Quiescence: a mechanism for escaping the effects of drug on cell populations

Normalization of the tumor microvasculature based on targeting and modulation of the tumor microenvironment

Angiogenesis is an essential process for tumor development. Owing to the imbalance between pro- and anti-angiogenic factors, the tumor vasculature possesses the characteristics of tortuous, hyperpermeable vessels and compressive force, resulting in a reduction in the effect of traditional chemotherapy and radiotherapy. Anti-angiogenesis has emerged as a promising strategy for cancer treatment. Tumor angiogenesis, however, has been proved to be a complex process in which the tumor microenvironment (TME) plays a vital role in the initiation and development of the tumor microvasculature. The host stromal cells in the TME, such as cancer associated fibroblasts (CAFs), tumor associated macrophages (TAMs) and Treg cells, contribute to angiogenesis. Furthermore, the abnormal metabolic environment, such as hypoxia and acidosis, leads to the up-regulated expression of angiogenic factors. Indeed, normalization of the tumor microvasculature via targeting and modulating the TME has become a promising strategy for anti-angiogenesis and anti-tumor therapy. In this review, we summarize the abnormalities of the tumor microvasculature, tumor angiogenesis induced by an abnormal metabolic environment and host stromal cells, as well as drug delivery therapies to restore the balance between pro- and anti-angiogenic factors by targeting and normalizing the tumor vasculature in the TME.

A branching process model for dormancy and seed banks in randomly fluctuating environments

The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank consisting of dormant individuals when facing fluctuating environmental conditions. To this end, we discuss a class of '2-type' branching processes describing populations of individuals that may switch between 'active' and 'dormant' states in a random environment oscillating between a 'healthy' and a 'harsh' state. We incorporate different switching strategies and suggest a method of 'fair comparison' to incorporate potentially varying reproductive costs. We then use this concept to compare the fitness of the different strategies in terms of maximal Lyapunov exponents. This gives rise to a 'fitness map' depicting the environmental regimes where certain switching strategies are uniquely supercritical.

Role of FBXW7 in the quiescence of gefitinib-resistant lung cancer stem cells in EGFR-mutant non-small cell lung cancer

Several recent studies suggest that cancer stem cells (CSCs) are involved in intrinsic resistance to cancer treatment. Maintenance of quiescence is crucial for establishing resistance of CSCs to cancer therapeutics. F-box/WD repeat-containing protein 7 (FBXW7) is a ubiquitin ligase that regulates quiescence by targeting the c-MYC protein for ubiquitination. We previously reported that gefitinib-resistant persisters (GRPs) in EGFR-mutant non-small cell lung cancer (NSCLC) cells highly expressed octamer-binding transcription factor 4 (Oct-4) as well as the lung CSC marker CD133, and they exhibited distinctive features of the CSC phenotype. However, the role of FBXW7 in lung CSCs and their resistance to epidermal growth factor receptor (EGFR)-tyrosine kinase inhibitors in NSCLC is not fully understood. In this study, we developed GRPs from the two NSCLC cell lines PC9 and HCC827, which express an EGFR exon 19 deletion mutation, by treatment with a high concentration of gefitinib. The GRPs from both PC9 and HCC827 cells expressed high levels of CD133 and FBXW7, but low levels of c-MYC. Cell cycle analysis demonstrated that the majority of GRPs existed in the G0/G1 phase. Knockdown of the FBXW7 gene significantly reduced the cell number of CD133-positive GRPs and reversed the cell population in the G0/G1-phase. We also found that FBXW7 expression in CD133-positive cells was increased and c-MYC expression was decreased in gefitinib-resistant tumors of PC9 cells in mice and in 9 out of 14 tumor specimens from EGFR-mutant NSCLC patients with acquired resistance to gefitinib. These findings suggest that FBXW7 plays a pivotal role in the maintenance of quiescence in gefitinib-resistant lung CSCs in EGFR mutation-positive NSCLC.

