Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr

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That a statistical test for association between predictive scores and the binary classifications that they are used to predict is not significant at the 5% level does not mean that there is no valid or useful predictive relation between the scores and the classification. It only means that association may not be the best way to describe that relation. Figure 8.2 shows a direct plot of the fraction of chemicals classified by EPA as possible, probable, or likely rodent carcinogens against the predictive score (i.e., the count of the number of HTS assays considered positive, as previously discussed). Among 25 test set chemicals with scores less than 7, fewer than half (48%) are classified as rodent carcinogens. Among the remaining 8 chemicals, having scores of 7 or more, 100% are classified as rodent carcinogens. Thus, the score provides useful predictive information, although the relation is not smoothly increasing, and hence ordinal association measures may not be the best way to characterize it.

Fig 8.2. The fraction of chemicals classified as rodent carcinogens is 100% if and only if the predictive score (count of positive HTS assays) exceeds 6

In summary, rather than testing the significance of measures of ordinal association, an alternative, simple characterization of the predictive relation between HTS-derived scores and EPA classifications of the rodent carcinogenicity of these pesticides is that the pesticides with more than six “hits” (positive assays) are very likely to be classified as rodent carcinogens. This high-scoring fraction comprised 8/33, or just under 25%, of the test data set.

Predicting Cancer in Rodents, not Humans

Following Kleinstreuer et al., we have focused so far on predicting cancer hazard in rodents, not in humans. In developing their prediction model, Kleinstreuer et al. extracted information from ToxRefDB for chemicals with entries corresponding to preneoplastic and carcinogenic pathologies in mouse and rat. For mice, the data extracted corresponded to effects in mice classified as “liver preneoplastic”, “liver neoplastic”, “lung preneoplastic”, and “spleen preneoplastic” and in rats “kidney preneoplastic”, “liver preneoplastic”, “liver neoplastic”, “testes preneoplastic”, “testes neoplastic”, “thyroid preneoplastic”, and “thyroid neoplastic” (Kleinstreuer et al. 2013, Supplemental Table 1. However, mouse liver tumorigenesis often lacks relevance to human cancer risk, can occur at high background rates, or may havedose-response thresholdsand modes of action not relevant to human cancer (Maronpot, R.R. 2009. Toxicol. Pathol. 22:11-33). Likewise, thyroid lesions in rats, both preneoplastic and neoplastic, often result from mechanisms of little to no concern for human health due to well-recognized species differences in sensitivity and mechanisms which alter thyroid hormone homeostasis in the ratbut not in humans (Hill et al. 1998). Similarly, testicular preneoplastic and neoplastic lesions in rats are not be indicative of substantive cancer hazard to humans (Cook et al. 1999). Thus, the relevance of the predictive relation in Figure 2 for predicting human carcinogenicity remains an open question.

In determining potential cancer risk to humans, EPA seeks to integrate all of the relevant and reliable information, and to reachconclusionson potential hazards and risks to humans based on the knowledge of nature and incidence of the pathological responses, species specificity and sensitivity, and dose response. The predictive relation in Figure 2 includes substances as positive even when EPA concludes that the level of evidence does not indicate a “likely” or “sufficient” or “probable” cancer risk to humans. Appendix A examines carcinogen classifications from the standpoint of possible human relevance. It concludes that, of the rodent carcinogenicity classifications shown by Kleinstreuer et al. (2013)for 154 chemicals, 104 might be changed if the hazard classification were to be made more relevant to humans.
Discussion and Conclusions
Although we were able to replicate most of the data and results reported by Kleinstreuer et al. (2013), their key conclusions on predictive power of HTS data proved to be very sensitive to the uncertain classifications of two chemicals and to the choice of statistical methods.  The carcinogenic potential classifications for 2 of 60 chemicals differed from those in EPA/OPP published data (, and more recent data suggest reclassifying additional chemicals if the goal is to identify potential human carcinogens (Appendix A).  Moreover, the Mann-Whitney-Wilcoxon rank sum test used was not appropriate for the data due to many tied ranks.  Correcting these two chemical classifications and applying a test (Kendall tau-b) that correctly adjusts for ties, we found that the HTS-based cancer hazard scores no longer significantly predict in vivo cancer results.  A change of classification to a single chemical can change the original study conclusion, which is therefore not robust.  This outcome suggests a clear need for more robust predictions (e.g., based on application of current model ensemble machine learning methods) and highlights the potential value of using multiple subsets of training data to achieve predictive models and quantitative conclusions that are less sensitive to minor changes in chemical classifications and statistical methods.

A plausible reaction to the replication and reanalysis results presented here is that, even if the Kleinstreuer et al. results are not statistically significant at a conventional 0.05 significance level, the fact that they are statistically significant at the 0.10 level is still encouraging. In the reconstructed model we developed, we observed that chemicals with a score of 7 or more were all classified as rodent carcinogens (in the test set), but each chemical with a score of 0-6 had one or more chemicals that are not rodent carcinogens. Thus, the simple scoring system proposed by Kleinstreuer et al. appears to have genuine predictive power, although its predictions are strong only for scores of at least 7 (about 25% of the chemicals examined).

The generalizability of these results to other data sets (e.g., outside the EPA-OPP data sets used in this study) remains unknown, and the probable error rates for applications of the procedure to new chemicals have not been characterized. For developing models to predict human cancer hazard from HTS data and data extracted from ToxRefDB, or other similar databases of chemically-induced rodent histopathological responses, we posit that the overall weight of evidence determinations for human risks are key, and assay-endpoint combinations should not include rodent pathologies known to be of little or no relevance to humans.

