Proteins as networks: usefulness of graph theory in protein science.

The network paradigm is based on the derivation of emerging properties of studied systems by their representation as oriented graphs: any system is traced back to a set of nodes (its constituent elements) linked by edges (arcs) correspondent to the relations existing between the nodes. This allows for a straightforward quantitative formalization of systems by means of the computation of mathematical descriptors of such graphs (graph theory). The network paradigm is particularly useful when it is clear which elements of the modelled system must play the role of nodes and arcs respectively, and when topological constraints have a major role with respect to kinetic ones. In this review we demonstrate how nodes and arcs of protein topology are characterized at different levels of definition: 1. Recurrence matrix of hydrophobicity patterns along the sequence 2. Contact matrix of alpha carbons of 3D structures 3. Correlation matrix of motions of different portion of the molecule in molecular dynamics. These three conditions represent different but potentially correlated reticular systems that can be profitably analysed by means of network analysis tools.

Magnetosensory evoked potentials: consistent nonlinear phenomena.

Electromagnetic fields (EMFs) having strengths typically found in the general environment can alter brain activity, but the reported effects have been inconsistent. We theorized that the problem arose from the use of linear methods for analyzing what were actually nonlinear phenomena, and therefore studied whether the nonlinear signal-processing technique known as recurrence quantification analysis (RQA) could be employed as the basis of a reliable method for demonstrating consistent changes in brain activity. Our primary purpose was to develop such a method for observing the occurrence of evoked potentials in individual subjects exposed to magnetic fields (2G, 30 and 60 Hz). After all conditions that affected the analysis of the EEG were specified in advance, we detected magnetosensory evoked potentials (MEPs) in all 15 subjects (P<0.05 in each experiment). The MEPs, which occurred within the predicted latency interval of 109-504 ms, were independent of the frequency and the direction of the field, and were not detected using the traditional linear method of analysis, time averaging. When the results obtained within subjects were averaged across subjects, the evoked potentials could not be detected, indicating how real nonlinear phenomena can be averaged away when the incorrect method of analysis is used. Recurrence quantification analysis, but not linear analysis, permitted consistent demonstration of MEPs. The use of nonlinear analysis might also resolve apparent inconsistencies in other kinds of brain studies.

Women tolerate drug therapy for coronary artery disease as well as men do, but are treated less frequently with aspirin, beta-blockers, or statins.

BACKGROUND: Women have worse morbidity, mortality, and health-related quality-of-life outcomes associated with coronary artery disease (CAD) compared with men. This may be related to underutilization of drug therapies, such as aspirin, beta-blockers, angiotensin-converting enzyme (ACE) inhibitors, or statins. No studies have sought to describe the relationship of gender with adverse reactions to drug therapy (ADRs) for CAD in clinical practice. OBJECTIVE: The aim of this study was to determine the prevalence of ADRs associated with common CAD drug therapies in women and men in clinical practice. METHODS: In a cohort of consecutive outpatients with CAD, detailed chart abstraction was performed to determine the use of aspirin, beta-blocker, ACE inhibitor, and statin therapy, as well as the ADRs reported for these treatments. Baseline clinical characteristics were also determined to identify the independent association of gender with use of standard drug treatments for CAD. RESULTS: Consecutive patients with CAD (153 men, 151 women) were included in the study. Women and men were observed to have a similar prevalence of cardiac risk factors and comorbidities, except that men had significantly higher prevalence of atrial fibrillation (30 [19.6%] men vs 15 [9.9%] women; P = 0.03) and significantly lower mean (SD) high-density lipoprotein cholesterol concentrations (45 [16] mg/dL for men vs 55 [19] mg/dL for women; P < 0.001). No significant differences were observed between the sexes in the prevalence of ADRs; however, significantly fewer women than men were treated with statins (118 [78.1%] vs 139 [90.8%], respectively; P = 0.003). After adjusting for clinical characteristics, women were also found to be less likely than men to receive aspirin (odds ratio [OR] = 0.164; 95% CI, 0.083-0.322; P = 0.001) and beta-blockers (OR = 0.184; 95% CI, 0.096-0.351; P = 0.001). CONCLUSIONS: Women and men experienced a similar prevalence of ADRs in the treatment of CAD; however, women were significantly less likely to be treated with aspirin, beta-blockers, and statins than were their male counterparts. To optimize care for women with CAD, further study is needed to identify the cause of this gender disparity in therapeutic drug use.

Is physiology the locus of health/health promotion?

