Elucidating protein secondary structures using alpha-carbon recurrence quantifications.

Secondary structures of proteins were studied by recurrence quantification analysis (RQA). High-resolution, 3-dimensional coordinates of alpha-carbon atoms comprising a set of 68 proteins were downloaded from the Protein Data Bank. By fine-tuning four recurrence parameters (radius, line, residue, separation), it was possible to establish excellent agreement between percent contribution of alpha-helix and beta-sheet structures determined independently by RQA and that of the DSSP algorithm (Define Secondary Structure of Proteins). These results indicate that there is an equivalency between these two techniques, which are based upon totally different pattern recognition strategies. RQA enhances qualitative contact maps by quantifying the arrangements of recurrent points of alpha carbons close in 3-dimensional space. For example, the radius was systematically increased, moving the analysis beyond local alpha-carbon neighborhoods in order to capture super-secondary and tertiary structures. However, differences between proteins could only be detected within distances up to about 6-11 A, but not higher. This result underscores the complexity of alpha-carbon spacing when super-secondary structures appear at larger distances. Finally, RQA-defined secondary structures were found to be robust against random displacement of alpha carbons upwards of 1 A. This finding has potential import for the dynamic functions of proteins in motion.

Heart rate and blood pressure response to short-term head-down bed rest: a nonlinear approach.

Although it is well-known that prolonged exposure to microgravity environment such as in space travel results in derangements of orthostasis, recent evidence suggests that even short-term exposure may have similar effects and parallels such common examples as prolonged bed rest. Whereas spectral analysis of heart rate and systolic blood pressure have been unable to detect changes, we hypothesized that nonlinear indexes may be better able to uncover such perturbations. Eighteen healthy subjects were exposed to 4-hour head-down tilt, and of these, 4 exhibited fainting. Two nonlinear indexes, mutual information and recurrence quantification were used to analyze the data. Only recurrence quantification was able to detect a "decoupling" of heart rate and systolic blood pressure at rest using discriminant analysis (p < 0.05). These results suggest that orthostatic intolerance may be due to a decoupling of heart rate from systolic blood pressure reflexive activity occurring at rest.

Nonlinear time-course of lumbar muscle fatigue using recurrence quantifications.

Isometric skeletal muscle fatigue is usually assumed to be a linear process based upon the monotonic decrease in spectral frequency of the EMG. Since spectral analysis by fast Fourier transform (FFT) constitutes a linear transformation of the data, the present study was designed to reevaluate the time-course of muscle fatigue with a nonlinear tool, recurrence quantification analysis (RQA). Surface EMG recordings were obtained from the multifidus muscle of 17 human subjects during isometric posture-holding of the upper torso. The process of muscle fatigue was found to be linear for 59% of the subjects by FFT criteria, but nonlinear for 76% by RQA criteria. As a demonstrative control, both slow and fast transients occurring within a nonlinear mathematical process could be accurately depicted by RQA, but not by FFT. It is concluded that assessment of EMG patterns by nonlinear techniques can give insight into the time-course of fatiguing muscles attributed to the summation of several nonlinear and competing processes.

The role of hydrophobicity patterns in prion folding as revealed by recurrence quantification analysis of primary structure.

It has been suggested that the number and strength of local contacts are the major factors governing conformation accessibility of model two ground-state polypeptide chains. This phenomenology has been posed as a possible factor influencing prion folding. To test this conjecture, recurrence quantification analysis was applied to two model 36mers, and the Syrian hamster prion protein. A unique divergence of the radius function for the recurrence quantification variable %DET of hydrophobicity patterns was observed for both 36mers, and in a critical region of the hamster prion protein. This divergence suggests a partition between strong short- and long-range hydrophobicity patterns, and may be an important factor in prion phenomenology, along with other global thermodynamic factors.

Nonlinear methods in the analysis of protein sequences: a case study in rubredoxins.

