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PubMed1991

Long-term optical recording of patterns of electrical activity in ensembles of cultured Aplysia neurons.

1. Left upper quadrant (LUQ) cells isolated from the abdominal ganglion of Aplysia were maintained in culture to study how the cellular and synaptic properties of individual neurons contribute to the generation of patterns of electrical activity by neuronal ensembles. 2. Conventional microelectrodes were used to examine the spiking characteristics of individually cultured LUQ cells in vitro and to characterize their synaptic interactions. 3. In vitro, in contrast to in situ, LUQ neurons innervate other LUQ neurons. Intracellular recordings from pairs of LUQ cells showed that the prevalent type of postsynaptic potential was purely inhibitory. The other type of response was a dual-action postsynaptic potential, with inhibition followed by a delayed, slow excitation. 4. We established a set of criteria for the use of multiple-site optical recording techniques, in combination with impermeant probes of membrane potential, to observe the patterns of electrical activity generated by ensembles of co-cultured LUQ cells. 5. The spiking activity of individual cells within the neuronal ensembles was detected by means of the change in optical absorption of cells that were vitally stained with the dye RH155. The change in absorption was typically delta A congruent to 4 X 10(-4) per spike. We achieved a signal-to-noise (peak-to-peak) ratio of approximately 10 for a 50 X 50-microns photodetector field and an incident intensity of approximately 10 mW/cm2, close to the theoretical limit. 6. These conditions permitted, for the first time, continuous optical recording from cultured neurons for periods of up to 3 h with no discernible photodynamic damage or photobleaching. This long-term optical recording permitted examination of the different patterns of electrical activity generated by individual neuronal ensembles under several different experimental conditions. 7. An elaborate tracery of regenerated neurites present in these cultures resulted in individual photodetectors recording simultaneously the activity of multiple neurons. We reconstructed the temporal firing patterns for individual neurons within ensembles even with all the neurons active simultaneously and determined the functional connections in the ensemble by analyzing the temporal relationships between firing patterns of individual neurons. Excitatory as well as inhibitory functional interactions could be observed within the neuronal ensemble, the latter after the tonic activity of the neurons was increased by reducing the extracellular [Mg2+]. 8. Examination of the optical data from ensembles constructed from identified cells having characteristic physiological responses allowed us to address the question of how cellular and synaptic properties affect the patterns of electrical activity generated by neuronal ensembles.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed2001

Calculation of ensembles of structures representing the unfolded state of an SH3 domain.

The N-terminal SH3 domain of drk (drkN SH3 domain) exists in equilibrium between a folded (F(exch)) and an unfolded (U(exch)) form under non-denaturing conditions. In order to further our previous descriptions of the U(exch) state, we have developed a protocol for calculating ensembles of structures, based on experimental spectroscopic data, which broadly represent the unfolded state. A large number of unfolding trajectories were generated, starting from the folded state structure of the protein, in order to provide a reasonable sampling of the conformational space accessible to this sequence. Unfolded state ensembles have been "calculated" using a newly developed program ENSEMBLE, which optimizes the population weights assigned to each structure based on experimental properties of the U(exch) state. Pseudo-energy terms for nuclear Overhauser effects, J-coupling constants, (13)C chemical shifts, translational diffusion coefficients and tryptophan ring burial based on NMR and fluorescence data have been implemented. The population weight assignment procedure was performed for different starting ensembles. Small numbers of structures (<60) dominate the final ensembles compared to the total number in the starting ensembles, suggesting that the drkN SH3 domain U(exch) state can be described by a limited number of lower-energy conformations. The calculated U(exch) state ensembles are much more compact than a "random coil" chain, with significant native-like residual structure observed. In particular, a sizable population of conformers having the n-src loop and distal beta-hairpin structures exist in the calculated U(exch) state ensembles, and Trp36 is involved in a large number of interactions, both native and non-native.

Animals↗

PubMed2002

Lung cancer cell identification based on artificial neural network ensembles.

