The Cancer Stem Cell Fraction in Hierarchically Organized Tumors Can Be Estimated Using Mathematical Modeling and Patient-Specific Treatment Trajectories

Stochastic journeys of cell progenies through compartments and the role of self-renewal, symmetric and asymmetric division

Division and differentiation events by which cell populations with specific functions are generated often take place as part of a developmental programme, which can be represented by a sequence of compartments. A compartment is the set of cells with common characteristics; sharing, for instance, a spatial location or a phenotype. Differentiation events are transitions from one compartment to the next. Cells may also die or divide. We consider three different types of division events: (i) where both daughter cells inherit the mother's phenotype (self-renewal), (ii) where only one of the daughters changes phenotype (asymmetric division), and (iii) where both daughters change phenotype (symmetric division). The self-renewal probability in each compartment determines whether the progeny of a single cell, moving through the sequence of compartments, is finite or grows without bound. We analyse the progeny stochastic dynamics with probability generating functions. In the case of self-renewal, by following one of the daughters after any division event, we may construct lifelines containing only one cell at any time. We analyse the number of divisions along such lines, and the compartment where lines terminate with a death event. Analysis and numerical simulations are applied to a five-compartment model of the gradual differentiation of hematopoietic stem cells and to a model of thymocyte development: from pre-double positive to single positive (SP) cells with a bifurcation to either SP4 or SP8 in the last compartment of the sequence.

Measures of genetic diversification in somatic tissues at bulk and single-cell resolution

Intra-tissue genetic heterogeneity is universal to both healthy and cancerous tissues. It emerges from the stochastic accumulation of somatic mutations throughout development and homeostasis. By combining population genetics theory and genomic information, genetic heterogeneity can be exploited to infer tissue organization and dynamics in vivo. However, many basic quantities, for example the dynamics of tissue-specific stem cells remain difficult to quantify precisely. Here, we show that single-cell and bulk sequencing data inform on different aspects of the underlying stochastic processes. Bulk-derived variant allele frequency spectra (VAF) show transitions from growing to constant stem cell populations with age in samples of healthy esophagus epithelium. Single-cell mutational burden distributions allow a sample size independent measure of mutation and proliferation rates. Mutation rates in adult hematopietic stem cells are higher compared to inferences during development, suggesting additional proliferation-independent effects. Furthermore, single-cell derived VAF spectra contain information on the number of tissue-specific stem cells. In hematopiesis, we find approximately 2 × 105 HSCs, if all stem cells divide symmetrically. However, the single-cell mutational burden distribution is over-dispersed compared to a model of Poisson distributed random mutations. A time-associated model of mutation accumulation with a constant rate alone cannot generate such a pattern. At least one additional source of stochasticity would be needed. Possible candidates for these processes may be occasional bursts of stem cell divisions, potentially in response to injury, or non-constant mutation rates either through environmental exposures or cell-intrinsic variation.

On tumoural growth and treatment under cellular dedifferentiation

Differentiated cancer cells may regain stem cell characteristics; however, the effects of such a cellular dedifferentiation on tumoural growth and treatment are currently understudied. Thus, we here extend a mathematical model of cancer stem cell (CSC) driven tumour growth to also include dedifferentiation. We show that dedifferentiation increases the likelihood of tumorigenesis and the speed of tumoural growth, both modulated by the proliferative potential of the non-stem cancer cells (NSCCs). We demonstrate that dedifferentiation also may lead to treatment evasion, especially when a treatment solely targets CSCs. Conversely, targeting both CSCs and NSCCs in parallel is shown to be more robust to dedifferentiation. Despite dedifferentiation, perturbing CSC-related parameters continues to exert the largest relative effect on tumoural growth; however, we show the existence of synergies between specific CSC- and NSCC-directed treatments which cause superadditive reductions of tumoural growth. Overall, our study demonstrates various effects of dedifferentiation on growth and treatment of tumoural lesions, and we anticipate our results to be helpful in guiding future molecular and clinical research on limiting tumoural growth in vivo.

Cells and material-based strategies for regenerative endodontics

<p class = "Abstract" style = "margin: 0 cm; line-height: 32px; font-size: 12 pt; font-family: "Times New Roman", serif; color: rgb(0, 0, 0); "><span lang = "EN-US">The carious process leads to inflammation of pulp tissue. Current care options include root canal treatment or apexification. These procedures, however, result in the loss of tooth vitality, sensitivity, and healing. Pulp capping and dental pulp regeneration are continually evolving techniques to regenerate pulp tissue, avoiding necrosis and loss of vitality. Many studies have successfully employed stem/progenitor cell populations, revascularization approaches, scaffolds or material-based strategies for pulp regeneration. Here we outline advantages and disadvantages of different methods and techniques which are currently being used in the field of regenerative endodontics. We also summarize recent findings on efficacious peptide-based materials which target the dental niche.<o:p></o:p></span></p>

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Pulp infection necessitates removal of necrotic, inflamed and infected tissue.

