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.

Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.

Experimental studies of lobe growth in the lichen Parmelia conspersa (Ehrh. Ex Ach.) Ach.

The radial growth of individual lobes of the foliose lichen, Parmelia conspersa (Ehrh. Ex Ach.) Ach. was studied to determine whether (1) adjacent lobes exchange carbohydrate and (2) marginal competition between lobes influences radial growth. In a survey of thalli of different size, the number of marginal lobes was linearly related to thallus circumference. However, the relationship between mean lobe width and thallus circumference was fitted by a second order polynomial. Hence, mean lobe width may reach a maximum in thalli approx. 3 cm in diameter. The interactions between marginal lobes were studied by either painting single lobes with acrylic paint or by removing lobes from the thallus. Painting the whole lobe virtually stopped its radial growth while partially painted lobes grew less than control lobes. The radial growth of a lobe was unaffected by either completely painting or removing its neighbour. Removal of both neighbouring lobes did not influence the radial growth of a lobe but severing the lobe from the thallus reduced its radial growth. In addition, lobe width increased significantly when both neighbouring lobes were removed. These results suggest that adjacent lobes have a considerable degree of independence and that there is little exchange of carbohydrate between them. In addition, marginal competition between adjacent lobes may restrict the lateral extension of the lobe and this may maintain a more constant mean lobe width in larger thalli. It is possible that the intensity of marginal competition between adjacent lobes may vary with thallus size and this could be a factor determining the growth curve of a foliose lichen throughout its life.

Detergent-free purification of ABC (ATP-binding-cassette) transporters

ABC (ATP-binding-cassette) transporters carry out many vital functions and are involved in numerous diseases, but study of the structure and function of these proteins is often hampered by their large size and membrane location. Membrane protein purification usually utilizes detergents to solubilize the protein from the membrane, effectively removing it from its native lipid environment. Subsequently, lipids have to be added back and detergent removed to reconstitute the protein into a lipid bilayer. In the present study, we present the application of a new methodology for the extraction and purification of ABC transporters without the use of detergent, instead, using a copolymer, SMA (polystyrene-co-maleic acid). SMA inserts into a bilayer and assembles into discrete particles, essentially solubilizing the membrane into small discs of bilayer encircled by a polymer, termed SMALPs (SMA lipid particles). We show that this polymer can extract several eukaryotic ABC transporters, P-glycoprotein (ABCB1), MRP1 (multidrug-resistance protein 1; ABCC1), MRP4 (ABCC4), ABCG2 and CFTR (cystic fibrosis transmembrane conductance regulator; ABCC7), from a range of different expression systems. The SMALP-encapsulated ABC transporters can be purified by affinity chromatography, and are able to bind ligands comparably with those in native membranes or detergent micelles. A greater degree of purity and enhanced stability is seen compared with detergent solubilization. The present study demonstrates that eukaryotic ABC transporters can be extracted and purified without ever being removed from their lipid bilayer environment, opening up awide range of possibilities for the future study of their structure and function. © The Authors Journal compilation © 2014 Biochemical Society.

Removing the redundancy from randomised gene libraries

Amino acid substitution plays a vital role in both the molecular engineering of proteins and analysis of structure-activity relationships. High-throughput substitution is achieved by codon randomisation, which generates a library of mutants (a randomised gene library) in a single experiment. For full randomisation, key codons are typically replaced with NNN (64 sequences) or NNG CorT (32 sequences). This obligates cloning of redundant codons alongside those required to encode the 20 amino acids. As the number of randomised codons increases, there is therefore a progressive loss of randomisation efficiency; the number of genes required per protein rises exponentially. The redundant codons cause amino acids to be represented unevenly; for example, methionine is encoded just once within NNN, whilst arginine is encoded six times. Finally, the organisation of the genetic code makes it impossible to encode functional subsets of amino acids (e.g. polar residues only) in a single experiment. Here, we present a novel solution to randomisation where genetic redundancy is eliminated; the number of different genes equals the number of encoded proteins, regardless of codon number. There is no inherent amino acid bias and any required subset of amino acids may be encoded in one experiment. This generic approach should be widely applicable in studies involving randomisation of proteins. © 2003 Elsevier Ltd. All rights reserved.