An artificial neural network ensemble is a learning paradigm where several artificial neural networks are jointly used to solve a problem. In this paper, an automatic pathological diagnosis procedure named Neural Ensemble-based Detection (NED) is proposed, which utilizes an artificial neural network ensemble to identify lung cancer cells in the images of the specimens of needle biopsies obtained from the bodies of the subjects to be diagnosed. The ensemble is built on a two-level ensemble architecture. The first-level ensemble is used to judge whether a cell is normal with high confidence where each individual network has only two outputs respectively normal cell or cancer cell. The predictions of those individual networks are combined by a novel method presented in this paper, i.e. full voting which judges a cell to be normal only when all the individual networks judge it is normal. The second-level ensemble is used to deal with the cells that are judged as cancer cells by the first-level ensemble, where each individual network has five outputs respectively adenocarcinoma, squamous cell carcinoma, small cell carcinoma, large cell carcinoma, and normal, among which the former four are different types of lung cancer cells. The predictions of those individual networks are combined by a prevailing method, i.e. plurality voting. Through adopting those techniques, NED achieves not only a high rate of overall identification, but also a low rate of false negative identification, i.e. a low rate of judging cancer cells to be normal ones, which is important in saving lives due to reducing missing diagnoses of cancer patients.

Adenocarcinoma↗

PubMed2006

Evaluation of stability of k-means cluster ensembles with respect to random initialization.

Many clustering algorithms, including cluster ensembles, rely on a random component. Stability of the results across different runs is considered to be an asset of the algorithm. The cluster ensembles considered here are based on k-means clusterers. Each clusterer is assigned a random target number of clusters, k and is started from a random initialization. Here, we use 10 artificial and 10 real data sets to study ensemble stability with respect to random k, and random initialization. The data sets were chosen to have a small number of clusters (two to seven) and a moderate number of data points (up to a few hundred). Pairwise stability is defined as the adjusted Rand index between pairs of clusterers in the ensemble, averaged across all pairs. Nonpairwise stability is defined as the entropy of the consensus matrix of the ensemble. An experimental comparison with the stability of the standard k-means algorithm was carried out for k from 2 to 20. The results revealed that ensembles are generally more stable, markedly so for larger k. To establish whether stability can serve as a cluster validity index, we first looked at the relationship between stability and accuracy with respect to the number of clusters, k. We found that such a relationship strongly depends on the data set, varying from almost perfect positive correlation (0.97, for the glass data) to almost perfect negative correlation (-0.93, for the crabs data). We propose a new combined stability index to be the sum of the pairwise individual and ensemble stabilities. This index was found to correlate better with the ensemble accuracy. Following the hypothesis that a point of stability of a clustering algorithm corresponds to a structure found in the data, we used the stability measures to pick the number of clusters. The combined stability index gave best results.

Algorithms↗

PubMed2005

Trial-by-trial discrimination of three enantiomer pairs by neural ensembles in mammalian olfactory bulb.

Populations of output neurons in the mammalian olfactory bulb (OB) exhibit distinct, widespread spatial and temporal activation patterns when stimulated with odorants. However, questions remain as to how ensembles of mitral/tufted (M/T) neurons in the mammalian OB represent odorant information. In this report, the single-trial encoding limits of random ensembles of putative single- and multiunit M/T cells in the anesthetized rat OB during presentations of enantiomers of limonene, carvone, and 2-butanol are investigated using simultaneous multielectrode recording techniques. The results of these experiments are: the individual constituents of our recorded ensembles broadly represent information about the presented odorants, the ensemble single-trial response of small spatially distributed populations of M/T neurons can readily discriminate between six different odorants, and the most consistent odorant discrimination is attained when the ensemble consists of all available units and their responses are integrated over an entire breathing cycle. These results suggest that small differences in spike counts among the ensemble members become significant when taken within the context of the entire ensemble. This may explain how ensembles of broadly tuned OB neurons contribute to olfactory perception and may explain how small numbers of individual units receiving input from distinct olfactory receptor neurons can be combined to form a robust representation of odorants.

Action Potentials↗

PubMed1995

Information coding in the rodent prefrontal cortex. II. Ensemble activity in orbitofrontal cortex.

