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Canalizing Kauffman networks: nonergodicity and its effect on their critical behavior.

Boolean networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean systems built from arbitrary ensembles of Boolean functions. In particular, we solve the critical condition for systems of units operating according to canalizing functions and present strong numerical evidence that our approach correctly predicts the phase transition from order to chaos in such systems.

Biophysics↗

Phase coexistence and dynamic properties of water in nanopores.

The dynamical properties of a confined fluid depend strongly on the (spatially varying) density. Its knowledge is therefore an important prerequisite for molecular-dynamics (MD) simulations and the analysis of experimental data. In a mixed Gibbs ensemble Monte Carlo (GEMC)/MD simulation approach we first apply the GEMC method to find possible phase states of water in hydrophilic and hydrophobic nanopores. The obtained phase diagrams evidence that a two-phase state is the most probable state of a fluid in incompletely filled pores in a wide range of temperature and level of pore filling. Pronounced variations of the average and local densities are observed. Subsequently, we apply constant-volume MD simulations to obtain water diffusion coefficients and to study their spatial variation along the pore radius. In general, water diffusivity slightly decreases in a hydrophilic pore and noticeably increases in a hydrophobic pore (up to about 40% with respect to the bulk value). In the range of gradual density variations the local diffusivity essentially follows the inverse density and the water binding energy. The diffusivity in the quasi-two-dimensional water layers near the hydrophilic wall decreases by 10 to 20% with respect to the bulk value. The average diffusivity of water in incompletely filled pore is discussed on the basis of the water diffusivities in the coexisting phases.

Computer Simulation↗

Analyzing neural responses to natural signals: maximally informative dimensions.

We propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli that are nongaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of a high-dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear. Existing analysis methods are based on correlation functions between stimuli and responses, but these methods are guaranteed to work only in the case of gaussian stimulus ensembles. As an alternative to correlation functions, we maximize the mutual information between the neural responses and projections of the stimulus onto low-dimensional subspaces. The procedure can be done iteratively by increasing the dimensionality of this subspace. Those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. If the dimensionality of the relevant subspace indeed is small, it becomes feasible to map the neuron's input-output function even under fully natural stimulus conditions. These ideas are illustrated in simulations on model visual and auditory neurons responding to natural scenes and sounds, respectively.

Acoustic Stimulation↗

Vertebrate gene finding from multiple-species alignments using a two-level strategy.

BACKGROUND: One way in which the accuracy of gene structure prediction in vertebrate DNA sequences can be improved is by analyzing alignments with multiple related species, since functional regions of genes tend to be more conserved. RESULTS: We describe DOGFISH, a vertebrate gene finder consisting of a cleanly separated site classifier and structure predictor. The classifier scores potential splice sites and other features, using sequence alignments between multiple vertebrate species, while the structure predictor hypothesizes coding transcripts by combining these scores using a simple model of gene structure. This also identifies and assigns confidence scores to possible additional exons. Performance is assessed on the ENCODE regions. We predict transcripts and exons across the whole human genome, and identify over 10,000 high confidence new coding exons not in the Ensembl gene set. CONCLUSION: We present a practical multiple species gene prediction method. Accuracy improves as additional species, up to at least eight, are introduced. The novel predictions of the whole-genome scan should support efficient experimental verification.

Animals↗

Influence of a reduced G-suit pressure schedule on G-duration tolerance using enhanced G-protection ensembles.

BACKGROUND: Reducing pressure to enhanced G-protection ensembles may diminish potential undesirable physiologic effects, as well as improve wear comfort and garment durability. HYPOTHESIS: G-duration tolerance will not be affected by reducing pressure to the Swedish tactical flight combat suit (TFCS). A second objective tested the similarity in G-duration tolerance between the TFCS and Combined Advanced Technology Enhanced Design G-Ensemble (COMBAT EDGE) combined with a prototype enhanced coverage G-suit. METHODS: There were 12 Swedish pilots (mean = 30 yr) who experienced gradual onset (+0.1 G.s-1) runs (GOR) to +9 Gz, rapid (+6 G.s-1) onset runs (ROR) and simulated aerial combat maneuvers (SACM) with +5 to +9 Gz cycles. The GOR and ROR profiles had a sustained times of 60 s after reaching +9 Gz. RESULTS: GOR duration tolerance was statistically decreased (p < 0.01) by the lower pressure (1.1 psig.G-1) when compared to standard pressure (1.5 psig.G-1). No statistical difference between TFCS and COMBAT EDGE was observed during the GOR trials. For all conditions, during the RORs, 90% of the subjects completed at least 30 s at +9 Gz. Many technical or medical difficulties during SACM trials limited statistical treatment of these data. However, no obvious among-condition differences were observed. Noteworthy among SACM trials were those of 3 subjects enduring more than 9 min before stopping; one completing 12.5 min (35 cycles). Neither heart rate, blood pressure, nor perceived exertion data revealed a condition-effect difference. CONCLUSION: Moderately reduced pressure to the extended coverage anti-G suit, combined with positive pressure breathing, may yield decreased G-tolerance results during laboratory evaluation; however, observed differences are sufficiently small they are likely operationally insignificant.

