Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation.

Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor development, cancer dormancy, and immunotherapies. In fact, early immunotherapy failures were partly due to a lack in understanding of the nonlinear growth dynamics these competing immune actions may cause. To study this biological phenomenon theoretically, we construct a minimally parameterized framework that incorporates all aspects of the immune response. We combine the effects of all immune cell types, general principles of self-limited logistic growth, and the physical process of inflammation into one quantitative setting. Simulations suggest that while there are pro-tumor or antitumor immunogenic responses characterized by larger or smaller final tumor volumes, respectively, each response involves an initial period where tumor growth is stimulated beyond that of growth without an immune response. The mathematical description is non-identifiable which allows an ensemble of parameter sets to capture inherent biological variability in tumor growth that can significantly alter tumor-immune dynamics and thus treatment success rates. The ability of this model to predict non-intuitive yet clinically observed patterns of immunomodulated tumor growth suggests that it may provide a means to help classify patient response dynamics to aid identification of appropriate treatments exploiting immune response to improve tumor suppression, including the potential attainment of an immune-induced dormant state.

Evolution and phenotypic selection of cancer stem cells.

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change, and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cells(CSC), as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits, including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of non-stem cancer cells(CC) that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The sub-population of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.

Classical mathematical models for description and prediction of experimental tumor growth.

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics.

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis--a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division--we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.

Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers.

Although optimal control theory has been used for the theoretical study of anti-cancerous drugs scheduling optimization, with the aim of reducing the primary tumor volume, the effect on metastases is often ignored. Here, we use a previously published model for metastatic development to define an optimal control problem at the scale of the entire organism of the patient. In silico study of the impact of different scheduling strategies for anti-angiogenic and cytotoxic agents (either in monotherapy or in combination) is performed to compare a low-dose, continuous, metronomic administration scheme with a more classical maximum tolerated dose schedule. Simulation results reveal differences between primary tumor reduction and control of metastases but overall suggest use of the metronomic protocol.

An integrated multidisciplinary model describing initiation of cancer and the Warburg hypothesis.

BACKGROUND: In this paper we propose a chemical physics mechanism for the initiation of the glycolytic switch commonly known as the Warburg hypothesis, whereby glycolytic activity terminating in lactate continues even in well-oxygenated cells. We show that this may result in cancer via mitotic failure, recasting the current conception of the Warburg effect as a metabolic dysregulation consequent to cancer, to a biophysical defect that may contribute to cancer initiation. MODEL: Our model is based on analogs of thermodynamic concepts that tie non-equilibrium fluid dynamics ultimately to metabolic imbalance, disrupted microtubule dynamics, and finally, genomic instability, from which cancers can arise. Specifically, we discuss how an analog of non-equilibrium Rayleigh-Benard convection can result in glycolytic oscillations and cause a cell to become locked into a higher-entropy state characteristic of cancer. CONCLUSIONS: A quantitative model is presented that attributes the well-known Warburg effect to a biophysical mechanism driven by a convective disturbance in the cell. Contrary to current understanding, this effect may precipitate cancer development, rather than follow from it, providing new insights into carcinogenesis, cancer treatment, and prevention.

The tumor growth paradox and immune system-mediated selection for cancer stem cells.

Cancer stem cells (CSCs) drive tumor progression, metastases, treatment resistance, and recurrence. Understanding CSC kinetics and interaction with their nonstem counterparts (called tumor cells, TCs) is still sparse, and theoretical models may help elucidate their role in cancer progression. Here, we develop a mathematical model of a heterogeneous population of CSCs and TCs to investigate the proposed "tumor growth paradox"--accelerated tumor growth with increased cell death as, for example, can result from the immune response or from cytotoxic treatments. We show that if TCs compete with CSCs for space and resources they can prevent CSC division and drive tumors into dormancy. Conversely, if this competition is reduced by death of TCs, the result is a liberation of CSCs and their renewed proliferation, which ultimately results in larger tumor growth. Here, we present an analytical proof for this tumor growth paradox. We show how numerical results from the model also further our understanding of how the fraction of cancer stem cells in a solid tumor evolves. Using the immune system as an example, we show that induction of cell death can lead to selection of cancer stem cells from a minor subpopulation to become the dominant and asymptotically the entire cell type in tumors.

