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PubMed2001

Decomposition of protein tryptophan fluorescence spectra into log-normal components. III. Correlation between fluorescence and microenvironment parameters of individual tryptophan residues.

In our previous paper (Reshetnyak, Ya. K., and E. A. Burstein. 2001. Biophys. J. 81:1710-1734) we confirmed the existence of five statistically discrete classes of emitting tryptophan fluorophores in proteins. The differences in fluorescence properties of tryptophan residues of these five classes reflect differences in interactions of excited states of tryptophan fluorophores with their microenvironment in proteins. Here we present a system of describing physical and structural parameters of microenvironments of tryptophan residues based on analysis of atomic crystal structures of proteins. The application of multidimensional statistical methods of cluster and discriminant analyses for the set of microenvironment parameters of 137 tryptophan residues of 48 proteins with known three-dimensional structures allowed us to 1) demonstrate the discrete nature of ensembles of structural parameters of tryptophan residues in proteins; 2) assign spectral components obtained after decomposition of tryptophan fluorescence spectra to individual tryptophan residues; 3) find a correlation between spectroscopic and physico-structural features of the microenvironment; and 4) reveal differences in structural and physical parameters of the microenvironment of tryptophan residues belonging to various spectral classes.

Analysis of Variance↗
PubMed2026

Seeing and Feeling DNA Methylation: Single-Molecule Biophysics Meets Machine Learning.

DNA methylation at 5-methylcytosine (5mC) is crucial for embryonic development and cellular function, while aberrant patterns strongly drive disease onset and progression. Its reversible nature offers substantial therapeutic potential, emphasizing the need for precise, context-specific genome wide 5mC mapping. Conventional techniques such as bisulfite sequencing and ensemble biosensor assays are hindered by DNA degradation, amplification bias, high cost, and inability to resolve single-molecule structural and mechanical effects of methylation. This review examines advances in single-molecule biophysical methods (nanopore sensing, smFRET, optical/magnetic tweezers, and AFM) that provide direct, label-free/minimally invasive 5mC detection, along with quantitative insights into DNA conformation, mechanics, and protein-DNA interactions. These techniques complement traditional methylome mapping by linking genomic localization to molecular mechanisms. Emerging machine-learning approaches are revolutionizing analysis, particularly in nanopore sensing, while promising applications in smFRET, tweezers, and AFM address throughput and reproducibility challenges. Their convergence promises scalable, high-resolution epigenetic profiling, advancing precision epigenomics toward clinical application.

DNA Methylation↗
PubMed2003

Quantitative description of human skin water dynamics by a disposition-decomposition analysis (DDA) of trans-epidermal water loss and epidermal capacitance.

BACKGROUND: In vivo water assessment would greatly benefit from a dynamical approach since the evaluation of common related variables such as trans-epidermal water loss or "capacitance" measurements is always limited to instantaneous data. Mathematical modelling is still an attractive alternative already attempted with bi-exponential empirical models. A classical two-compartment interpretation of such models raises a number of questions about the underlying fundamentals, which can hardly be experimentally confirmed. However, in a system analysis sense, skin water dynamics may be approached as an ensemble of many factors, impossible to discretize, but conceptually grouped in terms of feasible properties of the system. The present paper explores the applicability of this strategy to the in vivo water dynamics assessment. METHODS: From the plastic occlusion stress test (POST) skin water balance is assessed by modelling trans-epidermal water loss (TEWL) and "capacitance" data obtained at skin's surface. With system analysis (disposition-decomposition analysis) the distribution function, H(t), modelled as a sum of exponential terms, covers only the distribution characteristics of water molecules traversing the skin. This may correspond macroscopically to the experimental data accessed by "corneometry". Separately, the hyperbolic elimination function Q(TEWL) helps to characterise the dynamic aspects of water influx through the skin. DISCUSSION AND CONCLUSION: In the observable range there seems to be a linear relationship between the net amount of water lost at the surface by evaporation, and the capability of the system to replenish that loss. This may be a specific characteristic of the system related to what may be described as the skin's "intrinsic hydration capacity" (IHC) a new functional parameter only identified by this strategy. These new quantitative tools are expected to find different applicabilities (from the in vivo skin characterisation to efficacy testing) contributing to disclose the dynamical nature of the skin water balance process.

