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

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.

Molecular panorama of therapy resistance in prostate cancer: a pre-clinical and bioinformatics analysis for clinical translation

Prostate cancer (PCa) is a malignant disorder of prostate gland being asymptomatic in early stages and high metastatic potential in advanced stages. The chemotherapy and surgical resection have provided favourable prognosis of PCa patients, but advanced and aggressive forms of PCa including CRPC and AVPC lack response to therapy properly, and therefore, prognosis of patients is deteriorated. At the advanced stages, PCa cells do not respond to chemotherapy and radiotherapy in a satisfactory level, and therefore, therapy resistance is emerged. Molecular profile analysis of PCa cells reveals the apoptosis suppression, pro-survival autophagy induction, and EMT induction as factors in escalating malignant of cancer cells and development of therapy resistance. The dysregulation in molecular profile of PCa including upregulation of STAT3 and PI3K/Akt, downregulation of STAT3, and aberrant expression of non-coding RNAs are determining factor for response of cancer cells to chemotherapy. Because of prevalence of drug resistance in PCa, combination therapy including co-utilization of anti-cancer drugs and nanotherapeutic approaches has been suggested in PCa therapy. As a result of increase in DNA damage repair, PCa cells induce radioresistance and RelB overexpression prevents irradiation-mediated cell death. Similar to chemotherapy, nanomaterials are promising for promoting radiosensitivity through delivery of cargo, improving accumulation in PCa cells, and targeting survival-related pathways. In respect to emergence of immunotherapy as a new tool in PCa suppression, tumour cells are able to increase PD-L1 expression and inactivate NK cells in mediating immune evasion. The bioinformatics analysis for evaluation of drug resistance-related genes has been performed.

Fluctuations in tissue growth portray homeostasis as a critical state and long-time non-Markovian cell proliferation as Markovian

Tissue growth is an emerging phenomenon that results from the cell-level interplay between proliferation and apoptosis, which is crucial during embryonic development, tissue regeneration, as well as in pathological conditions such as cancer. In this theoretical article, we address the problem of stochasticity in tissue growth by first considering a minimal Markovian model of tissue size, quantified as the number of cells in a simulated tissue, subjected to both proliferation and apoptosis. We find two dynamic phases, growth and decay, separated by a critical state representing a homeostatic tissue. Since the main limitation of the Markovian model is its neglect of the cell cycle, we incorporated a refractory period that temporarily prevents proliferation immediately following cell division, as a minimal proxy for the cell cycle, and studied the model in the growth phase. Importantly, we obtained from this last model an effective Markovian rate, which accurately describes general trends of tissue size. This study shows that the dynamics of tissue growth can be theoretically conceptualized as a Markovian process where homeostasis is a critical state flanked by decay and growth phases. Notably, in the growing non-Markovian model, a Markovian-like growth process emerges at large time scales.

A review on cell damage, viability, and functionality during 3D bioprinting

Three-dimensional (3D) bioprinting fabricates 3D functional tissues/organs by accurately depositing the bioink composed of the biological materials and living cells. Even though 3D bioprinting techniques have experienced significant advancement over the past decades, it remains challenging for 3D bioprinting to artificially fabricate functional tissues/organs with high post-printing cell viability and functionality since cells endure various types of stress during the bioprinting process. Generally, cell viability which is affected by several factors including the stress and the environmental factors, such as pH and temperature, is mainly determined by the magnitude and duration of the stress imposed on the cells with poorer cell viability under a higher stress and a longer duration condition. The maintenance of high cell viability especially for those vulnerable cells, such as stem cells which are more sensitive to multiple stresses, is a key initial step to ensure the functionality of the artificial tissues/organs. In addition, maintaining the pluripotency of the cells such as proliferation and differentiation abilities is also essential for the 3D-bioprinted tissues/organs to be similar to native tissues/organs. This review discusses various pathways triggering cell damage and the major factors affecting cell viability during different bioprinting processes, summarizes the studies on cell viabilities and functionalities in different bioprinting processes, and presents several potential approaches to protect cells from injuries to ensure high cell viability and functionality.

Model scenarios for cell cycle re-entry in Alzheimer's disease

Alzheimer's disease (AD) is the most prevalent neurodegenerative disease. Aberrant production and aggregation of amyloid beta (Aβ) peptide into plaques is a frequent feature of AD, but therapeutic approaches targeting Aβ accumulation fail to inhibit disease progression. The approved cholinesterase inhibitor drugs are symptomatic treatments. During human brain development, the progenitor cells differentiate into neurons and switch to a postmitotic state. However, cell cycle re-entry often precedes loss of neurons. We developed mathematical models of multiple routes leading to cell cycle re-entry in neurons that incorporate the crosstalk between cell cycle, neuronal, and apoptotic signaling mechanisms. We show that the integration of multiple feedback loops influences disease severity making the switch to pathological state irreversible. We observe that the transcriptional changes associated with this transition are also characteristics of the AD brain. We propose that targeting multiple arms of the feedback loop may bring about disease-modifying effects in AD.

