Endogenous molecular-cellular hierarchical modeling of prostate carcinogenesis uncovers robust structure

Heterogeneous Evolution of Breast Cancer Cells-An Endogenous Molecular-Cellular Network Study

Breast cancer heterogeneity presents a significant challenge in clinical therapy, such as over-treatment and drug resistance. These challenges are largely due to its obscure normal epithelial origins, evolutionary stability, and transitions on the cancer subtypes. This study aims to elucidate the cellular emergence and maintenance of heterogeneous breast cancer via quantitative bio-process modeling, with potential benefit to therapeutic strategies for the disease. An endogenous molecular-cellular hypothesis posits that both pathological and physiological states are phenotypes evolved from and shaped by interactions among a number of conserved modules and cellular factors within a biological network. We hereby developed a model of core endogenous network for breast cancer in accordance with the theory, quantifying its intrinsic dynamic properties with dynamic modeling. The model spontaneously generates cell states that align with molecular classifications at both the molecular and modular level, replicating four widely recognized molecular subtypes of the cancer and validating against data extracted from the TCGA database. Further analysis shows that topologically, a singular progression gateway from normal breast cells to cancerous states is identified as the Luminal A-type breast cancer. Activated positive feedback loops are found to stabilize cellular states, while negative feedback loops facilitate state transitions. Overall, more routes are revealed on the cellular transition between stable states, and a traceable count explains the origin of breast cancer heterogeneity. Ultimately, the research intended to strength the search for therapeutic targets.

Potential therapeutic targets of gastric cancer explored under endogenous network modeling of clinical data

Improvement in the survival rate of gastric cancer, a prevalent global malignancy and the leading cause of cancer-related mortality calls for more avenues in molecular therapy. This work aims to comprehend drug resistance and explore multiple-drug combinations for enhanced therapeutic treatment. An endogenous network modeling clinic data with core gastric cancer molecules, functional modules, and pathways is constructed, which is then transformed into dynamics equations for in-silicon studies. Principal component analysis, hierarchical clustering, and K-means clustering are utilized to map the attractor domains of the stochastic model to the normal and pathological phenotypes identified from the clinical data. The analyses demonstrate gastric cancer as a cluster of stable states emerging within the stochastic dynamics and elucidate the cause of resistance to anti-VEGF monotherapy in cancer treatment as the limitation of the single pathway in preventing cancer progression. The feasibility of multiple objectives of therapy targeting specified molecules and/or pathways is explored. This study verifies the rationality of the platform of endogenous network modeling, which contributes to the development of cross-functional multi-target combinations in clinical trials.

Cancer Niches and Their Kikuchi Free Energy

Biological forms depend on a progressive specialization of pluripotent stem cells. The differentiation of these cells in their spatial and functional environment defines the organism itself; however, cellular mutations may disrupt the mutual balance between a cell and its niche, where cell proliferation and specialization are released from their autopoietic homeostasis. This induces the construction of cancer niches and maintains their survival. In this paper, we characterise cancer niche construction as a direct consequence of interactions between clusters of cancer and healthy cells. Explicitly, we evaluate these higher-order interactions between niches of cancer and healthy cells using Kikuchi approximations to the free energy. Kikuchi's free energy is measured in terms of changes to the sum of energies of baseline clusters of cells (or nodes) minus the energies of overcounted cluster intersections (and interactions of interactions, etc.). We posit that these changes in energy node clusters correspond to a long-term reduction in the complexity of the system conducive to cancer niche survival. We validate this formulation through numerical simulations of apoptosis, local cancer growth, and metastasis, and highlight its implications for a computational understanding of the etiopathology of cancer.

Extended Robust Boolean Network of Budding Yeast Cell Cycle

Background:

How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling.

Methods:

We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable.

Results:

Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved.

Conclusion:

The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.

