Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses

Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²⁺ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λ_alt) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ_alt≤−1. For different BCLs, control values of λ_alt were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ_alt. Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ_alt. In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.     

Effect of molecular confinement on internal enzyme dynamics: frequency domain fluorometry and molecular dynamics simulation studies

The tryptophanyl emission decay of the mesophilic beta-galactosidase from Aspergillus oryzae free in buffer and entrapped in agarose gel is investigated as a function of temperature and compared to that of the hyperthermophilic enzyme from Sulfolobus solfataricus. Both enzymes are tetrameric proteins with a large number of tryptophanyl residues, so the fluorescence emission can provide information on the conformational dynamics of the overall protein structure rather than that of the local environment. The tryptophanyl emission decays are best fitted by bimodal Lorentzian distributions. The long-lived component is ascribed to close, deeply buried tryptophanyl residues with reduced mobility; the short-lived one arises from tryptophanyl residues located in more flexible external regions of each subunit, some of which are involved in forming the catalytic site. The center of both lifetime distribution components at each temperature increases when going from the free in solution mesophilic enzyme to the gel-entrapped and hyperthermophilic enzyme, thus indicating that confinement of the mesophilic enzyme in the agarose gel limits the freedom of the polypeptide chain. A more complex dependence is observed for the distribution widths. Computer modeling techniques are used to recognize that the catalytic sites are similar for the mesophilic and hyperthermophilic beta-galactosidases. The effect due to gel entrapment is considered in dynamic simulations by imposing harmonic restraints to solvent-exposed atoms of the protein with the exclusion of those around the active site. The temperature dependence of the tryptophanyl fluorescence emission decay and the dynamic simulation confirm that more rigid structures, as in the case of the immobilized and/or hyperthermophilic enzyme, require higher temperatures to achieve the requisite conformational dynamics for an effective catalytic action and strongly suggest a link between conformational rigidity and enhanced thermal stability.     

Uncovering interactions in the frequency domain

Oscillatory activity plays a critical role in regulating biological processes at levels ranging from subcellular, cellular, and network to the whole organism, and often involves a large number of interacting elements. We shed light on this issue by introducing a novel approach called partial Granger causality to reliably reveal interaction patterns in multivariate data with exogenous inputs and latent variables in the frequency domain. The method is extensively tested with toy models, and successfully applied to experimental datasets, including (1) gene microarray data of HeLa cell cycle; (2) in vivo multi-electrode array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of a sheep; and (3) in vivo LFPs recorded from distributed sites in the right hemisphere of a macaque monkey.     

Ionic contacts at DnaK substrate binding domain involved in the allosteric regulation of lid dynamics

To gain further insight into the interactions involved in the allosteric transition of DnaK we have characterized wild-type (wt) protein and three mutants in which ionic interactions at the interface between the two subdomains of the substrate binding domain, and within the lid subdomain have been disrupted. Our data show that ionic contacts, most likely forming an electrically charged network, between the N-terminal region of helix B and an inner loop of the beta-sandwich are involved in maintaining the position of the lid relative to the beta-subdomain in the ADP state but not in the ATP state of the protein. Disruption of the ionic interactions between the C-terminal region of helix B and the outer loops of the beta-sandwich, known as the latch, does not have the same conformational consequences but results equally in an inactive protein. This indicates that a variety of mechanisms can inactivate this complex allosteric machine. Our results identify the ionic contacts at the subdomain and interdomain interfaces that are part of the hinge region involved in the ATP-induced allosteric displacement of the lid away from the peptide binding site. These interactions also stabilize peptide-Hsp70 complexes at physiological (37 degrees C) and stress (42 degrees C) temperatures, a requirement for productive substrate (re)folding.     

Implications of SH3 domain structure and dynamics for protein regulation and drug design

SH3 Domains provide interesting targets for investigations of protein structure and dynamics because of their compact size and importance for signal transduction. The present review summarizes recent research investigating SH3 domain structure and dynamics, the discovery of novel SH3 domains, the role of SH3 domains in disease, and progress in targeting SH3 domains for the development of novel therapeutics. Particular emphasis is placed on the unfolding/refolding characteristics of SH3 domains and the potential importance of these processes for regulation of signal transduction.     

