Modeling dynamics of cell-to-cell variability in TRAIL-induced apoptosis explains fractional killing and predicts reversible resistance

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Stochastic chemical kinetics is a widely used formalism for studying stochasticity of chemical reactions inside single cells. Experimental studies of reaction networks are generally performed with cells that are part of a growing population, yet the population context is rarely taken into account when models are developed. Models that neglect the population context lose their validity whenever the studied system influences traits of cells that can be selected in the population, a property that naturally arises in the complex interplay between single-cell and population dynamics of cell fate decision systems. Here, we represent such systems as absorbing continuous-time Markov chains. We show that conditioning on non-absorption allows one to derive a modified master equation that tracks the time evolution of the expected population composition within a growing population. This allows us to derive consistent population dynamics models from a specification of the single-cell process. We use this approach to classify cell fate decision systems into two types that lead to different characteristic phases in emerging population dynamics. Subsequently, we deploy the gained insights to experimentally study a recurrent problem in biology: how to link plasmid copy number fluctuations and plasmid loss events inside single cells to growth of cell populations in dynamically changing environments.

Quantifying cancer cell plasticity with gene regulatory networks and single-cell dynamics

Phenotypic plasticity of cancer cells can lead to complex cell state dynamics during tumor progression and acquired resistance. Highly plastic stem-like states may be inherently drug-resistant. Moreover, cell state dynamics in response to therapy allow a tumor to evade treatment. In both scenarios, quantifying plasticity is essential for identifying high-plasticity states or elucidating transition paths between states. Currently, methods to quantify plasticity tend to focus on 1) quantification of quasi-potential based on the underlying gene regulatory network dynamics of the system; or 2) inference of cell potency based on trajectory inference or lineage tracing in single-cell dynamics. Here, we explore both of these approaches and associated computational tools. We then discuss implications of each approach to plasticity metrics, and relevance to cancer treatment strategies.

Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFβ-SMAD Signaling Pathway

Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFβ/SMAD signaling pathway.

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.

Using single-cell models to predict the functionality of synthetic circuits at the population scale

SignificanceAt the single-cell level, biochemical processes are inherently stochastic. For many natural systems, the resulting cell-to-cell variability is exploited by microbial populations. In synthetic biology, however, the interplay of cell-to-cell variability and population processes such as selection or growth often leads to circuits not functioning as predicted by simple models. Here we show how multiscale stochastic kinetic models that simultaneously track single-cell and population processes can be obtained based on an augmentation of the chemical master equation. These models enable us to quantitatively predict complex population dynamics of a yeast optogenetic differentiation system from a specification of the circuit's components and to demonstrate how cell-to-cell variability can be exploited to purposefully create unintuitive circuit functionality.

Two-level modeling approach to identify the regulatory dynamics capturing drug response heterogeneity in single-cells

Single-cell multimodal technologies reveal the scales of cellular heterogeneity impairing cancer treatment, yet cell response dynamics remain largely underused to decipher the mechanisms of drug resistance they take part in. As the phenotypic heterogeneity of a clonal cell population informs on the capacity of each single-cell to recapitulate the whole range of observed behaviors, we developed a modeling approach utilizing single-cell response data to identify regulatory reactions driving population heterogeneity in drug response. Dynamic data of hundreds of HeLa cells treated with TNF-related apoptosis-inducing ligand (TRAIL) were used to characterize the fate-determining kinetic parameters of an apoptosis receptor reaction model. Selected reactions sets were augmented to incorporate a mechanism that leads to the separation of the opposing response phenotypes. Using a positive feedback loop motif to identify the reaction set, we show that caspase-8 is able to encapsulate high levels of heterogeneity by introducing a response delay and amplifying the initial differences arising from natural protein expression variability. Our approach enables the identification of fate-determining reactions that drive the population response heterogeneity, providing regulatory targets to curb the cell dynamics of drug resistance.

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.

Pattern formation during embryonic development and pathological tissue dynamics, such as cancer invasion, emerge from individual intercellular interactions. In order to study the impact of single cell dynamics and cell-cell interactions on tissue behaviour, one needs to develop space-time-dependent on- or off-lattice agent-based models (ABMs), which consider the behaviour of individual cells. However, classical on-lattice agent-based models also known as cellular automata fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. Here, we present the rule- and lattice-based BIO-LGCA modelling class which allows for (i) rigorous derivation of rules from biophysical laws and/or experimental data, (ii) mathematical analysis of collective migration, and (iii) computationally efficient simulations.

