A systems biology approach to cancer: fractals, attractors, and nonlinear dynamics

Coherent light scattering from cellular dynamics in living tissues

This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.

Fractal Analysis in Clinical Neurosciences: An Overview

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and astrocytes) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the pattern representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, neuro-ophthalmology, and cognitive neurosciences, with special emphasis on the translation of the fractal dimension and other fractal parameters as clinical biomarkers useful from bench to bedside.

System dynamics modeling for cancer prevention and control: A systematic review

Cancer prevention and control requires consideration of complex interactions between multilevel factors. System dynamics modeling, which consists of diagramming and simulation approaches for understanding and managing such complexity, is being increasingly applied to cancer prevention and control, but the breadth, characteristics, and quality of these studies is not known. We searched PubMed, Scopus, APA PsycInfo, and eight peer-reviewed journals to identify cancer-related studies that used system dynamics modeling. A dual review process was used to determine eligibility. Included studies were assessed using quality criteria adapted from prior literature and mapped onto the cancer control continuum. Characteristics of studies and models were abstracted and qualitatively synthesized. 32 studies met our inclusion criteria. A mix of simulation and diagramming approaches were used to address diverse topics, including chemotherapy treatments (16%), interventions to reduce tobacco or e-cigarettes use (16%), and cancer risk from environmental contamination (13%). Models spanned all focus areas of the cancer control continuum, with treatment (44%), prevention (34%), and detection (31%) being the most common. The quality assessment of studies was low, particularly for simulation approaches. Diagramming-only studies more often used participatory approaches. Involvement of participants, description of model development processes, and proper calibration and validation of models showed the greatest room for improvement. System dynamics modeling can illustrate complex interactions and help identify potential interventions across the cancer control continuum. Prior efforts have been hampered by a lack of rigor and transparency regarding model development and testing. Supportive infrastructure for increasing awareness, accessibility, and further development of best practices of system dynamics for multidisciplinary cancer research is needed.

Is Cancer Reversible? Rethinking Carcinogenesis Models-A New Epistemological Tool

A growing number of studies shows that it is possible to induce a phenotypic transformation of cancer cells from malignant to benign. This process is currently known as "tumor reversion". However, the concept of reversibility hardly fits the current cancer models, according to which gene mutations are considered the primary cause of cancer. Indeed, if gene mutations are causative carcinogenic factors, and if gene mutations are irreversible, how long should cancer be considered as an irreversible process? In fact, there is some evidence that intrinsic plasticity of cancerous cells may be therapeutically exploited to promote a phenotypic reprogramming, both in vitro and in vivo. Not only are studies on tumor reversion highlighting a new, exciting research approach, but they are also pushing science to look for new epistemological tools capable of better modeling cancer.

Fractal Pennes and Cattaneo-Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

In this study, the Pennes and Cattaneo-Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified gradient operator which depends on two parameters: R which represents the radius of the tumour and R0 which represents the radius of the spherical living tissue. Both the steady and unsteady states for each fractal bioheat equation were obtained and their implications on living cells in the presence of growth of a large tumour were analysed. Assuming a specific heating/cooling by a constant heat flux equivalent to the metabolic heat generation in the tissue, it was observed that the solutions of the fractal bioheat equations are robustly affected by fractal dimensions, the radius of the tumour growth and the dimensions of the living cell tissue. The ranges of both the fractal dimensions and temperature were obtained, analysed and compared with recent studies. This study confirms the importance of fractals in medicine.

Attractor Concepts to Evaluate the Transcriptome-wide Dynamics Guiding Anaerobic to Aerobic State Transition in Escherichia coli

For any dynamical system, like living organisms, an attractor state is a set of variables or mechanisms that converge towards a stable system behavior despite a wide variety of initial conditions. Here, using multi-dimensional statistics, we investigate the global gene expression attractor mechanisms shaping anaerobic to aerobic state transition (AAT) of Escherichia coli in a bioreactor at early times. Out of 3,389 RNA-Seq expression changes over time, we identified 100 sharply changing genes that are key for guiding 1700 genes into the AAT attractor basin. Collectively, these genes were named as attractor genes constituting of 6 dynamic clusters. Apart from the expected anaerobic (glycolysis), aerobic (TCA cycle) and fermentation (succinate pathways) processes, sulphur metabolism, ribosome assembly and amino acid transport mechanisms together with 332 uncharacterised genes are also key for AAT. Overall, our work highlights the importance of multi-dimensional statistical analyses for revealing novel processes shaping AAT.