The recent work by NCCT was presented as showing that “A simple scoring function built from these associated genes was significantly predictive of cancer hazard classifications for an external test set.” Figure 8.2 supports this description for the pesticides studied, especially the roughly 25% of them with score greater than 6. For the remaining chemicals, it is not clear that the scoring system can predict cancer hazard classifications well, consistent with the poor performance of previous systems in predicting rodent carcinogens in external validation studies (e.g., Valerio et al. 2010; Walmsley and Billinton 2011; Benigni and Zito, 2004; Snyder at al., 2004). We do not interpret these limitations as undermining the exciting program of research described by Kleinstreuer et al. (2013), but as showing that more (straight-forward) work needs to continue to be done to allow the results and predictive performance of these models be rigorously documented, thoroughly evaluated, and compared to the results of previous approaches across a wide range of chemicals.


Benigni R, Zito R.The second National Toxicology Program comparative exercise on the prediction of rodent carcinogenicity: definitive results.Mutat Res. 2004 Jan;566(1):49-63.

Cook et al. 1999. Crit Rev. Toxicol. 29:169-261

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Guyton KZ, Kyle AD, Aubrecht J, Cogliano VJ, Eastmond DA, Jackson M, Keshava N, Sandy MS, Sonawane B, Zhang L, Waters MD, Smith MT.

Improving prediction of chemical carcinogenicity by considering multiple mechanisms and applying toxicogenomic approaches.Mutat Res. 2009 Mar-Jun;681(2-3):230-40.

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Hill et al. 1998. Assessment of Thyroid Follicular Cell Tumors. EPA/630/R-97/002. MarchKirkland D, Aardema M, Henderson L, Müller L. Evaluation of the ability of a battery of three in vitro genotoxicity tests to discriminate rodent carcinogens and non-carcinogens I. Sensitivity, specificity and relative predictivity.Mutat Res. 2005 Jul 4;584(1-2):1-256. Erratum in: Mutat Res. 2005 Dec 7;588(1):70.

Kleinstreuer NC, Dix DJ, Houck KA, Kavlock RJ, Knudsen TB, Martin MT, Paul KB, Reif DM, Crofton KM, Hamilton K, Hunter R, Shah I, Judson RS. In vitro perturbations of targets in cancer hallmark processes predict rodent chemical carcinogenesis.Toxicol Sci. 2013 Jan;131(1):40-55.
Knight A, Bailey J, Balcombe J. Animal carcinogenicity studies: 1. Poor human predictivity.Altern Lab Anim. 2006 Feb;34(1):19-27.
Patlewicz G, Rodford R, Walker JD. Quantitative structure-activity relationships for predicting mutagenicity and carcinogenicity.Environ Toxicol Chem. 2003 Aug;22(8):1885-93.
Snyder RD, Pearl GS, Mandakas G, Choy WN, Goodsaid F, Rosenblum IY. Assessment of the sensitivity of the computational programs DEREK, TOPKAT, and MCASE in the prediction of the genotoxicity of pharmaceutical molecules.Environ Mol Mutagen. 2004;43(3):143-58. Erratum in: Environ Mol Mutagen. 2006 Apr;47(3):225.
Valerio LG Jr, Arvidson KB, Chanderbhan RF, Contrera JF. Prediction of rodent carcinogenic potential of naturally occurring chemicals in the human diet using high-throughput QSAR predictive modeling.Toxicol Appl Pharmacol. 2007 Jul 1;222(1):1-16.
Valerio LG Jr, Arvidson KB, Busta E, Minnier BL, Kruhlak NL, Benz RD.Testing computational toxicology models with phytochemicals.Mol Nutr Food Res. 2010 Feb;54(2):186-94. doi: 10.1002/mnfr.200900259.
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Chapter 9

Mechanistic Causality: Biological Mechanisms of Dose-Response Thresholds for Inflammation-Mediated Diseases Caused by Asbestos Fibers and Mineral Particles
As explained in Chapter 2, mechanistic causal models of how effects propagate through a system typically require more detailed information to build and validate than other forms of causal analysis, including predictive and attributive causal modeling. Substantial applied and computational mathematical research, modeling, and algorithm development is sometimes needed to describe with useful accuracy how a system evolves over time. On the other hand, mathematical analysis can also reveal robust qualitative properties of a system’s dynamic response to inputs. For example, many complex feedback control networks exhibit the qualitative property of bistability, in which a sufficiently long and intense stimulus or exogenous input causes the system to shift from its normal state to a new one with different properties that then becomes the new stable state of the system. Such stimulus-driven switches in behaviors occur frequently in biological regulatory networks and in other (e.g., socioeconomic) systems with positive feedback loops. This chapter considers the implications of recent advances in molecular biological understanding of the causal mechanisms of inflammation-mediated diseases for quantitative dose-response modeling. It focuses on the dynamic behavior of the NLRP3 (nucleotide-binding oligomerization domain-, leucine-rich repeat- and pyrin domain-containing) inflammasome, a signaling complex that is activated in response to sufficiently large exposures to potentially injurious agents including Staphylococcus aureus or Listeria monocytogenes bacteria, influenza and other viruses, radiation, asbestos fibers, and respirable crystalline silica (RCS) and that has been implicated in a host of inflammation-mediated diseases including asbestosis, fibrosis, mesothelioma, lung cancer, heart disease, gout, arthritis, and diabetes. Given this large and diverse array of agents and diseases for which NRLP3 provides a key to pathological responses, we will focus on how mineral particles and fibers such as asbestoscan activate the NRLP3 inflamasome and on the consequences for the shape of the dose-response relationship for inflammation-mediated responses to exposure.

