Receptor cross-talk in angiogenesis: mapping environmental cues to cell phenotype using a stochastic, Boolean signaling network model

Game-theoretical description of the go-or-grow dichotomy in tumor development for various settings and parameter constellations

A medically important feature of several types of tumors is their ability to "decide" between staying at a primary site in the body or leaving it and forming metastases. The present theoretical study aims to provide a better understanding of the ultimate reasons for this so-called "go-or-grow" dichotomy. To that end, we use game theory, which has proven to be useful in analyzing the competition between tumors and healthy tissues or among different tumor cells. We begin by determining the game types in the Basanta-Hatzikirou-Deutsch model, depending on the parameter values. Thereafter, we suggest and analyze five modified variants of the model. For example, in the basic model, the deadlock game, Prisoner's Dilemma, and hawk-dove game can occur. The modified versions lead to several additional game types, such as battle of the sexes, route-choice, and stag-hunt games. For some game types, all cells are predicted to stay on their original site ("grow phenotype"), while for other types, only a certain fraction stay and the other cells migrate away ("go phenotype"). If the nutrient supply at a distant site is high, all the cells are predicted to go. We discuss our predictions in terms of the pros and cons of caloric restriction and limitations of the supply of vitamins or methionine. Our results may help devise treatments to prevent metastasis.

Decoding dysregulated angiogenesis in HTLV-1 asymptomatic carriers compared to healthy individuals

Human T-cell lymphotropic virus type 1 (HTLV-1) is the first identified human retrovirus responsible for two significant diseases: HTLV-1-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and adult T-cell leukemia/lymphoma (ATLL). Although the majority of infected individuals remain asymptomatic carriers, a small percentage may develop ATLL or HAM/TSP. In tumorigenesis, a crucial process is angiogenesis, which involves the formation of new blood vessels. However, the precise mechanism of HTLV-1 associated angiogenesis remains unclear. This study aims to investigate the gene regulation involved in the angiogenesis signaling pathway associated with HTLV-1 infection. The research enrolled 20 male participants, including asymptomatic carriers and healthy individuals. Blood samples were collected and screened using ELISA for HTLV-1 confirmation, and PCR was performed for both Tax and HBZ for validation. RNA extraction and cDNA synthesis were carried out, followed by RT-qPCR analysis targeting cellular genes involved in angiogenesis. Our findings indicate that gene expression related to angiogenesis was elevated in HTLV-1 ACs patients. However, the differences in gene expression of the analyzed genes, including HSP27, Paxillin, PDK1, PTEN, RAF1, SOS1, and VEGFR2 between ACs and healthy individuals were not statistically significant. This suggests that although angiogenesis-related genes may show increased expression in HTLV-1 infection, they might not be robust indicators of ATLL progression in asymptomatic carriers. The results of our study demonstrate that angiogenesis gene expression is altered in ACs of HTLV-1, indicating potential involvement of angiogenesis in the early stages before ATLL development. While we observed elevated angiogenesis gene expression in ACs, the lack of statistical significance between ACs and healthy individuals suggests that these gene markers may not be sufficient on their own to predict the development of ATLL in asymptomatic carriers.

Combining Multikinase Tyrosine Kinase Inhibitors Targeting the Vascular Endothelial Growth Factor and Cluster of Differentiation 47 Signaling Pathways Is Predicted to Increase the Efficacy of Antiangiogenic Combination Therapies

Angiogenesis is a critical step in tumor growth, development, and invasion. Nascent tumor cells secrete vascular endothelial growth factor (VEGF) that significantly remodels the tumor microenvironment through interaction with multiple receptors on vascular endothelial cells, including type 2 VEGF receptor (VEGFR2). The complex pathways initiated by VEGF binding to VEGFR2 lead to enhanced proliferation, survival, and motility of vascular endothelial cells and formation of a new vascular network, enabling tumor growth. Antiangiogenic therapies that inhibit VEGF signaling pathways were among the first drugs that targeted stroma rather than tumor cells. Despite improvements in progression-free survival and higher response rates relative to chemotherapy in some types of solid tumors, the impact on overall survival (OS) has been limited, with the majority of tumors eventually relapsing due to resistance or activation of alternate angiogenic pathways. Here, we developed a molecularly detailed computational model of endothelial cell signaling and angiogenesis-driven tumor growth to investigate combination therapies targeting different nodes of the endothelial VEGF/VEGFR2 signaling pathway. Simulations predicted a strong threshold-like behavior in extracellular signal-regulated kinases 1/2 (ERK1/2) activation relative to phosphorylated VEGFR2 levels, as continuous inhibition of at least 95% of receptors was necessary to abrogate phosphorylated ERK1/2 (pERK1/2). Combinations with mitogen-activated protein kinase/ERK kinase (MEK) and spingosine-1-phosphate inhibitors were found to be effective in overcoming the ERK1/2 activation threshold and abolishing activation of the pathway. Modeling results also identified a mechanism of resistance whereby tumor cells could reduce pERK1/2 sensitivity to inhibitors of VEGFR2 by upregulation of Raf, MEK, and sphingosine kinase 1 (SphK1), thus highlighting the need for deeper investigation of the dynamics of the crosstalk between VEGFR2 and SphK1 pathways. Inhibition of VEGFR2 phosphorylation was found to be more effective at blocking protein kinase B, also known as AKT, activation; however, to effectively abolish AKT activation, simulations identified Axl autophosphorylation or the Src kinase domain as potent targets. Simulations also supported activating cluster of differentiation 47 (CD47) on endothelial cells as an effective combination partner with tyrosine kinase inhibitors to inhibit angiogenesis signaling and tumor growth. Virtual patient simulations supported the effectiveness of CD47 agonism in combination with inhibitors of VEGFR2 and SphK1 pathways. Overall, the rule-based system model developed here provides new insights, generates novel hypothesis, and makes predictions regarding combinations that may enhance the OS with currently approved antiangiogenic therapies.