Adult↗
PubMed1996

Spiral laminar flow in vivo.

1. Blood flow patterns are poorly understood despite their impact on arterial disease. There have been few measurements in vivo of the three-dimensional blood flow patterns; we present the results of such studies using a new non-invasive in-vivo method of examining biplanar arterial blood flow patterns. 2. Multiple colour Doppler ultrasound directional velocity images were obtained at two different beam target angles from the artery in the plane perpendicular to its axis. Ensemble average images were constructed; the absolute velocity and direction were calculated by compounding the left and right averaged images. Simple directional, non-directional velocity and vector maps were constructed. 3. Flow patterns were sampled in 11 healthy male volunteers at four points of the pulse cycle; peak systole, systolic downswing, diastolic reverse flow and diastolic forward flow and at three sites; the right common and distal superficial femoral and the left common femoral arteries. 4. Stable rotational flow was observed in all subjects, the direction of rotation varying between sides and individuals. 5. There are theoretical advantages to spiral laminar blood flow; the forward-directed, rotationally induced stability and reduction of laterally directed forces may reduce turbulence in the tapering branching arterial tree and at stenoses and have a beneficial effect on mechanisms of endothelial damage and repair.

Blood Flow Velocity↗
PubMed2006

Nonstatistical effects in the dissociation of ethyl radical: Finding order in chaos.

How does one identify order in complex dynamical systems? A Born-Oppenheimer molecular dynamics simulation of the dissociation of ethyl radical, C(2)H(5), produces an ensemble of classical trajectories which are decomposed in the time-frequency domain using wavelets. A time-dependent scalar metric, the normalized instantaneous orbital complexity, is constructed and shown to correlate not only to the more conventional Lyapunov exponents but also to the dissociation time for an individual trajectory. The analysis of the ensemble of trajectories confirms that the long-lived trajectories are associated with a low degree of ergodicity. While the analysis of molecular dissociation dynamics is the narrow focus of the present work, the method is more general for discovery and identification of ordered regimes within large sets of chaotic data.

Journal Article↗
PubMed2006

Application of the multiensemble sampling to the equilibrium folding of proteins.

MOTIVATION: Conventional Monte Carlo and molecular dynamics simulations of proteins in the canonical ensemble are of little use, because they tend to get trapped in states of energy local minima at low temperatures. One way to surmount this difficulty is to use a non-Boltzmann sampling method in which conformations are sampled upon a general weighting function instead of the conventional Boltzmann weighting function. The multiensemble sampling (MES) method is a non-Boltzmann sampling method that was originally developed to estimate free energy differences between systems with different potential energies and/or at different thermodynamic states. The method has not yet been applied to studies of complex molecular systems such as proteins. RESULTS: MES Monte Carlo simulations of small proteins have been carried out using a united-residue force field. The proteins at several temperatures from the unfolded to the folded states were simulated in a single MC run at a time and their equilibrium thermodynamic properties were calculated correctly. The distributions of sampled conformations clearly indicate that, when going through states of energy local minima, the MES simulation did not get trapped in them but escaped from them so quickly that all the relevant parts of conformation space could be sampled properly. A two-step folding process consisting of a collapse transition followed by a folding transition is observed. This study demonstrates that the use of MES alleviates the multiple-minima problem greatly. AVAILABILITY: Available on request from the authors.

Algorithms↗
PubMed2001

Ground-state fluctuations in finite Fermi systems.

We consider a small and fixed number of fermions in a trap. The ground state of the system is defined at T=0. For a given excitation energy, there are several ways of exciting the particles from this ground state. We formulate a method for calculating the number fluctuation in the ground state using microcanonical counting, and implement it for noninteracting fermions in harmonic confinement. This exact calculation for fluctuation, when compared with canonical or grand canonical ensemble averaging, gives considerably different results. This difference is expected to persist at low excitation even when the fermion number in the trap is large. For comparison, the well-known bosonic results are also given.

