Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.

Signal processing for molecular and cellular biological physics:an emerging field

Recent advances in our ability to watch the molecular and cellular processes of life in action-such as atomic force microscopy, optical tweezers and Forster fluorescence resonance energy transfer-raise challenges for digital signal processing (DSP) of the resulting experimental data. This article explores the unique properties of such biophysical time series that set them apart from other signals, such as the prevalence of abrupt jumps and steps, multi-modal distributions and autocorrelated noise. It exposes the problems with classical linear DSP algorithms applied to this kind of data, and describes new nonlinear and non-Gaussian algorithms that are able to extract information that is of direct relevance to biological physicists. It is argued that these new methods applied in this context typify the nascent field of biophysical DSP. Practical experimental examples are supplied.

Receptor activity-modifying proteins 2 and 3 generate adrenomedullin receptor subtypes with distinct molecular properties

Adrenomedullin (AM) is a peptide hormone with numerous effects in the vascular systems. AM signals through the AM1 and AM2 receptors formed by the obligate heterodimerization of a G protein-coupled receptor, the calcitonin receptor-like receptor (CLR), and receptor activity-modifying proteins (RAMP) 2 and 3, respectively. These different CLR-RAMP interactions yield discrete receptor pharmacology and physiological effects. The effective design of therapeutics that target the individual AM receptors is dependent on understanding the molecular details of the effects of RAMPs on CLR. To understand the role of RAMPs 2 and 3 on the activation and conformation of the CLR subunit of AM receptors we mutated 68 individual amino acids in the juxtamembrane region of CLR, a key region for activation of AM receptors and determined the effects on cAMP signalling. Sixteen CLR mutations had differential effects between the AM1 and AM2 receptors. Accompanying this, independent molecular modelling of the full-length AM-bound AM1 and AM2 receptors predicted differences in the binding pocket, and differences in the electrostatic potential of the two AM receptors. Druggability analysis indicated unique features that could be used to develop selective small molecule ligands for each receptor. The interaction of RAMP2 or RAMP3 with CLR induces conformational variation in the juxtamembrane region, yielding distinct binding pockets, probably via an allosteric mechanism. These subtype-specific differences have implications for the design of therapeutics aimed at specific AM receptors and for understanding the mechanisms by which accessory proteins affect G protein-coupled receptor function.