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Materials used clinically are inert (such as gutta percha, mineral trioxide aggregate).

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Recent developments in materials (angiogenic hydrogels, stem cell composites) have tuneable bioactivity.

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Dental pulp regeneration may now be possible through the use of bioactive systems, that guide regeneration.

A modified fluctuation-test framework characterizes the population dynamics and mutation rate of colorectal cancer persister cells

Compelling evidence shows that cancer persister cells represent a major limit to the long-term efficacy of targeted therapies. However, the phenotype and population dynamics of cancer persister cells remain unclear. We developed a quantitative framework to study persisters by combining experimental characterization and mathematical modeling. We found that, in colorectal cancer, a fraction of persisters slowly replicates. Clinically approved targeted therapies induce a switch to drug-tolerant persisters and a temporary 7- to 50-fold increase of their mutation rate, thus increasing the number of persister-derived resistant cells. These findings reveal that treatment may influence persistence and mutability in cancer cells and pinpoint inhibition of error-prone DNA polymerases as a strategy to restrict tumor recurrence.

Data-Driven Discovery of Mathematical and Physical Relations in Oncology Data Using Human-Understandable Machine Learning

For decades, researchers have used the concepts of rate of change and differential equations to model and forecast neoplastic processes. This expressive mathematical apparatus brought significant insights in oncology by describing the unregulated proliferation and host interactions of cancer cells, as well as their response to treatments. Now, these theories have been given a new life and found new applications. With the advent of routine cancer genome sequencing and the resulting abundance of data, oncology now builds an "arsenal" of new modeling and analysis tools. Models describing the governing physical laws of tumor-host-drug interactions can be now challenged with biological data to make predictions about cancer progression. Our study joins the efforts of the mathematical and computational oncology community by introducing a novel machine learning system for data-driven discovery of mathematical and physical relations in oncology. The system utilizes computational mechanisms such as competition, cooperation, and adaptation in neural networks to simultaneously learn the statistics and the governing relations between multiple clinical data covariates. Targeting an easy adoption in clinical oncology, the solutions of our system reveal human-understandable properties and features hidden in the data. As our experiments demonstrate, our system can describe nonlinear conservation laws in cancer kinetics and growth curves, symmetries in tumor's phenotypic staging transitions, the preoperative spatial tumor distribution, and up to the nonlinear intracellular and extracellular pharmacokinetics of neoadjuvant therapies. The primary goal of our work is to enhance or improve the mechanistic understanding of cancer dynamics by exploiting heterogeneous clinical data. We demonstrate through multiple instantiations that our system is extracting an accurate human-understandable representation of the underlying dynamics of physical interactions central to typical oncology problems. Our results and evaluation demonstrate that, using simple-yet powerful-computational mechanisms, such a machine learning system can support clinical decision-making. To this end, our system is a representative tool of the field of mathematical and computational oncology and offers a bridge between the data, the modeler, the data scientist, and the practicing clinician.

The Multiple Dimensions of Networks in Cancer: A Perspective

This perspective article gathers the latest developments in mathematical and computational oncology tools that exploit network approaches for the mathematical modelling, analysis, and simulation of cancer development and therapy design. It instigates the community to explore new paths and synergies under the umbrella of the Special Issue “Networks in Cancer: From Symmetry Breaking to Targeted Therapy”. The focus of the perspective is to demonstrate how networks can model the physics, analyse the interactions, and predict the evolution of the multiple processes behind tumour-host encounters across multiple scales. From agent-based modelling and mechano-biology to machine learning and predictive modelling, the perspective motivates a methodology well suited to mathematical and computational oncology and suggests approaches that mark a viable path towards adoption in the clinic.

Inferring Tumor Proliferative Organization from Phylogenetic Tree Measures in a Computational Model

We use a computational modeling approach to explore whether it is possible to infer a solid tumor's cellular proliferative hierarchy under the assumptions of the cancer stem cell hypothesis and neutral evolution. We work towards inferring the symmetric division probability for cancer stem cells, since this is believed to be a key driver of progression and therapeutic response. Motivated by the advent of multiregion sampling and resulting opportunities to infer tumor evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumor's evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumors by this biological parameter and also generate a number of actionable clinical and biological hypotheses regarding changes during therapy, and through tumor evolutionary time. [Cancer; evolution; phylogenetics.].