Role of Complex Networks for Integrating Medical Images and Radiomic Features of Intracranial Ependymoma Patients in Response to Proton Radiotherapy

Human cancers exhibit phenotypic diversity that medical imaging can precisely and non-invasively detect. Multiple factors underlying innovations and progresses in the medical imaging field exert diagnostic and therapeutic impacts. The emerging field of radiomics has shown unprecedented ability to use imaging information in guiding clinical decisions. To achieve clinical assessment that exploits radiomic knowledge sources, integration between diverse data types is required. A current gap is the accuracy with which radiomics aligns with clinical endpoints. We propose a novel methodological approach that synergizes data volumes (images), tissue-contextualized information breadth, and network-driven resolution depth. Following the Precision Medicine paradigm, disease monitoring and prognostic assessment are tackled at the individual level by examining medical images acquired from two patients affected by intracranial ependymoma (with and without relapse). The challenge of spatially characterizing intratumor heterogeneity is tackled by a network approach that presents two main advantages: (a) Increased detection in the image domain power from high spatial resolution, (b) Superior accuracy in generating hypotheses underlying clinical decisions.

Cell-cell bioelectrical interactions and local heterogeneities in genetic networks: a model for the stabilization of single-cell states and multicellular oscillations

Genetic networks operate in the presence of local heterogeneities in single-cell transcription and translation rates. Bioelectrical networks and spatio-temporal maps of cell electric potentials can influence multicellular ensembles. Could cell-cell bioelectrical interactions mediated by intercellular gap junctions contribute to the stabilization of multicellular states against local genetic heterogeneities? We theoretically analyze this question on the basis of two well-established experimental facts: (i) the membrane potential is a reliable read-out of the single-cell electrical state and (ii) when the cells are coupled together, their individual cell potentials can be influenced by ensemble-averaged electrical potentials. We propose a minimal biophysical model for the coupling between genetic and bioelectrical networks that associates the local changes occurring in the transcription and translation rates of an ion channel protein with abnormally low (depolarized) cell potentials. We then analyze the conditions under which the depolarization of a small region (patch) in a multicellular ensemble can be reverted by its bioelectrical coupling with the (normally polarized) neighboring cells. We show also that the coupling between genetic and bioelectric networks of non-excitable cells, modulated by average electric potentials at the multicellular ensemble level, can produce oscillatory phenomena. The simulations show the importance of single-cell potentials characteristic of polarized and depolarized states, the relative sizes of the abnormally polarized patch and the rest of the normally polarized ensemble, and intercellular coupling.

Microenvironmental influence on microtumour infiltration patterns: 3D-mathematical modelling supported by in vitro studies

Mathematical modelling approaches have become increasingly abundant in cancer research. Tumour infiltration extent and its spatial organization depend both on the tumour type and stage and on the bio-physicochemical characteristics of the microenvironment. This sets a complex scenario that often requires a multidisciplinary and individually adjusted approach. The ultimate goal of this work is to present an experimental/numerical combined method for the development of a three-dimensional mathematical model with the ability to reproduce the growth and infiltration patterns of a given avascular microtumour in response to different microenvironmental conditions. The model is based on a diffusion-convection reaction equation that considers logistic proliferation, volumetric growth, a rim of proliferative cells at the tumour surface, and invasion with diffusive and convective components. The parameter values of the model were fitted to experimental results while radial velocity and diffusion coefficients were made spatially variable in a case-specific way through the introduction of a shape function and a diffusion-limited-aggregation (DLA)-derived fractal matrix, respectively, according to the infiltration pattern observed. The in vitro model consists of multicellular tumour spheroids (MTSs) of an epithelial mammary tumour cell line (LM3) immersed in a collagen I gel matrix with a standard culture medium ("naive" matrix) or a conditioned medium from adipocytes or preadipocytes ("conditioned" matrix). It was experimentally determined that both adipocyte and preadipocyte conditioned media had the ability to change the MTS infiltration pattern from collective and laminar to an individual and atomized one. Numerical simulations were able to adequately reproduce qualitatively and quantitatively both kinds of infiltration patterns, which were determined by area quantification, analysis of fractal dimensions and lacunarity, and Bland-Altman analysis. These results suggest that the combined approach presented here could be established as a new framework with interesting potential applications at both the basic and clinical levels in the oncology area.

Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate: A Systems Biology Approach

The thermodynamical formalism of irreversible processes offers a theoretical framework appropriate to explain the complexity observed at the macroscopic level of dynamic systems. In this context, together with the theory of complex systems and systems biology, the thermodynamical formalism establishes an appropriate conceptual framework to address the study of biological systems, in particular cancer.The Chapter is organized as follows: In Subheading 1, an integrative view of these disciplines is offered, for the characterization of the emergence and evolution of cancer, seen as a self-organized dynamic system far from the thermodynamic equilibrium. Development of a thermodynamic framework, based on the entropy production rate, is presented in Subheading 2. Subheading 3 is dedicated to all tumor growth, as seen through a "phase transitions" far from equilibrium. Subheading 4 is devoted to complexity of cancer glycolysis. Finally, some concluding remarks are presented in Subheading 5.

Symmetry and symmetry breaking in cancer: a foundational approach to the cancer problem

Symmetry and symmetry breaking concepts from physics and biology are applied to the problem of cancer. Three categories of symmetry breaking in cancer are examined: combinatorial, geometric, and functional. Within these categories, symmetry breaking is examined for relevant cancer features, including epithelial-mesenchymal transition (EMT); tumor heterogeneity; tensegrity; fractal geometric and information structure; functional interaction networks; and network stabilizability and attack tolerance. The new cancer symmetry concepts are relevant to homeostasis loss in cancer and to its origin, spread, treatment and resistance. Symmetry and symmetry breaking could provide a new way of thinking and a pathway to a solution of the cancer problem.

An Emergence Framework of Carcinogenesis

Experimental paradigms provide the framework for the understanding of cancer, and drive research and treatment, but are rarely considered by clinicians. The somatic mutation theory (SMT), in which cancer is considered a genetic disease, has been the predominant traditional model of cancer for over 50 years. More recently, alternative theories have been proposed, such as tissue organization field theory (TOFT), evolutionary models, and inflammatory models. Key concepts within the various models have led to them being difficult to reconcile. Progressively, it has been recognized that biological systems cannot be fully explained by the physicochemical properties of their constituent parts. There is an increasing call for a 'systems' approach. Incorporating the concepts of 'emergence', 'systems', 'thermodynamics', and 'chaos', a single integrated framework for carcinogenesis has been developed, enabling existing theories to become compatible as alternative mechanisms, facilitating the integration of bioinformatics and providing a structure in which translational research can flow from both 'benchtop to bedside' and 'bedside to benchtop'. In this review, a basic understanding of the key concepts of 'emergence', 'systems', 'system levels', 'complexity', 'thermodynamics', 'entropy', 'chaos', and 'fractals' is provided. Non-linear mathematical equations are included where possible to demonstrate compatibility with bioinformatics. Twelve principles that define the 'emergence framework of carcinogenesis' are developed, with principles 1-10 encapsulating the key concepts upon which the framework is built and their application to carcinogenesis. Principle 11 relates the framework to cancer progression. Principle 12 relates to the application of the framework to translational research. The 'emergence framework of carcinogenesis' collates current paradigms, concepts, and evidence around carcinogenesis into a single framework that incorporates previously incompatible viewpoints and ideas. Any researcher, scientist, or clinician involved in research, treatment, or prevention of cancer can employ this framework.

