A modified Ising model of Barabási–Albert network with gene-type spins

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

     

Emergent behaviors from a cellular automaton model for invasive tumor growth in heterogeneous microenvironments

Understanding tumor invasion and metastasis is of crucial importance for both fundamental cancer research and clinical practice. In vitro experiments have established that the invasive growth of malignant tumors is characterized by the dendritic invasive branches composed of chains of tumor cells emanating from the primary tumor mass. The preponderance of previous tumor simulations focused on non-invasive (or proliferative) growth. The formation of the invasive cell chains and their interactions with the primary tumor mass and host microenvironment are not well understood. Here, we present a novel cellular automaton (CA) model that enables one to efficiently simulate invasive tumor growth in a heterogeneous host microenvironment. By taking into account a variety of microscopic-scale tumor-host interactions, including the short-range mechanical interactions between tumor cells and tumor stroma, degradation of the extracellular matrix by the invasive cells and oxygen/nutrient gradient driven cell motions, our CA model predicts a rich spectrum of growth dynamics and emergent behaviors of invasive tumors. Besides robustly reproducing the salient features of dendritic invasive growth, such as least-resistance paths of cells and intrabranch homotype attraction, we also predict nontrivial coupling between the growth dynamics of the primary tumor mass and the invasive cells. In addition, we show that the properties of the host microenvironment can significantly affect tumor morphology and growth dynamics, emphasizing the importance of understanding the tumor-host interaction. The capability of our CA model suggests that sophisticated in silico tools could eventually be utilized in clinical situations to predict neoplastic progression and propose individualized optimal treatment strategies.     

The effects of CA IX catalysis products within tumor microenvironment

Solid tumors are composed of both cancer cells and various types of accessory cells, mainly fibroblasts, that collectively compose the so called tumor-microenvironment. Cancer-associated fibroblasts have been described to actively participate in cancer progression by establishing a cytokine-mediated as well as metabolic crosstalk with cancer cells. In the present paper we show that activated human fibroblasts are able to boost tumor cells proliferation and that this effect is greatly dependent on stromal carbonic anhydrase IX (CA IX) activity. In fact fibroblasts show a strong upregulation of CA IX expression upon activation by cancer cells, while CA IX products, protons and bicarbonate, exert differential effects on cancer cells proliferation. While acidification of extracellular pH, a typical condition of rapidly growing solid tumors, is detrimental for tumor cells proliferation, bicarbonate, through its organication, supplies cancer cells with intermediates useful to sustain their high proliferation rate. Here we propose a new kind of fibroblasts/tumor cells crosstalk within tumor microenvironment, mediated by stromal CA IX products, aimed to favor cancer cells growth, opening new perspectives on CA IX role in tumor microenvironment.     

Corosolic acid inhibits cancer progression by decreasing the level of CDK19-mediated O-GlcNAcylation in liver cancer cells

Diabetes is an important risk factor for liver cancer, but its mechanism is unknown. Corosolic acid (CA) has been proven to have both hypoglycemic and antitumor effects, so revealing the function of CA can help us understand the relationship between diabetes and liver cancer. In previous studies, we confirmed that CA can effectively inhibit the expression of YAP, an important oncoprotein in HCC cells, and the proliferation of HCC cells. In addition, we also found that O-GlcNAcylation plays an indispensable role in HCC tumorigenesis. However, it is not clear whether CA can inhibit the effect of O-GlcNAcylation on HCC cells. In this study, the antitumor ability of CA was investigated by inhibiting the O-GlcNAcylation level and its corresponding mechanism. The results showed that HG (high glucose) could promote the proliferation of liver cancer cells, while CA could inhibit cell growth under HG conditions and tumor growth in a xenotransplantation model. CA can inhibit the activation of the HBP pathway and reduce the expression of YAP and OGT under HG conditions. Importantly, we found that CA can reduce YAP expression and O-GlcNAcylation by inhibiting the activity of CDK19. Overexpression of CDK19 partially reversed the CA-induced decrease in YAP and O-GlcNAcylation. This is the first evidence that CA can reduce the proliferative capacity of cells with high glucose levels and further inhibit tumor growth by inactivating the CDK19/YAP/O-GlcNAcylation pathway, suggesting that CA is a candidate drug for the development of treatments against diabetes-associated liver cancer.Subject terms: Oncogenes, Tumour angiogenesis     

Reconstruction of DNA sequences using genetic algorithms and cellular automata: Towards mutation prediction?