The host support niche as a control point for tumor dormancy: implications for tumor development and beyond.

An increasingly appreciated focus of carcinogenesis research is on mechanisms governing tumor growth after the fact of cancer cell creation. Of particular interest are dynamical interactions between tumor and host cell populations that can themselves strongly impact the fate of established cancer lesions. Regardless of tumor type, all cancers face the common problem of having to breach the barrier of angiogenic competency in order to advance from a microscopic lesion to symptomatic disease. If pre-angiogenic tumor cells are held in dormancy due to cell cycle arrest, this will postpone the need to traverse this higher-level barrier. On the other hand, the barrier itself may prove limiting to a tumor at its diffusion-limited size, creating a population-level dormancy characterized by balanced proliferation and cell death. In both cases of dormancy, the "angiogenic switch" has not yet occurred. We here describe and mathematically quantify an underappreciated third dormancy state defined by an angiogenic balance following the angiogenic switch. In this state we term "post-vascular dormancy," a tumor has attained angiogenic competency, but again demonstrates balanced proliferation and cell death because ambient pro- and anti-angiogenic influences are offsetting. Interestingly, autopsies have shown virtually all of us carry latent tumors in pre- or post-vascular states, many of which lie under the threshold of routine clinical detection. We show how, in the post-vascular case, tumor latency can arise from an elaborate mechanism of self-controlled growth, mediated through the tumor-vascular interaction. Underlying this observation is the finding that a tumor produces both angiogenesis stimulators and inhibitors, with the latter having greater influence, both locally and systemically, as the tumor grows-a mechanism we hypothesize is an aberrant co-option of normal organogenic regulation. That a tumor can limit its own growth raises the prospect that chronic therapies aimed at suppressing this tumor-host dynamic may compare favorably to current strategies which often yield favorable short-term responses but fail to deliver long-term tumor suppression.

Immunoediting: evidence of the multifaceted role of the immune system in self-metastatic tumor growth.

BACKGROUND: The role of the immune system in tumor progression has been a subject for discussion for many decades. Numerous studies suggest that a low immune response might be beneficial, if not necessary, for tumor growth, and only a strong immune response can counter tumor growth and thus inhibit progression. METHODS: We implement a cellular automaton model previously described that captures the dynamical interactions between the cancer stem and non-stem cell populations of a tumor through a process of self-metastasis. By overlaying on this model the diffusion of immune reactants into the tumor from a peripheral source to target cells, we simulate the process of immune-system-induced cell kill on tumor progression. RESULTS: A low cytotoxic immune reaction continuously kills cancer cells and, although at a low rate, thereby causes the liberation of space-constrained cancer stem cells to drive self-metastatic progression and continued tumor growth. With increasing immune system strength, however, tumor growth peaks, and then eventually falls below the intrinsic tumor sizes observed without an immune response. With this increasing immune response the number and proportion of cancer stem cells monotonically increases, implicating an additional unexpected consequence, that of cancer stem cell selection, to the immune response. CONCLUSIONS: Cancer stem cells and immune cytotoxicity alone are sufficient to explain the three-step "immunoediting" concept - the modulation of tumor growth through inhibition, selection and promotion.

Non-stem cancer cell kinetics modulate solid tumor progression.

BACKGROUND: Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are believed to drive tumor progression, but the relative frequencies of CSCs versus non-stem cancer cells span wide ranges even within tumors arising from the same tissue type. Tumor growth kinetics and composition can be studied through an agent-based cellular automaton model using minimal sets of biological assumptions and parameters. Herein we describe a pivotal role for the generational life span of non-stem cancer cells in modulating solid tumor progression in silico. RESULTS: We demonstrate that although CSCs are necessary for progression, their expansion and consequently tumor growth kinetics are surprisingly modulated by the dynamics of the non-stem cancer cells. Simulations reveal that slight variations in non-stem cancer cell proliferative capacity can result in tumors with distinctly different growth kinetics. Longer generational life spans yield self-inhibited tumors, as the emerging population of non-stem cancer cells spatially impedes expansion of the CSC compartment. Conversely, shorter generational life spans yield persistence-limited tumors, with symmetric division frequency of CSCs determining tumor growth rate. We show that the CSC fraction of a tumor population can vary by multiple orders of magnitude as a function of the generational life span of the non-stem cancer cells. CONCLUSIONS: Our study suggests that variability in the growth rate and CSC content of solid tumors may be, in part, attributable to the proliferative capacity of the non-stem cancer cell population that arises during asymmetric division of CSCs. In our model, intermediate proliferative capacities give rise to the fastest-growing tumors, resulting in self-metastatic expansion driven by a balance between symmetric CSC division and expansion of the non-stem cancer population. Our results highlight the importance of non-stem cancer cell dynamics in the CSC hypothesis, and may offer a novel explanation for the large variations in CSC fractions reported in vivo.

