistable activation of UPA-PLS is possible in the presence of substrate competition. An ultrasensitive threshold for activation of PLS and UPA would have ramifications for normal and disease processes, including angiogenesis, metastasis, wound healing, and fibrosis.

Computational modeling of signaling pathways mediating cell cycle checkpoint control and apoptotic responses to ionizing radiation-induced DNA damage

The shape of dose response of ionizing radiation (IR) induced cancer at low dose region, either linear non-threshold or J-shaped, has been a debate for a long time. This dose response relationship can be influenced by built-in capabilities of cells that minimize the fixation of IR-mediated DNA damage as pro-carcinogenic mutations. Key capabilities include sensing of damage, activation of cell cycle checkpoint arrests that provide time needed for repair of the damage as well as apoptosis. Here we describe computational modeling of the signaling pathways that link sensing of DNA damage and checkpoint arrest activation/apoptosis to investigate how these molecular-level interactions influence the dose response relationship for IR induced cancer. The model provides qualitatively accurate descriptions of the IR-mediated activation of cell cycle checkpoints and the apoptotic pathway, and of time-course activities and dose response of relevant regulatory proteins (e.g. p53 and p21). Linking to a two-stage clonal growth cancer model, the model described here successfully captured a monotonically increasing to a J-shaped dose response curve and identified one potential mechanism leading to the J-shape: the cell cycle checkpoint arrest time saturates with the increase of the dose.

Dynamic modelling of oestrogen signalling and cell fate in breast cancer cells

Cancers of the breast and other tissues arise from aberrant decision-making by cells regarding their survival or death, proliferation or quiescence, damage repair or bypass. These decisions are made by molecular signalling networks that process information from outside and from within the breast cancer cell and initiate responses that determine the cell's survival and reproduction. Because the molecular logic of these circuits is difficult to comprehend by intuitive reasoning alone, we present some preliminary mathematical models of the basic decision circuits in breast cancer cells that may aid our understanding of their susceptibility or resistance to endocrine therapy.

Bistability in apoptosis by receptor clustering

Apoptosis is a highly regulated cell death mechanism involved in many physiological processes. A key component of extrinsically activated apoptosis is the death receptor Fas which, on binding to its cognate ligand FasL, oligomerize to form the death-inducing signaling complex. Motivated by recent experimental data, we propose a mathematical model of death ligand-receptor dynamics where FasL acts as a clustering agent for Fas, which form locally stable signaling platforms through proximity-induced receptor interactions. Significantly, the model exhibits hysteresis, providing an upstream mechanism for bistability and robustness. At low receptor concentrations, the bistability is contingent on the trimerism of FasL. Moreover, irreversible bistability, representing a committed cell death decision, emerges at high concentrations which may be achieved through receptor pre-association or localization onto membrane lipid rafts. Thus, our model provides a novel theory for these observed biological phenomena within the unified context of bistability. Importantly, as Fas interactions initiate the extrinsic apoptotic pathway, our model also suggests a mechanism by which cells may function as bistable life/death switches independently of any such dynamics in their downstream components. Our results highlight the role of death receptors in deciding cell fate and add to the signal processing capabilities attributed to receptor clustering.

Many prominent diseases, most notably cancer, arise from an imbalance between the rates of cell growth and death in the body. This is often due to mutations that disrupt a cell death program called apoptosis. Here, we focus on the extrinsic pathway of apoptotic activation which is initiated upon detection of an external death signal, encoded by a death ligand, by its corresponding death receptor. Through the tools of mathematical analysis, we find that a novel model of death ligand-receptor interactions based on recent experimental data possesses the capacity for bistability. Consequently, the model supports threshold-like switching between unambiguous life and death states; intuitively, the defining characteristic of an effective cell death mechanism. We thus highlight the role of death receptors, the first component along the apoptotic pathway, in deciding cell fate. Furthermore, the model suggests an explanation for various biologically observed phenomena, including the trimeric character of the death ligand and the tendency for death receptors to colocalize, in terms of bistability. Our work hence informs the molecular basis of the apoptotic point-of-no-return, and may influence future drug therapies against cancer and other diseases.