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

Modeling Variability in Populations of Cells Using Approximated Multivariate Distributions

We are interested in studying the evolution of large homogeneous populations of cells, where each cell is assumed to be composed of a group of biological players (species) whose dynamics is governed by a complex biological pathway, identical for all cells. Modeling the inherent variability of the species concentrations in different cells is crucial to understand the dynamics of the population. In this work, we focus on handling this variability by modeling each species by a random variable that evolves over time. This appealing approach runs into the curse of dimensionality since exactly representing a joint probability distribution involving a large set of random variables quickly becomes intractable as the number of variables grows. To make this approach amenable to biopathways, we explore different techniques to (i) approximate the exact joint distribution at a given time point, and (ii) to track its evolution as time elapses. We start with the problem of approximating the probability distribution of biological species in a population of cells at some given time point. Data come from different fine-grained models of biological pathways of increasing complexities, such as (perturbed) Ordinary Differential Equations (ODEs). Classical approximations rely on the strong and unrealistic assumption that variables/species are independent, or that they can be grouped into small independent clusters. We propose instead to use the Chow-Liu tree representation, based on overlapping clusters of two variables, which better captures correlations between variables. Our experiments show that the proposed approximation scheme is more accurate than existing ones to model probability distributions deriving from biopathways. Then we address the problem of tracking the dynamics of a population of cells, that is computing from an initial distribution the evolution of the (approximate) joint distribution of species over time, called the inference problem. We evaluate several approximate inference algorithms (e.g., [14] , [17] ) for coarse-grained abstractions [12], [16] of biological pathways. Using the Chow-Liu tree approximation, we develop a new inference algorithm which is very accurate according to the experiments we report, for a minimal computation overhead. Our implementation is available at https://codeocean.com/capsule/6491669/tree.

A systematic approach to decipher crosstalk in the p53 signaling pathway using single cell dynamics

The transcription factors NF-κB and p53 are key regulators in the genotoxic stress response and are critical for tumor development. Although there is ample evidence for interactions between both networks, a comprehensive understanding of the crosstalk is lacking. Here, we developed a systematic approach to identify potential interactions between the pathways. We perturbed NF-κB signaling by inhibiting IKK2, a critical regulator of NF-κB activity, and monitored the altered response of p53 to genotoxic stress using single cell time lapse microscopy. Fitting subpopulation-specific computational p53 models to this time-resolved single cell data allowed to reproduce in a quantitative manner signaling dynamics and cellular heterogeneity for the unperturbed and perturbed conditions. The approach enabled us to untangle the integrated effects of IKK/ NF-κB perturbation on p53 dynamics and thereby derive potential interactions between both networks. Intriguingly, we find that a simultaneous perturbation of multiple processes is necessary to explain the observed changes in the p53 response. Specifically, we show interference with the activation and degradation of p53 as well as the degradation of Mdm2. Our results highlight the importance of the crosstalk and its potential implications in p53-dependent cellular functions.

Cells can respond to external and internal inputs by transducing information to the nucleus where transcription factors initiate corresponding cellular responses. Cellular signaling is mediated by several pathways; molecular networks that can interact with each other, which alters signal processing and modulates cellular responses. As deregulated signaling can lead to the development of tumors it is important to understand not only how signaling pathways function but also the contribution of their interaction on the signaling dynamics. Here, we analyzed the interplay of the IKK/ NF-κB and p53 pathway, which are both critical for the cellular response to DNA damage and have been implicated in tumor development. To systematically identify interaction points between both pathways, we perturbed IKK/ NF-κB signaling and tracked the changes in the response of p53 to DNA damage. Using computational methods, we show that several reactions in the p53 pathway are simultaneously affected by NF-κB signaling and that this combined action is necessary to explain altered behaviour of the p53 pathway. Hence, our results provide new insights into the interplay between the NF-κB and p53 pathway and help to gain a more comprehensive understanding of the crosstalk.

