Food-webs within ecosystems describe the trophic relationship between species of an ecological community. There can be predators, prey and resources, where different species find themselves consuming those on a lower trophic level, while being consumed by those on a higher one (Rosenzweig, 1971; Oksanen et al., 1981). Predators exploit prey, prey exploit resources, and resource renewal fuels the food-web. For species on the same trophic level, competition is often indirect. One individual competes with another by consuming and depressing the availability of shared resources. Such ecosystems may have two, three, four, or possibly even more trophic levels (Oksanen and Oksanen, 2000).

A key element of consumer-resource dynamics is the nutritional relationship of resources to the consumer, often showcased by the “beer and pretzel” example of complementary resources. To a consumer, two resources may be perfect substitutes, complementary, hemi-essential or essential (Tilman, 1980). Two nutrients are perfect substitutes if the value of a given diet is a linear, weighted average of the two nutrients in the diet. They are complementary if there are diminishing returns to fitness from consuming more of one of the resources. They are hemi-essential if (i) a non-zero amount of each must be consumed, (ii) there are diminishing returns to consuming more of one, and (iii) consuming more of one resource increases the value of consuming the other (Letnic and Crowther, 2013).

Two resources are essential if some ratio of the two must be consumed to achieve higher reward. That is, increasing consumption of the first resource has no value if consumption of the second resource limits the diet’s value, and vice-versa. Such resources conform to Liebig’s Law of the Minimum (Liebig, 1876). In the context of agriculture, Justus Freiherr von Liebig (von Liebig, 1840; Liebig, 1876) noted that beyond a certain point adding more of one nutrient, such as nitrogen, did not increase yields as some other nutrient, such as phosphorus, was now the limiting resource. With two resources, at any given time just one or the other resource is limiting unless they conform to a specific ratio in the diet. Essential resources impact the dynamics of both more traditional ecosystems, such as plants or microbes, as well as the dynamics within the ecosystem of the human body. Essential resources may characterize the nutrient or molecular requirements of normal cells, as well as cancer cells within their host.

While normal cells are not free-living single celled organisms, they do rely on consumption of blood-born or tissue-generated nutrients that can serve as fuel, as structural molecules, or as functional molecules (Thompson, 2011). Some of these nutrients can be thought of as general resources that are used by all cells in the human body (Palm and Thompson, 2017; Amend et al., 2018). These can include glucose, oxygen, and amino acids. Among these, some are essential, such as the essential amino acids (e.g., lysine) that cannot be synthesized from other amino acids or obtained in another way. Many other molecules can be used as fuel or metabolically transformed into the building blocks for structural and functional purposes (Hosios et al., 2016).

Some nutrients can be described as specific resources in that only a subset of cell types or tissues need and use them. For instance, in humans only a subset of cells in the liver and brain can, in general, take up and metabolize fructose; most of our cells cannot (Oppelt et al., 2017). Furthermore, in some cases, the need for a specific resource by a subset of cell types has evolved as an adaption for the whole organism to control the proliferation or metabolic activity of these cell subsets without impacting other cells. Hormones are examples of such specific resources that serve to regulate specific cells within specific tissues; examples of such resources include estrogen for glandular tissue in the breast and testosterone for glandular tissue in the prostate that are necessary for these cells to proliferate. Even as all other nutrients are in ample supply, proliferation of subsets of cells can be controlled by regulating the hormone supply. Hormones, therefore, serve as essential resources relative to the pool of other resources. Yet, as growth factors, they do not provide fuel or material for the cell. Nevertheless, specific cells have evolved to be metabolically wired to require these growth factors as keys (they generally form a dimer with another molecule within the cell (Duffy, 2006; Razandi et al., 2004; Lallous et al., 2013) to initiate metabolic pathways, including the possibility of cell division. They are used up in the process and metabolically broken down. As such, they are a faux resource, whose adaptive value is for the whole organism and not for the individual cell (Tilman, 1982).

Breast cancer cells, at least initially, carry the ancestral trait of requiring estrogen as an essential resource. The ability of cells to recognize and utilize estrogen is mediated through estrogen receptors (ER), which have been an appealing therapeutic target for patients with breast cancer since their discovery over a century ago. Beatson (1896) first observed in 1896 that removing the ovaries can lead to breast cancer remission. Over half a century later, estrogen and its receptors were confirmed as key actors in breast cancer (Jensen et al., 1971), marking the beginning of therapies to interfere with ER signaling to treat the disease.

