Non-local Parabolic and Hyperbolic Models for Cell Polarisation in Heterogeneous Cancer Cell Populations

Tumours consist of heterogeneous populations of cells. The sub-populations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell–cell interactions, i.e. attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell–cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.     

The malignant social network: Cell-cell adhesion and communication in cancer stem cells

Tumors contain a vastly complicated cellular network that relies on local communication to execute malignant programs. The molecular cues that are involved in cell-cell adhesion orchestrate large-scale tumor behaviors such as proliferation and invasion. We have recently begun to appreciate that many tumors contain a high degree of cellular heterogeneity and are organized in a cellular hierarchy, with a cancer stem cell (CSC) population identified at the apex in multiple cancer types. CSCs reside in unique microenvironments or niches that are responsible for directing their behavior through cellular interactions between CSCs and stromal cells, generating a malignant social network. Identifying cell-cell adhesion mechanisms in this network has implications for the basic understanding of tumorigenesis and the development of more effective therapies. In this review, we will discuss our current understanding of cell-cell adhesion mechanisms used by CSCs and how these local interactions have global consequences for tumor biology.     

The malignant social network

Tumors contain a vastly complicated cellular network that relies on local communication to execute malignant programs. The molecular cues that are involved in cell-cell adhesion orchestrate large-scale tumor behaviors such as proliferation and invasion. We have recently begun to appreciate that many tumors contain a high degree of cellular heterogeneity and are organized in a cellular hierarchy, with a cancer stem cell (CSC) population identified at the apex in multiple cancer types. CSCs reside in unique microenvironments or niches that are responsible for directing their behavior through cellular interactions between CSCs and stromal cells, generating a malignant social network. Identifying cell-cell adhesion mechanisms in this network has implications for the basic understanding of tumorigenesis and the development of more effective therapies. In this review, we will discuss our current understanding of cell-cell adhesion mechanisms used by CSCs and how these local interactions have global consequences for tumor biology.     

Cell invasion through basement membrane: the anchor cell breaches the barrier

Cell invasion through basement membrane (BM) is a specialized cellular behavior critical to many normal developmental events, immune surveillance, and cancer metastasis. A highly dynamic process, cell invasion involves a complex interplay between cell-intrinsic elements that promote the invasive phenotype, and cell-cell and cell-BM interactions that regulate the timing and targeting of BM transmigration. The intricate nature of these interactions has made it challenging to study cell invasion in vivo and model in vitro. Anchor cell invasion in Caenorhabditis elegans is emerging as an important experimental paradigm for comprehensive analysis of BM invasion, revealing the gene networks that specify invasive behavior and the interactions that occur at the cell-BM interface.     

Trait positions for elevated invasiveness in adaptive ecological networks

Our ability to predict the outcome of invasion declines rapidly as non-native species progress through intertwined ecological barriers to establish and spread in recipient ecosystems. This is largely due to the lack of systemic knowledge on key processes at play as species establish self-sustaining populations within the invaded range. To address this knowledge gap, we present a mathematical model that captures the eco-evolutionary dynamics of native and non-native species interacting within an ecological network. The model is derived from continuous-trait evolutionary game theory (i.e., Adaptive Dynamics) and its associated concept of invasion fitness which depicts dynamic demographic performance that is both trait mediated and density dependent. Our approach allows us to explore how multiple resident and non-native species coevolve to reshape invasion performance, or more precisely invasiveness, over trait space. The model clarifies the role of specific traits in enabling non-native species to occupy realised opportunistic niches. It also elucidates the direction and speed of both ecological and evolutionary dynamics of residing species (natives or non-natives) in the recipient network under different levels of propagule pressure. The versatility of the model is demonstrated using four examples that correspond to the invasion of (i) a horizontal competitive community; (ii) a bipartite mutualistic network; (iii) a bipartite antagonistic network; and (iv) a multi-trophic food web. We identified a cohesive trait strategy that enables the success and establishment of non-native species to possess high invasiveness. Specifically, we find that a non-native species can achieve high levels of invasiveness by possessing traits that overlap with those of its facilitators (and mutualists), which enhances the benefits accrued from positive interactions, and by possessing traits outside the range of those of antagonists, which mitigates the costs accrued from negative interactions. This ‘central-to-reap, edge-to-elude’ trait strategy therefore describes the strategic trait positions of non-native species to invade an ecological network. This model provides a theoretical platform for exploring invasion strategies in complex adaptive ecological networks.

