Interpretation of ANOVA models for microarray data using PCA.

MOTIVATION: ANOVA is a technique, which is frequently used in the analysis of microarray data, e.g. to assess the significance of treatment effects, and to select interesting genes based on P-values. However, it does not give information about what exactly is causing the effect. Our purpose is to improve the interpretation of the results from ANOVA on large microarray datasets, by applying PCA on the individual variance components. Interaction effects can be visualized by biplots, showing genes and variables in one plot, providing insight in the effect of e.g. treatment or time on gene expression. Because ANOVA has removed uninteresting sources of variance, the results are much more interpretable than without ANOVA. Moreover, the combination of ANOVA and PCA provides a simple way to select genes, based on the interactions of interest. RESULTS: It is shown that the components from an ANOVA model can be summarized and visualized with PCA, which improves the interpretability of the models. The method is applied to a real time-course gene expression dataset of mesenchymal stem cells. The dataset was designed to investigate the effect of different treatments on osteogenesis. The biplots generated with the algorithm give specific information about the effects of specific treatments on genes over time. These results are in agreement with the literature. The biological validation with GO annotation from the genes present in the selections shows that biologically relevant groups of genes are selected. AVAILABILITY: R code with the implementation of the method for this dataset is available from http://www.cac.science.ru.nl under the heading "Software".

Identification of functional and unfolding motions of cutinase as obtained from molecular dynamics computer simulations.

The implementation of cutinase from Fusarium solani pisi as a fat-stain removing ingredient in laundry washing is hampered by its unfolding in the presence of anionic surfactants. In this work we present molecular dynamics (MD) computer simulations on cutinase and analysis procedures to distinguish the movements related to its functional behavior (e.g., substrate binding) from those related to the unfolding of the enzyme. Two kinds of MD-simulations were performed: a simulation mimicking the thermal motion at room temperature, and several simulations in which unfolding is induced either by high temperature or by using a modified water-protein interaction potential. Essential dynamics analyses (A. Amadei et al., Proteins 17:412-425, 1993) on the simulations identify distinct regions in the molecular structure of cutinase in which the motions occur for function and initial unfolding. The unfolding in various simulations starts in a similar way, suggesting that mutations in the regions involved might stabilize the enzyme without affecting its functionality.

The nature of antibody heavy chain residue H6 strongly influences the stability of a VH domain lacking the disulfide bridge.

Monoclonal antibody mAb 03/01/01, directed against the musk odorant traseolide, carries a serine residue instead of the conserved Cys H92 in the heavy chain variable domain, and is thus lacking the highly conserved disulfide bridge. We investigated the energetic consequence of restoring the disulfide bond and the nature of residue H6 (Glu or Gln), which is poised to interact with Ser H92 in the recombinant scFv fragment obtained from this antibody. In the scFv fragment derived from this antibody, the stabilizing effect of Gln H6 over Glu was found to be as large as the effect of reintroducing the disulfide bond. We have analyzed the conformation and hydrogen bond pattern of Gln H6 and Glu H6 in antibodies carrying these residues and suggest mechanisms by which this residue could contribute to VH domain stability. We also show that the unpaired cysteine H22 is buried, and conforms to the expected VH structure. The antibody appears to have acquired two somatic mutations (Ser H52 and Arg H66), which had been previously characterized as having a positive effect on VH stability. The overall domain stability is the decisive factor for generating functional, disulfide-free antibody domains, and several key residues play dominant roles.

Lipoxygenase is irreversibly inactivated by the hydroperoxides formed from the enynoic analogues of linoleic acid.

