A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype

We present a cellular automaton model of clonal evolution in cancer aimed at investigating the emergence of the glycolytic phenotype. In the model each cell is equipped with a micro-environment response network that determines the behaviour or phenotype of the cell based on the local environment. The response network is modelled using a feed-forward neural network, which is subject to mutations when the cells divide. This implies that cells might react differently to the environment and when space and nutrients are limited only the fittest cells will survive. With this model we have investigated the impact of the environment on the growth dynamics of the tumour. In particular, we have analysed the influence of the tissue oxygen concentration and extra-cellular matrix density on the dynamics of the model. We found that the environment influences both the growth and the evolutionary dynamics of the tumour. For low oxygen concentration we observe tumours with a fingered morphology, while increasing the matrix density gives rise to more compact tumours with wider fingers. The distribution of phenotypes in the tumour is also affected, and we observe that the glycolytic phenotype is most likely to emerge in a poorly oxygenated tissue with a high matrix density. Our results suggest that it is the combined effect of the oxygen concentration and matrix density that creates an environment where the glycolytic phenotype has a growth advantage and consequently is most likely to appear.     

An evolutionary hybrid cellular automaton model of solid tumour growth

We propose a cellular automaton model of solid tumour growth, in which each cell is equipped with a micro-environment response network. This network is modelled using a feed-forward artificial neural network, that takes environmental variables as an input and from these determines the cellular behaviour as the output. The response of the network is determined by connection weights and thresholds in the network, which are subject to mutations when the cells divide. As both available space and nutrients are limited resources for the tumour, this gives rise to clonal evolution where only the fittest cells survive. Using this approach we have investigated the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. The results show that the oxygen concentration affects the selection pressure, cell population diversity and morphology of the tumour. A low oxygen concentration in the tissue gives rise to a tumour with a fingered morphology that contains aggressive phenotypes with a small apoptotic potential, while a high oxygen concentration in the tissue gives rise to a tumour with a round morphology containing less evolved phenotypes. The tissue oxygen concentration thus affects the tumour at both the morphological level and on the phenotype level.     

Modelling evolutionary cell behaviour using neural networks: Application to tumour growth

In this paper, we present a modelling framework for cellular evolution that is based on the notion that a cell’s behaviour is driven by interactions with other cells and its immediate environment. We equip each cell with a phenotype that determines its behaviour and implement a decision mechanism to allow evolution of this phenotype. This decision mechanism is modelled using feed-forward neural networks, which have been suggested as suitable models of cell signalling pathways. The environmental variables are presented as inputs to the network and result in a response that corresponds to the phenotype of the cell. The response of the network is determined by the network parameters, which are subject to mutations when the cells divide. This approach is versatile as there are no restrictions on what the input or output nodes represent, they can be chosen to represent any environmental variables and behaviours that are of importance to the cell population under consideration. This framework was implemented in an individual-based model of solid tumour growth in order to investigate the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. Our results show that the oxygen concentration affects the tumour at the morphological level, but more importantly has a direct impact on the evolutionary dynamics. When the supply of oxygen is limited we observe a faster divergence away from the initial genotype, a higher population diversity and faster evolution towards aggressive phenotypes. The implementation of this framework suggests that this approach is well suited for modelling systems where evolution plays an important role and where a changing environment exerts selection pressure on the evolving population.     

Explicit Separation of Growth and Motility in a New Tumor Cord Model

We investigate a new model of tumor growth in which cell motility is considered an explicitly separate process from growth. Bulk tumor expansion is modeled by individual cell motility in a density-dependent diffusion process. This model is implemented in the context of an in vivo system, the tumor cord. We investigate numerically microscale density distributions of different cell classes and macroscale whole tumor growth rates as functions of the strength of transitions between classes. Our results indicate that the total tumor growth follows a classical von Bertalanffy growth profile, as many in vivo tumors are observed to do. This provides a quick validation for the model hypotheses. The microscale and macroscale properties are both sensitive to fluctuations in the transition parameters, and grossly adopt one of two phenotypic profiles based on their parameter regime. We analyze these profiles and use the observations to classify parameter regimes by their phenotypes. This classification yields a novel hypothesis for the early evolutionary selection of the metastatic phenotype by selecting against less motile cells which grow to higher densities and may therefore induce local collapse of the vascular network.     

