Experiments show that simple diffusion of nutrients and waste molecules is not sufficient to explain the typical multilayered structure of solid tumours, where an outer rim of proliferating cells surrounds a layer of quiescent but viable cells and a central necrotic region. These experiments challenge models of tumour growth based exclusively on diffusion. Here we propose a model of tumour growth that incorporates the volume dynamics and the distribution of cells within the viable cell rim. The model is suggested by in silico experiments and is validated using in vitro data. The results correlate with in vivo data as well, and the model can be used to support experimental and clinical oncology.

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Tumour metabolism is an outstanding topic of cancer research, as it determines the growth rate and the global activity of tumours. Recently, by combining the diffusion of oxygen, nutrients, and metabolites in the extracellular environment, and the internal motions that mix live and dead cells, we derived a growth law of solid tumours which is linked to parameters at the cellular level 1 . Here we use this growth law to obtain a metabolic scaling law for solid tumours, which is obeyed by tumours of different histotypes both in vitro and in vivo, and we display its relation with the fractal dimension of the distribution of live cells in the tumour mass. The scaling behaviour is related to measurable parameters, with potential applications in the clinical practice.R ecently we derived a growth law for solid tumours 1 , where growth depends on the distribution of live cells in the tumour mass. The model was suggested by the results of computer simulations 2 , and it has been validated using data from in vitro experiments. In this model the inter-vascular micro-regions of solid tumours contain both live and dead cells, and the fraction of live cells is exponentially smaller as the distance from the sources of nutrients and oxygen increases. Although the decay length l is weakly dependent on tumour size, we found that an effective, size-independent l works nearly as well, and that l has values mostly in the range 50-150 mm. Notably, this is also the distance from the nearest blood vessel where the interstitial pO 2 assumes hypoxic and anoxic values and pH drops to acidic values in the micro-regions of vascularized tumours 3 , and corresponds to the typical thickness of the viable tumour cell layer around blood vessels 4 . Here we show how the growth law can be combined with basic metabolic parameters to yield a seemingly universal metabolic scaling law for tumours, that holds both in vitro and in vivo.We start from the tumour growth law, that can be expressed as a differential equation for tumour volume, and combines proliferation of live cells in the tumour with the gradual shrinking of dead cells 1whereis the fraction of live cells in the tumour, derived from the assumption of exponential decay of the density of live cells, so that the total volume of live cells is V a 5 F(V)V, and where the parameter a defines the individual cell proliferation rate, while the parameter d is the shrinking rate of dead cells. The tumour volume is proportional to x 3 , where x is some characteristic length of the tumour, i.e., V 5 Ax 3 . In the case of spherical tumours A 5 4p/3 < 4.2, and x is the tumour radius, but here we consider the possibility of departure from a spherical shape. Still, we assume that the tumour keeps roughly the same shape as it grows, so that x can be chosen as a substitute for radius, e.g., as the length of a given chord between two fixed, recognizable surface features of the tumour shape. We note that A is one of the factors that set the rate of tumour growth, at least for large tumour sizes, since in that c...

Podosomes are protrusive structures implicated in macrophage extracellular matrix degradation and three-dimensional migration through cell barriers and the interstitium. Podosome formation and assembly are regulated by cytoskeleton remodeling requiring cytoplasmic tyrosine kinases of the Src and the Abl families. Considering that Abl has been reported to phosphorylate the guanine nucleotide exchange factor Sos1, eliciting its Rac-guanine nucleotide exchange factor activity, and Rac regulates podosome formation in myeloid cells and invadopodia formation in cancer cells, we addressed whether Sos1 is implicated in podosome formation and function in macrophages. We found that ectopically expressed Abl or the Src kinase Fgr phosphorylate Sos1, and the Src kinases Hck and Fgr are required for Abl and Sos1 phosphorylation and Abl/Sos1 interaction in macrophages. Sos1 localizes to podosomes in both murine and human macrophages, and its silencing by small interfering RNA results in disassembly of murine macrophage podosomes and a marked reduction of GTP loading on Rac. Matrix degradative capacity, three-dimensional migration through Matrigel, and transmigration through an endothelial cell monolayer of Sos1-silenced macrophages were inhibited. In addition, Sos1- or Abl-silenced macrophages, or macrophages treated with the selective Abl inhibitor imatinib mesylate had a reduced capability to migrate into breast tumor spheroids, the majority of cells remaining at the margin and the outer layers of the spheroid itself. Because of the established role of Src and Abl kinases to regulate also invadopodia formation in cancer cells, our findings suggest that targeting the Src/Abl/Sos1/Rac pathway may represent a double-edged sword to control both cancer-invasive capacities and cancer-related inflammation.

It is generally accepted that radiotherapy must target clonogenic cells, i.e., those cells in a tumour that have self-renewing potential. Focussing on isolated clonogenic cells, however, may lead to an underestimate or even to an outright neglect of the importance of biological mechanisms that regulate tumour cell sensitivity to radiation. We develop a new statistical and experimental approach to quantify the effects of radiation on cell populations as a whole. In our experiments, we change the proximity relationships of the cells by culturing them in wells with different shapes, and we find that the radiosensitivity of T47D human breast carcinoma cells in tight clusters is different from that of isolated cells. Molecular analyses show that T47D cells express a Syncytin-1 homologous protein (SyHP). We observe that SyHP translocates to the external surface of the plasma membrane of cells killed by radiation treatment. The data support the fundamental role of SyHP in the formation of intercellular cytoplasmic bridges and in the enhanced radioresistance of surviving cells. We conclude that complex and unexpected biological mechanisms of tumour radioresistance take place at the cell population level. These mechanisms may significantly bias our estimates of the radiosensitivity of breast carcinomas in vivo and thereby affect treatment plans, and they call for further investigations.