Tracking the Adaptation and Compensation Processes of Patients' Brain Arterial Network to an Evolving Glioblastoma.

The brain's vascular network dynamically affects its development and core functions. It rapidly responds to abnormal conditions by adjusting properties of the network, aiding stabilization and regulation of brain activities. Tracking prominent arterial changes has clear clinical and surgical advantages. However, the arterial network functions as a system; thus, local changes may imply global compensatory effects that could impact the dynamic progression of a disease. We developed automated personalized system-level analysis methods of the compensatory arterial changes and mean blood flow behavior from a patient's clinical images. By applying our approach to data from a patient with aggressive brain cancer compared with healthy individuals, we found unique spatiotemporal patterns of the arterial network that could assist in predicting the evolution of glioblastoma over time. Our personalized approach provides a valuable analysis tool that could augment current clinical assessments of the progression of glioblastoma and other neurological disorders affecting the brain.

Phenotype stability under dynamic brain-tumor environment stimuli maps glioblastoma progression in patients.

Although tumor invasiveness is known to drive glioblastoma (GBM) recurrence, current approaches to treatment assume a fairly simple GBM phenotype transition map. We provide new analyses to estimate the likelihood of reaching or remaining in a phenotype under dynamic, physiologically likely perturbations of stimuli ("phenotype stability"). We show that higher stability values of the motile phenotype (Go) are associated with reduced patient survival. Moreover, induced motile states are capable of driving GBM recurrence. We found that the Dormancy and Go phenotypes are equally represented in advanced GBM samples, with natural transitioning between the two. Furthermore, Go and Grow phenotype transitions are mostly driven by tumor-brain stimuli. These are difficult to regulate directly, but could be modulated by reprogramming tumor-associated cell types. Our framework provides a foundation for designing targeted perturbations of the tumor-brain environment, by assessing their impact on GBM phenotypic plasticity, and is corroborated by analyses of patient data.

Computational modeling demonstrates that glioblastoma cells can survive spatial environmental challenges through exploratory adaptation.

Glioblastoma (GBM) is an aggressive type of brain cancer with remarkable cell migration and adaptation capabilities. Exploratory adaptation-utilization of random changes in gene regulation for adaptive benefits-was recently proposed as the process enabling organisms to survive unforeseen conditions. We investigate whether exploratory adaption explains how GBM cells from different anatomic regions of the tumor cope with micro-environmental pressures. We introduce new notions of phenotype and phenotype distance, and determine probable spatial-phenotypic trajectories based on patient data. While some cell phenotypes are inherently plastic, others are intrinsically rigid with respect to phenotypic transitions. We demonstrate that stochastic exploration of the regulatory network structure confers benefits through enhanced adaptive capacity in new environments. Interestingly, even with exploratory capacity, phenotypic paths are constrained to pass through specific, spatial-phenotypic ranges. This work has important implications for understanding how such adaptation contributes to the recurrence dynamics of GBM and other solid tumors.

Mathematical Modeling Reveals That Changes to Local Cell Density Dynamically Modulate Baseline Variations in Cell Growth and Drug Response.

Cell-to-cell variations contribute to drug resistance with consequent therapy failure in cancer. Experimental techniques have been developed to monitor tumor heterogeneity, but estimates of cell-to-cell variation typically fail to account for the expected spatiotemporal variations during the cell growth process. To fully capture the extent of such dynamic variations, we developed a mechanistic mathematical model supported by in vitro experiments with an ovarian cancer cell line. We introduce the notion of dynamic baseline cell-to-cell variation, showing how the emerging spatiotemporal heterogeneity of one cell population can be attributed to differences in local cell density and cell cycle. Manipulation of the geometric arrangement and spatial density of cancer cells revealed that given a fixed global cell density, significant differences in growth, proliferation, and paclitaxel-induced apoptosis rates were observed based solely on cell movement and local conditions. We conclude that any statistical estimate of changes in the level of heterogeneity should be integrated with the dynamics and spatial effects of the baseline system. This approach incorporates experimental and theoretical methods to systematically analyze biologic phenomena and merits consideration as an underlying reference model for cell biology studies that investigate dynamic processes affecting cancer cell behavior. Cancer Res; 76(10); 2882-90. ©2016 AACR.

Toward a Better Understanding of the Complexity of Cancer Drug Resistance.

Resistance to anticancer drugs is a complex process that results from alterations in drug targets; development of alternative pathways for growth activation; changes in cellular pharmacology, including increased drug efflux; regulatory changes that alter differentiation pathways or pathways for response to environmental adversity; and/or changes in the local physiology of the cancer, such as blood supply, tissue hydrodynamics, behavior of neighboring cells, and immune system response. All of these specific mechanisms are facilitated by the intrinsic hallmarks of cancer, such as tumor cell heterogeneity, redundancy of growth-promoting pathways, increased mutation rate and/or epigenetic alterations, and the dynamic variation of tumor behavior in time and space. Understanding the relative contribution of each of these factors is further complicated by the lack of adequate in vitro models that mimic clinical cancers. Several strategies to use current knowledge of drug resistance to improve treatment of cancer are suggested.

