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PubMed2000

Sampling rate and the estimation of ensemble variability for repetitive signals.

The measurement of ensemble variability in time-aligned event signals is studied in relation to sampling rate requirements. The theoretical analysis is based on statistical modelling of time misalignment in which the time resolution is limited by the length of the sampling interval. For different signal-to-noise ratios (SNRs), the sampling rate is derived which limits the misalignment effect to less than 10% of the noise effect. Each signal is assumed to be corrupted by additive noise. Using a normal QRS complex with a high SNR (approximately equal to 30 dB), a sampling rate of approximately 3 kHz is needed for accurate ensemble variability measurements. This result is surprising since it implies that the Nyquist rate is far too low for accurate variability measurements. The theoretical results are supplemented with results obtained from an ECG database of 94 subjects for which the ensemble variability is computed at different sampling rates using signal interpolation. The ensemble variability is substantially reduced (40%) when increasing the rate from 1 to 3 kHz, thus corroborating the results suggested by the theoretical analysis.

Electrocardiography↗

PubMed1996

A numerical simulation of muscle spindle ensemble encoding during planar movement of the human arm.

We address the issue of what proprioceptive information, regarding movement of the human arm, may be provided to the central nervous system by proprioceptors located within muscles of this limb. To accomplish this we developed a numerical simulation which could provide estimates of the length regimes experienced by a set of model receptors located within some of the principal muscles of the human arm during planar movement of this limb. These receptors were assumed to have characteristics analogous to those associated with a simple model of muscle spindle signalling of movement. To this end each spindle had proprioceptive 'channels' associated with it. These corresponded to primary and secondary spindle afferent fibers which could provide independent afferent output regarding the parent muscle the spindle monitored. The angles of the shoulder and elbow joints attained by subjects performing a task requiring movement of the right arm in a horizontal plane to a static visual target were recorded. For this angular data the lengths and rates of change of lengths experienced by muscle fascicles, and hence the model spindles, during movement were calculated by means of the numerical simulation. The discharge rates of the simulated spindles during the movement were calculated to derive a measure of the depth of modulation, induced by the movement, for each spindle. These values were then summed for all spindles to provide a first-order approximation of spindle ensemble coding of the movement. Significant correlations (P < 0.0001, Spearman's rank order) were found between the resulting ensemble encodings and, in order of significance, the angular velocity of the shoulder joint (rS = 0.945), the tangential velocity of the hand (rS = 0.942), and the angular velocity of the elbow joint (rS = 0.917). Correlations between the angular positions of the shoulder (rS = -0.623) and elbow (rS = 0.628) were lower. These findings indicate that the ensemble profiles of the simulated muscle spindles, encode information regarding kinematic parameters of movements related to both intrinsic and extrinsic coordinate systems. This suggests that motor structures capable of deriving such an ensemble encoding would be in a position to perform the sensory-motor transformations between intrinsic and extrinsic frames of reference necessary for controlling movements planned in extrinsic coordinates.

Arm↗

PubMed2006

A command chemical triggers an innate behavior by sequential activation of multiple peptidergic ensembles.

BACKGROUND: At the end of each molt, insects shed their old cuticle by performing the ecdysis sequence, an innate behavior consisting of three steps: pre-ecdysis, ecdysis, and postecdysis. Blood-borne ecdysis-triggering hormone (ETH) activates the behavioral sequence through direct actions on the central nervous system. RESULTS: To elucidate neural substrates underlying the ecdysis sequence, we identified neurons expressing ETH receptors (ETHRs) in Drosophila. Distinct ensembles of ETHR neurons express numerous neuropeptides including kinin, FMRFamides, eclosion hormone (EH), crustacean cardioactive peptide (CCAP), myoinhibitory peptides (MIP), and bursicon. Real-time imaging of intracellular calcium dynamics revealed sequential activation of these ensembles after ETH action. Specifically, FMRFamide neurons are activated during pre-ecdysis; EH, CCAP, and CCAP/MIP neurons are active prior to and during ecdysis; and activity of CCAP/MIP/bursicon neurons coincides with postecdysis. Targeted ablation of specific ETHR ensembles produces behavioral deficits consistent with their proposed roles in the behavioral sequence. CONCLUSIONS: Our findings offer novel insights into how a command chemical orchestrates an innate behavior by stepwise recruitment of central peptidergic ensembles.

