Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift

The size of the basin of attraction in ecosystems with alternative stable states is often referred to as "ecological resilience." Ecosystems with a low ecological resilience may easily be tipped into an alternative basin of attraction by a stochastic event. Unfortunately, it is very difficult to measure ecological resilience in practice. Here we show that the rate of recovery from small perturbations (sometimes called "engineering resilience") is a remarkably good indicator of ecological resilience. Such recovery rates decrease as a catastrophic regime shift is approached, a phenomenon known in physics as "critical slowing down." We demonstrate the robust occurrence of critical slowing down in six ecological models and outline a possible experimental approach to quantify differences in recovery rates. In all the models we analyzed, critical slowing down becomes apparent quite far from a threshold point, suggesting that it may indeed be of practical use as an early warning signal. Despite the fact that critical slowing down could also indicate other critical transitions, such as a stable system becoming oscillatory, the robustness of the phenomenon makes it a promising indicator of loss of resilience and the risk of upcoming regime shifts in a system.     

An insight into tumor dormancy equilibrium via the analysis of its domain of attraction

The trajectories of the dynamic system which regulates the competition between the populations of malignant cells and immune cells may tend to an asymptotically stable equilibrium in which the sizes of these populations do not vary, which is called tumor dormancy. Especially for lower steady-state sizes of the population of malignant cells, this equilibrium represents a desirable clinical condition since the tumor growth is blocked. In this context, it is of mandatory importance to analyze the robustness of this clinical favorable state of health in the face of perturbations. To this end, the paper presents an optimization technique to determine whether an assigned rectangular region, which surrounds an asymptotically stable equilibrium point of a quadratic systems, is included into the domain of attraction of the equilibrium itself. The biological relevance of the application of this technique to the analysis of tumor growth dynamics is shown on the basis of a recent quadratic model of the tumor–immune system competition dynamics. Indeed the application of the proposed methodology allows to ensure that a given safety region, determined on the basis of clinical considerations, belongs to the domain of attraction of the tumor blocked equilibrium; therefore for the set of perturbed initial conditions which belong to such region, the convergence to the healthy steady state is guaranteed. The proposed methodology can also provide an optimal strategy for cancer treatment.     

Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis

From the perspective of systems science, tumorigenesis can be hypothesized as a critical transition (an abrupt shift from one state to another) between proliferative and apoptotic attractors on the state space of a molecular interaction network, for which an attractor is defined as a stable state to which all initial states ultimately converge, and the region of convergence is called the basin of attraction. Before the critical transition, a cellular state might transit between the basin of attraction for an apoptotic attractor and that for a proliferative attractor due to the noise induced by the inherent stochasticity in molecular interactions. Such a flickering state transition (state transition between the basins of attraction for alternative attractors from the impact of noise) would become more frequent as the cellular state approaches near the boundary of the basin of attraction, which can increase the variation in the estimate of the respective basin size. To investigate this for colorectal tumorigenesis, we have constructed a stochastic Boolean network model of the molecular interaction network that contains an important set of proteins known to be involved in cancer. In particular, we considered 100 representative sequences of 20 gene mutations that drive colorectal tumorigenesis. We investigated the appearance of cancerous cells by examining the basin size of apoptotic, quiescent, and proliferative attractors along with the sequential accumulation of gene mutations during colorectal tumorigenesis. We introduced a measure to detect the flickering state transition as the variation in the estimate of the basin sizes for three-phenotype attractors from the impact of noise. Interestingly, we found that this measure abruptly increases before a cell becomes cancerous during colorectal tumorigenesis in most of the gene mutation sequences under a certain level of stochastic noise. This suggests that a frequent flickering state transition can be a precritical phenomenon of colorectal tumorigenesis.     

How Hives Collapse: Allee Effects,Ecological Resilience,and the Honey Bee

We construct a mathematical model to quantify the loss of resilience in collapsing honey bee colonies due to the presence of a strong Allee effect. In the model, recruitment and mortality of adult bees have substantial social components, with recruitment enhanced and mortality reduced by additional adult bee numbers. The result is an Allee effect, a net per-individual rate of hive increase that increases as a function of adult bee numbers. The Allee effect creates a critical minimum size in adult bee numbers, below which mortality is greater than recruitment, with ensuing loss of viability of the hive. Under ordinary and favorable environmental circumstances, the critical size is low, and hives remain large, sending off viably-sized swarms (naturally or through beekeeping management) when hive numbers approach an upper stable equilibrium size (carrying capacity). However, both the lower critical size and the upper stable size depend on many parameters related to demographic rates and their enhancement by bee sociality. Any environmental factors that increase mortality, decrease recruitment, or interfere with the social moderation of these rates has the effect of exacerbating the Allee effect by increasing the lower critical size and substantially decreasing the upper stable size. As well, the basin of attraction to the upper stable size, defined by the model potential function, becomes narrower and shallower, indicating the loss of resilience as the hive becomes subjected to increased risk of falling below the critical size. Environmental effects of greater severity can cause the two equilibria to merge and the basin of attraction to the upper stable size to disappear, resulting in collapse of the hive from any initial size. The model suggests that multiple proximate causes, among them pesticides, mites, pathogens, and climate change, working singly or in combinations, could trigger hive collapse.     