Sufficiently high and prolonged inhalation exposures to some respirable elongated mineral particles (REMPs), notably including amphibole asbestos fibers, can increase risk of inflammation-mediated diseases including malignant mesothelioma, pleural diseases, fibrosis, and lung cancer. Although the molecular mechanisms of pathogenesis are still being elucidated, it is now clear that chronic inflammation sustained by ongoing activation of the NLRP3 inflammasome plays a crucial causal role, enabling immune cells to produce the potent proinflammatory cytokines IL-1 and IL-18. This insight, which has been developed in detail largely over the past decade, harmonizes with previous understanding that had identified upregulation of reactive oxygen species (ROS) as playing a central role in creating and maintaining a pro-inflammatory environment in these diseases and others, such as COPD. It is now understood that ROS (in particular, mitochondrial ROS) contributes to NRLP3 activation via a well-elucidated mechanism involving oxidation of reduced thioredoxin and association of thioredoxin-interacting protein with NLRP3, although the precise roles of ROS in the two-step priming and activation of NLRP3 are still being clarified. Lysosomal destabilization, efflux of cytosolic potassium ions and influx of calcium ions, signals from damaged mitochondria, both translational and post-translational controls, and prion-like polymerization have increasingly clear roles in regulating NLRP3 activation.

As the molecular biology of inflammation-mediated responses to REMP exposure becomes clearer, a practical question looms: What do these mechanisms imply for the shape of the dose-response function relating exposure concentrations and durations for EMPs of different shapes, sizes, and surface chemistries to the risk of pathological responses? For example, does increasing understanding of how REMP exposures affect the NLRP3 inflammasome have any clear implications for the existence of dose-response thresholds or threshold-like nonlinearities? How much knowledge must be accumulated before useful answers can be given to such questions? We propose that the partial understanding of NLRP3-mediated REMP effects available today is already sufficient to show that threshold-like dose-response nonlinearities should be expected. Biomathematical analysis of regulatory mechanisms and networks provides general conditions that lead to such thresholds; these include (a) Cooperativity in the assembly of supramolecular signaling complexes such as the inflammasome and apoptosome, leading to a characteristic all-or-nothing response; (b) Positive feedback loops in regulatory networks, leading to bistability in the network response; (c) Overwhelming or suppression of defensive barriers for maintaining homeostasis, such as IL-1-mediated suppression of antioxidant defenses; and (d) Damage thresholds below which responses are controlled and above which they are not, as in lysosome destabilization-induced activation of NLRP3. Each of these general classes of mechanisms for generating exposure-response thresholds is already known to hold for NLRP3 activation in response to stimuli such as REMP exposures. Moreover, some of them (such as bistability induced by positive feedback loops) are robust qualitative features of dose-response, insensitive to further details of the underlying biochemical mechanisms. It is therefore timely to start considering the implications of these advances in biological understanding for human health risk assessment with dose-response thresholds.

Understanding of the toxicological mechanisms of health risks caused by inhaling mineral particles, including respirable crystalline silica (RCS), elongated mineral particles (EMPs), and asbestos fibers, has been greatly advanced over the past decade by the discovery and gradual elucidation of the functioning of inflammasomes that coordinate inflammatory responses to inhalation exposures. It is plausible that the NLRP3 inflammasome plays a decisive role in initiation and progression of various inflammation-mediated diseases caused by such inhalation exposures, including silicosis, fibrosis, lung cancer, and malignant mesothelioma (Sayan and Mossman, 2016), as well as in diseases of other organs and organ systems, such as gout, acute myocardial infarction and inflammatory bowel disease (Veltman et al., 2017). However, these substantial advances in biological insights have yet to be matched by corresponding advances in understanding their implications for quantitative dose-response modeling, health risk assessment, and uncertainty characterization. This chapter examines the biomathematical implications for dose-response relations and health risks of what is now known about exposure-induced NLRP3 assembly and activation dynamics and subsequent disruptions of normal homeostasis resulting in chronic inflammation and increased risks of inflammation-mediated diseases. Crucial questions for dose-response modeling include the following:

  1. Is there an exposure concentration threshold below which adverse responses of interest do not occur?

  2. For any exposure concentration, is there an exposure duration threshold before which adverse responses of interest do not occur?

  3. If such thresholds exist, how large are they, and on what factors do they depend?

  4. What is the shape of the concentration-duration-risk relationship for exposures above the exposure concentrations and duration thresholds (if any)? How do physiochemical properties of inhaled materials and pharmacokinetic and biochemical parameters for exposed individuals affect the answer?

  5. How sure can we be about the answers to the preceding questions, and what information would most help to reduce remaining uncertainties?

To address these questions, the following sections examine biomathematical implications for dose-response relationships of currently known biochemistry and toxicology of NLRP3-mediated inflammation and disease processes.

Biological Background: NLRP3 Inflammasome Responses to Mineral Particles
Excellent reviews of the biology of the NLRP3 inflammasome and its roles in various inflammation- and immune system-mediated diseases are already available. Sayan and Mossman (2016) discuss NLRP3 inflammasome priming, activation, and signaling specifically for mineral particles. Figure 9.1 depicts a common contemporary view of the causal cascades that can trigger priming, assembly, and activation of this inflammasome in various cells, including monocytes, macrophages, dendritic cells, and human mesothelial cells (Thompson et al., 2017) in response to a variety of environmental triggers. In brief, exposures producing pathogen-associated molecular patterns (PAMPs) and danger-associated molecular patterns (DAMPs) trigger a signaling cascade (“Signal 1”) via phosphorylation of Toll-like receptors (TLRs) that stimulate NF-κB-mediated upregulation of nuclear transcription of the genes for NLRP3, proIL-1β, and proIL-18. These genes are translated into corresponding proteins that are released to the cytoplasm as inactive building blocks, thus “priming” the inflammasome by making these components available in the cytosol for assembly and activation. Priming also deubiquitinates the NLRP3 protein (via pathways that can involve mitochondrial ROS or ATP signaling), allowing it be activated.

Fig. 9.1 NLRP3 inflammasomes within a cell’s cytosol use active caspase-1 to cleave ProIL-1 and ProIL-18, forming mature inflammatory cytokines IL-1 and IL-18, in response to exposures to mineral particles and other stimuli.