Two computational methods widely used in time series analysis were applied to protein sequences, and their ability to derive structural information not directly accessible through classical sequence comparisons methods was assessed. The primary structures of 19 rubredoxins of both mesophilic and thermophilic bacteria, coded with hydrophobicity values of amino acid residues, were considered as time series and were analyzed by 1) recurrence quantification analysis and 2) spectral analysis of the sequence major eigenfunctions. The results of the two methods agreed to a large extent and generated a classification consistent with known 3D structural characteristics of the studied proteins. This classification separated in a clearcut manner a thermophilic protein from mesophilic proteins. The classification of primary structures given by the two dynamical methods was demonstrated to be basically different from classification stemming from classical sequence homology metrics. Moreover, on a more detailed scale, the method was able to discriminate between thermophilic and mesophilic proteins from a set of chimeric sequences generated from the mixing of a mesophilic (Rubr Clopa) and a thermophilic (Rubr Pyrfu) protein. Overall, our results point to a new way of looking at protein sequence comparisons.

Recurrence quantification analysis in structure-function relationships of proteins: an overview of a general methodology applied to the case of TEM-1 beta-lactamase.

Protein structure-function relationships have been increasingly scrutinized by a variety of correlational and information theoretic measures. In an effort to extend this methodology, a technique originally developed in non-linear science, recurrence quantification analysis, was combined with traditional principal components analysis to study a large number (56) of TEM-1 beta-lactamase mutants. The hydrophobicity profiles corresponding to the primary structure of 13 naturally occurring mutations partially impairing function, together with 43 artificial non-tolerated mutations were subjected to discriminant analysis, derived from the results of recurrence quantification analysis, coupled to a principal exponents extraction. Eleven (85%) of the naturally occurring mutants and 36 (84%) of the artificial mutants were correctly classified (p < 0.0001). We conclude that this technique may be useful in protein engineering and, in general, in structure-function studies of biopolymers.

A terminal dynamics model of the heartbeat.

It is widely assumed that heartbeat dynamics are chaotic, although there has been no evidence confirming such an opinion, and some evidence to the contrary. Additionally, the deterministic assumptions of such dynamics cannot be demonstrated. An alternative model is presented based upon the notion of terminal dynamics, which can more faithfully represent key features of the heartbeat: namely, piecewise determinism, and singular points between beats, which allow for adaptability while maintaining stability.

Effect of HeartMate left ventricular assist device on cardiac autonomic nervous activity.

BACKGROUND: Clinical performance of a left ventricular assist device is assessed via hemodynamic parameters and end-organ function. This study examined effect of a left ventricular assist device on human neurophysiology. METHODS: This study evaluated the time course change of cardiac autonomic activity of 3 patients during support with a left ventricular assist device before cardiac transplantation. Cardiac autonomic activity was determined by power spectral analysis of short-term heart rate variability. The heart rate variability before cardiac transplantation was compared with that on the day before left ventricular assist device implantation. RESULTS: The standard deviation of the mean of the R-R intervals of the electrocardiogram, an index of vagal activity, increased to 27 +/- 7 ms from 8 +/- 0.6 ms. The modulus of power spectral components increased. Low frequency (sympathetic activity) and high frequency power (vagal activity) increased by a mean of 9 and 22 times of each baseline value (low frequency power, 5.2 +/- 3.0 ms2; high frequency power, 2.1 +/- 0.7 ms2). The low over high frequency power ratio decreased substantially, indicating an improvement of cardiac sympatho-vagal balance. CONCLUSIONS: The study results suggest that left ventricular assist device support before cardiac transplantation may exert a favorable effect on cardiac autonomic control in patients with severe heart failure.

A Markovian formalization of heart rate dynamics evinces a quantum-like hypothesis.

