A Thermodynamic Approach to the Metaboloepigenetics of Cancer.

We present a novel thermodynamic approach to the epigenomics of cancer metabolism. Here, any change in a cancer cell's membrane electric potential is completely irreversible, and as such, cells must consume metabolites to reverse the potential whenever required to maintain cell activity, a process driven by ion fluxes. Moreover, the link between cell proliferation and the membrane's electric potential is for the first time analytically proven using a thermodynamic approach, highlighting how its control is related to inflow and outflow of ions; consequently, a close interaction between environment and cell activity emerges. Lastly, we illustrate the concept by evaluating the Fe2+-flux in the presence of carcinogenesis-promoting mutations of the TET1/2/3 gene family.

The importance of ion fluxes for cancer proliferation and metastasis: A thermodynamic analysis.

Following a thermodynamic approach, we develop a new theoretical analysis of ion transfer across cell membranes. Supported also by experimental data from the literature, we highlight that ion channels determine the typical features of cancer cells, i.e. independence from growth-regulatory signals, avoidance of apoptosis, indefinite proliferative potential, and the capability of inducing angiogenesis. Specifically, we analyse how ion transport, with particular regards to Ca2+ fluxes, modulates cancer cell proliferation, and regulates cell cycle checkpoints. Finally, our analysis also suggests that in malignant tumours aerobic glycolysis is the more efficient metabolic process when taking the required solvent capacity into account.

Simulating cancer growth with multiscale agent-based modeling.

There have been many techniques developed in recent years to in silico model a variety of cancer behaviors. Agent-based modeling is a specific discrete-based hybrid modeling approach that allows simulating the role of diversity in cell populations as well as within each individual cell; it has therefore become a powerful modeling method widely used by computational cancer researchers. Many aspects of tumor morphology including phenotype-changing mutations, the adaptation to microenvironment, the process of angiogenesis, the influence of extracellular matrix, reactions to chemotherapy or surgical intervention, the effects of oxygen and nutrient availability, and metastasis and invasion of healthy tissues have been incorporated and investigated in agent-based models. In this review, we introduce some of the most recent agent-based models that have provided insight into the understanding of cancer growth and invasion, spanning multiple biological scales in time and space, and we further describe several experimentally testable hypotheses generated by those models. We also discuss some of the current challenges of multiscale agent-based cancer models.

Integrated PK-PD and agent-based modeling in oncology.

Mathematical modeling has become a valuable tool that strives to complement conventional biomedical research modalities in order to predict experimental outcome, generate new medical hypotheses, and optimize clinical therapies. Two specific approaches, pharmacokinetic-pharmacodynamic (PK-PD) modeling, and agent-based modeling (ABM), have been widely applied in cancer research. While they have made important contributions on their own (e.g., PK-PD in examining chemotherapy drug efficacy and resistance, and ABM in describing and predicting tumor growth and metastasis), only a few groups have started to combine both approaches together in an effort to gain more insights into the details of drug dynamics and the resulting impact on tumor growth. In this review, we focus our discussion on some of the most recent modeling studies building on a combined PK-PD and ABM approach that have generated experimentally testable hypotheses. Some future directions are also discussed.

A Thermodynamic Perspective of Cancer Cells' Volume/Area Expansion Ratio.

The constructal law is used to improve the analysis of the resonant heat transfer in cancer cells. The result highlights the fundamental role of the volume/area ratio and its role in cancer growth and invasion. Cancer cells seek to increase their surface area to facilitate heat dissipation; as such, the tumour expansion ratio declines as malignant cells start to migrate and the cancer expands locally and systemically. Consequently, we deduce that effective anticancer therapy should be based on the control of some ion transport phenomena in an effort to increase the volume/area ratio. This emphasises restricting the local and systemic spatial expansion of the tumour system and thus gives further credence to the superior role of novel anti-migratory and anti-invasive treatment strategies over conventional anti-proliferative options only.

Multiscale cancer modeling.

Simulating cancer behavior across multiple biological scales in space and time, i.e., multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine hypotheses, focus experiments, and enable more accurate predictions. A growing number of examples illustrate the value of this approach in providing quantitative insights in the initiation, progression, and treatment of cancer. In this review, we introduce the most recent and important multiscale cancer modeling works that have successfully established a mechanistic link between different biological scales. Biophysical, biochemical, and biomechanical factors are considered in these models. We also discuss innovative, cutting-edge modeling methods that are moving predictive multiscale cancer modeling toward clinical application. Furthermore, because the development of multiscale cancer models requires a new level of collaboration among scientists from a variety of fields such as biology, medicine, physics, mathematics, engineering, and computer science, an innovative Web-based infrastructure is needed to support this growing community.

