Structural classification of multi-input nonlinear systems

We present new structural classification and parameter estimation results that are applicable to multi-input nonlinear systems. The mathematical relationships between the self- and cross-(Volterra and Wiener) kernels are derived for a basic two-input nonlinear structure. These results are then used to develop classification methods for more complicated two-input structures. Algorithms for estimating the parameters (linear and nonlinear subsystems) of these structures are also presented.     

Recognizing protein–protein interfaces with empirical potentials and reduced amino acid alphabets

Background  

In structural genomics, an important goal is the detection and classification of protein–protein interactions, given the structures of the interacting partners. We have developed empirical energy functions to identify native structures of protein–protein complexes among sets of decoy structures. To understand the role of amino acid diversity, we parameterized a series of functions, using a hierarchy of amino acid alphabets of increasing complexity, with 2, 3, 4, 6, and 20 amino acid groups. Compared to previous work, we used the simplest possible functional form, with residue–residue interactions and a stepwise distance-dependence. We used increased computational ressources, however, constructing 290,000 decoys for 219 protein–protein complexes, with a realistic docking protocol where the protein partners are flexible and interact through a molecular mechanics energy function. The energy parameters were optimized to correctly assign as many native complexes as possible. To resolve the multiple minimum problem in parameter space, over 64000 starting parameter guesses were tried for each energy function. The optimized functions were tested by cross validation on subsets of our native and decoy structures, by blind tests on series of native and decoy structures available on the Web, and on models for 13 complexes submitted to the CAPRI structure prediction experiment.     

A comparative analysis of the triloops in all high-resolution RNA structures reveals sequence structure relationships

Despite an increasing number of experimentally determined RNA structures, the gap between the number of structures and that of RNA families is still growing. To overcome this limitation, efficient and reliable RNA modeling methodologies must be developed. In order to reach this goal, here, we show how triloop sequence-structure relationships have been inferred through a systematic analysis of all triloops found in available high-resolution structures. The structural annotation of all triloops allowed us to define discrete states of the triloop's conformational space, and therefore an explicit sequence-to-structure relation. The sequence-structure relationships inferred from this explicit relation are presented in a convenient modeling table that provides a limited set of possible three-dimensional structures given any triloop sequence. The table is indexed by the two nucleotides that form the triloop's flanking base pair, since they are shown to provide the most information about the triloop three-dimensional structures. We also report the observations in the X-ray crystallographic structures of important conformational variations, which we believe might be the result of RNA dynamic.     

Relationships between protein structure and dynamics from a database of NMR-derived backbone order parameters

The amplitude of protein backbone NH group motions on a time-scale faster than molecular tumbling may be determined by analysis of (15)N NMR relaxation data according to the Lipari-Szabo model free formalism. An internet-accessible database has been compiled containing 1855 order parameters from 20 independent NMR relaxation studies on proteins whose three-dimensional structures are known. A series of statistical analyses has been performed to identify relationships between the structural features and backbone dynamics of these proteins. Comparison of average order parameters for different amino acid types indicates that amino acids with small side-chains tend to have greater backbone flexibility than those with large side-chains. In addition, the motions of a given NH group are also related to the sizes of the neighboring amino acids in the primary sequence. The secondary structural environment appears to influence backbone dynamics relatively weakly, with only subtle differences between the order parameter distributions of loop structures and regular hydrogen bonded secondary structure elements. However, NH groups near helix termini are more mobile on average than those in the central regions of helices. Tertiary structure influences are also relatively weak but in the expected direction, with more exposed residues being more flexible on average than residues that are relatively inaccessible to solvent.     

Self-consistent quasineutral dust structures

Distributions of the dusty plasma parameters (electron, ion, and dust densities; dust grain charge; and ion drift velocity) in quasineutral dust structures whose dimensions are much greater than the mean free path of the ions in their interactions with neutral particles are calculated numerically under conditions such that ionization sources are located outside the structures. Planar, cylindrical, and spherical structures are investigated. It is shown that static equilibrium structures are governed by a single (basic) parameter: the electrostatic potential drop between the center of the structure and its boundary. It is found that the maximum value of the basic parameter (in energy units) does not exceed the electron temperature. The basic parameter also determines the total number of dust grains in the structure and the power of external ionization sources that are necessary to sustain this structure. The fact that the basic parameter varies within a limited range allows one to consider all the possible structures with a given dimensionality (planar, cylindrical, and spherical).     