Sample-based modeling reveals bidirectional interplay between cell cycle progression and extrinsic apoptosis

Apoptotic cell death can be initiated through the extrinsic and intrinsic signaling pathways. While cell cycle progression promotes the responsiveness to intrinsic apoptosis induced by genotoxic stress or spindle poisons, this has not yet been studied conclusively for extrinsic apoptosis. Here, we combined fluorescence-based time-lapse monitoring of cell cycle progression and cell death execution by long-term time-lapse microscopy with sampling-based mathematical modeling to study cell cycle dependency of TRAIL-induced extrinsic apoptosis in NCI-H460/geminin cells. In particular, we investigated the interaction of cell death timing and progression of cell cycle states. We not only found that TRAIL prolongs cycle progression, but in reverse also that cell cycle progression affects the kinetics of TRAIL-induced apoptosis: Cells exposed to TRAIL in G1 died significantly faster than cells stimulated in S/G2/M. The connection between cell cycle state and apoptosis progression was captured by developing a mathematical model, for which parameter estimation revealed that apoptosis progression decelerates in the second half of the cell cycle. Similar results were also obtained when studying HCT-116 cells. Our results therefore reject the null hypothesis of independence between cell cycle progression and extrinsic apoptosis and, supported by simulations and experiments of synchronized cell populations, suggest that unwanted escape from TRAIL-induced apoptosis can be reduced by enriching the fraction of cells in G1 phase. Besides novel insight into the interrelation of cell cycle progression and extrinsic apoptosis signaling kinetics, our findings are therefore also relevant for optimizing future TRAIL-based treatment strategies.

Protein level variability determines phenotypic heterogeneity in proteotoxic stress response

Cell-to-cell variability in stress response is a bottleneck for the construction of accurate and predictive models which could guide clinical diagnosis and treatment of certain diseases, for example, cancer. Indeed, such phenotypic heterogeneity can lead to fractional killing and persistence of a subpopulation of cells which are resistant to a given treatment. The heat shock response network plays a major role in protecting the proteome against several types of injuries. Here, we combine high-throughput measurements and mathematical modeling to unveil the molecular origin of the phenotypic variability in the heat shock response network. Although the mean response coincides with known biochemical measurements, we found a surprisingly broad diversity in single-cell dynamics with a continuum of response amplitudes and temporal shapes for several stimulus strengths. We theoretically predict that the broad phenotypic heterogeneity is due to network ultrasensitivity together with variations in the expression level of chaperones controlled by the transcription factor heat shock factor 1. Furthermore, we experimentally confirm this prediction by mapping the response amplitude to chaperone and heat shock factor 1 expression levels.

Stochastic fluctuations in apoptotic threshold of tumour cells can enhance apoptosis and combat fractional killing

Fractional killing, which is a significant impediment to successful chemotherapy, is observed even in a population of genetically identical cancer cells exposed to apoptosis-inducing agents. This phenomenon arises not from genetic mutation but from cell-to-cell variation in the activation timing and level of the proteins that regulates apoptosis. To understand the mechanism behind the phenomenon, we formulate complex fractional killing processes as a first-passage time (FPT) problem with a stochastically fluctuating boundary. Analytical calculations are performed for the FPT distribution in a toy model of stochastic p53 gene expression, where the cancer cell is killed only when the p53 expression level crosses an active apoptotic threshold. Counterintuitively, we find that threshold fluctuations can effectively enhance cellular killing by significantly decreasing the mean time that the p53 protein reaches the threshold level for the first time. Moreover, faster fluctuations lead to the killing of more cells. These qualitative results imply that fluctuations in threshold are a non-negligible stochastic source, and can be taken as a strategy for combating fractional killing of cancer cells.

TRAIL-induced variation of cell signaling states provides nonheritable resistance to apoptosis

TNFα-related apoptosis-inducing ligand (TRAIL), specifically initiates programmed cell death, but often fails to eradicate all cells, making it an ineffective therapy for cancer. This fractional killing is linked to cellular variation that bulk assays cannot capture. Here, we quantify the diversity in cellular signaling responses to TRAIL, linking it to apoptotic frequency across numerous cell systems with single-cell mass cytometry (CyTOF). Although all cells respond to TRAIL, a variable fraction persists without apoptotic progression. This cell-specific behavior is nonheritable where both the TRAIL-induced signaling responses and frequency of apoptotic resistance remain unaffected by prior exposure. The diversity of signaling states upon exposure is correlated to TRAIL resistance. Concomitantly, constricting the variation in signaling response with kinase inhibitors proportionally decreases TRAIL resistance. Simultaneously, TRAIL-induced de novo translation in resistant cells, when blocked by cycloheximide, abrogated all TRAIL resistance. This work highlights how cell signaling diversity, and subsequent translation response, relates to nonheritable fractional escape from TRAIL-induced apoptosis. This refined view of TRAIL resistance provides new avenues to study death ligands in general.

