A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

Conformational flexibility of DNA: polymorphism and handedness

It is shown that left-handed duplexes are possible for A, B, and D forms of DNA. These duplexes are stereochemically satisfactory and are consistent with the observed x-ray intensity data. On scrutiny the refined right-handed models of B and D DNA by Arnott and coworkers are found to be stereochemically unacceptable. It was possible to formulate a stereochemical guideline for molecular model building based on theory and analysis of single-crystal structure data of dinucleoside monophosphate and higher oligomers. This led to both right- and left-handed DNA duplexes. The right-handed B and D DNA duplexes so obtained are stereochemically superior to earlier models and agree well with the observed x-ray intensity data. The observation that DNA can exist in either handedness for all the polymorphous forms of DNA at once explained A in equilibrium B and B in equilibrium D transitions. Hence it is confirmed that polymorphism of DNA is a reflection on the conformational flexibility inherent in DNA, the same cause that ultimately allows DNA in either handedness. The possibility of various types of right- and left-handed duplexes generated by using dinucleoside monophosphate and trinucleoside diphosphate as repeating units resulted in a variety of models, called RL models. All these models have alternating right and left helical segments and inverted stacking at the bend region as suggested by us earlier. It turns out that the B-Z DNA model of Wang et al. is only an example of RL models.

Molecular conformation of N,N -diarylthioureas: An assessment by 1H NMR and infrared spectroscopy

Several N,N -dipyridyl- and N-phenyl-N -pyridyl-thioureas were examined in different solvents at various temperatures by 1H NMR in order to study their conformational properties. The influence of concentration and the methyl substituent in the pyridine ring on the chemical shifts of the NH and pyridine groups was investigated. The observed chemical shifts are analysed in terms of the conformational properties of the molecules. Free energy barriers to the internal rotation about the C N bonds have been determined. Infrared spectra have been measured to supplement the NMR studies. Intramolecular hydrogen bonding played a major role in the preferred conformation of pyridylthioureas. The data further revealed an interesting dynamic exchange phenomenon occurring in symmetric N,N -dipyridylthioureas between two intramolecularly hydrogen bonded conformers.

Left-handed helices for DNA: studies on poly[d(I-C)]

Earlier, we showed that, for the D form (n = 8 and h = 3.03 A, where n is number of nucleotide units per turn and h is height per nucleotide unit) of poly[d(A-T)], both right- and left-handed double helical models are stereochemically satisfactory and give good agreement with the observed fiber diffraction data. It was also noted that the conformations of the right- and left-handed D-DNA models are very similar to those of the right- and left-handed B-DNA models. This observation was consistent with the D leads to B transition in the solid phase. As a continuation of our earlier studies, we have carried out similar experiments with poly[d(I-C)]. We could obtain a crystalline D-form pattern (n = 8, h = 3.13 A) of the fiber at 75% relative humidity (r.h.); the hydrated (r.h. approximately equal to 95%) form of the same fiber gave the classical B-form pattern (n = 10, h = 3.40 A). In the present report, we show that both right- and left-handed double-helical models are consistent with the fiber diffraction data of poly[d(I-C)] in the D-form. Theoretical energy calculations also suggest that the right- and left-handed B- and D-DNA models are almost equally stable. Hence, we conclude that the right- and left-handed double-helical models of poly[d(I-C)] in a given form (B or D) are equally likely and that the fiber diffraction data do not permit discrimination.

Geometry Of Proline And Hydroxyproline .1. An Analysis Of X-Ray Crystal-Structure Data

We have carried out an analysis of crystal structure data on prolyl and hydroxyprolyl moieties in small molecules. The flexibility of the pyrrolidine ring due to the pyramidal character of nitrogen has been defined in terms of two projection angles δ1 and δ2. The distribution of these parameters in the crystal structures is found to be consistent with results of the energy calculations carried out on prolyl moieties in our laboratory.

Proton magnetic resonance study of molecular dynamics in (NH4)2CdI4

Proton magnetic resonance and spin-lattice relaxation studies have been carried out on (NH4)2CdI4 as a function of temperature (77–400 K) and Larmor frequency (10, 20 and 30 MHz). The T1 data indicate isotropic tumbling of ammonium ions at equivalent sites till 160 K. There is an indication of a phase transition at 265 K, the activation energy for molecular reorientation increases from 2.8 kcal/mole to 4.6 kcal/mole. The relaxation results and the linewidth data support the presence of two inequivalent sites at low temperatures, one having an environment corresponding to near-rigid-lattice limit and the other undergoing fast reorientations. The behaviour of the free induction decay with temperature below 120 K suggests a coherent motion for the faster species.