Biofilm image reconstruction for assessing structural parameters

The structure of biofilms can be numerically quantified from microscopy images using structural parameters. These parameters are used in biofilm image analysis to compare biofilms, to monitor temporal variation in biofilm structure, to quantify the effects of antibiotics on biofilm structure and to determine the effects of environmental conditions on biofilm structure. It is often hypothesized that biofilms with similar structural parameter values will have similar structures; however, this hypothesis has never been tested. The main goal was to test the hypothesis that the commonly used structural parameters can characterize the differences or similarities between biofilm structures. To achieve this goal (1) biofilm image reconstruction was developed as a new tool for assessing structural parameters, (2) independent reconstructions using the same starting structural parameters were tested to see how they differed from each other, (3) the effect of the original image parameter values on reconstruction success was evaluated, and (4) the effect of the number and type of the parameters on reconstruction success was evaluated. It was found that two biofilms characterized by identical commonly used structural parameter values may look different, that the number and size of clusters in the original biofilm image affect image reconstruction success and that, in general, a small set of arbitrarily selected parameters may not reveal relevant differences between biofilm structures.     

A Riemannian manifold analysis of endothelial cell monolayer impedance parameter precision

Endothelial cell adhesion and barrier function play a critical role in many biological and pathophysiological processes. The decomposition of endothelial cell adhesion and barrier function into cell–cell and cell–matrix components using frequency dependent cellular micro-impedance measurements has, therefore, received widespread application. Few if any studies, however, have examined the precision of these model parameters. This study presents a parameter sensitivity analysis of a representative cellular barrier function model using a concise geometric formulation that includes instrumental data acquisition settings. Both model state dependence and instrumental noise distributions are accounted for within the framework of Riemannian manifold theory. Experimentally acquired microimpedance measurements of attached endothelial cells define the model state domain, while experimentally measured noise statistics define the data space Riemannian metric based on the Fisher information matrix. The results of this analysis show that the sensitivity of cell–cell and cell–matrix impedance components are highly model state dependent and several well defined regions of low precision exist. The results of this study further indicate that membrane resistive components can significantly reduce the precision of the remaining parameters in these models. This work was supported by a National Science Foundation CAREER Award (AE), BES-0238905, and in part by the American Heart Association under Grant 0265029B (AE).     

On the other hand: The stereoselectivity of drug action at ion channels

Ion channels are pharmacological receptors with specific drug binding sites. These binding sites define specific structure–function relationships for the actions of drug classes. Interpretation of these structure–function relationships may be complex because of state-dependent drug-channel interactions. These state-dependent interactions determine affinity and access of drug to binding sites and may result in both quantitative and qualitative changes in structure–function relationships including stereoselectivity. A channel-active drug may exhibit antagonist or activator properties according to membrane potential and the stereoselectivity of interaction may also change with channel state. © 1994 Wiley-Liss, Inc.     

Structural parameters of communication networks

Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.     

On the possibility for a protein to exist in a manifold of partially folded states

With the help of the methods of tryptophan fluorescence and room-temperature phosphorescence and using Escherichia coli alkaline phosphatase as an example, the ability of a protein to exist in a manifold of partially folded thermodynamically stable states differing in conformation, the internal dynamics, and functional activity was shown. Such intermediate (between native and unfolded) structures may form during unfolding or folding of the protein. It was shown that the degree of destruction of the native structural organization of the globule depends on both the nature and the mode of action of the destroying agent and the structure of the protein. Conformational transitions of the globule can change the kind of the internal dynamics (fast, slow), and shifts of dynamics can initiate conformation changes of the protein and precede them. A scheme of the structural and functional transformations of the protein during denaturation is presented, which takes into account the possibility of globule transitions into a manifold of functional active and inactive partially folded states. The role of partially folded forms of cell proteins in the development of pathology is discussed.     