Quantitative modeling of tumor dynamics and radiotherapy.

Cancer is a complex disease, necessitating research on many different levels; at the subcellular level to identify genes, proteins and signaling pathways associated with the disease; at the cellular level to identify, for example, cell-cell adhesion and communication mechanisms; at the tissue level to investigate disruption of homeostasis and interaction with the tissue of origin or settlement of metastasis; and finally at the systems level to explore its global impact, e.g. through the mechanism of cachexia. Mathematical models have been proposed to identify key mechanisms that underlie dynamics and events at every scale of interest, and increasing effort is now being paid to multi-scale models that bridge the different scales. With more biological data becoming available and with increased interdisciplinary efforts, theoretical models are rendering suitable tools to predict the origin and course of the disease. The ultimate aims of cancer models, however, are to enlighten our concept of the carcinogenesis process and to assist in the designing of treatment protocols that can reduce mortality and improve patient quality of life. Conventional treatment of cancer is surgery combined with radiotherapy or chemotherapy for localized tumors or systemic treatment of advanced cancers, respectively. Although radiation is widely used as treatment, most scheduling is based on empirical knowledge and less on the predictions of sophisticated growth dynamical models of treatment response. Part of the failure to translate modeling research to the clinic may stem from language barriers, exacerbated by often esoteric model renderings with inaccessible parameterization. Here we discuss some ideas for combining tractable dynamical tumor growth models with radiation response models using biologically accessible parameters to provide a more intuitive and exploitable framework for understanding the complexity of radiotherapy treatment and failure.

Stochastic population dynamic effects for lung cancer progression.

The multistage paradigm is widely used in quantitative analyses of radiation-influenced carcinogenesis. Steps such as initiation, promotion and transformation have been investigated in detail. However, progression, a later step during which malignant cells produced in the earlier steps can develop into clinical cancer, has received less attention in computational radiobiology; it has often been approximated deterministically as a fixed, comparatively short, lag time. This approach overlooks important mechanisms in progression, including stochastic extinction, possible radiation effects on tumor growth, immune suppression and angiogenic bottlenecks. Here we analyze tumor progression in background and in radiation-induced lung cancers, emphasizing tumor latent times and the stochastic extinction of malignant lesions. A Monte Carlo cell population dynamics formalism is developed by supplementing the standard two-stage clonal expansion (TSCE) model with a stochastic birth-death model for proliferation of malignant cells. Simulation results for small cell lung cancers and lung adenocarcinomas show that the effects of stochastic malignant cell extinction broaden progression time distributions drastically. We suggest that fully stochastic cancer progression models incorporating malignant cell kinetics, dormancy (a phase in which tumors remain asymptomatic), escape from dormancy, and invasiveness, with radiation able to act directly on each phase, need to be considered for a better assessment of radiation-induced lung cancer risks.

Chromosomes are predominantly located randomly with respect to each other in interphase human cells.

To test quantitatively whether there are systematic chromosome-chromosome associations within human interphase nuclei, interchanges between all possible heterologous pairs of chromosomes were measured with 24-color whole-chromosome painting (multiplex FISH), after damage to interphase lymphocytes by sparsely ionizing radiation in vitro. An excess of interchanges for a specific chromosome pair would indicate spatial proximity between the chromosomes comprising that pair. The experimental design was such that quite small deviations from randomness (extra pairwise interchanges within a group of chromosomes) would be detectable. The only statistically significant chromosome cluster was a group of five chromosomes previously observed to be preferentially located near the center of the nucleus. However, quantitatively, the overall deviation from randomness within the whole genome was small. Thus, whereas some chromosome-chromosome associations are clearly present, at the whole-chromosomal level, the predominant overall pattern appears to be spatially random.