The ecology of cancer differentiation therapy

A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.

Evidence for hypoxia increasing the tempo of evolution in glioblastoma

BACKGROUND

Tumour hypoxia is associated with metastatic disease, and while there have been many mechanisms proposed for why tumour hypoxia is associated with metastatic disease, it remains unclear whether one precise mechanism is the key reason or several in concert. Somatic evolution drives cancer progression and treatment resistance, fuelled not only by genetic and epigenetic mutation but also by selection from interactions between tumour cells, normal cells and physical micro-environment. Ecological habitats influence evolutionary dynamics, but the impact on tempo of evolution is less clear.

METHODS

We explored this complex dialogue with a combined clinical-theoretical approach by simulating a proliferative hierarchy under heterogeneous oxygen availability with an agent-based model. Predictions were compared against histology samples taken from glioblastoma patients, stained to elucidate areas of necrosis and TP53 expression heterogeneity.

RESULTS

Results indicate that cell division in hypoxic environments is effectively upregulated, with low-oxygen niches providing avenues for tumour cells to spread. Analysis of human data indicates that cell division is not decreased under hypoxia, consistent with our results.

CONCLUSIONS

Our results suggest that hypoxia could be a crucible that effectively warps evolutionary velocity, making key mutations more likely. Thus, key tumour ecological niches such as hypoxic regions may alter the evolutionary tempo, driving mutations fuelling tumour heterogeneity.

Modeling Resistance and Recurrence Patterns of Combined Targeted-Chemoradiotherapy Predicts Benefit of Shorter Induction Period

Optimal integration of molecularly targeted therapies, such as tyrosine kinase inhibitors (TKI), with concurrent chemotherapy and radiation (CRT) to improve outcomes in genotype-defined cancers remains a current challenge in clinical settings. Important questions regarding optimal scheduling and length of induction period for neoadjuvant use of targeted agents remain unsolved and vary among clinical trial protocols. Here, we develop and validate a biomathematical framework encompassing drug resistance and radiobiology to simulate patterns of local versus distant recurrences in a non-small cell lung cancer (NSCLC) population with mutated EGFR receiving TKIs and CRT. Our model predicted that targeted induction before CRT, an approach currently being tested in clinical trials, may render adjuvant targeted therapy less effective due to proliferation of drug-resistant cancer cells when using very long induction periods. Furthermore, simulations not only demonstrated the competing effects of drug-resistant cell expansion versus overall tumor regression as a function of induction length, but also directly estimated the probability of observing an improvement in progression-free survival at a given cohort size. We thus demonstrate that such stochastic biological simulations have the potential to quantitatively inform the design of multimodality clinical trials in genotype-defined cancers. SIGNIFICANCE: A biomathematical framework based on fundamental principles of evolution and radiobiology for in silico clinical trial design allows clinicians to optimize administration of TKIs before chemoradiotherapy in oncogene-driven NSCLC.

An Optimal Control Framework for the Automated Design of Personalized Cancer Treatments

One of the key challenges in current cancer research is the development of computational strategies to support clinicians in the identification of successful personalized treatments. Control theory might be an effective approach to this end, as proven by the long-established application to therapy design and testing. In this respect, we here introduce the Control Theory for Therapy Design (CT4TD) framework, which employs optimal control theory on patient-specific pharmacokinetics (PK) and pharmacodynamics (PD) models, to deliver optimized therapeutic strategies. The definition of personalized PK/PD models allows to explicitly consider the physiological heterogeneity of individuals and to adapt the therapy accordingly, as opposed to standard clinical practices. CT4TD can be used in two distinct scenarios. At the time of the diagnosis, CT4TD allows to set optimized personalized administration strategies, aimed at reaching selected target drug concentrations, while minimizing the costs in terms of toxicity and adverse effects. Moreover, if longitudinal data on patients under treatment are available, our approach allows to adjust the ongoing therapy, by relying on simplified models of cancer population dynamics, with the goal of minimizing or controlling the tumor burden. CT4TD is highly scalable, as it employs the efficient dCRAB/RedCRAB optimization algorithm, and the results are robust, as proven by extensive tests on synthetic data. Furthermore, the theoretical framework is general, and it might be applied to any therapy for which a PK/PD model can be estimated, and for any kind of administration and cost. As a proof of principle, we present the application of CT4TD to Imatinib administration in Chronic Myeloid leukemia, in which we adopt a simplified model of cancer population dynamics. In particular, we show that the optimized therapeutic strategies are diversified among patients, and display improvements with respect to the current standard regime.

