A Minimal Model of Signaling Network Elucidates Cell-to-Cell Stochastic Variability in Apoptosis

Background

Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The structure of this minimal network is derived based on some simple assumptions on its differential response to external stimuli.

Methodology

We employ stochastic differential equations and probability distributions obtained from stochastic simulations to characterize differential signaling response in our minimal network model. Gillespie''s stochastic simulation algorithm (SSA) is used in this study.

Conclusions/Significance

We show that the proposed minimal signaling network displays two distinct types of response as the strength of the stimulus is decreased. The signaling network has a deterministic part that undergoes rapid activation by a strong stimulus in which case cell-to-cell fluctuations can be ignored. As the strength of the stimulus decreases, the stochastic part of the network begins dominating the signaling response where slow activation is observed with characteristic large cell-to-cell stochastic variability. Interestingly, this proposed stochastic signaling network can capture some of the essential signaling behaviors of a complex apoptotic cell death signaling network that has been studied through experiments and large-scale computer simulations. Thus we claim that the proposed signaling network is an appropriate minimal model of apoptosis signaling. Elucidating the fundamental design principles of complex cellular signaling pathways such as apoptosis signaling remains a challenging task. We demonstrate how our proposed minimal model can help elucidate the effect of a specific apoptotic inhibitor Bcl-2 on apoptotic signaling in a cell-type independent manner. We also discuss the implications of our study in elucidating the adaptive strategy of cell death signaling pathways.     

Estimating the Stochastic Bifurcation Structure of Cellular Networks

High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. Since cellular networks are inherently noisy, we generalize the traditional bifurcation diagram of deterministic systems theory to stochastic dynamical systems. We demonstrate how statistical methods for density estimation, in particular, mixture density and conditional mixture density estimators, can be employed to establish empirical bifurcation diagrams describing the bistable genetic switch network controlling galactose utilization in yeast Saccharomyces cerevisiae. These approaches allow us to make novel qualitative and quantitative observations about the switching behavior of the galactose network, and provide a framework that might be useful to extract information needed for the development of quantitative network models.     

Monte Carlo simulation of cell death signaling predicts large cell-to-cell stochastic fluctuations through the type 2 pathway of apoptosis

Apoptosis, or genetically programmed cell death, is a crucial cellular process that maintains the balance between life and death in cells. The precise molecular mechanism of apoptosis signaling and the manner in which type 1 and type 2 pathways of the apoptosis signaling network are differentially activated under distinct apoptotic stimuli is poorly understood. Based on Monte Carlo stochastic simulations, we show that the type 1 pathway becomes activated under strong apoptotic stimuli, whereas the type 2 mitochondrial pathway dominates apoptotic signaling in response to a weak death signal. Our results also show signaling in the type 2 pathway is stochastic; the population average over many cells does not capture the cell-to-cell fluctuations in the time course (~1–10 h) of downstream caspase-3 activation. On the contrary, the probability distribution of caspase-3 activation for the mitochondrial pathway shows a distinct bimodal behavior that can be used to characterize the stochastic signaling in type 2 apoptosis and other similar complex signaling processes. Interestingly, such stochastic fluctuations in apoptosis signaling occur even in the presence of large numbers of signaling molecules.     

Bcl-2 inhibits apoptosis by increasing the time-to-death and intrinsic cell-to-cell variations in the mitochondrial pathway of cell death

BH3 mimetics have been proposed as new anticancer therapeutics. They target anti-apoptotic Bcl-2 proteins, up-regulation of which has been implicated in the resistance of many cancer cells, particularly leukemia and lymphoma cells, to apoptosis. Using probabilistic computational modeling of the mitochondrial pathway of apoptosis, verified by single-cell experimental observations, we develop a model of Bcl-2 inhibition of apoptosis. Our results clarify how Bcl-2 imparts its anti-apoptotic role by increasing the time-to-death and cell-to-cell variability. We also show that although the commitment to death is highly impacted by differences in protein levels at the time of stimulation, inherent stochastic fluctuations in apoptotic signaling are sufficient to induce cell-to-cell variability and to allow single cells to escape death. This study suggests that intrinsic cell-to-cell stochastic variability in apoptotic signaling is sufficient to cause fractional killing of cancer cells after exposure to BH3 mimetics. This is an unanticipated facet of cancer chemoresistance.     

