Inducing catastrophe in malignant growth.

Mathematical catastrophe theory is used to describe cancer growth during any time-dependent program a(t) of therapeutic activity. The program may be actively imposed, e.g.

Causes and consequences of increased glucose metabolism of cancers.

In this review we examine the mechanisms (causes) underlying the increased glucose consumption observed in tumors within a teleological context (consequences). In other words, we will ask not only "How do cancers have high glycolysis?" but also, "Why?" We believe that the insights gained from answering the latter question support the conclusion that elevated glucose consumption is a necessary component of carcinogenesis. Specifically we propose that glycolysis is elevated because it produces acid, which provides an evolutionary advantage to cancer cells vis-à-vis normal parenchyma into which they invade.

Adaptation to hypoxia and acidosis in carcinogenesis and tumor progression.

Carcinogenesis is a complex, multistep, multipath process often described as "somatic evolution". Conventional models of cancer progression are typically based on the genetic and epigenetic changes observed in malignant and premalignant tumors. We have explored an alternative approach that emphasizes the selection forces within adaptive landscapes governing growth and evolution in in situ, microinvasive, and metastatic cancers.

Optimization of synchronization in complex clustered networks.

There has been mounting evidence that many types of biological or technological networks possess a clustered structure. As many system functions depend on synchronization, it is important to investigate the synchronizability of complex clustered networks. Here we focus on one fundamental question: Under what condition can the network synchronizability be optimized? In particular, since the two basic parameters characterizing a complex clustered network are the probabilities of intercluster and intracluster connections, we investigate, in the corresponding two-dimensional parameter plane, regions where the network can be best synchronized.

An evolutionary model for initiation, promotion, and progression in carcinogenesis.

Human carcinogenesis is a multistep process in which epithelial cells progress through a series of premalignant phenotypes until an invasive cancer emerges. Extensive experimental observations in carcinogenesis have demonstrated this process can be divided into three general eras: initiation, promotion, and progression. However, this empirically derived, tissue-level explanation of carcinogenesis has not been reconciled with the step-wise genotypic and phenotypic changes encompassed in evolutionary paradigms such as the Feoron-Vogelstein diagram.

Alternating synchronizability of complex clustered networks with regular local structure.

Small network distance and homogeneous degree distribution have been found to be critical to efficient network synchronization. In this paper, we investigate the synchronizability of clustered networks with regular subnetworks and report a counterintuitive phenomenon: As the density of intracluster links is increased, the network exhibits strong and weak synchronizability in an alternating manner. A theory based on analyzing the eigenvalues and eigenvectors of the coupling matrix is provided to explain this phenomenon.

Acid treatment of melanoma cells selects for invasive phenotypes.

Solid tumors become acidic due to hypoxia and upregulated glycolysis. We have hypothesized that this acidosis leads to more aggressive invasive behavior during carcinogenesis (Nature Reviews Cancer 4:891-899, 2004). Previous work on this subject has shown mixed results.

A microenvironmental model of carcinogenesis.

We propose that carcinogenesis requires tumour populations to surmount six distinct microenvironmental proliferation barriers that arise in the adaptive landscapes of normal and premalignant populations growing from epithelial surfaces. Somatic evolution of invasive cancer can then be viewed as a sequence of phenotypical adaptations to these barriers. The genotypical and phenotypical heterogeneity of cancer populations is explained by an equivalence principle in which multiple strategies can successfully adapt to the same barrier.

Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer.

Conceptual models of carcinogenesis typically consist of an evolutionary sequence of heritable changes in genes controlling proliferation, apoptosis, and senescence. We propose that these steps are necessary but not sufficient to produce invasive breast cancer because intraductal tumour growth is also constrained by hypoxia and acidosis that develop as cells proliferate into the lumen and away from the underlying vessels. This requires evolution of glycolytic and acid-resistant phenotypes that, we hypothesise, is critical for emergence of invasive cancer.

Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth.

Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology.

Adaptive landscapes and emergent phenotypes: why do cancers have high glycolysis?

Investigating the causes of increased aerobic glycolysis in tumors (Warburg Effect) has gone in and out of fashion many times since it was first described almost a century ago. The field is currently in ascendance due to two factors. Over a million FDG-PET studies have unequivocally identified increased glucose uptake as a hallmark of metastatic cancer in humans.

Glycolysis in cancer: a potential target for therapy.

Clinical imaging of primary and metastatic cancers with Fluoro deoxy-d-Glucose Positron Emission Tomography (FdG PET) has clearly demonstrated that increased glucose flux compared to normal tissue is a common trait of human malignancies (Gambhir, 2002) This is a consequence of a shift of glucose metabolism to less efficient glycolytic pathways in response to regional hypoxia and evolution of aerobic glycolysis in many cancer phenotypes. This distinctive metabolic profile presents an inviting target for cancer treatment and prevention. Here, we summarize the therapeutic strategies under investigation to exploit or interrupt tumor glycolytic metabolism.

Hypoxia and adaptive landscapes in the evolution of carcinogenesis.