A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration

Stem cell heterogeneity is essential for homeostasis in tissue development. This paper establishes a general mathematical framework to model the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The framework generalizes the classical G0 cell cycle model and incorporates the epigenetic states of individual cells represented by a continuous multidimensional variable. In the model, the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, are dependent on their epigenetic states, and the random transitions of epigenetic states between cell cycles are represented by an inheritance probability function that describes the conditional probability of cell state changes. Moreover, the model can be extended to include genotypic changes and describe the process of gene mutation-induced tumor development. The proposed mathematical framework provides a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.

Mathematical modeling reveals the factors involved in the phenomena of cancer stem cells stabilization

Cancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, isolated CSCs rapidly regenerate the original population of stem and non-stem cells (non-CSCs) as shown by various investigators. This phenomenon still remains to be explained. We propose a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and non-CSCs sub-populations, and taking into account the stabilization phenomenon. The analysis of the model allows determination of time-varying corridors of probabilities for different cell fates, given the particular dynamics of cancer cells populations; and determination of a cell-cell communication factors influencing these time-varying probabilities of cell behavior (division, transition) scenarios. Though the results of the model have to be experimentally confirmed, we can anticipate the development of several fundamental and practical applications based on the theoretical results of the model.

Patient-Specific Tumor Growth Trajectories Determine Persistent and Resistant Cancer Cell Populations during Treatment with Targeted Therapies

The importance of preexisting versus acquired drug resistance in patients with cancer treated with small-molecule tyrosine kinase inhibitors (TKI) remains controversial. The goal of this study is to provide a general estimate of the size and dynamics of a preexisting, drug-resistant tumor cell population versus a slow-growing persister population that is the precursor of acquired TKI resistance. We describe a general model of resistance development, including persister evolution and preexisting resistance, solely based on the macroscopic trajectory of tumor burden during treatment. We applied the model to 20 tumor volume trajectories of EGFR-mutant lung cancer patients treated with the TKI erlotinib. Under the assumption of only preexisting resistant cells or only persister evolution, it is not possible to explain the observed tumor trajectories with realistic parameter values. Assuming only persister evolution would require very high mutation induction rates, while only preexisting resistance would lead to very large preexisting populations of resistant cells at the initiation of treatment. However, combining preexisting resistance with persister populations can explain the observed tumor volume trajectories and yields an estimated preexisting resistant fraction varying from 10-4 to 10-1 at the time of treatment initiation for this study cohort. Our results also demonstrate that the growth rate of the resistant population is highly correlated to the time to tumor progression. These estimates of the size of the resistant and persistent tumor cell population during TKI treatment can inform combination treatment strategies such as multi-agent schedules or a combination of targeted agents and radiotherapy. SIGNIFICANCE: These findings quantify pre-existing resistance and persister cell populations, which are essential for the integration of targeted agents into the management of locally advanced disease and the timing of radiotherapy in metastatic patients.

Engineered 3D Model of Cancer Stem Cell Enrichment and Chemoresistance

Intraperitoneal dissemination of ovarian cancers is preceded by the development of chemoresistant tumors with malignant ascites. Despite the high levels of chemoresistance and relapse observed in ovarian cancers, there are no in vitro models to understand the development of chemoresistance in situ. Method: We describe a highly integrated approach to establish an in vitro model of chemoresistance and stemness in ovarian cancer, using the 3D hanging drop spheroid platform. The model was established by serially passaging non-adherent spheroids. At each passage, the effectiveness of the model was evaluated via measures of proliferation, response to treatment with cisplatin and a novel ALDH1A inhibitor. Concomitantly, the expression and tumor initiating capacity of cancer stem-like cells (CSCs) was analyzed. RNA-seq was used to establish gene signatures associated with the evolution of tumorigenicity, and chemoresistance. Lastly, a mathematical model was developed to predict the emergence of CSCs during serial passaging of ovarian cancer spheroids. Results: Our serial passage model demonstrated increased cellular proliferation, enriched CSCs, and emergence of a platinum resistant phenotype. In vivo tumor xenograft assays indicated that later passage spheroids were significantly more tumorigenic with higher CSCs, compared to early passage spheroids. RNA-seq revealed several gene signatures supporting the emergence of CSCs, chemoresistance, and malignant phenotypes, with links to poor clinical prognosis. Our mathematical model predicted the emergence of CSC populations within serially passaged spheroids, concurring with experimentally observed data. Conclusion: Our integrated approach illustrates the utility of the serial passage spheroid model for examining the emergence and development of chemoresistance in ovarian cancer in a controllable and reproducible format.