A new view of radiation-induced cancer: integrating short- and long-term processes. Part II: second cancer risk estimation.

As the number of cancer survivors grows, prediction of radiotherapy-induced second cancer risks becomes increasingly important. Because the latency period for solid tumors is long, the risks of recently introduced radiotherapy protocols are not yet directly measurable. In the accompanying article, we presented a new biologically based mathematical model, which, in principle, can estimate second cancer risks for any protocol. The novelty of the model is that it integrates, into a single formalism, mechanistic analyses of pre-malignant cell dynamics on two different time scales: short-term during radiotherapy and recovery; long-term during the entire life span. Here, we apply the model to nine solid cancer types (stomach, lung, colon, rectal, pancreatic, bladder, breast, central nervous system, and thyroid) using data on radiotherapy-induced second malignancies, on Japanese atomic bomb survivors, and on background US cancer incidence. Potentially, the model can be incorporated into radiotherapy treatment planning algorithms, adding second cancer risk as an optimization criterion.

A new view of radiation-induced cancer: integrating short- and long-term processes. Part I: approach.

Mathematical models of radiation carcinogenesis are important for understanding mechanisms and for interpreting or extrapolating risk. There are two classes of such models: (1) long-term formalisms that track pre-malignant cell numbers throughout an entire lifetime but treat initial radiation dose-response simplistically and (2) short-term formalisms that provide a detailed initial dose-response even for complicated radiation protocols, but address its modulation during the subsequent cancer latency period only indirectly. We argue that integrating short- and long-term models is needed. As an example of this novel approach, we integrate a stochastic short-term initiation/inactivation/repopulation model with a deterministic two-stage long-term model. Within this new formalism, the following assumptions are implemented: radiation initiates, promotes, or kills pre-malignant cells; a pre-malignant cell generates a clone, which, if it survives, quickly reaches a size limitation; the clone subsequently grows more slowly and can eventually generate a malignant cell; the carcinogenic potential of pre-malignant cells decreases with age.

PPARgamma ligands inhibit primary tumor growth and metastasis by inhibiting angiogenesis.

Several drugs approved for a variety of indications have been shown to exhibit antiangiogenic effects. Our study focuses on the PPARgamma ligand rosiglitazone, a compound widely used in the treatment of type 2 diabetes. We demonstrate, for the first time to our knowledge, that PPARgamma is highly expressed in tumor endothelium and is activated by rosiglitazone in cultured endothelial cells. Furthermore, we show that rosiglitazone suppresses primary tumor growth and metastasis by both direct and indirect antiangiogenic effects. Rosiglitazone inhibits bovine capillary endothelial cell but not tumor cell proliferation at low doses in vitro and decreases VEGF production by tumor cells. In our in vivo studies, rosiglitazone suppresses angiogenesis in the chick chorioallantoic membrane, in the avascular cornea, and in a variety of primary tumors. These results suggest that PPARgamma ligands may be useful in treating angiogenic diseases such as cancer by inhibiting angiogenesis.

Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth.

Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. Here, we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bearing two simultaneously implanted tumors, growth of only one of the tumors was significantly suppressed (61% size reduction at day 15, P < 0.05). The competition model had to be rejected, whereas the angiogenesis inhibition and proliferation inhibition models were able to describe the data. Additional models including a theory based on distant cytotoxic log-kill effects were unable to fit the data. The proliferation inhibition model was identifiable and minimal (four parameters), and its descriptive power was validated against the data, including consistency in predictions of single tumor growth when no secondary tumor was present. This theory may also shed new light on single cancer growth insofar as it offers a biologically translatable picture of how local and global action may combine to control local tumor growth and, in particular, the role of tumor-tumor inhibition. This model offers a depiction of concomitant resistance that provides an improved theoretical basis for tumor growth control and may also find utility in therapeutic planning to avoid postsurgery metastatic acceleration. Cancer Res; 77(18); 5183-93. ©2017 AACR.