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Developed mathematical models of cell cycle re-entry in Alzheimer's disease (AD)

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Integration of multiple feedback loops drives irreversible transition to AD

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Predicted transcriptional dysregulation is validated using AD gene expression data

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Inhibition of self-amplifying feedback loops brings about disease-modifying effects

Dual roles of SIRT1 in the BAX switch through the P53 module: A mathematical modeling study

SIRT1 is a multifunctional deacetylase that participates in a variety of cellular physiological processes to cope with stress. The anticancer protein P53 is an important target of SIRT1. It has been found that SIRT1 is involved in apoptosis by regulating the activity and intracellular location of P53. Moreover, P53-dependent apoptosis is inseparable from the BCL-2 protein family. Among the members of this family, BAX’s switching dynamics may play a key role in apoptosis. Therefore, a challenging question arises: what effect does SIRT1 have on the BAX switch? To answer this question, we built a small-scale protein network model. Through computer simulation, the properties of SIRT1 that on the one hand promote and on the other inhibit apoptosis are revealed. We found that the opening time of the BAX switch will be delayed in the case of either SIRT1 excess or deficiency. Similarly, the stimulus threshold required for apoptosis will also increase in the above two scenarios. Thereby, we proposed that SIRT1 has an optimal content at which the probability of apoptosis is greatest. In addition, P53 oscillation requires the concentration of SIRT1 to be higher than the optimal value. This work may be helpful both experimentally and clinically.

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.

CASPAM: A Triple-Modality Biosensor for Multiplexed Imaging of Caspase Network Activity

Understanding signal propagation across biological networks requires to simultaneously monitor the dynamics of several nodes to uncover correlations masked by inherent intercellular variability. To monitor the enzymatic activity of more than two components over short time scales has proven challenging. Exploiting the narrow spectral width of homo-FRET-based biosensors, up to three activities can be imaged through fluorescence polarization anisotropy microscopy. We introduce Caspase Activity Sensor by Polarization Anisotropy Multiplexing (CASPAM) a single-plasmid triple-modality reporter of key nodes of the apoptotic network. Apoptosis provides an ideal molecular framework to study interactions between its three composing pathways (intrinsic, extrinsic, and effector). We characterized the biosensor performance and demonstrated the advantages that equimolar expression has in both simplifying experimental procedure and reducing observable variation, thus enabling robust data-driven modeling. Tools like CASPAM become essential to analyze molecular pathways where multiple nodes need to be simultaneously monitored.

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 systems biology approach to discovering pathway signaling dysregulation in metastasis

Total metastatic burden is the primary cause of death for many cancer patients. While the process of metastasis has been studied widely, much remains to be understood. Moreover, few agents have been developed that specifically target the major steps of the metastatic cascade. Many individual genes and pathways have been implicated in metastasis but a holistic view of how these interact and cooperate to regulate and execute the process remains somewhat rudimentary. It is unclear whether all of the signaling features that regulate and execute metastasis are yet fully understood. Novel features of a complex system such as metastasis can often be discovered by taking a systems-based approach. We introduce the concepts of systems modeling and define some of the central challenges facing the application of a multidisciplinary systems-based approach to understanding metastasis and finding actionable targets therein. These challenges include appreciating the unique properties of the high-dimensional omics data often used for modeling, limitations in knowledge of the system (metastasis), tumor heterogeneity and sampling bias, and some of the issues key to understanding critical features of molecular signaling in the context of metastasis. We also provide a brief introduction to integrative modeling that focuses on both the nodes and edges of molecular signaling networks. Finally, we offer some observations on future directions as they relate to developing a systems-based model of the metastatic cascade.

The role of time delays in P53 gene regulatory network stimulated by growth factor

In this paper, a delayed mathematical model for the P53-Mdm2 network is developed. The P53-Mdm2 network we study is triggered by growth factor instead of DNA damage and the amount of DNA damage is regarded as zero. We study the influences of time delays, growth factor and other important chemical reaction rates on the dynamic behaviors in the system. It is shown that the time delay is a critical factor and its length determines the period, amplitude and stability of the P53 oscillation. Furthermore, as for some important chemical reaction rates, we also obtain some interesting results through numerical simulation. Especially, S (growth factor), k₃ (rate constant for Mdm2_p dephosphorylation), k₁₀ (basal expression of PTEN) and k₁₄ (Rate constant for PTEN-induced Akt dephosphorylation) could undermine the dynamic behavior of the system in different degree. These findings are expected to understand the mechanisms of action of several carcinogenic and tumor suppressor factors in humans under normal conditions.