Drugs modulating stochastic gene expression affect the erythroid differentiation process

To better understand the mechanisms behind cells decision-making to differentiate, we assessed the influence of stochastic gene expression (SGE) modulation on the erythroid differentiation process. It has been suggested that stochastic gene expression has a role in cell fate decision-making which is revealed by single-cell analyses but studies dedicated to demonstrate the consistency of this link are still lacking. Recent observations showed that SGE significantly increased during differentiation and a few showed that an increase of the level of SGE is accompanied by an increase in the differentiation process. However, a consistent relation in both increasing and decreasing directions has never been shown in the same cellular system. Such demonstration would require to be able to experimentally manipulate simultaneously the level of SGE and cell differentiation in order to observe if cell behavior matches with the current theory. We identified three drugs that modulate SGE in primary erythroid progenitor cells. Both Artemisinin and Indomethacin decreased SGE and reduced the amount of differentiated cells. On the contrary, a third component called MB-3 simultaneously increased the level of SGE and the amount of differentiated cells. We then used a dynamical modelling approach which confirmed that differentiation rates were indeed affected by the drug treatment. Using single-cell analysis and modeling tools, we provide experimental evidence that, in a physiologically relevant cellular system, SGE is linked to differentiation.

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.

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.

Systems Biology Approaches Toward Understanding Primary Mitochondrial Diseases

Primary mitochondrial diseases form one of the most common and severe groups of genetic disease, with a birth prevalence of at least 1 in 5000. These disorders are multi-genic and multi-phenotypic (even within the same gene defect) and span the entire age range from prenatal to late adult onset. Mitochondrial disease typically affects one or multiple high-energy demanding organs, and is frequently fatal in early life. Unfortunately, to date there are no known curative therapies, mostly owing to the rarity and heterogeneity of individual mitochondrial diseases, leading to diagnostic odysseys and difficulties in clinical trial design. This review aims to discuss recent advances and challenges of systems approaches for the study of primary mitochondrial diseases. Although there has been an explosion in the generation of omics data, few studies have progressed toward the integration of multiple levels of omics. It is evident that the integration of different types of data to create a more complete representation of biology remains challenging, perhaps due to the scarcity of available integrative tools and the complexity inherent in their use. In addition, "bottom-up" systems approaches have been adopted for use in the iterative cycle of systems biology: from data generation to model prediction and validation. Primary mitochondrial diseases, owing to their complex nature, will most likely benefit from a multidisciplinary approach encompassing clinical, molecular and computational studies integrated together by systems biology to elucidate underlying pathomechanisms for better diagnostics and therapeutic discovery. Just as next generation sequencing has rapidly increased diagnostic rates from approximately 5% up to 60% over two decades, more recent advancing technologies are encouraging; the generation of multi-omics, the integration of multiple types of data, and the ability to predict perturbations will, ultimately, be translated into improved patient care.

Hidden heterogeneity and circadian-controlled cell fate inferred from single cell lineages

The origin of lineage correlations among single cells and the extent of heterogeneity in their intermitotic times (IMT) and apoptosis times (AT) remain incompletely understood. Here we developed single cell lineage-tracking experiments and computational algorithms to uncover correlations and heterogeneity in the IMT and AT of a colon cancer cell line before and during cisplatin treatment. These correlations could not be explained using simple protein production/degradation models. Sister cell fates were similar regardless of whether they divided before or after cisplatin administration and did not arise from proximity-related factors, suggesting fate determination early in a cell's lifetime. Based on these findings, we developed a theoretical model explaining how the observed correlation structure can arise from oscillatory mechanisms underlying cell fate control. Our model recapitulated the data only with very specific oscillation periods that fit measured circadian rhythms, thereby suggesting an important role of the circadian clock in controlling cellular fates.