     

Probabilistic model of the human protein-protein interaction network

A catalog of all human protein-protein interactions would provide scientists with a framework to study protein deregulation in complex diseases such as cancer. Here we demonstrate that a probabilistic analysis integrating model organism interactome data, protein domain data, genome-wide gene expression data and functional annotation data predicts nearly 40,000 protein-protein interactions in humans-a result comparable to those obtained with experimental and computational approaches in model organisms. We validated the accuracy of the predictive model on an independent test set of known interactions and also experimentally confirmed two predicted interactions relevant to human cancer, implicating uncharacterized proteins into definitive pathways. We also applied the human interactome network to cancer genomics data and identified several interaction subnetworks activated in cancer. This integrative analysis provides a comprehensive framework for exploring the human protein interaction network.     

Defining invasiveness and invasibility in ecological networks

The success of a biological invasion is context dependent, and yet two key concepts—the invasiveness of species and the invasibility of recipient ecosystems—are often defined and considered separately. We propose a framework that can elucidate the complex relationship between invasibility and invasiveness. It is based on trait-mediated interactions between species and depicts the response of an ecological network to the intrusion of an alien species, drawing on the concept of community saturation. Here, invasiveness of an introduced species with a particular trait is measured by its per capita population growth rate when the initial propagule pressure of the introduced species is very low. The invasibility of the recipient habitat or ecosystem is dependent on the structure of the resident ecological network and is defined as the total width of an opportunity niche in the trait space susceptible to invasion. Invasibility is thus a measure of network instability. We also correlate invasibility with the asymptotic stability of resident ecological network, measured by the leading eigenvalue of the interaction matrix that depicts trait-based interaction intensity multiplied by encounter rate (a pairwise product of propagule pressure of all members in a community). We further examine the relationship between invasibility and network architecture, including network connectance, nestedness and modularity. We exemplify this framework with a trait-based assembly model under perturbations in ways to emulate fluctuating resources and random trait composition in ecological networks. The maximum invasiveness of a potential invader (greatest intrinsic population growth rate) was found to be positively correlated with invasibility of the recipient ecological network. Additionally, ecosystems with high network modularity and high ecological stability tend to exhibit high invasibility. Where quantitative data are lacking we propose using a qualitative interaction matrix of the ecological network perceived by a potential invader so that the structural network stability and invasibility can be estimated from the literature or from expert opinion. This approach links network structure, invasiveness and invasibility in the context of trait-mediated interactions, such as the invasion of insects into mutualistic and antagonistic networks.     

Systems biology analysis reveals new insights into invasive lung cancer

Background

Adenocarcinoma in situ (AIS) is a pre-invasive lesion in the lung and a subtype of lung adenocarcinoma. The patients with AIS can be cured by resecting the lesion completely. In contrast, the patients with invasive lung adenocarcinoma have very poor 5-year survival rate. AIS can develop into invasive lung adenocarcinoma. The investigation and comparison of AIS and invasive lung adenocarcinoma at the genomic level can deepen our understanding of the mechanisms underlying lung cancer development.

Results

In this study, we identified 61 lung adenocarcinoma (LUAD) invasive-specific differentially expressed genes, including nine long non-coding RNAs (lncRNAs) based on RNA sequencing techniques (RNA-seq) data from normal, AIS, and invasive tissue samples. These genes displayed concordant differential expression (DE) patterns in the independent stage III LUAD tissues obtained from The Cancer Genome Atlas (TCGA) RNA-seq dataset. For individual invasive-specific genes, we constructed subnetworks using the Genetic Algorithm (GA) based on protein-protein interactions, protein-DNA interactions and lncRNA regulations. A total of 19 core subnetworks that consisted of invasive-specific genes and at least one putative lung cancer driver gene were identified by our study. Functional analysis of the core subnetworks revealed their enrichment in known pathways and biological progresses responsible for tumor growth and invasion, including the VEGF signaling pathway and the negative regulation of cell growth.

Conclusions

Our comparison analysis of invasive cases, normal and AIS uncovered critical genes that involved in the LUAD invasion progression. Furthermore, the GA-based network method revealed gene clusters that may function in the pathways contributing to tumor invasion. The interactions between differentially expressed genes and putative driver genes identified through the network analysis can offer new targets for preventing the cancer invasion and potentially increase the survival rate for cancer patients.