Conceptual models of epithelial carcinogenesis typically depict a sequence of heritable changes that give rise to a population of cells possessing the hallmarks of invasive cancer. We propose the evolutionary dynamics that give rise to the phenotypic properties of malignant cells must be understood within the context of specific selection forces generated by the microenvironment. This can be accomplished by using an "inverse problem" approach in which we use observed typical phenotypic traits of primary and metastatic cancers to infer the evolutionary dynamics.

Information theory in living systems, methods, applications, and challenges.

Living systems are distinguished in nature by their ability to maintain stable, ordered states far from equilibrium. This is despite constant buffeting by thermodynamic forces that, if unopposed, will inevitably increase disorder. Cells maintain a steep transmembrane entropy gradient by continuous application of information that permits cellular components to carry out highly specific tasks that import energy and export entropy.

Metabolic changes during carcinogenesis: potential impact on invasiveness.

Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the cell-microenvironmental interactions that mediate somatic evolution of cancer cells. This allows investigation of the hypothesis that regions of premalignant lesions develop a substrate-limited environment as proliferation carries cells away from blood vessels which remain separated by the intact basement membrane.

Acid-mediated tumor invasion: a multidisciplinary study.

The acid-mediated tumor invasion hypothesis proposes altered glucose metabolism and increased glucose uptake, observed in the vast majority of clinical cancers by fluorodeoxyglucose-positron emission tomography, are critical for development of the invasive phenotype. In this model, increased acid production due to altered glucose metabolism serves as a key intermediate by producing H(+) flow along concentration gradients into adjacent normal tissue. This chronic exposure of peritumoral normal tissue to an acidic microenvironment produces toxicity by: (a) normal cell death caused by the collapse of the transmembrane H(+) gradient inducing necrosis or apoptosis and (b) extracellular matrix degradation through the release of cathepsin B and other proteolytic enzymes.

An integrated computational/experimental model of tumor invasion.

The intracellular and extracellular dynamics that govern tumor growth and invasiveness in vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and growth factor concentrations are key variables. In previous work, using a reaction-diffusion mathematical model based on variables that directly describe tumor cell cycle and biology, we formulated the hypothesis that tumor morphology is determined by the competition between heterogeneous cell proliferation caused by spatial diffusion gradients, e.

Power laws of complex systems from extreme physical information.

Many complex systems obey allometric, or power, laws y=Y x(a) . Here y > or = 0 is the measured value of some system attribute a , Y> or =0 is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values n/4 , n=0, +/-1, +/-2.

Morphologic instability and cancer invasion.

Purpose: A solid tumor embedded in host tissue is a three-dimensional arrangement of cells and extracellular matrix that acts as a sink of oxygen and cell nutrients, thus establishing diffusional gradients. This and variations in vascular density and blood flow typically produce intratumoral regions of hypoxia and acidosis, and may result in spatially heterogeneous cell proliferation and migration. Here, we formulate the hypothesis that through these mechanisms, microenvironmental substrate gradients may drive morphologic instability with separation of cell clusters from the tumor edge and infiltration into surrounding normal tissue.

The role of acidity in solid tumour growth and invasion.

Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this paper, we develop a simple model of three-dimensional tumour growth to examine the role of acidosis in the interaction between normal and tumour cell populations.

The role of non-genomic information in maintaining thermodynamic stability in living systems.

Living systems represent a local exception, albeit transient, to the second law of thermodynamics, which requires entropy or disorder to increase with time. Cells maintain a stable ordered state by generating a steep transmembrane entropy gradient in an open thermodynamic system far from equilibrium through a variety of entropy exchange mechanisms. Information storage in DNA and translation of that information into proteins is central to maintenance thermodynamic stability, through increased order that results from synthesis of specific macromolecules from monomeric precursors while heat and other reaction products are exported into the environment.

pH imaging. A review of pH measurement methods and applications in cancers.

Acid-base balance is altered in a variety of common pathologies, including COPD, ischemia, renal failure, and cancer. Because of robust cellular pH homeostatic mechanisms, most of the pathological alterations in pH are expressed as changes in the extracellular, systemic pH. There are data to indicate that altered pH is not simply an epiphenomenon of metabolic or physiologic imbalance but that chronic pH alterations can have important sequelae.

Information dynamics in carcinogenesis and tumor growth.

The storage and transmission of information is vital to the function of normal and transformed cells. We use methods from information theory and Monte Carlo theory to analyze the role of information in carcinogenesis. Our analysis demonstrates that, during somatic evolution of the malignant phenotype, the accumulation of genomic mutations degrades intracellular information.

Why do cancers have high aerobic glycolysis?

If carcinogenesis occurs by somatic evolution, then common components of the cancer phenotype result from active selection and must, therefore, confer a significant growth advantage. A near-universal property of primary and metastatic cancers is upregulation of glycolysis, resulting in increased glucose consumption, which can be observed with clinical tumour imaging. We propose that persistent metabolism of glucose to lactate even in aerobic conditions is an adaptation to intermittent hypoxia in pre-malignant lesions.