Change of DNA sequence that fuels evolution is, to a certain extent, a deterministic process because mutagenesis does not occur in an absolutely random manner. So far, it has not been possible to decipher the rules that govern DNA sequence evolution due to the extreme complexity of the entire process. In our attempt to approach this issue we focus solely on the mechanisms of mutagenesis and deliberately disregard the role of natural selection. Hence, in this analysis, evolution refers to the accumulation of genetic alterations that originate from mutations and are transmitted through generations without being subjected to natural selection. We have developed a software tool that allows modelling of a DNA sequence as a one-dimensional cellular automaton (CA) with four states per cell which correspond to the four DNA bases, i.e. A, C, T and G. The four states are represented by numbers of the quaternary number system. Moreover, we have developed genetic algorithms (GAs) in order to determine the rules of CA evolution that simulate the DNA evolution process. Linear evolution rules were considered and square matrices were used to represent them. If DNA sequences of different evolution steps are available, our approach allows the determination of the underlying evolution rule(s). Conversely, once the evolution rules are deciphered, our tool may reconstruct the DNA sequence in any previous evolution step for which the exact sequence information was unknown. The developed tool may be used to test various parameters that could influence evolution. We describe a paradigm relying on the assumption that mutagenesis is governed by a near-neighbour-dependent mechanism. Based on the satisfactory performance of our system in the deliberately simplified example, we propose that our approach could offer a starting point for future attempts to understand the mechanisms that govern evolution. The developed software is open-source and has a user-friendly graphical input interface.     

A Cellular Automaton Model for Tumor Dormancy: Emergence of a Proliferative Switch

Malignant cancers that lead to fatal outcomes for patients may remain dormant for very long periods of time. Although individual mechanisms such as cellular dormancy, angiogenic dormancy and immunosurveillance have been proposed, a comprehensive understanding of cancer dormancy and the “switch” from a dormant to a proliferative state still needs to be strengthened from both a basic and clinical point of view. Computational modeling enables one to explore a variety of scenarios for possible but realistic microscopic dormancy mechanisms and their predicted outcomes. The aim of this paper is to devise such a predictive computational model of dormancy with an emergent “switch” behavior. Specifically, we generalize a previous cellular automaton (CA) model for proliferative growth of solid tumor that now incorporates a variety of cell-level tumor-host interactions and different mechanisms for tumor dormancy, for example the effects of the immune system. Our new CA rules induce a natural “competition” between the tumor and tumor suppression factors in the microenvironment. This competition either results in a “stalemate” for a period of time in which the tumor either eventually wins (spontaneously emerges) or is eradicated; or it leads to a situation in which the tumor is eradicated before such a “stalemate” could ever develop. We also predict that if the number of actively dividing cells within the proliferative rim of the tumor reaches a critical, yet low level, the dormant tumor has a high probability to resume rapid growth. Our findings may shed light on the fundamental understanding of cancer dormancy.     

Simulating tumor growth in confined heterogeneous environments

The holy grail of computational tumor modeling is to develop a simulation tool that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies. In order to develop such a predictive model, one must account for many of the complex processes involved in tumor growth. One interaction that has not been incorporated into computational models of neoplastic progression is the impact that organ-imposed physical confinement and heterogeneity have on tumor growth. For this reason, we have taken a cellular automaton algorithm that was originally designed to simulate spherically symmetric tumor growth and generalized the algorithm to incorporate the effects of tissue shape and structure. We show that models that do not account for organ/tissue geometry and topology lead to false conclusions about tumor spread, shape and size. The impact that confinement has on tumor growth is more pronounced when a neoplasm is growing close to, versus far from, the confining boundary. Thus, any clinical simulation tool of cancer progression must not only consider the shape and structure of the organ in which a tumor is growing, but must also consider the location of the tumor within the organ if it is to accurately predict neoplastic growth dynamics.     

