A survey of some tensor analysis techniques for biological systems

Background: Since biological systems are complex and often involve multiple types of genomic relationships, tensor analysis methods can be utilized to elucidate these hidden complex relationships. There is a pressing need for this, as the interpretation of the results of high-throughput experiments has advanced at a much slower pace than the accumulation of data.Results: In this review we provide an overview of some tensor analysis methods for biological systems.Conclusions: Tensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics, mathematics and many other areas. Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations.     

An improved hydrogen bond potential: impact on medium resolution protein structures

A new semi-empirical force field has been developed to describe hydrogen-bonding interactions with a directional component. The hydrogen bond potential supports two alternative target angles, motivated by the observation that carbonyl hydrogen bond acceptor angles have a bimodal distribution. It has been implemented as a module for a macromolecular refinement package to be combined with other force field terms in the stereochemically restrained refinement of macromolecules. The parameters for the hydrogen bond potential were optimized to best fit crystallographic data from a number of protein structures. Refinement of medium-resolution structures with this additional restraint leads to improved structure, reducing both the free R-factor and over-fitting. However, the improvement is seen only when stringent hydrogen bond selection criteria are used. These findings highlight common misconceptions about hydrogen bonding in proteins, and provide explanations for why the explicit hydrogen bonding terms of some popular force field sets are often best switched off.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

In vivo protein complex topologies: sights through a cross-linking lens

Proteins are a remarkable class of molecules that exhibit wide diversity of shapes or topological features that underpin protein interactions and give rise to biological function. In addition to quantitation of abundance levels of proteins in biological systems under a variety of conditions, the field of proteome research has as a primary mission the assignment of function for proteins and if possible, illumination of factors that enable function. For many years, chemical cross-linking methods have been used to provide structural data on single purified proteins and purified protein complexes. However, these methods also offer the alluring possibility to extend capabilities to complex biological samples such as cell lysates or intact living cells where proteins may exhibit native topological features that do not exist in purified form. Recent efforts are beginning to provide glimpses of protein complexes and topologies in cells that suggest continued development will yield novel capabilities to view functional topological features of many proteins and complexes as they exist in cells, tissues, or other complex samples. This review will describe rationale, challenges, and a few success stories along the path of development of cross-linking technologies for measurement of in vivo protein interaction topologies.     

Neuronal plasticity and cellular immunity: shared molecular mechanisms

It is becoming evident that neurons express an unusual number of molecules that were originally thought to be specific to immune functions. One such molecule, class I major histocompatibility complex, is required in the activity-dependent refinement and plasticity of connections in the developing and adult central nervous system, demonstrating that molecules can perform critical roles in both systems. Recent studies reveal striking parallels between cellular signaling mechanisms in the immune and nervous systems that may provide unexpected insights into the development, function, and diseases of both systems.     

How accurately can oligonucleotide structures be determined from the hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics approach?

The accuracy and precision of structures derived from a combined hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics methodology were examined with simulations that included typical experimental errors. NOESY data were simulated for a DNA dodecamer duplex, d-(CGCGAATTCGCG)2, with added volume error of approximately 20% and low-level thermal noise. Distances derived from a hybrid relaxation matrix analysis of the NOE data were used as constraints in molecular dynamics driven structural refinements of several initial model geometries. The final structures were compared against results obtained from the traditional isolated two-spin approximation treatment of these NOESY volumes and also against refined structures that employed error-free data. Results show that the structures derived from the relaxation rate matrix analysis of the NOESY data are more accurate than those derived from a simple two-spin approximation analysis and it is possible to achieve refinement to the level of simulated experimental error. Results may be significantly improved with the use of either more accurately measured NOESY volumes or additional matrix-derived constraints. Many of the helical parameters and backbone torsional angles may be accurately reproduced by the hybrid matrix methodology.     

Prediction of protein oligomer structures using GALAXY in CASP13

Many proteins need to form oligomers to be functional, so oligomer structures provide important clues to biological roles of proteins. Prediction of oligomer structures therefore can be a useful tool in the absence of experimentally resolved structures. In this article, we describe the server and human methods that we used to predict oligomer structures in the CASP13 experiment. Performances of the methods on the 42 CASP13 oligomer targets consisting of 30 homo-oligomers and 12 hetero-oligomers are discussed. Our server method, Seok-assembly, generated models with interface contact similarity measure greater than 0.2 as model 1 for 11 homo-oligomer targets when proper templates existed in the database. Model refinement methods such as loop modeling and molecular dynamics (MD)-based overall refinement failed to improve model qualities when target proteins have domains not covered by templates or when chains have very small interfaces. In human predictions, additional experimental data such as low-resolution electron microscopy (EM) map were utilized. EM data could assist oligomer structure prediction by providing a global shape of the complex structure.     