A current trend in physiology education involves the use of clinical vignettes to demonstrate the importance of knowing normal physiology to appreciate pathophysiology. Although laudable, in effect, such tactics promote the so-called "disease" model of medicine while at the same time suggesting that the only utility for the knowledge of physiology is to understand pathophysiology. This would seem to be at odds with health professions and institutions, who maintain their goal is to promote health. Yet, a search for the locus of "health" education in typical curricula is not easily found. Given the developing interest in biological systems as well as aging, it is suggested that these topics may provide a basis for locating physiology as the locus for understanding "health."

A topologically related singularity suggests a maximum preferred size for protein domains.

A variety of protein physicochemical as well as topological properties, demonstrate a scaling behavior relative to chain length. Many of the scalings can be modeled as a power law which is qualitatively similar across the examples. In this article, we suggest a rational explanation to these observations on the basis of both protein connectivity and hydrophobic constraints of residues compactness relative to surface volume. Unexpectedly, in an examination of these relationships, a singularity was shown to exist near 255-270 residues length, and may be associated with an upper limit for domain size. Evaluation of related G-factor data points to a wide range of conformational plasticity near this point. In addition to its theoretical importance, we show by an application of CASP experimental and predicted structures, that the scaling is a practical filter for protein structure prediction.

Entropic criteria for protein folding derived from recurrences: six residues patch as the basic protein word.

Some research has suggested that patches of six constitute an important amino acid window length in proteins for conveying information. We present database evidence that supports this conjecture, as well as additional recurrence-based data that characterization and quantification of these words affect the folding/aggregation features of proteins. Other indirect evidence is presented and discussed.

Detection of cardiac variability in the isolated rat heart.

Cardiac variability can be assessed from two perspectives: beat-to-beat performance and continuous performance during the cardiac cycle. Linear analysis techniques assess cardiac variability by measuring the physical attributes of a signal, whereas nonlinear techniques evaluate signal dynamics. This study sought to determine if recurrence quantification analysis (RQA), a nonlinear technique, could detect pharmacologically induced autonomic changes in the continuous left ventricular pressure (LVP) and electrographic (EC) signals from an isolated rat heart-a model that theoretically contains no inherent variability. LVP and EC signal data were acquired simultaneously during Langendorff perfusion of isolated rat hearts before and after the addition of acetylcholine (n = 11), norepinephrine (n = 12), or no drug (n = 12). Two-minute segments of the continuous LVP and EC signal data were analyzed by RQA. Findings showed that%recurrence,%determinism, entropy, maxline, and trend from the continuous LVP signal significantly increased in the presence of both acetylcholine and norepinephrine, although systolic LVP significantly increased only with norepinephrine. In the continuous EC signal, the RQA trend variable significantly increased in the presence of norepinephrine. These results suggest that when either the sympathetic or parasympathetic division of the autonomic nervous system overwhelms the other, the dynamics underlying cardiac variability become stationary. This study also shows that information concerning inherent variability in the isolated rat heart can be gained via RQA of the continuous cardiac signal. Although speculative, RQA may be a tool for detecting alterations in cardiac variability and evaluating signal dynamics as a nonlinear indicator of cardiac pathology.

Early events in protein aggregation: molecular flexibility and hydrophobicity/charge interaction in amyloid peptides as studied by molecular dynamics simulations.

In a previous article (Zbilut et al., Biophys J 2003;85:3544-3557), we demonstrated how an aggregation versus folding choice could be approached considering hydrophobicity distribution and charge. In this work, our aim is highlighting the mutual interaction of charge and hydrophobicity distribution in the aggregation process. Use was made of two different peptides, both derived from a transmembrane protein (amyloid precursor protein; APP), namely, Abeta(1-28) and Abeta(1-40). Abeta(1-28) has a much lower aggregation propensity than Abeta(1-40). The results obtained by means of molecular dynamics simulations show that, when submitted to the most "aggregation-prone" environment, corresponding to the isoelectric point and consequently to zero net charge, both peptides acquire their maximum flexibility, but Abeta(1-40) has a definitely higher conformational mobility than Abeta(1-28). The absence of a hydrophobic "tail," which is the most mobile part of the molecule in Abeta(1-40), is the element lacking in Abeta(1-28) for obtaining a "fully aggregating" phenotype. Our results suggest that conformational flexibility, determined by both hydrophobicity and charge effect, is the main mechanistic determinant of aggregation propensity.