Redundancy: a critical obstacle to improving cancer therapy.

A system characterized by redundancy has various elements that are able to act in the same biologic or dynamic manner, where the inhibition of one of those elements has no significant effect on the global biologic outcome or on the system's dynamic behavior. Methods that aim to predict the effectiveness of cancer therapies must include evolutionary and dynamic features that would change the static view that is widely accepted. Here, we explore several important issues about mechanisms of redundancy, heterogeneity, biologic importance, and drug resistance and describe methodologic challenges that, if overcome, would significantly contribute to cancer research.

Modeling intrinsic heterogeneity and growth of cancer cells.

Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multidrug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level.

Network features suggest new hepatocellular carcinoma treatment strategies.

BACKGROUND: Resistance to therapy remains a major cause of the failure of cancer treatment. A major challenge in cancer therapy is to design treatment strategies that circumvent the higher-level homeostatic functions of the robust cellular network that occurs in resistant cells. There is a lack of understanding of mechanisms responsible for the development of cancer and the basis of therapy-resistance mechanisms. Cellular signaling networks have an underlying architecture guided by universal principles. A robust system, such as cancer, has the fundamental ability to survive toxic anticancer drug treatments or a stressful environment mainly due to its mechanisms of redundancy. Consequently, inhibition of a single component/pathway would probably not constitute a successful cancer therapy. RESULTS: We developed a computational method to study the mechanisms of redundancy and to predict communications among the various pathways based on network theory, using data from gene expression profiles of hepatocellular carcinoma (HCC) of patients with poor and better prognosis cancers. Our results clearly indicate that immune system pathways tightly regulate most cancer pathways, and when those pathways are targeted by drugs, the network connectivity is dramatically changed. We examined the main HCC targeted treatments that are currently being evaluated in clinical trials. One prediction of our study is that Sorafenib combined with immune system treatments will be a more effective combination strategy than Sorafenib combined with any other targeted drugs. CONCLUSIONS: We developed a computational framework to analyze gene expression data from HCC tumors with varying degrees of responsiveness and non-tumor samples, based on both Gene and Pathway Co-expression Networks. Our hypothesis is that redundancy is one of the major causes of drug resistance, and can be described as a function of the network structure and its properties. From this perspective, we believe that integration of the redundant variables could lead to the development of promising new methodologies to selectively identify and target the most significant resistance mechanisms of HCC. We describe three mechanisms of redundancy based on their levels of generalization and study the possible impact of those redundancy mechanisms on HCC treatments.

The impact of cell density and mutations in a model of multidrug resistance in solid tumors.

In this paper we develop a mathematical framework for describing multidrug resistance in cancer. To reflect the complexity of the underlying interplay between cancer cells and the therapeutic agent, we assume that the resistance level is a continuous parameter. Our model is written as a system of integro-differential equations that are parameterized by the resistance level. This model incorporates the cell density and mutation dependence. Analysis and simulations of the model demonstrate how the dynamics evolves to a selection of one or more traits corresponding to different levels of resistance. The emerging limit distribution with nonzero variance is the desirable modeling outcome as it represents tumor heterogeneity.

Simplifying the complexity of resistance heterogeneity in metastasis.

The main goal of treatment regimens for metastasis is to control growth rates, not eradicate all cancer cells. Mathematical models offer methodologies that incorporate high-throughput data with dynamic effects on net growth. The ideal approach would simplify, but not over-simplify, a complex problem into meaningful and manageable estimators that predict the response of a patient to specific treatments. We explore here three fundamental approaches with different assumptions concerning resistance mechanisms in which the cells are categorized into either discrete compartments or described by a continuous range of resistance levels. We argue in favor of modeling resistance as a continuum, and demonstrate how integrating cellular growth rates, density-dependent versus exponential growth, and intratumoral heterogeneity improves predictions concerning the resistance heterogeneity of metastases.

The role of cell density and intratumoral heterogeneity in multidrug resistance.

Recent data have demonstrated that cancer drug resistance reflects complex biologic factors, including tumor heterogeneity, varying growth, differentiation, apoptosis pathways, and cell density. As a result, there is a need to find new ways to incorporate these complexities in the mathematical modeling of multidrug resistance. Here, we derive a novel structured population model that describes the behavior of cancer cells under selection with cytotoxic drugs. Our model is designed to estimate intratumoral heterogeneity as a function of the resistance level and time. This updated model of the multidrug resistance problem integrates both genetic and epigenetic changes, density dependence, and intratumoral heterogeneity. Our results suggest that treatment acts as a selection process, whereas genetic/epigenetic alteration rates act as a diffusion process. Application of our model to cancer treatment suggests that reducing alteration rates as a first step in treatment causes a reduction in tumor heterogeneity and may improve targeted therapy. The new insight provided by this model could help to dramatically change the ability of clinical oncologists to design new treatment protocols and analyze the response of patients to therapy.