Heterogeneity in the structural dynamics of Sulfolobus solfataricus beta-glycosidase revealed by electron paramagnetic resonance and frequency domain fluorometry

The local and global dynamics of the Sulfolobus solfataricus beta-glycosidase were studied by electron spin resonance and time-resolved fluorescence techniques. For electron paramagnetic resonance (EPR) investigations, the protein was covalently modified by the maleimido nitroxide spin label, which is specific for cysteine -SH groups, at position 344 and at position 101, where Ser-101 was changed into a cysteine by site-directed mutagenesis. The greater reactivity of exposed Cys-101 suggested the exclusive modification of this amino acid compared with Cys-344. The labeled proteins underwent temperature perturbation in the range 290-335 K and the values of the spin-label rotation correlation frequencies (nu(c)) ranged from 6 x 10(7) to 2 x 10(8) sec(-1) for the protein labeled at position C344 and from 5.62 x 10(7) to 1.10 x 10(8) sec(-1) for the protein labeled at C101. These rotation correlation values are related to the local dynamic characteristics of the protein matrix. The temperature dependence of rotation correlation frequencies expressed in terms of Arrhenius coordinates (log (nu(c)) vs. 1/T) for the protein labeled at C344 exhibited a linear dependence but with a change in the slope at 311 K. For the protein labeled at C101, no change in the slope was observed at the same temperature. General dynamic information was deduced from the analysis of the fluorescence emission decay of the tryptophanyl residues that are present in each region of the protein structure. Fluorescence data analysis highlighted a bimodal distribution of fluorescence lifetimes arising from the contribution of two emitting groups: one consisting of closely clustered tryptophans responsible for the long-lived emission component (7.1 nsec) and the other composed of tryptophans nearer to the protein surface, which can be associated to the short-lived component (2.5 nsec). The temperature dependence of lifetime distribution parameters linked to the long-lived and short-lived components, expressed in Arrhenius coordinates, showed two different points in which the change in the slope occurred (i.e., 328 K and 338 K, respectively). The Arrhenius analysis of data provided the activation energy relative to the conformational changes characterizing the local and global movements running through the protein matrix.     

Objective response detection in the frequency domain

Several different and related measures have been proposed for objective response detection in the frequency domain. We compared magnitude-squared coherence (MSC) to phase coherence (PC) using simulations with specified signal-to-noise ratios (SNRs) and varying numbers of subaverages; the performance measure was area unde a receiver operating characteristic (ROC) curve. MSC was superior to PC; test time required for equivalent performance is about 3 times greater PC than for MSC. MSC performance for a given final SNR increased with the number of subaverages, but reached a plateau at 16 subaverages. Simulations of noise non-stationarity (high-amplitude noise in some subaverages compared to the others) led to decreased performance advantage for MSC over PC. However, weighted averaging restored this advantage. MSC is shown to be a simple algebraic transform of Victor and Mast's (1991) “circular T²” statistic and of two earlier statistics; all have identical statistical power.     

Color vision in the comb frequency domain

In 1982, Horace Barlow considered the question of human trichromacy in the context of information theory: according to the Sampling Theorem, three types of receptors covering the visible spectrum (400-700 nm) might be sufficient to reconstruct the color signal. Although Barlow was led to reject the direct application of the Sampling Theorem to explain color dimensionality, the theoretical framework offers a fresh point of view for analyzing the color system in conjunction with the physical characteristics of natural color signals. This review aims to illustrate that if the strict mathematical reconstruction (as implied by the Sampling Theorem) is replaced by a pragmatic approximation of color signals, then trichromacy, with its subsequent opponent-color process, could be regarded as an optimization of color constancy abilities in the spectral environment of primates. Higher dimension systems (tetrachromacy) found in other species can also serve the purpose of color constancy optimization in environments where color signals exhibit a finer spectral structure.     