Animals↗

PubMed2005

Mutational analysis demonstrates that specific electrostatic interactions can play a key role in the denatured state ensemble of proteins.

The nature of the denatured state ensemble has been controversial for decades owing, in large part, to the difficulty in characterizing the structure and energetics of denatured state interactions. There is increasing evidence for relatively non-specific hydrophobic clustering in the denatured states of some proteins but other types of interactions are much less well characterized. Here, we report the characterization of highly specific electrostatic interactions in the denatured state of a small alpha-beta protein, the N-terminal domain of the ribosomal protein L9 (NTL9). Mutation of Lys12 to Met has been shown to increase the stability of NTL9 significantly through the disruption of denatured state interactions. Here, we describe the analysis of the pH-dependent stability of 13 mutants designed to probe the nature of the Lys12 denatured state interaction. Lys12 is located in a lysine-rich region of the protein but analysis of a set of Lys to Met mutants shows that it plays a unique role in the denatured state. Analysis of mutants of all of the acidic residues in NTL9 shows that Lys12 forms a specific non-native electrostatic interaction with Asp8 in the denatured state ensemble. Thus the distribution of charge-charge interactions in the denatured state ensemble of NTL9 appears to be biased by few key interactions and is very different from that expected in a random coil. We propose that these interactions are not encoded by local sequence effects but rather reflect interactions among residues more distant in sequence. These results demonstrate that electrostatic as well as hydrophobic interactions can play an important role in the denatured state ensemble.

Hydrogen-Ion Concentration↗

PubMed2006

Fibrillogenic and non-fibrillogenic ensembles of SDS-bound human alpha-synuclein.

Fibril formation of alpha-synuclein is associated with several neurodegenerative diseases, including Parkinson's disease in humans. The anionic detergent sodium dodecyl sulfate (SDS) can accelerate the fibril formation in vitro. However, the molecular basis of this acceleration is not clear. Our study shows that native alpha-synuclein exhibits relatively less fibril growth despite providing fibril seeds for nucleation. The presence of SDS promotes the seeded fibril growth in a concentration-dependent manner, with an optimal concentration of 0.5-0.75 mM. We used isothermal calorimetry, hydrophobic dye binding and circular dichroism spectroscopy to characterize the protein-detergent interactions as a function of the concentration of SDS. Interaction of SDS with alpha-synuclein when studied by isothermal titration calorimetry and hydrophobic dye-binding reveals a similar characteristic optimal behavior between 0.5 mM and 0.75 mM SDS. The study shows two types of ensembles of alpha-synuclein and SDS: the fibrillogenic ensembles formed with optimal concentration of SDS around 0.5-0.75 mM are characterized by enhanced accessible hydrophobic surfaces and extended to partially helical conformation, while the less or non-fibrillogenic ensembles formed above 2 mM SDS are characterized by less accessible hydrophobic surfaces and maximal helical content. Little or no fibrillogenicity of the ensembles observed above 2 mM SDS could be partly because of the observed intrinsic instability of the fibrils under the condition.

Circular Dichroism↗

PubMed1995

Probability assessment of conformational ensembles: sugar repuckering in a DNA duplex in solution.