     

Mathematical modelling of the influence of heat shock proteins on cancer invasion of tissue

Tumour cell invasion is crucial for cancer metastasis, which is the main cause of cancer mortality. An important group of proteins involved in cancer invasion are the Heat Shock Proteins (HSPs). According to experimental data, inhibition of one of these proteins, Hsp90, slows down cancer cells while they are invading tissue, but does not affect the synthesis of matrix metalloproteinases (MMP2 and MMP9), which are very important for cancer metastasis, acting as extracellular matrix (ECM) degrading enzymes. To test different biological hypotheses regarding how precisely Hsp90 influences tumour invasion, in this paper we use a model of solid tumour growth which accounts for the interactions between Hsp90 dynamics and the migration of cancer cells and, alternatively, between Hsp90 dynamics and the synthesis of matrix degrading enzymes (MDEs). The model consists of a system of reaction-diffusion-taxis partial differential equations describing interactions between cancer cells, MDE, and the host tissue (ECM). Using numerical simulations we investigate the effects of the administration of Hsp90 inhibitors on the dynamics of tumour invasion. Alternative mechanisms of reduction of cancer invasiveness result in different simulated patterns of the invading tumour cells. Therefore, predictions of the model suggest experiments which might be performed to develop a deeper understanding of the tumour invasion process.     

A novel knowledge-driven systems biology approach for phenotype prediction upon genetic intervention

Deciphering the biological networks underlying complex phenotypic traits, e.g., human disease is undoubtedly crucial to understand the underlying molecular mechanisms and to develop effective therapeutics. Due to the network complexity and the relatively small number of available experiments, data-driven modeling is a great challenge for deducing the functions of genes/proteins in the network and in phenotype formation. We propose a novel knowledge-driven systems biology method that utilizes qualitative knowledge to construct a Dynamic Bayesian network (DBN) to represent the biological network underlying a specific phenotype. Edges in this network depict physical interactions between genes and/or proteins. A qualitative knowledge model first translates typical molecular interactions into constraints when resolving the DBN structure and parameters. Therefore, the uncertainty of the network is restricted to a subset of models which are consistent with the qualitative knowledge. All models satisfying the constraints are considered as candidates for the underlying network. These consistent models are used to perform quantitative inference. By in silico inference, we can predict phenotypic traits upon genetic interventions and perturbing in the network. We applied our method to analyze the puzzling mechanism of breast cancer cell proliferation network and we accurately predicted cancer cell growth rate upon manipulating (anti)cancerous marker genes/proteins.     

Facilitation promotes invasions in plant‐associated microbial communities

While several studies have established a positive correlation between community diversity and invasion resistance, it is less clear how species interactions within resident communities shape this process. Here, we experimentally tested how antagonistic and facilitative pairwise interactions within resident model microbial communities predict invasion by the plant–pathogenic bacterium Ralstonia solanacearum. We found that facilitative resident community interactions promoted and antagonistic interactions suppressed invasions both in the lab and in the tomato plant rhizosphere. Crucially, pairwise interactions reliably explained observed invasion outcomes also in multispecies communities, and mechanistically, this was linked to direct inhibition of the invader by antagonistic communities (antibiosis), and to a lesser degree by resource competition between members of the resident community and the invader. Together, our findings suggest that the type and strength of pairwise interactions can reliably predict the outcome of invasions in more complex multispecies communities.     

Cell invasion through basement membranes: an anchor of understanding

To metastasize, cancer cells must acquire the ability to breach several basement membrane barriers. Cell invasions through basement membranes also occur during normal development and immune system function, enabling organ formation and cell dispersal. The mechanisms that cells use to cross basement membranes in vivo remain elusive. In cancer and development, these invasions occur in complex and inaccessible environments, which are difficult to study in vivo. Anchor-cell invasion in Caenorhabditis elegans is a simple, visually and experimentally accessible model of basement membrane invasion that is beginning to reveal a network of cellular and molecular control mechanisms that regulate the fundamental cellular process of invasion through basement membranes.     

Tumor microenvironment: Interactions and therapy

Tumor microenvironment (TME) is a host for a complex network of heterogeneous stromal cells with overlapping or opposing functions depending on the dominant signals within this milieu. Reciprocal paracrine interactions between cancer cells with cells within the tumor stroma often reshape the TME in favor of the promotion of tumor. These complex interactions require more sophisticated approaches for cancer therapy, and, therefore, advancing knowledge about dominant drivers of cancer within the TME is critical for designing therapeutic schemes. This review will provide knowledge about TME architecture, multiple signaling, and cross communications between cells within this milieu, and its targeting for immunotherapy of cancer.     