MicroRNA-375 inhibits colorectal cancer growth by targeting PIK3CA

Colorectal cancer (CRC) is the second most common cause of death from cancer. MicroRNAs (miRNAs) represent a class of small non-coding RNAs that control gene expression by triggering RNA degradation or interfering with translation. Aberrant miRNA expression is involved in human disease including cancer. Herein, we showed that miR-375 was frequently down-regulated in human colorectal cancer cell lines and tissues when compared to normal human colon tissues. PIK3CA was identified as a potential miR-375 target by bioinformatics. Overexpression of miR-375 in SW480 and HCT15 cells reduced PIK3CA protein expression. Subsequently, using reporter constructs, we showed that the PIK3CA untranslated region (3′-UTR) carries the directly binding site of miR-375. Additionally, miR-375 suppressed CRC cell proliferation and colony formation and led to cell cycle arrest. Furthermore, miR-375 overexpression resulted in inhibition of phosphatidylinositol 3-kinase (PI3K)/Akt signaling pathway. SiRNA-mediated silencing of PIK3CA blocked the inhibitory effect of miR-375 on CRC cell growth. Lastly, we found overexpressed miR-375 effectively repressed tumor growth in xenograft animal experiments. Taken together, we propose that overexpression of miR-375 may provide a selective growth inhibition for CRC cells by targeting PI3K/Akt signaling pathway.     

A Mathematical-Biological Joint Effort to Investigate the Tumor-Initiating Ability of Cancer Stem Cells

The involvement of Cancer Stem Cells (CSCs) in tumor progression and tumor recurrence is one of the most studied subjects in current cancer research. The CSC hypothesis states that cancer cell populations are characterized by a hierarchical structure that affects cancer progression. Due to the complex dynamics involving CSCs and the other cancer cell subpopulations, a robust theory explaining their action has not been established yet. Some indications can be obtained by combining mathematical modeling and experimental data to understand tumor dynamics and to generate new experimental hypotheses. Here, we present a model describing the initial phase of ErbB2⁺ mammary cancer progression, which arises from a joint effort combing mathematical modeling and cancer biology. The proposed model represents a new approach to investigate the CSC-driven tumorigenesis and to analyze the relations among crucial events involving cancer cell subpopulations. Using in vivo and in vitro data we tuned the model to reproduce the initial dynamics of cancer growth, and we used its solution to characterize observed cancer progression with respect to mutual CSC and progenitor cell variation. The model was also used to investigate which association occurs among cell phenotypes when specific cell markers are considered. Finally, we found various correlations among model parameters which cannot be directly inferred from the available biological data and these dependencies were used to characterize the dynamics of cancer subpopulations during the initial phase of ErbB2⁺ mammary cancer progression.     

Oscillations in an epidemiological model based on asynchronous probabilistic cellular automaton

Consider a contagious disease affecting a host population composed of two groups with distinct habits. At each time step, each individual of this population can be in one of two states: susceptible (S) or infective (I). Here, a SIS epidemic model based on cellular automaton (CA) is proposed to study the disease spreading in such a population. In this model, the state transitions are described by probabilistic rules and each group has its own schedule to update the states of its individuals. We also propose a set of difference equations (DE) to analyze this population dynamics and we show how these two approaches (CA and DE) can be equivalent. We noticed that oscillations can be found in the composition of the group with more active social life, but not in the composition of the other group.     

A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis—a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division—we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.     

The Tumor Growth Paradox and Immune System-Mediated Selection for Cancer Stem Cells

Cancer stem cells (CSCs) drive tumor progression, metastases, treatment resistance, and recurrence. Understanding CSC kinetics and interaction with their nonstem counterparts (called tumor cells, TCs) is still sparse, and theoretical models may help elucidate their role in cancer progression. Here, we develop a mathematical model of a heterogeneous population of CSCs and TCs to investigate the proposed “tumor growth paradox”—accelerated tumor growth with increased cell death as, for example, can result from the immune response or from cytotoxic treatments. We show that if TCs compete with CSCs for space and resources they can prevent CSC division and drive tumors into dormancy. Conversely, if this competition is reduced by death of TCs, the result is a liberation of CSCs and their renewed proliferation, which ultimately results in larger tumor growth. Here, we present an analytical proof for this tumor growth paradox. We show how numerical results from the model also further our understanding of how the fraction of cancer stem cells in a solid tumor evolves. Using the immune system as an example, we show that induction of cell death can lead to selection of cancer stem cells from a minor subpopulation to become the dominant and asymptotically the entire cell type in tumors.     

