H-Bonds in Crambin: Coherence in an α-Helix

We applied coherence analysis-used by engineers to identify linear interactions in stochastic systems-to molecular dynamics simulations of crambin, a thionin storage protein found in Abyssinian cabbage. A key advantage of coherence over other analyses is that it is robust, independent of the properties, or even the existence of probability distributions often relied on in statistical mechanics. For frequencies between 0.391 and 5.08 GHz (corresponding reciprocally to times of 2.56 and 0.197 ns), the displacements of oxygen and nitrogen atoms across α-helix H-bonds are strongly correlated, with a coherence greater than 0.9; the secondary structure causes the H-bonds to effectively act as a spring. Similar coherence behavior is observed for covalent bonds and other noncovalent interactions including H-bonds in β-sheets and salt bridges. In contrast, arbitrary pairs of atoms that are physically distant have uncorrelated motions and negligible coherence. These results suggest that coherence may be used to objectively identify atomic interactions without subjective thresholds such as H-bond lengths angles and angles. Strong coherence is also observed between the average position of adjacent leaves (groups of atoms) in an α-helix, suggesting that the harmonic analysis of classical molecular dynamics can successfully describe the propagation of allosteric interactions through the structure.

Using high-throughput multi-omics data to investigate structural balance in elementary gene regulatory network motifs

MOTIVATION

The simultaneous availability of ATAC-seq and RNA-seq experiments allows to obtain a more in-depth knowledge on the regulatory mechanisms occurring in gene regulatory networks. In this article, we highlight and analyze two novel aspects that leverage on the possibility of pairing RNA-seq and ATAC-seq data. Namely we investigate the causality of the relationships between transcription factors, chromatin and target genes and the internal consistency between the two omics, here measured in terms of structural balance in the sample correlations along elementary length-3 cycles.

RESULTS

We propose a framework that uses the a priori knowledge on the data to infer elementary causal regulatory motifs (namely chains and forks) in the network. It is based on the notions of conditional independence and partial correlation, and can be applied to both longitudinal and non-longitudinal data. Our analysis highlights a strong connection between the causal regulatory motifs that are selected by the data and the structural balance of the underlying sample correlation graphs: strikingly, >97% of the selected regulatory motifs belong to a balanced subgraph. This result shows that internal consistency, as measured by structural balance, is close to a necessary condition for 3-node regulatory motifs to satisfy causality rules.

AVAILABILITY AND IMPLEMENTATION

The analysis was carried out in MATLAB and the code can be found at https://github.com/albertozenere/Multi-omics-elementary-regulatory-motifs.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Power spectrum of the rectified EMG: when and why is rectification beneficial for identifying neural connectivity?

OBJECTIVE

The identification of common oscillatory inputs to motor neurons in the electromyographic (EMG) signal power spectrum is often preceded by EMG rectification for enhancing the low-frequency oscillatory components. However, rectification is a nonlinear operator and its influence on the EMG signal spectrum is not fully understood. In this study, we aim at determining when EMG rectification is beneficial in the study of oscillatory inputs to motor neurons.

APPROACH

We provide a full mathematical description of the power spectrum of the rectified EMG signal and the influence of the average shape of the motor unit action potentials on it. We also provide a validation of these theoretical results with both simulated and experimental EMG signals.

MAIN RESULTS

Simulations using an advanced computational model and experimental results demonstrated the accuracy of the theoretical derivations on the effect of rectification on the EMG spectrum. These derivations proved that rectification is beneficial when assessing the strength of low-frequency (delta and alpha bands) common synaptic inputs to the motor neurons, when the duration of the action potentials is short, and when the level of cancellation is relatively low. On the other hand, rectification may distort the estimation of common synaptic inputs when studying higher frequencies (beta and gamma), in a way dependent on the duration of the action potentials, and may introduce peaks in the coherence function that do not correspond to physiological shared inputs.

SIGNIFICANCE

This study clarifies the conditions when rectifying the surface EMG is appropriate for studying neural connectivity.