Evolutionary game theory elucidates the role of glycolysis in glioma progression and invasion

Abstract. Objectives: Tumour progression has been described as a sequence of traits or phenotypes that cells have to acquire if the neoplasm is to become an invasive and malignant cancer. Although genetic mutations that lead to these phenotypes are random, the process by which some of these mutations become successful and cells spread is influenced by tumour microenvironment and the presence of other cell phenotypes. It is thus likely that some phenotypes that are essential in tumour progression will emerge in the tumour population only with prior presence of other different phenotypes. Materials and methods: In this study, we use evolutionary game theory to analyse the interactions between three different tumour cell phenotypes defined by autonomous growth, anaerobic glycolysis, and cancer cell invasion. The model allows us to understand certain specific aspects of glioma progression such as the emergence of diffuse tumour cell invasion in low‐grade tumours. Results: We have found that the invasive phenotype is more likely to evolve after appearance of the glycolytic phenotype which would explain the ubiquitous presence of invasive growth in malignant tumours. Conclusions: The result suggests that therapies, which increase the fitness cost of switching to anaerobic glycolysis, might decrease probability of the emergence of more invasive phenotypes.     

Inhibitory effects of novel integrin-targeting peptides on angiogenesis activity in HUVEC cells in vitro

Integrins are critically involved in many tumour-promoting activities. The development of inhibitors against integrins may suppress tumour growth by inhibiting tumour angiogenic signalling. In this study, we investigated the effects of two novel peptides containing the integrin binding arginine-glycine-aspartic acid-motif on inhibiting diverse cell behaviours, including cell adhesion, motility, invasion, tube formation and cell cytoskeleton. Cell adhesion and motility assays demonstrated that cyclopeptides c-Gly and c-Lys might inhibit the adhesive and motile activity at the concentration of 25 μM. There was no significant effect on cell invasion, indicating the importance of extracellular matrix degradation in modulating the anti-invasive effect of human umbilical vein endothelial cells (HUVECs). More importantly, the tubular network formation of HUVECs was significantly inhibited by cyclopeptide c-Lys besides causing a remarkable inhibition of cytoskeletal organization, disrupting the focal adhesion and actin stress fibres formation. In conclusion, this study results indicated that the novel peptide c-Lys has the ability to inhibit diverse cell behaviours of HUVECs, and the effects may be mediated at different levels of the tumour growth. Therefore, c-Lys is perhaps proposed to be a potent anti-angiogenic drug candidate.     

A Multiscale Mathematical Model of Tumour Invasive Growth

Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57–70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309–335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279–1289, 2012).     

Collective dynamics of cancer cells confined in a confluent monolayer of normal cells

Tumorigenesis often involves specific changes in cell motility and intercellular adhesion. Understanding the collective cancer cell behavior associated with these specific changes could facilitate the detection of malignant characteristics during tumor growth and invasion. In this study, a cellular vertex model is developed to investigate the collective dynamics of a disk-like aggregate of cancer cells confined in a confluent monolayer of normal cells. The effects of intercellular adhesion and cell motility on tumor progression are examined. It is found that the stresses in both the cancer cells and the normal cells increase with tumor growth, resulting in a crowded environment and enhanced cell apoptosis. The intercellular adhesion between cancer cells and normal cells is revealed to promote tumor growth and invasion. The tumor invasion dynamics hinges on the motility of cancer cells. The cancer cells could orchestrate into different collective migration modes, e.g., directional migration and rotational oscillations, dictated by the competition between cell persistence and local coordination. Phase diagrams are established to reveal the competitive mechanisms. This work highlights the role of mechanics in regulating tumor growth and invasion.     

Short-lived, transitory cell-cell interactions foster migration-dependent aggregation

During embryonic development, motile cells aggregate into cohesive groups, which give rise to tissues and organs. The role of cell migration in regulating aggregation is unclear. The current paradigm for aggregation is based on an equilibrium model of differential cell adhesivity to neighboring cells versus the underlying substratum. In many biological contexts, however, dynamics is critical. Here, we provide evidence that multicellular aggregation dynamics involves both local adhesive interactions and transport by cell migration. Using time-lapse video microscopy, we quantified the duration of cell-cell contacts among migrating cells that collided and adhered to another cell. This lifetime of cell-cell interactions exhibited a monotonic decreasing dependence on substratum adhesivity. Parallel quantitative measurements of cell migration speed revealed that across the tested range of adhesive substrata, the mean time needed for cells to migrate and encounter another cell was greater than the mean adhesion lifetime, suggesting that aggregation dynamics may depend on cell motility instead of the local differential adhesivity of cells. Consistent with this hypothesis, aggregate size exhibited a biphasic dependence on substratum adhesivity, matching the trend we observed for cell migration speed. Our findings suggest a new role for cell motility, alongside differential adhesion, in regulating developmental aggregation events and motivate new design principles for tuning aggregation dynamics in tissue engineering applications.     