Multi-scale model of lumen formation via inverse membrane blebbing mechanism during sprouting angiogenesis process

Cancer is one of the leading causes of mortality and morbidity among people worldwide. Cancer appears as solid tumors in many cases. Angiogenesis is the growth of blood vessels from the existing vasculature and is one of the imperative processes in tumor growth. Another vital phenomenon for formation and functionality of this vasculature network is lumen formation. The results of recent studies indicate the importance of blood pressure in this mechanism. Computational modeling can study these processes in different scales. Hence, wide varieties of these models have been proposed during recent years. In this research, a multi-scale model is developed for the angiogenesis process. In the extracellular scale, the growth factor concentration is calculated via the reaction diffusion equation. At the cellular scale, growth, migration, and the adhesion of endothelial cells are modeled by the Potts cellular model. At the intra-cellular scale by considering biochemical signals, a Boolean network model describes migration, division, or apoptosis of endothelial cells. A stochastic model developed for lumen formation via inverse membrane blebbing mechanism. A CFD simulation was also used to investigate the role of pulsated blood pressure in the inverse membrane blebbing mechanism. The lumen formation model shows stochastic behavior in blebs expansion and lumen expansion. Comparing the stochastic model's results with the CFD simulation also shows the vital role of pressure pulse and the topology of the blebs in bleb retraction.

Relative importance of composition structures and biologically meaningful logics in bipartite Boolean models of gene regulation

Boolean networks have been widely used to model gene networks. However, such models are coarse-grained to an extent that they abstract away molecular specificities of gene regulation. Alternatively, bipartite Boolean network models of gene regulation explicitly distinguish genes from transcription factors (TFs). In such bipartite models, multiple TFs may simultaneously contribute to gene regulation by forming heteromeric complexes, thus giving rise to composition structures. Since bipartite Boolean models are relatively recent, an empirical investigation of their biological plausibility is lacking. Here, we estimate the prevalence of composition structures arising through heteromeric complexes. Moreover, we present an additional mechanism where composition structures may arise as a result of multiple TFs binding to cis-regulatory regions and provide empirical support for this mechanism. Next, we compare the restriction in BFs imposed by composition structures and by biologically meaningful properties. We find that though composition structures can severely restrict the number of Boolean functions (BFs) driving a gene, the two types of minimally complex BFs, namely nested canalyzing functions (NCFs) and read-once functions (RoFs), are comparatively more restrictive. Finally, we find that composition structures are highly enriched in real networks, but this enrichment most likely comes from NCFs and RoFs.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach

OBJECTIVES

Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies.

MATERIALS AND METHODS

A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network.

RESULTS

Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens.

CONCLUSIONS

Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

Systems biology of angiogenesis signaling: Computational models and omics

Angiogenesis is a highly regulated multiscale process that involves a plethora of cells, their cellular signal transduction, activation, proliferation, differentiation, as well as their intercellular communication. The coordinated execution and integration of such complex signaling programs is critical for physiological angiogenesis to take place in normal growth, development, exercise, and wound healing, while its dysregulation is critically linked to many major human diseases such as cancer, cardiovascular diseases, and ocular disorders; it is also crucial in regenerative medicine. Although huge efforts have been devoted to drug development for these diseases by investigation of angiogenesis‐targeted therapies, only a few therapeutics and targets have proved effective in humans due to the innate multiscale complexity and nonlinearity in the process of angiogenic signaling. As a promising approach that can help better address this challenge, systems biology modeling allows the integration of knowledge across studies and scales and provides a powerful means to mechanistically elucidate and connect the individual molecular and cellular signaling components that function in concert to regulate angiogenesis. In this review, we summarize and discuss how systems biology modeling studies, at the pathway‐, cell‐, tissue‐, and whole body‐levels, have advanced our understanding of signaling in angiogenesis and thereby delivered new translational insights for human diseases.