The colorectal cancer stem-like cell hypothesis: a pathologist's point of view

Colorectal cancer is the fourth most common cancer in men and the third most common cancer in women worldwide. The partial failure of classic therapeutic options makes scientists to doubt the efficacy of systemic treatments in targeting the essential cell populations and achieving cure as a final goal. Overgrowing data suggest that cancer is a disease closely linked to stem cells (SCs). It is well known that the first identification of cancer stem-like cells in acute myeloid leukaemia was soon followed by similar results in solid malignancies, including colorectal cancer, and the classic model for colon carcinogenesis supports the development of sudden mutations that will lead to the activation or inactivation of certain oncogenes or tumor suppressors. Thus, this process may go on for years before the first symptoms and the only cells able to withstand for many years, avoid apoptosis and have a high regenerative capacity are the progenitor cells found at the lower part of colon crypts. A more profound study of the mechanisms and molecular signalling pathways that control the basic characteristics of SCs, such as asymmetrical division or self-renewal, may help comprehend the basic mechanisms of cancer genesis and progression. This will result in the development of new therapeutic agents that may target chemoresistant cell populations and improve the therapeutic results. In the current review we point out the importance of cancer stem-like cells in colorectal oncology from a pathologist's point of view, stating the obvious correlation between histology, embryology and surgical pathology.     

肿瘤干细胞与卵巢癌研究进展

近年来,肿瘤干细胞学说作为肿瘤发生发展的重要原因获得越来越多的认可。肿瘤干细胞是指肿瘤中存在的含量极少、具有无限增殖潜能的干细胞样肿瘤细胞,它们能自我更新、分化、迁徙,是导致肿瘤发生、发展、转移和耐药的重要原因。卵巢癌也可能是卵巢癌干细胞所致的疾病。卵巢癌干细胞的分离鉴定正处于起始阶段,针对卵巢癌干细胞的靶向治疗可能在卵巢癌治疗中具有重要作用,为临床彻底治愈卵巢癌带来希望。     

Critical slowing down as an indicator of transitions in two-species models

Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator-prey and competition models. The models exhibit three types of transition: the predator-prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator-prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems.     

Metabolic interplay between glycolysis and mitochondrial oxidation: The reverse Warburg effect and its therapeutic implication

Aerobic glycolysis, i.e., the Warburg effect, may contribute to the aggressive phenotype of hepatocellular carcinoma. However, increasing evidence highlights the limitations of the Warburg effect, such as high mitochondrial respiration and low glycolysis rates in cancer cells. To explain such contradictory phenomena with regard to the Warburg effect, a metabolic interplay between glycolytic and oxidative cells was proposed, i.e., the "reverse Warburg effect". Aerobic glycolysis may also occur in the stromal compartment that surrounds the tumor; thus, the stromal cells feed the cancer cells with lactate and this interaction prevents the creation of an acidic condition in the tumor microenvironment. This concept provides great heterogeneity in tumors, which makes the disease difficult to cure using a single agent. Understanding metabolic flexibility by lactate shuttles offers new perspectives to develop treatments that target the hypoxic tumor microenvironment and overcome the limitations of glycolytic inhibitors.     

Modeling adaptive drug resistance of colorectal cancer and therapeutic interventions with tumor spheroids

Drug resistance is a major barrier against successful treatments of cancer patients. Various intrinsic mechanisms and adaptive responses of tumor cells to cancer drugs often lead to failure of treatments and tumor relapse. Understanding mechanisms of cancer drug resistance is critical to develop effective treatments with sustained anti-tumor effects. Three-dimensional cultures of cancer cells known as spheroids present a biologically relevant model of avascular tumors and have been increasingly incorporated in tumor biology and cancer drug discovery studies. In this review, we discuss several recent studies from our group that utilized colorectal tumor spheroids to investigate responses of cancer cells to cytotoxic and molecularly targeted drugs and uncover mechanisms of drug resistance. We highlight our findings from both short-term, one-time treatments and long-term, cyclic treatments of tumor spheroids and discuss mechanisms of adaptation of cancer cells to the treatments. Guided by mechanisms of resistance, we demonstrate the feasibility of designing specific drug combinations to effectively block growth and resistance of cancer cells in spheroid cultures. Finally, we conclude with our perspectives on the utility of three-dimensional tumor models and their shortcomings and advantages for phenotypic and mechanistic studies of cancer drug resistance.     