Antipsychotic agent pimozide promotes reversible proliferative suppression by inducing cellular quiescence in liver cancer

The antipsychotic drug pimozide has been found to exhibit anticancer effects. Previously, it was demonstrated that pimozide inhibits hepatocellular carcinoma (HCC) cell growth, but its pharmacodynamic characteristics remain unclear. The aim of the present study was to investigate the reversibility and mechanism of the ability of pimozide to inhibit cell proliferation in liver cancer. Cell viability was determined by Cell Counting Kit‑8 and colony formation assay. The cell cycle distribution was analyzed by flow cytometry with Ki‑67 and PI staining. ROS production of HCC cells was detected with DCFH‑DA and inhibited with NAC treatment. Western blot assay was performed to detect the expression of related signaling molecules in HCC cells. Our results showed that pimozide promoted G0/G1 phase arrest in HCC cell lines without significant cell death. Its anti‑proliferative effects on HCC cells were reversible, consistent with involvement of cell quiescence and reactive oxygen species (ROS) production. Pimozide enhanced inhibition of HCC cell proliferation by sorafenib. In conclusion, elucidation of pimozide's reversible proliferation inhibition in liver cancer and additive activity with a well‑established anticancer drug warrants further exploration of the potential of pimozide as an adjuvant anticancer therapy.

Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance to therapy since the rescued population is less sensitive to therapy.

Evolutionary escape on complex genotype-phenotype networks

We study the problem of evolutionary escape that is the process whereby a population under sudden changes in the selective pressures acting upon it try to evade extinction by evolving from previously well-adapted phenotypes to those that are favoured by the new selective pressure. We perform a comparative analysis between results obtained by modelling genotype space as a regular hypercube (H-graphs), which is the scenario considered in previous work on the subject, to those corresponding to a complex genotype-phenotype network (B-graphs). In order to analyse the properties of the escape process on both these graphs, we apply a general theory based on multi-type branching processes to compute the evolutionary dynamics and probability of escape. We show that the distribution of distances between phenotypes in B-graphs exhibits a much larger degree of heterogeneity than in H-graphs. This property, one of the main structural differences between both types of graphs, causes heterogeneous behaviour in all results associated to the escape problem. We further show that, due to the heterogeneity characterising escape on B-graphs, escape probability can be underestimated by assuming a regular hypercube genotype network, even if we compare phenotypes at the same distance in H-graphs. Similarly, it appears that the complex structure of B-graphs slows down the rate of escape.

Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy

HIV-1 infected patients are effectively treated with highly active anti-retroviral therapy (HAART). Whilst HAART is successful in keeping the disease at bay with average levels of viral load well below the detection threshold of standard clinical assays, it fails to completely eradicate the infection, which persists due to the emergence of a latent reservoir with a half-life time of years and is immune to HAART. This implies that life-long administration of HAART is, at the moment, necessary for HIV-1-infected patients, which is prone to drug resistance and cumulative side effects as well as imposing a considerable financial burden on developing countries, those more afflicted by HIV, and public health systems. The development of therapies which specifically aim at the removal of this latent reservoir has become a focus of much research. A proposal for such therapy consists of elevating the rate of activation of the latently infected cells: by transferring cells from the latently infected reservoir to the active infected compartment, more cells are exposed to the anti-retroviral drugs thus increasing their effectiveness. In this paper, we present a stochastic model of the dynamics of the HIV-1 infection and study the effect of the rate of latently infected cell activation on the average extinction time of the infection. By analysing the model by means of an asymptotic approximation using the semi-classical quasi steady state approximation (QSS), we ascertain that this therapy reduces the average life-time of the infection by many orders of magnitudes. We test the accuracy of our asymptotic results by means of direct simulation of the stochastic process using a hybrid multi-scale Monte Carlo scheme.