Visualization and Molecular Analysis of Actin Assembly in Living Cells

Actin filament assembly is critical for eukaryotic cell motility. Arp2/3 complex and capping protein (CP) regulate actin assembly in vitro. To understand how these proteins regulate the dynamics of actin filament assembly in a motile cell, we visualized their distribution in living fibroblasts using green flourescent protein (GFP) tagging. Both proteins were concentrated in motile regions at the cell periphery and at dynamic spots within the lamella. Actin assembly was required for the motility and dynamics of spots and for motility at the cell periphery. In permeabilized cells, rhodamine-actin assembled at the cell periphery and at spots, indicating that actin filament barbed ends were present at these locations. Inhibition of the Rho family GTPase rac1, and to a lesser extent cdc42 and RhoA, blocked motility at the cell periphery and the formation of spots. Increased expression of phosphatidylinositol 5-kinase promoted the movement of spots. Increased expression of LIM–kinase-1, which likely inactivates cofilin, decreased the frequency of moving spots and led to the formation of aggregates of GFP–CP. We conclude that spots, which appear as small projections on the surface by whole mount electron microscopy, represent sites of actin assembly where local and transient changes in the cortical actin cytoskeleton take place.     

Behavioral remodeling of normal and cancerous epithelial cell lines with differing invasion potential induced by substrate elastic modulus

ABSTRACT

The micro-environment of cancer cells in the body is mechanically stiffer than that of normal cells. We cultured three breast cell lines of MCF10A-normal, MCF7-noninvasive, and MDA-MB-231-invasive on PDMS substrates with different elastic moduli and different cellular features were examined.Effects of substrate stiffness on cell behavior were evident among all cell lines. Cancerous cells were more sensitive to substrate stiffness for cell behaviors related to cell motility and migration which are necessary for invasion. The invasive cancerous cells were the most motile on substrates with moderate stiffness followed by non-invasive cancerous cells. Gene markers alterations were generally according to the analyzed cell movement parameters. Results suggest that alterations in matrix stiffness may be related to cancer disease and progression.     

Redundant mechanisms for stable cell locomotion revealed by minimal models

Crawling of eukaryotic cells on flat surfaces is underlain by the protrusion of the actin network, the contractile activity of myosin II motors, and graded adhesion to the substrate regulated by complex biochemical networks. Some crawling cells, such as fish keratocytes, maintain a roughly constant shape and velocity. Here we use moving-boundary simulations to explore four different minimal mechanisms for cell locomotion: 1), a biophysical model for myosin contraction-driven motility; 2), a G-actin transport-limited motility model; 3), a simple model for Rac/Rho-regulated motility; and 4), a model that assumes that microtubule-based transport of vesicles to the leading edge limits the rate of protrusion. We show that all of these models, alone or in combination, are sufficient to produce half-moon steady shapes and movements that are characteristic of keratocytes, suggesting that these mechanisms may serve redundant and complementary roles in driving cell motility. Moving-boundary simulations demonstrate local and global stability of the motile cell shapes and make testable predictions regarding the dependence of shape and speed on mechanical and biochemical parameters. The models shed light on the roles of membrane-mediated area conservation and the coupling of mechanical and biochemical mechanisms in stabilizing motile cells.     

Septins promote stress fiber–mediated maturation of focal adhesions and renal epithelial motility

Organogenesis and tumor metastasis involve the transformation of epithelia to highly motile mesenchymal-like cells. Septins are filamentous G proteins, which are overexpressed in metastatic carcinomas, but their functions in epithelial motility are unknown. Here, we show that a novel network of septin filaments underlies the organization of the transverse arc and radial (dorsal) stress fibers at the leading lamella of migrating renal epithelia. Surprisingly, septin depletion resulted in smaller and more transient and peripheral focal adhesions. This phenotype was accompanied by a highly disorganized lamellar actin network and rescued by the actin bundling protein α-actinin-1. We show that preassembled actin filaments are cross-linked directly by Septin 9 (SEPT9), whose expression is increased after induction of renal epithelial motility with the hepatocyte growth factor. Significantly, SEPT9 overexpression enhanced renal cell migration in 2D and 3D matrices, whereas SEPT9 knockdown decreased migration. These results suggest that septins promote epithelial motility by reinforcing the cross-linking of lamellar stress fibers and the stability of nascent focal adhesions.     

Redistribution of cytosolic FGFR1 after induced migration of urothelial cells in culture

The distribution of cytosolic fibroblast growth factor receptor 1 (FGFR1) was studied in correlation to cell migration in urothelial cell line g/G. Cell motility was analysed with a new method using consecutive series of photographs of cells relocated on CELLocate coverslips and with image analysis software. The results confirmed that FGF1 stimulated cell motility only when cells were grown on collagen I coating. During the transition from sessile to motile cell phenotype a complete redistribution of cytosolic FGFR1 was revealed. In sessile cells, FGFR1 had a filamentous distribution and its location matched cytokeratin 7. In cells of the migrating phenotype, the distribution of FGFR1 was diffuse, mainly located in cytosol. Our data reveal that the location of cytosolic FGFR1 depends on the motile characteristics of the cell. The results also indicate that attachment of cells to collagen I is crucial for the induction of urothelial cell motility with FGF1.     