Fate decisions mediated by crosstalk of autophagy and apoptosis in mammalian cells

Autophagy is an important cell activity which is the process of formation of autophagosomes, docking with lysosomes and degradation. The intrinsic pathway of apoptosis involves mitochondrial outer membrane permeabilization (MOMP) and cytochrome c release followed by caspase activation. Many molecules, e.g., Ca²⁺ and mTOR, and different stresses such as endoplasmic reticulum (ER) stress and nutritional stress take part in these two processes. However, the mechanism of how they work together so as to determine cell fate decisions remains to be clarified. Here, we present a computational model for cell fate decisions based on intertwined dynamics with autophagy and apoptosis involving Ca²⁺, mTOR, and both ER stress and nutritional stress. In agreement with experimental observations, the model predicts that both Ca²⁺ and the stresses play critical roles in regulating the choice between autophagy and apoptosis in a combinatorial way. The model presented here might be a good candidate for providing the qualitative mechanism of cell fate decisions mediated by Ca²⁺, mTOR, and two kinds of stress.

Detection of biological switches using the method of Gröebner bases

BACKGROUND

Bistability and ability to switch between two stable states is the hallmark of cellular responses. Cellular signaling pathways often contain bistable switches that regulate the transmission of the extracellular information to the nucleus where important biological functions are executed.

RESULTS

In this work we show how the method of Gröebner bases can be used to detect bistability and output switchability. The method of Gröebner bases can be seen as a multivariate, non-linear generalization of the Gaussian elimination for linear systems which conveniently seperates the variables and drastically simplifies the simultaneous solution of polynomial equations. A necessary condition for fixed-point state bistability is for the Gröbner basis to have three distinct solutions for the state. A sufficient condition is provided by the eigenvalues of the local Jacobians. We also introduce the concept of output switchability which is defined as the ability of an output of a bistable system to switch between two different stable steady-state values. It is shown that bistability does not necessarily guarantee switchability of every state variable of the system. We further show that, for a bistable system, the necessary conditions for output switchability can be derived using the Gröebner basis. The theoretical results are incorporated into an analysis procedure and applied to several systems including the AKT (Protein kinase B), RAS (Rat Sarcoma) and MAPK (Mitogen-activated protein kinase) signal transduction pathways. Results demonstrate that the Gröebner bases can be conveniently used to analyze biological switches by simultaneously detecting bistability and output switchability.

CONCLUSION

The Gröebner bases provides a novel methodology to analyze bistability. Results clarify the distinction between bistability and output switchability which is lacking in the literature. We have shown that theoretically, it is possible to have an output subspace of an n-dimensional bistable system where certain variables cannot switch. It is possible to construct such systems as we have done with two reaction networks.

System-based approaches as prognostic tools for glioblastoma

BACKGROUND

The evasion of apoptosis is a hallmark of cancer. Understanding this process holistically and overcoming apoptosis resistance is a goal of many research teams in order to develop better treatment options for cancer patients. Efforts are also ongoing to personalize the treatment of patients. Strategies to confirm the therapeutic efficacy of current treatments or indeed to identify potential novel additional options would be extremely beneficial to both clinicians and patients. In the past few years, system medicine approaches have been developed that model the biochemical pathways of apoptosis. These systems tools incorporate and analyse the complex biological networks involved. For their successful integration into clinical practice, it is mandatory to integrate systems approaches with routine clinical and histopathological practice to deliver personalized care for patients.

RESULTS

We review here the development of system medicine approaches that model apoptosis for the treatment of cancer with a specific emphasis on the aggressive brain cancer, glioblastoma.

CONCLUSIONS

We discuss the current understanding in the field and present new approaches that highlight the potential of system medicine approaches to influence how glioblastoma is diagnosed and treated in the future.

Mathematical Modeling of p53 Pathways

Cells have evolved balanced systems that ensure an appropriate response to stress. The systems elicit repair responses in temporary or moderate stress but eliminate irreparable cells via apoptosis in detrimental conditions of prolonged or severe stress. The tumor suppressor p53 is a central player in these stress response systems. When activated under DNA damage stress, p53 regulates hundreds of genes that are involved in DNA repair, cell cycle, and apoptosis. Recently, increasing studies have demonstrated additional regulatory roles of p53 in metabolism and mitochondrial physiology. Due to the inherent complexity of feedback loops between p53 and its target genes, the application of mathematical modeling has emerged as a novel approach to better understand the multifaceted functions and dynamics of p53. In this review, we discuss several mathematical modeling approaches in exploring the p53 pathways.

Designing combination therapies with modeling chaperoned machine learning

Chemotherapy resistance is a major challenge to the effective treatment of cancer. Thus, a systematic pipeline for the efficient identification of effective combination treatments could bring huge biomedical benefit. In order to facilitate rational design of combination therapies, we developed a comprehensive computational model that incorporates the available biological knowledge and relevant experimental data on the life-and-death response of individual cancer cells to cisplatin or cisplatin combined with the TNF-related apoptosis-inducing ligand (TRAIL). The model's predictions, that a combination treatment of cisplatin and TRAIL would enhance cancer cell death and exhibit a "two-wave killing" temporal pattern, was validated by measuring the dynamics of p53 accumulation, cell fate, and cell death in single cells. The validated model was then subjected to a systematic analysis with an ensemble of diverse machine learning methods. Though each method is characterized by a different algorithm, they collectively identified several molecular players that can sensitize tumor cells to cisplatin-induced apoptosis (sensitizers). The identified sensitizers are consistent with previous experimental observations. Overall, we have illustrated that machine learning analysis of an experimentally validated mechanistic model can convert our available knowledge into the identity of biologically meaningful sensitizers. This knowledge can then be leveraged to design treatment strategies that could improve the efficacy of chemotherapy.