Source: Shao et al., 2015. This picture is provided under the terms of the Creative Commons Attribution License (CC BY)
In macrophages and dendritic cells, the inflammasome is assembled and activated upon receipt of a second signal, denoted by “Signal 2” in Figure 9.1, that triggers oligomerization of its inactive NLRP3, apoptosis-associated speck-like protein (ASC), which is linearly ubiquitinated and phosphorylated in the process, and procaspase-1 components (Guo et al., 2015; Bednash and Mallampalli, 2016). (In monocytes, no second signal is needed (ibid).) These components (the “mers” or units in the oligomer) come together via oligomerization to form a fully assembled and active inflammasome. The Signal 2 that triggers this process typically involves calcium ion fluxes and K+ efflux (via a P2X7-dependent pore); PAMP- and DAMP-associated production of reactive oxygen species (ROS); mitochondrial damage and production of mitochondrial ROS (mtROS); or, most importantly for crystalline silica and asbestos fiber-induced diseases, frustrated phagocytosis of mineral particles leading to lysosomal membrane rupture and release of cathepsin B and other pro-inflammatory contents (Guo et al., 2015; Sayan and Mossman, 2016). In a positive feedback loop, cytoplasmic ROS and mitochondrial ROS stimulate translocation of thioredoxin-interacting protein (TXNIP) from the nucleus into the cytoplasm and mitochondria, where it binds to and inhibits the activity of the antioxidant thioredoxins TRX1 and TRX2, respectively, thus further elevating of cytoplasmic and mitochondrial ROS (Harijith et al., 2014).

Elevated ROS and molecules from ruptured lysosomes activate the primed NLRP3 inflammasomes in the cytoplasm, causing them to cleave the protective tails from ProIL-1 and ProIL-18 (using active caspase-1) to form mature inflammatory cytokines IL-1 and IL-18. These potent pro-inflammatory cytokines, in turn, act as signals stimulating and coordinating other inflammatory events in other cells, eventually leading to pyroptosis (i.e., inflammatory cell death) of the host cell, recruitment of activated macrophages and neutrophils, and chronic unresolved inflammation in the lung or other target tissues. NLRP3 protein nucleates growth of prion-like filaments of ASC, from which pro-caspase-1 filaments subsequently grow and become activated via autoproteolysis, generating active caspase-1 (Guo et al., 2015). Repeated and widespread cycles of epithelial cell injury and tissue damage, partial repair (eventually leading to fibrosis and scarring in the alveolar epithelium), and stimulated cell division and proliferation of progenitor cells can increase the risks of inflammation-mediated diseases and pathologies, including fibrosis, silicosis, asbestosis, lung cancer, and malignant mesothelioma.

We will refine this basic description of NLRP3 inflammasome biology later to emphasize the roles of several other positive feedback loops, but the version just described and depicted in Figure 1 suffices to understand the main steps where thresholds might arise in dose-response modeling. They are priming, assembly, activation, and signaling by the activated inflammasomes within and between cells.
Thresholds in NLRP3 priming: Receptor-mediated signal transduction and critical mass of NLRP3 protein required for activation
Receptor-mediated responses such as priming of the inflammasome typically exhibit thresholds or threshold-like nonlinearities if a sufficiently large (threshold) fraction of receptors must be simultaneously bound by a ligand to trigger a signaling cascade (Andersen et al., 2014). Lower ligand concentrations almost certainly fail to trigger a response, with probability near 1; concentrations that are higher trigger a response with probability close to 1; and the interval of concentrations that gives intermediate probabilities of triggering a response tends to be very short, corresponding to a “sharp transition” threshold in response probability (Cox, 2006; Wu, 2013). For example, for Toll-like receptor 4 (TLR4) ligand-activated signaling, Gottschalk et al., 2016 identify distinct thresholds for NF-κB and MAPK signaling activation in both mouse and human macrophages. Such thresholds protect the cell against responding to low levels of exposures (e.g., from endogenous bacteria) while allowing high levels to trigger inflammatory signaling.

The NRLP3 inflammasome cannot be assembled and activated until a sufficient quantity of the NRLP3 protein has accumulated in a cell’s cytosol (Bednash and Mallampalli, 2016). Accumulation of NRLP3 protein depends on a dynamic balance between its production, which is triggered by NF-κB signaling to the nucleus (Figure 1), and its inactivation or destruction. NRLP3 protein can be temporarily inactivated by ubiquitinization and then activated relatively rapidly via deubiquitinating enzymes (Py et al., 2013). Fully assembled NLRP3 inflammasomes are also removed by autophagy in autophagosomes formed in response to, and partly co-localized with, the inflammasomes (Shi et al., 2012). As NRLP3 protein accumulates, the threshold for signal 2 to trigger assembly and activation of the inflammasome decreases (Bednash and Mallampalli, 2016). Once a tipping point is reached in which the rate of production of active (deubiquitinated) protein has exceeded the rate of inactivation and removal for long enough for active NLRP3 protein levels to accumulate to a critical level, even low levels of signal 2 will result in NLRP3 inflammasome activation. Conversely, if the signals that stimulate NLRP3 protein production and deubiquitination are insufficiently strong and protracted to enable its accumulation to overwhelm the inactivation and degradation processes, then assembly and activation do not occur: priming fails to lead to activated NLRP3 inflammasomes. Thus, effective priming does not occur if exposure concentration and duration do not generate a large enough supply of deubiquitinated NLRP3 protein so that assembly and activation of NLRP3 inflammasomes can proceed (Bednash and Mallampalli, 2016). Exposures cannot cause NLRP3 inflammasome-mediated responses unless they are sufficiently high and sustained for such effective priming to be completed.