Adult↗

Replacement of steric 6-12 potential-derived interaction energies by atom-based indicator variables in CoMFA leads to models of higher consistency.

The steric descriptors commonly used in CoMFA--Lennard-Jones 6-12 potential-derived interaction energies calculated between a probe atom and the molecules under investigation--have been replaced by variables indicating the presence of an atom of a particular molecule in predefined volume elements (cubes) within the region enclosing the ensemble of superimposed molecules. The resulting 'atom indicator vectors' were used as steric fields in the subsequent PLS analyses, with and without inclusion of electrostatic Coulomb interaction-derived fields. Application of this method to five training sets (80 compounds each) and five test sets (60 compounds each), randomly selected from an ensemble of 256 dihydrofolate reductase inhibitors, leads to models of significantly higher consistency, as indicated by the cross-validated r2 values for the training sets and the predictive r2 values for the test sets.

Computer Simulation↗

Precision of mean transit time measurements in 99Tcm-DTPA renal scintigraphy: a Monte Carlo study.

The precision of renal mean transit time (MTT) measurements by 99Tcm-DTPA scintigraphy was studied by a Monte Carlo procedure. Data were obtained from twenty mild essential hypertensives with normal renal function. An ensemble of equivalent data sequences was constructed for each renal time-activity curve (TAC), assuming the dominant noise in the data to be Poisson in character. TACS were deconvolved by the matrix method and MTT was inferred from retention functions by a procedure entailing a nonlinear least-squares minimization. For every ensemble of data sequences a distribution of MTTs was generated. The population-averaged coefficients of variation for these distributions were 1.6% and 2.6%, for whole-kidney and cortical data, respectively. We conclude that the precision of MTT determination from clinical data is comparable to that from simulated data. MTT measurements may be useful for detecting functional changes in individual kidneys following an intervention such as angiotensin-converting-enzyme inhibition.

Algorithms↗

Error estimates for results of nonstationary noise analysis derived with linear least squares methods.

Nonstationary noise analysis of electrophysiological data is applied to the estimation of the single-channel current, i, and the number of active channels, N(C), whenever they cannot be determined directly due to limited resolution. Using least squares methods, the accuracy of estimating i and N(C) chiefly depends on the statistical error of the ensemble variance. It is shown that if the correlation among the binned data points is taken into account correctly, the variability of i and N(C) can be remarkably reduced and exact confidence limits of the parameters can be calculated. Least-squares methods are introduced which consider the measured error-covariance matrix of the binned variance in a model-independent fashion. Employing Monte Carlo methods, it is demonstrated that both the error predictions and the confidence limits are correct. The method is used to investigate the performance of nonstationary noise analysis at low channel open-probabilities. The application of the approach to simulated data as well as to experimental, i.e. non-ideal, data is discussed.

Animals↗

Range- and azimuth-dependent variability of image texture in two-dimensional echocardiograms.

Regional two-dimensional (2D) echocardiographic amplitude patterns, or image texture, may be of diagnostic importance. Echocardiographic image texture is due in part to acoustic speckle, a complex pattern of interference of reflections from many small scatterers in tissue. The regional speckle pattern appears to be altered in several disorders associated with abnormalities in myocardial structure but also may be altered by a variety of characteristics of the scanning instrument. We hypothesized that quantitative measures of regional 2D echocardiographic image texture would vary as a function of position in range and azimuth within the field of view, even when imaging a uniform ensemble of scatterers. We tested this hypothesis by imaging a tissue-equivalent phantom with two phased-array scanners and two different methods of digitization. We analyzed the texture in several regions of interest separated in range and azimuth and found significant differences in quantitative texture measures as a function of position of the region of interest in the sector field of view (p values .006 to .0001 by multivariate analysis of variance). We found significant regional variability in texture with both scanners and both methods of digitization. We conclude that regional quantitative image texture in 2D echocardiograms varies as a function of range and azimuth, even when imaging a uniform ensemble of scatterers. This variability is related to several physical and instrument-related phenomena and precludes interpreting all regional texture alterations as indicating tissue structural abnormalities.