Triple bond analogues of natural fatty acids irreversibly inactivate lipoxygenase during their enzymatic conversion [Nieuwenhuizen, W. F., et al. (1995) Biochemistry 34, 10538-10545]. To gain insight into the mechanism of the irreversible inactivation of soybean lipoxygenase-1, we studied the enzymatic conversion of two linoleic acid analogues, 9(Z)-octadec-9-en-12-ynoic acid (9-ODEYA) and 12(Z)-octadec-12-en-9-ynoic acid (12-ODEYA). During the inactivation process, Fe(III)-lipoxygenase converts 9-ODEYA into three products, i.e. 11-oxooctadec-9-en-12-ynoic acid, racemic 9-hydroxy-10(E)-octadec-10-en-12-ynoic acid, and racemic 9-hydroperoxy-10(E)-octadec-10-en-12-ynoic acid. Fe(II)-lipoxygenase does not convert the inhibitor and is not inactivated by 9-ODEYA. Fe(III)-lipoxygenase converts 12-ODEYA into 13-hydroperoxy-11(Z)-octadec-11-en-9-ynoic acid (34/66 R/S), 13-hydroperoxy11(E)-octadec-11-en-9-ynoic acid (36/64 R/S), 11-hydroperoxyoctadec-12-en-9-ynoic acid (11-HP-12-ODEYA, enantiomeric composition of 33/67), and 11-oxooctadec-12-en-9-ynoic acid (11-oxo-12-ODEYA) during the inactivation process. Also, Fe(II)-lipoxygenase is inactivated by 12-ODEYA. It converts the inhibitor into the same products as Fe(III)-lipoxygenase does, but two additional products are formed, viz. 13-oxo-11(E)-octadec-11-en-9-ynoic acid and 13-oxo-11(Z)-octadec-11-en-9-ynoic acid. The purified reaction products were tested for their lipoxygenase inhibitory activities. The oxo compounds, formed in the reaction of 9-ODEYA and 12-ODEYA, do not inhibit Fe(II)- or Fe(III)-lipoxygenase. The 9- and 13-hydroperoxide products that are formed from 9-ODEYA and 12-ODEYA, respectively, oxidize Fe(II)-lipoxygenase to its Fe(III) state and are weak lipoxygenase inhibitors. 11-HP-12-ODEYA is, however, the most powerful inhibitor and is able to oxidize Fe(II)-lipoxygenase to Fe(III)-lipoxygenase. 11-HP-12-ODEYA is converted into 11-oxo-12-ODEYA by Fe(III)-lipoxygenase. We propose a mechanism for the latter reaction in which Fe(III)-lipoxygenase abstracts the bisallylic hydrogen H-11 from 11-HP-12-ODEYA, yielding a hydroperoxyl radical which is subsequently cleaved into 11-oxo-ODEYA and a hydroxyl radical which may inactivate the enzyme.

1H, 13C, and 15N resonance assignments of Fusarium solani pisi cutinase and preliminary features of the structure in solution.

Essentially complete (96%) sequence-specific assignments were made for the backbone and side-chain 1H, 13C, and 15N resonances of Fusarium solani pisi cutinase, produced as a 214-residue heterologous protein in Escherichia coli, using heteronuclear NMR techniques. Three structural features were noticed during the assignment. (1) The secondary structure in solution corresponds mostly with the structure from X-ray diffraction, suggesting that both structures are globally similar. (2) The HN of Ala32 has a strongly upfield-shifted resonance at 3.97 ppm, indicative of an amide-aromatic hydrogen bond to the indole ring of Trp69 that stabilizes the N-terminal side of the parallel beta-sheet. (3) The NMR data suggest that the residues constituting the oxyanion hole are quite mobile in the free enzyme in solution, in contrast to the existence of a preformed oxyanion hole as observed in the crystal structure. Apparently, cutinase forms its oxyanion hole upon binding of the substrate like true lipases.

Internal mobility of the basic pancreatic trypsin inhibitor in solution: a comparison of NMR spin relaxation measurements and molecular dynamics simulations.

Order parameters as well as longitudinal and transverse relaxation rates are calculated for the backbone 15N and 13C alpha nuclei of the basic pancreatic trypsin inhibitor (BPTI) from a 1000 ps molecular dynamics trajectory in explicit water at 277 K using the "model free" approach of Lipari and Szabo. New NMR relaxation data at 277 K are presented, and a comparison is made between NMR relaxation measurements and molecular dynamics relaxation data. It is found that the relaxation processes determining the longitudinal (T1) relaxation rates are inadequately sampled even during this length of simulation. In effect, the calculated relaxation rates are determined almost solely by the order parameters and the overall rotational correlation time of the protein, which appears to be in clear contrast to experimental relaxation rates.