Potential landscape of high dimensional nonlinear stochastic dynamics with large noise

Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including the cell-fate decision in developmental processes as well as the genesis and progression of cancers. While various attempts have been made to construct potential landscape in high dimensional systems and to estimate transition rates, they are practically limited to the cases where either noise is small or detailed balance condition holds. A general and practical approach to investigate real-world nonequilibrium systems, which are typically high-dimensional and subject to large multiplicative noise and the breakdown of detailed balance, remains elusive. Here, we formulate a computational framework that can directly compute the relative probabilities between locally stable states of such systems based on a least action method, without the necessity of simulating the steady-state distribution. The method can be applied to systems with arbitrary noise intensities through A-type stochastic integration, which preserves the dynamical structure of the deterministic counterpart dynamics. We demonstrate our approach in a numerically accurate manner through solvable examples. We further apply the method to investigate the role of noise on tumor heterogeneity in a 38-dimensional network model for prostate cancer, and provide a new strategy on controlling cell populations by manipulating noise strength.

Beyond cancer genes: colorectal cancer as robust intrinsic states formed by molecular interactions

Colorectal cancer (CRC) has complex pathological features that defy the linear-additive reasoning prevailing in current biomedicine studies. In pursuing a mechanistic understanding behind such complexity, we constructed a core molecular–cellular interaction network underlying CRC and investigated its nonlinear dynamical properties. The hypothesis and modelling method has been developed previously and tested in various cancer studies. The network dynamics reveal a landscape of several attractive basins corresponding to both normal intestinal phenotype and robust tumour subtypes, identified by their different molecular signatures. Comparison between the modelling results and gene expression profiles from patients collected at the second affiliated hospital of Zhejiang University is presented as validation. The numerical ‘driving’ experiment suggests that CRC pathogenesis may depend on pathways involved in gastrointestinal track development and molecules associated with mesenchymal lineage differentiation, such as Stat5, BMP, retinoic acid signalling pathways, Runx and Hox transcription families. We show that the multi-faceted response to immune stimulation and therapies, as well as different carcinogenesis and metastasis routes, can be straightforwardly understood and analysed under such a framework.

Evolutionary Origins of Cancer Driver Genes and Implications for Cancer Prognosis

The cancer atavistic theory suggests that carcinogenesis is a reverse evolution process. It is thus of great interest to explore the evolutionary origins of cancer driver genes and the relevant mechanisms underlying the carcinogenesis. Moreover, the evolutionary features of cancer driver genes could be helpful in selecting cancer biomarkers from high-throughput data. In this study, through analyzing the cancer endogenous molecular networks, we revealed that the subnetwork originating from eukaryota could control the unlimited proliferation of cancer cells, and the subnetwork originating from eumetazoa could recapitulate the other hallmarks of cancer. In addition, investigations based on multiple datasets revealed that cancer driver genes were enriched in genes originating from eukaryota, opisthokonta, and eumetazoa. These results have important implications for enhancing the robustness of cancer prognosis models through selecting the gene signatures by the gene age information.

Phenotypic Plasticity and Cell Fate Decisions in Cancer: Insights from Dynamical Systems Theory

Waddington's epigenetic landscape, a famous metaphor in developmental biology, depicts how a stem cell progresses from an undifferentiated phenotype to a differentiated one. The concept of "landscape" in the context of dynamical systems theory represents a high-dimensional space, in which each cell phenotype is considered as an "attractor" that is determined by interactions between multiple molecular players, and is buffered against environmental fluctuations. In addition, biological noise is thought to play an important role during these cell-fate decisions and in fact controls transitions between different phenotypes. Here, we discuss the phenotypic transitions in cancer from a dynamical systems perspective and invoke the concept of "cancer attractors"-hidden stable states of the underlying regulatory network that are not occupied by normal cells. Phenotypic transitions in cancer occur at varying levels depending on the context. Using epithelial-to-mesenchymal transition (EMT), cancer stem-like properties, metabolic reprogramming and the emergence of therapy resistance as examples, we illustrate how phenotypic plasticity in cancer cells enables them to acquire hybrid phenotypes (such as hybrid epithelial/mesenchymal and hybrid metabolic phenotypes) that tend to be more aggressive and notoriously resilient to therapies such as chemotherapy and androgen-deprivation therapy. Furthermore, we highlight multiple factors that may give rise to phenotypic plasticity in cancer cells, such as (a) multi-stability or oscillatory behaviors governed by underlying regulatory networks involved in cell-fate decisions in cancer cells, and (b) network rewiring due to conformational dynamics of intrinsically disordered proteins (IDPs) that are highly enriched in cancer cells. We conclude by discussing why a therapeutic approach that promotes "recanalization", i.e., the exit from "cancer attractors" and re-entry into "normal attractors", is more likely to succeed rather than a conventional approach that targets individual molecules/pathways.

