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PubMed2004

Estimation of critical behavior from the density of states in classical statistical models.

We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.

Journal Article↗
PubMed2000

A dendritic cable model for the amplification of synaptic potentials by an ensemble average of persistent sodium channels.

The persistent sodium current density (I(NaP)) at the soma measured with the 'whole-cell' patch-clamp recording method is linearized about the resting state and used as a current source along the dendritic cable (depicting the spatial distribution of voltage-dependent persistent sodium ionic channels). This procedure allows time-dependent analytical solutions to be obtained for the membrane depolarization. Computer simulated response to a dendritic current injection in the form of synaptically-induced voltage change located at a distance from the recording site in a cable with unequally distributed persistent sodium ion channel densities per unit length of cable (the so-called 'hot-spots') is used to obtain conclusions on the density and distribution of persistent sodium ion channels. It is shown that the excitatory postsynaptic potentials (EPSPs) are amplified if hot-spots of persistent sodium ion channels are spatially distributed along the dendritic cable, with the local density of I(NaP) with respect to the recording site shown to specifically increase the peak amplitude of the EPSP for a proximally placed synaptic input, while the spatial distribution of I(NaP) serves to broaden the time course of the amplified EPSP. However, in the case of a distally positioned synaptic input, both local and nonlocal densities yield an approximately identical enhancement of EPSPs in contradiction to the computer simulations performed by Lipowsky et al. [J. Neurophysiol. 76 (1996) 2181]. The results indicate that persistent sodium channels produce EPSP amplification even when their distribution is relatively sparse (i.e. , approximately 1-2% of the transient sodium channels are found in dendrites of CA1 hippocampal pyramidal neurons). This gives a strong impetus for the use of the theory as a novel approach in the investigation of synaptic integration of signals in active dendrites represented as ionic cables.

Animals↗
PubMed1991

Physical characterization of pharmaceutical solids.

A general review of the methods available for the physical characterization of pharmaceutical solids is presented. The techniques are classified as being on the molecular level (properties capable of being detected in an ensemble of individual molecules), the particulate level (properties which can be detected through the analysis of an ensemble of particles), and the bulk level (properties which can be measured only using a relatively large amount of material). The molecular-level properties discussed are infrared spectroscopy and nuclear magnetic resonance spectrometry, the particulate-level properties discussed are particle morphology, particle size distribution, powder X-ray diffraction, and thermal methods of analysis, and the bulk-level properties discussed are surface area, porosity and pore size distribution, and powder flow characteristics. Full physical characterization of three modifications of lactose (hydrous, anhydrous, and Fast-Flo) is presented to illustrate the type of information which can be obtained using each of the techniques discussed.

Magnetic Resonance Spectroscopy↗
PubMed2004

Commitment and nucleation in the protein G transition state.

An accurate characterization of the transition state ensemble (TSE) is central to furthering our understanding of the protein folding reaction. We have extensively tested a recently reported method for studying a protein's TSE, utilizing phi-value data from protein engineering experiments and computational studies as restraints in all-atom Monte Carlo (MC) simulations. The validity of interpreting experimental phi-values as the fraction of native contacts made by a residue in the TSE was explored, revealing that this definition is unable to uniquely specify a TSE. The identification of protein G's second hairpin, in both pre and post-transition conformations demonstrates that high experimental phi-values do not guarantee a residue's importance in the TSE. An analysis of simulations based on structures restrained by experimental phi-values is necessary to yield this result, which is not obvious from a simplistic interpretation of individual phi-values. The TSE that we obtain corresponds to a single, specific nucleation event, characterized by six residues common to all three observed, convergent folding pathways. The same specific nucleus was independently identified from computational and experimental data, and "Conservation of Conservation" analysis in the protein G fold. When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event. Once the nucleus has formed, the folding reaction enters a slow relaxation process associated with side-chain packing and small, local backbone rearrangements. A detailed analysis of phi-values and their relationship to the transition state ensemble allows us to construct a unified theoretical model of protein G folding.

Models, Molecular↗
PubMed2002

Cell population modelling of yeast glycolytic oscillations.

We investigated a cell-population modelling technique in which the population is constructed from an ensemble of individual cell models. The average value or the number distribution of any intracellular property captured by the individual cell model can be calculated by simulation of a sufficient number of individual cells. The proposed method is applied to a simple model of yeast glycolytic oscillations where synchronization of the cell population is mediated by the action of an excreted metabolite. We show that smooth one-dimensional distributions can be obtained with ensembles comprising 1000 individual cells. Random variations in the state and/or structure of individual cells are shown to produce complex dynamic behaviours which cannot be adequately captured by small ensembles.