SMT and TOFT: Why and How They are Opposite and Incompatible Paradigms

The Somatic Mutation Theory (SMT) has been challenged on its fundamentals by the Tissue Organization Field Theory of Carcinogenesis (TOFT). However, a recent publication has questioned whether TOFT could be a valid alternative theory of carcinogenesis to that presented by SMT. Herein we critically review arguments supporting the irreducible opposition between the two theoretical approaches by highlighting differences regarding the philosophical, methodological and experimental approaches on which they respectively rely. We conclude that SMT has not explained carcinogenesis due to severe epistemological and empirical shortcomings, while TOFT is gaining momentum. The main issue is actually to submit SMT to rigorous testing. This concern includes the imperatives to seek evidence for disproving one's hypothesis, and to consider the whole, and not just selective evidence.

The Significance of an Enhanced Concept of the Organism for Medicine

Recent developments in evolutionary biology, comparative embryology, and systems biology suggest the necessity of a conceptual shift in the way we think about organisms. It is becoming increasingly evident that molecular and genetic processes are subject to extremely refined regulation and control by the cell and the organism, so that it becomes hard to define single molecular functions or certain genes as primary causes of specific processes. Rather, the molecular level is integrated into highly regulated networks within the respective systems. This has consequences for medical research in general, especially for the basic concept of personalized medicine or precision medicine. Here an integrative systems concept is proposed that describes the organism as a multilevel, highly flexible, adaptable, and, in this sense, autonomous basis for a human individual. The hypothesis is developed that these properties of the organism, gained from scientific observation, will gradually make it necessary to rethink the conceptual framework of physiology and pathophysiology in medicine.

Towards a Neuronal Gauge Theory

Given the amount of knowledge and data accruing in the neurosciences, is it time to formulate a general principle for neuronal dynamics that holds at evolutionary, developmental, and perceptual timescales? In this paper, we propose that the brain (and other self-organised biological systems) can be characterised via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we show that a gauge theory for neuronal dynamics--based on approximate Bayesian inference--has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception.

Knowing one's place: a free-energy approach to pattern regulation

Understanding how organisms establish their form during embryogenesis and regeneration represents a major knowledge gap in biological pattern formation. It has been recently suggested that morphogenesis could be understood in terms of cellular information processing and the ability of cell groups to model shape. Here, we offer a proof of principle that self-assembly is an emergent property of cells that share a common (genetic and epigenetic) model of organismal form. This behaviour is formulated in terms of variational free-energy minimization-of the sort that has been used to explain action and perception in neuroscience. In brief, casting the minimization of thermodynamic free energy in terms of variational free energy allows one to interpret (the dynamics of) a system as inferring the causes of its inputs-and acting to resolve uncertainty about those causes. This novel perspective on the coordination of migration and differentiation of cells suggests an interpretation of genetic codes as parametrizing a generative model-predicting the signals sensed by cells in the target morphology-and epigenetic processes as the subsequent inversion of that model. This theoretical formulation may complement bottom-up strategies-that currently focus on molecular pathways-with (constructivist) top-down approaches that have proved themselves in neuroscience and cybernetics.

Quantitative dynamic modelling of the gene regulatory network controlling adipogenesis

Gene regulatory networks (GRNs) coherently coordinate the expressions of genes and control the behaviors of cellular systems. The complexity in modeling a quantitative GRN usually results from inaccurate parameter estimation, which is mostly due to small sample sizes. For better modeling of GRNs, we have designed a small-sample iterative optimization algorithm (SSIO) to quantitatively model GRNs with nonlinear regulatory relationships. The algorithm utilizes gene expression data as the primary input and it can be applied in case of small-sized samples. Using SSIO, we have quantitatively constructed the dynamic models for the GRNs controlling human and mouse adipogenesis. Compared with two other commonly-used methods, SSIO shows better performance with relatively lower residual errors, and it generates rational predictions on the adipocyte responses to external signals and steady-states. Sensitivity analysis further indicates the validity of our method. Several differences are observed between the GRNs of human and mouse adipocyte differentiations, suggesting the differences in regulatory efficiencies of the transcription factors between the two species. In addition, we use SSIO to quantitatively determine the strengths of the regulatory interactions as well as to optimize regulatory models. The results indicate that SSIO facilitates better investigation and understanding of gene regulatory processes.