Detection of nonlinear interactions of EEG alpha waves in the brain by a new coherence measure and its application to epilepsy and anti-epileptic drug therapy

EEG and field potential rhythms established in the cortex and thalamus may accommodate the propagation of seizures. This article describes the interaction between thalamus and cortex during pentylenetetrazol (PTZ) seizures in rats with and without prior treatment with ethosuximide (ESM), a well-known antiepileptic drug (AED) that raises the threshold for seizures, was given before PTZ. The AED was given before PTZ convulsant administration. We track this thalamo-cortical association with a novel measure we have called the cross-bicoherence gain, or BISCOH. This quantity allows us to measure the spectral coherence in a purely higher order spectralmethodology. BISCOH is able to track the formation of nonlinearities at specific frequencies in the recorded EEG. BISCOH showed a strong increase in low alpha wave harmonic generationat 10 and 12.5 Hz after ESM treatment (p < 0.02 and p < 0.007, respectively). Conventional coherence failed to show distinctive and significant changes in thalamo-cortical coupling after ESM treatment at those frequencies and instead showed changes at 5 Hz. This rise in cortical rhythms is evidence of harmonic generation or new frequency formation in the thalamo-cortical system withAED therapy. BISCOH could become a powerful tool in unraveling changes in coherence due to neuroelectric modulation resulting from drug treatment or electrical stimulation.

Spinal cord integrity monitoring by adaptive coherence measurement

OBJECTIVE

Injury during routine spinal cord procedures could result in devastating consequences for the surgical patient. Spinal cord monitoring through somatosensory evoked potentials (SEPs) remains a viable method for prevention of serious injury.

METHODS

The adaptive coherence estimation (ACE) is a method to iteratively calculate signal match quality through successive filter entrainment. Here we compare the speed of detection with ACE to conventional amplitude measurements. Both absolute magnitude of ACE and amplitude as well as slope change detector algorithm (Farley-Hinich) was run as well to determine the earliest time when a significant change occurred.

RESULTS

The standard error for the ACE algorithm is close to one tenth of the amplitude measure, Since the ACE algorithm achieved low variance during baseline measurement, we were able to achieve rapid detection of injury. For absolute magnitude detection ACE was faster than amplitude for the 20 g injury weight class. It took an average of 10 epochs to detect the injury with adaptive coherence and nearly 19 with standard amplitude metrics using absolute magnitude changes. Abrupt change detection methods using slope change show that ACE provides more favorable detection capabilities comparable to amplitude. Additionally, there was a significant increase in the ROC curve between ACE and amplitude alone (p<0.05).

CONCLUSIONS

Because of its excellent detection capabilities, the adaptive coherence method provides an excellent supplement to traditional amplitude for capturing injury-related changes in SEPs.

SIGNIFICANCE

Adaptive coherence remains a viable method for rapidly and accurately detecting spinal injury.

Experimental approach for testing the uncoupling between cardiovascular variability series

In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parametric autoregressive (AR) method (model order M= 4, 8, 12, 16), on time series with length L = 180, 300, 420, 540 s. Te decreased with increasing B and L and with decreasing M (range: 0.11-0.54 for WC estimator, 0.06-0.46 for AR estimator). Values for the typical parameter settings of WC and AR estimation (B = 0.025 Hz; M = 8; L = 300 s) were, respectively, 0.24 and 0.17. Moreover, Tt was always higher (range: 0.12-0.65) and the results were less dependable than those for Te in defining the zero level of MSC. Thus, with the proposed method, the hypothesis of uncoupling is rejected by accounting for the parameters that affect the confidence of spectral and cross-spectral estimates. The broad applicability of this approach should favour its introduction for assessing the significance of the coupling between cardiovascular variability series.

Nonlinear changes in brain's response in the event of injury as detected by adaptive coherence estimation of evoked potentials

Injury-related changes in evoked potentials are studied with the aid of the coherence function, which effectively measures the degree of linear association between a pair of signals recorded during normal and abnormal states of the brain. The performance of an adaptive algorithm for estimating coherence function is studied, and the effects of additive noise on the estimated coherence function is discussed. Further, a linearity index is formulated and, through analysis and simulations, the index is shown to respond in a predictable manner to increasing nonlinearity while maintaining the robustness to the observation noise. Somatosensory evoked potentials are shown to be sensitive to injury resulting from acute cerebral hypoxia. We analyze the somatosensory evoked potentials recorded from anesthetized cats during inhalation of 8-9% oxygen gas mixtures and during recovery with 100% oxygen. Analyses of the experimental data show a very sharp drop in the magnitude coherence estimates during hypoxic injury and a corresponding rapid decline in the linearity index at the very early stages of the hypoxic injury. Thus, injury may lead to nonlinearities in the electrical response of the brain, and such measurements analyzed by the adaptive coherence estimation method may be used for diagnostic purposes.