Collective behavior in cancer cell populations.

In recent years the argument has been made that malignant tumors represent complex dynamic and self-organizing biosystems. Furthermore, there is increasing evidence that collective cell migration is common during invasion and metastasis of malignant tumors. Here, we argue that cancer systems may be capable of developing multicellular collective patterns that resemble evolved adaptive behavior known from other biological systems including collective sensing of environmental conditions and collective decision-making. We present a concept as to how these properties could arise in tumors and why the emergence of such swarm-like patterns would confer advantageous properties to the spatiotemporal expansion of tumors, and consequently, why understanding and ultimately targeting such collectivity should be of interest for basic and clinical cancer research alike.

Discovering Molecular Targets in Cancer with Multiscale Modeling.

Multiscale modeling is increasingly being recognized as a promising research area in computational cancer systems biology. Here, exemplified by two pioneering studies, we attempt to explain why and how such a multiscale approach paired with an innovative cross-scale analytical technique can be useful in identifying high-value molecular therapeutic targets. This novel, integrated approach has the potential to offer a more effective in silico framework for target discovery and represents an important technical step towards systems medicine.

Cross-scale, cross-pathway evaluation using an agent-based non-small cell lung cancer model.

We present a multiscale agent-based non-small cell lung cancer model that consists of a 3D environment with which cancer cells interact while processing phenotypic changes. At the molecular level, transforming growth factor beta (TGFbeta) has been integrated into our previously developed in silico model as a second extrinsic input in addition to epidermal growth factor (EGF). The main aim of this study is to investigate how the effects of individual and combinatorial change in EGF and TGFbeta concentrations at the molecular level alter tumor growth dynamics on the multi-cellular level, specifically tumor volume and expansion rate. Our simulation results show that separate EGF and TGFbeta fluctuations trigger competing multi-cellular phenotypes, yet synchronous EGF and TGFbeta signaling yields a spatially more aggressive tumor that overall exhibits an EGF-driven phenotype. By altering EGF and TGFbeta concentration levels simultaneously and asynchronously, we discovered a particular region of EGF-TGFbeta profiles that ensures phenotypic stability of the tumor system. Within this region, concentration changes in EGF and TGFbeta do not impact the resulting multi-cellular response substantially, while outside these concentration ranges, a change at the molecular level will substantially alter either tumor volume or tumor expansion rate, or both. By evaluating tumor growth dynamics across different scales, we show that, under certain conditions, therapeutic targeting of only one signaling pathway may be insufficient. Potential implications of these in silico results for future clinico-pharmacological applications are discussed.

The κ-statistics approach to epidemiology.

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced [Formula: see text]-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of [Formula: see text]-statistics in fitting empirical data. In this paper, we use [Formula: see text]-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived [Formula: see text]-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the [Formula: see text]-Weibull model has universal features.

In silico cancer modeling: is it ready for prime time?

At the dawn of the era of personalized, systems-driven medicine, computational or in silico modeling and the simulation of disease processes is becoming increasingly important for hypothesis generation and data integration in both experiments and clinics alike. Arguably, the use of these techniques is nowhere more visible than in oncology. To illustrate the field's vast potential, as well as its current limitations, we briefly review selected studies on modeling malignant brain tumors. Implications for clinical practice, and for clinical trial design and outcome prediction, are also discussed.

Life Sciences and the web: a new era for collaboration.

The World Wide Web has revolutionized how researchers from various disciplines collaborate over long distances. This is nowhere more important than in the Life Sciences, where interdisciplinary approaches are becoming increasingly powerful as a driver of both integration and discovery. Data access, data quality, identity, and provenance are all critical ingredients to facilitate and accelerate these collaborative enterprises and it is here where Semantic Web technologies promise to have a profound impact. This paper reviews the need for, and explores advantages of as well as challenges with these novel Internet information tools as illustrated with examples from the biomedical community.

Simulating Brain Tumor Heterogeneity with a Multiscale Agent-Based Model: Linking Molecular Signatures, Phenotypes and Expansion Rate.