Discrimination of single amino acid mutations of the p53 protein by means of deterministic singularities of recurrence quantification analysis.

p53 is mutated in roughly 50% of all human tumors, predominantly in the DNA-binding domain codons. Structural, biochemical, and functional studies have reported that the different p53 mutants possess a broad range of behaviors that include the elimination of the tumor-suppression function of wild-type protein, the acquisition of dominant-negative function over the wild-type form, and the establishment of gain-of-function activities. The contribution of each of these types of mutations to tumor progression, grade of malignancy, and response to anticancer treatments has been so far analyzed only for a few "hot-spots." In an attempt to identify new approaches to systematically characterize the complete spectrum of p53 mutations, we applied recurrence quantification analysis (RQA), a non-linear signal analysis technique, to p53 primary structure. Moving from the study of the p53 hydrophobicity pattern, which revealed important similarities with the singular deterministic structuring of prions, we could statistically discriminate, on a pure amino acid sequence basis, between experimentally characterized DNA-contact defective and conformational p53 mutants with a very high percentage of success. This result indicates that RQA is a mathematical tool particularly advantageous for the development of a database of p53 mutations that integrates epidemiological data with structural and functional categorizations.

Review of nonlinear analysis of proteins through recurrence quantification.

This review considers the use of a nonlinear signal analysis tool, recurrence quantification analysis, as a method to study sequence/structure relationships of proteins. Four broad categories are discussed: (1) a point of view involving information contained in deterministic aspects of hydrophobicity; (2) the analysis of protein hydrophobicity "singularities"; (3) time-series analysis of protein dynamics simulations; and (4) prediction of protein secondary structure.

Application of trilinear SLICING to analyse a single relaxation curve.

Determining the time constants and amplitudes of exponential decays from relaxation data is a common task in LF-NMR. In this communication, we present an application of the SLICING algorithm to evaluate its possibilities for solving this problem. The method, originally introduced to compare different samples, is applied here to analyse a single relaxation curve, using the embedding technique. To test this procedure, we acquired data sets from samples of liquids properly separated, and characterized by different relaxation times. The results show a good estimation of parameters, comparable with those obtained applying Marquardt's algorithm, when the components have sufficiently different relaxation times.

Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals.

The complexity, nonlinearity and nonstationarity of the cardiovascular system typically defy comprehensive and deterministic mathematical modeling, except from a statistical perspective. Living systems are governed by numerous, continuously changing, interacting variables in the presence of noise. Cardiovascular signals can be shown to be discontinuous alternations between deterministic trajectories and stochastic pauses (terminal dynamics). One promising approach for assessing such nondeterministic complexity is recurrence quantification analysis (RQA). As reviewed in this paper, strategies implementing quantification of recurrences have been successful in diagnosing changes in nonstationary cardiac signals not easily detected by traditional methods. It is concluded that recurrence quantification analysis is a powerful discriminatory tool which, when properly applied to cardiac signals, can provide objectivity regarding the degree of determinism characterizing the system, state changes, as well as degrees of complexity and/or randomness.

Biosignatures of health.

The term health is commonplace in both everyday parlance and professional discourse. Unfortunately, the term has little objective specification, especially in physiologic terms. When critically examined, even time-honored terms such as homeostasis lack specific measurable referents. The last three decades, however, have witnessed an explosion of information from diverse fields regarding the dynamical basis of biology. This brief review explores a few main ideas, which appear to be coming together to provide biosignatures of health.

Biological uncertainty.

Heisenberg's uncertainty relation has inspired speculations in a variety of scientific fields. Most of these speculations have wandered significantly far from the original formulation; yet, they may have been useful for a critical examination of methodological issues. As molecular genetics and its complexities evolve amid a backdrop of technological innovation, new "uncertainties" may have emerged. We present some of these uncertainties not as impediments, but as challenges to be recognized and managed.

Implications from a network-based topological analysis of ubiquitin unfolding simulations.

BACKGROUND: The architectural organization of protein structures has been the focus of intense research since it can hopefully lead to an understanding of how proteins fold. In earlier works we had attempted to identify the inherent structural organization in proteins through a study of protein topology. We obtained a modular partitioning of protein structures with the modules correlating well with experimental evidence of early folding units or "foldons". Residues that connect different modules were shown to be those that were protected during the transition phase of folding. METHODOLOGY/PRINCIPAL FINDINGS: In this work, we follow the topological path of ubiquitin through molecular dynamics unfolding simulations. We observed that the use of recurrence quantification analysis (RQA) could lead to the identification of the transition state during unfolding. Additionally, our earlier contention that the modules uncovered through our graph partitioning approach correlated well with early folding units was vindicated through our simulations. Moreover, residues identified from native structure as connector hubs and which had been shown to be those that were protected during the transition phase of folding were indeed more stable (less flexible) well beyond the transition state. Further analysis of the topological pathway suggests that the all pairs shortest path in a protein is minimized during folding. CONCLUSIONS: We observed that treating a protein native structure as a network by having amino acid residues as nodes and the non-covalent interactions among them as links allows for the rationalization of many aspects of the folding process. The possibility to derive this information directly from 3D structure opens the way to the prediction of important residues in proteins, while the confirmation of the minimization of APSP for folding allows for the establishment of a potentially useful proxy for kinetic optimality in the validation of sequence-structure predictions.