Cancer stem cells in solid tumors: is 'evading apoptosis' a hallmark of cancer?

Conventional wisdom has long held that once a cancer cell has developed it will inevitably progress to clinical disease. Updating this paradigm, it has more recently become apparent that the tumor interacts with its microenvironment and that some environmental bottlenecks, such as the angiogenic switch, must be overcome for the tumor to progress. In parallel, attraction has been drawn to the concept that there is a minority population of cells - the cancer stem cells - bestowed with the exclusive ability to self-renew and regenerate the tumor. With therapeutic targeting issues at stake, much attention has shifted to the identification of cancer stem cells, the thinking being that the remaining non-stem population, already fated to die, will play a negligible role in tumor development.In fact, the newly appreciated importance of intercellular interactions in cancer development also extends in a unique and unexpected way to interactions between the stem and non-stem compartments of the tumor. Here we discuss recent findings drawn from a hybrid mathematical-cellular automaton model that simulates growth of a heterogeneous solid tumor comprised of cancer stem cells and non-stem cancer cells. The model shows how the introduction of cell fate heterogeneity paradoxically influences the tumor growth dynamic in response to apoptosis, to reveal yet another bottleneck to tumor progression potentially exploitable for disease control.     

Combining Perturbations and Parameter Variation to Influence Mean First Passage Times

Perturbations are relatively large shocks to state variables that can drive transitions between stable states, while drift in parameter values gradually alters equilibrium magnitudes. This latter effect can lead to equilibrium bifurcation, the generation, or annihilation of equilibria. Equilibrium annihilations reduce the number of equilibria and so are associated with catastrophic population collapse. We study the combination of perturbations and parameter drift, using a two-species intraguild predation (IGP) model. For example, we use bifurcation analysis to understand how parameter drift affects equilibrium number, showing that both competition and predation rates in this model are bifurcating parameters. We then introduce a stochastic process to model the effects of population perturbations. We demonstrate how to evaluate the joint effects of perturbations and drift using the common currency of mean first passage time to transitions between stable states. Our methods and results are quite general, and for example, can relate to issues in both pest control and sustainable harvest. Our results show that parameter drift (1) does not importantly change the expected time to reach target points within a basin of attraction, but (2) can dramatically change the expected time to shift between basins of attraction, through its effects on equilibrium resilience.     

Mathematical modeling of ovarian cancer treatments: sequencing of surgery and chemotherapy

Ovarian cancer has long been one of the most common forms of cancer in women. The main treatment for ovarian cancer comprises a combination of surgery and chemotherapy. In an effort to improve treatment strategies, a variety of mathematical models have been developed in the literature. In this paper, we consider a simple mathematical model that incorporates tumor growth as well as the effects of chemotherapeutic and surgical treatments in ovarian cancer. We consider several growth models and combine them with different cell-kill hypotheses. Surgery is assumed to eliminate a fixed fraction of tumor cells instantaneously. We discuss how different models predict the optimal sequencing of chemotherapeutic and surgical treatments. This work has been carried out in the context of ovarian cancer; however, the results may also be useful for other kind of cancers.     

Analysis of Tumor Suppressor Genes Based on Gene Ontology and the KEGG Pathway

Cancer is a serious disease that causes many deaths every year. We urgently need to design effective treatments to cure this disease. Tumor suppressor genes (TSGs) are a type of gene that can protect cells from becoming cancerous. In view of this, correct identification of TSGs is an alternative method for identifying effective cancer therapies. In this study, we performed gene ontology (GO) and pathway enrichment analysis of the TSGs and non-TSGs. Some popular feature selection methods, including minimum redundancy maximum relevance (mRMR) and incremental feature selection (IFS), were employed to analyze the enrichment features. Accordingly, some GO terms and KEGG pathways, such as biological adhesion, cell cycle control, genomic stability maintenance and cell death regulation, were extracted, which are important factors for identifying TSGs. We hope these findings can help in building effective prediction methods for identifying TSGs and thereby, promoting the discovery of effective cancer treatments.     