Journal Article↗
PubMed2004

Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms.

We suggest a method for suppression of synchrony in a globally coupled oscillator network, based on the time-delayed feedback via the mean field. Having in mind possible applications for suppression of pathological rhythms in neural ensembles, we present numerical results for different models of coupled bursting neurons. A theory is developed based on the consideration of the synchronization transition as a Hopf bifurcation.

Action Potentials↗
PubMed2005

Thermodynamics of the self-gravitating ring model.

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the self-gravitating-ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply an iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state.

Journal Article↗
PubMed2006

Solution structure of GOPC PDZ domain and its interaction with the C-terminal motif of neuroligin.

GOPC (Golgi-associated PDZ and coiled-coil motif-containing protein) represents a PDZ domain-containing protein associated with the Golgi apparatus, which plays important roles in vesicular trafficking in secretory and endocytic pathways. GOPC interacts with many other proteins, such as the Wnt receptors Frizzled 8 and neuroligin via its PDZ domain. Neuroligin is a neural cell-adhesion molecule of the post-synapse, which binds to the presynapse molecule neurexin to form a heterotypic intercellular junction. Here we report the solution structure of the GOPC PDZ domain by NMR. Our results show that it is a canonical class I PDZ domain, which contains two alpha-helices and six beta-strands. Using chemical shift perturbation experiments, we further studied the binding properties of the GOPC PDZ domain with the C-terminal motif of neuroligin. The observations showed that the ensemble of the interaction belongs to fast exchange with low affinity. The 3D model of the GOPC PDZ domain/neuroligin C-terminal peptide complex was constructed with the aid of the molecular dynamics simulation method. Our discoveries provide insight into the specific interaction of the GOPC PDZ domain with the C-terminal peptide of Nlg and also provide a general insight about the possible binding mode of the interaction of Nlg with other PDZ domain-containing proteins.

Adaptor Proteins, Signal Transducing↗
PubMed2006

Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data.

BACKGROUND: Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made. RESULTS: We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogeneous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations. CONCLUSION: We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.

Bayes Theorem↗
PubMed2025

MaxComp: Predicting single-cell chromatin compartments from 3D chromosome structures.

The genome is organized into distinct chromatin compartments with at least two main classes, a transcriptionally active A and an inactive B compartment, broadly corresponding to euchromatin and heterochromatin. Chromatin regions within the same compartment preferentially interact with each other over regions in the opposite compartment. A/B compartments are traditionally identified from ensemble Hi-C contact frequency matrices using principal component analysis of their covariance matrices. However, defining compartments at the single-cell level from sparse single-cell Hi-C data is challenging, especially since homologous copies are often not resolved. To address this, we present MaxComp, an unsupervised method, for inferring single-cell A/B compartments based on 3D geometric considerations in single-cell chromosome structures-derived either from multiplexed FISH-omics imaging or 3D structure models derived from Hi-C data. By representing each 3D chromosome structure as an undirected graph with edge-weights encoding structural information, MaxComp reformulates compartment prediction as a variant of the Max-cut problem, solved using semidefinite graph programming (SPD) to optimally partition the graph into two structural compartments. Our results show that the population average of MaxComp single-cell compartment annotations closely matches those derived from ensemble Hi-C principal component analysis, demonstrating that compartmentalization can be recovered from geometric principles alone, using only the 3D coordinates and nuclear microenvironment of chromatin regions. Our approach reveals widespread cell-to-cell variability in compartment organization, with substantial heterogeneity across genomic loci. When applied to multiplexed FISH imaging data, MaxComp also uncovers relationships between compartment annotations and transcriptional activity at the single-cell level. In summary, MaxComp offers a new framework for understanding chromatin compartmentalization in single cells, connecting 3D genome architecture, and transcriptional activity with the cell-to-cell variations of chromatin compartments.