1. Neural activity was recorded from the orbitofrontal cortex (OF) of rats performing an eight-odor discrimination task that included predictable associations between particular odor pairs. A modified linear discriminant analysis was employed to characterize the population response in each trial of the task as a point in an N-dimensional activity space with the firing rate of each cell in the population represented on one of the N dimensions. The ability of the ensemble to discriminate among conditions of a variable was reflected in the tendency of population responses to cluster together in this activity space for repetitions of a given condition. We assessed coding of several variables describing the period of odor sampling, focusing on aspects of current, past, and future events reflected in single-neuron firing patterns, in ensembles composed of 22-138 cells active during the period when the rats sampled the discriminative stimulus in each trial. 2. OF ensembles performed well at discriminating variables with relevance to task demands represented in single-neuron firing patterns, specifically the physical attributes and assigned reward contingency of the current odor as well as the expectation of reward in the following trial that could be inferred from the predictable associations between particular pairs of odors. OF ensembles were able to correctly identify the identity and assigned reward contingency of the current odor in up to 52% (chance = 12.5%) and 99% (chance = 50%) of all trials, respectively, such that the observed behavioral performance required a population of 5,364 odor-responsive cells in the case of odor identity and only 40 cells in the case of valence. Expectations regarding upcoming rewards based on both assigned response contingency and associations between particular pairs of odors were correctly classified in up to 67% (chance = 20%) of all trials such that the observed level of behavioral performance required a population of 3,169 cells. 3. Other information represented in the single-neuron firing patterns, such as the identity and reward contingency of the preceding odor and specific odor-odor associations, was poorly encoded by OF ensembles. Thus neural ensembles in OF may represent only some of the information reflected in single-neuron activity. Stable coding of only the most useful and relevant information by the ensemble might emerge from the tuning properties of single neurons under the influence of the task at hand, producing in the well-trained animal the observed pattern of broad and diverse coding by single neurons and selective, task-relevant coding by neural ensembles in OF.

Animals↗

PubMed1996

A numerical simulation of muscle spindle ensemble encoding during planar movement of the human arm: correlation sensitivity and parameter dependence.

We extend the analysis developed in the preceding paper in which we correlated kinematic parameters of planar movements of the human arm made by subjects moving to a visual target with numerical estimates of the ensemble encoding of muscle spindles within some of the muscles of this limb. Three possible models for the inclusion of noise in the calculations of the ensemble encodings are considered: (i) random errors in the angular coordinates from which muscle fascicle, and hence spindle length are calculated, (ii) variability of spindle discharge rates, and (iii) variability in the calculation of the ensemble encoding. In each case the correlations between kinematic variables of the movements and the resultant ensemble encodings decrease as the contribution of the noise term to the calculation of the encodings increases. Subject to the constraint that the magnitude of the noise term remains within physiologically realistic limits, however, the observed correlations persist at statistically significant levels. We also investigate the dependence of the observed correlations on the choice of model parameters, namely (i) the absolute and relative contributions made by simulated spindle primary and secondary afferents to the ensemble encoding, (ii) the inclusion of explicit length-related terms in the model of muscle spindle discharge, and (iii) the fractional power of velocity experienced by the model spindles during movement. The resulting correlations are approximately independent of both the fractional power of velocity and absolute firing levels of both the primary and secondary afferents of the spindle model. The inclusion of explicit length-dependent terms in the model does result in differences in the observed correlation coefficients. In this case, however, the magnitudes of the differences are small. On the basis of these findings we conclude that the correlations between kinematic variables of movement and the associated ensemble encodings are robust with regard to both the choice of model parameters and noise inherent at all stages of the transduction and processing of proprioceptive information. The findings of the present study provide further evidence, therefore, to support the hypothesis that motor structures capable of deriving such an ensemble encoding would be provided with information regarding ongoing movements in both intrinsic (body-centered) and extrinsic (Cartesian) coordinate systems.

Animals↗

PubMed2026

One chromatin, many structures: From ensemble contact maps to single-cell 3D organization.