A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer

Ductal carcinoma in situ (DCIS) is an early stage noninvasive breast cancer that originates in the epithelial lining of the milk ducts, but it can evolve into comedo DCIS and ultimately, into the most common type of breast cancer, invasive ductal carcinoma. Understanding the progression and how to effectively intervene in it presents a major scientific challenge. The extracellular matrix (ECM) surrounding a duct contains several types of cells and several types of growth factors that are known to individually affect tumor growth, but at present the complex biochemical and mechanical interactions of these stromal cells and growth factors with tumor cells is poorly understood. Here we develop a mathematical model that incorporates the cross-talk between stromal and tumor cells, which can predict how perturbations of the local biochemical and mechanical state influence tumor evolution. We focus on the EGF and TGF-β signaling pathways and show how up- or down-regulation of components in these pathways affects cell growth and proliferation. We then study a hybrid model for the interaction of cells with the tumor microenvironment (TME), in which epithelial cells (ECs) are modeled individually while the ECM is treated as a continuum, and show how these interactions affect the early development of tumors. Finally, we incorporate breakdown of the epithelium into the model and predict the early stages of tumor invasion into the stroma. Our results shed light on the interactions between growth factors, mechanical properties of the ECM, and feedback signaling loops between stromal and tumor cells, and suggest how epigenetic changes in transformed cells affect tumor progression.     

Niche-Dependent Gene Expression Profile of Intratumoral Heterogeneous Ovarian Cancer Stem Cell Populations

Intratumoral heterogeneity challenges existing paradigms for anti-cancer therapy. We have previously demonstrated that the human embryonic stem cells (hESC)-derived cellular microenvironment in immunocompromised mice, enables functional distinction of heterogeneous tumor cells, including cells which do not grow into a tumor in a conventional direct tumor xenograft platform. We have identified and characterized six cancer cell subpopulations each clonally expanded from a single cell, derived from human ovarian clear cell carcinoma of a single tumor, to demonstrate striking intratumoral phenotypic heterogeneity that is dynamically dependent on the tumor growth microenvironment. These cancer cell subpopulations, characterized as cancer stem cell subpopulations, faithfully recapitulate the full spectrum of histological phenotypic heterogeneity known for human ovarian clear cell carcinoma. Each of the six subpopulations displays a different level of morphologic and tumorigenic differentiation wherein growth in the hESC-derived microenvironment favors growth of CD44+/aldehyde dehydrogenase positive pockets of self-renewing cells that sustain tumor growth through a process of tumorigenic differentiation into CD44-/aldehyde dehydrogenase negative derivatives. Strikingly, these derivative cells display microenvironment-dependent plasticity with the capacity to restore self-renewal markers and CD44 expression. In the current study, we delineate the distinct gene expression and epigenetic profiles of two such subpopulations, representing extremes of phenotypic heterogeneity in terms of niche-dependent self-renewal and tumorigenic differentiation. By combining Gene Set Enrichment, Gene Ontology and Pathway-focused array analyses with methylation status, we propose a suite of robust differences in tumor self-renewal and differentiation pathways that underlie the striking intratumoral phenotypic heterogeneity which characterize this and other solid tumor malignancies.     

Bayesian Calibration,Validation and Uncertainty Quantification for Predictive Modelling of Tumour Growth: A Tutorial

In this work, we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example, we calibrate the model against experimental data that are subject to measurement errors, and then validate the resulting uncertain model predictions. We then analyse the sensitivity of the model predictions to the underlying measurement model. Finally, we propose an elementary learning approach for tuning a threshold parameter in the validation procedure in order to maximize predictive accuracy of our validated model.     