Decoding early myelopoiesis from dynamics of core endogenous network

A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states. They reveal the developmental routes-how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore, recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.

Cancer as robust intrinsic state shaped by evolution: a key issues review

Cancer is a complex disease: its pathology cannot be properly understood in terms of independent players-genes, proteins, molecular pathways, or their simple combinations. This is similar to many-body physics of a condensed phase that many important properties are not determined by a single atom or molecule. The rapidly accumulating large 'omics' data also require a new mechanistic and global underpinning to organize for rationalizing cancer complexity. A unifying and quantitative theory was proposed by some of the present authors that cancer is a robust state formed by the endogenous molecular-cellular network, which is evolutionarily built for the developmental processes and physiological functions. Cancer state is not optimized for the whole organism. The discovery of crucial players in cancer, together with their developmental and physiological roles, in turn, suggests the existence of a hierarchical structure within molecular biology systems. Such a structure enables a decision network to be constructed from experimental knowledge. By examining the nonlinear stochastic dynamics of the network, robust states corresponding to normal physiological and abnormal pathological phenotypes, including cancer, emerge naturally. The nonlinear dynamical model of the network leads to a more encompassing understanding than the prevailing linear-additive thinking in cancer research. So far, this theory has been applied to prostate, hepatocellular, gastric cancers and acute promyelocytic leukemia with initial success. It may offer an example of carrying physics inquiring spirit beyond its traditional domain: while quantitative approaches can address individual cases, however there must be general rules/laws to be discovered in biology and medicine.

Gene regulatory network underlying the immortalization of epithelial cells

BACKGROUND

Tumorigenic transformation of human epithelial cells in vitro has been described experimentally as the potential result of spontaneous immortalization. This process is characterized by a series of cell-state transitions, in which normal epithelial cells acquire first a senescent state which is later surpassed to attain a mesenchymal stem-like phenotype with a potentially tumorigenic behavior. In this paper we aim to provide a system-level mechanistic explanation to the emergence of these cell types, and to the time-ordered transition patterns that are common to neoplasias of epithelial origin. To this end, we first integrate published functional and well-curated molecular data of the components and interactions that have been found to be involved in such cell states and transitions into a network of 41 molecular components. We then reduce this initial network by removing simple mediators (i.e., linear pathways), and formalize the resulting regulatory core into logical rules that govern the dynamics of each of the network components as a function of the states of its regulators.

RESULTS

Computational dynamic analysis shows that our proposed Gene Regulatory Network model recovers exactly three attractors, each of them defined by a specific gene expression profile that corresponds to the epithelial, senescent, and mesenchymal stem-like cellular phenotypes, respectively. We show that although a mesenchymal stem-like state can be attained even under unperturbed physiological conditions, the likelihood of converging to this state is increased when pro-inflammatory conditions are simulated, providing a systems-level mechanistic explanation for the carcinogenic role of chronic inflammatory conditions observed in the clinic. We also found that the regulatory core yields an epigenetic landscape that restricts temporal patterns of progression between the steady states, such that recovered patterns resemble the time-ordered transitions observed during the spontaneous immortalization of epithelial cells, both in vivo and in vitro.

CONCLUSION

Our study strongly suggests that the in vitro tumorigenic transformation of epithelial cells, which strongly correlates with the patterns observed during the pathological progression of epithelial carcinogenesis in vivo, emerges from underlying regulatory networks involved in epithelial trans-differentiation during development.