We have extended our previously developed 3D multi-scale agent-based brain tumor model to simulate cancer heterogeneity and to analyze its impact across the scales of interest. While our algorithm continues to employ an epidermal growth factor receptor (EGFR) gene-protein interaction network to determine the cells' phenotype, it now adds an implicit treatment of tumor cell adhesion related to the model's biochemical microenvironment. We simulate a simplified tumor progression pathway that leads to the emergence of five distinct glioma cell clones with different EGFR density and cell 'search precisions'. The in silico results show that microscopic tumor heterogeneity can impact the tumor system's multicellular growth patterns. Our findings further confirm that EGFR density results in the more aggressive clonal populations switching earlier from proliferation-dominated to a more migratory phenotype. Moreover, analyzing the dynamic molecular profile that triggers the phenotypic switch between proliferation and migration, our in silico oncogenomics data display spatial and temporal diversity in documenting the regional impact of tumorigenesis, and thus support the added value of multi-site and repeated assessments in vitro and in vivo. Potential implications from this in silico work for experimental and computational studies are discussed.

Multi-scale, multi-resolution brain cancer modeling.

In advancing discrete-based computational cancer models towards clinical applications, one faces the dilemma of how to deal with an ever growing amount of biomedical data that ought to be incorporated eventually in one form or another. Model scalability becomes of paramount interest. In an effort to start addressing this critical issue, here, we present a novel multi-scale and multi-resolution agent-based in silico glioma model. While 'multi-scale' refers to employing an epidermal growth factor receptor (EGFR)-driven molecular network to process cellular phenotypic decisions within the micro-macroscopic environment, 'multi-resolution' is achieved through algorithms that classify cells to either active or inactive spatial clusters, which determine the resolution they are simulated at. The aim is to assign computational resources where and when they matter most for maintaining or improving the predictive power of the algorithm, onto specific tumor areas and at particular times. Using a previously described 2D brain tumor model, we have developed four different computational methods for achieving the multi-resolution scheme, three of which are designed to dynamically train on the high-resolution simulation that serves as control. To quantify the algorithms' performance, we rank them by weighing the distinct computational time savings of the simulation runs versus the methods' ability to accurately reproduce the high-resolution results of the control. Finally, to demonstrate the flexibility of the underlying concept, we show the added value of combining the two highest-ranked methods. The main finding of this work is that by pursuing a multi-resolution approach, one can reduce the computation time of a discrete-based model substantially while still maintaining a comparably high predictive power. This hints at even more computational savings in the more realistic 3D setting over time, and thus appears to outline a possible path to achieve scalability for the all-important clinical translation.

Dynamic Targeting in Cancer Treatment.

With the advent of personalized medicine, design and development of anti-cancer drugs that are specifically targeted to individual or sets of genes or proteins has been an active research area in both academia and industry. The underlying motivation for this approach is to interfere with several pathological crosstalk pathways in order to inhibit or at the very least control the proliferation of cancer cells. However, after initially conferring beneficial effects, if sub-lethal, these artificial perturbations in cell function pathways can inadvertently activate drug-induced up- and down-regulation of feedback loops, resulting in dynamic changes over time in the molecular network structure and potentially causing drug resistance as seen in clinics. Hence, the targets or their combined signatures should also change in accordance with the evolution of the network (reflected by changes to the structure and/or functional output of the network) over the course of treatment. This suggests the need for a "dynamic targeting" strategy aimed at optimizing tumor control by interfering with different molecular targets, at varying stages. Understanding the dynamic changes of this complex network under various perturbed conditions due to drug treatment is extremely challenging under experimental conditions let alone in clinical settings. However, mathematical modeling can facilitate studying these effects at the network level and beyond, and also accelerate comparison of the impact of different dosage regimens and therapeutic modalities prior to sizeable investment in risky and expensive clinical trials. A dynamic targeting strategy based on the use of mathematical modeling can be a new, exciting research avenue in the discovery and development of therapeutic drugs.

A new concept for cancer therapy: out-competing the aggressor.

Cancer expansion depends on host organ conditions that permit growth. Since such microenvironmental nourishment is limited we argue here that an autologous, therapeutically engineered and faster metabolizing cell strain could potentially out-compete native cancer cell populations for available resources which in turn should contain further cancer growth. This hypothesis aims on turning cancer progression, and its microenvironmental dependency, into a therapeutic opportunity. To illustrate our concept, we developed a three-dimensional computational model that allowed us to investigate the growth dynamics of native tumor cells mixed with genetically engineered cells that exhibit a higher proliferation rate. The simulation results confirm in silico efficacy of such therapeutic cells to combating cancer cells on site in that they can indeed control tumor growth once their proliferation rate exceeds a certain level. While intriguing from a theoretical perspective, this bold, innovative ecology-driven concept bears some significant challenges that warrant critical discussion in the community for further refinement.

Cancer stem cells as the engine of unstable tumor progression.