Cancer stem cell, niche and EGFR decide tumor development and treatment response: A bio-computational simulation study

Recent research in cancer biology has suggested the hypothesis that tumors are initiated and driven by a small group of cancer stem cells (CSCs). Furthermore, cancer stem cell niches have been found to be essential in determining fates of CSCs, and several signaling pathways have been proven to play a crucial role in cellular behavior, which could be two important factors in cancer development. To better understand the progression, heterogeneity and treatment response of breast cancer, especially in the context of CSCs, we propose a mathematical model based on the cell compartment method. In this model, three compartments of cellular subpopulations are constructed: CSCs, progenitor cells (PCs), and terminal differentiated cells (TCs). Moreover, (1) the cancer stem cell niche is, considered by modeling its effect on division patterns (symmetric or asymmetric) of CSCs, and (2) the EGFR signaling pathway is integrated by modeling its role in cell proliferation, apoptosis. Our simulation results indicate that (1) a higher probability for symmetric division of CSC may result in a faster expansion of tumor population, and for a larger number of niches, the tumor grows at a slower rate, but the final tumor volume is larger; (2) higher EGFR expression correlates to tumors with larger volumes while a saturation function is observed, and (3) treatments that inhibit tyrosine kinase activity of EGFR may not only repress the tumor volume, but also decrease the CSCs percentages by shifting CSCs from symmetric divisions to asymmetric divisions. These findings suggest that therapies should be designed to effectively control or eliminate the symmetric division of CSCs and to reduce or destroy the CSC niches.     

A self-contained enzyme activating prodrug cytotherapy for preclinical melanoma

Gene-directed enzyme prodrug therapy (GDEPT) has been investigated as a means of cancer treatment without affecting normal tissues. This system is based on the delivery of a suicide gene, a gene encoding an enzyme which is able to convert its substrate from non-toxic prodrug to cytotoxin. In this experiment, we have developed a targeted suicide gene therapeutic system that is completely contained within tumor-tropic cells and have tested this system for melanoma therapy in a preclinical model. First, we established double stable RAW264.7 monocyte/macrophage-like cells (Mo/Ma) containing a Tet-On^? Advanced system for intracellular carboxylesterase (InCE) expression. Second, we loaded a prodrug into the delivery cells, double stable Mo/Ma. Third, we activated the enzyme system to convert the prodrug, irinotecan, to the cytotoxin, SN-38. Our double stable Mo/Ma homed to the lung melanomas after 1?day and successfully delivered the prodrug-activating enzyme/prodrug package to the tumors. We observed that our system significantly reduced tumor weights and numbers as targeted tumor therapy after activation of the InCE. Therefore, we propose that this system may be a useful targeted melanoma therapy system for pulmonary metastatic tumors with minimal side effects, particularly if it is combined with other treatments.     

Flickering as an early warning signal

Most work on generic early warning signals for critical transitions focuses on indicators of the phenomenon of critical slowing down that precedes a range of catastrophic bifurcation points. However, in highly stochastic environments, systems will tend to shift to alternative basins of attraction already far from such bifurcation points. In fact, strong perturbations (noise) may cause the system to “flicker” between the basins of attraction of the system’s alternative states. As a result, under such noisy conditions, critical slowing down is not relevant, and one would expect its related generic leading indicators to fail, signaling an impending transition. Here, we systematically explore how flickering may be detected and interpreted as a signal of an emerging alternative attractor. We show that—although the two mechanisms differ—flickering may often be reflected in rising variance, lag-1 autocorrelation and skewness in ways that resemble the effects of critical slowing down. In particular, we demonstrate how the probability distribution of a flickering system can be used to map potential alternative attractors and their resilience. Thus, while flickering systems differ in many ways from the classical image of critical transitions, changes in their dynamics may carry valuable information about upcoming major changes.     

Quantification of Rare Cancer Cells in Patients With Gastrointestinal Cancer by Nanostructured Substrate