A cellular automaton model for tumour growth in inhomogeneous environment

Most of the existing mathematical models for tumour growth and tumour-induced angiogenesis neglect blood flow. This is an important factor on which both nutrient and metabolite supply depend. In this paper we aim to address this shortcoming by developing a mathematical model which shows how blood flow and red blood cell heterogeneity influence the growth of systems of normal and cancerous cells. The model is developed in two stages. First we determine the distribution of oxygen in a native vascular network, incorporating into our model features of blood flow and vascular dynamics such as structural adaptation, complex rheology and red blood cell circulation. Once we have calculated the oxygen distribution, we then study the dynamics of a colony of normal and cancerous cells, placed in such a heterogeneous environment. During this second stage, we assume that the vascular network does not evolve and is independent of the dynamics of the surrounding tissue. The cells are considered as elements of a cellular automaton, whose evolution rules are inspired by the different behaviour of normal and cancer cells. Our aim is to show that blood flow and red blood cell heterogeneity play major roles in the development of such colonies, even when the red blood cells are flowing through the vasculature of normal, healthy tissue.     

Correlating single cell motility with population growth dynamics for flagellated bacteria

Many bacteria used for biotechnological applications are naturally motile. Their "bio-nanopropeller" driven movement allows searching for better environments in a process called chemotaxis. Since bacteria are extremely small in size compared to the bulk fluid volumes in bioreactors, single cell motility is not considered to influence bioreactor operations. However, with increasing interest in localized fluid flow inside reactors, it is important to ask whether individual motility characteristics of bacteria are important in bioreactor operations. The first step in this direction is to try to correlate single cell measurements with population data of motile bacteria in a bioreactor. Thus, we observed the motility behavior of individual bacterial cells, using video microscopy with 33 ms time resolution, as a function of population growth dynamics of batch cultures in shake flasks. While observing the motility behavior of the most intensively studied bacteria, Escherichia coli, we find that overall bacterial motility decreases with progression of the growth curve. Remarkably, this is due to a decrease in a specific motility behavior called "running". Our results not only have direct implications on biofilm formations, but also provide a new direction in bioprocess design research highlighting the role of individual bacterial cell motility as an important parameter.     

Metastasis is driven by sequential elevation of H-ras and Smad2 levels

Metastasis is a multistep process that involves local tumour invasion followed by dissemination to, and re-establishment at, distant sites. Here we show that during multistage tumorigenesis, discrete expression thresholds of activated Smad2 and H-ras are sequentially surpassed, driving tumour progression through distinct phases from a differentiated squamous carcinoma to a motile invasive stage, followed by an overt change from epithelial to mesenchymal cell type, finally culminating in metastatic tumour spread. Smad2 activation alone induces migration of tumour cells. Elevated H-ras levels, however, are required for nuclear accumulation of Smad2, both of which are essential for the epithelial mesenchymal transition (EMT). Having undergone EMT, fibroblastoid carcinoma cells with elevated levels of activated Smad2, gain the capability to spread to a wide variety of tissues by a further increase in Smad2 expression. These findings have far-reaching implications for the prevention of tumour growth, invasion and metastasis.     

Local calcium transients contribute to disappearance of pFAK, focal complex removal and deadhesion of neuronal growth cones and fibroblasts

Cell adhesion is crucial for migration of cells during development, and cell-substrate adhesion of motile cells is accomplished through the formation and removal of focal complexes that are sites of cell-substrate contact. Because Ca2+ signaling regulates the rate of axon outgrowth and growth cone turning, we investigated the potential role of Ca2+ in focal complex dynamics. We describe a novel class of localized, spontaneous transient elevations of cytosolic Ca2+ observed both in Xenopus neuronal growth cones and fibroblasts that are 2-6 mum in spatial extent and 2-4 s in duration. They are distributed throughout growth cone lamellipodia and at the periphery of fibroblast pseudopodia, which are regions of high motility. In both cell types, these Ca2+ transients lead to disappearance of phosphorylated focal adhesion kinase (pFAK) and deadhesion from the substrate as assessed by confocal and internal reflection microscopy, respectively. The loss of pFAK is inhibited by cyclosporin A, suggesting that these Ca2+ transients exert their effects via calcineurin. These results identify an intrinsic mechanism for local cell detachment that may be modulated by agents that regulate motility.