pH effects on the conformational preferences of amyloid beta-peptide (1-40) in HFIP aqueous solution by NMR spectroscopy.

The structure and aggregation state of amyloid beta-peptide (Abeta) in membrane-like environments are important determinants of pathological events in Alzheimer's disease. In fact, the neurotoxic nature of amyloid-forming peptides and proteins is associated with specific conformational transitions proximal to the membrane. Under certain conditions, the Abeta peptide undergoes a conformational change that brings the peptide in solution to a "competent state" for aggregation. Conversion can be obtained at medium pH (5.0-6.0), and in vivo this appears to take place in the endocytic pathway. The combined use of (1)H NMR spectroscopy and molecular dynamics-simulated annealing calculations in aqueous hexafluoroisopropanol simulating the membrane environment, at different pH conditions, enabled us to get some insights into the aggregation process of Abeta, confirming our previous hypotheses of a relationship between conformational flexibility and aggregation propensity. The conformational space of the peptide was explored by means of an innovative use of principal component analysis as applied to residue-by-residue root-mean-square deviations values from a reference structure. This procedure allowed us to identify the aggregation-prone regions of the peptide.

A contemporary pathology of science.

A contemporary pathology of science is outlined. This pathology suggests that "previous knowledge" drastically limits innovative thinking in science. In very raw "Bayesian" terms it is affirmed that a too rich and flexible a priori knowledge is detrimental to the appreciation of novelty coming from experimental results by both lowering the relative weight assigned to a posteriori contrasting evidence and adapting potentially revolutionary findings to an already existing frame.

Will systems biology offer new holistic paradigms to life sciences?

A biological system, like any complex system, blends stochastic and deterministic features, displaying properties of both. In a certain sense, this blend is exactly what we perceive as the "essence of complexity" given we tend to consider as non-complex both an ideal gas (fully stochastic and understandable at the statistical level in the thermodynamic limit of a huge number of particles) and a frictionless pendulum (fully deterministic relative to its motion). In this commentary we make the statement that systems biology will have a relevant impact on nowadays biology if (and only if) will be able to capture the essential character of this blend that in our opinion is the generation of globally ordered collective modes supported by locally stochastic atomisms.

Network scaling invariants help to elucidate basic topological principles of proteins.

The structural architecture of proteins continues to be an area of active research. Despite the difference in models dealing with the way proteins fold into their tertiary structures, it is recognized that small regions of proteins tend to fold independently and are then stabilized by interactions between these distinct subunits. However, there are a number of different definitions of what comprises an independent subunit. In the belief that an unequivocal definition of a domain must be based on the most fundamental property of protein 3D structure, namely, the adjacency matrix of inter-residues contact, we adopt a network representation of the protein. In this work, we used a well-established, global method for identifying modules in networks, without any specific reference to the kind of network being analyzed. The algorithm converges toward the maximization of the modularity of the given protein network and, in doing so, allows the representation of the residues of the protein in terms of their intramodule degree, z, and participation coefficient, P. We demonstrate that the labeling of residues in terms of these invariants allows for information-rich representations of the studied proteins as well as to sketch a new way to link sequence, structure, and the dynamical properties of proteins. We discovered a strong invariant character of protein molecules in terms of P/z characterization, pointing to a common topological design of all protein structures. This invariant representation, applied to different protein systems, enabled us to identify the possible functional role of high P/z residues during the folding process. Additionally, we observe a hierarchical behavior of protein structural organization that provides a sequence-secondary-tertiary structure link. The discovery of similar and repeatable scaling laws at different level of definitions going from hydrophobicity patterning along the sequence up to the size of an autonomous folding unit (AFU) and general contact distribution of the entire molecule suggest a hierarchical-like behavior of protein architecture. This implies the possibility to select different privileged scales of observation for deriving useful information on protein systems.