Molecular Dynamics in [(CH8)aN]z Cd14 A Proton Magnetic Relaxation Study

second moment measurements are carried out on [(CH,),N], CdI, in the temperature range 77 to 400 K. The results are interpreted based on a molecular dynamical model of randomly reorienting methyl groups and isotropically tumbling tetramethyl ammonium group. The relaxation data show contributions from spin-rotation interaction at high temperatures and presence of inequivalent methyl groups. The correlation times and associated activation energies, connected with this model, are calculated from the data. The structure in the absorption line and in the free-induction decay signal at 77 K indicates the possibility of tunnelling motion of the methyl groups. Im Temperaturbereich 77 bis 400 K werden an [(CH,),N],CdI, Protonen-Spin-Gitter-Relaxationsexperimente (bei Larmorfrequenzen von 10,20 und 30 MHz) und Messungen des zweiten Moments durchgefiihrt. Die Ergebnisse werden an Hand eines molekularen dynamischen Modells sich statistisch umorientierender Methylgruppen und isotrop taumelnder Tetramethyl-Ammoniumgruppen interpretiert. Die Relaxationswerte zeigen Beitriige von Spin-Rotations-Wechselwirkung bei hohen Temperaturen und die Anwesenheit von inaquivalenten Methylgruppen. Die Korrelationszeiten und verknupften Aktivierungsenergien, die mit diesem Model1 verbunden sind, werden am den Werten berechnet. Die Struktur in der Absorptionslinie und im Abklingsignal der freien Induktion bei 77 K zeigt die Moglichkeit einer Tunnelbewegung der Methylgruppen.

Strategies for collecting screen-less oscillation data

Screen-less oscillation photography is the method of choice for recording three-dimensional X-ray diffraction data for crystals of biological macromolecules. The geometry of an oscillation camera is extremely simple. However, the manner in which the reciprocal lattice is recorded in any experiment is fairly complex. This depends on the Laue symmetry of the reciprocal lattice, the lattice type, the orientation of the crystal on the camera and to a lesser extent on the unit-cell dimensions. Exploring the relative efficiency of collecting X-ray diffraction data for different crystal orientations prior to data collection might reduce the number of films required to record most of the unique data and the consequent amount of time required for processing these films. Here algorithms are presented suitable for this purpose and results are reported for the 11 Laue groups, different lattice types and crystal orientations often employed in data collection.

Flexibility of the furanose ring in nucleic acids: a compilation of crystal data

A compilation of crystal structure data on deoxyribo- and ribonucleosides and their higher derivatives is presented. The aim of this paper is to highlight the flexibility of deoxyribose and ribose rings. So far, the conformational parameters of nucleic acids constituents of ribose and deoxyribose have not been analysed separately. This paper aims to correlate the conformational parameters with the nature and puckering of the sugar. Deoxyribose puckering occurs in the C2′ endo region while ribose puckering is observed both in the C3′ endo and C2′ endo regions. A few endocyclic and exocyclic bond angles depend on the puckering and the nature of the sugar. The majority of structures have an anti conformation about the glycosyl bond. There appears to be a puckering dependence on the torsion angle about the C4′---C5′ bonds. Such stereochemical information is useful in model building studies of polynucleotides and nucleic acids.

Proline-containing β-turns in peptides and proteins: Analysis of structural data on globular proteins

Tetrapeptide sequences of the type Z-Pro-Y-X were obtained from the crystal structure data on 34 globular proteins, and used in an analysis of the positional preferences of the individual amino acid residues in the β-turn conformation. The effect of fixing proline as the second position residue in the tetrapeptide sequence was studied by comparing the data obtained on the positional preferences with the corresponding data obtained by Chou and Fasman using the Z-R-Y-X sequence, where no particular residue was fixed in any of the four positions. While, in general, several amino acid residues having relatively very high or very low preferences for specific positions were found to be common to both the Z-Pro-Y-X and Z-R-Y-X sequences, many significant differences were found between the two sets of data, which are to be attributed to specific interactions arising from the presence of the proline residue.

Molecular structure of a cyclic tetrapeptide disulfide. A novel 310 helical conformation with an S-S bridge

The crystal structure of the cyclic peptide disulfide Boc-Cys-Pro-Aib-Cys-NHMe has been determined by X-ray diffraction. The peptide crystallizes in the space group P212121, with A = 8.646(1), B = 18.462(2), C = 19.678(3)Å and Z = 4. The molecules adopt a highly folded compact conformation, stabilized by two intramolecular 4→ 1 hydrogen bonds between the Cys (1) and Pro (2) CO groups and the Cys (4) and methylamide NH groups, respectively. The backbone conformational angles for the peptide lie very close to those expected for a 310 helix. The S-S bridge adopts a right handed twist with a dihedral angle of 82°. The structure illustrates the role of stereochemically constrained residues, in generating novel peptide conformations. Aib, α-aminoisobutyric acid; Z, benzyloxycarbonyl; Boc, t-butyloxycarbonyl; OMe, methyl ester; OBz, benzyl ester; NHMe, N-methylamide; Tosyl, p-toluenesulfonyl.