Understanding how chromatin folds in three dimensions remains challenging because most experimental assays capture low-dimensional projections of an underlying, highly heterogeneous polymer. Here, we present an ensemble-based interpretive framework built on the previously introduced Self-Returning Excluded Volume (SR-EV) model, a minimal generator of chromatin conformations using a nucleosome-indexed coarse-grained representation based on stochastic return rules and excluded-volume geometry. Despite its simplicity, SR-EV recapitulates key experimental signatures across scales: heterogeneous nanoscale packing domains resembling ChromEMT and ChromSTEM observations, sparse and highly variable single-configuration contact patterns analogous to single-cell chromosome conformation capture (Hi-C), and robust ensemble-level contact enrichment consistent with topologically associating domains (TADs). In this framework, Hi-C loop and TAD signatures are interpreted as ensemble-level statistical enrichments rather than invariant features of single-cell conformations. SR-EV is explicitly designed to generate large ensembles of complete three-dimensional chromatin configurations that can be projected consistently onto two-dimensional contact maps and one-dimensional genomic profiles. By introducing architectural-protein effects only through ensemble selection rather than explicit forces, SR-EV supports a separation between intrinsic polymer geometry and regulatory bias and suggests that TAD-like features can emerge as statistical enrichments rather than deterministic three-dimensional structures. Coordination number and probe-based accessibility computed directly from SR-EV provide a unified link between three-dimensional packing, two-dimensional contact maps, and one-dimensional genomic profiles. The main contribution of this work is to show, within a single coarse-grained framework, how these multimodal observables arise as linked projections of the same heterogeneous chromatin ensemble through averaging and conditional sampling. Together, these results establish SR-EV as a minimal and geometrically grounded mesoscale reference framework for interpreting how heterogeneous chromatin ensembles give rise to multimodal experimental observables while remaining consistent with the fact that chromatin organization is realized in individual cells.

Chromatin↗

PubMed2025

Pioneer in Molecular Biology: Conformational Ensembles in Molecular Recognition, Allostery, and Cell Function.

In 1978, for my PhD, I developed the efficient O(n3) dynamic programming algorithm for the-then open problem of RNA secondary structure prediction. This algorithm, now dubbed the "Nussinov algorithm", "Nussinov plots", and "Nussinov diagrams", is still taught across Europe and the U.S. As sequences started coming out in the 1980s, I started seeking genome-encoded functional signals, later becoming a bioinformatics trend. In the early 1990s I transited to proteins, co-developing a powerful computer vision-based docking algorithm. In the late 1990s, I proposed the foundational role of conformational ensembles in molecular recognition and allostery. At the time, conformational ensembles and free energy landscapes were viewed as physical properties of proteins but were not associated with function. The classical view of molecular recognition and binding was based on only two conformations captured by crystallography: open and closed. I proposed that all conformational states preexist. Proteins always have not one folded form-nor two-but many folded forms. Thus, rather than inducing fit, binding can work by shifting the ensembles between states, and this shifting, or redistributing the ensembles to maintain equilibrium, is the origin of the allosteric effect and protein, thus cell, function. This transformative paradigm impacted community views in allosteric drug design, catalysis, and regulation. Dynamic conformational ensemble shifts are now acknowledged as the origin of recognition, allostery, and signaling, underscoring that conformational ensembles-not proteins-are the workhorses of the cell, pioneering the fundamental idea that dynamic ensembles are the driving force behind cellular processes. Nussinov was recognized as pioneer in molecular biology by JMB.

Molecular Biology↗

PubMed2001

Pulsed flow modulation for high-speed GC using a pressure-tunable column ensemble.

A computer-driven pressure controller is used to deliver pressure pulses to the junction point of two series-coupled columns using different stationary-phase chemistries. The column ensemble consists of a trifluoropropylmethyl polysiloxane column followed by a dimethyl polysiloxane column. Each pressure pulse causes a differential change in the carrier gas velocities in the two columns, which lasts for the duration of the pulse. A pressure pulse is used to selectively increase the separation of a component pair that is separated by the first column but coelutes from the series-coupled ensemble. If both components are on the same column when the pulse is applied, a small change in the ensemble separation occurs. If one component of the pair is on the first column and the other component is on the second column, a pressure pulse can result in a much larger change in the ensemble separation for the component pair. A model with a spreadsheet algorithm is used to predict the effects of a pressure pulse on the trajectories of component bands on the column ensemble. The effect of the initiation time of a pressure pulse is investigated for a two-component mixture that coelutes from the column ensemble. For the case where the entire pressure pulse occurs when one of the components is on the first column and the other component is on the second column, the peak separation from the ensemble increases nearly linearly with the product of the pressure pulse amplitude and the pulse duration. Peak shape artifacts are observed if the pressure pulse occurs when a solute band is migrating across the column junction point.