Regulation of ionizing radiation-induced apoptosis by mitochondrial NADP+-dependent isocitrate dehydrogenase

Ionizing radiation induces the production of reactive oxygen species, which play an important causative role in apoptotic cell death. By supplying NADPH for antioxidant systems, we recently demonstrated that the control of mitochondrial redox balance and the cellular defense against oxidative damage are some of the primary functions of mitochondrial NADP(+)-dependent isocitrate dehydrogenase (IDPm). In this study, we demonstrate that modulation of IDPm activity in U937 cells regulates ionizing radiation-induced apoptosis. When we examined the regulatory role of IDPm against ionizing radiation-induced apoptosis in U937 cells transfected with the cDNA for mouse IDPm in sense and antisense orientations, a clear inverse relationship was observed between the amount of IDPm expressed in target cells and their susceptibility to apoptosis. Upon exposure to 2 gray gamma-irradiation, there was a distinct difference between the IDPm transfectant cells in regard to the morphological evidence of apoptosis, DNA fragmentation, cellular redox status, oxidative damage to cells, mitochondrial function, and the modulation of apoptotic marker proteins. In addition, transfection of HeLa cells with an IDPm small interfering RNA decreased the activity of IDPm, enhancing the susceptibility of radiation-induced apoptosis. Taken together, these results indicate that IDPm may play an important role in regulating the apoptosis induced by ionizing radiation, and the effect of IDPm small interfering RNA on HeLa cells offers the possibility of developing a modifier of radiation therapy.     

Robustness analysis identifies the plausible model of the Bcl-2 apoptotic switch

In this paper two competing models of the B-cell lymphoma 2 (Bcl-2) apoptotic switch were contrasted by mathematical modeling and robustness analysis. Since switch-like behaviors are required for models that attempt to explain the all-or-none decisions of apoptosis, ultrasensitivity was employed as a criterion for comparison. Our results successfully exhibit that the direct activation model operates more reliably to achieve a robust switch in cellular conditions. Moreover, by investigating the robustness of other important features of the Bcl-2 apoptotic switch (including low Bax basal activation, inhibitory role of anti-apoptotic proteins and insensitivity to small perturbations) the direct activation model was further supported. In all, we identified the direct activation model as a more plausible explanation for the Bcl-2 apoptotic switch.     

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

Background

The complex interplay between B-cell lymphoma 2 (Bcl-2) family proteins constitutes a crucial checkpoint in apoptosis. Its detailed molecular mechanism remains controversial. Our former modeling studies have selected the ‘Direct Activation Model’ as a better explanation for experimental observations. In this paper, we continue to extend this model by adding interactions according to updating experimental findings.

Methodology/Principal Findings

Through mathematical simulation we found bistability, a kind of switch, can arise from a positive (double negative) feedback in the Bcl-2 interaction network established by anti-apoptotic group of Bcl-2 family proteins. Moreover, Bax/Bak auto-activation as an independent positive feedback can enforce the bistability, and make it more robust to parameter variations. By ensemble stochastic modeling, we also elucidated how intrinsic noise can change ultrasensitive switches into gradual responses. Our modeling result agrees well with recent experimental data where bimodal Bax activation distributions in cell population were found.

Conclusions/Significance

Along with the growing experimental evidences, our studies successfully elucidate the switch mechanism embedded in the Bcl-2 interaction network and provide insights into pharmacological manipulation of Bcl-2 apoptotic switch as further cancer therapies.     

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomycescerevisiae yeast, and (2) the SOS DNA repair network in Escherichiacoli.     

Role of Intracellular Stochasticity in Biofilm Growth. Insights from Population Balance Modeling

There is increasing recognition that stochasticity involved in gene regulatory processes may help cells enhance the signal or synchronize expression for a group of genes. Thus the validity of the traditional deterministic approach to modeling the foregoing processes cannot be without exception. In this study, we identify a frequently encountered situation, i.e., the biofilm, which has in the past been persistently investigated with intracellular deterministic models in the literature. We show in this paper circumstances in which use of the intracellular deterministic model appears distinctly inappropriate. In Enterococcus faecalis, the horizontal gene transfer of plasmid spreads drug resistance. The induction of conjugation in planktonic and biofilm circumstances is examined here with stochastic as well as deterministic models. The stochastic model is formulated with the Chemical Master Equation (CME) for planktonic cells and Reaction-Diffusion Master Equation (RDME) for biofilm. The results show that although the deterministic model works well for the perfectly-mixed planktonic circumstance, it fails to predict the averaged behavior in the biofilm, a behavior that has come to be known as stochastic focusing. A notable finding from this work is that the interception of antagonistic feedback loops to signaling, accentuates stochastic focusing. Moreover, interestingly, increasing particle number of a control variable could lead to an even larger deviation. Intracellular stochasticity plays an important role in biofilm and we surmise by implications from the model, that cell populations may use it to minimize the influence from environmental fluctuation.     