Quantitative single cell analysis uncovers the life/death decision in CD95 network

CD95/Fas/APO-1 is a member of the death receptor family that triggers apoptotic and anti-apoptotic responses in particular, NF-κB. These responses are characterized by a strong heterogeneity within a population of cells. To determine how the cell decides between life and death we developed a computational model supported by imaging flow cytometry analysis of CD95 signaling. Here we show that CD95 stimulation leads to the induction of caspase and NF-κB pathways simultaneously in one cell. The related life/death decision strictly depends on cell-to-cell variability in the formation of the death-inducing complex (DISC) on one side (extrinsic noise) vs. stochastic gene expression of the NF-κB pathway on the other side (intrinsic noise). Moreover, our analysis has uncovered that the stochasticity in apoptosis and NF-kB pathways leads not only to survival or death of a cell, but also causes a third type of response to CD95 stimulation that we termed ambivalent response. Cells in the ambivalent state can undergo cell death or survive which was subsequently validated by experiments. Taken together, we have uncovered how these two competing pathways control the fate of a cell, which in turn plays an important role for development of anti-cancer therapies.

Activation of death receptor (DR) family has been reported to activate both apoptotic as well as anti-apoptotic responses. Molecular mechanisms underlying the intricate details of this crosstalk have not been established yet. Here we show that these pathways are triggered simultaneously in one cell. Furthermore, using stochastic computational modeling we uncovered how an individual cell undergoes apoptosis, while other cells survive upon the same DR activation conditions. This was only possible by combination of computational modeling supported by experimental validation based on the state of the art single cell analysis. The latter included cutting edge technology of imaging flow cytometry, which combines microscopy and flow cytometry in one measurement circuit enabling quantitative analysis of endogenous cellular protein levels estimated from a large number of cells simultaneously. This allowed to shed the light on the question how a single cell possibly avoids apoptosis, which is a highly actual topic in the field of cancer research and development of efficient anti-cancer therapies.

Abstracting the dynamics of biological pathways using information theory: a case study of apoptosis pathway

Motivation

Quantitative models are increasingly used in systems biology. Usually, these quantitative models involve many molecular species and their associated reactions. When simulating a tissue with thousands of cells, using these large models becomes computationally and time limiting.

Results

In this paper, we propose to construct abstractions using information theory notions. Entropy is used to discretize the state space and mutual information is used to select a subset of all original variables and their mutual dependencies. We apply our method to an hybrid model of TRAIL-induced apoptosis in HeLa cell. Our abstraction, represented as a Dynamic Bayesian Network (DBN), reduces the number of variables from 92 to 10, and accelerates numerical simulation by an order of magnitude, yet preserving essential features of cell death time distributions.

Availability and Implementation

This approach is implemented in the tool DBNizer, freely available at http://perso.crans.org/genest/DBNizer .

Contact

gregory.batt@inria.fr or bgenest@irisa.fr.

Supplementary information

Supplementary data are available at Bioinformatics online.

The impact of non-genetic heterogeneity on cancer cell death

The goal of cancer chemotherapy is to induce homogeneous cell death within the population of targeted cancer cells. However, no two cells are exactly alike at the molecular level, and sensitivity to drug-induced cell death, therefore, varies within a population. Genetic alterations can contribute to this variability and lead to selection for drug resistant clones. However, there is a growing appreciation for the role of non-genetic variation in producing drug-tolerant cellular states that exhibit reduced sensitivity to cell death for extended periods of time, from hours to weeks. These cellular states may result from individual variation in epigenetics, gene expression, metabolism, and other processes that impact drug mechanism of action or the execution of cell death. Such population-level non-genetic heterogeneity may contribute to treatment failure and provide a cellular "substrate" for the emergence of genetic alterations that confer frank drug resistance.

Mitochondrial levels determine variability in cell death by modulating apoptotic gene expression

Fractional killing is the main cause of tumour resistance to chemotherapy. This phenomenon is observed even in genetically identical cancer cells in homogeneous microenvironments. To understand this variable resistance, here we investigate the individual responses to TRAIL in a clonal population of HeLa cells using live-cell microscopy and computational modelling. We show that the cellular mitochondrial content determines the apoptotic fate and modulates the time to death, cells with higher mitochondrial content are more prone to die. We find that all apoptotic protein levels are modulated by the mitochondrial content. Modelling the apoptotic network, we demonstrate that these correlations, and especially the differential control of anti- and pro-apoptotic protein pairs, confer mitochondria a powerful discriminatory capacity of apoptotic fate. We find a similar correlation between the mitochondria and apoptotic proteins in colon cancer biopsies. Our results reveal a different role of mitochondria in apoptosis as the global regulator of apoptotic protein expression.