Thresholds for NLRP3 Assembly: Cooperativity in Oligomerization Kinetics
If exposure is sufficient for priming to occur and if further exposure generates signal 2 while the primed state lasts, then NLRP3 inflammasomes will begin to assemble via energetically favorable oligomerization. Several types of signaling complexes with multiple domains assembled into functional units (oligomers), including the apoptosome and the inflammasome, are formed via oligomerization exhibiting kinetic cooperativity: attachment of further units becomes progressively easier following initial nucleation and increasing availability of binding sites for additional units as the oligomerized array expands (Bagci et al., 2006; Wu, 2013). Wu (2013) emphasizes the importance of replacing a traditional view of signal transduction and “signalsome” assembly as a cascade of events (Figure 9.1) with a view in which large spatial arrays of oligomer components undergo these cascades side by side, in parallel, with the parallel cascades facilitating each other, leading to sharp transitions in the responses of cells to concentrations of signals that stimulate assembly of the oligomers. Figure 9.2 shows the mathematical implications (from the Hill equation in biochemistry or the equivalent Langmuir adsorption isotherm in surface chemistry) of increasing cooperativity in attachment of units to binding sites during parallel assembly of oligomers.
Figure 9.2. Cooperativity in oligomerization processes leads to sharp transitions in responses. N = Hill coefficient measuring cooperativity; a.u.= arbitrary units.

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Source: Wu (2013) (Reproduced with permission from Elsevier)
In the left panel, the “Dose” on the horizontal axis refers to concentration of a ligand (e.g., deubiquitinated NRLP3 protein) in arbitrary units (a.u.), scaled so that a dose of 5 is defined as the level that elicits 50% of the maximum response. Thus, all dose-response curves must pass through this point, which is fixed by definition. The “Response” on the vertical axis shows the fraction of the maximum response (e.g., maximum production of fully assembled oligomers) achieved. As cooperativity in oligomerization increases (indicated by increasing values of the Hill coefficient, N), the dose-response curves become steeper and increasingly threshold-like and the minimum concentration needed to elicit a significant positive response increases while the minimum dose needed to achieve maximum response decreases. The right panel shows that higher cooperativity also induces an increased time delay before the response departs significantly from zero, as initialization (successful nucleation) of the oligomerization process takes longer. These patterns are predicted to hold for assembly of signaling complexes – higher-order assemblies of oligomers consisting of intracellular adapters, signaling enzymes and their substrates – that can be well approximated by the Hill equation; the NLRP3 inflammasome is only one of many examples (Qiao and Wu, 2015). The threshold-like nonlinearities in concentration-response curves (left side of Figure 9.2) and in the time needed to respond significantly (right side of Figure 9.2) protect macrophages and other cells against continually responding to low-level stimuli.
Thresholds in NLRP3 Activation: Lysosome Disruption and ROS
Signal 2 is generated by several inter-linked processes involving mitochondrial damage, release of mitochondrial ROS (mtROS), increase in lysosomal membrane permeabilization (LMP), disruption of the lysosome, and release of lysosomal hydrolases, including cathepsins, to the cytosol (Figure 9.1); these events can trigger a cell death pathway (Boya and Kroemer, 2008; Repnik et al., 2014). Moreover, human monocytes sequester iron and use iron ions to activate the NLRP3 inflammasome (Nakamura et al., 2016). Studies of carbon nanotubes suggest that fiber geometry is important. Stiff fibers beyond a critical length poke against the inner leaflet of the soft lysosomal membrane, causing lysosomal permeabilization (Zhu et al., 2016). Despite this complexity, it is now clear that accumulation of protonated lysosomotropic agents above a concentration threshold triggers detergent-like disruption of the lysosomal membrane and that accumulation of iron in the lysosome – possibly accelerated by phagocytosis of mineral particles with iron ions available to participate in Fenton reactions – catalyzes ROS-induced disruption of its membrane (Boya and Kroemer, 2008; Schilling, 2016). Rupture of the lysosome membrane activates a MAPK signaling pathway that, in turn, contributes to activation of the NRLP3 inflammasome via oligomerization of its ASC component (Okada et al., 2014). Rupture of a membrane triggered by accumulation of destabilizing contents past a critical level is inherently a threshold-like response. In addition, LMP, ROS, and the NLRP3 inflammasome participate in several positive feedback loops. As discussed next, such loops can create threshold-like responses for the set of variables involved, even if none of them by itself has such a threshold-like response.

Thresholds in NLRP3 Signaling: Positive Feedback Loops and Bistability
A bistable dynamical system is one with two stable equilibrium states. Figure 9.3 illustrates bistability visually: the position of a ball, indicated by X, has stable local equilibria at both position 1 and position 3. Pushing the ball rightward from position 1 will eventually cause it to cross a threshold (position 2), leaving the basin of attraction for position 1 (to which it would otherwise have returned when the force was removed) and entering the basin of attraction for position 3, to which it will now spontaneously move in the absence of further exposure to the driving force. This is a visual metaphor for switch-like transition thresholds in bistable systems: sufficient exposure to an outside force that exogenously increases a variable eventually drives the system past a threshold and causes it to enter a new stable equilibrium with permanently increased levels of the variable.
Figure 9.3. Concept of a bistable system. A ball can be in stable equilibrium (a local minimum of the energy, E) in positions 1 or 3. Position 2 is an unstable equilibrium. For the NLRP3 inflammasome, the “position” variable X can be reinterpreted as ROS.