This article is categorized under:

Cardiovascular Diseases > Computational Models

Cancer > Computational Models

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels' growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development-the avascular and vascular phases-and in each stage two cases are considered-with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).

Towards understanding the messengers of extracellular space: Computational models of outside-in integrin reaction networks

The interactions between cells and their extracellular matrix (ECM) are critically important for homeostatic control of cell growth, proliferation, differentiation and apoptosis. Transmembrane integrin molecules facilitate the communication between ECM and the cell. Since the characterization of integrins in the late 1980s, there has been great advancement in understanding the function of integrins at different subcellular levels. However, the versatility in molecular pathways integrins are involved in, the high diversity in their interaction partners both outside and inside the cell as well as on the cell membrane and the short lifetime of events happening at the cell-ECM interface make it difficult to elucidate all the details regarding integrin function experimentally. To overcome the experimental challenges and advance the understanding of integrin biology, computational modeling tools have been used extensively. In this review, we summarize the computational models of integrin signaling while we explain the function of integrins at three main subcellular levels (outside the cell, cell membrane, cytosol). We also discuss how these computational modeling efforts can be helpful in other disciplines such as biomaterial design. As such, this review is a didactic modeling summary for biomaterial researchers interested in complementing their experimental work with computational tools or for seasoned computational scientists that would like to advance current in silico integrin models.

Markers of Cancer Cell Invasion: Are They Good Enough?

Invasion, or directed migration of tumor cells into adjacent tissues, is one of the hallmarks of cancer and the first step towards metastasis. Penetrating to adjacent tissues, tumor cells form the so-called invasive front/edge. The cellular plasticity afforded by different kinds of phenotypic transitions (epithelial-mesenchymal, collective-amoeboid, mesenchymal-amoeboid, and vice versa) significantly contributes to the diversity of cancer cell invasion patterns and mechanisms. Nevertheless, despite the advances in the understanding of invasion, it is problematic to identify tumor cells with the motile phenotype in cancer tissue specimens due to the absence of reliable and acceptable molecular markers. In this review, we summarize the current information about molecules such as extracellular matrix components, factors of epithelial-mesenchymal transition, proteases, cell adhesion, and actin cytoskeleton proteins involved in cell migration and invasion that could be used as invasive markers and discuss their advantages and limitations. Based on the reviewed data, we conclude that future studies focused on the identification of specific invasive markers should use new models one of which may be the intratumor morphological heterogeneity in breast cancer reflecting different patterns of cancer cell invasion.

Computational modeling of synergistic interaction between αVβ3 integrin and VEGFR2 in endothelial cells: Implications for the mechanism of action of angiogenesis-modulating integrin-binding peptides

Cooperation between VEGFR2 and integrin αVβ3 is critical for neovascularization in wound healing, cardiovascular ischemic diseases, ocular diseases, and tumor angiogenesis. In the present study, we developed a rule-based computational model to investigate the potential mechanism by which the Src-induced integrin association with VEGFR2 enhances VEGFR2 activation. Simulations demonstrated that the main function of integrin is to reduce the degradation of VEGFR2 and hence stabilize the activation signal. In addition, receptor synthesis rate and recruitment from internal compartment were found to be sensitive determinants of the activation state of VEGFR2. The model was then applied to simulate the effect of integrin-binding peptides such as tumstatin and cilengitide on VEGFR2 signaling. Further, computational modeling proposed potential molecular mechanisms for the angiogenesis-modulating activity of other integrin-binding peptides. The model highlights the complexity of the crosstalk between αVβ3 integrin and VEGFR2 and the necessity of utilizing models to elucidate potential mechanisms in angiogenesis-modulating peptide therapy.

Optimal stabilization of Boolean networks through collective influence

Boolean networks have attracted much attention due to their wide applications in describing dynamics of biological systems. During past decades, much effort has been invested in unveiling how network structure and update rules affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. For locally treelike Boolean networks with biased truth tables, we propose a greedy algorithm to identify influential nodes in Boolean networks by minimizing the largest eigenvalue of a modified nonbacktracking matrix. We test the performance of the proposed collective influence algorithm on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes compared with other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying virulence genes that lead to serious diseases.