The dynamics of drug resistance: a mathematical perspective.

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance, induced resistance and acquired resistance. In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intracellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance.

Regulation of modular Cyclin and CDK feedback loops by an E2F transcription oscillator in the mammalian cell cycle.

The cell cycle is regulated by a large number of enzymes and transcription factors. We have developed a modular description of the cell cycle, based on a set of interleaved modular feedback loops, each leading to a cyclic behavior. The slowest loop is the E2F transcription and ubiquitination, which determines the cycling frequency of the entire cell cycle. Faster feedback loops describe the dynamics of each Cyclin by itself. Our model shows that the cell cycle progression as well as the checkpoints of the cell cycle can be understood through the interactions between the main E2F feedback loop and the driven Cyclin feedback loops. Multiple models were proposed for the cell cycle dynamics; each with differing basic mechanisms. We here propose a new generic formalism. In contrast with existing models, the proposed formalism allows a straightforward analysis and understanding of the dynamics, neglecting the details of each interaction. This model is not sensitive to small changes in the parameters used and it reproduces the observed behavior of the transcription factor E2F and different Cyclins in continuous or regulated cycling conditions. The modular description of the cell cycle resolves the gap between cyclic models, solely based on protein-protein reactions and transcription reactions based models. Beyond the explanation of existing observations, this model suggests the existence of unknown interactions, such as the need for a functional interaction between Cyclin B and retinoblastoma protein (Rb) de-phosphorylation.

Effect of vaccination in environmentally induced diseases.

Along with the constant improvement in hygiene in the last few decades there has been a continuous increase in the incidence of particular diseases, mainly of autoimmune or allergic etiology, but also of diseases caused by infectious agents, such as listeriosis. We here present a model for the effect of exposure to agents causing or inducing the disease on the incidence of morbidity. The proposed model is an expansion of the SIR model to non-contagious diseases and aims to estimate the balance between immunization and disease probability. The model results indicate that, paradoxically in a wide range of parameters, a decrease in exposure to the disease inducing agent results in an increase in disease incidence. This can occur if: (a) the probability of developing disease, given an exposure to the agent increases with age, (b) immunity to the agent is long. The inverse relation between exposure and disease incidence results from a decrease in the adult immunized population following a previous decrease in the exposure rate. Therefore, a lower exposure can lead to lower incidence in the short term but to higher incidence in the long term.

What cycles the cell? -Robust autonomous cell cycle models.

The cell cycle is one of the best studied cellular mechanisms at the experimental and theoretical levels. Although most of the important biochemical components and reactions of the cell cycle are probably known, the precise way the cell cycle dynamics are driven is still under debate. This phenomenon is not atypical to many other biological systems where the knowledge of the molecular building blocks and the interactions between them does not lead to a coherent picture of the appropriate dynamics. We here propose a methodology to develop plausible models for the driving mechanisms of embryonic and cancerous cell cycles. We first define a key property of the system (a cyclic behaviour in the case of the embryonic cell cycle) and set mathematical constraints on the types of two variable simplified systems robustly reproducing such a cyclic behaviour. We then expand these robust systems to three variables and reiterate the procedure. At each step, we further limit the type of expanded systems to fit the known microbiology until a detailed description of the system is obtained. This methodology produces mathematical descriptions of the required biological systems that are more robust to changes in the precise function and rate constants. This methodology can be extended to practically any type of subcellular mechanism.

Listeriosis: a model for the fine balance between immunity and morbidity.

BACKGROUND: Listeriosis is a severe food-borne disease caused by Listeria monocytogenes. It mostly affects immune-compromised individuals, pregnant women, and the elderly, and it is associated with huge economic losses, especially to the food industry. In the last decade, a sharp increase in listeriosis incidence was observed in several European countries. No suitable explanation was found for this increase, which occurred only in old patients and not in pregnant women. METHODS: We developed a mathematical model to explore this upsurge by studying the balance between the immunized population fraction and the force of infection, and its influence on the incidence of listeriosis. RESULTS: The model shows that the current upsurge could be the result of a decrease in exposure to the pathogen in food a few decades ago and hence decreased level of population immunity. The model also suggests that, counterintuitively, the incidence of listeriosis can be higher under reduced exposure to L. monocytogenes than under high exposure. These results rely on the accepted assumption that immunity to L. monocytogenes is long-lived (at least 20 years) or that there is a long-lived boosting effect by previous exposure to L. monocytogenes. The results are robust to wide changes in all other model parameters. CONCLUSIONS: Historical alterations in exposure to L. monocytogenes might explain current changes in incidence of listeriosis. The model may also be implied for other noncontagious infectious diseases (eg, food borne diseases or vector-borne diseases for which humans are considered dead-end hosts) for which susceptibility increases with age.