Dual Antagonist of cIAP/XIAP ASTX660 Sensitizes HPV- and HPV+ Head and Neck Cancers to TNFα, TRAIL, and Radiation Therapy

PURPOSE

Human papillomavirus-negative (HPV^-) head and neck squamous cell carcinomas (HNSCC) harbor frequent genomic amplification of Fas-associated death domain, with or without concurrent amplification of Baculovirus inhibitor of apoptosis repeat containing (BIRC2/3) genes encoding cellular inhibitor of apoptosis proteins 1/2 (cIAP1/2). Antagonists targeting cIAP1 have been reported to enhance sensitivity of HPV^-, but not HPV⁺ tumors, to TNF family death ligands (TNF and TRAIL) and radiation.Experimental Design: We tested a novel dual cIAP/XIAP antagonist ASTX660 in HPV⁺ and HPV^- cell lines in combination with death ligands TNFα and TRAIL, and in preclinical xenograft models with radiation, an inducer of death ligands. The dependence of activity on TNF was examined by antibody depletion.

RESULTS

ASTX660 sensitized subsets of HPV^- and HPV⁺ HNSCC cell lines to TNFα and TRAIL. These antitumor effects of ASTX660 are the result of both apoptosis and/or necroptosis among HPV^- cells, and primarily by apoptosis (caspase 3 and caspase 8 cleavage) in HPV⁺ cells. ASTX660 enhanced restoration of protein expression and inhibitory activity of proapoptotic tumor suppressor TP53 in HPV⁺ HNSCC. Furthermore, ASTX660 combined with radiotherapy, an inducer of death ligands, significantly delayed growth of both HPV^- and HPV⁺ human tumor xenografts, an effect attenuated by anti-TNFα pretreatment blockade.

CONCLUSIONS

IAP1/XIAP antagonist, ASTX660, sensitizes HPV⁺ HNSCC to TNFα via a mechanism involving restoration of TP53. These findings serve to motivate further studies of dual cIAP/XIAP antagonists and future clinical trials combining these antagonists with radiotherapy to treat both HPV⁺ and HPV^- HNSCC.

Apoptosis: A mammalian cell bioprocessing perspective

Apoptosis is a form of programmed and controlled cell death that accounts for the majority of cellular death in bioprocesses. Cell death affects culture longevity and product quality; it is instigated by several stresses experienced by the cells within a bioreactor. Understanding the factors that cause apoptosis as well as developing strategies that can protect cells is crucial for robust bioprocess development. This review aims to a) address apoptosis from a bioprocess perspective; b) describe the significant apoptotic mechanisms linking them to the most relevant stresses encountered in bioreactors; c) discuss the design of operating conditions in order to avoid cell death; d) focus on industrially relevant cell lines; and e) present anti-apoptosis strategies including cell engineering and model-based optimization of bioprocesses. In addition, the importance of apoptosis in quality-by-design bioprocess development from clone screening to production scale are highlighted.

MiR-35 buffers apoptosis thresholds in the C. elegans germline by antagonizing both MAPK and core apoptosis pathways

Apoptosis is a genetically programmed cell death process with profound roles in development and disease. MicroRNAs modulate the expression of many proteins and are often deregulated in human diseases, such as cancer. C. elegans germ cells undergo apoptosis in response to genotoxic stress by the combined activities of the core apoptosis and MAPK pathways, but how their signalling thresholds are buffered is an open question. Here we show mir-35–42 miRNA family play a dual role in antagonizing both NDK-1, a positive regulator of MAPK signalling, and the BH3-only pro-apoptotic protein EGL-1 to regulate the magnitude of DNA damage-induced apoptosis in the C. elegans germline. We show that while miR-35 represses EGL-1 by promoting transcript degradation, repression of NDK-1 may be through sequestration of the transcript to inhibit translation. Importantly, dramatic increase in NDK-1 expression was observed in cells about to die. In the absence of miR-35, increased NDK-1 activity enhanced MAPK signalling that lead to significant increases in germ cell death. Our findings demonstrate that NDK-1 acts upstream of (or in parallel to) EGL-1, and that miR-35 targets both egl-1 and ndk-1 to fine-tune cell killing in response to genotoxic stress.