From invasion to latency: intracellular noise and cell motility as key controls of the competition between resource-limited cellular populations

In this paper we analyse stochastic models of the competition between two resource-limited cell populations which differ in their response to nutrient availability: the resident population exhibits a switch-like response behaviour while the invading population exhibits a bistable response. We investigate how noise in the intracellular regulatory pathways and cell motility influence the fate of the incumbent and invading populations. We focus initially on a spatially homogeneous system and study in detail the role of intracellular noise. We show that in such well-mixed systems, two distinct regimes exist: In the low (intracellular) noise limit, the invader has the ability to invade the resident population, whereas in the high noise regime competition between the two populations is found to be neutral and, in accordance with neutral evolution theory, invasion is a random event. Careful examination of the system dynamics leads us to conclude that (i) even if the invader is unable to invade, the distribution of survival times, PS(t), has a fat-tail behaviour (PS(t) ∼ t(-1)) which implies that small colonies of mutants can coexist with the resident population for arbitrarily long times, and (ii) the bistable structure of the invading population increases the stability of the latent population, thus increasing their long-term likelihood of survival, by decreasing the intensity of the noise at the population level. We also examine the effects of spatial inhomogeneity. In the low noise limit we find that cell motility is positively correlated with the aggressiveness of the invader as defined by the time the invader takes to invade the resident population: the faster the invasion, the more aggressive the invader.

Surviving evolutionary escape on complex genotype-phenotype networks

We study the problem of evolutionary escape and survival of cell populations with a genotype-phenotype structure. We refer to evolutionary escape as the process where a cell of a given ill-adapted population to reach a well-adapted phenotype. Similarly, survival refers to the dynamics of the population once the escape phenotype has been reached. The aim of this paper is to analyse the influence of topological properties associated to robustness and evolvability on the probability of escape and on the probability of survival. In order to explore these issues, we formulate a population dynamics model, consisting of a multi-type time-continuous branching process, where types are associated to genotypes and their birth and death probabilities depend on the associated phenotype (non-escape or escape). We exploit the separation of time scales introduced by the the difference in reproductive ratios between the ill-adapted phenotypes and the escape phenotype. Two dynamical regimes emerge: a fast-decaying regime associated to the escape process itself, and a slow regime which corresponds to the survival dynamics of the population once the escape phenotype has been reached. We exploit this separation of time scales to analyse the topological factors which determine escape and survival probabilities. We show that, while the escape probability depends on the degree of escape phenotype, the probability of survival is essentially determined by its robustness, measured in terms of a weighted clustering coefficient.

Hydrogen peroxide modulates the proliferation/quiescence switch in the liver during embryonic development and posthepatectomy regeneration

AIMS

The liver undergoes marked changes in the rate of proliferation during normal development and regeneration through the coordinated activity of numerous signaling pathways. Little is known, however, about the events that act upstream of these signaling pathways. Here, we explore the modulatory effects of hydrogen peroxide (H2O2) on these pathways in the context of liver development and regeneration.

RESULTS

We show that H2O2 production during liver development and after partial hepatectomy is tightly regulated in time by specific H2O2-producing and scavenging proteins and dose dependently triggers two distinct pathways. Sustained elevated H2O2 levels are required for the activation of ERK signaling and trigger a shift from quiescence to proliferation. Contrastingly, sustained decreased H2O2 levels are required for the activation of p38 signaling and trigger a shift from proliferation to quiescence. Both events impact the cyclin D and Rb pathways and are involved in liver development and regeneration. Pharmacological lowering of H2O2 levels reduces the extent of fetal hepatocyte proliferation and delays the onset of liver regeneration. Chemical augmentation of H2O2 levels in adult hepatocytes triggers proliferation and delays the termination of liver regeneration.

INNOVATION

Our results challenge the traditional view of H2O2 as a deleterious stressor in response to liver damage and identify a novel role of endogenous H2O2 in liver development and regeneration.

CONCLUSIONS

Endogenous H2O2 production is tightly regulated during liver development and regeneration. H2O2 constitutes an important trigger for the proliferation and quiescence transition in hepatocytes via the concentration-dependent activation of the ERK or p38 pathway.

