Occupancy of new habitats through dispersion is a central process in nature. In particular, long range dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves spread to new tissues. We show that the early spread of cancer cells is similar to the species individuals spread and that both processes are represented by a common spatio-temporal signature, characterized by a particular fractal geometry of the boundaries of patches generated, and a power law-scaled, disrupted patch size distribution. We show that both properties are a direct result of long-distance dispersal, and that they reflect homologous ecological processes of population self-organization. Our results are significant for processes involving long-range dispersal like biological invasions, epidemics and cancer metastasis.
Deep Dive into Similar self-organizing scale-invariant properties characterize early cancer invasion and long range species spread.
Occupancy of new habitats through dispersion is a central process in nature. In particular, long range dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves spread to new tissues. We show that the early spread of cancer cells is similar to the species individuals spread and that both processes are represented by a common spatio-temporal signature, characterized by a particular fractal geometry of the boundaries of patches generated, and a power law-scaled, disrupted patch size distribution. We show that both properties are a direct result of long-distance dispersal, and that they reflect homologous ecological processes of population self-organization. Our results are significant for processes involving long-range dispersal like biological invasions, epidemics and cancer metastasis.
Long-distance dispersal (LDD) (1), even if represented by rare events, is one of the main factors explaining the fast spread of different organisms in new habitats, for example in paleocolonization events (2), plant pathogens (3), and invasive species (4). In addition, spread from primary tumors can be thought as a biological invasion from cancer cells spreading and invading new tissues. Considering cancer as an ecological process (5), the fitness of a neoplastic cell is shaped in part by its interactions with cells and other factors in its microenvironment, the surrounding tissues. Colonization begins with a single or few cells previously dispersed from the primary tumor (6), originating different clone lines that evolve independently across the new tissues and organs invaded (7) in a process we can consider as LDD. In spite of the remarkable similarity with species spread, at present no detailed mechanism has been proposed for an ecological interpretation of cancer spread.
In this paper we show that the spread of cells in cancer invasion and of invasive species generates a similar patchy pattern characterized by fractal and power law scaling. Furthermore, we show that this common pattern originates from self-organized, homologous mechanisms driven by LDD.
Fat-tailed functions like the power law seem to adequately describe LDD (1), and evidence for this is coming from crop pathogens distributions determined experimentally (8) and from model simulations (9,10). Power law functions and fractal geometry characterize species dispersal by LDD (9), and they reflect the invariance of some property over a range of temporal and spatial scales. There is increasing consensus in that they can be a byproduct of self-organizing processes of populations and communities (11,12). The capacity of a system to evolve to an organized state due to intrinsic mechanisms, i.e., self-organization, often characterized by a scale free geometry, has been attributed to diverse natural phenomena (13). However, the fundamental dynamics that determine selforganization scaling properties have remained obscure in many cases. Performing independent simulations we show that the pattern properties we found in real data from cancer invasion and species spread are specific of long range dispersal mediated by a power law distribution function.
We performed simulations using a spatially explicit, individual-based model based on a cellular automaton originally developed for the study of biological invasions (14,15). We simulated long ranged dispersal mechanisms using the power law dispersal function f (r) = A / r α (9). The main biological significance of the inclusion of the power law in the model is that dispersion is allowed to reach the whole area considered without distance limits. This is drastically different respect to the use of distribution functions allowing only short-distance dispersal (SDD), where dispersion can reach just close areas to the initial focus (9). The power law function allows for the inclusion of local and LDD events in the same dispersal function, depending on the value of the α exponent (9). To characterize the spatial pattern of spread produced by the simulations, we calculated the mean fractal dimension D of patch borders using a box counting algorithm (16), and determined the patch size distribution. We explored the pattern of spread produced by the model to understand the observed patterns of spread of cells from an invasive human glioma and of an invasive tree (English elm, Ulmus minor Mill.). We analyzed the spread of human glioma U87MG cells engineered to express an angiogenic regulator, angiopoietin-2 (Ang2) (U87MG/Ang2 cells), capable of promoting glioma cell infiltration into the brain parenchyma, established by intracranial cross-species transplantations in the brain of mice (17). Invasion of glioma cells involves the attachment of invading tumor cells to the extracellular matrix and its disruption, and subsequent invading cell penetration into brain tissues adjacent to primary tumor. This process is mediated by tumor-secreted enzymes called matrix metalloproteases (MMPs) that degrade the extracellular matrix at tumor-invasive borders and invasive areas (17).
We recorded the spread of English elm into a native forest from an initial small focus using aerial photographs taken in 1970, 1987 and 1996. Fruits of English elm are dispersed by wind (usually assumed to be a LDD mechanism) in high numbers but many seeds remain near the parent providing also local dispersal.
The analysis of pattern generation process with LDD during the simulations allows understanding its mechanism (Fig. 1a, Movie S1), which is essentially different from SDD mechanism (Movie S2, 9, 17 Fig. 2a). In LDD, beginning with an initially reproductive individual, a single patch appears surrounded by isolated, immature individuals (green dots, Movie S1) scattered all over the field. At times longer than the time of first reproduction, som
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