Apoptosis propagates through the cytoplasm as trigger waves

Apoptosis is an evolutionarily conserved form of programmed cell death critical for development and tissue homeostasis in animals. The apoptotic control network includes several positive feedback loops that may allow apoptosis to spread through the cytoplasm in self-regenerating trigger waves. We tested this possibility in cell-free Xenopus laevis egg extracts and observed apoptotic trigger waves with speeds of ~30 micrometers per minute. Fractionation and inhibitor studies implicated multiple feedback loops in generating the waves. Apoptotic oocytes and eggs exhibited surface waves with speeds of ~30 micrometers per minute, which were tightly correlated with caspase activation. Thus, apoptosis spreads through trigger waves in both extracts and intact cells. Our findings show how apoptosis can spread over large distances within a cell and emphasize the general importance of trigger waves in cell signaling.

Digital signaling network drives the assembly of the AIM2-ASC inflammasome

The AIM2-ASC inflammasome is a filamentous signaling platform essential for mounting host defense against cytoplasmic dsDNA arising not only from invading pathogens but also from damaged organelles. Currently, the design principles of its underlying signaling network remain poorly understood at the molecular level. We show here that longer dsDNA is more effective in inducing AIM2 assembly, its self-propagation, and downstream ASC polymerization. This observation is related to the increased probability of forming the base of AIM2 filaments, and indicates that the assembly discerns small dsDNA as noise at each signaling step. Filaments assembled by receptor AIM2, downstream ASC, and their joint complex all persist regardless of dsDNA, consequently generating sustained signal amplification and hysteresis. Furthermore, multiple positive feedback loops reinforce the assembly, as AIM2 and ASC filaments accelerate the assembly of nascent AIM2 with or without dsDNA. Together with a quantitative model of the assembly, our results indicate that an ultrasensitive digital circuit drives the assembly of the AIM2-ASC inflammasome.

In silico modelling of apoptosis induced by photodynamic therapy

Photodynamic therapy (PDT) is an emergent technique used for the treatment of several diseases. After PDT, cells die by necrosis, apoptosis or autophagy. Necrosis is produced immediately during photodynamic therapy by high concentration of reactive oxygen species, apoptosis and autophagy are triggered by mild or low doses of light and photosensitizer. In this work we model the cell response to low doses of PDT assuming a bi-dimensional matrix of interacting cells. For each cell of the matrix we simulate in detail, with the help of the Gillespie's algorithm, the two main chemical pathways leading to apoptosis. We unveil the role of both pathways in the cell death rate of the tumor, as well as the relevance of several molecules in the process. Our model suggests values of concentrations for several species of molecules to enhance the effectiveness of PDT.

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.

Printing-induced cell injury evaluation during laser printing of 3T3 mouse fibroblasts

Three-dimensional bioprinting has emerged as a promising solution for the freeform fabrication of living cellular constructs, which can be used for tissue/organ transplantation and tissue models. During bioprinting, some living cells are unavoidably injured and may become necrotic or apoptotic cells. This study aims to investigate the printing-induced cell injury and evaluates injury types of post-printing cells using the annexin V/7-aminoactinomycin D and FAM-DEVD-FMK/propidium iodide assays during laser printing of NIH 3T3 mouse fibroblasts. As observed, the percentage of post-printing early apoptotic mouse fibroblasts increases with the incubation time, indicating that post-printing apoptotic mouse fibroblasts have different initiation lag times of apoptosis due to different levels of mechanical stress exerted during laser printing. Post-printing necrotic mouse fibroblasts can be detected immediately after printing, while post-printing early apoptotic mouse fibroblasts need time to develop into a late apoptotic stage. The minimum time needed for post-printing early apoptotic mouse fibroblasts to complete their apoptosis pathway and transition into late apoptotic mouse fibroblasts is from 4 h to 5 h post-printing. The resulting knowledge of the evolution of different apoptotic post-printing mouse fibroblasts will help better design future experiments to quantitatively determine, model, and mitigate the post-printing cell injury based on molecular signal pathway modeling.

Recent progress and open challenges in modeling p53 dynamics in single cells

In mammalian cells, the tumor suppressor p53 is activated upon a variety of cellular stresses and ensures an appropriate response ranging from arrest and repair to the induction of senescence and apoptosis. Quantitative measurements in individual living cells showed stimulus-dependent dynamics of p53 accumulation upon stress induction. Due to the complexity of the underlying biochemical interactions, mathematical models were indispensable for understanding the topology of the network regulating p53 dynamics. Recent work provides furhter insights into the causes of heterogeneous responses in individual cells, the rewiring of the network in response to different inputs and the role of the downstream processes in determining the cellular fate upon stress.

Unraveling cellular pathways contributing to drug-induced liver injury by dynamical modeling

INTRODUCTION

Drug-induced liver injury (DILI) is a significant threat to human health and a major problem in drug development. It is hard to predict due to its idiosyncratic nature and which does not show up in animal trials. Hepatic adaptive stress response pathway activation is generally observed in drug-induced liver injury. Dynamical pathway modeling has the potential to foresee adverse effects of drugs before they go in trial. Ordinary differential equation modeling can offer mechanistic insight, and allows us to study the dynamical behavior of stress pathways involved in DILI. Areas covered: This review provides an overview on the progress of the dynamical modeling of stress and death pathways pertinent to DILI, i.e. pathways relevant for oxidative stress, inflammatory stress, DNA damage, unfolded proteins, heat shock and apoptosis. We also discuss the required steps for applying such modeling to the liver. Expert opinion: Despite the strong progress made since the turn of the century, models of stress pathways have only rarely been specifically applied to describe pathway dynamics for DILI. We argue that with minor changes, in some cases only to parameter values, many of these models can be repurposed for application in DILI research. Combining both dynamical models with in vitro testing might offer novel screening methods for the harmful side-effects of drugs.