Most investigations into heart rate dynamics have emphasized continuous functions, whereas the heart beat itself is a discrete event. We present experimental evidence that by considering this quality, the dynamics may be appreciated as a result of singular dynamics arising out of non-Lipschitz formalisms. Markov process analysis demonstrates that heart beats may then be considered in terms of quantum-like constraints.

Treatment of sepsis and septic shock: a review.

Septic shock is one of the leading causes of death in intensive care units, and its incidence is increasing. Mortality rates as high as 95% are reported, with rates of 60% or more even when diagnosed and treated promptly. This review examines the definition of septic shock, its pathogenesis, and supportive therapy, with particular attention to intervention during the septic shock cascade.

Dynamical assessment of physiological systems and states using recurrence plot strategies.

Physiological systems are best characterized as complex dynamical processes that are continuously subjected to and updated by nonlinear feedforward and feedback inputs. System outputs usually exhibit wide varieties of behaviors due to dynamical interactions between system components, external noise perturbations, and physiological state changes. Complicated interactions occur at a variety of hierarchial levels and involve a number of interacting variables, many of which are unavailable for experimental measurement. In this paper we illustrate how recurrence plots can take single physiological measurements, project them into multidimensional space by embedding procedures, and identify time correlations (recurrences) that are not apparent in the one-dimensional time series. We extend the original description of recurrence plots by computing an array of specific recurrence variables that quantify the deterministic structure and complexity of the plot. We then demonstrate how physiological states can be assessed by making repeated recurrence plot calculations within a window sliding down any physiological dynamic. Unlike other predominant time series techniques, recurrence plot analyses are not limited by data stationarity and size constraints. Pertinent physiological examples from respiratory and skeletal motor systems illustrate the utility of recurrence plots in the diagnosis of nonlinear systems. The methodology is fully applicable to any rhythmical system, whether it be mechanical, electrical, neural, hormonal, chemical, or even spacial.

Phase-dependent properties of the cardiac sarcoplasmic reticulum oscillator in cat right atrium: a mechanism contributing to dysrhythmias induced by Ca2+ overload.

These experiments analyse the phase-dependent properties of spontaneous oscillations of the sarcoplasmic reticulum (SR) induced by Ca2+ overload. Right atrial tissue was loaded with intracellular Ca2+ by exposure to a modified Tyrode solution containing 50% of normal Na+ and 0.5 mM K+. Verapamil (2 microM) was added to block regenerative activity. Intracellular Ca2+ overload elicited spontaneous, rhythmic voltage and tension oscillations that were phase locked 1:1. Voltage and tension oscillations were abolished by exposure to low (0.9 mM) external Ca2+, 1 microM ryanodine, or 10 mM caffeine, indicating that both voltage and tension oscillations resulted from spontaneous oscillations in SR Ca2+ release. Single pulses of nerve-stimulated ACh release elicited phase shifts in both voltage and tension oscillations. Sinusoidal current was used as a periodic stimulus to drive membrane voltage and elicit periodic voltage oscillations. Stimulated voltage oscillations entrained spontaneous tension oscillations 1:1 in a range of frequencies close to the basic spontaneous SR oscillatory cycle length, or 2:1 at frequencies close to one-half the spontaneous SR oscillatory cycle length. Stimulation frequencies between these two regions entrained tension oscillations in predictable fixed coupled ratios (4:3, 3:2) and resulted in Wenckeback-like voltage patterns. Stimulation frequencies between phase-locked regions resulted in complex coupling relationships and irregular voltage patterns. Exposure to 1 microM ryanodine, 0.9 mM external Ca2+, or 10 mM caffeine abolished irregular voltage patterns and tension. We conclude that the SR oscillator exhibits phase-dependent sensitivity to perturbations at the surface membrane. As a result, external perturbations can elicit phase differences between spontaneous SR oscillations and membrane voltage that cause either phase-locked or irregular voltage patterns. These findings identify an intracellular mechanism that may contribute to the development of cardiac dysrhythmias resulting from intracellular Ca2+ overload.