Illuminating the Numbers: Integrating Mathematical Models to Optimize Photomedicine Dosimetry and Combination Therapies

Cancer photomedicine offers unique mechanisms for inducing local tumor damage with the potential to stimulate local and systemic anti-tumor immunity. Optically-active nanomedicine offers these features as well as spatiotemporal control of tumor-focused drug release to realize synergistic combination therapies. Achieving quantitative dosimetry is a major challenge, and dosimetry is fundamental to photomedicine for personalizing and tailoring therapeutic regimens to specific patients and anatomical locations. The challenge of dosimetry is perhaps greater for photomedicine than many standard therapies given the complexity of light delivery and light-tissue interactions as well as the resulting photochemistry responsible for tumor damage and drug-release, in addition to the usual intricacies of therapeutic agent delivery. An emerging multidisciplinary approach in oncology utilizes mathematical and computational models to iteratively and quantitively analyze complex dosimetry, and biological response parameters. These models are parameterized by preclinical and clinical observations and then tested against previously unseen data. Such calibrated and validated models can be deployed to simulate treatment doses, protocols, and combinations that have not yet been experimentally or clinically evaluated and can provide testable optimal treatment outcomes in a practical workflow. Here, we foresee the utility of these computational approaches to guide adaptive therapy, and how mathematical models might be further developed and integrated as a novel methodology to guide precision photomedicine.

Mathematical modeling of bone marrow - peripheral blood dynamics in the disease state based on current emerging paradigms, part II

The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction. Accordingly, the mathematical challenges brought on by the model that mirror general challenges in dealing with nonlinear phenomena are discussed and placed in context. The proposed model describes the logical occurrence of discrete time delays, that by themselves present mathematical challenges, in the evolving cell populations under consideration. Under the challenging circumstances, the steady state properties of the model system of delay differential equations are obtained, analyzed, and the resulting mathematical predictions arising therefrom are interpreted and placed within the framework of findings regarding CSCs. Simulations of the model are carried out by considering various parameter scenarios that reflect different experimental situations involving disease evolution in human hosts. Model analyses and simulations suggest that the emergence of the cancer stem cell population alongside other malignant cells engenders higher dimensions of complexity in the evolution of malignancy in the bone marrow and peripheral blood at the expense of healthy hematopoietic development. The model predicts the evolution of an aberrant environment in which the malignant population particularly in the bone marrow shows tendencies of reaching an uncontrollable equilibrium state. Essentially, the model shows that a structural relationship exists between CSCs and non-stem malignant cells that confers on CSCs the role of temporally enhancing and stimulating the expansion of non-stem malignant cells while also benefitting from increases in their own population and these CSCs may be the main protagonists that drive the ultimate evolution of the uncontrollable equilibrium state of such malignant cells and these may have implications for treatment.

Modelling of the SDF-1/CXCR4 regulated in vivo homing of therapeutic mesenchymal stem/stromal cells in mice

Background

Mesenchymal stem/stromal cells (MSCs) are a promising tool for cell-based therapies in the treatment of tissue injury. The stromal cell-derived factor-1 (SDF-1)/CXC chemokine receptor 4 (CXCR4) axis plays a significant role in directing MSC homing to sites of injury. However in vivo MSC distribution following intravenous transplantation remains poorly understood, potentially hampering the precise prediction and evaluation of therapeutic efficacy.

Methods

A murine model of partial ischemia/reperfusion (I/R) is used to induce liver injury, increase the hepatic levels of SDF-1, and study in vivo MSC distribution. Hypoxia-preconditioning increases the expression of CXCR4 in human bone marrow-derived MSCs. Quantitative assays for human DNA using droplet digital PCR (ddPCR) allow us to examine the in vivo kinetics of intravenously infused human MSCs in mouse blood and liver. A mathematical model-based system is developed to characterize in vivo homing of human MSCs in mouse models with SDF-1 levels in liver and CXCR4 expression on the transfused MSCs. The model is calibrated to experimental data to provide novel estimates of relevant parameter values.