Modeling triple-negative breast cancer heterogeneity: Effects of stromal macrophages, fibroblasts and tumor vasculature

A hallmark of breast tumors is its spatial heterogeneity that includes its distribution of cancer stem cells and progenitor cells, but also heterogeneity in the tumor microenvironment. In this study we focus on the contributions of stromal cells, specifically macrophages, fibroblasts, and endothelial cells on tumor progression. We develop a computational model of triple-negative breast cancer based on our previous work and expand it to include macrophage infiltration, fibroblasts, and angiogenesis. In vitro studies have shown that the secretomes of tumor-educated macrophages and fibroblasts increase both the migration and proliferation rates of triple-negative breast cancer cells. In vivo studies also demonstrated that blocking signaling of selected secreted factors inhibits tumor growth and metastasis in mouse xenograft models. We investigate the influences of increased migration and proliferation rates on tumor growth, the effect of the presence on fibroblasts or macrophages on growth and morphology, and the contributions of macrophage infiltration on tumor growth. We find that while the presence of macrophages increases overall tumor growth, the increase in macrophage infiltration does not substantially increase tumor growth and can even stifle tumor growth at excessive rates.

A Network Model to Explore the Effect of the Micro-environment on Endothelial Cell Behavior during Angiogenesis

Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.

Applying attractor dynamics to infer gene regulatory interactions involved in cellular differentiation

The dynamics of gene regulatory networks (GRNs) guide cellular differentiation. Determining the ways regulatory genes control expression of their targets is essential to understand and control cellular differentiation. The way a regulatory gene controls its target can be expressed as a gene regulatory function. Manual derivation of these regulatory functions is slow, error-prone and difficult to update as new information arises. Automating this process is a significant challenge and the subject of intensive effort. This work presents a novel approach to discovering biologically plausible gene regulatory interactions that control cellular differentiation. This method integrates known cell type expression data, genetic interactions, and knowledge of the effects of gene knockouts to determine likely GRN regulatory functions. We employ a genetic algorithm to search for candidate GRNs that use a set of transcription factors that control differentiation within a lineage. Nested canalyzing functions are used to constrain the search space to biologically plausible networks. The method identifies an ensemble of GRNs whose dynamics reproduce the gene expression pattern for each cell type within a particular lineage. The method's effectiveness was tested by inferring consensus GRNs for myeloid and pancreatic cell differentiation and comparing the predicted gene regulatory interactions to manually derived interactions. We identified many regulatory interactions reported in the literature and also found differences from published reports. These discrepancies suggest areas for biological studies of myeloid and pancreatic differentiation. We also performed a study that used defined synthetic networks to evaluate the accuracy of the automated search method and found that the search algorithm was able to discover the regulatory interactions in these defined networks with high accuracy. We suggest that the GRN functions derived from the methods described here can be used to fill gaps in knowledge about regulatory interactions and to offer hypotheses for experimental testing of GRNs that control differentiation and other biological processes.

Activation of Apoptotic Signal in Endothelial Cells through Intracellular Signaling Molecules Blockade in Tumor-Induced Angiogenesis

Tumor-induced angiogenesis is the bridge between avascular and vascular tumor growth phases. In tumor-induced angiogenesis, endothelial cells start to migrate and proliferate toward the tumor and build new capillaries toward the tumor. There are two stages for sprout extension during angiogenesis. The first stage is prior to anastomosis, when single sprouts extend. The second stage is after anastomosis when closed flow pathways or loops are formed and blood flows in the closed loops. Prior to anastomosis, biochemical and biomechanical signals from extracellular matrix regulate endothelial cell phenotype; however, after anastomosis, blood flow is the main regulator of endothelial cell phenotype. In this study, the critical signaling pathways of each stage are introduced. A Boolean network model is used to map environmental and flow induced signals to endothelial cell phenotype (proliferation, migration, apoptosis, and lumen formation). Using the Boolean network model, blockade of intracellular signaling molecules of endothelial cell is investigated prior to and after anastomosis and the cell fate is obtained in each case. Activation of apoptotic signal in endothelial cell can prevent the extension of new vessels and may inhibit angiogenesis. It is shown that blockade of a few signaling molecules in endothelial cell activates apoptotic signal that are proposed as antiangiogenic strategies.