The high-resolution structure of the histidine-containing phosphocarrier protein HPr from Escherichia coli determined by restrained molecular dynamics from nuclear magnetic resonance nuclear Overhauser effect data.

The solution structure of the histidine-containing phosphocarrier protein HPr from Escherichia coli has been determined by NMR in combination with distance geometry and restrained molecular dynamics. The structure is based on 1520 experimental restraints identified from both three-dimensional 1H-1H-13C and 1H-1H-15N nuclear Overhauser effect multiple-quantum coherence spectroscopy and two-dimensional 1H-1H nuclear Overhauser effect spectra. Thirty-two four-dimensional coordinate frames were produced by metric matrix distance geometry, subjected to distance bounds driven dynamics, projected into three-dimensional space and again subjected to distance-bounds driven dynamics. These 32 distance geometry structures were refined further by restrained molecular dynamics (40 ps) in the GROMOS in vacuo force field. All 32 structures reached acceptable energy minima while satisfying the imposed restraints. Two of these structures were subjected to a further 200 ps of molecular dynamics simulation in water, using time-dependent distance restraining, followed by a 200 ps free simulation without any distance restraining. The resulting structure is very similar to the X-ray structure of Bacillus subtilis HPr, but differs mainly in the position of the two loops containing the active site histidine residue 15 and residues 53 to 57 relative to the rest of the structure. The unfavorable phi torsion angle that was found for residue 16 in the active center of unphosphorylated Streptococcus faecalis HPr was proposed to play a role in the activity of the protein. Although present at the early stages of the structure calculations, this torsion-angle strain disappeared in the final model obtained from molecular dynamics simulations in water using time-averaged distance restraining and upon releasing the distance restraints. This suggests that the strain may be an artifact of crystallization conditions instead of an essential element in the phosphorylation/dephosphorylation process.

A structure refinement method based on molecular dynamics in four spatial dimensions.

We have developed a method for structure refinement based on molecular dynamics in four spatial dimensions (4D-MD). The method was applied with success to the structure refinement of Cyclosporin A (CPA) and the lac-repressor headpiece (LAC) using atom-atom distance restraints derived from NMR data, two cases where conventional MD refinement methods failed. In the case of CPA we were able to refine seven out of nine substantially different structures, while conventional MD only refines three structures. Previously, it had appeared to be impossible to refine a given LAC structure with conventional MD methods, manual modifications were necessary in order to fulfil all the distance restraints. In this study we show that LAC can be refined without manual interference and using only 5000 steps (10 ps) of 4D-MD. The latter result is particularly interesting because it indicates that this method may be a very useful tool when modelling loops in proteins.

Conformational search by potential energy annealing: algorithm and application to cyclosporin A.

A major problem in modelling (biological) macromolecules is the search for low-energy conformations. The complexity of a conformational search problem increases exponentially with the number of degrees of freedom which means that a systematic search can only be performed for very small structures. Here we introduce a new method (PEACS) which has a far better performance than conventional search methods. To show the advantages of PEACS we applied it to the refinement of Cyclosporin A and compared the results with normal molecular dynamics (MD) refinement. The structures obtained with PEACS were lower in energy and agreed with the NMR parameters much better than those obtained with MD. From the results it is further clear that PEACS samples a much larger part of the available conformational space than MD does.

On deriving spatial protein structure from NMR or X-ray diffraction data.

During the last decade it has become possible to derive the spatial structure of small proteins in solution using multidimensional NMR spectroscopy measurements and interpreting the data in terms of a chemical atomic model. The NMR experiments generate a set of interproton distance constraints, which is subsequently used to generate spatial structures that satisfy the experimental data. Correspondingly, crystallographic least-squares and molecular dynamics refinement is routinely applied to obtain a protein structure that is compatible with the observed structure factor amplitudes. The quality of the structure obtained will depend on the number and quality of the experimental data and on the searching power of the refinement method and protocol. The potential energy annealing conformational search (PEACS) algorithm is shown to be an improvement over standard molecular dynamics search methods. The use of time-dependent distance or structure factor restraints in molecular dynamics refinement yields a much better representation of experimental information than the fixed, static restraints which have generally been used until now. Conventional structure refinement methods lead to a too static and rigid picture of a protein in solution or in the crystalline state.