The integrated stress response

In response to diverse stress stimuli, eukaryotic cells activate a common adaptive pathway, termed the integrated stress response (ISR), to restore cellular homeostasis. The core event in this pathway is the phosphorylation of eukaryotic translation initiation factor 2 alpha (eIF2α) by one of four members of the eIF2α kinase family, which leads to a decrease in global protein synthesis and the induction of selected genes, including the transcription factor ATF4, that together promote cellular recovery. The gene expression program activated by the ISR optimizes the cellular response to stress and is dependent on the cellular context, as well as on the nature and intensity of the stress stimuli. Although the ISR is primarily a pro-survival, homeostatic program, exposure to severe stress can drive signaling toward cell death. Here, we review current understanding of the ISR signaling and how it regulates cell fate under diverse types of stress.

S100A4 and its role in metastasis – computational integration of data on biological networks

Characterising signal transduction networks is fundamental to our understanding of biology. However, redundancy and different types of feedback mechanisms make it difficult to understand how variations of the network components contribute to a biological process. In silico modelling of signalling interactions therefore becomes increasingly useful for the development of successful therapeutic approaches. Unfortunately, quantitative information cannot be obtained for all of the proteins or complexes that comprise the network, which limits the usability of computational models. We developed a flexible computational framework for the analysis of biological signalling networks. We demonstrate our approach by studying the mechanism of metastasis promotion by the S100A4 protein, and suggest therapeutic strategies. The advantage of the proposed method is that only limited information (interaction type between species) is required to set up a steady-state network model. This permits a straightforward integration of experimental information where the lack of details are compensated by efficient sampling of the parameter space. We investigated regulatory properties of the S100A4 network and the role of different key components. The results show that S100A4 enhances the activity of matrix metalloproteinases (MMPs), causing higher cell dissociation. Moreover, it leads to an increased stability of the pathological state. Thus, avoiding metastasis in S100A4-expressing tumours requires multiple target inhibition. Moreover, the analysis could explain the previous failure of MMP inhibitors in clinical trials. Finally, our method is applicable to a wide range of biological questions that can be represented as directional networks.

A mathematical model for apoptotic switch in Drosophila

Apoptosis is an evolutionarily-conserved process of autonomous cell death. The molecular switch mechanism underlying the fate decision of apoptosis in mammalian cells has been intensively studied by mathematical modeling. In contrast, the apoptotic switch in invertebrates, with highly conserved signaling proteins and pathway, remains poorly understood mechanistically and calls for theoretical elucidation. In this study, we develop a mathematical model of the apoptosis pathway in Drosophila and compare the switch mechanism to that in mammals. Enumeration of the elementary reactions for the model demonstrates that the molecular interactions among the signaling components are considerably different from their mammalian counterparts. A notable distinction in network organization is that the direct positive feedback from the effector caspase (EC) to the initiator caspase in mammalian pathway is replaced by a double-negative regulation in Drosophila. The model is calibrated by experimental input-output relationship and the simulated trajectories exhibit all-or-none bimodal behavior. Bifurcation diagrams confirm that the model of Drosophila apoptotic switch possesses bistability, a well-recognized feature for an apoptosis system. Since the apoptotic protease activating factor-1 (APAF1) induced irreversible activation of caspase is an essential and beneficial property for the mammalian apoptotic switch, we perform analysis of the bistable caspase activation with respect to the input of DARK protein, the Drosophila homolog of APAF1. Interestingly, this bistable behavior in Drosophila is predicted to be reversible. Further analysis suggests that the mechanism underlying the systems property of reversibility is the double-negative feedback from the EC to the initiator caspase. Using theoretical modeling, our study proposes plausible evolution of the switch mechanism for apoptosis between organisms.

Dynamic Modeling of the Interaction Between Autophagy and Apoptosis in Mammalian Cells

Autophagy is a conserved biological stress response in mammalian cells that is responsible for clearing damaged proteins and organelles from the cytoplasm and recycling their contents via the lysosomal pathway. In cases of mild stress, autophagy acts as a survival mechanism, while in cases of severe stress cells may switch to programmed cell death. Understanding the decision process that moves a cell from autophagy to apoptosis is important since abnormal regulation of autophagy occurs in many diseases, including cancer. To integrate existing knowledge about this decision process into a rigorous, analytical framework, we built a mathematical model of cell fate decisions mediated by autophagy. Our dynamical model is consistent with existing quantitative measurements of autophagy and apoptosis in rat kidney proximal tubular cells responding to cisplatin-induced stress.