Multi-parametric analysis and modeling of relationships between mitochondrial morphology and apoptosis

Mitochondria exist as a network of interconnected organelles undergoing constant fission and fusion. Current approaches to study mitochondrial morphology are limited by low data sampling coupled with manual identification and classification of complex morphological phenotypes. Here we propose an integrated mechanistic and data-driven modeling approach to analyze heterogeneous, quantified datasets and infer relations between mitochondrial morphology and apoptotic events. We initially performed high-content, multi-parametric measurements of mitochondrial morphological, apoptotic, and energetic states by high-resolution imaging of human breast carcinoma MCF-7 cells. Subsequently, decision tree-based analysis was used to automatically classify networked, fragmented, and swollen mitochondrial subpopulations, at the single-cell level and within cell populations. Our results revealed subtle but significant differences in morphology class distributions in response to various apoptotic stimuli. Furthermore, key mitochondrial functional parameters including mitochondrial membrane potential and Bax activation, were measured under matched conditions. Data-driven fuzzy logic modeling was used to explore the non-linear relationships between mitochondrial morphology and apoptotic signaling, combining morphological and functional data as a single model. Modeling results are in accordance with previous studies, where Bax regulates mitochondrial fragmentation, and mitochondrial morphology influences mitochondrial membrane potential. In summary, we established and validated a platform for mitochondrial morphological and functional analysis that can be readily extended with additional datasets. We further discuss the benefits of a flexible systematic approach for elucidating specific and general relationships between mitochondrial morphology and apoptosis.     

The Dynamics of Stress p53-Mdm2 Network Regulated by p300 and HDAC1

We construct a stress p53-Mdm2-p300-HDAC1 regulatory network that is activated and stabilised by two regulatory proteins, p300 and HDAC1. Different activation levels of observed due to these regulators during stress condition have been investigated using a deterministic as well as a stochastic approach to understand how the cell responds during stress conditions. We found that these regulators help in adjusting p53 to different conditions as identified by various oscillatory states, namely fixed point oscillations, damped oscillations and sustain oscillations. On assessing the impact of p300 on p53-Mdm2 network we identified three states: first stabilised or normal condition where the impact of p300 is negligible, second an interim region where p53 is activated due to interaction between p53 and p300, and finally the third regime where excess of p300 leads to cell stress condition. Similarly evaluation of HDAC1 on our model led to identification of the above three distinct states. Also we observe that noise in stochastic cellular system helps to reach each oscillatory state quicker than those in deterministic case. The constructed model validated different experimental findings qualitatively.     

Apoptotic microtubule network organization and maintenance depend on high cellular ATP levels and energized mitochondria

Microtubule cytoskeleton is reformed during apoptosis, forming a cortical structure beneath plasma membrane, which plays an important role in preserving cell morphology and plasma membrane integrity. However, the maintenance of the apoptotic microtubule network (AMN) during apoptosis is not understood. In the present study, we examined apoptosis induced by camptothecin (CPT), a topoisomerase I inhibitor, in human H460 and porcine LLCPK-1α cells. We demonstrate that AMN was organized in apoptotic cells with high ATP levels and hyperpolarized mitochondria and, on the contrary, was dismantled in apoptotic cells with low ATP levels and mitochondrial depolarization. AMN disorganization after mitochondrial depolarization was associated with increased plasma membrane permeability assessed by enhancing LDH release and increased intracellular calcium levels. Living cell imaging monitoring of both, microtubule dynamics and mitochondrial membrane potential, showed that AMN persists during apoptosis coinciding with cycles of mitochondrial hyperpolarization. Eventually, AMN was disorganized when mitochondria suffered a large depolarization and cell underwent secondary necrosis. AMN stabilization by taxol prevented LDH release and calcium influx even though mitochondria were depolarized, suggesting that AMN is essential for plasma membrane integrity. Furthermore, high ATP levels and mitochondria polarization collapse after oligomycin treatment in apoptotic cells suggest that ATP synthase works in “reverse” mode during apoptosis. These data provide new explanations for the role of AMN and mitochondria during apoptosis.     

