Model-based Comparison of Cell Density-dependent Cell Migration Strategies

Here, we investigate different cell density-dependent migration strategies. In particular, we consider strategies which differ in the precise regulation of transitions between resting and motile phenotypes. We develop a lattice-gas cellular automaton (LGCA) model for each migration strategy. Using a mean-field approximation we quantify the corresponding spreading dynamics at the cell population level. Our results allow for the prediction of cell population spreading based on experimentally accessible single cell migration parameters

A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates

Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions

Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of vascularized tumor growth, where the main novelty is the modeling of the interplay between functional tumor vasculature and effector cell recruitment dynamics. Parameters are calibrated on the basis of different in vivo immunocompromised Rag1-/- and wild-type (WT) BALB/c murine tumor growth experiments. The model analysis supports that tumor vasculature normalization can be a plausible and effective strategy to treat cancer when combined with appropriate immuno-stimulations. We find that improved levels of functional tumor vasculature, potentially mediated by normalization or stress alleviation strategies, can provide beneficial outcomes in terms of tumor burden reduction and growth control. Normalization of tumor blood vessels opens a therapeutic window of opportunity to augment the antitumor immune responses, as well as to reduce the intratumoral immunosuppression and induced-hypoxia due to vascular abnormalities. The potential success of normalizing tumor-associated vasculature closely depends on the effector cell recruitment dynamics and tumor sizes. Furthermore, an arbitrary increase of initial effector cell concentration does not necessarily imply a better tumor control. We evidence the existence of an optimal concentration range of effector cells for tumor shrinkage. Based on these findings, we suggest a theory-driven therapeutic proposal that optimally combines immuno- and vaso-modulatory interventions

Cellular automaton models for time-correlated random walks: derivation and analysis.

Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is "data-driven". Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.The authors thank the Centre for Information Services and High Performance Computing (ZIH) at TU Dresden for providing an excellent infrastructure. The authors acknowledge support by the German Research Foundation and the Open Access Publication Funds of the TU Dresden.The authors would like to thank Anja Voß-Böhme, Lutz Brusch, Fabian Rost, Osvaldo Chara, Simon Syga, and Oleksandr Ostrenko for their helpful comments and fruitful discussions. Andreas Deutsch is grateful to the Deutsche Krebshilfe for support. Andreas Deutsch is supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) within the projects SFB-TR 79 “Materials for tissue regeneration within systemically altered bones” and Research Cluster of Excellence “Center for Advancing Electronics Dresden” (cfaed). Haralampos Hatzikirou would like to acknowledge the SYSMIFTA ERACoSysMed grant (031L0085B) for the financial support of this work and the German Federal Ministry of Education and Research within the Measures for the Establishment of Systems Medicine, project SYSIMIT (BMBF eMed project SYSIMIT, FKZ: 01ZX1308D). Josué Manik Nava-Sedeño is supported by the joint scolarship program DAAD-CONACYT-Regierungsstipendien (50017046) by the German Academic Exchange Service and the National Council on Science and Technology of Mexico

‘Go or Grow': the key to the emergence of invasion in tumour progression?

Uncontrolled proliferation and abnormal cell migration are two of the main characteristics of tumour growth. Of ultimate importance is the question what are the mechanisms that trigger the progression from benign neoplasms (uncontrolled/autonomous proliferation) to malignant invasive tumours (high migration). In the following, we challenge the currently prevailing view that the emergence of invasiveness is mainly the consequence of acquired cancer cell mutations. To study this, we mainly focus on the ‘glioblastoma multiforme' (GBM) tumour which is a particularly aggressive and invasive tumour. In particular, with the help of a simple growth model, we demonstrate that the short time required for the recurrence of a GBM tumour after a gross total resection cannot be deduced solely from a mutation-based theory. We propose that the transition to invasive tumour phenotypes can be explained on the basis of the microscopic ‘Go or Grow' mechanism (migration/proliferation dichotomy) and the oxygen shortage, i.e. hypoxia, in the environment of a growing tumour. We test this hypothesis with the help of a lattice-gas cellular automaton. Finally, we suggest possible therapies that could help prevent the progression towards malignancy and invasiveness of benign tumour

Studying the emergence of invasiveness in tumours using game theory

Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative mathematical model based on game theory and computer simulations using cellular automata. With this model we study the circumstances under which mutations that confer increased motility to cells can spread through a tumour made of rapidly proliferating cells. The analysis suggests therapies that could help prevent the progression towards malignancy and invasiveness of benign tumours

In-silico insights on the prognostic potential of immune cell infiltration patterns in the breast lobular epithelium

Scattered inflammatory cells are commonly observed in mammary gland tissue, most likely in response to normal cell turnover by proliferation and apoptosis, or as part of immunosurveillance. In contrast, lymphocytic lobulitis (LLO) is a recurrent inflammation pattern, characterized by lymphoid cells infiltrating lobular structures, that has been associated with increased familial breast cancer risk and immune responses to clinically manifest cancer. The mechanisms and pathogenic implications related to the inflammatory microenvironment in breast tissue are still poorly understood. Currently, the definition of inflammation is mainly descriptive, not allowing a clear distinction of LLO from physiological immunological responses and its role in oncogenesis remains unclear. To gain insights into the prognostic potential of inflammation, we developed an agent-based model of immune and epithelial cell interactions in breast lobular epithelium. Physiological parameters were calibrated from breast tissue samples of women who underwent reduction mammoplasty due to orthopedic or cosmetic reasons. The model allowed to investigate the impact of menstrual cycle length and hormone status on inflammatory responses to cell turnover in the breast tissue. Our findings suggested that the immunological context, defined by the immune cell density, functional orientation and spatial distribution, contains prognostic information previously not captured by conventional diagnostic approaches. Several studies provided conclusive evidence that a delicate balance between mammary epithelial cell proliferation and apoptosis regulates homeostasis in the healthy breast tissue 1-7. After menarche, and in the absence of pregnancy, the adult female mammary gland is subjected to cyclic fluctuations depending on hormonal stimulation 1,8. In response to such systemic hormonal changes, the breast epithelium undergoes a tightly regulated sequence of cell proliferation and apoptosis during each ovarian/menstrual cycle 1-3. The peak of epithelial cell proliferation has been reported to occur during the luteal phase, suggesting a synergistic influence of steroid hormones, such as estrogen and progesterone 2-5. In turn, the peak of apoptotic activity would be expected in response to decreasing hormone levels towards the end of the menstrual cycle 2-5. However, recent histologic findings indicate that apoptosis reaches its maximum levels in the middle of the luteal phase, although there is also a peak at about the third day of the menstrual cycle 6,7. Experimental measurements of cell turnover, i.e. programmed cell death and proliferation, demonstrated that an imbalance between the mitotic and apoptotic activity might lead to malignant transformation of epithelial cells and tumorigenic processes 9-11. Indeed, excessive cell proliferation promotes accumulation of DNA damage due to insufficient timely repair and mutations 12,13. There is also recent evidence that hormones suppress effective DNA repair and alter DNA damage response (DDR) 13-15

A toy model of fractal glioma development under RF electric field treatment

A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating-field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered. The model is based on a modification of a comb model for cancer cells, where the migration-proliferation dichotomy becomes naturally apparent. Considering glioma cancer as a fractal dielectric composite of cancer cells and normal tissue cells, a new effective mechanism of glioma treatment is suggested in the form of a giant enhancement of the TTF. This leads to the irreversible electroporation that may be an effective non-invasive method of treating brain cancer.Comment: Submitted for publication in European Physical Journal