Discovery of Drug Synergies in Gastric Cancer Cells Predicted by Logical Modeling

Discovery of efficient anti-cancer drug combinations is a major challenge, since experimental testing of all possible combinations is clearly impossible. Recent efforts to computationally predict drug combination responses retain this experimental search space, as model definitions typically rely on extensive drug perturbation data. We developed a dynamical model representing a cell fate decision network in the AGS gastric cancer cell line, relying on background knowledge extracted from literature and databases. We defined a set of logical equations recapitulating AGS data observed in cells in their baseline proliferative state. Using the modeling software GINsim, model reduction and simulation compression techniques were applied to cope with the vast state space of large logical models and enable simulations of pairwise applications of specific signaling inhibitory chemical substances. Our simulations predicted synergistic growth inhibitory action of five combinations from a total of 21 possible pairs. Four of the predicted synergies were confirmed in AGS cell growth real-time assays, including known effects of combined MEK-AKT or MEK-PI3K inhibitions, along with novel synergistic effects of combined TAK1-AKT or TAK1-PI3K inhibitions. Our strategy reduces the dependence on a priori drug perturbation experimentation for well-characterized signaling networks, by demonstrating that a model predictive of combinatorial drug effects can be inferred from background knowledge on unperturbed and proliferating cancer cells. Our modeling approach can thus contribute to preclinical discovery of efficient anticancer drug combinations, and thereby to development of strategies to tailor treatment to individual cancer patients.

The Vital Role of Blood Flow-Induced Proliferation and Migration in Capillary Network Formation in a Multiscale Model of Angiogenesis

Sprouting angiogenesis and capillary network formation are tissue scale phenomena. There are also sub-scale phenomena involved in angiogenesis including at the cellular and intracellular (molecular) scales. In this work, a multiscale model of angiogenesis spanning intracellular, cellular, and tissue scales is developed in detail. The key events that are considered at the tissue scale are formation of closed flow path (that is called loop in this article) and blood flow initiation in the loop. At the cellular scale, growth, migration, and anastomosis of endothelial cells (ECs) are important. At the intracellular scale, cell phenotype determination as well as alteration due to blood flow is included, having pivotal roles in the model. The main feature of the model is to obtain the physical behavior of a closed loop at the tissue scale, relying on the events at the cellular and intracellular scales, and not by imposing physical behavior upon it. Results show that, when blood flow is considered in the loop, the anastomosed sprouts stabilize and elongate. By contrast, when the loop is modeled without consideration of blood flow, the loop collapses. The results obtained in this work show that proper determination of EC phenotype is the key for its survival.

NetCooperate: a network-based tool for inferring host-microbe and microbe-microbe cooperation

Background

Host-microbe and microbe-microbe interactions are often governed by the complex exchange of metabolites. Such interactions play a key role in determining the way pathogenic and commensal species impact their host and in the assembly of complex microbial communities. Recently, several studies have demonstrated how such interactions are reflected in the organization of the metabolic networks of the interacting species, and introduced various graph theory-based methods to predict host-microbe and microbe-microbe interactions directly from network topology. Using these methods, such studies have revealed evolutionary and ecological processes that shape species interactions and community assembly, highlighting the potential of this reverse-ecology research paradigm.

Results

NetCooperate is a web-based tool and a software package for determining host-microbe and microbe-microbe cooperative potential. It specifically calculates two previously developed and validated metrics for species interaction: the Biosynthetic Support Score which quantifies the ability of a host species to supply the nutritional requirements of a parasitic or a commensal species, and the Metabolic Complementarity Index which quantifies the complementarity of a pair of microbial organisms’ niches. NetCooperate takes as input a pair of metabolic networks, and returns the pairwise metrics as well as a list of potential syntrophic metabolic compounds.

Conclusions

The Biosynthetic Support Score and Metabolic Complementarity Index provide insight into host-microbe and microbe-microbe metabolic interactions. NetCooperate determines these interaction indices from metabolic network topology, and can be used for small- or large-scale analyses. NetCooperate is provided as both a web-based tool and an open-source Python module; both are freely available online at http://elbo.gs.washington.edu/software_netcooperate.html.

Systems biology of the microvasculature

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell-cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.

On the interplay between mathematics and biology: hallmarks toward a new systems biology

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach.

Synergistic effects of curcumin and bevacizumab on cell signaling pathways in hepatocellular carcinoma

The aim of the present study was to explore the effects of curcumin in combination with bevacizumab on the vascular endothelial growth factor (VEGF)/VEGF receptor (VEGFR)/K-ras pathway in hepatocellular carcinoma. A total of 30 Sprague Dawley (SD) rats were randomly divided into five groups: Control, model, curcumin, VEGF blocker, and curcumin + VEGF blocker groups. The mRNA levels of VEGF and VEGFR in all groups were subsequently measured by quantitative reverse transcriptase-polymerase chain reaction and the protein expression of K-ras was detected by western blot analysis. Compared with the control group, the mRNA levels of VEGF and VEGFR were revealed to be significantly increased in the model, curcumin and VEGF blocker groups. The VEGF mRNA levels in the curcumin, VEGF blocker and curcumin + VEGF blocker groups were all decreased when compared with the model group. In addition, the VEGF mRNA levels in the curcumin + VEGF blocker group were significantly lower compared with the curcumin group (P<0.05). The VEGF mRNA levels in the curcumin, VEGF blocker and curcumin + VEGF blocker groups were decreased when compared with the model group (P=0.0001). No significant differences in VEGF mRNA levels were identified between the VEGF blocker and curcumin groups (P=0.863), whereas the VEGF mRNA levels in the curcumin + VEGF blocker group were significantly lower than that of the curcumin group (P=0.025). Curcumin and the VEGF blocker are each capable of inhibiting hepatocellular carcinoma progression by regulating the VEGF/VEGFR/K-ras pathway. The combination of the two compounds has a synergistic effect on the inhibition of the effects of the VEGF signaling pathways in hepatocellular carcinoma progression.