Mechanism of fenretinide (4-HPR)-induced cell death

4-HPR (fenretinide) is a synthetic analog of retinoic acid (RA) whose potential as a chemopreventative agent has gained support from in vitro and animal experiments and in limited clinical trials. Comparative analyses of cellular, biochemical, and molecular properties of fenretinide with RA using various tissue culture cells reveal that a key distinction between these two retinoids lies in the ability of fenretinide to induce programmed cell death, also known as apoptosis. Here we review the composite evidence for induction of apoptosis in fenretinide-treated cells. Assays used to validate apoptosis in various cell types are also summarized. Apoptosis in response to fenretinide primarily occurs by a receptor-independent mechanism, which is accompanied by increases in signaling molecules, e.g., ceramide, and cysteine-dependent aspartate-directed proteases, termed caspases, including execution caspase-3. Both caspase-3 inhibitor DEVD-CHO and ceramide synthase inhibitor fumonisin B₁ (FB₁) block fenretinide-induced apoptosis. Increase in caspase-3 appears to result from fenretinide-elicited stabilization of procaspase-3 zymogen. We also review apoptotic regulatory proteins such as inhibitor of apoptosis (IAPs) and second mitochondria-derived activator of caspase (SMACs) that participate in the coordinate control of caspase activities. The existence of a large number of proteins capable of modulating apoptosis via activation or inhibition of caspases, coupled with the fact that both the initiation and execution phases of apoptosis utilize pre-existing zymogens, which, once set in motion, culminates in an irreversible apoptotic cascade, raise the possibility that the on/off switch of apoptosis is linked to an intricate intracellular regulatory network, capable of responding to external stimuli such as fenretinide. This network functions to provide checks/balances of the need for apoptosis as well as to minimize and prevent untimely errors in apoptosis. We suggest that dynamic and coordinated regulation of apoptosis by such a hypothetical network in vivo may involve co-localization of pro- and anti-apoptotic proteins and their respective activators/inhibitors in a macromolecular modular unit which we propose to be named caspasomes. Fenretinide also induces apoptosis by elevating reactive oxygen species (ROS), unrelated to changes in ceramide-caspases. Thus multiple, distinct pathways contribute to the induction of apoptosis by fenretinide.     

Comparison of Deterministic and Stochastic Models of the lac Operon Genetic Network

The lac operon has been a paradigm for genetic regulation with positive feedback, and several modeling studies have described its dynamics at various levels of detail. However, it has not yet been analyzed how stochasticity can enrich the system's behavior, creating effects that are not observed in the deterministic case. To address this problem we use a comparative approach. We develop a reaction network for the dynamics of the lac operon genetic switch and derive corresponding deterministic and stochastic models that incorporate biological details. We then analyze the effects of key biomolecular mechanisms, such as promoter strength and binding affinities, on the behavior of the models. No assumptions or approximations are made when building the models other than those utilized in the reaction network. Thus, we are able to carry out a meaningful comparison between the predictions of the two models to demonstrate genuine effects of stochasticity. Such a comparison reveals that in the presence of stochasticity, certain biomolecular mechanisms can profoundly influence the region where the system exhibits bistability, a key characteristic of the lac operon dynamics. For these cases, the temporal asymptotic behavior of the deterministic model remains unchanged, indicating a role of stochasticity in modulating the behavior of the system.     

Viral pro-survival proteins block separate stages in Bax activation but changes in mitochondrial ultrastructure still occur

Mitochondrial dysfunction mediated by Bax and Bak is a critical step in mammalian cell apoptosis. However, the molecular mechanism of Bax activation remains unknown and has been difficult to investigate due to its rapid and stochastic nature. It is currently unclear whether mitochondria play a passive role in the initiation of apoptosis, remaining unaffected by cell stresses until Bax and Bak are active, or whether they actively participate in Bax/Bak activation. Here, two viral proteins, E1B19K and BHRF1, are examined for their ability to block Bax activation at different steps and thereby reveal the timing of mitochondrial changes during apoptosis. We demonstrate that BHRF1 strongly inhibits Bax activation but not upstream apoptotic signaling events, while E1B19K permits initial stages of Bax activation but prevents the subsequent oligomerization of Bax that is required for mitochondrial dysfunction. In this defined system we show that changes in mitochondrial ultrastructure, characteristic of cells undergoing apoptosis, precede Bax activation and are not blocked by E1B19K and BHRF1. We suggest that the ability of mitochondria to respond to apoptotic stress prior to Bax activation indicates that these organelles may play a direct role in activating Bax.     