Once a patient’s breast cancer is clinically detectable, cells of the tumor can be classified as ER⁺ (requiring estrogen) or ER^– (lacking estrogen receptors) by immunohistochemical staining of tumor biopsies. Most primary breast cancers possess both types of cells coexisting within the tumor. Breast cancers are scored pathologically as ER⁺ or ER^– based on the percentage of cells exhibiting the estrogen receptor. Patients with ER⁺ breast cancer typically have a more favorable prognosis compared to ER^– patients, with the arsenal of therapeutic interventions expanded to include therapies that interfere with estrogen production or estrogen signaling. Women that score as ER^– have fewer therapy options (Hammond et al., 2010).

Ecologically, within a breast cancer tumor we expect to observe at least three distinct types of communities: all ER⁺, all ER^– or a community of the two coexisting together. Coexistence seems to be the norm (Jensen et al., 1971; Harvey et al., 1999; Caruana et al., 2020). Here, we want to leverage ecological insights about consumer-resource dynamics and resource subsistence levels to explore the circumstances favoring ER⁺ vs. ER^– breast cancer. We explore the possibilities for evolutionarily steering cancer cell frequencies through nutrient manipulations. To achieve this goal, we model interactions of cancer cells with a general (glucose) and a specific (estrogen) resource subject to Liebig’s Law of the Minimum as a consumer-resource interaction. We consider nutrient uptake rates, resource supply rates, and the proliferation and survival consequences to cancer cells of their nutrient uptake. We identify conditions favoring ER⁺ or ER^– cancer cells in the tumor microenvironment and discuss strategies that may impact success of hormone-based therapeutic interventions.

In our modeling framework, we consider two types of consumers. Consumers using strategy 1, S₁, use both specific and general resources (ER⁺ cells), while consumers using strategy 2, S₂, rely only on general resources (ER^– cells). Evidence suggests that in some cases these consumer strategies are heritably distinct and as such are pure strategies that breed true. In other cases, cancer cells can switch between the strategies.

Let the individuals within the population of cancer cells be denoted as x_α(t), where α represents a mixed strategy of using S₁ with probability α. If α = 1, cells only use S₁, and if α = 0, cells only use S₂.

Cells utilizing strategy S₁ depend on both the specific resourceR₁(t), such as estrogen, and the general resourceR₂(t), such as glucose, as essential resources to the cell. Parameters a_ij (per time) represent the probability of encountering a given item of the resource, while parameters b_ijrepresent the conversion rate of resources into the proliferation daughter cells; we also assume that there exists some intrinsic cell death rate δ. Finally, we can describe the fitness (per capita proliferation rate), F₁(t), of cells using strategy S₁ based on Liebig’s Law of the Minimum as F₁(t) = min⁡(b₁₁a₁₁R₁(t),a₂₁b₂₁R₂(t)). Cells that use strategy S₂ depend only on general resource R₂(t) and grow at a rate F₂(t) = a₂₂b₂₂R₂(t). Together, the change over time in a population with ER⁺ (x_{α = 0}) and ER^– (x_{α = 1}) cancer cells can be described as:

Next, we assume that resources R₁(t) and R₂(t) have constant inflow rates R₀₁ and R₀₂, respectively, and are cleared or consumed by normal cells at rates k₁ and k₂ per unit of the resources R₁(t) andR₂(t), respectively. Resource R₂(t) can be consumed by cells using strategy S₁ or strategy S₂, while R₁(t) can only be consumed by cells using strategy S₁. These assumptions are captured by the following system of equations:

In formulating these dynamics, we assume that cancer cells using strategy S₁ do not overconsume either of the essential resources. If resource 1 is limiting, then the cancer cell will consume all encountered items of resource 1 but only some of the encountered items of resource 2. The amount of resource 2 consumed when it is not limiting is just that amount needed to fully utilize resource 1. And vice-versa if resource 2 is limiting.

In the absence of consumption by the cancer cells, resources will achieve a steady state level at R1′=R01k1 for specific resource R₁, and R2′=R02k2 for general resource R₂. In consumer-resource theory, these levels are referred to as resource supply points. This represents the highest standing crop of resources that is achievable within the tumor.