Computational systems biology approaches to anti-angiogenic cancer therapeutics

Angiogenesis is an exquisitely regulated process that is required for physiological processes and is also important in numerous diseases. Tumors utilize angiogenesis to generate the vascular network needed to supply the cancer cells with nutrients and oxygen, and many cancer drugs aim to inhibit tumor angiogenesis. Anti-angiogenic therapy involves inhibiting multiple cell types, molecular targets, and intracellular signaling pathways. Computational tools are useful in guiding treatment strategies, predicting the response to treatment, and identifying new targets of interest. Here, we describe progress that has been made in applying mathematical modeling and bioinformatics approaches to study anti-angiogenic therapeutics in cancer.

Multistable switches and their role in cellular differentiation networks

Background

Cellular differentiation during development is controlled by gene regulatory networks (GRNs). This complex process is always subject to gene expression noise. There is evidence suggesting that commonly seen patterns in GRNs, referred to as biological multistable switches, play an important role in creating the structure of lineage trees by providing stability to cell types.

Results

To explore this question a new methodology is developed and applied to study (a) the multistable switch-containing GRN for hematopoiesis and (b) a large set of random boolean networks (RBNs) in which multistable switches were embedded systematically. In this work, each network attractor is taken to represent a distinct cell type. The GRNs were seeded with one or two identical copies of each multistable switch and the effect of these additions on two key aspects of network dynamics was assessed. These properties are the barrier to movement between pairs of attractors (separation) and the degree to which one direction of movement between attractor pairs is favored over another (directionality). Both of these properties are instrumental in shaping the structure of lineage trees. We found that adding one multistable switch of any type had a modest effect on increasing the proportion of well-separated attractor pairs. Adding two identical switches of any type had a much stronger effect in increasing the proportion of well-separated attractors. Similarly, there was an increase in the frequency of directional transitions between attractor pairs when two identical multistable switches were added to GRNs. This effect on directionality was not observed when only one multistable switch was added.

Conclusions

This work provides evidence that the occurrence of multistable switches in networks that control cellular differentiation contributes to the structure of lineage trees and to the stabilization of cell types.

Modeling and visualizing cell type switching

Understanding cellular differentiation is critical in explaining development and for taming diseases such as cancer. Differentiation is conventionally represented using bifurcating lineage trees. However, these lineage trees cannot readily capture or quantify all the types of transitions now known to occur between cell types, including transdifferentiation or differentiation off standard paths. This work introduces a new analysis and visualization technique that is capable of representing all possible transitions between cell states compactly, quantitatively, and intuitively. This method considers the regulatory network of transcription factors that control cell type determination and then performs an analysis of network dynamics to identify stable expression profiles and the potential cell types that they represent. A visualization tool called CellDiff3D creates an intuitive three-dimensional graph that shows the overall direction and probability of transitions between all pairs of cell types within a lineage. In this study, the influence of gene expression noise and mutational changes during myeloid cell differentiation are presented as a demonstration of the CellDiff3D technique, a new approach to quantify and envision all possible cell state transitions in any lineage network.

A systems biology view of blood vessel growth and remodelling

Blood travels throughout the body in an extensive network of vessels – arteries, veins and capillaries. This vascular network is not static, but instead dynamically remodels in response to stimuli from cells in the nearby tissue. In particular, the smallest vessels – arterioles, venules and capillaries – can be extended, expanded or pruned, in response to exercise, ischaemic events, pharmacological interventions, or other physiological and pathophysiological events. In this review, we describe the multi-step morphogenic process of angiogenesis – the sprouting of new blood vessels – and the stability of vascular networks in vivo. In particular, we review the known interactions between endothelial cells and the various blood cells and plasma components they convey. We describe progress that has been made in applying computational modelling, quantitative biology and high-throughput experimentation to the angiogenesis process.