Results

Images of immunohistochemistry for SDF-1 in the mouse liver with I/R injury show a significantly higher SDF-1 level in the I/R injured liver than that in the control. Correspondingly, the ddPCR results illustrate a higher MSC concentration in the I/R injured liver than the normal liver. CXCR4 is overexpressed in hypoxia-preconditioned MSCs. An increased number of hypoxia-preconditioned MSCs in the I/R injured liver is observed from the ddPCR results. The model simulations align with the experimental data of control and hypoxia-preconditioned human MSC distribution in normal and injured mouse livers, and accurately predict the experimental outcomes with different MSC doses.

Discussion

The modelling results suggest that SDF-1 in organs is an effective in vivo attractant for MSCs through the SDF-1/CXCR4 axis and reveal the significance of the SDF-1/CXCR4 chemotaxis on in vivo homing of MSCs. This in vivo modelling approach allows qualitative characterization and prediction of the MSC homing to normal and injured organs on the basis of clinically accessible variables, such as the MSC dose and SDF-1 concentration in blood. This model could also be adapted to abnormal conditions and/or other types of circulating cells to predict in vivo homing patterns.

Effect of cellular de-differentiation on the dynamics and evolution of tissue and tumor cells in mathematical models with feedback regulation

Tissues are maintained by adult stem cells that self-renew and also differentiate into functioning tissue cells. Homeostasis is achieved by a set of complex mechanisms that involve regulatory feedback loops. Similarly, tumors are believed to be maintained by a minority population of cancer stem cells, while the bulk of the tumor is made up of more differentiated cells, and there is indication that some of the feedback loops that operate in tissues continue to be functional in tumors. Mathematical models of such tissue hierarchies, including feedback loops, have been analyzed in a variety of different contexts. Apart from stem cells giving rise to differentiated cells, it has also been observed that more differentiated cells can de-differentiate into stem cells, both in healthy tissue and tumors, aspects of which have also been investigated mathematically. This paper analyses the effect of de-differentiation on the basic and evolutionary dynamics of cells in the context of tissue hierarchy models that include negative feedback regulation of the cell populations. The models predict that in the presence of de-differentiation, the fixation probability of a neutral mutant is lower than in its absence. Therefore, if de-differentiation occurs, a mutant with identical parameters compared to the wild-type cell population behaves like a disadvantageous mutant. Similarly, the process of de-differentiation is found to lower the fixation probability of an advantageous mutant. These results indicate that the presence of de-differentiation can lower the rates of tumor initiation and progression in the context of the models considered here.

Emerging functional markers for cancer stem cell-based therapies: Understanding signaling networks for targeting metastasis

Metastasis is one of the most challenging issues in cancer patient management, and effective therapies to specifically target disease progression are missing, emphasizing the urgent need for developing novel anti-metastatic therapeutics. Cancer stem cells (CSCs) gained fast attention as a minor population of highly malignant cells within liquid and solid tumors that are responsible for tumor onset, self-renewal, resistance to radio- and chemotherapies, and evasion of immune surveillance accelerating recurrence and metastasis. Recent progress in the identification of their phenotypic and molecular characteristics and interactions with the tumor microenvironment provides great potential for the development of CSC-based targeted therapies and radical improvement in metastasis prevention and cancer patient prognosis. Here, we report on newly uncovered signaling mechanisms controlling CSC's aggressiveness and treatment resistance, and CSC-specific agents and molecular therapeutics, some of which are currently under investigation in clinical trials, gearing towards decisive functional CSC intrinsic or surface markers. One special research focus rests upon subverted regulatory pathways such as insulin-like growth factor 1 receptor signaling and its interactors in metastasis-initiating cell populations directly related to the gain of stem cell- and EMT-associated properties, as well as key components of the E2F transcription factor network regulating metastatic progression, microenvironmental changes, and chemoresistance. In addition, the study provides insight into systems biology tools to establish complex molecular relationships behind the emergence of aggressive phenotypes from high-throughput data that rely on network-based analysis and their use to investigate immune escape mechanisms or predict clinical outcome-relevant CSC receptor signaling signatures. We further propose that customized vector technologies could drastically enhance systemic drug delivery to target sites, and summarize recent progress and remaining challenges. This review integrates available knowledge on CSC biology, computational modeling approaches, molecular targeting strategies, and delivery techniques to envision future clinical therapies designed to conquer metastasis-initiating cells.