A robust procedure for removing background damage in assays of radiation-induced DNA fragment distributions.

The non-random distribution of DNA breakage in PFGE (pulsed-field gel electrophoresis) experiments poses a problem of proper subtraction of the background DNA damage to obtain a fragment-size distribution due to radiation only. A naive bin-to-bin subtraction of the background signal will not result in the right DNA mass distribution histogram. This problem could become more pronounced for high-LET (linear energy transfer) radiation, because the fragment-size distribution manifests a higher frequency of smaller fragments. Previous systematic subtraction methods have been based on random breakage, appropriate for low-LET radiation. Moreover, an investigation is needed to determine whether the background breakage is itself random or non-random. We consider two limiting cases: (1) the background damage is present in all cells, and (2) it is present in only a small subset of cells, while other cells are not contributing to the background DNA fragmentation. We give a generalized formalism based on stochastic processes for the subtraction of the background damage in PFGE experiments for any LET and apply it to two sets of PFGE data for iron ions.

SU5416 and SU6668 attenuate the angiogenic effects of radiation-induced tumor cell growth factor production and amplify the direct anti-endothelial action of radiation in vitro.

In recent decades, radiation research has concentrated primarily on the cancer cell compartment. Much less is known about the effect of ionizing radiation on the endothelial cell compartment and the complex interaction between tumor cells and their microenvironment. Here we report that ionizing radiation is a potent antiangiogenic agent that inhibits endothelial cell survival, proliferation, tube formation and invasion. Vascular endothelial growth factor (VEGF) and basic fibroblast growth factor were able to reduce the radiosensitivity of endothelial cells. Yet, it is also found that radiation induces angiogenic factor production by tumor cells that can be abrogated by the addition of antiangiogenic agents. Receptor tyrosine kinase inhibitors of Flk-1/KDR/VEGFR2, FGFR1 and PDGFR beta, SU5416, and SU6668 enhanced the antiangiogenic effects of direct radiation of the endothelial cells. In a coculture system of PC3 prostate cancer cells and endothelial cells, isolated irradiation of the PC3 cells enhanced endothelial cell invasiveness through a Matrigel matrix, which was inhibited by SU5416 and SU6668. Furthermore, ionizing radiation up-regulated VEGF and basic fibroblast growth factor in PC3 cells and VEGFR2 in endothelial cells. Together these findings suggest a radiation-inducible protective role for tumor cells in the support of their associated vasculature that may be down-regulated by coadministration of angiogenesis inhibitors. These results rationalize concurrent administration of angiogenesis inhibitors and radiotherapy in cancer treatment.

Combined therapy with direct and indirect angiogenesis inhibition results in enhanced antiangiogenic and antitumor effects.

The multifaceted nature of the angiogenic process in malignant neoplasms suggests that protocols that combine antiangiogenic agents may be more effective than single-agent therapies. However it is unclear which combination of agents would be most efficacious and will have the highest degree of synergistic activity while maintaining low overall toxicity. Here we investigate the concept of combining a "direct" angiogenesis inhibitor (endostatin) with an "indirect" antiangiogenic compound [SU5416, a vascular endothelial growth factor receptor 2 (VEGFR2) receptor tyrosine kinase (RTK) inhibitor]. These angiogenic agents were more effective in combination than when used alone in vitro (endothelial cell proliferation, survival, migration/invasion, and tube formation tests) and in vivo. The combination of SU5416 and low-dose endostatin further reduced tumor growth versus monotherapy in human prostate (PC3), lung (A459), and glioma (U87) xenograft models, and reduced functional microvessel density, tumor microcirculation, and blood perfusion as detected by intravital microscopy and contrast-enhanced Doppler ultrasound. One plausible explanation for the efficacious combination could be that, whereas SU5416 specifically inhibits vascular endothelial growth factor signaling, low-dose endostatin is able to inhibit a broader spectrum of diverse angiogenic pathways directly in the endothelium. The direct antiangiogenic agent might be able to suppress alternative angiogenic pathways up-regulated by the tumor in response to the indirect, specific pathway inhibition. For future clinical evaluation of the concept, a variety of agents with similar mechanistic properties could be tested.