Haralampos Hatzikirou

Mathematical modelling of glioblastoma tumour development: A review

During the past several years mathematical models have been applied to various aspects of cancer dynamics, in particular avascular and vascular tumour growth, invasion, angiogenesis, and metastasis. This paper focuses on the most common and malignant brain tumour, glioblastoma, and surveys the growing number of studies dealing with mathematical modelling of this tumour. We attempt to classify these studies by their biomedical relevance and critically analyse their results. The aim of this review is to provide a meaningful reference, to both biomedical and mathematical researchers, of the current state of the art of glioma tumour modelling. The discussion attempts to identify current open problems as well as new research perspectives in the mathematical modelling of glioblastoma growth.

In Silico Analysis of Cell Cycle Synchronisation Effects in Radiotherapy of Tumour Spheroids

Tumour cells show a varying susceptibility to radiation damage as a function of the current cell cycle phase. While this sensitivity is averaged out in an unperturbed tumour due to unsynchronised cell cycle progression, external stimuli such as radiation or drug doses can induce a resynchronisation of the cell cycle and consequently induce a collective development of radiosensitivity in tumours. Although this effect has been regularly described in experiments it is currently not exploited in clinical practice and thus a large potential for optimisation is missed. We present an agent-based model for three-dimensional tumour spheroid growth which has been combined with an irradiation damage and kinetics model. We predict the dynamic response of the overall tumour radiosensitivity to delivered radiation doses and describe corresponding time windows of increased or decreased radiation sensitivity. The degree of cell cycle resynchronisation in response to radiation delivery was identified as a main determinant of the transient periods of low and high radiosensitivity enhancement. A range of selected clinical fractionation schemes is examined and new triggered schedules are tested which aim to maximise the effect of the radiation-induced sensitivity enhancement. We find that the cell cycle resynchronisation can yield a strong increase in therapy effectiveness, if employed correctly. While the individual timing of sensitive periods will depend on the exact cell and radiation types, enhancement is a universal effect which is present in every tumour and accordingly should be the target of experimental investigation. Experimental observables which can be assessed non-invasively and with high spatio-temporal resolution have to be connected to the radiosensitivity enhancement in order to allow for a possible tumour-specific design of highly efficient treatment schedules based on induced cell cycle synchronisation.

The biology and mathematical modelling of glioma invasion: a review.

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

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

Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.

Cancer therapeutic potential of combinatorial immuno- and vasomodulatory interventions.

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

From Immune Cells to Self-Organizing Ultra-Dense Small Cell Networks

In order to cope with the wireless traffic demand explosion within the next decade, operators are underlying their macrocellular networks with low power base stations in a more dense manner. Such networks are typically referred to as heterogeneous or ultra-dense small cell networks, and their deployment entails a number of challenges in terms of backhauling, capacity provision, and dynamics in spatio-temporally fluctuating traffic load. Self-organizing network (SON) solutions have been defined to overcome these challenges. Since self-organization occurs in a plethora of biological systems, we identify the design principles of immune system self-regulation and draw analogies with respect to ultra-dense small cell networks. In particular, we develop a mathematical model of an artificial immune system (AIS) that autonomously activates or deactivates small cells in response to the local traffic demand. The main goal of the proposed AIS-based SON approach is the enhancement of energy efficiency and improvement of cell-edge throughput. As a proof of principle, system level simulations are carried out in which the bio-inspired algorithm is evaluated for various parameter settings, such as the speed of small cell activation and the delay of deactivation. Analysis using spatio-temporally varying traffic exhibiting uncertainty through geo-location demonstrates the robustness of the AIS-based SON approach proposed.

Therapeutic Potential of Bacteria against Solid Tumors

Intentional bacterial infections can produce efficacious antitumor responses in mice, rats, dogs, and humans. However, low overall success rates and intense side effects prevent such approaches from being employed clinically. In this work, we titered bacteria and/or the proinflammatory cytokine TNFα in a set of established murine models of cancer. To interpret the experiments conducted, we considered and calibrated a tumor-effector cell recruitment model under the influence of functional tumor-associated vasculature. In this model, bacterial infections and TNFα enhanced immune activity and altered vascularization in the tumor bed. Information to predict bacterial therapy outcomes was provided by pretreatment tumor size and the underlying immune recruitment dynamics. Notably, increasing bacterial loads did not necessarily produce better long-term tumor control, suggesting that tumor sizes affected optimal bacterial loads. Short-term treatment responses were favored by high concentrations of effector cells postinjection, such as induced by higher bacterial loads, but in the longer term did not correlate with an effective restoration of immune surveillance. Overall, our findings suggested that a combination of intermediate bacterial loads with low levels TNFα administration could enable more favorable outcomes elicited by bacterial infections in tumor-bearing subjects. Cancer Res; 77(7); 1553-63. ©2017 AACR.