A statistical method for identifying differential gene-gene co-expression patterns

MOTIVATION: To understand cancer etiology, it is important to explore molecular changes in cellular processes from normal state to cancerous state. Because genes interact with each other during cellular processes, carcinogenesis related genes may form differential co-expression patterns with other genes in different cell states. In this study, we develop a statistical method for identifying differential gene-gene co-expression patterns in different cell states. RESULTS: For efficient pattern recognition, we extend the traditional F-statistic and obtain an Expected Conditional F-statistic (ECF-statistic), which incorporates statistical information of location and correlation. We also propose a statistical method for data transformation. Our approach is applied to a microarray gene expression dataset for prostate cancer study. For a gene of interest, our method can select other genes that have differential gene-gene co-expression patterns with this gene in different cell states. The 10 most frequently selected genes, include hepsin, GSTP1 and AMACR, which have recently been proposed to be associated with prostate carcinogenesis. However, genes GSTP1 and AMACR cannot be identified by studying differential gene expression alone. By using tumor suppressor genes TP53, PTEN and RB1, we identify seven genes that also include hepsin, GSTP1 and AMACR. We show that genes associated with cancer may have differential gene-gene expression patterns with many other genes in different cell states. By discovering such patterns, we may be able to identify carcinogenesis related genes.     

Stress-mediated progression of solid tumors: effect of mechanical stress on tissue oxygenation,cancer cell proliferation,and drug delivery

Oxygen supply plays a central role in cancer cell proliferation. While vascular density increases at the early stages of carcinogenesis, mechanical solid stresses developed during growth compress tumor blood vessels and, thus, drastically reduce not only the supply of oxygen, but also the delivery of drugs at inner tumor regions. Among other effects, hypoxia and reduced drug delivery compromise the efficacy of radiation and chemo/nanotherapy, respectively. In the present study, we developed a mathematical model of tumor growth to investigate the interconnections among tumor oxygenation that supports cancer cell proliferation, the heterogeneous accumulation of mechanical stresses owing to tumor growth, the non-uniform compression of intratumoral blood vessels due to the mechanical stresses, and the insufficient delivery of oxygen and therapeutic agents because of vessel compression. We found that the high vascular density and increased cancer cell proliferation often observed in the periphery compared to the interior of a tumor can be attributed to heterogeneous solid stress accumulation. Highly vascularized peripheral regions are also associated with greater oxygenation compared with the compressed, less vascularized inner regions. We also modeled the delivery of drugs of two distinct sizes, namely chemotherapy and nanomedicine. Model predictions suggest that drug delivery is affected negatively by vessel compression independently of the size of the therapeutic agent. Finally, we demonstrated the applicability of our model to actual geometries, employing a breast tumor model derived from MR images.     

A model of NSCLC microenvironment predicts optimal receptor targets

Background: Tumor microenvironment plays an essential role in the growth of malignancy. Understanding how tumor cells co-evolve with tumor-associated immune cells and stromal cells is important for tumor treatment. Methods: In this paper, we propose a logistic population dynamics model for quantifying the intercellular signaling network in non-small-cell lung cancer (NSCLC). The model describes the evolutionary dynamics of cells and signaling proteins and was used to predict effective receptor targets through combination strategy analysis. Then, we optimized a multi-target strategy analysis algorithm that was verified by applying it to virtual patients with heterogeneous conditions. Furthermore, to deal with acquired resistance which was commonly observed in patients with NSCLC, we proposed a novel targeting strategy — tracking targeted therapy, to optimize the treatment by improving the therapeutic strategy periodically. Results: The synergistic effect when inhibiting multiple signaling pathways may help significantly retard carcinogenic processes associated with disease progression, compared with suppression of a single signaling pathway. While traditional treatment (surgery, radiotherapy and chemotherapy) tends to attack tumor cells directly, the multi-target therapy we suggested here is aimed to inhibit the development of tumor by emasculating the relative competitive advantages of tumor cells and promoting that of normal cells. Conclusion: The combination of traditional and targeted therapy, as an interesting experiment, was significantly more effective in treatment of virtual patients due to a clear complementary relationship between the two therapeutic schemes.