Reduced tyrosine kinase inhibitor dose is predicted to be as effective as standard dose in chronic myeloid leukemia: a simulation study based on phase III trial data

Continuing tyrosine kinase inhibitor (TKI)-mediated targeting of the BCR-ABL1 oncoprotein is the standard therapy for chronic myeloid leukemia (CML) and allows for a sustained disease control in the majority of patients. While therapy cessation for patients appeared as a safe option for about half of those patients with optimal response, no systematic assessment of long-term TKI dose de-escalation has been made. We use a mathematical model to analyze and consistently describe biphasic treatment responses from TKI-treated patients from two independent clinical phase III trials. Scale estimates reveal that drug efficiency determines the initial response while the long-term behavior is limited by the rare activation of leukemic stem cells. We use this mathematical framework to investigate the influence of different dosing regimens on the treatment outcome. We provide strong evidence to suggest that TKI dose de-escalation (at least 50%) does not lead to a reduction of long-term treatment efficiency for most patients, who have already achieved sustained remission, and maintains the secondary decline of BCR-ABL1 levels. We demonstrate that continuous BCR-ABL1 monitoring provides patient-specific predictions of an optimal reduced dose without decreasing the anti-leukemic effect on residual leukemic stem cells. Our results are consistent with the interim results of the DESTINY trial and provide clinically testable predictions. Our results suggest that dose-halving should be considered as a long-term treatment option for CML patients with good response under continuing maintenance therapy with TKIs. We emphasize the clinical potential of this approach to reduce treatment-related side-effects and treatment costs.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

gDNA qPCR is statistically more reliable than mRNA analysis in detecting leukemic cells to monitor CML

Chronic Myeloid Leukemia (CML) is a stem cell cancer that arises when t(9;22) translocation occurs in a hematopoietic stem cells. This event results in the expression of the BCR-ABL1 fusion gene, which codes for a constitutively active tyrosine kinase that is responsible for the transformation of a HSC into a CML stem cell, which then gives rise to a clonal myeloproliferative disease. The introduction of Tyrosine Kinase Inhibitors (TKIs) has revolutionized the management of the disease. However, these drugs do not seem to be able to eradicate the malignancy. Indeed, discontinuation trials (STIM; TWISER; DADI) for those patients who achieved a profound molecular response showed 50% relapsing within 12 months. We performed a comparative analysis on 15 CML patients and one B-ALL patient, between the standard quantitative reverse-transcriptase PCR (qRT-PCR) and our genomic DNA patient-specific quantitative PCR assay (gDNA qPCR). Here we demonstrate that gDNA qPCR is better than standard qRT-PCR in disease monitoring after an average follow-up period of 200 days. Specifically, we statistically demonstrated that DNA negativity is more reliable than RNA negativity in indicating when TKIs therapy can be safely stopped.

A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment

Targeting key regulators of the cancer stem cell phenotype to overcome their critical influence on tumor growth is a promising new strategy for cancer treatment. Here we present a modeling framework that operates at both the cellular and molecular levels, for investigating IL-6 mediated, cancer stem cell driven tumor growth and targeted treatment with anti-IL6 antibodies. Our immediate goal is to quantify the influence of IL-6 on cancer stem cell self-renewal and survival, and to characterize the subsequent impact on tumor growth dynamics. By including the molecular details of IL-6 binding, we are able to quantify the temporal changes in fractional occupancies of bound receptors and their influence on tumor volume. There is a strong correlation between the model output and experimental data for primary tumor xenografts. We also used the model to predict tumor response to administration of the humanized IL-6R monoclonal antibody, tocilizumab (TCZ), and we found that as little as 1mg/kg of TCZ administered weekly for 7 weeks is sufficient to result in tumor reduction and a sustained deceleration of tumor growth.

A small population of cancer stem cells that share many of the biological characteristics of normal adult stem cells are believed to initiate and sustain tumor growth for a wide variety of malignancies. Growth and survival of these cancer stem cells is highly influenced by tumor micro-environmental factors and molecular signaling initiated by cytokines and growth factors. This work focuses on quantifying the influence of IL-6, a pleiotropic cytokine secreted by a variety of cell types, on cancer stem cell self-renewal and survival. We present a mathematical model for IL-6 mediated, cancer stem cell driven tumor growth that operates at the following levels: (1) the molecular level—capturing cell surface dynamics of receptor-ligand binding and receptor activation that lead to intra-cellular signal transduction cascades; and (2) the cellular level—describing tumor growth, cellular composition, and response to treatments targeted against IL-6.

Extinction rates in tumour public goods games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.