Cell migration or cytokinesis and proliferation?--revisiting the "go or grow" hypothesis in cancer cells in vitro

The mortality of patients with solid tumors is mostly due to metastasis that relies on the interplay between migration and proliferation. The "go or grow" hypothesis postulates that migration and proliferation spatiotemporally excludes each other. We evaluated this hypothesis on 35 cell lines (12 mesothelioma, 13 melanoma and 10 lung cancer) on both the individual cell and population levels. Following three-day-long videomicroscopy, migration, proliferation and cytokinesis-length were quantified. We found a significantly higher migration in mesothelioma cells compared to melanoma and lung cancer while tumor types did not differ in mean proliferation or duration of cytokinesis. Strikingly, we found in melanoma and lung cancer a significant positive correlation between mean proliferation and migration. Furthermore, non-dividing melanoma and lung cancer cells displayed slower migration. In contrast, in mesothelioma there were no such correlations. Interestingly, negative correlation was found between cytokinesis-length and migration in melanoma. FAK activation was higher in melanoma cells with high motility. We demonstrate that the cancer cells studied do not defer proliferation for migration. Of note, tumor cells from various organ systems may differently regulate migration and proliferation. Furthermore, our data is in line with the observation of pathologists that highly proliferative tumors are often highly invasive.

Reaction-contingency based bipartite Boolean modelling

Background

Intracellular signalling systems are highly complex, rendering mathematical modelling of large signalling networks infeasible or impractical. Boolean modelling provides one feasible approach to whole-network modelling, but at the cost of dequantification and decontextualisation of activation. That is, these models cannot distinguish between different downstream roles played by the same component activated in different contexts.

Results

Here, we address this with a bipartite Boolean modelling approach. Briefly, we use a state oriented approach with separate update rules based on reactions and contingencies. This approach retains contextual activation information and distinguishes distinct signals passing through a single component. Furthermore, we integrate this approach in the rxncon framework to support automatic model generation and iterative model definition and validation. We benchmark this method with the previously mapped MAP kinase network in yeast, showing that minor adjustments suffice to produce a functional network description.

Conclusions

Taken together, we (i) present a bipartite Boolean modelling approach that retains contextual activation information, (ii) provide software support for automatic model generation, visualisation and simulation, and (iii) demonstrate its use for iterative model generation and validation.

Multiscale computational models of complex biological systems

Integration of data across spatial, temporal, and functional scales is a primary focus of biomedical engineering efforts. The advent of powerful computing platforms, coupled with quantitative data from high-throughput experimental methodologies, has allowed multiscale modeling to expand as a means to more comprehensively investigate biological phenomena in experimentally relevant ways. This review aims to highlight recently published multiscale models of biological systems, using their successes to propose the best practices for future model development. We demonstrate that coupling continuous and discrete systems best captures biological information across spatial scales by selecting modeling techniques that are suited to the task. Further, we suggest how to leverage these multiscale models to gain insight into biological systems using quantitative biomedical engineering methods to analyze data in nonintuitive ways. These topics are discussed with a focus on the future of the field, current challenges encountered, and opportunities yet to be realized.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time.

Background

There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature.

Results

Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions.

Conclusions

Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

Dynamical systems approach to endothelial heterogeneity

Endothelial cells display remarkable phenotypic heterogeneity. An important goal is to elucidate the scope and mechanisms of endothelial heterogeneity and to use this information to develop vascular bed-specific therapies. We reexamine our current understanding of the molecular basis of endothelial heterogeneity. We introduce multistability as a new explanatory framework in vascular biology. We draw on the field of nonlinear dynamics to propose a dynamical systems framework for modeling multistability and its derivative properties, including robustness, memory, and plasticity. Our perspective allows for both a conceptual and quantitative description of system-level features of endothelial regulation.

Integration of experimental and computational approaches to sprouting angiogenesis

PURPOSE OF REVIEW

We summarize recent experimental and computational studies that investigate molecular and cellular mechanisms of sprouting angiogenesis. We discuss how experimental tools have unveiled new opportunities for computational modeling by providing detailed phenomenological descriptions and conceptual models of cell-level behaviors underpinned by high-quality molecular data. Using recent examples, we show how new understanding results from bridging computational and experimental approaches.

RECENT FINDINGS

Experimental data extends beyond the tip cell vs. stalk cell paradigm, and involves numerous molecular inputs such as vascular endothelial growth factor and Notch. This data is being used to generate and validate computational models, which can then be used to predict the results of hypothetical experiments that are difficult to perform in the laboratory, and to generate new hypotheses that account for system-wide interactions. As a result of this integration, descriptions of critical gradients of growth factor-receptor complexes have been generated, and new modulators of cell behavior have been described.