Stochastic modelling of viral blips in HIV-1-infected patients: effects of inhomogeneous density fluctuations

We propose a stochastic model of HIV-1 infection dynamics under HAART in order to analyse the origin and dynamics of the so-called viral blips, i.e. episodes of transient viremia that occur in the phase of where the disease remains in a latent state during which the viral load raises above the detection limit of standard clinical assays. Based on prior work in the subject, we consider an infection model in which latently infected cell compartment sustains a residual (latent) infection over long periods of time. Unlike previous models, we include the effects of inhomogeneities in cell and virus concentration in the blood stream. We further consider the effect of burst virion production. By comparing with the experimental results obtained during a study in which intensive sampling was carried out on HIV-1-infected patients undergoing HAART over a long period of time, we conclude that our model supports the hypothesis that viral blips are consistent with random fluctuations around the average viral load. We further observe that agreement between our simulation results and the blip statistics obtained in the aforementioned study improves when burst virion production is considered. We also study the effect of sample manipulation artifacts on the results produced by our model, in particular, that of the post-extraction handling time, i.e. the time elapsed between sample extraction and actual test. Our results support the notion that the statistics of viral blips can be critically affected by such artifacts.

Robustness of differentiation cascades with symmetric stem cell division

Stem cells (SCs) perform the task of maintaining tissue homeostasis by both self-renewal and differentiation. While it has been argued that SCs divide asymmetrically, there is also evidence that SCs undergo symmetric division. Symmetric SC division has been speculated to be key for expanding cell numbers in development and regeneration after injury. However, it might lead to uncontrolled growth and malignancies such as cancer. In order to explore the role of symmetric SC division, we propose a mathematical model of the effect of symmetric SC division on the robustness of a population regulated by a serial differentiation cascade and we show that this may lead to extinction of such population. We examine how the extinction likelihood depends on defining characteristics of the population such as the number of intermediate cell compartments. We show that longer differentiation cascades are more prone to extinction than systems with less intermediate compartments. Furthermore, we have analysed the possibility of mixed symmetric and asymmetric cell division against invasions by mutant invaders in order to find optimal architecture. Our results show that more robust populations are those with unfrequent symmetric behaviour.

A mathematical model of HiF-1α-mediated response to hypoxia on the G1/S transition

Hypoxia is known to influence the cell cycle by increasing the G1 phase duration or by inducing a quiescent state (arrest of cell proliferation). This entry into quiescence is a mean for the cell to escape from hypoxia-induced apoptosis. It is suggested that some cancer cells have gain the advantage over normal cells to easily enter into quiescence when environmental conditions, such as oxygen pressure, are unfavorable [43,1]. This ability contributes in the appearance of highly resistant and aggressive tumor phenotypes [2]. The HiF-1α factor is the key actor of the intracellular hypoxia pathway. As tumor cells undergo chronic hypoxic conditions, HiF-1α is present in higher level in cancer than in normal cells. Besides, it was shown that genetic mutations promoting overstabilization of HiF-1α are a feature of various types of cancers [7]. Finally, it is suggested that the intracellular level of HiF-1α can be related to the aggressiveness of the tumors [53,24,4,10]. However, up to now, mathematical models describing the G1/S transition under hypoxia, did not take into account the HiF-1α factor in the hypoxia pathway. Therefore, we propose a mathematical model of the G1/S transition under hypoxia, which explicitly integrates the HiF-1α pathway. The model reproduces the slowing down of G1 phase under moderate hypoxia, and the entry into quiescence of proliferating cells under severe hypoxia. We show how the inhibition of cyclin D by HiF-1α can induce quiescence; this result provides a theoretical explanation to the experimental observations of Wen et al. (2010) [50]. Thus, our model confirms that hypoxia-induced chemoresistance can be linked, for a part, to the negative regulation of cyclin D by HiF-1α.

Parameter non-identifiability of the Gyllenberg-Webb ODE model

An ODE model introduced by Gyllenberg and Webb (Growth Develop Aging 53:25-33, 1989) describes tumour growth in terms of the dynamics between proliferating and quiescent cell states. The passage from one state to another and vice versa is modelled by two functions r0 and ri depending on the total tumour size. As these functions do not represent any observable quantities, they have to be identified from the observations. In this paper we show that there is an infinite number of pairs (r0, ri) corresponding to the same solution of the ODE system and the functions (r0, ri) will be classified in terms of this equivalence. Surprisingly, the technique used for this classification permits a uniqueness proof of the solution of the ODE model in a non-Lipschitz case. The reasoning can be widened to a more general setting including an extension of the Gyllenberg-Webb model with a nonlinear birth rate. The relevance of this result is discussed in a preclinical application scenario.