Nonlinear polarization spectroscopy in the frequency domain of light-harvesting complex II: absorption band substructure and exciton dynamics.

Spectral substructure and ultrafast excitation dynamics have been investigated in the chlorophyll (Chl) a and b Qy region of isolated plant light-harvesting complex II (LHC II). We demonstrate the feasibility of Nonlinear Polarization Spectroscopy in the frequency domain, a novel photosynthesis research laser spectroscopic technique, to determine not only ultrafast population relaxation (T1) and dephasing (T2) times, but also to reveal the complex spectral substructure in the Qy band as well as the mode(s) of absorption band broadening at room temperature (RT). The study gives further direct evidence for the existence of up to now hypothetical "Chl forms". Of particular interest is the differentiated participation of the Chl forms in energy transfer in trimeric and aggregated LHC II. Limits for T2 are given in the range of a few ten fs. Inhomogeneous broadening does not exceed the homogeneous widths of the subbands at RT. The implications of the results for the energy transfer mechanisms in the antenna are discussed.     

Molecular organization and dynamics of the outer membrane of Salmonella thyphimurium mutant strains detected by frequency domain fluorometry

The fluorescence decay of 1,6-diphenyl-1,3,5-hexatriene (DPH) in the outer membrane bilayer of two mutant strains of Salmonella thyphimurium, i.e., SH 5014 and SH 6261, at different temperatures was analyzed in terms of continuous Lorentzian lifetime distributions. The results were compared with those obtained for the free fluorophore in an isotropic nonviscous solvent. The incorporation of DPH in the outer membrane fragments resulted in a broadening of the lifetime distribution which was attributed to the microenvironmental heterogeneity of the membrane bilayer for the extrinsic fluorophore. The differences observed between the two types of membrane bilayers were interpreted in terms of a different molecular organization and, to a lesser extent, in terms of a different fluidity. The comparison between the DPH lifetime distributions obtained using two different excitation wavelengths, i.e., 280 and 350 nm, suggested that the structural organization of the membrane domains, which are richest in proteins, is almost identical in the two examined mutant strains. This observation indicates that the different susceptibility of the two mutant strains toward phagocytosis and complement-mediated lytic action may depend on the molecular organization and dynamics of the lipid regions far from those containing proteins.     

The identification of recirculating systems in the frequency domain

A method for the identification of flow systems by frequency domain analysis has been extended to include systems with recirculation and truncated data curves. Application of the technique to clinical indicator-dilution curves indicates that the method may be useful in the quantitation of intracardiac shunts. A number of numerical examples which demonstrate the accuracy of the method are included.     

Registration of pedobarographic image data in the frequency domain

Image registration has been used to support pixel-level data analysis on pedobarographic image data sets. Some registration methods have focused on robustness and sacrificed speed, but a recent approach based on external contours offered both high computational processing speed and high accuracy. However, since contours can be influenced by local perturbations, we sought more global methods. Thus, we propose two new registration methods based on the Fourier transform, cross-correlation and phase correlation which offer high computational speed. We found out that both proposed methods revealed high accuracy for the similarity measures considered, using control geometric transformations. Additionally, both methods revealed high computational processing speed which, combined with their accuracy and robustness, allows their implementation in near-real-time applications. Furthermore, we found that the current methods were robust to moderate levels of noise, and consequently, do not require noise removal procedure like the contours method does.     