Glycolysis↗
PubMed2001

Rigorous classical-mechanical derivation of a multiple-copy algorithm for sampling statistical mechanical ensembles.

We derive a rigorous, multiple-copy simulation algorithm that is formally equivalent to conventional classical molecular dynamics for an ensemble of systems, but may be used for rapid geometry optimizations. The derivation is accomplished by starting from an ensemble of copies of the entire system and applying a point coordinate transformation to a large subsystem defined as the bath. After the transformation, each atom of the bath is described by one "major" set of coordinates located at the average position of the ensemble of equivalent atoms and a set of "minor" coordinates that when combined with the "major" coordinates represent exact dynamics. Neglecting the "minor" set of coordinates results in a Hamiltonian and a probability density equivalent to those used in existing multiple-copy methods. Neglecting Hamilton's equations of motion for the minor variables gives the equations of motion for locally enhanced sampling. Numerical tests indicate that the algorithm can recover exact molecular dynamics of the ensemble, conventional multiple-copy dynamics, or results of intermediate accuracy. Thus, the algorithm provides a rigorous basis for multiple-copy dynamics, resolves many of the uncertainties associated with their current implementations, and offers the potential for calculating ensemble average properties in conjunction with finding a system's global minimum energy geometry.

Journal Article↗
PubMed2024

Deep-Learning Model for Tumor-Type Prediction Using Targeted Clinical Genomic Sequencing Data.

UNLABELLED: Tumor type guides clinical treatment decisions in cancer, but histology-based diagnosis remains challenging. Genomic alterations are highly diagnostic of tumor type, and tumor-type classifiers trained on genomic features have been explored, but the most accurate methods are not clinically feasible, relying on features derived from whole-genome sequencing (WGS), or predicting across limited cancer types. We use genomic features from a data set of 39,787 solid tumors sequenced using a clinically targeted cancer gene panel to develop Genome-Derived-Diagnosis Ensemble (GDD-ENS): a hyperparameter ensemble for classifying tumor type using deep neural networks. GDD-ENS achieves 93% accuracy for high-confidence predictions across 38 cancer types, rivaling the performance of WGS-based methods. GDD-ENS can also guide diagnoses of rare type and cancers of unknown primary and incorporate patient-specific clinical information for improved predictions. Overall, integrating GDD-ENS into prospective clinical sequencing workflows could provide clinically relevant tumor-type predictions to guide treatment decisions in real time. SIGNIFICANCE: We describe a highly accurate tumor-type prediction model, designed specifically for clinical implementation. Our model relies only on widely used cancer gene panel sequencing data, predicts across 38 distinct cancer types, and supports integration of patient-specific nongenomic information for enhanced decision support in challenging diagnostic situations. See related commentary by Garg, p. 906. This article is featured in Selected Articles from This Issue, p. 897.

Humans↗
PubMed1993

A Monte Carlo method for generating structures of short single-stranded DNA sequences.

A Monte Carlo method has been developed for generating the conformations of short single-stranded DNAs from arbitrary starting states. The chain conformers are constructed from energetically favorable arrangements of the constituent mononucleotides. Minimum energy states of individual dinucleotide monophosphate molecules are identified using a torsion angle minimizer. The glycosyl and acyclic backbone torsions of the dimers are allowed to vary, while the sugar rings are held fixed in one of the two preferred puckered forms. A total of 108 conformationally distinct states per dimer are considered in this first stage of minimization. The torsion angles within 5 kcal/mole of the global minimum in the resulting optimized states are then allowed to vary by +/- 10 degrees in an effort to estimate the breadth of the different local minima. The energies of a total of 2187 (3(7)) angle combinations are examined per local conformational minimum. Finally, the energies of all dinucleotide conformers are scaled so that the populations of differently puckered sugar rings in the theoretical sample match those found in nmr solution studies. This last step is necessitated by limitations in the theoretical methods to predict DNA sugar puckering accurately. The conformer populations of the individual acyclic torsion angles in the composite dimer ensembles are found to be in good agreement with the distributions of backbone conformations deduced from nmr coupling constants and the frequencies of glycosyl conformations in x-ray crystal structures, suggesting that the low energy states are reasonable. The low energy dimer forms (consisting of 150-325 conformational states per dimer step) are next used as variables in a Monte Carlo algorithm, which generates the conformations of single-stranded d(CXnG) chains, where X = A, T and n = 3, 4, 5. The oligonucleotides are built sequentially from the 5' end of the chain using random numbers to select the conformations of overlapping dimer units. The simulations are very fast, involving a total of 10(6) conformations per chain sequence. The potential errors in the buildup procedure are minimized by taking advantage of known rotational interdependences in the sugar-phosphate backbone. The distributions of oligonucleotide conformations are examined in terms of the magnitudes, positions, and orientations of the end-to-end vectors of the chains. The differences in overall flexibility and extension of the oligomers are discussed in terms of the conformations of the constituent dinucleotide steps, while the general methodology is discussed and compared with other nucleic acid model building techniques.