Each consumer strategy, S₁ and S₂, will have a subsistence level of resource abundance, R₁^∗ and R₂^∗, below which it will have negative fitness (declining numbers) and above which fitness will be positive (increasing numbers). The subsistence level of resources can be found by setting the fitness of a consumer strategy equal to zero and solving for the associated R^∗.

When α = 1, cells require both resources (ER⁺ cells), and thus subsistence levels for both resources are R1*=δa11⁢b11 when R2≥δa21⁢b21, or R2*=δa21⁢b21 when R1≥δa11⁢b11. That is, these are the minimal levels of both resources that an ER⁺ cell requires for survival. In consumer resource theory, the graph of this in the state space of R₂ vs. R₁ forms an elbow, and it describes the zero net growth isocline (ZNGI) for a consumer harvesting essential resources (see Figure 1).

Conversely, for cells with α = 0, which depend only on the general resource R₂, the resource subsistence level is given by R2*=δa22⁢b22. In the state space of R₂ vs. R₁, this describes a horizontal line, and it is the zero net growth isocline of strategy S₂ (Figure 1). Above this line, cells with strategy S₂ have positive fitness and below this line their fitness is negative. By the definition of this strategy, the fitness of individuals with S₂ is independent of the availability of the specific resource, R₁.

In a consumer-resource model there are limits to growth for the consumers. Consumers, intra- and inter-specifically, compete with each other. This competition is indirect via depletion of the standing crop of resources. This means that each species has a carrying capacity determined by the population size that depresses resource availability to its R^∗. At population sizes above this level, R will be driven below R^∗ and the consumer’s population growth will be negative, and vice-versa for population sizes below this level.

In this section we address the question of how a population that is heterogeneous with respect to resource consumption strategy will evolve over time with respect to both its initial composition and properties of cells and the environment, i.e., with respect to variations in parameters R₀₁,R₀₂,a_ij,b_ij as defined in Table 1. For that, we assume that each individual cell in the population possesses a strategy parameter of α that belongs to the interval [0,1]. With this assumption, the population can consist of individuals that use either the pure strategy (cases analyzed in the previous section), or any mixture of the two pure strategies. There is value in allowing for both possibilities: a mix of two pure strategies vs. a continuum of mixed strategies. In the case of estrogen receptor status in breast cancer, evidence suggests cases in which ER⁺ and ER^– are heritably distinct and other cases where the trait is phenotypically plastic (Polyak, 2007; Dai et al., 2017; Sahoo et al., 2021).

We can consider the dynamics of any starting distribution of mixed strategies through the application of the Hidden Keystone Variable (HKV) method (Kareva and Karev, 2019); the specific details of transformations necessary to apply the HKV method to this system of equations are given in Supplementary Appendix. The final system of equations reads as follows:

where E^t[α] is the expected value of the strategy parameter that changes over time as the population evolves, and N(t) is the total population size of all the cells. Derivations for expression describing E^t[α] and N(t) are given in Supplementary Appendix. Using this transformed system of equations we can now calculate change in population size, expected value and variance of α over time, thus enabling us to track evolution of the population with respect to resource consumption strategy subject to variations in environmental conditions.

The direct impact of nutrient inflow rates on population composition raises the possibility of “evolutionary steering” (Stanková et al., 2019), aimed at promoting a more therapeutically susceptible composition of cancer cell types. Ideally, we would devise strategies to steer the populations toward a point where neither ER⁺ nor ER^– cells can persist (Region 0 in Figure 1). However, this cannot be achieved directly through nutrient manipulation without harming the host, since the general resources (glucose) are required by all cells of the body.