Geometric parameters defining the structure of proteins--relation to early-stage folding step

Two geometrical parameters describing the structure of a polypeptide: V-dihedral angle between two sequential peptide bond planes and R-radius of curvature are used for structural classification of polypeptide structure in proteins. The relation between these two parameters was the basis for the definition of the conformational sub-space for early-stage structural forms. The cluster analysis of V and lnR, applied to the selected proteins of well-defined secondary structure (according to DSSP classification) and to proteins without any introductory classified analysis, revealed that several of the discriminated groups of proteins agree with the assumed model of early-stage conformational sub-space. This analysis shows that protein structures may be represented in VR space instead of Phi, Psi angles space, thus lowering the conformational space dimensionality. The VR model allows classification of traditional secondary structure elements as well as different Random Coil motifs, which broadens the range of recognized structural categories (compared to standard secondary structure elements).     

Hopf bifurcations in multiple-parameter space of the Hodgkin-Huxley equations I. Global organization of bistable periodic solutions

 The Hodgkin-Huxley equations (HH) are parameterized by a number of parameters and shows a variety of qualitatively different behaviors depending on the parameter values. We explored the dynamics of the HH for a wide range of parameter values in the multiple-parameter space, that is, we examined the global structure of bifurcations of the HH. Results are summarized in various two-parameter bifurcation diagrams with I _ext (externally applied DC current) as the abscissa and one of the other parameters as the ordinate. In each diagram, the parameter plane was divided into several regions according to the qualitative behavior of the equations. In particular, we focused on periodic solutions emerging via Hopf bifurcations and identified parameter regions in which either two stable periodic solutions with different amplitudes and periods and a stable equilibrium point or two stable periodic solutions coexist. Global analysis of the bifurcation structure suggested that generation of these regions is associated with degenerate Hopf bifurcations. Received: 23 April 1999 / Accepted in revised form: 24 September 1999     

A Refined Prediction Method for Gel Retardation of DNA Oligonucleotides from Dinucleotide Step Parameters: Reconciliation of DNA Bending Models with Crystal Structure Data

Abstract

The development and assessment of a prediction method for gel retardation and sequence dependent curvature of DNA based on dinucleotide step parameters are described. The method is formulated using the Babcock-Olson equations for base pair step geometry (1) and employs Monte Carlo simulated annealing for parameter optimization against experimental data. The refined base pair step parameters define a structural construct which, when the width of observed parameter distributions is taken into account, is consistent with the results of DNA oligonucleotide crystal structures. The predictive power of the method is demonstrated and tested via comparisons with DNA bending data on sets of sequences not included in the training set, including A-tracts with and without periodic helix phasing, phased A₄T₄ and T₄A₄ motifs, a sequence with a phased GGGCCC motif, some “unconventional” helix phasing sequences, and three short fragments of kinetoplast DNA from Crithidia fasiculata that exhibit significantly different behavior on non-denaturing polyacrylamide gels. The nature of the structural construct produced by the methodology is discussed with respect to static and dynamic models of structure and representations of bending and bendability. An independent theoretical account of sequence dependent chemical footprinting results is provided. Detailed analysis of sequences with A-tract induced axis bending forms the basis for a critical discussion of the applicability of wedge models, junction models and non A-tract, general sequence models for understanding the origin of DNA curvature at the molecular level.     

Exploring protein domain structure

The protein databank contains coordinates of over 10,000 protein structures, which constitute more than 25,000 structural domains in total. The investigation of protein structural, functional and evolutionary relationships is fundamental to many important fields in bioinformatics research, and will be crucial in determining the function of the human and other genomes.This review describes the SCOP and CATH databases of protein structure classification, which define, classify and annotate each domain in the protein databank. The hierarchical structure, use and annotation of the databases are explained. Other tools for exploring protein structure relationships are also described.     

Analysis of oscillations in yeast continuous cultures by a new simplified model

The autonomous oscillations in yeast continuous cultures are investigated analytically and related to the behaviour of the single cell by means of a suitable modified version of Monod’s classical chemostat model. Two main cell phases or states are considered to account for the experimentally observed changes occurring in the cell growth course: the budded phase and the unbudded one. Thus, a sort of two compartment structure is given to the total biomass. The model so far obtained allows one to analyse the local properties of the predicted steady states under various assumptions, both on the yield coefficients and the specific growth rates. Necessary conditions for the local instability are derived and the existence of stable limit cycles is shown by computer simulation. With respect to the qualitative changes in the metabolic parameters, this analysis agrees with the results obtained by simulation of complex structured and segregated models. However, the oscillation period is too long compared with the experimental one and this fact may be mainly due to the strong simplifying assumptions on the dynamic evolution of the transfer rates between the two compartments. The model’s usefulness seems until now restricted to the identification of the relationships between the cell cycle regulation and the oscillation triggering.     