Genomic instability is considered by many authors the key engine of tumorigenesis. However, mounting evidence indicates that a small population of drug resistant cancer cells can also be a key component of tumor progression. Such cancer stem cells would define a compartment effectively acting as the source of most tumor cells. Here we study the interplay between these two conflicting components of cancer dynamics using two types of tissue architecture. Both mean field and multicompartment models are studied. It is shown that tissue architecture affects the pattern of cancer dynamics and that unstable cancers spontaneously organize into a heterogeneous population of highly unstable cells. This dominant population is in fact separated from the low-mutation compartment by an instability gap, where almost no cancer cells are observed. The possible implications of this prediction are discussed.

Using magnetic resonance microscopy to study the growth dynamics of a glioma spheroid in collagen I: A case study.

BACKGROUND: Highly malignant gliomas are characterized by rapid growth, extensive local tissue infiltration and the resulting overall dismal clinical outcome. Gaining any additional insights into the complex interaction between this aggressive brain tumor and its microenvironment is therefore critical. Currently, the standard imaging modalities to investigate the crucial interface between tumor growth and invasion in vitro are light and confocal laser scanning microscopy. While immensely useful in cell culture, integrating these modalities with this cancer's clinical imaging method of choice, i.e. MRI, is a non-trivial endeavour. However, this integration is necessary, should advanced computational modeling be able to utilize these in vitro data to eventually predict growth behaviour in vivo. We therefore argue that employing the same imaging modality for both the experimental setting and the clinical situation it represents should have significant value from a data integration perspective. In this case study, we have investigated the feasibility of using a specific form of MRI, i.e. magnetic resonance microscopy or MRM, to study the expansion dynamics of a multicellular tumor spheroid in a collagen type I gel. METHODS: An U87mEGFR human giloblastoma multicellular spheroid (MTS) containing approximately 4.103 cells was generated and pipetted into a collagen I gel. The sample was then imaged using a T2-weighted 3D spoiled gradient echo pulse sequence on a 14T MRI scanner over a period of 12 hours with a temporal resolution of 3 hours at room temperature. Standard histopathology was performed on the MRM sample, as well as on control samples. RESULTS: We were able to acquire three-dimensional MR images with a spatial resolution of 24 x 24 x 24 microm3. Our MRM data successfully documented the volumetric growth dynamics of an MTS in a collagen I gel over the 12-hour period. The histopathology results confirmed cell viability in the MRM sample, yet displayed distinct patterns of cell proliferation and invasion as compared to control. CONCLUSION: In this study, we demonstrate that a specific form of MRI, i.e. magnetic resonance microscopy or MRM, can be used to study the dynamic growth of a multicellular tumor spheroid (MTS) with a single cell scale spatial resolution that approaches the level of light microscopy. We argue that MRM can be employed as a complementary non-invasive tool to characterize microscopic MTS expansion, and thus, together with integrative computational modeling, may allow bridging of the experimental and clinical scales more readily.

Cross-scale sensitivity analysis of a non-small cell lung cancer model: linking molecular signaling properties to cellular behavior.

Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a two-dimensional, multiscale non-small cell lung cancer (NSCLC) model, we examine the effects of perturbations in system parameters which span both molecular and cellular levels, i.e. across scales of interest. This is achieved by first linking molecular and cellular activities and then assessing the influence of parameters at the molecular level on the tumor's spatio-temporal expansion rate, which serves as the output behavior at the cellular level. Overall, the algorithm operated reliably over relatively large variations of most parameters, hence confirming the robustness of the model. However, three pathway components (proteins PKC, MEK, and ERK) and eleven reaction steps were determined to be of critical importance by employing a sensitivity coefficient as an evaluation index. Each of these sensitive parameters exhibited a similar changing pattern in that a relatively larger increase or decrease in its value resulted in a lesser influence on the system's cellular performance. This study provides a novel cross-scaled approach to analyzing sensitivities of computational model parameters and proposes its application to interdisciplinary biomarker studies.

Cancer: a profit-driven biosystem?

The argument is made that solid malignant tumors behave as profit-driven biological systems in that they expand their nutrient-uptaking surface to increase energetic revenue, at a comparably low metabolic cost. Within this conceptual framework, cancer cell migration is a critical mechanism as it maximizes systemic surface expansion while minimizing diffusion distance. Treating these tumor systems with adjuvant anti-proliferative regimen only should increase the energetic net gain of the viable cancer cells left behind, hence would facilitate tumor recurrence. Therapeutic attempts to better control tumor (re)growth should therefore aim primarily at containing its surface expansion, thus reducing its energetic revenue, or increasing its metabolic costs or better yet, both.