Conformational flexibility of molecules in solution implies that different conformers contribute to the NMR signal. This may lead to internal inconsistencies in the 2D NOE-derived interproton distance restraints and to conflict with scalar coupling-based torsion angle restraints. Such inconsistencies have been revealed and analyzed for the DNA octamer GTATAATG.CATATTAC, containing the Pribnow box consensus sequence. A number of subsets of distance restraints were constructed and used in the restrained Monte Carlo refinement of different double-helical conformers. The probabilities of conformers were then calculated by a quadratic programming algorithm, minimizing a relaxation rate-base residual index. The calculated distribution of conformers agrees with the experimental NOE data as an ensemble better than any single structure. A comparison with the results of this procedure, which we term PARSE (Probability Assessment via Relaxation rates of a Structural Ensemble), to an alternative method to generate solution ensembles showed, however, that the detailed multi-conformational description of solution DNA structure remains ambiguous at this stage. Nevertheless, some ensemble properties can be deduced with confidence, the most prominent being a distribution of sugar puckers with minor populations in the N-region and major populations in the S-region. Importantly, such a distribution is in accord with the analysis of independent experimental data--deoxyribose proton-proton scalar coupling constants.

Algorithms↗

PubMed1996

Grand canonical ensemble Monte Carlo simulation of the dCpG/proflavine crystal hydrate.

The grand canonical ensemble Monte Carlo molecular simulation method is used to investigate hydration patterns in the crystal hydrate structure of the dCpG/proflavine intercalated complex. The objective of this study is to show by example that the recently advocated grand canonical ensemble simulation is a computationally efficient method for determining the positions of the hydrating water molecules in protein and nucleic acid structures. A detailed molecular simulation convergence analysis and an analogous comparison of the theoretical results with experiments clearly show that the grand ensemble simulations can be far more advantageous than the comparable canonical ensemble simulations.

Binding Sites↗

PubMed2002

Native-like mean structure in the unfolded ensemble of small proteins.

The nature of the unfolded state plays a great role in our understanding of proteins. However, accurately studying the unfolded state with computer simulation is difficult, due to its complexity and the great deal of sampling required. Using a supercluster of over 10,000 processors we have performed close to 800 micros of molecular dynamics simulation in atomistic detail of the folded and unfolded states of three polypeptides from a range of structural classes: the all-alpha villin headpiece molecule, the beta hairpin tryptophan zipper, and a designed alpha-beta zinc finger mimic. A comparison between the folded and the unfolded ensembles reveals that, even though virtually none of the individual members of the unfolded ensemble exhibits native-like features, the mean unfolded structure (averaged over the entire unfolded ensemble) has a native-like geometry. This suggests several novel implications for protein folding and structure prediction as well as new interpretations for experiments which find structure in ensemble-averaged measurements.

Amino Acid Sequence↗

PubMed1989

Ensemble proprioceptive activity in the cat step cycle: towards a representative look-up chart.

Analysis of the control of movement in tasks such as stepping is severely restricted by the lack of quantitative data on the ensemble activity of afferents in the numerous muscles involved. We have started to build up a quantitative "look-up-chart" of the ensemble afferent and efferent profiles in the cat step cycle. To this end, we have developed software which allows us to digitize afferent firing, muscle length and electromyogram (EMG) activity, and to align segments for averaging by choosing one or more reference points in the step cycle. The ensemble firing of triceps surae Ia afferents showed lower than expected mean and peak rates, whereas triceps group II and Ib afferents were more active than predicted. There were small but significant transients in Ia firing at foot-off and touch-down which could not be explained in terms of origin-to-insertion length lone. They were most likely caused by propagated mechanical transients or tendon compliance effects giving rise to small differences between the origin-to-insertion length and the intramuscular length "seen" by spindles. Net ensemble Ia rates, based on previous estimates of spindle populations, probably exceed 25 kilo-impulses/second (ki.p.s.) in some muscles. Inputs as large as this are likely to contribute significantly to reflex control.

Animals↗

PubMed1998

Alterations in information transmission in ensembles of primary muscle spindle afferents after muscle fatigue in heteronymous muscle.