It is unclear what causes variation in cell death in response to chemotherapy. Here, the authors show that cellular mitochondrial content modulates apoptotic protein levels, which in turn regulates response to agents such as TRAIL.

Epigenetic and Transcriptional Variability Shape Phenotypic Plasticity

Epigenetic and transcriptional variability contribute to the vast diversity of cellular and organismal phenotypes and are key in human health and disease. In this review, we describe different types, sources, and determinants of epigenetic and transcriptional variability, enabling cells and organisms to adapt and evolve to a changing environment. We highlight the latest research and hypotheses on how chromatin structure and the epigenome influence gene expression variability. Further, we provide an overview of challenges in the analysis of biological variability. An improved understanding of the molecular mechanisms underlying epigenetic and transcriptional variability, at both the intra- and inter-individual level, provides great opportunity for disease prevention, better therapeutic approaches, and personalized medicine.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

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.

Integrating network reconstruction with mechanistic modeling to predict cancer therapies

Signal transduction networks are often rewired in cancer cells. Identifying these alterations will enable more effective cancer treatment. We developed a computational framework that can identify, reconstruct, and mechanistically model these rewired networks from noisy and incomplete perturbation response data and then predict potential targets for intervention. As a proof of principle, we analyzed a perturbation data set targeting epidermal growth factor receptor (EGFR) and insulin-like growth factor 1 receptor (IGF1R) pathways in a panel of colorectal cancer cells. Our computational approach predicted cell line-specific network rewiring. In particular, feedback inhibition of insulin receptor substrate 1 (IRS1) by the kinase p70S6K was predicted to confer resistance to EGFR inhibition, suggesting that disrupting this feedback may restore sensitivity to EGFR inhibitors in colorectal cancer cells. We experimentally validated this prediction with colorectal cancer cell lines in culture and in a zebrafish (Danio rerio) xenograft model.

The role of stochastic gene switching in determining the pharmacodynamics of certain drugs: basic mechanisms

In this paper we analyze the impact of the stochastic fluctuation of genes between their ON and OFF states on the pharmacodynamics of a potentially large class of drugs. We focus on basic mechanisms underlying the onset of in vitro experimental dose-response curves, by investigating two elementary molecular circuits. Both circuits consist in the transcription of a gene and in the successive translation into the corresponding protein. Whereas in the first the activation/deactivation rates of the single gene copy are constant, in the second the protein, now a transcription factor, amplifies the deactivation rate, so introducing a negative feedback. The drug is assumed to enhance the elimination of the protein, and in both cases the success of therapy is assured by keeping the level of the given protein under a threshold for a fixed time. Our numerical simulations suggests that the gene switching plays a primary role in determining the sigmoidal shape of dose-response curves. Moreover, the simulations show interesting phenomena related to the magnitude of the average gene switching time and to the drug concentration. In particular, for slow gene switching a significant fraction of cells can respond also in the absence of drug or with drug concentrations insufficient for the response in a deterministic setting. For higher drug concentrations, the non-responding fraction exhibits a maximum at intermediate values of the gene switching rates. For fast gene switching, instead, the stochastic prediction follows the prediction of the deterministic approximation, with all the cells responding or non-responding according to the drug dose.

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

BACKGROUND

Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level.

SCOPE OF REVIEW

We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies.

MAJOR CONCLUSIONS

Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies.

GENERAL SIGNIFICANCE

Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a variety of settings where the network might operate. These settings are representative of distinct cellular types, abundance of transcription factors and ratio between gene switching and protein synthesis rates. By investigating noise-induced transitions among the different network operative states, our results suggest that gene switching rates are key parameters to shape network response to external perturbations, and that such response depends on the particular biological setting, i.e. the characteristic time scales and protein abundance. These results might have implications on our understanding of irreversible transitions for noise-related phenomena such as cellular differentiation. In addition these evidences suggest to adopt the appropriate mathematical model of the network in order to analyze the system consistently to the reference biological setting.