Theoretical analysis of the relation between the cell state and pathways of carbon isotope fractionation in metabolic processes

On a dynamic model of fractionation of carbon isotopes in the living cell there are considered relationships between the distribution of carbon isotopes in the structures approximating basic biochemical fractions, their isotopic composition and parameters characterizing the dynamics of carbon metabolism, i.e. efficient carbon isotope separation factor in pyruvate enzymic decarboxylation, degree of its transformation at primary and secondary decarboxylation and ratios between the currents of carbon substrates. A wide range of variations of cell isotope parameters resulting from the change of its functional states was revealed. Possible applications of the relationships observed for studying biological systems are shown.     

Characterization of dynamic behavior of side groups of globular proteins by spin-label, NMR and luminescence polarization methods

In this work we suggest a quantitative estimation of a complicated motion of side groups of globular proteins. In the general case, three basic parameters determine the motion: (a) rotational correlation time of a side unit under study, or covalently bound spin label, or dye, (b) parameter S that reflects sterical restrictions for re-orientation of the given unit (these two parameters depending on the side-chain structure and its conformational change within the immediate dynamic protein surrounding whereas correlation times of side units on microviscosity in addition), (c) rotational correlation time of protein globule. These parameters can be measured by spin-label, NMR and fluorescence polarization techniques. An attempt to describe a complicated dynamic behaviour of side units of protein macromolecules with a single dynamics parameter--rotational correlation time--not only leads to a loss of part of information about the local structural dynamics of macromolecules but also can diminish the tau value.     

Data-based identifiability analysis of non-linear dynamical models

MOTIVATION: Mathematical modelling of biological systems is becoming a standard approach to investigate complex dynamic, non-linear interaction mechanisms in cellular processes. However, models may comprise non-identifiable parameters which cannot be unambiguously determined. Non-identifiability manifests itself in functionally related parameters, which are difficult to detect. RESULTS: We present the method of mean optimal transformations, a non-parametric bootstrap-based algorithm for identifiability testing, capable of identifying linear and non-linear relations of arbitrarily many parameters, regardless of model size or complexity. This is performed with use of optimal transformations, estimated using the alternating conditional expectation algorithm (ACE). An initial guess or prior knowledge concerning the underlying relation of the parameters is not required. Independent, and hence identifiable parameters are determined as well. The quality of data at disposal is included in our approach, i.e. the non-linear model is fitted to data and estimated parameter values are investigated with respect to functional relations. We exemplify our approach on a realistic dynamical model and demonstrate that the variability of estimated parameter values decreases from 81 to 1% after detection and fixation of structural non-identifiabilities.     

Interpreting Dynamically-Averaged Scalar Couplings in Proteins

The experimental determination of scalar three-bond coupling constants represents a powerful method to probe both the structure and dynamics of proteins. The detailed structural interpretation of such coupling constants is usually based on Karplus relationships, which allow the measured couplings to be related to the torsion angles of the molecules. As the measured couplings are sensitive to thermal fluctuations, the parameters in the Karplus relationships are better derived from ensembles representing the distributions of dihedral angles present in solution, rather than from single conformations. We present a method to derive such parameters that uses ensembles of conformations determined through dynamic-ensemble refinement – a method that provides structural ensembles that simultaneously represent both the structure and the associated dynamics of a protein.     

Reconstruction of biofilm images: combining local and global structural parameters

Digitized images can be used for quantitative comparison of biofilms grown under different conditions. Using biofilm image reconstruction, it was previously found that biofilms with a completely different look can have nearly identical structural parameters and that the most commonly utilized global structural parameters were not sufficient to uniquely define these biofilms. Here, additional local and global parameters are introduced to show that these parameters considerably increase the reliability of the image reconstruction process. Assessment using human evaluators indicated that the correct identification rate of the reconstructed images increased from 50% to 72% with the introduction of the new parameters into the reconstruction procedure. An expanded set of parameters especially improved the identification of biofilm structures with internal orientational features and of structures in which colony sizes and spatial locations varied. Hence, the newly introduced structural parameter sets helped to better classify the biofilms by incorporating finer local structural details into the reconstruction process.