In biological systems and chemical reaction networks, bistability commonly arises from positive feedback loops among variables, and switch-like behavior generated by such loops is a common motif found in a wide variety of regulatory networks (e.g., Siegal-Gaskins et al., 2011; Chakravarty and Barik, 2017). That a system can have multiple equilibrium states is easily illustrated. Consider a system with two variables, x and y, with each increasing the level of the other, as follows:

dy/dt = x - y

dx/dt =y - 2xy

This pair of coupled ordinary differential equations (ODEs) states that y is formed at a rate proportional to the level of x and is removed at a rate proportional to its own level, where both rates are measured in units of y per unit time formed or removed. Likewise, x is formed at a rate proportional to y and is removed at a rate proportional to the product of x and y. In steady-state equilibrium, if one exists, dy/dt = dx/dt = 0, and so y = x (from the first equation) and the second equation then implies y = 2y2. The system has two possible equilibria: x = y = 0 and x = y = 0.5. Bistable systems have the additional feature that each of the two equilibrium states is locally stable, meaning that the system will return to it after small perturbations.

How bistability emerges from positive feedback loops is easy to see for a single feedback loop; Figure 9.4 sketches the main idea. Write the loop as a chain XY …. ZX with the same first and last variable. Now, imagine fixing the value of the first variable at some value and letting each variable in turn adjust to the new equilibrium value determined by its predecessor’s value (assuming that such an equilibrium value exists). A new value of X is determined by this equilibration process at the right end of the chain. From this perspective, each value of X supplied at the start of the chain determines a new value at the end of it. This relation can be described as Xt+1 = f(Xt) where t indexes iterations and f is a function mapping the starting value of X to its ending value by traversing the loop once, as just described. Equilibrium values of X are fixed points of this function, i.e., values such that X = f(X); starting from such a point, the iterative mapping leaves the value of unchanged. In biological systems, it is common for f to have a sigmoid shape, as illustrated in Figure 9.4. In this diagram, the horizontal axis consists of possible starting values for X; the vertical axis represents the next value of X, determined from the starting value by traversing the feedback loop once; the sigmoid function represents the feedback loop mapping f, and the line Xt+1 = Xt is the locus of possible equilibrium points. The left end of the function f is usually flat because one or more elements in the loop, possibly being stabilized by their own negative feedback networks, respond very little to small perturbations in low levels of X.

Figure 9.4. A bistable system has two stable equilibria (values X1 and X3) separated by an unstable one (X2).

The right end of f is flat because one or more variables is saturated: it has reached a maximum possible value, and the loop as a whole cannot be driven to higher levels of all its variables once any of them is saturated. Between these two regions, in which the next value of X is insensitive to the current value, is a region where the function f is increasing. Between X1 and X2, f lies below the equilibrium line, meaning that the next value of X is less than its starting value, and the system moves leftward, back toward the stable equilibrium X1. (The subscripts on X1, X2 and X3 denote specific values, not successive iterations.) Between X2 and X3, f lies above the equilibrium line, and the system moves rightward, toward the stable equilibrium X3. The tipping point, or threshold, separating the basins of attraction for these two equilibria is the unstable equilibrium point X2.

Interpretively, the bistability model in Figure 9.4 shows that there is a normal healthy equilibrium state, corresponding to X1, in which variables in the feedback loop are at their unperturbed levels. This is a locally stable state, maintained by homeostatic mechanisms, and hence is restored following small perturbations, such as after an exposure that is insufficiently high and prolonged to push the system past X2. However, exposures large enough to increase X past X2 induce a transition to a new, pathological state, X3, which is also stable. For example, if X represents ROS and is part of one or more positive feedback loops, then one or more high-ROS disease states may be reachable via sufficiently large exposure-related increases in ROS that will then remain stable, corresponding to a chronic inflammatory state. Unresolved chronic inflammation with persistently elevated levels of ROS, inflammasome activation, macrophage and neutrophil infiltration and activation, and proinflammatory cytokines can thus be viewed as a stable pathological equilibrium, analogous to X3 in Figure 9.4 (Cox, 2011). We shall add inflammasomes to this picture momentarily.

Many aspects of inflammation, including EMP-induced inflammation, are now known to involve positive feedback loops. Bistability has been noted for mitochondrial ROS production (Pereira et al., 2016);  IL-1β upregulation in response to TNFα in a model of inflammatory responses to influenza (Jin et al., 2014); cytokine network signaling and immune cell responses in cancer (Li and Levine, 2017); and bacterial infections (Malka et al., 2010). Both asbestos and erionite fibers prime and activate the NLRP3 inflammasome in human mesothelial cells via an autocrine feedback loop that passes through the IL-1R receptor (Hillegass et al., 2013). Table 9.1 summarizes multiple positive feedback loops identified for NLRP3 inflammasome activation, ROS generation, and signaling. In these diagrams, an arrow between two quantities means that an increase in the one at the arrow’s tail increases the one at its head. Each chain starts and ends with the same variable, indicating a positive feedback loop.
Table 9.1. Positive feedback loops for production of reactive oxygen species (ROS) and activation of the NLRP3 inflammasome


Description of positive feedback loop


ROS ® LMP ® lysosomal enzymes released ® phospholipase A2 activated ® mitochondrial outer membrane permeabilization (MOMP) ® ROS


LMP ® lysosomal enzymes released ® phospholipase A2 activated ® LMP


ROS ® thioredoxin-interacting protein (TXNIP) translocated from nucleus to cytoplasm and mitochondria ® antioxidant thioredoxins inhibited ® ROS (cytoplasmic and mitochondrial)


ROS ® NLRP3 activation ® IL-1, IL-18 ® inflammatory cytokines ® cell damage ® pyroptosis ® release of cell contents ® ROS


ROS ® NLRP3 activation ® DNA damage ® pyroptosis ® release of cell contents ® ROS


ROS ® decrease in antioxidants ® secretion of matrix metalloproteinase 12 (MMP-12) and neutrophil elastase (NE) ® neutrophil and macrophage recruitment and activation ® NE, ROS

Loops 1 and 2 are discussed in more detail by Boya and Kroemer (2008). Harijith et al. (2014) provide details of loops 3-5 and Cox (2011) discusses the neutrophil and macrophage loops summarized in loop 6.