Journal Article↗

PubMed1999

Correct microcanonical ensemble in molecular dynamics.

The statistical-mechanics ensemble corresponding to equilibrium molecular dynamics simulations is different than the usual microcanonical EVN ensemble. Historically molecular dynamics has been associated with the EVNM ensemble, where M is the constant total linear momentum of the system. We show that the correct ensemble associated with molecular dynamics is the EVNMG ensemble where G is the constant of the motion associated with Galilean boosts. The ensemble associated with molecular dynamics simulations has, apparently, not been previously recognized. An earlier problem with the pressure in the new ensemble disappears.

Journal Article↗

PubMed2000

Molecular dynamics ensemble, equation of state, and ergodicity.

The variant of the NVE ensemble known as the molecular dynamics ensemble was recently redefined by Ray and Zhang [Phys. Rev. E 59, 4781 (1999)] to include the specification of a time invariant G (a function of phase and, explicitly, the time) in addition to the total linear momentum M. We reformulate this ensemble slightly as the NVEMR ensemble, in which R/N is the center-of-mass position, and consider the equation of state of the hard-sphere system in this ensemble through both the virial function and the Boltzmann entropy. We test the quasiergodic hypothesis by a comparison of old molecular dynamics and Monte Carlo results for the compressibility factor of the 12-particle, hard-disk systems. The virial approach, which had previously been found to support the hypothesis in the NVEM ensemble, remains unchanged in the NVEMR ensemble. The entropy S approach depends on whether S is defined through the phase integral over the energy sphere or the energy shell, the parameter straight theta being 0 or 1, respectively. The ergodic hypothesis is found to be supported for straight theta=0 but not for straight theta=1.

Journal Article↗

PubMed2002

Skew-orthogonal polynomials and random-matrix ensembles.

There is considerable interest in understanding the relation between random-matrix ensembles and quantum chaotic systems in the context of the universality of energy-level correlations. In this connection, while Gaussian ensembles of random matrices have been studied extensively, not much is known about ensembles with non-Gaussian weight functions. Dyson has shown that the n-level correlation functions can be expressed in terms of a kernel function involving orthogonal and skew-orthogonal polynomials--orthogonal for matrix ensembles with unitary invariance and skew orthogonal for ensembles with orthogonal and symplectic invariances. We have obtained the following results. (1) Skew-orthogonal polynomials of both types are derived for the Jacobi class of weight functions including the limiting cases of associated Laguerre and Hermite (or Gaussian). (2) Matrix-integral representations are given for the general weight functions. (3) Asymptotic forms of the polynomials are obtained rigorously for the Jacobi class and in the form of an ansatz for the general case. (4) For the three types of ensembles, the (asymptotic) n-level correlation functions with appropriate scaling are shown to be universal, being independent of the weight function and location in the spectrum, and identical with the well-known Gaussian results. This provides a rigorous justification for the universality of the Gaussian ensemble results observed in quantum chaotic systems. As expected, the level density is not universal.

Journal Article↗

PubMed2004

Random matrix ensembles from nonextensive entropy.

The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S(BGS) = -integral dH[P(H)]ln[P(H)], with suitable constraints. Here, we construct and analyze random-matrix ensembles arising from the generalized entropy S(q) = [1- integral dH [P(H)](q)] /(q-1) (thus, S1 = S(BGS) ). The resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form. Making q-->1 recovers the Gaussian ensembles. If q not equal 1, the joint probability distributions P(H) cannot be factorized, i.e., the matrix elements of H are correlated. In the limit of large matrices two different regimes are observed. When q<1, P(H) has compact support, and the fluctuations tend asymptotically to those of the Gaussian ensembles. Anomalies appear for q>1 : Both P(H) and the marginal distributions P( H(ij) ) show power-law tails. Numerical analyses reveal that the nearest-neighbor spacing distribution is also long-tailed (not Wigner-Dyson) and, after proper scaling, very close to the result for the 2 x 2 case--a generalization of Wigner's surmise. We discuss connections of these "nonextensive" ensembles with other non-Gaussian ones, such as the so-called Lévy ensembles and those arising from soft confinement.

