Symmetric projection attractor reconstruction: Embedding in higher dimensions.

Symmetric Projection Attractor Reconstruction (SPAR) provides an intuitive visualization and simple quantification of the morphology and variability of approximately periodic signals. The original method takes a three-dimensional delay coordinate embedding of a signal and subsequently projects this phase space reconstruction to a two-dimensional image with threefold symmetry, providing a bounded visualization of the waveform. We present an extension of the original work to apply delay coordinate embedding in any dimension N≥3 while still deriving a two-dimensional output with some rotational symmetry property that provides a meaningful visualization of the higher dimensional attractor. A generalized result is developed for taking N≥3 delay coordinates from a continuous periodic signal, where we determine invariant subspaces of the phase space that provide a two-dimensional projection with the required rotational symmetry. The result in each subspace is shown to be equivalent to following each pair of coefficients of the trigonometric interpolating polynomial of N evenly spaced points as the signal is translated horizontally. Bounds on the mean and the frequency response of our new coordinates are derived. We demonstrate how this aids our understanding of the attractor properties and its relationship to the underlying waveform. Our generalized result is then extended to real, approximately periodic signals, where we demonstrate that the higher dimensional SPAR method provides information on subtle changes in different parts of the waveform morphology.

Robustness of convolutional neural networks to physiological electrocardiogram noise.

The electrocardiogram (ECG) is a widespread diagnostic tool in healthcare and supports the diagnosis of cardiovascular disorders. Deep learning methods are a successful and popular technique to detect indications of disorders from an ECG signal. However, there are open questions around the robustness of these methods to various factors, including physiological ECG noise. In this study, we generate clean and noisy versions of an ECG dataset before applying symmetric projection attractor reconstruction (SPAR) and scalogram image transformations. A convolutional neural network is used to classify these image transforms. For the clean ECG dataset, F1 scores for SPAR attractor and scalogram transforms were 0.70 and 0.79, respectively. Scores decreased by less than 0.05 for the noisy ECG datasets. Notably, when the network trained on clean data was used to classify the noisy datasets, performance decreases of up to 0.18 in F1 scores were seen. However, when the network trained on the noisy data was used to classify the clean dataset, the decrease was less than 0.05. We conclude that physiological ECG noise impacts classification using deep learning methods and careful consideration should be given to the inclusion of noisy ECG signals in the training data when developing supervised networks for ECG classification. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Simulating the influence of plasma protein on measured receptor affinity in biochemical assays reveals the utility of Schild analysis for estimating compound affinity for plasma proteins.

BACKGROUND AND PURPOSE: Plasma protein binding (PPB) influences the free fraction of drug available to bind to its target and is therefore an important consideration in drug discovery. While traditional methods for assessing PPB (e.g. rapid equilibrium dialysis) are suitable for comparing compounds with relatively weak PPB, they are not able to accurately discriminate between highly bound compounds (typically >99.5%). The aim of the present work was to use mathematical modelling to explore the potential utility of receptor binding and cellular functional assays to estimate the affinity of compounds for plasma proteins. Plasma proteins are routinely added to in vitro assays, so a secondary goal was to investigate the effect of plasma proteins on observed ligand-receptor interactions. EXPERIMENTAL APPROACH: Using the principle of conservation of mass and the law of mass action, a cubic equation was derived describing the ligand-receptor complex [LR] in the presence of plasma protein at equilibrium. KEY RESULTS: The model demonstrates the profound influence of PPB on in vitro assays and identifies the utility of Schild analysis, which is usually applied to determine receptor-antagonist affinities, for calculating affinity at plasma proteins (termed KP ). We have also extended this analysis to functional effects using operational modelling and demonstrate that these approaches can also be applied to cell-based assay systems. CONCLUSIONS AND IMPLICATIONS: These mathematical models can potentially be used in conjunction with experimental data to estimate drug-plasma protein affinities in the earliest phases of drug discovery programmes.

From Luc and Phot genes to the hospital bed.

The Luc gene from the firefly Photinus pyralis has been isolated by cloning it in pcDV1 PL plasmid primer and Honjo linker and the Phot gene isolated from Aequorea victoria using the polymerase chain reaction. A method has been established using SP6 RNA polymerase for transcribing and translating bioluminescent genes in vitro. It should now be possible to engineer these genes to measure intracellular ATP and the covalent modification of proteins in single, live cells, providing unique insights into the molecular basis of disease.