An integrative analysis of meningioma tumors reveals the determinant genes and pathways of malignant transformation

Meningiomas are frequent central nervous system neoplasms, which despite their predominant benignity, show sporadically malignant behavior. Type 2 neurofibromatosis and polymorphisms in several genes have been associated with meningioma risk and are probably involved in its pathogenesis. Although GWAS studies have found loci related to meningioma risk, little is known about the factors determining malignant transformation. Thus, this study is aimed to identify the genomic and transcriptomic factors influencing evolution from benignity toward aggressive phenotypes. By applying an integrative bioinformatics pipeline combining public information on a wealth of biological layers of complexity (from genetic polymorphisms to protein interactions), this study identified a module of co-expressed genes highly correlated with tumor stage and statistically linked to several genomic regions (module Quantitative Trait Loci, mQTLs). Ontology analysis of the transcription hub genes identified microtubule-associated cell-cycle processes as key drivers of such network. mQTLs and single nucleotide polymorphisms associated with meningioma stage were replicated in an alternative meningioma cohort, and integration of these results with up-to-date scientific literature and several databases retrieved a list of genes and pathways with a potentially important role in meningioma malignancy. As a result, cytoskeleton and cell-cell adhesion pathways, calcium-channels and glutamate receptors, as well as oxidoreductase and endoplasmic reticulum-associated degradation pathways were found to be the most important and redundant findings associated to meningioma progression. This study presents an integrated view of the pathways involved in meningioma malignant conversion and paves the way for the development of new research lines that will improve our understanding of meningioma biology.

Tumor and the microenvironment: a chance to reframe the paradigm of carcinogenesis?

The somatic mutation theory of carcinogenesis has eventually accumulated an impressive body of shortfalls and paradoxes, as admittedly claimed by its own supporters given that the cell-based approach can hardly explain the emergence of tissue-based processes, like cancer. However, experimental data and alternatives theories developed during the last decades may actually provide a new framework on which cancer research should be reframed. Such issue may be fulfilled embracing new theoretical perspectives, taking the cells-microenvironment interplay as the privileged level of observation and assuming radically different premises as well as new methodological frameworks. Within that perspective, the tumor microenvironment cannot be merely considered akin to new “factor” to be added to an already long list of “signaling factors”; microenvironment represents the physical-biochemical support of the morphogenetic field which drives epithelial cells towards differentiation and phenotype transformation, according to rules understandable only by means of a systems biology approach. That endeavour entails three fundamental aspects: general biological premises, the level of observation (i.e., the systems to which we are looking for), and the principles of biological organization that would help in integrating and understanding experimental data.

A linear-encoding model explains the variability of the target morphology in regeneration

A fundamental assumption of today's molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This 'inverse problem' is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila, hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering.

Dynamics of tissue topology during cancer invasion and metastasis

During tumor progression, cancer cells mix with other cell populations including epithelial and endothelial cells. Although potentially important clinically as well as for our understanding of basic tumor biology, the process of mixing is largely a mystery. Furthermore, there is no rigorous, analytical measure available for quantifying the mixing of compartments within a tumor. I present here a mathematical model of tissue repair and tumor growth based on collective cell migration that simulates a wide range of observed tumor behaviors with correct tissue compartmentalization and connectivity. The resulting dynamics are analyzed in light of the Euler characteristic number (χ), which describes key topological features such as fragmentation, looping and cavities. The analysis predicts a number of regimes in which the cancer cells can encapsulate normal tissue, form a co-interdigitating mass, or become fragmented and encapsulated by endothelial or epithelial structures. Key processes that affect the topological changes are the production of provisional matrix in the tumor, and the migration of endothelial or epithelial cells on this matrix. Furthermore, the simulations predict that topological changes during tumor invasion into blood vessels may contribute to metastasis. The topological analysis outlined here could be useful for tumor diagnosis or monitoring response to therapy and would only require high resolution, 3D image data to resolve and track the various cell compartments.