Conformational dynamics of the anticodon loop in yeast tRNAPhe as sensed by the fluorescence of wybutine

Conformational and dynamic properties of the anticodon loop of yeast tRNA^Phe were investigated by analyzing the time resolved fluorescence of wybutine serving as a local structural probe adjacent to the anticodon GmAA on its 3 side. The influence of Mg²⁺, important for stabilizing the tertiary structure of tRNA, and of the complementary anticodon s²UUC of E. coli tRNA ₂ ^Glu were investigated.Fluorescence lifetimes and anisotropies were measured with ps time resolution using time correlated single photon counting and a mode locked synchronously pumped and frequency doubled dye laser as excitation source. From the analysis of lifetimes () and rotational relaxation times ( _R ) we conclude that wybutine occurs in various structural states: (i) one stacked conformation where the base has no free mobility and the only rotational motion reflects the mobility of the whole tRNA molecule (=6 ns, _R =19 ns), (ii) an unstacked conformation where the base can freely rotate (=100 ps, _R = 370 ps) and (iii) an intermediary state (=2 ns, _R = 1.6 ns).Under biological conditions, i. e. in the presence of Mg²⁺ and neutral salts, wybutine is found in a stacked and immobile state which is consistent with the crystallographic picture. In the presence of the complementary codon however, as exemplified by the E. coli-tRNA ₂ ^Glu anticodon, our analysis indicates that the codon-anticodon complex exists in an equilibrium of structural states with different rotational mobility of wybutine. The conformation with wybutine freely mobile is the predominant one and suggests that this conformation of the codon-anticodon structure differs from the canonical 3–5 stack.     

A method of nonlinear analysis in the frequency domain.

A method is developed for the analysis of nonlinear biological systems based on an input temporal signal that consists of a sum of a large number of sinusoids. Nonlinear properties of the system are manifest by responses at harmonics and intermodulation frequencies of the input frequencies. The frequency kernels derived from these nonlinear responses are similar to the Fourier transforms of the Wiener kernels. Guidelines for the choice of useful input frequency sets, and examples satisfying these guidelines, are given. A practical algorithm for varying the relative phases of the input sinusoids to separate high-order interactions is presented. The utility of this technique is demonstrated with data obtained from a cat retinal ganglion cell of the Y type. For a high spatial frequency grafting, the entire response is contained in the even-order nonlinear components. Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.     

SMP domain proteins in membrane lipid dynamics

Synaptotagmin-like mitochondrial-lipid-binding (SMP) domain proteins are evolutionarily conserved family of proteins in eukaryotes that localize between the endoplasmic reticulum (ER) and either the plasma membrane (PM) or other organelles. They are involved in tethering of these membrane contact sites through interaction with other proteins and membrane lipids. Recent structural and biochemical studies have demonstrated that SMP domain proteins transport a wide variety of lipid species by the ability of the SMP domain to harbor lipids through its unique hydrophobic cavity. Growing evidence suggests that SMP domain proteins play critical roles in cell physiology by their actions at membrane contact sites. In this review, we summarize the functions of SMP domain proteins and their direct roles in lipid transport across different membrane compartments. We also discuss their physiological functions in organisms as well as “bypass” pathways that act in parallel with SMP domain proteins at membrane contact sites.     

Conformational dynamics of unfolded peptides as a function of chain length: a frequency domain fluorescence approach

The fluorescence emission decays of single-tryptophan-containing peptides of different chain lengths in their unfolded state were investigated in the frequency domain. The data were analyzed using different functions, i.e., exponential fit and probability-density functions of different shape. We found that unimodal Lorentzian distributions best describe the fluorescence decays. This finding agrees with the point of view, now broadly accepted, that rapid motions exist in polypeptides. As a consequence of this flexibility, a large variety of conformations, with an unequal perturbation of tryptophan in its excited state, is generated. The lifetime distribution center was independent of the length of the polypeptide chain but strongly related to the nature of the amino acid residues located in the proximity of the tryptophan in the primary structure. The full width at half maximum, W, of the lifetime distribution was found to be related to the length of unfolded polypeptide by the empirical logarithmic relationship W = 0.83 log n, where n indicates the number of residues. For short peptides, a single lifetime or a narrow range of lifetimes is observed because of the fast relaxation of the tryptophanyl environment. On peptide lengthening, the spectrum of conformations, which the peptide can assume, increases; this causes a complex fluorescence decay represented by a lifetime distribution. For long polypeptide chains, the motions of the regions far from tryptophan do not significantly perturb the chromophore environment.