Echocardiography↗

Improving the ensemble average of visual evoked potentials. II. Simulations and experiments.

Ensemble averaging is generally used for the estimation of Evoked Potentials. This paper deals with the assessment of correction procedures for the time variability of the ensemble components, this time variability reduces the improvement of the signal-to-noise ratio (SNR) by averaging. Evoked potentials were estimated by ensemble averaging, synchronized to a periodic stimulus. It is assumed that VEP-instability is partly caused by time-variability of the evoked potentials. Two time-variate models were used, from which procedures were derived to correct the single VEP-responses prior to ensemble averaging. The models are: (1) variation in response delay (jitter), (2) variable compression/expansion of the time scale of the response (wow). The Spectral Phase Difference method was applied to estimate both the delay time jitter and the wow factor of single responses with respect to a template (conventional ensemble average). The effects of the devised correction on the average VEP waveform and on the SNR of the ensemble were investigated by using data from realistic simulations and from experiments (n = 23) with a number of healthy human volunteers (n = 17). Jitter- and wow-corrections were effective on simulations with time variability due to delay time jitter and time scale distortion (wow), respectively. Both wow- and jitter correction of the single responses improved the SNR of the VEP measurements significantly and to the same amount. A combined wow-jitter approach resulted in significantly better results than the exclusive application of jitter- or wow correction.

Computer Simulation↗

A rapid computational method for lead evolution: description and application to alpha(1)-adrenergic antagonists.

The high failure rate of drugs in the development phase requires a strategy to reduce risks by generating lead candidates from different chemical classes. We describe a new three-dimensional computational approach for lead evolution, based on multiple pharmacophore hypotheses. Using full conformational models for both active and inactive compounds, a large number of pharmacophore hypotheses are analyzed to select the set or "ensemble" of hypotheses that, when combined, is most able to discriminate between active and inactive molecules. The ensemble hypothesis is then used to search virtual chemical libraries to identify compounds for synthesis. This method is very rapid, allowing very large virtual libraries on the order of a million compounds to be filtered efficiently. In applying this method to alpha(1)-adrenergic receptor ligands, we have demonstrated lead evolution from heterocyclic alpha(1)-adrenergic receptor ligands to highly dissimilar active N-substituted glycine compounds. Our results also show that the active N-substituted glycines are part of our smaller filtered library and thus could have been identified by synthesizing only a portion of the N-substituted glycine library.

Adrenergic alpha-Antagonists↗

[Experimental investigation on the reproducibility of ensemble-averaged electromyographic gait analysis data in the area of experimental and clinical orthopaedics].

With suitable application and signal processing methods, surface electromyography is a comparatively simple instrument for investigating the temporal pattern of the muscular activity of a walking subject. The influence of changes both in the external experimental conditions (e.g. orthopedic shoe design) and in the human locomotor system (due to disease or therapy) on the individual muscular gait characteristics can be documented in this way. The usefulness of this kind of investigation is basically limited by the reproducibility of the gait analytical findings of the subject, who is examined at different times with unchanged bodily state and under identical experimental conditions unchanged. In our experiments we observed that the reproducibility of electromyographic activity curves obtained by ensemble averaging over a sufficiently high number of full strides differs for different muscles and in different subjects. Within the same experimental session it is very high and considerably better than in experiments done on different days. In examinations done on different days the basic characteristics of the activity curves are reproduced better than the absolute height of the amplitudes. In view of these findings the differences observed in the gait analysis of patients in the course of operative or conservative therapy have to be interpreted very carefully as to their true origin.

Algorithms↗

Understanding ensemble protein folding at atomic detail.

It has long been known that a protein's amino acid sequence dictates its native structure. However, despite significant recent advances, an ensemble description of how a protein achieves its native conformation from random coil under physiologically relevant conditions remains incomplete. Here we present a detailed all-atom model with a transferable potential that is capable of ab initio folding of entire protein domains using only sequence information. The computational efficiency of this model allows us to perform thousands of microsecond-time scale-folding simulations of the engrailed homeodomain and to observe thousands of complete independent folding events. We apply a graph-theoretic analysis to this massive data set to elucidate which intermediates and intermediary states are common to many trajectories and thus important for the folding process. This method provides an atomically detailed and complete picture of a folding pathway at the ensemble level. The approach that we describe is quite general and could be used to study the folding of proteins on time scales orders of magnitude longer than currently possible.