Data-driven docking for the study of biomolecular complexes

With the amount of genetic information available, a lot of attention has focused on systems biology, in particular biomolecular interactions. Considering the huge number of such interactions, and their often weak and transient nature, conventional experimental methods such as X-ray crystallography and NMR spectroscopy are not sufficient to gain structural insight into these. A wealth of biochemical and/or biophysical data can, however, readily be obtained for biomolecular complexes. Combining these data with docking (the process of modeling the 3D structure of a complex from its known constituents) should provide valuable structural information and complement the classical structural methods. In this review we discuss and illustrate the various sources of data that can be used to map interactions and their combination with docking methods to generate structural models of the complexes. Finally a perspective on the future of this kind of approach is given.     

Advances in plant cell type-specific genome-wide studies of gene expression

Cell is the functional unit of life.To study the complex interactions of systems of biological molecules,it is crucial to dissect these molecules at the cell level.In recent years,major progresses have been made by plant biologists to profile gene expression in specific cell types at the genome-wide level.Approaches based on the isolation of cells,polysomes or nuclei have been developed and successfully used for studying the cell types from distinct organs of several plant species.These cell-level data sets revealed previously unrecognized cellular properties,such as cell-specific gene expression modules and hormone response centers,and should serve as essential resources for functional genomic analyses.Newly developed technologies are more affordable to many laboratories and should help to provide new insights at the cellular resolution in the near future.     

A component-based software environment for visualizing large macromolecular assemblies

The interactive visualization of large biological assemblies poses a number of challenging problems, including the development of multiresolution representations and new interaction methods for navigating and analyzing these complex systems. An additional challenge is the development of flexible software environments that will facilitate the integration and interoperation of computational models and techniques from a wide variety of scientific disciplines. In this paper, we present a component-based software development strategy centered on the high-level, object-oriented, interpretive programming language: Python. We present several software components, discuss their integration, and describe some of their features that are relevant to the visualization of large molecular assemblies. Several examples are given to illustrate the interoperation of these software components and the integration of structural data from a variety of experimental sources. These examples illustrate how combining visual programming with component-based software development facilitates the rapid prototyping of novel visualization tools.     

Fluorescence correlation spectroscopy and quantitative cell biology

Fluorescence correlation spectroscopy (FCS) analyzes fluctuations in fluorescence within a small observation volume. Autocorrelation analysis of FCS fluctuation data can be used to measure concentrations, diffusion properties, and kinetic constants for individual fluorescent molecules. Photon count histogram analysis of fluorescence fluctuation data can be used to study oligomerization of individual fluorescent molecules. If the FCS observation volume is positioned inside a living cell, these parameters can be measured in vivo. FCS can provide the requisite quantitative data for analysis of molecular interaction networks underlying complex cell biological processes.     

Parameter estimation in stochastic biochemical reactions

Gene regulatory, signal transduction and metabolic networks are major areas of interest in the newly emerging field of systems biology. In living cells, stochastic dynamics play an important role; however, the kinetic parameters of biochemical reactions necessary for modelling these processes are often not accessible directly through experiments. The problem of estimating stochastic reaction constants from molecule count data measured, with error, at discrete time points is considered. For modelling the system, a hidden Markov process is used, where the hidden states are the true molecule counts, and the transitions between those states correspond to reaction events following collisions of molecules. Two different algorithms are proposed for estimating the unknown model parameters. The first is an approximate maximum likelihood method that gives good estimates of the reaction parameters in systems with few possible reactions in each sampling interval. The second algorithm, treating the data as exact measurements, approximates the number of reactions in each sampling interval by solving a simple linear equation. Maximising the likelihood based on these approximations can provide good results, even in complex reaction systems.     