The individual feedback loops in Table 9.1 clearly intersect with each other, forming a network of overlapping positive feedback loops. A fuller picture of the cytokine signaling network and immune cell population responses (such as recruitment and activation of macrophages and neutrophils, cross-talk with T cells, activation and eventual depletion or overwhelming of additional antioxidant defenses, and so forth) would be far more complex than these few feedback loops and would include negative feedback loops that attempt to maintain healthy homeostasis (Cox, 2011). However, the existence and prominence of positive feedback loops is consonant with the existence of observed bistable (or multistable) dose-response relationships in which sustained high exposures eventually overcome stabilizing loops or reservoirs (e.g., reducing active antioxidant production and depleting antioxidant pools) and shift the immune network from a normal low-ROS healthy state to a pathological high-ROS chronic inflammation state, accompanied by increases in the variables in loops 1-6 that increase, and are increased by, ROS. This includes priming and activation of NLRP3 inflammasomes in loops 4 and 5.
From Cells to Tissues: Percolation Thresholds for Spread of Inflammation
Activation of NLRP3 inflammasomes, secretion of inflammatory cytokines, induction of a high-ROS state, and apoptosis or pyroptosis are all normal parts of acute inflammation, e.g., in response to bacterial infections. They do not normally cause the previously mentioned diseases associated with chronic inflammation. What determines whether inflammation resolves itself, subsiding back into homeostasis, or progresses to pathological chronic inflammation and increased risks of diseases? Bistability is likely an important part of the answer. As suggested by the ball metaphor in Figure 9.3, exposure must be large enough for long enough to move the system from its normal homeostatic basin of attraction past the unstable equilibrium threshold and into the pathological basin of attraction in order to create chronic inflammation as a new equilibrium. The positive feedback loops in Table 9.1 add detail to this metaphor by specifying variables such as ROS, events such as NLRP3 activation, processes such as pyroptosis, and conditions such as LMP that are involved in the shift between basins of attraction. However, they are still rather abstract, leaving aside details such as which specific cell populations (e.g., monocytes, macrophages, dendritic cells, alveolar epithelial cells, mesothelial cells, and so forth) are involved in each change, and how strongly. Further information about specific exposures and responses can be added within the framework when it is available. For example, the recent discovery that crocidolite asbestos fibers oxidize Thioredoxin-1 (Trx1), releasing TXNI and activating inflammasomes in human mesothelial cells (Thompson et al., 2014) shows that feedback loop 3 in Table 9.1, and other loops that it activates, are relevant for crocidolite asbestos exposures. However, the feedback loops and mechanisms of NLRP3 priming, assembly, activation, and signaling discussed so far have focused primarily on events within individual cells and their compartments, especially the nucleus, cytosol, mitochondria, and lysosome. It is useful to also consider how inflammation spreads between cells.

Intracellular spread of inflammation and ROS activation is facilitated by the release of NLRP3 inflammasomes into extracellular spaces following pyroptosis. The released inflammasomes continue to broadcast inflammatory cytokines and act as danger signals to neighboring cells, which may then mount their own inflammasome-mediated defense if the signaling is strong enough and lasts long enough (Baroja-Mazo et al., 2014). Inflammation also spreads among neighboring cells via prion-like propagation mediated by release and subsequent uptake of ASC specks (Franklin et al., 2014). In extracellular space, these specks continue to promote IL-1 maturation, which increases inflammatory cytokine signaling to nearby cells. In addition, when phagocytized by macrophages, the previously released ASC specks induce lysosomal damage, nucleation of ASC oligomerization and fiber growth, and IL-1 activation in the macrophages, initiating a new round of inflammatory responses in these new cells (Franklin et al., 2014). For the population of cells, this leads to a further positive feedback loop:

pyroptosis of inflamed macrophage  NLRP3 inflammasome and ASC speck release into extracellular space  NLRP3 inflammasome and ASC signaling, IL-1 activation in extracellular space  uptake of ASC speck by new macrophage  inflammation of new macrophage  pyroptosis of inflamed macrophage

This loop has an important spatial component, as it takes place within a volume of tissue where cell populations, recruited immune cells, and NLRP3 inflammasomes and ASC specks in extracellular space interact. Moreover, there is considerable heterogeneity in the responses of cells within the same local volume of tissue. Being surrounded by other cells undergoing inflammation and pyroptosis increases the probability that a cell will also succumb to them, but not all cells respond the same, suggesting that the spread of inflammation can best be regarded as a spatial stochastic process, somewhat analogous to the spread of a forest fire through a population of heterogeneous trees. For such a spatial stochastic process, the question of how widely an initially localized inflammation will spread through the affected tissue (analogous to how far a forest fire will spread if an edge or area is initially ignited) can be addressed using stochastic percolation models (Guisoni et al., 2011; Squires et al., 2013). Such models consider the conditional probability that a cell will become inflamed (or, in our context, undergo pyroptosis) if its neighbors do. A common finding is that there is a percolation threshold for this conditional probability: above the percolation threshold, the inflammation spreads throughout the available area or volume where these strong dependencies hold, and below it, the inflammation is self-limiting and spreads only a finite distance before dying out. We conjecture that percolation models, thresholds, and phase transitions will prove to be useful for describing the spread of NLRP3-mediated inflammation through affected tissue, but this is currently only a conjecture.