Core level regulatory network of osteoblast as molecular mechanism for osteoporosis and treatment

To develop and evaluate the long-term prophylactic treatment for chronic diseases such as osteoporosis requires a clear view of mechanism at the molecular and systems level. While molecular signaling pathway studies for osteoporosis are extensive, a unifying mechanism is missing. In this work, we provide experimental and systems-biology evidences that a tightly connected top-level regulatory network may exist, which governs the normal and osteoporotic phenotypes of osteoblast. Specifically, we constructed a hub-like interaction network from well-documented cross-talks among estrogens, glucocorticoids, retinoic acids, peroxisome proliferator-activated receptor, vitamin D receptor and calcium-signaling pathways. The network was verified with transmission electron microscopy and gene expression profiling for bone tissues of ovariectomized (OVX) rats before and after strontium gluconate (GluSr) treatment. Based on both the network structure and the experimental data, the dynamical modeling predicts calcium and glucocorticoids signaling pathways as targets for GluSr treatment. Modeling results further reveal that in the context of missing estrogen signaling, the GluSr treated state may be an outcome that is closest to the healthy state.

From molecular interaction to acute promyelocytic leukemia: Calculating leukemogenesis and remission from endogenous molecular-cellular network

Acute promyelocytic leukemia (APL) remains the best example of a malignancy that can be cured clinically by differentiation therapy. We demonstrate that APL may emerge from a dynamical endogenous molecular-cellular network obtained from normal, non-cancerous molecular interactions such as signal transduction and translational regulation under physiological conditions. This unifying framework, which reproduces APL, normal progenitor, and differentiated granulocytic phenotypes as different robust states from the network dynamics, has the advantage to study transition between these states, i.e. critical drivers for leukemogenesis and targets for differentiation. The simulation results quantitatively reproduce microarray profiles of NB4 and HL60 cell lines in response to treatment and normal neutrophil differentiation, and lead to new findings such as biomarkers for APL and additional molecular targets for arsenic trioxide therapy. The modeling shows APL and normal states mutually suppress each other, both in "wiring" and in dynamical cooperation. Leukemogenesis and recovery under treatment may be a consequence of spontaneous or induced transitions between robust states, through "passes" or "dragging" by drug effects. Our approach rationalizes leukemic complexity and constructs a platform towards extending differentiation therapy by performing "dry" molecular biology experiments.

Three-Dimensional Gene Map of Cancer Cell Types: Structural Entropy Minimisation Principle for Defining Tumour Subtypes

In this study, we propose a method for constructing cell sample networks from gene expression profiles, and a structural entropy minimisation principle for detecting natural structure of networks and for identifying cancer cell subtypes. Our method establishes a three-dimensional gene map of cancer cell types and subtypes. The identified subtypes are defined by a unique gene expression pattern, and a three-dimensional gene map is established by defining the unique gene expression pattern for each identified subtype for cancers, including acute leukaemia, lymphoma, multi-tissue, lung cancer and healthy tissue. Our three-dimensional gene map demonstrates that a true tumour type may be divided into subtypes, each defined by a unique gene expression pattern. Clinical data analyses demonstrate that most cell samples of an identified subtype share similar survival times, survival indicators and International Prognostic Index (IPI) scores and indicate that distinct subtypes identified by our algorithms exhibit different overall survival times, survival ratios and IPI scores. Our three-dimensional gene map establishes a high-definition, one-to-one map between the biologically and medically meaningful tumour subtypes and the gene expression patterns, and identifies remarkable cells that form singleton submodules.

Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis

From the perspective of systems science, tumorigenesis can be hypothesized as a critical transition (an abrupt shift from one state to another) between proliferative and apoptotic attractors on the state space of a molecular interaction network, for which an attractor is defined as a stable state to which all initial states ultimately converge, and the region of convergence is called the basin of attraction. Before the critical transition, a cellular state might transit between the basin of attraction for an apoptotic attractor and that for a proliferative attractor due to the noise induced by the inherent stochasticity in molecular interactions. Such a flickering state transition (state transition between the basins of attraction for alternative attractors from the impact of noise) would become more frequent as the cellular state approaches near the boundary of the basin of attraction, which can increase the variation in the estimate of the respective basin size. To investigate this for colorectal tumorigenesis, we have constructed a stochastic Boolean network model of the molecular interaction network that contains an important set of proteins known to be involved in cancer. In particular, we considered 100 representative sequences of 20 gene mutations that drive colorectal tumorigenesis. We investigated the appearance of cancerous cells by examining the basin size of apoptotic, quiescent, and proliferative attractors along with the sequential accumulation of gene mutations during colorectal tumorigenesis. We introduced a measure to detect the flickering state transition as the variation in the estimate of the basin sizes for three-phenotype attractors from the impact of noise. Interestingly, we found that this measure abruptly increases before a cell becomes cancerous during colorectal tumorigenesis in most of the gene mutation sequences under a certain level of stochastic noise. This suggests that a frequent flickering state transition can be a precritical phenomenon of colorectal tumorigenesis.

Cell cycle gene expression networks discovered using systems biology: Significance in carcinogenesis

The early stages of carcinogenesis are linked to defects in the cell cycle. A series of cell cycle checkpoints are involved in this process. The G1/S checkpoint that serves to integrate the control of cell proliferation and differentiation is linked to carcinogenesis and the mitotic spindle checkpoint is associated with the development of chromosomal instability. This paper presents the outcome of systems biology studies designed to evaluate if networks of covariate cell cycle gene transcripts exist in proliferative mammalian tissues including mice, rats, and humans. The GeneNetwork website that contains numerous gene expression datasets from different species, sexes, and tissues represents the foundational resource for these studies (www.genenetwork.org). In addition, WebGestalt, a gene ontology tool, facilitated the identification of expression networks of genes that co-vary with key cell cycle targets, especially Cdc20 and Plk1 (www.bioinfo.vanderbilt.edu/webgestalt). Cell cycle expression networks of such covariate mRNAs exist in multiple proliferative tissues including liver, lung, pituitary, adipose, and lymphoid tissues among others but not in brain or retina that have low proliferative potential. Sixty-three covariate cell cycle gene transcripts (mRNAs) compose the average cell cycle network with P = e(-13) to e(-36) . Cell cycle expression networks show species, sex and tissue variability, and they are enriched in mRNA transcripts associated with mitosis, many of which are associated with chromosomal instability.

Modeling the epigenetic attractors landscape: toward a post-genomic mechanistic understanding of development

Robust temporal and spatial patterns of cell types emerge in the course of normal development in multicellular organisms. The onset of degenerative diseases may result from altered cell fate decisions that give rise to pathological phenotypes. Complex networks of genetic and non-genetic components underlie such normal and altered morphogenetic patterns. Here we focus on the networks of regulatory interactions involved in cell-fate decisions. Such networks modeled as dynamical non-linear systems attain particular stable configurations on gene activity that have been interpreted as cell-fate states. The network structure also restricts the most probable transition patterns among such states. The so-called Epigenetic Landscape (EL), originally proposed by C. H. Waddington, was an early attempt to conceptually explain the emergence of developmental choices as the result of intrinsic constraints (regulatory interactions) shaped during evolution. Thanks to the wealth of molecular genetic and genomic studies, we are now able to postulate gene regulatory networks (GRN) grounded on experimental data, and to derive EL models for specific cases. This, in turn, has motivated several mathematical and computational modeling approaches inspired by the EL concept, that may be useful tools to understand and predict cell-fate decisions and emerging patterns. In order to distinguish between the classical metaphorical EL proposal of Waddington, we refer to the Epigenetic Attractors Landscape (EAL), a proposal that is formally framed in the context of GRNs and dynamical systems theory. In this review we discuss recent EAL modeling strategies, their conceptual basis and their application in studying the emergence of both normal and pathological developmental processes. In addition, we discuss how model predictions can shed light into rational strategies for cell fate regulation, and we point to challenges ahead.