Shape in migration: quantitative image analysis of migrating chemoresistant HCT-8 colon cancer cells

Unsuccessful cytotoxic anticancer treatments may contribute to tumor morphologic instability and consequent tissue invasion, promoting the selection of a more malignant phenotype. Indeed, morphological changes have been demonstrated to be more pronounced in strongly vs. weakly metastatic cells. By means of normalized bending energy, we have previously quantitatively defined the link between cell shape modifications and the acquisition of a more malignant phenotype by 5-FU-resistant colon cancer cells (HCT-8FUres). Such changes were significantly correlated with an increase in motility speed. Herein, we propose a method to quantitatively analyze the shape of wild and chemoresistant HCT-8 migration front cells during wound healing assay. We evaluated the reliability of parameters (area/perimeter ratio [A/p], circularity, roundness, fractal dimension, and solidity) in describing the biological behavior of the two cell lines, enabling hence in distinguishing the chemoresistant line from the other one. We found solidity index the parameter that better described the difference between chemoresistant and wild cells. Moreover, solidity is able to capture the differences between chemoresistant and wild cells at each time point of the migration process. Indeed, motility speed was found to be inversely correlated with solidity, a quantitative index of cell deformability. Deformability is an outstanding hallmark of the process leading to metastatic spread; consequently, solidity may be considered a marker of acquired metastatic property.

Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis

Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed.

Theoretical aspects of Systems Biology

The natural world consists of hierarchical levels of complexity that range from subatomic particles and molecules to ecosystems and beyond. This implies that, in order to explain the features and behavior of a whole system, a theory might be required that would operate at the corresponding hierarchical level, i.e. where self-organization processes take place. In the past, biological research has focused on questions that could be answered by a reductionist program of genetics. The organism (and its development) was considered an epiphenomenona of its genes. However, a profound rethinking of the biological paradigm is now underway and it is likely that such a process will lead to a conceptual revolution emerging from the ashes of reductionism. This revolution implies the search for general principles on which a cogent theory of biology might rely. Because much of the logic of living systems is located at higher levels, it is imperative to focus on them. Indeed, both evolution and physiology work on these levels. Thus, by no means Systems Biology could be considered a 'simple' 'gradual' extension of Molecular Biology.

Implications of systemic dysfunction for the etiology of malignancy

The current approach to treatment in oncology is to replace the generally cytotoxic chemotherapies with pharmaceutical treatment which inactivates specific molecular targets associated with cancer development and progression. The goal is to limit cellular damage to pathways perceived to be directly responsible for the malignancy. Its underlying assumptions are twofold: (1) that individual pathways are the cause of malignancy; and (2) that the treatment objective should be destruction-either of the tumor or the dysfunctional pathway. However, the extent to which data actually support these assumptions has not been directly addressed. Accumulating evidence suggests that systemic dysfunction precedes the disruption of specific genetic/molecular pathways in most adult cancers and that targeted treatments such as kinase inhibitors may successfully treat one pathway while generating unintended changes to other, non-targeted pathways. This article discusses (1) the systemic basis of malignancy; (2) better profiling of pre-cancerous biomarkers associated with elevated risk so that preventive lifestyle modifications can be instituted early to revert high-risk epigenetic changes before tumors develop; (3) a treatment emphasis in early stage tumors that would target the restoration of systemic balance by strengthening the body's innate defense mechanisms; and (4) establishing better quantitative models of systems to capture adequate complexity for predictability at all stages of tumor progression.

Marker-free phenotyping of tumor cells by fractal analysis of reflection interference contrast microscopy images

Phenotyping of tumor cells by marker-free quantification is important for cancer diagnostics. For the first time, fractal analysis of reflection interference contrast microscopy images of single living cells was employed as a new method to distinguish between different nanoscopic membrane features of tumor cells. Since tumor progression correlates with a higher degree of chaos within the cell, it can be quantified mathematically by fractality. Our results show a high accuracy in identifying malignant cells with a failure chance of 3%, which is far better than today's applied methods.