The role of coupled positive feedback in the expression of the SPI1 type three secretion system in Salmonella

Salmonella enterica serovar Typhimurium is a common food-borne pathogen that induces inflammatory diarrhea and invades intestinal epithelial cells using a type three secretion system (T3SS) encoded within Salmonella pathogenicity island 1 (SPI1). The genes encoding the SPI1 T3SS are tightly regulated by a network of interacting transcriptional regulators involving three coupled positive feedback loops. While the core architecture of the SPI1 gene circuit has been determined, the relative roles of these interacting regulators and associated feedback loops are still unknown. To determine the function of this circuit, we measured gene expression dynamics at both population and single-cell resolution in a number of SPI1 regulatory mutants. Using these data, we constructed a mathematical model of the SPI1 gene circuit. Analysis of the model predicted that the circuit serves two functions. The first is to place a threshold on SPI1 activation, ensuring that the genes encoding the T3SS are expressed only in response to the appropriate combination of environmental and cellular cues. The second is to amplify SPI1 gene expression. To experimentally test these predictions, we rewired the SPI1 genetic circuit by changing its regulatory architecture. This enabled us to directly test our predictions regarding the function of the circuit by varying the strength and dynamics of the activating signal. Collectively, our experimental and computational results enable us to deconstruct this complex circuit and determine the role of its individual components in regulating SPI1 gene expression dynamics.

Evaluating bistability of Bax activation switch

Mitochondrial apoptotic pathway is precisely controlled by BCL-2 family. Complex interactions of BCL-2 family proteins constitute a bistable switch of which detailed experimental and theoretical delineation remains elusive. In this paper, combined approaches were used to explore the bistability of Bax activation switch. We found that Bax activation is indeed in an 'all-or-none' manner. The 'variable-delay, snap-action' nature for Bax activation is further explored theoretically. We suggest that bistability is largely attributed to topological structure and shows considerable robustness. Therefore, our study characterizes dynamics and sensitivities in intrinsic apoptotic pathway.

Building biological memory by linking positive feedback loops

A common topology found in many bistable genetic systems is two interacting positive feedback loops. Here we explore how this relatively simple topology can allow bistability over a large range of cellular conditions. On the basis of theoretical arguments, we predict that nonlinear interactions between two positive feedback loops can produce an ultrasensitive response that increases the range of cellular conditions at which bistability is observed. This prediction was experimentally tested by constructing a synthetic genetic circuit in Escherichia coli containing two well-characterized positive feedback loops, linked in a coherent fashion. The concerted action of both positive feedback loops resulted in bistable behavior over a broad range of inducer concentrations; when either of the feedback loops was removed, the range of inducer concentrations at which the system exhibited bistability was decreased by an order of magnitude. Furthermore, bistability of the system could be tuned by altering growth conditions that regulate the contribution of one of the feedback loops. Our theoretical and experimental work shows how linked positive feedback loops may produce the robust bistable responses required in cellular networks that regulate development, the cell cycle, and many other cellular responses.

Computational analysis of dynamical responses to the intrinsic pathway of programmed cell death

Multicellular organisms shape development and remove aberrant cells by programmed cell death ("apoptosis"). Because defective cell death (too little or too much) is implicated in various diseases (like cancer and autoimmunity), understanding how apoptosis is regulated is an important goal of molecular cell biologists. To this end, we propose a mathematical model of the intrinsic apoptotic pathway that captures three key dynamical features: a signal threshold to elicit cell death, irreversible commitment to the response, and a time delay that is inversely proportional to signal strength. Subdividing the intrinsic pathway into three modules (initiator, amplifier, executioner), we use computer simulation and bifurcation theory to attribute signal threshold and time delay to positive feedback in the initiator module and irreversible commitment to positive feedback in the executioner module. The model accounts for the behavior of mutants deficient in various genes and is used to design experiments that would test its basic assumptions. Finally, we apply the model to study p53-induced cellular responses to DNA damage. Cells first undergo cell cycle arrest and DNA repair, and then apoptosis if the damage is beyond repair. The model ascribes this cell-fate transition to a transformation of p53 from "helper" to "killer" forms.

Modeling the role of p53 pulses in DNA damage- induced cell death decision

Background

The tumor suppressor p53 plays pivotal roles in tumorigenesis suppression. Although oscillations of p53 have been extensively studied, the mechanism of p53 pulses and their physiological roles in DNA damage response remain unclear.

Results

To address these questions we presented an integrated model in which Ataxia-Telangiectasia Mutated (ATM) activation and p53 oscillation were incorporated with downstream apoptotic events, particularly the interplays between Bcl-2 family proteins. We first reproduced digital oscillation of p53 as the response of normal cells to DNA damage. Subsequent modeling in mutant cells showed that high basal DNA damage is a plausible cause for sustained p53 pulses observed in tumor cells. Further computational analyses indicated that p53-dependent PUMA accumulation and the PUMA-controlled Bax activation switch might play pivotal roles to count p53 pulses and thus decide the cell fate.