This study showed that fatigue of the ipsilateral medial gastrocnemius muscle caused a clear-cut reduction in the ability of ensembles of primary muscle spindle afferents from the lateral gastrocnemius muscle to discriminate between muscle stretches of varying amplitude. The results were probably caused by reflex-mediated effects from chemosensitive group III and IV afferents onto the gamma-motoneurons projecting to lateral gastrocnemius muscle spindles. The experiments were conducted on seven cats anaesthetized with alpha-chloralose and a total of 41 primary muscle spindle afferents from the lateral gastrocnemius were registered. Afferents were simultaneously recorded in ensembles of three to 10 afferents. A method based on principal component analysis and algorithms for quantification of stimulus discrimination in ensembles of muscle afferents was used prior to, immediately following and five or more minutes after muscle fatigue had been induced to the ipsilateral medial gastrocnemius muscle. It is well established that the primary muscle spindle afferents play an important role in proprioception and kinaesthesia. Therefore the decrease in the accuracy of the information transmitted by ensembles of primary muscle spindle afferents caused by fatigue in an ipsilateral muscle implies concomitant effects on proprioception and kinaesthesia.

Animals↗

PubMed1998

The ensemble-averaged impedance cardiogram: an evaluation of scoring methods and interrater reliability.

The interrater reliability and concurrent validity of two methods of scoring the ensemble-averaged impedance cardiogram were evaluated. Impedance cardiographic and electrocardiographic signals were recorded from 40 undergraduate men and women during a baseline rest period and a vocal mental arithmetic task period. Recordings were scored by four rates using a conventional method, involving ensemble averaging after careful editing of beat-to-beat waveforms, and a streamlined method, involving ensemble averaging without beat-to-beat editing. Intraclass correlations for interrater reliability exceeded .92, whereas intraclass correlations for concurrent validity exceeded .97, indicating excellent agreement between rates and scoring methods for all cardiac measures. The streamlined method was significantly faster than the conventional method. The results indicate that variations in beat-to-beat editing do not constitute a serious source of error in the ensemble-averaged impedance cardiogram and support the interrater reliability and concurrent validity of the two scoring methods.

Adult↗

PubMed2000

Hihg-speed GC/MS of gasoline-range hydrocarbon compounds using a pressure-tunable column ensemble and time-of-flight detection

A pressure-tunable series-coupled ensemble of two capillary GC columns is combined with a time-of-flight MS detector for the high-speed characterization of mixtures containing hydrocarbon compounds. The column ensemble consists of a nonpolar 5% phenyl poly(dimethylsiloxane) column and a very polar poly(ethylene glycol) column. The TOFMS instrument uses time-array detection to obtain up to 500 complete electron mass spectra per second. Instrument software allows for automated peak finding and the spectral deconvolution of severely overlapping unknown chromatographic peaks, if their fragmentation patterns are significantly different and if at least two spectra can be recorded between the peak apexes. By adjusting the carrier-gas pressure at the column-junction point, the separations between adjacent peak pairs can be adjusted to enhance the capabilities of the TOFMS detector. The sensitivity of peak-pair separation to changes in junction-point pressure is studied for combinations of alkanes, olefins, and aromatic compounds. When complete separation is required, the use of pressure-tunable column ensembles cannot always provide sufficient control of peak-pair separation for structurally similar compounds. However, complete chromatographic separation typically is not required with the TOFMS detection, and a pressure-tunable column ensemble is very useful for the high-speed characterization of hydrocarbon mixtures.

Journal Article↗

PubMed2005

Molecular simulations of aqueous electrolyte solubility: 1. The expanded-ensemble osmotic molecular dynamics method for the solution phase.