Discussion and Conclusions
The previous sections have outlined several different general mechanisms that can create exposure-response relationships with thresholds or threshold-like nonlinearities, meaning S-shaped exposure concentration-response or duration-response functions with a sharp transition from the low to the high levels. Table 9.2 summarizes these mechanisms. Most of them are now known to apply to the assembly, priming, activation, and signaling of the NLRP3 inflammasome, although percolation thresholds for the spread of inflammation are currently speculative. Bistability based on positive feedback loop motifs is plausible both within EMP-exposed target cells (specifically including monocytes, macrophages, and mesothelial cells) and also in the wider cytokine signaling and immune cell population response and cross-talk causal networks to which they belong (see Table 1). As summarized in Table 9.3, current knowledge strongly suggests that NLRP3 inflammasome-mediated responses to EMP and other (e.g., bacterial) exposures have exposure concentration and duration thresholds below which they do not occur. This is because relevant events do not occur unless exposure concentration is kept sufficiently high for sufficiently long to deplete or overwhelm protective resources such as antioxidant pools. Events with threshold-like response characteristics probably include assembly, priming, and activation of the NLRP3 inflammasome, involving initiation and completion of oligomerization and activation of ACS and NLRP3 proteins and accumulation of intralysosomal, mitochondrial, and cytosolic levels of key factors such as ROS to levels needed to generate System 2; activation of feedback loops; and transition from the low-ROS to the high-ROS state.

Table 9.2. Summary of five general mechanisms for exposure-response thresholds

Threshold mechanism

Main idea

Examples for NLRP3 inflammasome

Receptor-mediated signal transduction

Probability of activation switches from near 0 to near 1 as concentration crosses a threshold

  • NF-κB- signaling to -regulate NLRP3 transcription

Critical mass or concentration is required to trigger an event

Response occurs only if and when accumulated amount or concentration in a compartment reaches a critical point

  • Rupture of lysosome by accumulated intra-lysosomal ROS or other agents

  • NLRP3 priming and assembly of NLRP3 inflammasome require a threshold level of deubiquitinated NLRP3 protein to accumulate

Cooperativity in oligomerization

High cooperativity (Hill coefficient) in oligomerization creates threshold-like concentration-response and a time delay for response (see Figure 2)

  • Exposure concentration threshold for triggering assembly of NLRP3 inflammasome via oligomerization

  • Exposure duration threshold for triggering assembly of NLRP3 inflammasome via oligomerization

Bistability in networks with positive feedback loops

Sufficiently high and prolonged exposures shift move system with positive feedback loops to a new, stable chronic inflammation equilibrium (see Figures 3 and 4)

  • Positive feedback loops for ROS and NLRP3 inflammasome (see Table 1)

Percolation thresholds in spatial stochastic propagation processes

Spread of inflammation throughout a volume of tissue requires that the probability that a cell will become inflamed if its neighbors are must exceed a critical percolation threshold value

  • Prion-like transmission of inflammation among cells via ASC specks released upon pyroptosis has been identified, but percolation thresholds and phase transitions for tissue inflammation are currently only conjectured here.

Much biochemical detail can and should be added to the framework outlined in Tables 9.1-9.3. Such detail is needed to quantify the timing and speed of feedback loop activations in response to exposures for different substances (e.g., crystalline silica, asbestos fibers, other EMPs with different physiochemical properties) in different target organs and tissues with different biochemical parameters, e.g., reflecting genetic polymorphisms, prior smoking histories, and interindividual variability in biochemistry. More detail is also needed to quantify the subsequent time course of disease initiation and progression following induction of chronic inflammation. But it is already realistic to anticipate that detailed models will have threshold-like responses to exposure concentrations and durations, and to start considering implications for public and occupational health protection and risk analysis of exposure thresholds for inflammation-mediated diseases.

Table 9.3. Summary of proposed partial answers to risk analysis questions

Risk analysis question

Currently proposed partial answers

Q1: Is there an exposure concentration threshold below which adverse responses do not occur?

A1: Yes. Within a cell, NLRP3-mediated responses do not occur unless exposure concentrations are sufficient to trigger production of active NLRP3 protein (via NF-κB- signaling and deubiquitination), priming, assembly via oligomerization (see left side of Figure 2), and activation via Signal 2 (typically involving MOMP, ROS, LMP, and lysosome disruption). All of these are threshold-like processes. In addition, bistability (or multi-stability) of cytokine and inflammation networks, and perhaps percolation thresholds for spread of inflammation, create thresholds for the inflammatory responses of multiple cells in a tissue.

Q2: For any exposure concentration, is there an exposure duration threshold before which adverse responses of interest do not occur?

A2: Yes: If exposure durations are too brief, ASC polymerization and NLRP3 oligomerization will not be completed (see right side of Figure 2)

Q3: If such thresholds exist, how large are they, and on what factors do they depend?

A3: Exposure concentration and duration thresholds needed to cause persistent NLRP3 activation and chronic inflammation are probably the same as or similar to those needed to create a persistent high-ROS inflammatory state. Both probably involve the same overlapping major bistable positive feedback loops (Table 1). Thresholds for Signal 2 to activate the NLRP3 inflammasome in a cell decrease with accumulation of active NLRP3 protein in its cytosol.

Q4: What is the shape of the concentration-duration-risk relationship above the thresholds? How do physiochemical properties of EMPs and pharmacokinetic and biochemical parameters for exposed individuals affect the answer?

A4: The main shape of the dose-response relationship is probably switch-like, approximating all-or-nothing activation of various NLRP3 inflammasome activation and high-ROS loops. However, damage and disease from activated loops may progress over decades. Physiochemical properties (greater fiber length, stiffness, and availability of iron on the surface of EMPs) can reduce time to lysosome rupture and Signal 2 generation.

Q5: How sure can we be about the answers to the preceding questions, and what information would most help to reduce remaining uncertainties?

A5: Oligomerization-based assembly of NLRP3, induction of high levels of mitochondrial and cytosolic ROS, disruption of the lysosome to generate Signal 2, existence of autocrine and other positive feedback loops, and prion-like spread of inflammation are all well established. Percolation thresholds are speculative.

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