Chromatin↗
PubMed2003

Characterizing the unstructured intermediates in oxidative folding.

A recently developed method is used here to characterize some of the folding intermediates, and the oxidative folding processes, of RNase A. This method is based on the ability of trans-[Pt(en)(2)Cl(2)](2+) to oxidize cysteine residues to form disulfide bonds faster than the disulfide bonds can be rearranged by reshuffling or reduction. Variations of this method have enabled us to address three issues. (i) How the nature of the residual structure and/or conformational order that is present, or develops, during the initial stages of folding can be elucidated. It is shown here that there is a 10-fold increase in the propensity of the unfolded reduced forms of RNase A to form the native set of disulfides directly, compared to the propensity under strongly denaturing conditions (4-6 M GdnHCl). Thus, the unfolded reduced forms of RNase A are not statistical coils with a more condensed form than in the GdnHCl-denatured state; rather, it is suggested that reduced RNase A has a little bias toward a native topology. (ii) The structural characterization of oxidative folding intermediates in terms of disulfide pairing is demonstrated; specifically, a lower-limit estimate is made of the percentage of native disulfide-containing molecules in the two-disulfide ensemble of RNase A. (iii) The critical role of structured intermediate species in determining the oxidative folding pathways of proteins was shown previously. Here, we demonstrate that the presence of a structured intermediate in the oxidative folding of proteins can be revealed by this method.

Chromatography, High Pressure Liquid↗
PubMed2003

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations.

A method of statistical estimation is applied to the problem of one-dimensional internal rotation in a hindering potential of mean force. The hindering potential, which may have a completely general shape, is expanded in a Fourier series, the coefficients of which are estimated by fitting an appropriate statistical-mechanical distribution to the random variable of internal rotation angle. The function of reduced moment of inertia of an internal rotation is averaged over the thermodynamic ensemble of atomic configurations of the molecule obtained in stochastic simulations. When quantum effects are not important, an accurate estimate of the absolute internal rotation entropy of a molecule with a single rotatable bond is obtained. When there is more than one rotatable bond, the "marginal" statistical-mechanical properties corresponding to a given internal rotational degree of freedom are reduced. The method is illustrated using Monte Carlo simulations of two public health relevant halocarbon molecules, each having a single internal-rotation degree of freedom, and a molecular dynamics simulation of an immunologically relevant polypeptide, in which several dihedral angles are analyzed.

Algorithms↗
PubMed2001

MUSTA--a general, efficient, automated method for multiple structure alignment and detection of common motifs: application to proteins.

Here we present an algorithm designed to carry out multiple structure alignment and to detect recurring substructural motifs. So far we have implemented it for comparison of protein structures. However, this general method is applicable to comparisons of RNA structures and to detection of a pharmacophore in a series of drug molecules. Further, its sequence order independence permits its application to detection of motifs on protein surfaces, interfaces, and binding/active sites. While there are many methods designed to carry out pairwise structure comparisons, there are only a handful geared toward the multiple structure alignment task. Most of these tackle multiple structure comparison as a collection of pairwise structure comparison tasks. The multiple structural alignment algorithm presented here automatically finds the largest common substructure (core) of atoms that appears in all the molecules in the ensemble. The detection of the core and the structural alignment are done simultaneously. The algorithm begins by finding small substructures that are common to all the proteins in the ensemble. One of the molecules is considered the reference; the others are the source molecules. The small substructures are stored in special arrays termed combinatorial buckets, which define sets of multistructural alignments from the source molecules that coincide with the same small set of reference atoms (C(alpha)-atoms here). These substructures are initial small fragments that have congruent copies in each of the proteins. The substructures are extended, through the processing of the combinatorial buckets, by clustering the superpositions (transformations). The method is very efficient.

Algorithms↗
PubMed2002

Simulating proteins at constant pH: An approach combining molecular dynamics and Monte Carlo simulation.