Detecting the cancer cells in the peripheral blood, i.e. circulating tumor cell (CTC), have been considered as the “liquid biopsy” and become a particular area of focus. A deep insight into CTC provides a potential alternative method for early diagnosis of solid tumor. Previous studies showed that CTC counts could be regarded as an indicator in tumor diagnosis, predicting clinical outcomes and monitoring treatment responses. In this report, we utilize our facile and efficient CTC detection device made of hydroxyapatite/chitosan (HA/CTS) for rare cancer cells isolation and enumeration in clinical use. A biocompatible and surface roughness controllable nanofilm was deposited onto a glass slide to achieve enhanced topographic interactions with nanoscale cellular surface components, anti-EpCAM (epithelial cell adhesion molecule, EpCAM) were then coated onto the surface of nanosubstrate for specific capture of CTCs. This device performed a considerable and stable capture yields. We evaluated the relationship performance between serial CTC changes and the changes of tumor volume/serum tumor marker in gastrointestinal cancer patients undergoing anti-cancer treatments. The present study results showed that changes in the number of CTC were associated with tumor burden and progression. Enumeration of CTCs in cancer patients may predict clinical response. Longitudinal monitoring of individual patients during the therapeutic process showed a close correlation between CTC quantity and clinical response to anti-cancer therapy. Effectively capture of this device is capable of CTCs isolation and quantification for monitoring of cancer and predicting treatment response.     

Intratumoral heterogeneity: Clonal cooperation in epithelial-to-mesenchymal transition and metastasis

Although phenotypic intratumoral heterogeneity was first described many decades ago, the advent of next-generation sequencing has provided conclusive evidence that in addition to phenotypic diversity, significant genotypic diversity exists within tumors. Tumor heterogeneity likely arises both from clonal expansions, as well as from differentiation hierarchies existent in the tumor, such as that established by cancer stem cells (CSCs) and non-CSCs. These differentiation hierarchies may arise due to genetic mutations, epigenetic alterations, or microenvironmental influences. An additional differentiation hierarchy within epithelial tumors may arise when only a few tumor cells trans-differentiate into mesenchymal-like cells, a process known as epithelial-to-mesenchymal transition (EMT). Again, this process can be influenced by both genetic and non-genetic factors. In this review we discuss the evidence for clonal interaction and cooperation for tumor maintenance and progression, particularly with respect to EMT, and further address the far-reaching effects that tumor heterogeneity may have on cancer therapy.     

A new era of cancer therapy: cancer cell targeted therapies are coming of age

The large majority of today's cancer therapies are based on the removal of solid tumor masses (for example by surgery when possible) and a plethora of chemical or physical treatments such as chemo- and radiotherapy which induce death of particularly sensitive or rapidly growing cells. These approaches are variously combined in order to optimize therapeutic indices. While in some cases, such as childhood leukemia, these treatments may cure patients, it is common knowledge that they are associated with serious side effects. The main conceptual reason for this is that neither cancer cells nor the cancer cause(s) are directly targeted. In addition to a high toxicity and a low quality of life, these traditional therapies can give rise to therapy-induced secondary cancers. Here we will neither discuss the various optimization possibilities nor arguments for and against established therapies. Rather we want to reflect about recent advances, challenges and perspectives of cancer therapeutic concepts which aim at increasing cancer-selectivity. More precisely, we will discuss two such concepts from a cell biological and molecular oncology perspective, namely to (i) target the cause of the cancer and (ii) to (re)activate specific endogenous pathways for cancer cell-selective apoptosis.     

TGFβ secreted by B16 melanoma antagonizes cancer gene immunotherapy bystander effect

Tumor-targeted delivery of immune stimulatory genes, such as pro-inflammatory cytokines and suicide genes, has shown to cure mouse models of cancer. Total tumor eradication was also found to occur despite subtotal tumor engineering; a phenomenon coined the "bystander effect". The bystander effect in immune competent animals arises mostly from recruitment of a cancer lytic cell-mediated immune response to local and distant tumor cells which escaped gene modification. We have previously described a Granulocyte-Macrophage Colony Stimulating Factor (GM-CSF) and Interleukin 2 (IL2) fusokine (aka GIFT2) which serves as a potent anticancer cytokine and it here served as a means to understand the mechanistic underpinnings to the immune bystander effect in an immune competent model of B16 melanoma. As expected, we observed that GIFT2 secreted by genetically engineered B16 tumor cells induces a bystander effect on non modified B16 cells, when admixed in a 1:1 ratio. However, despite keeping the 1:1 ratio constant, the immune bystander effect was completely lost as the total B16 cell number was increased from 10(4) to 10(6) which correlated with a sharp reduction in the number of tumor-infiltrating NK cells. We found that B16 secrete biologically active TGFbeta which in turn inhibited GIFT2 dependent immune cell proliferation in vitro and downregulated IL-2R beta expression and IFN gamma secretion by NK cells. In vivo blockade of B16 originating TGFbeta significantly improved the immune bystander effect arising from GIFT2. We propose that cancer gene immunotherapy of pre-established tumors will be enhanced by blockade of tumor-derived TGFbeta.