A nonparametric statistical method for deconvolving densities in the analysis of proteomic data

Genomic or proteomic data are frequently affected by noise or are convolutions of different biological signals. This is, e.g., particularly relevant in skin aging research, in which intrinsic aging, driven by genetic factors, and extrinsic aging, caused by environmental exposure, are both investigated considering, e.g., the proteome of skin fibroblasts. Since all skin areas are affected by intrinsic aging, isolating the pure extrinsic signal from the mixture of the intrinsic and extrinsic effects is crucial to investigate extrinsic aging. In such settings, deconvolution methods can be used to estimate the density of the target component. However, existing nonparametric deconvolution approaches often fail when the variance of the mixed distribution is substantially greater than that of the target distribution, a common issue in genomic and proteomic data. We introduce a new nonparametric deconvolution method called N-power Fourier deconvolution (NPFD) that deals with this problem of differing variances by employing the N-th power of the Fourier transforms of the densities. Leveraging Fourier inversion and key properties of density transforms, NPFD reduces numerical instability, resulting in smooth and accurate density estimates. NPDF is able to effectively resolve smoothness- and variance-related challenges and performs comparably or better than existing methods in almost all considered scenarios, as a comprehensive simulation study shows. Moreover, applications to real proteomic data from skin fibroblasts demonstrate how NPFD can be employed to estimate the pure extrinsic aging signal. NPFD represents a new conceptual framework for nonparametric density deconvolution by exploiting the properties of Fourier transforms in a novel way. Its ability to address smoothness- and variance-related challenges makes it a versatile and powerful tool for deconvolving complex biological signals on the level of density functions across diverse applications.