What Population Reveals about Individual Cell Identity: Single-Cell Parameter Estimation of Models of Gene Expression in Yeast

Significant cell-to-cell heterogeneity is ubiquitously observed in isogenic cell populations. Consequently, parameters of models of intracellular processes, usually fitted to population-averaged data, should rather be fitted to individual cells to obtain a population of models of similar but non-identical individuals. Here, we propose a quantitative modeling framework that attributes specific parameter values to single cells for a standard model of gene expression. We combine high quality single-cell measurements of the response of yeast cells to repeated hyperosmotic shocks and state-of-the-art statistical inference approaches for mixed-effects models to infer multidimensional parameter distributions describing the population, and then derive specific parameters for individual cells. The analysis of single-cell parameters shows that single-cell identity (e.g. gene expression dynamics, cell size, growth rate, mother-daughter relationships) is, at least partially, captured by the parameter values of gene expression models (e.g. rates of transcription, translation and degradation). Our approach shows how to use the rich information contained into longitudinal single-cell data to infer parameters that can faithfully represent single-cell identity.

Because of non-genetic variability, cells in an isogenic population respond differently to a same stimulation. Therefore, the mean behavior of a cell population does not generally correspond to the behavior of the mean cell, and more generally, neglecting cell-to-cell differences biases our quantitative representation and understanding of the functioning of cellular systems. Here we introduce a statistical inference approach allowing for the calibration of (a population of) single cell models, differing by their parameter values. It enables to view time-lapse microscopy data as many experiments performed on one cell rather than one experiment performed on many cells. By harnessing existing cell-to-cell differences, one can then learn how environmental cues affect (non-observed) intracellular processes. Our approach is generic and enables to exploit in unprecedented manner the high informative content of single-cell longitudinal data.

Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space

Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space.

Variation is function: Are single cell differences functionally important?: Testing the hypothesis that single cell variation is required for aggregate function

There is a growing appreciation of the extent of transcriptome variation across individual cells of the same cell type. While expression variation may be a byproduct of, for example, dynamic or homeostatic processes, here we consider whether single-cell molecular variation per se might be crucial for population-level function. Under this hypothesis, molecular variation indicates a diversity of hidden functional capacities within an ensemble of identical cells, and this functional diversity facilitates collective behavior that would be inaccessible to a homogenous population. In reviewing this topic, we explore possible functions that might be carried by a heterogeneous ensemble of cells; however, this question has proven difficult to test, both because methods to manipulate molecular variation are limited and because it is complicated to define, and measure, population-level function. We consider several possible methods to further pursue the hypothesis that variation is function through the use of comparative analysis and novel experimental techniques.

The Importance of Neighborhood Scheme Selection in Agent-based Tumor Growth Modeling

Modeling tumor growth has proven a very challenging problem, mainly due to the fact that tumors are highly complex systems that involve dynamic interactions spanning multiple scales both in time and space. The desire to describe interactions in various scales has given rise to modeling approaches that use both continuous and discrete variables, known as hybrid approaches. This work refers to a hybrid model on a 2D square lattice focusing on cell movement dynamics as they play an important role in tumor morphology, invasion and metastasis and are considered as indicators for the stage of malignancy used for early prognosis and effective treatment. Considering various distributions of the microenvironment, we explore how Neumann vs. Moore neighborhood schemes affects tumor growth and morphology. The results indicate that the importance of neighborhood selection is critical under specific conditions that include i) increased hapto/chemo-tactic coefficient, ii) a rugged microenvironment and iii) ECM degradation.

Surviving apoptosis: life-death signaling in single cells

Tissue development and homeostasis are regulated by opposing pro-survival and pro-death signals. An interesting feature of the Tumor Necrosis Factor (TNF) family of ligands is that they simultaneously activate opposing signals within a single cell via the same ligand-receptor complex. The magnitude of pro-death events such as caspase activation and pro-survival events such as Nuclear Factor (NF)-κB activation vary not only from one cell type to the next but also among individual cells of the same type due to intrinsic and extrinsic noise. The molecules involved in these pro-survival and/or pro-death pathways, and the different phenotypes that result from their activities, have been recently reviewed. Here we focus on the impact of cell-to-cell variability in the strength of these opposing signals on shaping cell fate decisions.