Conclusion

The high levels of basal DNA damage are responsible for generating sustained pulses of p53 in the tumor cells. Meanwhile, the Bax activation switch can count p53 pulses through PUMA accumulation and transfer it into death signal. Our modeling provides a plausible mechanism about how cells generate and orchestrate p53 pulses to tip the balance between survival and death.

Mathematical model of a network of interaction between p53 and Bcl-2 during genotoxic-induced apoptosis

Ionizing radiation like UV light, gamma and X rays, can produce genotoxic damage in fibroblast cells. This injury can be reverted by activation of specific nuclear molecules. However, intense genotoxic damage induces the activation of the p53 dependent apoptotic pathway. Activated nuclear p53 has the role of a transcription factor that switches on the transcription of the Puma protein, which once released into the cytoplasm leads to the activation of a network of chemical processes that produces cell death. This network is built up with the chemical interaction between pro-apoptotic p53, Puma and Bax proteins and the anti-apoptotic Bcl2 and Bcl-x(L) proteins. In this work we present a mathematical model of this modular network under different regimes of Puma release into the cytoplasm. In this model we use a set of coupled nonlinear differential equations, which is solved by numerical methods, to determine the nature of the equilibrium points of the dynamical system. With this information we construct the phase portrait associated with Puma induced apoptosis and we found that once the genotoxic injury is produced, Bax levels continuously increase. In this work we propose that a possible mechanism for the control of apoptosis is the Bax level in the cytoplasm, i.e., Bax is continuously released into the cytoplasm, even in absence of Puma, according to the kinetic properties of the set of chemical interactions in which the Bcl2/Bax complex takes part. If the damage is reverted before the Bax level reaches a threshold value the apoptotic process is stopped, otherwise the process goes on until cell death.

Construction and analysis of a modular model of caspase activation in apoptosis

Background

A key physiological mechanism employed by multicellular organisms is apoptosis, or programmed cell death. Apoptosis is triggered by the activation of caspases in response to both extracellular (extrinsic) and intracellular (intrinsic) signals. The extrinsic and intrinsic pathways are characterized by the formation of the death-inducing signaling complex (DISC) and the apoptosome, respectively; both the DISC and the apoptosome are oligomers with complex formation dynamics. Additionally, the extrinsic and intrinsic pathways are coupled through the mitochondrial apoptosis-induced channel via the Bcl-2 family of proteins.

Results

A model of caspase activation is constructed and analyzed. The apoptosis signaling network is simplified through modularization methodologies and equilibrium abstractions for three functional modules. The mathematical model is composed of a system of ordinary differential equations which is numerically solved. Multiple linear regression analysis investigates the role of each module and reduced models are constructed to identify key contributions of the extrinsic and intrinsic pathways in triggering apoptosis for different cell lines.

Conclusion

Through linear regression techniques, we identified the feedbacks, dissociation of complexes, and negative regulators as the key components in apoptosis. The analysis and reduced models for our model formulation reveal that the chosen cell lines predominately exhibit strong extrinsic caspase, typical of type I cell, behavior. Furthermore, under the simplified model framework, the selected cells lines exhibit different modes by which caspase activation may occur. Finally the proposed modularized model of apoptosis may generalize behavior for additional cells and tissues, specifically identifying and predicting components responsible for the transition from type I to type II cell behavior.

Modeling a snap-action, variable-delay switch controlling extrinsic cell death

When exposed to tumor necrosis factor (TNF) or TNF-related apoptosis-inducing ligand (TRAIL), a closely related death ligand and investigational therapeutic, cells enter a protracted period of variable duration in which only upstream initiator caspases are active. A subsequent and sudden transition marks activation of the downstream effector caspases that rapidly dismantle the cell. Thus, extrinsic apoptosis is controlled by an unusual variable-delay, snap-action switch that enforces an unambiguous choice between life and death. To understand how the extrinsic apoptosis switch functions in quantitative terms, we constructed a mathematical model based on a mass-action representation of known reaction pathways. The model was trained against experimental data obtained by live-cell imaging, flow cytometry, and immunoblotting of cells perturbed by protein depletion and overexpression. The trained model accurately reproduces the behavior of normal and perturbed cells exposed to TRAIL, making it possible to study switching mechanisms in detail. Model analysis shows, and experiments confirm, that the duration of the delay prior to effector caspase activation is determined by initiator caspase-8 activity and the rates of other reactions lying immediately downstream of the TRAIL receptor. Sudden activation of effector caspases is achieved downstream by reactions involved in permeabilization of the mitochondrial membrane and relocalization of proteins such as Smac. We find that the pattern of interactions among Bcl-2 family members, the partitioning of Smac from its binding partner XIAP, and the mechanics of pore assembly are all critical for snap-action control.