We have developed a molecular-level simulation technique called the expanded-ensemble osmotic molecular dynamics (EEOMD) method, for studying electrolyte solution systems. The EEOMD method performs simulations at a fixed number of solvent molecules, pressure, temperature, and overall electrolyte chemical potential. The method combines elements of constant pressure-constant temperature molecular dynamics and expanded-ensemble grand canonical Monte Carlo. The simulated electrolyte solution systems contain, in addition to solvent molecules, full and fractional ions and undissociated electrolyte molecular units. The fractional particles are coupled to the system via a coupling parameter that varies between 0 (no interaction between the fractional particle and the other particles in the system) and 1 (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the constant pressure-constant temperature equations of motion and accompanied by random changes in the coupling parameter. The coupling-parameter changes are accepted with a probability derived from the expanded-ensemble osmotic partition function corresponding to the prescribed electrolyte chemical potential. The coupling-parameter changes mimic insertion/deletion of particles as in a crude grand canonical Monte Carlo simulation; if the coupling parameter becomes 0, the fractional particles disappear from the system, and as the coupling parameter reaches unity, the fractional particles become full particles. The method is demonstrated for a model of NaCl in water at ambient conditions. To test our approach, we first determine the chemical potential of NaCl in water by the thermodynamic integration technique and by the expanded-ensemble method. Then, we carry out EEOMD simulations for different specified values of the overall NaCl chemical potential and measure the concentration of ions resulting from the simulations. Both computations give consistent results, validating the EEOMD methodology.

Journal Article↗

PubMed1998

Effect of interparticulate interaction on release kinetics of microsphere ensembles.

The release kinetics of microsphere ensembles is complicated by the mutual influence of the microspheres which are entrapped in small compartments such as body cavities. This work focused on the effect of interparticulate interaction on the release kinetics of microsphere ensembles with limited spreading. Experiments and finite element modeling were conducted to investigate diffusional drug release from a single sphere, a monolayer, and multiple layers of microspheres. Poly(methyl methacrylate-co-methacrylic acid) (P(MMA/MAA)) microspheres and azidothymidine (AZT) were used in the experiments. The order of the release rate of AZT from various microsphere populations was observed to be single sphere > monolayer > multiple layers. This evidenced the importance of interparticulate interaction. The finite element simulations elucidated the influence of various factors on the release kinetics of microsphere ensembles including the separation distance, location of the spheres, and the drug accumulation in the medium. Calibration of overall release kinetics for the neighboring effect was proposed on the basis of the spreading factor. Overall release profiles of microsphere ensembles were predicted using the release profiles of individual microspheres at various locations.

Diffusion↗

PubMed2000

Imaging, image processing and pattern analysis of skin capillary ensembles.

BACKGROUND/AIMS: The capillary bed is recognized as the site where metabolic and nutrient processes occur for living tissues at all levels. The evaluation of this vital process is a major concern in microcirculation. Unlike traditional approaches that concentrated on the extreme local properties of this process, a more global analysis toward capillary ensembles is employed here, since capillaries work as a cooperative entirety. As a first step toward ensemble analysis, the static and planar geometric parameters are investigated. Parameters such as the capillary adjacency and size information are very important in predicting and analysing certain malfunctions in the microvascular bed. METHODS/RESULTS: In order to achieve an objective and accurate analysis of these vital parameters, a computerized imaging system is proposed. Not only the number of capillaries and the capillary cross-sectional areas are important in describing the microvascular bed but the planar distribution pattern of the capillaries also carries valid information. This information, unique to the ensemble analysis, can be used to reveal, visualise and quantify the clustering of capillaries; and this information, according to the Krogh model, is fundamental in estimating the tissue oxygen supply. Two spatial models, the closest neighbor and triangulation methods, have been applied to the captured images of capillary ensembles. The closest neighbor technique generates a minimal distance map or displays a distribution, which depicts the local clustering of capillaries. The triangulation technique, on the other hand, generates a mutual distance map, which is a global description of the capillary positions. Triangulation methods have been evaluated but all except the Greedy triangulation method have been rejected due to lack of robustness and model weakness. Therefore, the capillaries are triangulated by the Greedy triangulation method, and the capillary distribution uniformity is defined as one minus the coefficient of variance of the edge lengths of the mutual distance map. CONCLUSIONS: A series of advanced image processing methods have been developed that efficiently extract the capillary position, size and distribution information from the images. These results facilitate the automatic counting of capillaries and the capillary size-related pathological analysis.