Computational cell fate modelling for discovery of rewiring in apoptotic network for enhanced cancer drug sensitivity

The ongoing cancer research has shown that malignant tumour cells have highly disrupted signalling transduction pathways. In cancer cells, signalling pathways are altered to satisfy the demands of continuous proliferation and survival. The changes in signalling pathways supporting uncontrolled cell growth, termed as rewiring, can lead to dysregulation of cell fates e.g. apoptosis. Hence comparative analysis of normal and oncogenic signal transduction pathways may provide insights into mechanisms of cancer drug-resistance and facilitate the discovery of novel and effective anti-cancer therapies. Here we propose a hybrid modelling approach based on ordinary differential equation (ODE) and machine learning to map network rewiring in the apoptotic pathways that may be responsible for the increase of drug sensitivity of tumour cells in triple-negative breast cancer. Our method employs Genetic Algorithm to search for the most likely network topologies by iteratively generating simulated protein phosphorylation data using ODEs and the rewired network and then fitting the simulated data with real data of cancer signalling and cell fate. Most of our predictions are consistent with experimental evidence from literature. Combining the strengths of knowledge-driven and data-driven approaches, our hybrid model can help uncover molecular mechanisms of cancer cell fate at systems level.

Crosstalks between cytokines and Sonic Hedgehog in Helicobacter pylori infection: a mathematical model

Helicobacter pylori infection of gastric tissue results in an immune response dominated by Th1 cytokines and has also been linked with dysregulation of Sonic Hedgehog (SHH) signaling pathway in gastric tissue. However, since interactions between the cytokines and SHH during H. pylori infection are not well understood, any mechanistic understanding achieved through interpretation of the statistical analysis of experimental results in the context of currently known circuit must be carefully scrutinized. Here, we use mathematical modeling aided by restraints of experimental data to evaluate the consistency between experimental results and temporal behavior of H. pylori activated cytokine circuit model. Statistical analysis of qPCR data from uninfected and H. pylori infected wild-type and parietal cell-specific SHH knockout (PC-SHH^KO) mice for day 7 and 180 indicate significant changes that suggest role of SHH in cytokine regulation. The experimentally observed changes are further investigated using a mathematical model that examines dynamic crosstalks among pro-inflammatory (IL1β, IL-12, IFNγ, MIP-2) cytokines, anti-inflammatory (IL-10) cytokines and SHH during H. pylori infection. Response analysis of the resulting model demonstrates that circuitry, as currently known, is inadequate for explaining of the experimental observations; suggesting the need for additional specific regulatory interactions. A key advantage of a computational model is the ability to propose putative circuit models for in-silico experimentation. We use this approach to propose a parsimonious model that incorporates crosstalks between NFĸB, SHH, IL-1β and IL-10, resulting in a feedback loop capable of exhibiting cyclic behavior. Separately, we show that analysis of an independent time-series GEO microarray data for IL-1β, IFNγ and IL-10 in mock and H. pylori infected mice further supports the proposed hypothesis that these cytokines may follow a cyclic trend. Predictions from the in-silico model provide useful insights for generating new hypothesis and design of subsequent experimental studies.

Control of cell growth, division and death: information processing in living cells

By way of surface receptor molecules and internal surveillance mechanisms, the living cell receives information about its external environment and internal state. In light of this information, the cell must determine its most appropriate course of action under the circumstances and initiate the relevant response pathways. Typical responses include growth and division, sexual reproduction, movement, differentiation and programmed cell death. Similar to a digital computer that uses bistable electrical switches to store and process information, the living cell uses bistable biochemical switches to implement its decision-making capabilities. In this review article, we describe some of the lines of thought that led, over the last 50 years, to our current understanding of cellular information processing, particularly related to cell growth, division and death.

Modelling the effect of GRP78 on anti-oestrogen sensitivity and resistance in breast cancer

Understanding the origins of resistance to anti-oestrogen drugs is of critical importance to many breast cancer patients. Recent experiments show that knockdown of GRP78, a key gene in the unfolded protein response (UPR), can re-sensitize resistant cells to anti-oestrogens, and overexpression of GRP78 in sensitive cells can cause them to become resistant. These results appear to arise from the operation and interaction of three cellular systems: the UPR, autophagy and apoptosis. To determine whether our current mechanistic understanding of these systems is sufficient to explain the experimental results, we built a mathematical model of the three systems and their interactions. We show that the model is capable of reproducing previously published experimental results and some new data gathered specifically for this paper. The model provides us with a tool to better understand the interactions that bring about anti-oestrogen resistance and the effects of GRP78 on both sensitive and resistant breast cancer cells.

A plausible model for bimodal p53 switch in DNA damage response

p53 is a tumor suppressor and the p53 dynamics displays stimulus dependent patterns. Recent evidence suggests a bimodal p53 switch in cell fate decision. However, no theoretical studies have been proposed to investigate bimodal p53 induction. Here we constructed a model and showed that MDM2-p53 mRNA binding might contribute to bimodal p53 switch through an intrinsic positive feedback loop. Lower damage favored pulsing while monotonic increasing was generated with higher damage. Bimodal p53 dynamics was largely influenced by cellular MDM2 and elevated p53/MDM2 ratios with increasing etoposide favor mono-ubiquitination. Our model replicated recent experiments and provided potential insights into dynamic mechanisms of bimodal switch.