A chitotetrose specific lectin from Luffa acutangula :Physico-chemical properties and the assignment of orientation of sugars in the lectin binding site

A chitooligosaccharide specific lectin (Luffa acutangula agglutinin) has been purified from the exudate of ridge gourd fruits by affinity chromatography on soybean agglutininglycopeptides coupled to Sepharose-6B. The affinity purified lectin was found homogeneous by polyacrylamide gel electrophoresis, in sodium dodecyl sulphate-polyacrylamide gels, by gel filtration on Sephadex G-100 and by sedimentation velocity experiments. The relative molecular weight of this lectin is determined to be 48,000 ± 1,000 by gel chromatography and sedimentation equilibrium experiments. The sedimentation coefficient (S20, w) was obtained to be 4·06 S. The Stokes’ radius of the protein was found to be 2·9 nm by gel filtration. In sodium dodecyl sulphate-polyacrylamide gel electrophoresis the lectin gave a molecular weight of 24,000 in the presence as well as absence of 2-mercaptoethanol. The subunits in this dimeric lectin are therefore held by non-covalent interactions alone. The lectin is not a glycoprotein and circular dichroism spectral studies indicate that this lectin has 31% α-helix and no ß-sheet. The lectin is found to bind specifically to chitooligosaccharides and the affinity of the lectin increases with increasing oligosaccharide chain length as monitored by near ultra-violetcircular dichroism and intrinsic fluorescence titration. The values of ΔG, ΔΗ and ΔS for the binding process showed a pronounced dependence on the size of the oligosaccharide. The values for both ΔΗ and ΔS show a significant increase with increase in the oligosaccharide chain length showing that the binding of higher oligomers is progressively more favoured thermodynamically than chitobiose itself. The thermodynamic data is consistent with an extended binding site in the lectin which accommodates a tetrasaccharide. Based on the thermodynamic data, blue shifts and fluorescence enhancement, spatial orientation of chitooligosaccharides in the combining site of the lectin is assigned.

Is 3'-nucleotide rigid?

Conformational analysis of nucleic acids and polynucleotides is far more complex than that of proteins and polypeptides, due to five single bond rotations in addition to the sugar puckerings in the monomer. Sundaralingam1 proposed the concept of the 'rigid' nucleotides from analysis of crystal structure data, with the flexibility allowed only about the phosphodiester bonds. However, the crystal structure of deoxyguanosine-5'−phosphate2,3 indicates at gt conformation about the C-4'−C-5' bond against gg in a conformationally rigid nudeotide1. Jack et al. 4 considered the flexibility of nucleotides in tRNA about the C-4'−C-5' bond, thereby introducing the concept of 'non-rigid' ribonucleotides. Conformational flexibility of the f uranose ring in DNA and RNA and their energetics using classical and quantum chemical methods have been reported5−8. We have examined the flexibility of 3'-nucleotides. alpha, the most important of the conformational parameters defining the 3'-end of a nucleotide unit9, has a value in the range 195°−270° in all the 3'-nucleotides, dinucleoside monophosphates and higher oligomers which have been surveyed. A survey of the proposed structures of polyribonudeotides10,11 also shows the values of a to be greater than 200°. However, the structures proposed for B-DNA by Arnott and Hukins12,13 and D-DNA by Arnott et al. 14 have values of alpha of 155° and 141° respectively, much lower than the lowest observed value. The structure for B-DNA has two strong, short contacts (C-2'...OP-1 = 2.64 Å and HC-2"...OP-1 = 1.79 Å) which lead to an energetically unfavourable conformation. Hence, it is of interest to investigate whether, by allowing flexibility to the sugar moiety in the nucleotide unit, it is possible to make the structure energetically favourable. Here, conformational energy calculations were carried out to determine the range of alpha which would give rise to energetically favoured conformations with different sugar puckerings. Our analysis has shown that the theoretically obtained range is nearly the same as the preferred range in crystals, indicating the flexibility of the 3'-nucleotides.

The mean geometry of the peptide unit from crystal structure data

The average dimensions of the peptide unit have been obtained from the data reported in recent crystal structure analyses of di- and tripeptides. The bond lengths and bond angles agree with those in common use, except for the bond angle C---N---H, which is about 4° less than the accepted value, and the angle C2α---N---H which is about 4° more. The angle τ (Cα) has a mean value of 114° for glycyl residues and 110° for non-glycyl residues. Attention is directed to these mean values as observed in crystal structures, as they are relevant for model building of peptide chain structures.

Metal ions in molecular association of porphyrins

Molecular association of porphyrins and their metal derivatives has been recognized as one of the important properties for many of their biological functions. The association is classified into (i) self-aggregation, (ii) intermolecular association and (iii) intramolecular association. The presence of metal ions in the porphyrin cavity is shown to alter the magnitudes of binding constants and thermodynamic parameters of complexation. The interaction between the porphyrin unit and the acceptor is described in terms of π-π interaction. The manifestation of charge transfer states both in the ground and excited states of these complexes is shown to influence the rates of excited state electron transfer reactions. Owing to paucity of crystal structure data, the time-averaged geometries of many of these complexes have been derived from magnetic resonance data.