An alternative approach involves steering the population composition toward the ER⁺ phenotype, which is more susceptible to therapeutic interventions. Such interventions include several endocrine-based therapies, such as tamoxifen, fulvestrant and aromatase inhibitors (AIs). Development of tamoxifen, initially a contraceptive, has been a critical advance in breast cancer treatment (Jordan, 2003; Quirke, 2017). It acts as a selective ER modulator (SERM), interfering with signaling between ER and estrogen, although it has been shown to have both antagonist and weak agonist activity. Fulvestrant acts to not only block but also downregulate ER without agonist activity (Osborne et al., 2004). Both are effective in breast cancer, yet both can select for resistant cancer cells (Riggins et al., 2007; Mills et al., 2018), namely those that are ER^– or resistant through other mechanisms. AIs are small molecules that block conversion of precursor compounds into estrogenic molecules (Smith and Dowsett, 2003). AIs, such as anastrozole, letrozole, and exemestane, have proven effective as monotherapies (Mauri et al., 2006) and in combination with tamoxifen (Johnston et al., 2005; Winer et al., 2005; Early Breast Cancer Trialists’ Collaborative Group (Ebctcg), 2015).

With a range of options available for estrogen-dependent tumors, it is particularly important to provide therapeutic options to all patients who can benefit. Breast tumors can harbor a combination of ER⁺ and ER^– cells, but what fraction of ER⁺ cells within the tumor is high enough to qualify the patient for hormone therapies? This question is not as straightforward as one might believe. One issue concerns inconsistency between testing facilities in how they classify tumors as ER⁺ or ER^–. Typically, one or several sections from a biopsy are stained for ER expression using immunohistochemistry (IHC). Tumors may show a continuum of expression levels among the constituent cancer cells, some cells showing no expression at all (ER^– cells). Generally, all cells exhibiting expression “at any intensity” are reported as positive (Hammond et al., 2010). However, Layfield et al. (2003) showed that there exists considerable variability between ER classifications on the same tissue block when analyzed by different laboratories. Similar discrepancies have been reported by Goldstein et al. (2003) and Nkoy et al. (2010) highlighting differences in laboratory protocols (Ibarra et al., 2010). A nationwide assessment of positivity rates in the Netherlands (Dooijeweert et al., 2019) identified limited variability in a more recent analysis, but absolute variations still existed.

Next, even if there were no inter-laboratory inconsistencies, another question remains: what level of ER expression within the tumor is therapeutically relevant? Two main scoring methods have been used for evaluating the extent of ER positivity: H-score and Allred score. Allred score (Allred et al., 1998) combines the proportion of positive-staining tumor cells and the intensity of staining to give a score between 0 and 8. H-score (Goulding et al., 1995) aims to capture the full range of staining percentages and intensities in tumor samples rather than just the average intensity of the Allred score. H-scores range from 1 to 300. A larger score corresponds to a higher intensity of staining. A score of 1 corresponds to up to 1% ER⁺ cells among the cancer cells within the tumor.

Some studies however suggest that there are actually few cases of tumors being weakly ER⁺ vs. entirely ER^–. They suggest that ER staining results in a bimodal distribution of tumor types (Collins et al., 2005). The lack of consistency in testing and potential misclassification of weakly ER⁺ tumors as ER⁺ tumors prompted Collins et al. (2005) to perform internal IHC analysis of immune-stains of 825 breast cancer samples, estimating proportion of ER⁺ tumor cells, and grading samples using the Allred score. The authors showed that in 817 cases (99.0%), either all of the cancer cells in the tumor showed an absence of staining (all ER^– cells) or over 70% of the cells were ER⁺. Thus, 818 cases (99.2%) exhibited Allred scores of either 0 or 7/8. These results prompted the authors to conclude that in most cases, an overwhelming number of breast cancer patients’ tumors can be classified as completely ER^– or unambiguously ER⁺, with only a small fraction of tumors showing very small frequencies of ER⁺ cells and thus appearing weakly positive. It is noteworthy that Allred scores of 7 or 8 means there are still a sizeable frequency of ER^– cancer cells within the tumor.

The question of whether even weakly positive tumors should be treated with endocrine therapies was addressed in 2010 at the American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) meeting. A panel of experts agreed on setting a threshold of 1% ER⁺ cancer cells for reporting a patient’s breast cancer as ER positive (Hammond et al., 2010). With regards to scoring, this corresponds to a minimum Allred score of 3, which can be seen with as few as 1–10% weakly staining cells, and an H-score of over 1 (Table 10 in Hammond et al., 2010).