Role of neutrophil extracellular traps in regulation of lung cancer invasion and metastasis: Structural insights from a computational model

Lung cancer is one of the leading causes of cancer-related deaths worldwide and is characterized by hijacking immune system for active growth and aggressive metastasis. Neutrophils, which in their original form should establish immune activities to the tumor as a first line of defense, are undermined by tumor cells to promote tumor invasion in several ways. In this study, we investigate the mutual interactions between the tumor cells and the neutrophils that facilitate tumor invasion by developing a mathematical model that involves taxis-reaction-diffusion equations for the critical components in the interaction. These include the densities of tumor and neutrophils, and the concentrations of signaling molecules and structure such as neutrophil extracellular traps (NETs). We apply the mathematical model to a Boyden invasion assay used in the experiments to demonstrate that the tumor-associated neutrophils can enhance tumor cell invasion by secreting the neutrophil elastase. We show that the model can both reproduce the major experimental observation on NET-mediated cancer invasion and make several important predictions to guide future experiments with the goal of the development of new anti-tumor strategies. Moreover, using this model, we investigate the fundamental mechanism of NET-mediated invasion of cancer cells and the impact of internal and external heterogeneity on the migration patterning of tumour cells and their response to different treatment schedules.     

Extracellular heat shock protein (Hsp)70 and Hsp90α assist in matrix metalloproteinase-2 activation and breast cancer cell migration and invasion

Breast cancer is second only to lung cancer in cancer-related deaths in women, and the majority of these deaths are caused by metastases. Obtaining a better understanding of migration and invasion, two early steps in metastasis, is critical for the development of treatments that inhibit breast cancer metastasis. In a functional proteomic screen for proteins required for invasion, extracellular heat shock protein 90 alpha (Hsp90α) was identified and shown to activate matrix metalloproteinase 2 (MMP-2). The mechanism of MMP-2 activation by Hsp90α is unknown. Intracellular Hsp90α commonly functions with a complex of co-chaperones, leading to our hypothesis that Hsp90α functions similarly outside of the cell. In this study, we show that a complex of co-chaperones outside of breast cancer cells assists Hsp90α mediated activation of MMP-2. We demonstrate that the co-chaperones Hsp70, Hop, Hsp40, and p23 are present outside of breast cancer cells and co-immunoprecipitate with Hsp90α in vitro and in breast cancer conditioned media. These co-chaperones also increase the association of Hsp90α and MMP-2 in vitro. This co-chaperone complex enhances Hsp90α-mediated activation of MMP-2 in vitro, while inhibition of Hsp70 in conditioned media reduces this activation and decreases cancer cell migration and invasion. Together, these findings support a model in which MMP-2 activation by an extracellular co-chaperone complex mediated by Hsp90α increases breast cancer cell migration and invasion. Our studies provide insight into a novel pathway for MMP-2 activation and suggest Hsp70 as an additional extracellular target for anti-metastatic drug development.     

Overexpression of monocarboxylate anion transporter 1 and 4 in T24-induced cancer-associated fibroblasts regulates the progression of bladder cancer cells in a 3D microfluidic device

Stromal fibroblasts are essential for tumor proliferation and invasion. Here we presented a 3-dimensional (3D) microfluidic co-culture device to reconstruct an in vivo-like tumor microenvironment for investigation of the interactions of cancer-associated fibroblasts (CAFs) and bladder cancer cells. With this device, we verified that the cytokines secreted by bladder cancer cells T24 effectively transform the fibroblasts into CAFs. Compared to fibroblasts, the CAFs, which undergo the aerobic glycolysis, showed higher ability to produce lactate and provide energy for bladder cancer cell proliferation and invasion. We also demonstrated that this kind of tumor-promoting effect was associated with the upregulation of monocarboxylate anion transporter 1 (MCT1) and MCT4 expression in CAFs. We concluded that MCT1 and MCT4 are involved in bladder cancer cell proliferation and invasiveness. Moreover, this 3D microfluidic co-culture device allows for the assay to characterize various cellular events in a single device sequentially, facilitating a better understanding of the interactions among heterotypic cells in a sophisticated microenvironment.     

Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces

Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis.     

Three-Dimensional Quantification of Spheroid Degradation-Dependent Invasion and Invadopodia Formation

Invadopodia are actin-rich, proteolytic structures that enable cancer cell to invade into the surrounding tissues. Several in vitro invasion assays have been used in the literature ranging from directional quantitative assays to complex three-dimensional (3D) analyses. One of the main limitations of these assays is the lack of quantifiable degradation-dependent invasion in a three-dimensional (3D) environment that mimics the tumor microenvironment. In this article, we describe a new invasion and degradation assay based on the currently available tumor spheroid model that allows long-term high-resolution imaging of the tumor, precise quantification, and visualization of matrix degradation and multichannel immunocytochemistry. By incorporating a degradation marker (DQ-Green BSA) into a basement-membrane matrix, we demonstrate the ability to quantitate cancer cell-induced matrix degradation in 3D. Also, we describe a technique to generate histological sections of the tumor spheroid allowing the detection of invadopodia formation in the 3D tumor spheroid. This new technique provides a clear advantage for studying cancer in vitro and will help address critical questions regarding the dynamics of cancer cell invasion.     

Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation

The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.