Algorithms↗
PubMed2001

A new method for assembling metabolic networks, with application to the Krebs citric acid cycle.

To understand why a molecular network has a particular connectivity one can generate an ensemble of alternative networks, all of which meet the same performance criteria as the real network. We have generated alternatives to the Krebs cycle, allowing group transfers and B(12)-mediated shifts that were excluded in previous work. Our algorithm does not use a reaction list, but determines the reactants and products in generic reactions. It generates networks in order of increasing number of reaction steps. We find that alternatives to the Krebs cycle are very likely to be cycles. Many of the alternatives produce toxic or unstable compounds and use group transfer reactions, which have unfavorable consequences. Although alternatives are better than the Krebs cycle in some respects, the Krebs cycle has the most favorable combination of traits.

Algorithms↗
PubMed2004

Density of states for almost-diagonal random matrices.

We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost-diagonal Hermitian random matrices. The matrices have independent random entries H(i > or =j) with small off-diagonal elements: <|H(i not equal to j)|2> << <|H(ii)|2> approximately 1. Using the recently suggested method of a virial expansion in the number of interacting energy levels [J. Phys. A 36, 8265 (2003)], we calculate the leading correction to the Poissonian DOS in the cases of the Gaussian orthogonal and unitary ensembles. We apply the general formula to the critical power-law banded random matrices and the unitary Moshe-Neuberger-Shapiro model and compare the DOS's of these models.

Journal Article↗
PubMed1994

Scanning concentration correlation spectroscopy using the confocal laser microscope.

Concentration correlation spectroscopy allows the assessment of molecular motions in complex systems. The technique generally monitors concentration fluctuations by means of some method such as the intensity of fluorescent molecules (fluorescence correlation spectroscopy). We describe here the use of scanning confocal laser microscopy to measure correlation functions in both space and time. This methodology offers two major advantages over conventional methods. First, collecting data from different regions of the sample significantly increases the signal-to-noise ratio. Second, molecular motions of colloidal gold can be analyzed by correlation methods with high temporal and spatial resolution. Using a MRC 600 laser scanning system, we collect data from an ensemble of 768 independent subvolumes and determine the space-time correlation function. We demonstrate the technique using two different types of samples, fluorescently labeled DNA molecules in solution and colloidal gold-tagged lipids in a planar bilayer. This approach, which we term "scanning concentration correlation spectroscopy," provides a straightforward means of performing high resolution correlation analysis of molecular motions with available instrumentation.

Biophysical Phenomena↗
PubMed2005

Experimental validation of the docking orientation of Cdc25 with its Cdk2-CycA protein substrate.

Cdc25 phosphatases are key activators of the eukaryotic cell cycle and compelling anticancer targets because their overexpression has been associated with numerous cancers. However, drug discovery targeting these phosphatases has been hampered by the lack of structural information about how Cdc25s interact with their native protein substrates, the cyclin-dependent kinases. Herein, we predict a docked orientation for Cdc25B with its Cdk2-pTpY-CycA protein substrate by a rigid-body docking method and refine the docked models with full-scale molecular dynamics simulations and minimization. We validate the stable ensemble structure experimentally by a variety of in vitro and in vivo techniques. Specifically, we compare our model with a crystal structure of the substrate-trapping mutant of Cdc25B. We identify and validate in vivo a novel hot-spot residue on Cdc25B (Arg492) that plays a central role in protein substrate recognition. We identify a hot-spot residue on the substrate Cdk2 (Asp206) and confirm its interaction with hot-spot residues on Cdc25 using hot-spot swapping and double mutant cycles to derive interaction energies. Our experimentally validated model is consistent with previous studies of Cdk2 and its interaction partners and initiates the opportunity for drug discovery of inhibitors that target the remote binding sites of this protein-protein interaction.

Binding Sites↗
PubMed2000

Binding of a diverse set of ligands to avidin and streptavidin: an accurate quantitative prediction of their relative affinities by a combination of molecular mechanics and continuum solvent models.