Algorithms↗

Modification of a technique for support of thin, flexible tissues for microscopic examination: application to turkey air sac membranes.

Modifications to the ring-stabilization technique for collection of avian air sac membranes were developed to allow dehydration and paraffin embedding of samples to be done by an automated system and to simplify processing for transmission electron microscopy (TEM). The modified collection method utilized a pair of rings that were snapped together across an intervening membrane sample. The tissue and ring ensemble was embedded as a unit. Paraffin-embedded tissues were collected with aluminum rings, whereas samples for TEM were collected with rings made of polymerized embedding medium. Tissue sections of excellent quality were obtained with the method. The technique is shown to be applicable to immunohistochemical studies.

Air Sacs↗

The equilibrium partition function and base pair binding probabilities for RNA secondary structure.

A novel application of dynamic programming to the folding problem for RNA enables one to calculate the full equilibrium partition function for secondary structure and the probabilities of various substructures. In particular, both the partition function and the probabilities of all base pairs are computed by a recursive scheme of polynomial order N3 in the sequence length N. The temperature dependence of the partition function gives information about melting behavior for the secondary structure. The pair binding probabilities, the computation of which depends on the partition function, are visually summarized in a "box matrix" display and this provides a useful tool for examining the full ensemble of probable alternative equilibrium structures. The calculation of this ensemble representation allows a proper application and assessment of the predictive power of the secondary structure method, and yields important information on alternatives and intermediates in addition to local information about base pair opening and slippage. The results are illustrated for representative tRNA, 5S RNA, and self-replicating and self-splicing RNA molecules, and allow a direct comparison with enzymatic structure probes. The effect of changes in the thermodynamic parameters on the equilibrium ensemble provides a further sensitivity check to the predictions.

Animals↗

Comparison of free energy methods for molecular systems.

We present a detailed comparison of computational efficiency and precision for several free energy difference (DeltaF) methods. The analysis includes both equilibrium and nonequilibrium approaches, and distinguishes between unidirectional and bidirectional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration, and single-ensemble path sampling to more established methodologies. As test cases, we study relative solvation free energies of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation DeltaF estimates as compared to other methods used in this report, while also offering rapid estimation of DeltaF. The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the unidirectional, "fast-growth" nonequilibrium case. Closer examination of the path sampling approach on a two-dimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.

Models, Chemical↗

A mini-review of mass spectrometry using high-performance FTICR-MS methods.

Structural characterization of macromolecules is currently delivering new insights into the behavior of individual molecules or molecular ensembles. Technological advances have made it possible to examine smaller and smaller amounts (down to single molecules) of larger and larger molecular systems. Mass spectrometry in particular is capable of the detailed study of extremely small quantities (down to a single molecule) of very large (biological) molecules. The advent of new ionization techniques such as electrospray and matrix-assisted laser desorption are mainly responsible for these advances. As a result, mass spectrometry has evolved into an enabling discipline that plays an increasingly important role in combinatorial chemistry, polymer science, biochemistry, medicine, environmental and marine science, and archaeology and conservation science. This paper will review a selection of methodological developments in the field of high-performance Fourier transform ion cyclotron resonance mass spectrometry for structural analysis of these macromolecules.

Journal Article↗

DNA library design for molecular computation.

A novel approach to designing a DNA library for molecular computation is presented. The method is employed for encoding binary information in DNA molecules. It aims to achieve a practical discrimination between perfectly matched DNA oligomers and those with mismatches in a large pool of different molecules. The approach takes into account the ability of DNA strands to hybridize in complex structures like hairpins, internal loops, or bulge loops and computes the stability of the hybrids formed based on thermodynamic data. A dynamic programming algorithm is applied to calculate the partition function for the ensemble of structures, which play a role in the hybridization reaction. The applicability of the method is demonstrated by the design of a twelve-bit DNA library. The library is constructed and experimentally tested using molecular biology tools. The results show a high level of specific hybridization achieved for all library words under identical conditions. The method is also applicable for the design of primers for PCR, DNA sequences for isothermal amplification reactions, and capture probes in DNA-chip arrays. The library could be applied for integrated DNA computing of twelve-bit instances of NP-complete combinatorial problems by multi-step DNA selection in microflow reactors.

Algorithms↗