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In invasive breast cancer, cell clusters of varying sizes and shapes are embedded in the fibrous extracellular matrix (ECM). Although the prevailing view attributes this structure to increasing disorder resulting from loss of function and…
The availability of cancer measurements over time enables the personalised assessment of tumour growth and therapeutic response dynamics. However, many tumours are treated after diagnosis without collecting longitudinal data, and cancer…
In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the…
We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms.…
The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world…
The pancreatic innervation undergoes dynamic remodeling during the development of pancreatic ductal adenocarcinoma (PDAC). Denervation experiments have shown that different types of axons can exert either pro- or anti-tumor effects, but…
Mutations can arise from the chance misincorporation of nucleotides during DNA replication or from DNA lesions that are not repaired correctly. We introduce a model that relates the source of mutations to their accumulation with cell…
Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently…
Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins - proteins converting chemical energy into kinetic energy. It is known that motor proteins work in teams enabling unidirectional and…
We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…
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…
Tissue mechanical properties such as rigidity and fluidity, and changes in these properties driven by jamming-unjamming transitions (UJT), have come under recent highlight as mechanical markers of health and disease in various biological…
The ability to locally degrade the extracellular matrix (ECM) and interact with the tumour microenvironment is a key process distinguishing cancer from normal cells, and is a critical step in the metastatic spread of the tumour. The…
Single-cell trajectory analysis aims to reconstruct the biological developmental processes of cells as they evolve over time, leveraging temporal correlations in gene expression. During cellular development, gene expression patterns…
Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are termed Cancer Stem Cells (CSCs}, and as opposed to the more…
Cancer is increasingly perceived as a systems-level, network phenomenon. The major trend of malignant transformation can be described as a two-phase process, where an initial increase of network plasticity is followed by a decrease of…
In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is…
In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell…
Primary tumors often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical observations have suggested that these premalignant fields…
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…