Aging and lifelong calorie restriction result in adaptations of skeletal muscle apoptosis repressor, apoptosis-inducing factor, X-linked inhibitor of apoptosis, caspase-3, and caspase-12

The mechanisms of apoptosis in the loss of myocytes in skeletal muscle with age and the role of mitochondrial and sarcoplasmic reticulum-mediated pathways of apoptosis are unknown. Moreover, it is unknown whether lifelong calorie restriction prevents apoptosis in skeletal muscle and reverses age-related alterations in apoptosis signaling. We investigated key apoptotic regulatory proteins in the gastrocnemius muscle of 12 and 26 month old ad libitum fed and 26 month old calorie-restricted male Fischer-344 rats. We found that apoptosis increased with age and that calorie-restricted rats showed less apoptosis compared with their age-matched cohorts. Moreover, pro- and cleaved caspase-3 levels increased significantly with age and calorie-restricted rats had significantly lower levels than the aged ad libitum group. Neither age nor calorie restriction had any effect on muscle caspase-3 enzyme activity, but the levels of X-linked inhibitor of apoptosis, particularly an inhibitor of caspase-3, increased with age and were reduced significantly in the 26 month old calorie-restricted cohort. The apoptotic inhibitor apoptosis repressor with a caspase recruitment domain (ARC), which inhibits cytochrome c release, underwent an age-associated decline in the cytosol but increased with calorie restriction. In contrast, mitochondrial ARC levels increased with age and were lower in calorie-restricted rats than in age-matched controls, suggesting a translocation of this protein to attenuate oxidative stress. The translocation of ARC may explain the reduction in cytosolic cytochrome c levels observed with age and calorie restriction. Moreover, we found a striking approximately 350% increase in the expression of procaspase-12 (caspase located at the sarcoplasmic reticulum) with age which was significantly lower in the 26 month old calorie-restricted group. The total protein level of apoptosis-inducing factor in the plantaris muscle increased with age and was reduced calorie-restricted rats compared with age-matched controls, but there were no significant changes in this pro-apoptotic protein in the isolated nuclei. Calorie restriction is able to lower the apoptotic potential in aged skeletal muscle by altering several key apoptotic proteins toward cellular survival, thereby reducing the potential for sarcopenia.     

Recruitment of cellular prion protein to mitochondrial raft-like microdomains contributes to apoptosis execution

We examined the possibility that cellular prion protein (PrP(C)) plays a role in the receptor-mediated apoptotic pathway. We first found that CD95/Fas triggering induced a redistribution of PrP(C) to the mitochondria of T lymphoblastoid CEM cells via a mechanism that brings into play microtubular network integrity and function. In particular, we demonstrated that PrP(C) was redistributed to raft-like microdomains at the mitochondrial membrane, as well as at endoplasmic reticulum-mitochondria-associated membranes. Our in vitro experiments also demonstrated that, although PrP(C) had such an effect on mitochondria, it induced the loss of mitochondrial membrane potential and cytochrome c release only after a contained rise of calcium concentration. Finally, the involvement of PrP(C) in apoptosis execution was also analyzed in PrP(C)-small interfering RNA-transfected cells, which were found to be significantly less susceptible to CD95/Fas-induced apoptosis. Taken together, these results suggest that PrP(C) might play a role in the complex multimolecular signaling associated with CD95/Fas receptor-mediated apoptosis.     

Survivin withdrawal by nuclear export failure as a physiological switch to commit cells to apoptosis

Apoptosis is a tightly controlled process regulated by many signaling pathways; however, the mechanisms and cellular events that decide whether a cell lives or dies remain poorly understood. Here we showed that when a cell is under apoptotic stress, the prosurvival protein Survivin redistributes from the cytoplasm to the nucleus, thus acting as a physiological switch to commit the cell to apoptosis. The nuclear relocalization of Survivin is a result of inefficient assembly of functional RanGTP–CRM1–Survivin export complex due to apoptotic RanGTP gradient collapse. Subsequently, Survivin undergoes ubiquitination, which not only physically prevents its diffusion back to the cytoplasm but also facilitates its degradation. Together, this spatial and functional regulation of Survivin abolishes its cytoprotective effect toward the apoptotic executors and thus commits a cell to apoptosis. Our data indicate that the withdrawal of Survivin is a novel and active physiological regulatory mechanism that tilts the survival balance and promotes the progression of apoptosis.