Journal Article↗

PubMed2003

Medical diagnosis with C4.5 Rule preceded by artificial neural network ensemble.

Comprehensibility is very important for any machine learning technique to be used in computer-aided medical diagnosis. Since an artificial neural network ensemble is composed of multiple artificial neural networks, its comprehensibility is worse than that of a single artificial neural network. In this paper, C4.5 Rule-PANE which combines artificial neural network ensemble with rule induction by regarding the former as a preprocess of the latter, is proposed. At first, an artificial neural network ensemble is trained. Then, a new training data set is generated by feeding the feature vectors of the original training instances to the trained ensemble and replacing the expected class labels of the original training instances with the class labels output from the ensemble. Additional training data may also be appended by randomly generating feature vectors and combining them with their corresponding class labels output from the ensemble. Finally, a specific rule induction approach, i.e., C4.5 Rule, is used to learn rules from the new training data set. Case studies on diabetes, hepatitis, and breast cancer show that C4.5 Rule-PANE could generate rules with strong generalization ability, which profits from artificial neural network ensemble, and strong comprehensibility, which profits from rule induction.

Diagnosis↗

PubMed2004

Spatiotemporal encoding of a bar's direction of motion by neural ensembles in cat primary visual cortex.

Directionally selective neurons strongly fire when presented with a preferred direction of motion of a bar and only weakly respond otherwise. Intuition suggests these "specialist" neurons would be better suited to report this stimulus feature to higher visual centers than "generalist" neurons, neurons that broadly modulate their activity to the feature. However, as stimuli are encoded not by one cell but by large neural ensembles, we have studied the role of single-cell receptive field properties in stimulus representation. Using regression error statistics, we compared the performance of direction-of-motion estimators, using ensembles of neurons selectively responding to direction of motion and estimators using ensembles not specializing to direction. We found that direction-selective ensembles were no better at representing a bar's direction of motion than nonselective ensembles. Quite the opposite, the nonselective unit ensembles provided a better estimate of the direction (standard deviation of the error of 33 degrees) than the direction-selective ensembles (standard deviation of the error of 42 degrees). The nonselective neurons provided information through a latency code that is apparent only when a neuron's activity is considered in the context of the responses of neighboring neurons. These results suggest that models utilizing both generalist and specialist neurons may better reflect the encoding mechanisms that take place in sensory pathways.

Action Potentials↗

PubMed1995

Building clinical classifiers using incomplete observations--a neural network ensemble for hepatoma detection in patients with cirrhosis.

One objective of liver transplant evaluation is to identify patients that harbor a hepatoma, but standard screening techniques are not sensitive enough. We trained neural network ensembles to predict the presence of hepatoma in patients with cirrhosis, based on information collected at the time of transplant evaluation. Network architecture and training were modified to handle missing observations. Three ensembles were trained: ensemble A using the subset with no missing observations (528 patients); ensemble B using the complete set, which included missing observations (853 patients); and ensemble C using the smaller subset, originally with complete data, but after a fixed number of observations were deleted (i.e., made "missing"). Ensemble performance on testing sets was very good. The areas under the ROC curves were 0.91, 0.89, and 0.90, for ensembles A, B, and C, respectively. Neural networks can successfully perform this classification task, and strategies can be developed that allow use of incomplete observations.

Adult↗

PubMed2007

The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins.

While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure of proteins and their associated dynamics. We discuss the effects that under-restraining (overfitting) and over-restraining (underfitting) have on the structures generated in ensemble-averaged molecular simulations. We then introduce the MUMO (minimal under-restraining minimal over-restraining) method, a procedure in which different observables are averaged over a different number of molecules. As both over-restraining and under-restraining are significantly reduced in the MUMO method, it is possible to generate ensembles of conformations that accurately characterize both the structure and the dynamics of native states of proteins. The application of the MUMO method to the protein ubiquitin yields a high-resolution structural ensemble with an RDC Q-factor of 0.19.

Amino Acid Sequence↗