Towards an integrated systems-based modelling framework for drug transport and its effect on tumour cells

Background

A systematic understanding of chemotherapeutic influence on solid tumours is highly challenging and complex as it encompasses the interplay of phenomena occurring at multiple scales. It is desirable to have a multiscale systems framework capable of disentangling the individual roles of multiple contributing factors, such as transport and extracellular factors, and purely intracellular factors, as well as the interactions among these factors. Based on a recently developed systems-based modelling framework, we have developed a coupled system in order to further elucidate the role of drug transport, and its interplay with cellular signalling by incorporating intra- and extra-vascular drug transport in tumour, dynamic descriptions of intracellular signalling and tumour cell density dynamics.

Results

Different aspects of the interaction between transport and cell signalling and the effects of transport parameters have been investigated in silico. Limited drug penetration is found to be a major constraint in inducing drug effect; many aspects of the interaction of transport with cell signalling are independent of the details of cell signalling. A sensitivity analysis indicates that the effect of drug diffusivity depends on the balance between interstitial drug transport and the specific requirement for triggering apoptosis (governed by highly nonlinear signalling networks), suggesting that the effect of drug diffusivity in such cases must be considered in conjunction with descriptions of cellular dynamics.

Conclusions

The modelling framework developed in this study provides qualitative and mechanistic insights into the effect of drug on tumour cells. It provides an in silico experimental platform to investigate the interplay between extracellular factors (e.g. transport) and intracellular factors. Such a platform is essential to understanding the individual and combined effects of transport and cellular factors in solid tumour.

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.

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.

A mathematical model of the unfolded protein stress response reveals the decision mechanism for recovery, adaptation and apoptosis

Background

The unfolded protein response (UPR) is a major signalling cascade acting in the quality control of protein folding in the endoplasmic reticulum (ER). The cascade is known to play an accessory role in a range of genetic and environmental disorders including neurodegenerative and cardiovascular diseases, diabetes and kidney diseases. The three major receptors of the ER stress involved with the UPR, i.e. IRE1 α, PERK and ATF6, signal through a complex web of pathways to convey an appropriate response. The emerging behaviour ranges from adaptive to maladaptive depending on the severity of unfolded protein accumulation in the ER; however, the decision mechanism for the switch and its timing have so far been poorly understood.

Results

Here, we propose a mechanism by which the UPR outcome switches between survival and death. We compose a mathematical model integrating the three signalling branches, and perform a comprehensive bifurcation analysis to investigate possible responses to stimuli. The analysis reveals three distinct states of behaviour, low, high and intermediate activity, associated with stress adaptation, tolerance, and the initiation of apoptosis. The decision to adapt or destruct can, therefore, be understood as a dynamic process where the balance between the stress and the folding capacity of the ER plays a pivotal role in managing the delivery of the most appropriate response. The model demonstrates for the first time that the UPR is capable of generating oscillations in translation attenuation and the apoptotic signals, and this is supplemented with a Bayesian sensitivity analysis identifying a set of parameters controlling this behaviour.

Conclusions

This work contributes largely to the understanding of one of the most ubiquitous signalling pathways involved in protein folding quality control in the metazoan ER. The insights gained have direct consequences on the management of many UPR-related diseases, revealing, in addition, an extended list of candidate disease modifiers. Demonstration of stress adaptation sheds light to how preconditioning might be beneficial in manifesting the UPR outcome to prevent untimely apoptosis, and paves the way to novel approaches for the treatment of many UPR-related conditions.

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.

Computational modeling of apoptotic signaling pathways induced by cisplatin

Background

Apoptosis is an essential property of all higher organisms that involves extremely complex signaling pathways. Mathematical modeling provides a rigorous integrative approach for analyzing and understanding such intricate biological systems.

Results

Here, we constructed a large-scale, literature-based model of apoptosis pathways responding to an external stimulus, cisplatin. Our model includes the key elements of three apoptotic pathways induced by cisplatin: death receptor-mediated, mitochondrial, and endoplasmic reticulum-stress pathways. We showed that cisplatin-induced apoptosis had dose- and time-dependent characteristics, and the level of apoptosis was saturated at higher concentrations of cisplatin. Simulated results demonstrated that the effect of the mitochondrial pathway on apoptosis was the strongest of the three pathways. The cross-talk effect among pathways accounted for approximately 25% of the total apoptosis level.

Conclusions

Using this model, we revealed a novel mechanism by which cisplatin induces dose-dependent cell death. Our finding that the level of apoptosis was affected by not only cisplatin concentration, but also by cross talk among pathways provides in silico evidence for a functional impact of system-level characteristics of signaling pathways on apoptosis.