We report calculations of free energies of binding, DeltaG(bind), between a diverse set of nine ligands and avidin as well as between a peptide and streptavidin using the recently developed MM/PBSA approach. This method makes use of a molecular dynamics simulation of the ligand-protein complex to generate a thermally averaged ensemble of conformations of the molecules that are involved in the complex formation. Based on this set of structures, a free energy of binding is calculated using molecular mechanical and continuum solvent energies as well as including estimates of the nonpolar solvation free energy and solute entropy. We compare in our simulations different classes of ligands, involving biotin derivatives, the dye 2-(4'-hydroxyazobenzene)benzoic acid (HABA), and a cyclic hexapeptide, which cover a large range of binding free energies from -5 to -20 kcal/mol. Our calculations are able to reproduce experimental DeltaG(bind) values with a very good correlation coefficient of r(2) = 0.92. This agreement is considerably better than the results obtained with an alternate approach, the linear interaction energy approximation, for this system (r(2) = 0.55).

Avidin↗
PubMed2005

Free-energy calculations for the cubic ZrO2 crystal as an example of a system with a soft mode.

We calculate the free energy for a crystalline ZrO(2) with a soft mode by the first-principles method, using the double-well energy-displacement relation. The soft-mode branch is considered as an ensemble of independent anharmonic oscillators of the parabola-plus-Gaussian or of the 2-4 polynomial forms. The anharmonic contributions are included to reproduce the cubic-to-tetragonal phase transition, however, it appears that the cubic phase does not become the most stable within the framework of the independent oscillators approach.

Journal Article↗
PubMed2006

A kinetic theory of tertiary contact formation coupled to the helix-coil transition in polypeptides.

The framework model and the hydrophobic collapse model represent two canonical descriptions of the protein folding process. The first places primary reliance on the short-range interactions of secondary structure and the second assigns greater importance to the long-range interactions of tertiary structure. The availability of increasingly detailed information about the folding mechanisms of diverse proteins suggests that both are important and the folding mechanism of most proteins utilizes different combinations of such interactions. A prior report described the XHC model, an extended helix-coil theory, which treats the mutual stabilization of secondary and tertiary structure in simple alpha-helical proteins at equilibrium. In this study, a kinetic scheme describing tertiary contact formation has been developed which relaxes to the XHC equilibrium model. The relaxation is governed by the relative stabilities of the equilibrium states and an additional factor which represents an activation energy for formation of a tertiary contact. The model can be used to simulate time-dependent properties of the ensemble of conformations during the entire folding process, and the resulting predictions are applicable to a range of experimental methods. This XHC kinetic model enables investigation of the relative influence of secondary and tertiary interactions on folding mechanisms.

Algorithms↗
PubMed2004

Differences in the folding transition state of ubiquitin indicated by phi and psi analyses.

We compare the folding transition state (TS) of ubiquitin previously identified by using psi analysis to that determined by using analysis. Both methods attempt to identify interactions and their relative populations at the rate-limiting step for folding. The TS ensemble derived from psi analysis has an extensive native-like chain topology, with a four-stranded beta-sheet network and a portion of the major helix. According to analysis, however, the TS is much smaller and more polarized, with only a local helix/hairpin motif. We find that structured regions can have values far from unity, the canonical value for such sites, because of structural relaxation of the TS. Consequently, these sites may be incorrectly interpreted as contributing little to the structure of the TS. These results stress the need for caution when interpreting and drawing conclusions from analysis alone and highlight the need for more specific tools for examining the structure and energetics of the TS ensemble.

Computer Simulation↗
PubMed2004

Universal results from an alternate random-matrix model for QCD with a baryon chemical potential.

We introduce a new non-Hermitian random-matrix model for QCD with a baryon chemical potential. This model is a direct chiral extension of a previously studied model that interpolates between the Wigner-Dyson and Ginibre ensembles. We present exact results for all eigenvalue correlations for any number of quark flavors using the orthogonal polynomial method. We also find that the parameters of the model can be scaled to remove the effects of the chemical potential from all thermodynamic quantities until the finite density phase transition is reached. This makes the model and its extensions well suited for studying the phase diagram of QCD.

Journal Article↗
PubMed2002

Adaptive filtering of evoked potentials with radial-basis-function neural network prefilter.

Evoked potentials (EPs) are time-varying signals typically buried in relatively large background noise. To extract the EP more effectively from noise, we had previously developed an approach using an adaptive signal enhancer (ASE) (Chen et al., 1995). ASE requires a proper reference input signal for its optimal performance. Ensemble- and moving window-averages were formerly used with good results. In this paper, we present a new method to provide even more effective reference inputs for the ASE. Specifically, a Gaussian radial basis function neural network (RBFNN) was used to preprocess raw EP signals before serving as the reference input. Since the RBFNN has built-in nonlinear activation functions that enable it to closely fit any function mapping, the output of RBFNN can effectively track the signal variations of EP. Results confirmed the superior performance of ASE with RBFNN over the previous method.

Algorithms↗