Resting potential, oncogene-induced tumorigenesis, and metastasis: the bioelectric basis of cancer in vivo

Cancer may result from localized failure of instructive cues that normally orchestrate cell behaviors toward the patterning needs of the organism. Steady-state gradients of transmembrane voltage (V(mem)) in non-neural cells are instructive, epigenetic signals that regulate pattern formation during embryogenesis and morphostatic repair. Here, we review molecular data on the role of bioelectric cues in cancer and present new findings in the Xenopus laevis model on how the microenvironment's biophysical properties contribute to cancer in vivo. First, we investigated the melanoma-like phenotype arising from serotonergic signaling by 'instructor' cells-a cell population that is able to induce a metastatic phenotype in normal melanocytes. We show that when these instructor cells are depolarized, blood vessel patterning is disrupted in addition to the metastatic phenotype induced in melanocytes. Surprisingly, very few instructor cells need to be depolarized for the hyperpigmentation phenotype to occur; we present a model of antagonistic signaling by serotonin receptors that explains the unusual all-or-none nature of this effect. In addition to the body-wide depolarization-induced metastatic phenotype, we investigated the bioelectrical properties of tumor-like structures induced by canonical oncogenes and cancer-causing compounds. Exposure to carcinogen 4-nitroquinoline 1-oxide (4NQO) induces localized tumors, but has a broad (and variable) effect on the bioelectric properties of the whole body. Tumors induced by oncogenes show aberrantly high sodium content, representing a non-invasive diagnostic modality. Importantly, depolarized transmembrane potential is not only a marker of cancer but is functionally instructive: susceptibility to oncogene-induced tumorigenesis is significantly reduced by forced prior expression of hyperpolarizing ion channels. Importantly, the same effect can be achieved by pharmacological manipulation of endogenous chloride channels, suggesting a strategy for cancer suppression that does not require gene therapy. Together, these data extend our understanding of the recently demonstrated role of transmembrane potential in tumor formation and metastatic cell behavior. V(mem) is an important non-genetic biophysical aspect of the microenvironment that regulates the balance between normally patterned growth and carcinogenesis.

Fractal dimension and Shannon's entropy analyses of the architectural complexity caused by the inflammatory reactions induced by highly crystalline poly(vinyl alcohol) microspheres implanted in subcutaneous tissues of the Wistar rats

The results of the histopathological analyses after the implantation of highly crystalline PVA microspheres in subcutaneous tissues of Wistar rats are here in reported. Three different groups of PVA microparticles were systematically studied: highly crystalline, amorphous, and commercial ones. In addition to these experiments, complementary analyses of architectural complexity were performed using fractal dimension (FD), and Shannon's entropy (SE) concepts. The highly crystalline microspheres induced inflammatory reactions similar to the ones observed for the commercial ones, while the inflammatory reactions caused by the amorphous ones were less intense. Statistical analyses of the subcutaneous tissues of Wistar rats implanted with the highly crystalline microspheres resulted in FD and SE values significantly higher than the statistical parameters observed for the amorphous ones. The FD and SE parameters obtained for the subcutaneous tissues of Wistar rats implanted with crystalline and commercial microparticles were statistically similar. Briefly, the results indicated that the new highly crystalline microspheres had biocompatible behavior comparable to the commercial ones. In addition, statistical tools such as FD and SE analyses when combined with histopathological analyses can be useful tools to investigate the architectural complexity tissues caused by complex inflammatory reactions.

State of the art in silico tools for the study of signaling pathways in cancer

In the last several years, researchers have exhibited an intense interest in the evolutionarily conserved signaling pathways that have crucial roles during embryonic development. Interestingly, the malfunctioning of these signaling pathways leads to several human diseases, including cancer. The chemical and biophysical events that occur during cellular signaling, as well as the number of interactions within a signaling pathway, make these systems complex to study. In silico resources are tools used to aid the understanding of cellular signaling pathways. Systems approaches have provided a deeper knowledge of diverse biochemical processes, including individual metabolic pathways, signaling networks and genome-scale metabolic networks. In the future, these tools will be enormously valuable, if they continue to be developed in parallel with growing biological knowledge. In this study, an overview of the bioinformatics resources that are currently available for the analysis of biological networks is provided.