While the main rationale for the 1% cutoff is to expand access to treatment options to as many patients as possible, it may be too low for statistically significant efficacy. Morgan et al. (2011) showed that low levels of expression, defined as H-score ≤ 50, resulted in lower overall disease-free survival when treated with only endocrine therapy. Chen et al. (2018) showed that patients with ER⁺ staining between 1 and 9% gained no significant benefit from endocrine therapy, unlike ER⁺ tumors with over 10% positive staining. Raghav et al. (2012) also showed that patients with tumors with 1–5% ER positive expression gained no clinical benefit from endocrine therapy.

Even though weakly positive tumors are classified as eligible to receive endocrine therapies, it seems that therapeutic success would be greater if one could increase the proportion of ER⁺ cells in these tumors prior to administering endocrine therapy. Within the framework proposed here, this may be possible through resource manipulation.

As we have shown above, the proportion of ER⁺ cells that rely on both resources increases with increased estrogen inflow, or with reduced glucose inflow. Perhaps it might be feasible to externally increase estrogen concentration to favor ER⁺ cells over ER^– ones without compromising patient health, but as yet, this has not been explored experimentally. Such a therapy would fall into what has been termed an evolutionary gambit or suckers gambit (Maley et al., 2004; Gatenby and Brown, 2020). On the other hand, glucose deprivation may be able to achieve a similar effect (Barbosa and Martel, 2020), priming the tumor to becoming more receptive to hormone therapy by favoring an increase in the frequency of ER⁺ cells relative to ER^– ones (Figure 5).

If the tumor is primarily composed of ER⁺ cells, then estrogen deprivation therapies will have initial success but might eventually drive the tumor toward either all ER^– or a mixture of both ER⁺ and ER^– cells. Adding glucose deprivation or enhancing the resource supply of estrogen relative to other nutrients may set up an evolutionary double-bind (Gatenby et al., 2009), where the resulting resource dynamics force an ER⁺ tumor that is highly susceptible to hormone therapy (Figure 5).

Here we analyzed a consumer-resource model with two resources subject to Liebig’s Law of the Minimum to describe evolution of a heterogeneous population of cancer cells as influenced by resource availability. We evaluated the impact of a general resource, such as glucose, and a specific resource, such as estrogen, on the conditions for coexistence by a phenotype that requires both, and a phenotype that only requires the general resource. Our model was intended for breast cancer, where ER⁺ and ER^– cancer cells are frequently found coexisting within the same patient’s tumor. We solved analytically for conditions under which the tumor should have pure or mixed strategies (Figure 1). This involved calculating the subsistence levels of resources (R^∗) for the ER⁺ and ER^– cancer cell strategies, there zero net growth isoclines (ZNGI), and the effect of the resource supply points of glucose and estrogen on the composition of cancer cell strategies.

We then confirmed theoretical predictions these results by showing that if a heterogeneous population can evolve over time, it will evolve toward the predicted population composition and resource equilibrium levels. We assessed population evolution by changes in the mean and variance of a distribution of mixed strategies, where a given strategy gives the probability of exhibiting the ER^– or ER⁺ phenotype (Figure 2). We showed that in this system, population evolution is invariant to initial distribution of cell clones in the populations, and that over time the final population composition is dictated only by the supply of each resource (Figure 3), suggesting that resource manipulation can be used to impact the composition of the population (Figure 5).

To test this hypothesis, we varied relative inflow rates for both the general and specific resource and evaluated where the population evolved over time (Figure 4). Specifically, in our simulations we allowed the population to evolve to steady state, at which point we evaluated composition of the population (mean strategy and variance of strategies), as well as equilibrium abundances of resources. In addition to confirming predicted levels of both resources at a steady state, the model analysis revealed that the highest variance in the mixed strategies found among the cell lineages occurs for populations that have a mix of ER⁺ and ER^– cells.

In Lloyd et al. (2014) examined the frequency of ER⁺ and ER^– cancer cells from the biopsies of 24 patients; all biopsies were obtained from the primary tumor. Six exhibited 100% ER^– cells (corresponding to Region 1 of Figure 5), seven had both phenotypes at 5–10% ER^– cells (corresponding to Region 2 of Figure 5) and 11 were 100% ER⁺ cells (corresponding to Regions 3 or 4 of Figure 5). The authors found that ER^– tumors exhibit less vasculature. Lack of vasculature may reduce the inflow of both glucose (and other general resources) and estrogen, but the level of estrogen may drop below the subsistence level of the ER⁺ cells, leaving a higher standing crop of underutilized general resources, thereby favoring ER^– cells (to our knowledge, this prediction remains untested). The authors hypothesize that anti-estrogen therapy (e.g., Tamoxifen) can select for ER^–independent cells, while “cyclic introduction of estrogen may improve survival rate by continually altering, rather than unilaterally shifting, toward an ER^– population.” The authors suggest that “modulation (and not eradication or extinction of certain population) may prove to be an advantageous treatment strategy,” a hypothesis that is supported by the proposed mathematical model.