Journal Article↗

PubMed2004

Semiclassical Liouville method for the simulation of electronic transitions: single ensemble formulation.

In this paper, we describe a single ensemble implementation of the semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, one ensemble of trajectories supports the evolution of all semiclassical density matrix elements, rather than employing a distinct ensemble for each. The ensemble evolves classically under a single reference Hamiltonian, which is chosen based on physical grounds; for electronic relaxation of an initially excited state, the initially populated upper surface Hamiltonian is the natural choice. Classical trajectories evolving on the reference potential then represent the time-dependent upper state population density and also the electronic coherence and the ground state density created by electronic transition. The error made in the classical motion of the trajectories for these latter distributions is compensated for by incorporating the difference between the correct and reference Liouville propagators into the calculation of the coefficients of the individual trajectories. This approach gives very accurate results for a number of model problems and cases describing ultrafast electronic relaxation dynamics.

Journal Article↗

PubMed2005

Phase coexistence in heterogeneous porous media: a new extension to Gibbs ensemble Monte Carlo simulation method.

The effect of confinement on phase behavior of simple fluids is still an area of intensive research. In between experiment and theory, molecular simulation is a powerful tool to study the effect of confinement in realistic porous materials, containing some disorder. Previous simulation works aiming at establishing the phase diagram of a confined Lennard-Jones-type fluid, concentrated on simple pore geometries (slits or cylinders). The development of the Gibbs ensemble Monte Carlo technique by Panagiotopoulos [Mol. Phys. 61, 813 (1987)], greatly favored the study of such simple geometries for two reasons. First, the technique is very efficient to calculate the phase diagram, since each run (at a given temperature) converges directly to an equilibrium between a gaslike and a liquidlike phase. Second, due to volume exchange procedure between the two phases, at least one invariant direction of space is required for applicability of this method, which is the case for slits or cylinders. Generally, the introduction of some disorder in such simple pores breaks the initial invariance in one of the space directions and prevents to work in the Gibbs ensemble. The simulation techniques for such disordered systems are numerous (grand canonical Monte Carlo, molecular dynamics, histogram reweighting, N-P-T+test method, Gibbs-Duhem integration procedure, etc.). However, the Gibbs ensemble technique, which gives directly the coexistence between phases, was never generalized to such systems. In this work, we focus on two weakly disordered pores for which a modified Gibbs ensemble Monte Carlo technique can be applied. One of the pores is geometrically undulated, whereas the second is cylindrical but presents a chemical variation which gives rise to a modulation of the wall potential. In the first case almost no change in the phase diagram is observed, whereas in the second strong modifications are reported.

Journal Article↗

PubMed2006

Geometrical cluster ensemble analysis of random sphere packings.

We introduce a geometric analysis of random sphere packings based on the ensemble averaging of hard-sphere clusters generated via local rules including a nonoverlap constraint for hard spheres. Our cluster ensemble analysis matches well with computer simulations and experimental data on random hard-sphere packing with respect to volume fractions and radial distribution functions. To model loose as well as dense sphere packings various ensemble averages are investigated, obtained by varying the generation rules for clusters. Essential findings are a lower bound on volume fraction for random loose packing that is surprisingly close to the freezing volume fraction for hard spheres and, for random close packing, the observation of an unexpected split peak in the distribution of volume fractions for the local configurations. Our ensemble analysis highlights the importance of collective and global effects in random sphere packings by comparing clusters generated via local rules to random sphere packings and clusters that include collective effects.

Algorithms↗