Zero-Inflated Poisson Distribution of Sedimented Cells in Multi-Layered Microwell Arrays

Open arrays of micro-scale wells (microwells; MW) are a popular platform for trapping biological cells, as they are gentler than other methods and their openness circumvents several problems associated with enclosed alternatives. This paper presents a dual-layered polymeric film featuring an imprinted MW array (MWA) and various complimentary shallower features that streamline both optical microscopy and alignment with an immunobiosensing (IBS) slide. The dual-layered MWA design presented in this paper represents a substantial improvement over our previous designs. The most substantial contribution of this paper lies with its statistical analysis of the trapped cell count datasets obtained from experiments using this refined MWA design. This analysis confirms experimentally that the distribution of cells into a MWA following sedimentation is indeed naturally Poisson distributed. Moreover, this analysis also shows that a zero-inflated Poisson (ZIP) distribution provides a superior fit, by incorporating an additional variable quantifying dataset sparsity. Furthermore, it is shown that maximum likelihood estimators (MLEs) for the parameters of these Poisson fits are superior to method of moments-based alternatives. This paper should prove useful for those seeking to develop a MWA with which to trap cells via sedimentation, and to mathematically describe this trapping process.

Automated summary

This paper introduces an improved dual-layered MWA design and confirms experimentally that the distribution of cells into a MWA following sedimentation is naturally Poisson distributed. It proposes a zero-inflated Poisson distribution as a superior fit, incorporating an additional variable to quantify dataset sparsity. It also demonstrates that maximum likelihood estimators for the parameters of these Poisson fits are superior to method of moments-based alternatives.