Morphogenetic fields in embryogenesis, regeneration, and cancer: non-local control of complex patterning

Establishment of shape during embryonic development, and the maintenance of shape against injury or tumorigenesis, requires constant coordination of cell behaviors toward the patterning needs of the host organism. Molecular cell biology and genetics have made great strides in understanding the mechanisms that regulate cell function. However, generalized rational control of shape is still largely beyond our current capabilities. Significant instructive signals function at long range to provide positional information and other cues to regulate organism-wide systems properties like anatomical polarity and size control. Is complex morphogenesis best understood as the emergent property of local cell interactions, or as the outcome of a computational process that is guided by a physically encoded map or template of the final goal state? Here I review recent data and molecular mechanisms relevant to morphogenetic fields: large-scale systems of physical properties that have been proposed to store patterning information during embryogenesis, regenerative repair, and cancer suppression that ultimately controls anatomy. Placing special emphasis on the role of endogenous bioelectric signals as an important component of the morphogenetic field, I speculate on novel approaches for the computational modeling and control of these fields with applications to synthetic biology, regenerative medicine, and evolutionary developmental biology.

Quantitative shape analysis of chemoresistant colon cancer cells: correlation between morphotype and phenotype

Morphological, qualitative observations allow pathologists to correlate the shape the cells acquire with the progressive, underlying neoplastic transformation they are experienced. Cell morphology, indeed, roughly scales with malignancy. A quantitative parameter for characterizing complex irregular structures is the Normalized Bending Energy (NBE). NBE provides a global feature for shape characterization correspondent to the amount of energy needed to transform the specific shape under analysis into its lowest energy state. We hypothesized that a chemotherapy resistant cancer cell line would experience a significant change in its shape, and that such a modification might be quantified by means of NBE parameterization. We checked out the usefulness of a mathematical algorithm to distinguish wild and 5-fluorouracil (5-FU)-resistant colon cancer HCT-8 cells (HCT-8FUres). NBE values, as well as cellular and molecular parameters, were recorded in both cell populations. Results demonstrated that acquisition of drug resistance is accompanied by statistically significant morphological changes in cell membrane, as well as in biological parameters. Namely, NBE increased progressively meanwhile cells become more resistant to increasing 5-FU concentrations. These data indicate how tight the relationships between morphology and phenotype is, and they support the idea to follow a cell transition toward a drug-resistant phenotype by means of morphological monitoring.

Molecular bioelectricity in developmental biology: new tools and recent discoveries: control of cell behavior and pattern formation by transmembrane potential gradients

Significant progress in the molecular investigation of endogenous bioelectric signals during pattern formation in growing tissues has been enabled by recently developed techniques. Ion flows and voltage gradients produced by ion channels and pumps are key regulators of cell proliferation, migration, and differentiation. Now, instructive roles for bioelectrical gradients in embryogenesis, regeneration, and neoplasm are being revealed through the use of fluorescent voltage reporters and functional experiments using well-characterized channel mutants. Transmembrane voltage gradients (V(mem) ) determine anatomical polarity and function as master regulators during appendage regeneration and embryonic left-right patterning. A state-of-the-art recent study reveals that they can also serve as prepatterns for gene expression domains during craniofacial patterning. Continued development of novel tools and better ways to think about physical controls of cell-cell interactions will lead to mastery of the morphogenetic information stored in physiological networks. This will enable fundamental advances in basic understanding of growth and form, as well as transformative biomedical applications in regenerative medicine.

Chromatin remodeling system, cancer stem-like attractors, and cellular reprogramming

The cancer cell attractors theory provides a next-generation understanding of carcinogenesis and natural explanation of punctuated clonal expansions of tumor progression. The impressive notion of atavism of cancer is now updated but more evidence is awaited. Besides, the mechanisms that the ectopic expression of some germline genes result in somatic tumors such as melanoma and brain tumors are emerging but are not well understood. Cancer could be triggered by cells undergoing abnormal cell attractor transitions, and may be reversible with "cyto-education". From mammals to model organisms like Caenorhabditis elegans and Drosophila melanogaster, the versatile Mi-2β/nucleosome remodeling and histone deacetylation complexes along with their functionally related chromatin remodeling complexes (CRCs), i.e., the dREAM/Myb-MuvB complex and Polycomb group complex are likely master regulators of cell attractors. The trajectory that benign cells switch to cancerous could be the reverse of navigation of embryonic cells converging from a series of intermediate transcriptional states to a final adult state, which is supported by gene expression dynamics inspector assays and some cross-species genetic evidence. The involvement of CRCs in locking cancer attractors may help find the recipes of perturbing genes to achieve successful reprogramming such that the reprogrammed cancer cell function in the same way as the normal cells.