The Extrinsic Noise Effect on Lateral Inhibition Differentiation Waves

Multipotent differentiation, where cells adopt one of several cell fates, is a determinate and orchestrated procedure that often incorporates stochastic mechanisms in order to diversify cell types. How these stochastic phenomena interact to govern cell fate is poorly understood. Nonetheless, cell fate decision-making procedure is mainly regulated through the activation of differentiation waves and associated signaling pathways. In the current work, we focus on the Notch/Delta signaling pathway, which is not only known to trigger such waves but also is used to achieve the principle of lateral inhibition (i.e., a competition for exclusive fates through cross-signaling between neighboring cells). Such a process ensures unambiguous stochastic decisions influenced by intrinsic noise sources, such as those found in the regulation of signaling pathways, and extrinsic stochastic fluctuations attributed to microenvironmental factors. However, the effect of intrinsic and extrinsic noise on cell fate determination is an open problem. Our goal is to elucidate how the induction of extrinsic noise affects cell fate specification in a lateral inhibition mechanism. Using a stochastic Cellular Automaton with continuous state space, we show that extrinsic noise results in the emergence of steady-state furrow patterns of cells in a “frustrated/transient” phenotypic state.

Encoding of cellular positional information and maximum capacity of parallel coupled channels

Inspired by the parallels between information coding in morphogenesis and information coding in computer communication, we introduce a new model for coupled discrete memoryless channels in which the error probability of one channel depends on the output of the other channel. The model is motivated by a type of cell-cell communication. It is shown that coupling will lead to higher sum capacities with both optimal input distribution and with uniform input distribution under joint coding. Thereby, nature can achieve more than the sum of the individual capacities (synergistic effect). We compare this result with the maximum achievable sum capacity by arbitrary ideal coupling using Majorization theory. Finally, we illustrate the model with applications from wireless communications.

Hook length of the bacterial flagellum is controlled to nanometer-scale for optimal motility performance

Most bacteria swim in liquid environments by rotating one or several flagella. The long external filament of the flagellum is connected to a membrane-embedded basal-body by a flexible universal joint, the hook, which allows the transmission of motor torque to the filament. The length of the hook is controlled on a nanometer-scale by a sophisticated molecular ruler mechanism. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook-length variants of Salmonella enterica. Measurements of plate-assay motility, single-cell swimming speed and directional persistence in quasi 2D and population-averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild type hook-length. We conclude that too short hooks may be too stiff to function as a junction and too long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook-length control mechanism is therefore a prime example of how bacteria evolved elegant, but robust mechanisms to maximize their fitness under specific environmental constraints.Most bacteria swim in liquid environments by rotating one or several flagella. Each flagellum consists of a long external filament that is connected to a membrane-embedded basal-body by a short, curved structure: the hook. The length of the hook is controlled on a nanometer-scale by a sophisticated molecular ruler mechanism and it functions as a flexible universal joint allowing transmission of motor torque to the filament. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook length variants of Salmonella enterica. Measurements of plate-assay motility, single-cell swimming speed and directional persistence in quasi 2D and population-averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild type hook length. We conclude that too short hooks may be too stiff to function as a junction and too long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook length control mechanism is therefore a prime example of how bacteria evolved elegant, but robust mechanisms to maximize their fitness under specific environmental constraints. Significance statement Many bacteria use flagella for directed movement in liquid environments. The flexible hook connects the membrane-embedded basal-body of the flagellum to the long, external filament. Flagellar function relies on self-assembly processes that define or self-limit the lengths of major parts. The length of the hook is precisely controlled on a nanometer-scale by a molecular ruler mechanism. However, the physiological benefit of tight hook length control remains unclear. Here, we show that the molecular ruler mechanism evolved to control the optimal length of the flagellar hook, which is consistent with efficient motility performance. These results highlight the evolutionary forces that enable flagellated bacteria to optimize their fitness in diverse environments and might have important implications for the design of swimming micro-robots.