SUMMARY

We suggest that the recent emphasis on the different stages of sprouting angiogenesis, and integration of experimental and computational approaches, should provide a way to manage the complexity of this process and help identify new regulatory paradigms and therapeutic targets.

Information routing driven by background chatter in a signaling network

Living systems are capable of processing multiple sources of information simultaneously. This is true even at the cellular level, where not only coexisting signals stimulate the cell, but also the presence of fluctuating conditions is significant. When information is received by a cell signaling network via one specific input, the existence of other stimuli can provide a background activity –or chatter– that may affect signal transmission through the network and, therefore, the response of the cell. Here we study the modulation of information processing by chatter in the signaling network of a human cell, specifically, in a Boolean model of the signal transduction network of a fibroblast. We observe that the level of external chatter shapes the response of the system to information carrying signals in a nontrivial manner, modulates the activity levels of the network outputs, and effectively determines the paths of information flow. Our results show that the interactions and node dynamics, far from being random, confer versatility to the signaling network and allow transitions between different information-processing scenarios.

Far from being silent and static, the habitat of a cell is usually composed by multiple and simultaneous signals. We can consider nutrients, hormones, temperature, light, and other stimuli as elements building a default environment in which cells grow, divide and die. This environment, which has an intrinsically fluctuating nature, is the setting in which cells process all incoming stimuli. Here we examine the role that this background activity –or signaling chatter– plays in the transmission of information in a typical human cell. We address this question using a cellular model of signal transduction that we simulate using both random and periodic stimuli. We find that the level of background chatter determines the response of the whole signaling network to external stimuli. Different areas of the network are activated by specific levels of background activity, routing the information through chatter-dependent paths. In this way, different levels of chatter allow the network to select between different responses, given the same stimulus. These features depend on the architecture and functional connectivity of a truly biological network, since we find that randomized versions of the model are incapable of showing this behavior.

Integrative physical oncology

Cancer is arguably the ultimate complex biological system. Solid tumors are microstructured soft matter that evolves as a consequence of spatio-temporal events at the intracellular (e.g., signaling pathways, macromolecular trafficking), intercellular (e.g., cell-cell adhesion/communication), and tissue (e.g., cell-extracellular matrix interactions, mechanical forces) scales. To gain insight, tumor and developmental biologists have gathered a wealth of molecular, cellular, and genetic data, including immunohistochemical measurements of cell type-specific division and death rates, lineage tracing, and gain-of-function/loss-of-function mutational analyses. These data are empirically extrapolated to a diagnosis/prognosis of tissue-scale behavior, e.g., for clinical decision. Integrative physical oncology (IPO) is the science that develops physically consistent mathematical approaches to address the significant challenge of bridging the nano (nm)-micro (µm) to macro (mm, cm) scales with respect to tumor development and progression. In the current literature, such approaches are referred to as multiscale modeling. In the present article, we attempt to assess recent modeling approaches on each separate scale and critically evaluate the current 'hybrid-multiscale' models used to investigate tumor growth in the context of brain and breast cancers. Finally, we provide our perspective on the further development and the impact of IPO.

The "self-similarity logic" applied to the development of the vascular system

From a structural standpoint, living systems exhibit a hierarchical pattern of organization in which structures are nested within one another. From a temporal point of view, this type of organization is the outcome of a 'history' resulting from a set of developmental steps. Recently, it has been suggested that some auto similarity prevails at each nested level or time step and a principle of "self-similarity logic" has been proposed to convey the concept of a multi-level organization in which very similar rules (logic) apply at each level. In this study, the hypothesis is put forward that such a principle is particularly apparent in many morphological and developmental aspects of the vascular system. In fact, not only the morphology of the vascular system exhibits a high degree of geometrical self-similarity, but its remodelling processes also seem to be characterized by the application of almost the same rules, from the macroscopic to the endothelial cell to the sub-cellular levels, potentially allowing a unitary description of features such as sprouting and intussusceptive angiogenesis, and phenotypic differences of endothelial cells. The influence of the "self-similarity logic" shaping the vascular system on the organogenesis has been also discussed.

Relaxation dynamics and frequency response of a noisy cell signaling network

We investigate the dynamics of cell signaling using an experimentally based Boolean model of the human fibroblast signal transduction network. We determine via systematic numerical simulations the relaxation dynamics of the network in response to a constant set of inputs, both in the absence and in the presence of environmental fluctuations. We then study the network's response to periodically modulated signals, uncovering different types of behaviors for different pairs of driven input and output nodes. The phenomena observed include low-pass, high-pass, and band-pass filtering of the input modulations, among other nontrivial responses, at frequencies around the relaxation frequency of the network. The results reveal that the dynamic response to the external modulation of biologically realistic signaling networks is versatile and robust to noise.