The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually calculated by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the Search for ExtraTerrestrial Intelligence (SETI) field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression. An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation does not provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process that will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.
While the control of cell migration by biochemical and biophysical factors is largely documented, a precise quantification of cell migration parameters in different experimental contexts is still questionable. Indeed, these phenomenological parameters can be evaluated from data obtained either at the cell population level or at the individual cell level. However, the range within which both characterizations of cell migration are equivalent remains unclear. We analyse here to which extent both sources of data could be integrated within a unified description of cell migration by considering the motility of the endothelial cell line EAhy926. Using time-lapse video-microscopy and associated analysis of digital image time series, we quantified EAhy926 random motility coefficient, migration speed and trajectory persistence time in two different migration assays: the in vitro wound healing assay, and the cell-populated agarose drop assay. In order to analyse the agreement between independent quantifications of cell motility based either on individual cell analysis or cell population dynamic analysis, a theoretical multi-agents cellular model was developed and discussed as a possible theoretical framework able to unify these multi-scale data. Model simulations especially reveal the potential bias induced by cell proliferation and cell-cell adhesion when cell migration parameters are estimated from the extensively used in vitro wound healing assay.
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