The proposed model is built on the underlying theory of essential resources and Liebig’s Law of the Minimum. For ER⁺ cells, estrogen may be a hemi-essential resource (it certainly is not a perfectly substitutable one). Had we modeled estrogen as a hemi-essential resource for ER⁺ cancer cells, our results would remain qualitatively unchanged. The model, however, would lose much of its analytic tractability as fitness would now involve the product of consumption rates of estrogen and the general resource.

Direct evidence for estrogen acting as an essential resource is that ER⁺ cells cannot survive and proliferate in the absence of estrogen, no matter the abundance of other nutrients (Martin et al., 2003; Comsa et al., 2015). Furthermore, in the absence of sufficient quantities of other nutrients such as glucose, fatty acids and amino acids, cancer cells cannot survive or proliferate regardless of the availability of estrogen. Finally, like other resources, estrogen becomes depleted and used up by the cells rather than continuously being recycled (Gudas et al., 1995).

Indirect evidence suggests that estrogen may act as an essential or hemi-essential resource in line with Liebig’s Law. Mathews et al. (2020) quantified the effect of long-term glucose deprivation on various cancer cell lines in vitro. Cell lines were stabilized at typical human glucose level of 6 mmol/L, with the intervention group then receiving 3 mmol/L of glucose for 90 days. The authors observed that glucose deprivation had different effect on different cell lines, with MDA-MB-231 cell line (ER^–), the highly aggressive triple negative breast cancer cell line, being most sensitive to the metabolic intervention, while the non-tumorigenic epithelial cell line MCF 10A (ER⁺) was least affected. For the purposes of model validation, more decisive experiments involving ER⁺ and ER^– cell lines should include varying resource availabilities, and mono- vs. co-culturing to then quantify changes in population composition over time (Freischel et al., 2020). If estrogen and general nutrients function as essential resources, then nutrient modulation may be an effective strategy for cancer modulation.

The potential benefit on cancer therapy of glucose deprivation through a ketogenic diet has been discussed extensively in the last several years (Klement, 2017; Weber et al., 2018). Khodabakhshi et al. (2020) reported results of a randomized controlled clinical trial, evaluating the effects of ketogenic diet on patients with breast cancer undergoing chemotherapy. In neoadjuvant patients, they found that overall survival increased in the intervention group compared to the control group. In another trial by the same authors (Khodabakhshi et al., 2021) evaluated changes in biomarkers of breast cancer patients undergoing chemotherapy. Patients on a ketogenic diet showed significant decreases in TNF-alpha and insulin levels after 12 weeks of treatment, as well as increase in IL-10. All of these changes are associated with better patient outcomes. Additional experiments are needed to evaluate relative contributions of different mechanisms triggered by glucose deprivation in the presence and absence of estrogen. In addition to manipulating cancer-cell population composition and density, glucose deprivation may also influence immune modulation (Chang et al., 2015; Buck et al., 2017; Klein Geltink et al., 2018) and vasculature (Lloyd et al., 2014).

When a patient is diagnosed with breast cancer, it is standard approach to classify the tumor and start tumor treatment as expeditiously as possible, with tumor burden reduction being the goal of each step of the treatment. However, it may be more effective to first prime the tumor following the initial assessment of the frequency of ER⁺ and ER^– cancer cells. The first step in the treatment cascade could be aimed at modifying the tumor environment to favor ER⁺ cancer cells. By developing a long-term strategy rather than relying on short-term tumor burden reduction, it may be possible to expand the pool of patients that can maximally benefit from endocrine-based therapy through application of ecological principles to cancer.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author/s.

IK conducted MATLAB simulations. Both authors contributed to study design and manuscript preparation.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The handling Editor declared a past co-authorship with one of the authors IK.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.