Modelling the role of angiogenesis and vasculogenesis in solid tumuour growth

Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis involves the proliferation and migration of endothelial cells (ECs) in pre-existing vessels, vasculogenesis involves the mobilisation of bone-marrow-derived endothelial progenitor cells (EPCs) into the bloodstream. Once blood-borne, EPCs home in on the tumour site, where subsequently they may differentiate into ECs and form vascular structures. In this paper, we develop a mathematical model, formulated as a system of nonlinear ordinary differential equations (ODEs), which describes vascular tumour growth with both angiogenesis and vasculogenesis contributing to vessel formation. Submodels describing exclusively angiogenic and exclusively vasculogenic tumours are shown to exhibit similar growth dynamics. In each case, there are three possible scenarios: the tumour remains in an avascular steady state, the tumour evolves to a vascular equilibrium, or unbounded vascular growth occurs. Analysis of the full model reveals that these three behaviours persist when angiogenesis and vasculogenesis act simultaneously. However, when both vascularisation mechanisms are active, the tumour growth rate may increase, causing the tumour to evolve to a larger equilibrium size or to expand uncontrollably. Alternatively, the growth rate may be left unaffected, which occurs if either vascularisation process alone is able to keep pace with the demands of the growing tumour. To clarify further the effects of vasculogenesis, the full model is also used to compare possible treatment strategies, including chemotherapy and antiangiogenic therapies aimed at suppressing vascularisation. This investigation highlights how, dependent on model parameter values, targeting both ECs and EPCs may be necessary in order to effectively reduce tumour vasculature and inhibit tumour growth

Cancer disease: integrative modelling approaches

Cancer is a complex disease in which a variety of phenomena interact over a wide range of spatial and temporal scales. In this article a theoretical framework will be introduced that is capable of linking together such processes to produce a detailed model of vascular tumour growth. The model is formulated as a hybrid cellular automaton and contains submodels that describe subcellular, cellular and tissue level features. Model simulations will be presented to illustrate the effect that coupling between these different elements has on the tumour's evolution and its response to chemotherapy

Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons

Many reaction-diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction-diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting traveling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviors observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate

Pattern formation of scale cells in Lepidoptera by differential origin-dependent cell adhesion

We present a model for the formation of parallel rows of scale cells in the developing adult wing of moths and butterflies. Precursors of scale cells differentiate throughout each epithelial monolayer and migrate into rows that are roughly parallel to the body axis. Grafting experiments have revealed what appears to be a gradient of adhesivity along the wing. What is more, cell adhesivity character is maintained after grafting. Thus we suggest that it is a cell’s location prior to migration that determines its interactions during migration. We use nonlinear bifurcation analysis to show that differential origin-dependent cell adhesion can result in the stabilization of rows over spots

Neural crest migration is driven by a few trailblazer cells with a unique molecular signature narrowly confined to the invasive front

Neural crest (NC) cell migration is crucial to the formation of peripheral tissues during vertebrate development. However, how NC cells respond to different microenvironments to maintain persistence of direction and cohesion in multicellular streams remains unclear. To address this, we profiled eight subregions of a typical cranial NC cell migratory stream. Hierarchical clustering showed significant differences in the expression profiles of the lead three subregions compared with newly emerged cells. Multiplexed imaging of mRNA expression using fluorescent hybridization chain reaction (HCR) quantitatively confirmed the expression profiles of lead cells. Computational modeling predicted that a small fraction of lead cells that detect directional information is optimal for successful stream migration. Single-cell profiling then revealed a unique molecular signature that is consistent and stable over time in a subset of lead cells within the most advanced portion of the migratory front, which we term trailblazers. Model simulations that forced a lead cell behavior in the trailing subpopulation predicted cell bunching near the migratory domain entrance. Misexpression of the trailblazer molecular signature by perturbation of two upstream transcription factors agreed with the in silico prediction and showed alterations to NC cell migration distance and stream shape. These data are the first to characterize the molecular diversity within an NC cell migratory stream and offer insights into how molecular patterns are transduced into cell behaviors

Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation

The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology

Pattern formation in heterogeneous domains

Development of spatial pattern in the early embryo results from the interaction of several processes in a complex hierarchy of mechanisms. Most models for morphogenesis to date have, however, focussed on a particular mechanism. Although such models are capable of capturing some aspects of development they are inconsistent with key experimental observations. Here we consider a two-step hierarchy of patterning mechanisms in which the spatial pattern of a control chemical regulates morphogen diffusivity in an overlaying reaction diffusion system

Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

Immune-Mobilizing Monoclonal T Cell Receptors Mediate Specific and Rapid Elimination of Hepatitis B-Infected Cells

Background and Aims: Therapies for chronic hepatitis B virus (HBV) infection are urgently needed because of viral integration, persistence of viral antigen expression, inadequate HBV‐specific immune responses, and treatment regimens that require lifelong adherence to suppress the virus. Immune mobilizing monoclonal T Cell receptors against virus (ImmTAV) molecules represent a therapeutic strategy combining an affinity‐enhanced T Cell receptor with an anti‐CD3 T Cell‐activating moiety. This bispecific fusion protein redirects T cells to specifically lyse infected cells expressing the target virus‐derived peptides presented by human leukocyte antigen (HLA). Approach and Results: ImmTAV molecules specific for HLA‐A*02:01‐restricted epitopes from HBV envelope, polymerase, and core antigens were engineered. The ability of ImmTAV‐Env to activate and redirect polyclonal T cells toward cells containing integrated HBV and cells infected with HBV was assessed using cytokine secretion assays and imaging‐based killing assays. Elimination of infected cells was further quantified using a modified fluorescent hybridization of viral RNA assay. Here, we demonstrate that picomolar concentrations of ImmTAV‐Env can redirect T cells from healthy and HBV‐infected donors toward hepatocellular carcinoma (HCC) cells containing integrated HBV DNA resulting in cytokine release, which could be suppressed by the addition of a corticosteroid in vitro. Importantly, ImmTAV‐Env redirection of T cells induced cytolysis of antigen‐positive HCC cells and cells infected with HBV in vitro, causing a reduction of hepatitis B e antigen and specific loss of cells expressing viral RNA. Conclusions: The ImmTAV platform has the potential to enable the elimination of infected cells by redirecting endogenous non‐HBV‐specific T cells, bypassing exhausted HBV‐specific T cells. This represents a promising therapeutic option in the treatment of chronic hepatitis B, with our lead candidate now entering trials

A biochemical hypothesis on the formation of fingerprints using a turing patterns approach

<p>Abstract</p> <p>Background</p> <p>Fingerprints represent a particular characteristic for each individual. Characteristic patterns are also formed on the palms of the hands and soles of the feet. Their origin and development is still unknown but it is believed to have a strong genetic component, although it is not the only thing determining its formation. Each fingerprint is a papillary drawing composed by papillae and rete ridges (crests). This paper proposes a phenomenological model describing fingerprint pattern formation using reaction diffusion equations with Turing space parameters.</p> <p>Results</p> <p>Several numerical examples were solved regarding simplified finger geometries to study pattern formation. The finite element method was used for numerical solution, in conjunction with the Newton-Raphson method to approximate nonlinear partial differential equations.</p> <p>Conclusions</p> <p>The numerical examples showed that the model could represent the formation of different types of fingerprint characteristics in each individual.</p