Analysis of MicroRNA-mRNA Interactions in Stem Cell-Enriched Fraction of Oral Squamous Cell Carcinoma

This study is an integrated analysis of the transcriptome profile microRNA (miRNA) and its experimentally validated mRNA targets differentially expressed in the tumorigenic stem-like fraction of oral squamous cell carcinoma (OSCC). We had previously reported the coexistence of multiple drug-resistant tumorigenic fractions, termed side population (SP1, SP2, and MP2), and a nontumorigenic fraction, termed main population (MP1), in oral cancer. These fractions displayed a self-renewal, regenerative potential and expressed known stemness-related cell surface markers despite functional differences. Flow cytometrically sorted pure fractions of SP1 and MP1 cells were subjected to differential expression analysis of both mRNAs and miRNAs. A significant upregulation of genes associated with inflammation, cell survival, cell proliferation, drug transporters, and antiapoptotic pathways, in addition to enhanced transcriptome reprogramming mediated by DNA-histone binding proteins and pattern recognition receptor-mediated signaling, was found to play a crucial role in the transformation of the nontumorigenic MP1 fraction to the tumorigenic SP1 fraction. We also identified several differentially expressed miRNAs that specifically target genes distinctive of tumorigenic SP1 fraction. miRNA-mediated downregulation of stemness-associated markers CD44 and CD147 and upregulation of CD151 may also account for the emergence and persistence of multiple tumorigenic stem cell fractions with varying degrees of malignancy. The phenotypic switch of cancer cells to stem-like OSCC cells mediated by transcriptomal regulation is effectual in addressing biological tumor heterogeneity and subsequent therapeutic resistance leading to a minimal residual disease (MRD) condition in oral cancer. A detailed study of the interplay of miRNAs, mRNA, and the cellular phases involved in the gradual transition of nontumorigenic cancer cells to tumorigenic stem-like cells in solid tumors would enable detection and development of a treatment regimen that targets and successfully eliminates multiple, drug-resistant fractions of cancer cells.

Cellular Hierarchy as a Determinant of Tumor Sensitivity to Chemotherapy

Chemotherapy has been shown to enrich cancer stem cells in tumors. Recently, we demonstrated that administration of chemotherapy to human bladder cancer xenografts could trigger a wound-healing response that mobilizes quiescent tumor stem cells into active proliferation. This phenomenon leads to a loss of sensitivity to chemotherapy partly due to an increase in the number of tumor stem cells, which typically respond to chemotherapy-induced cell death less than more differentiated cells. Different bladder cancer xenografts, however, demonstrate differential sensitivities to chemotherapy, the basis of which is not understood. Using mathematical models, we show that characteristics of the tumor cell hierarchy can be crucial for determining the sensitivity of tumors to drug therapy, under the assumption that stem cell enrichment is the primary basis for drug resistance. Intriguingly, our model predicts a weaker response to therapy if there is negative feedback from differentiated tumor cells that inhibits the rate of tumor stem cell division. If this negative feedback is less pronounced, the treatment response is predicted to be enhanced. The reason is that negative feedback on the rate of tumor cell division promotes a permanent rise of the tumor stem cell population over time, both in the absence of treatment and even more so during drug therapy. Model application to data from chemotherapy-treated patient-derived xenografts indicates support for model predictions. These findings call for further research into feedback mechanisms that might remain active in cancers and potentially highlight the presence of feedback as an indication to combine chemotherapy with approaches that limit the process of tumor stem cell enrichment. Cancer Res; 77(9); 2231-41. ©2017 AACR.

Hierarchical tissue organization as a general mechanism to limit the accumulation of somatic mutations

How can tissues generate large numbers of cells, yet keep the divisional load (the number of divisions along cell lineages) low in order to curtail the accumulation of somatic mutations and reduce the risk of cancer? To answer the question we consider a general model of hierarchically organized self-renewing tissues and show that the lifetime divisional load of such a tissue is independent of the details of the cell differentiation processes, and depends only on two structural and two dynamical parameters. Our results demonstrate that a strict analytical relationship exists between two seemingly disparate characteristics of self-renewing tissues: divisional load and tissue organization. Most remarkably, we find that a sufficient number of progressively slower dividing cell types can be almost as efficient in minimizing the divisional load, as non-renewing tissues. We argue that one of the main functions of tissue-specific stem cells and differentiation hierarchies is the prevention of cancer.

To limit the accumulation of somatic mutations, renewing tissues must minimize the number of times each cell divides during differentiation. Here, the authors analytically derive the lower limit of lifetime divisional load of a tissue, show that hierarchically differentiating tissues can approach this limit, and that this depends on uneven divisional rates across the hierarchy.

An exactly solvable, spatial model of mutation accumulation in cancer

One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.