For the structure and function of proteins, the pH of the solution is one of the determining parameters. Current molecular dynamics (MD) simulations account for the solution pH only in a limited way by keeping each titratable site in a chosen protonation state. We present an algorithm that generates trajectories at a Boltzmann distributed ensemble of protonation states by a combination of MD and Monte Carlo (MC) simulation. The algorithm is useful for pH-dependent structural studies and to investigate in detail the titration behavior of proteins. The method is tested on the acidic residues of the protein hen egg white lysozyme. It is shown that small structural changes may have a big effect on the pK(A) values of titratable residues.

Algorithms↗
PubMed2026

Dynamic evolution of chaperone-mediated autophagy is associated with tumor microenvironment remodeling and prognostic stratification in lung adenocarcinoma: insights from single-cell transcriptomics, ensemble machine learning, and experimental validation.

BACKGROUND: Lung adenocarcinoma (LUAD) shows prognostic heterogeneity, and tumor-node-metastasis (TNM) staging is limited for individualized management. Chaperone-mediated autophagy (CMA) maintains proteostasis, but its role during adenocarcinoma in situ (AIS)-minimally invasive adenocarcinoma (MIA)-invasive adenocarcinoma (IAC) progression remains unclear. METHODS: Single-cell RNA sequencing (scRNA-seq) data from GSE189357 and bulk transcriptomes from The Cancer Genome Atlas (TCGA)-LUAD and Gene Expression Omnibus (GEO) cohorts were integrated. CMA activity, cell-cell communication, weighted gene co-expression network analysis (WGCNA), tumor-normal differential expression, machine-learning survival modeling, tumor microenvironment (TME) features, drug sensitivity, and EPC1 function were analyzed. RESULTS: CMA-high tumor epithelial cells increased from AIS (58.1%) to MIA (65.7%) but declined in IAC (44.4%; p < 0.001). CMA-low cells preferentially received fibroblast-derived extracellular matrix cues. A CMA-negatively correlated module identified 69 core genes. Random survival forest (RSF) performed best among 117 machine-learning combinations (mean concordance index > 0.873). High-risk patients had worse survival across cohorts, and the risk score was independently associated with overall survival (hazard ratio = 16.013, 95% confidence interval: 9.579-26.768, p < 0.001). High-risk tumors showed proliferative activation and M0 macrophage enrichment, whereas low-risk tumors showed stronger immune-related signaling. EPC1 overexpression suppressed malignant phenotypes in A549 cells. CONCLUSION: CMA dynamics are associated with stromal and immune remodeling during LUAD progression. A CMA-based model provides robust prognostic stratification and may offer a basis for future TME-guided studies.

Chaperone-mediated autophagy↗
PubMed1997

Enzyme-inhibitor association thermodynamics: explicit and continuum solvent studies.

Studying the thermodynamics of biochemical association reactions at the microscopic level requires efficient sampling of the configurations of the reactants and solvent as a function of the reaction pathways. In most cases, the associating ligand and receptor have complementary interlocking shapes. Upon association, loosely connected or disconnected solvent cavities at and around the binding site are formed. Disconnected solvent regions lead to severe statistical sampling problems when simulations are performed with explicit solvent. It was recently proposed that, when such limitations are encountered, they might be overcome by the use of the grand canonical ensemble. Here we investigate one such case and report the association free energy profile (potential of mean force) between trypsin and benzamidine along a chosen reaction coordinate as calculated using the grand canonical Monte Carlo method. The free energy profile is also calculated for a continuum solvent model using the Poisson equation, and the results are compared to the explicit water simulations. The comparison shows that the continuum solvent approach is surprisingly successful in reproducing the explicit solvent simulation results. The Monte Carlo results are analyzed in detail with respect to solvation structure. In the binding site channel there are waters bridging the carbonyl oxygen groups of Asp189 with the NH2 groups of benzamidine, which are displaced upon inhibitor binding. A similar solvent-bridging configuration has been seen in the crystal structure of trypsin complexed with bovine pancreatic trypsin inhibitor. The predicted locations of other internal waters are in very good agreement with the positions found in the crystal structures, which supports the accuracy of the simulations.

Benzamidines↗