Visualization of dynamic simulations of muscle thin filaments

Following a novel computational formalism, the thin filament of muscle can be modeled by a computational machine containing a large number of finite automata that have one-to-one correspondence with the constituent protein molecules.¹ Computer graphics can be used to visualize the correspondence between the states of finite automata and the configurations of protein molecules according to the structural data. The dynamic simulation of the muscle filament that corresponds to the concurrent state transitions of finite automata can be represented as a sequence of video images. The kinetic and structural knowledge of individual protein molecules is, therefore, integrated into a coherent and functional system. This type of computation and visualization can also be useful for the investigation of molecular structure, function, and interaction in various complex biological systems.     

LNB-TM7, a group of seven-transmembrane proteins related to family-B G-protein-coupled receptors

A number of unusual seven-transmembrane molecules have recently been characterized that have significant amino acid sequence similarity within the membrane-spanning hydrophobic regions and intervening loops to members of G-protein-coupled receptor family B. However, in contrast to the family-B G-protein-coupled receptors, these molecules have unusually large N-terminal extracellular domains that contain a number of well- characterized protein modules. The range of cell types expressing these complex molecules and their potential roles in cell adhesion and signalling have become a major focus of research in a number of biological systems.     

Structure-based systems biology: a zoom lens for the cell

Systems biology seeks to explain complex biological systems, such as the cell, through the integration of many different types of information. Here, we discuss how the incorporation of high-resolution structural data can provide key molecular details often necessary to understand the complex connection between individual molecules and cell behavior. We suggest a process of zooming on the cell, from global networks through pathways to the precise atomic contacts at the interfaces of interacting proteins.     

Symmetry-restrained flexible fitting for symmetric EM maps

Many large biological macromolecules have inherent structural symmetry, being composed of a few distinct subunits, repeated in a symmetric array. These complexes are often not amenable to traditional high-resolution structural determination methods, but can be imaged in functionally relevant states using cryo-electron microscopy (cryo-EM). A number of methods for fitting atomic-scale structures into cryo-EM maps have been developed, including the molecular dynamics flexible fitting (MDFF) method. However, quality and resolution of the cryo-EM map are the major determinants of a method's success. In order to incorporate knowledge of structural symmetry into the fitting procedure, we developed the symmetry-restrained MDFF method. The new method adds to the cryo-EM map-derived potential further restraints on the allowed conformations of a complex during fitting, thereby improving the quality of the resultant structure. The benefit of using symmetry-based restraints during fitting, particularly for medium to low-resolution data, is demonstrated for three different systems.     

BIOSENSORS: BLESSING OR BANE?

Biosensor technology is changing the methodology used to detect or characterize many microorganisms and/or their metabolites of importance to food microbiologists and the food industry. Biosensors have been developed to monitor the freshness of meat and fish. ATP and glucose concentrations have been monitored as well as continuous control operations in food processing. Enzyme-substrate transformations, DNA or RNA hybridizations and antibody-antigen interactions are examples of the types of molecules used in biosensor systems. Instrumentation coupled to the biological molecules and measuring the changes that occur include reactions on simple ion-sensing electrodes, as well as complex chips, optical fibers or piezoelectric crystals. In most cases, data can be obtained within a few minutes on very small amounts of compounds. However, the long term stability of the biological molecules involved in these procedures presents a major stumbling block. Partially or completely disposable devices are under consideration.     

Vertebrate protein glycosylation: diversity, synthesis and function

Protein glycosylation is a ubiquitous post-translational modification found in all domains of life. Despite their significant complexity in animal systems, glycan structures have crucial biological and physiological roles, from contributions in protein folding and quality control to involvement in a large number of biological recognition events. As a result, they impart an additional level of 'information content' to underlying polypeptide structures. Improvements in analytical methodologies for dissecting glycan structural diversity, along with recent developments in biochemical and genetic approaches for studying glycan biosynthesis and catabolism, have provided a greater understanding of the biological contributions of these complex structures in vertebrates.     

Structure determination of a new protein from backbone-centered NMR data and NMR-assisted structure prediction

Targeting of proteins for structure determination in structural genomic programs often includes the use of threading and fold recognition methods to exclude proteins belonging to well-populated fold families, but such methods can still fail to recognize preexisting folds. The authors illustrate here a method in which limited amounts of structural data are used to improve an initial homology search and the data are subsequently used to produce a structure by data-constrained refinement of an identified structural template. The data used are primarily NMR-based residual dipolar couplings, but they also include additional chemical shift and backbone-nuclear Overhauser effect data. Using this methodology, a backbone structure was efficiently produced for a 10 kDa protein (PF1455) from Pyrococcus furiosus. Its relationship to existing structures and its probable function are discussed.