Flux balance analysis of biological systems: applications and challenges

Systems level modelling and simulations of biological processes are proving to be invaluable in obtaining a quantitative and dynamic perspective of various aspects of cellular function. In particular, constraint-based analyses of metabolic networks have gained considerable popularity for simulating cellular metabolism, of which flux balance analysis (FBA), is most widely used. Unlike mechanistic simulations that depend on accurate kinetic data, which are scarcely available, FBA is based on the principle of conservation of mass in a network, which utilizes the stoichiometric matrix and a biologically relevant objective function to identify optimal reaction flux distributions. FBA has been used to analyse genome-scale reconstructions of several organisms; it has also been used to analyse the effect of perturbations, such as gene deletions or drug inhibitions in silico. This article reviews the usefulness of FBA as a tool for gaining biological insights, advances in methodology enabling integration of regulatory information and thermodynamic constraints, and finally addresses the challenges that lie ahead. Various use scenarios and biological insights obtained from FBA, and applications in fields such metabolic engineering and drug target identification, are also discussed. Genome-scale constraint-based models have an immense potential for building and testing hypotheses, as well as to guide experimentation.

Bottleneck assignment problems under categorization

This paper considers two special cases of bottleneck grouped assignment problems when n jobs belong to m distinct categories (m < n). Solving these special problems through the available branch and bound algorithms will result in a heavy computational burden. Sequentially identifying nonopitmal variables, this paper provides more efficient methods for those cases. Propositions leading to the algorithms have been established. Numerical examples illustrate the respective algorithms.

Stereochemical studies on cyclic peptides. XIII. Energy minimization studies on cyclic hexapeptides having hydrogen bonds

The basic cyclic hexapeptide conformations which accommodate hydrogen bonded β and γ turns in the backbone have been worked out using stereochemical criteria and energy minimization procedures. It was found that cyclic hexapeptides can be made up of all possible combinations of 4 ± 1 hydrogen bonded types I, I', II and II' β turns, giving rise to symmetric conformations having twofold and inversion symmetries as well as nonsymmetric structures. Conformations having exclusive features of 3 ± 1 hydrogen bonded γ turns were found to be possible in threefold and S6 symmetric cyclic hexapeptides. The results show that the cyclic hexapeptides formed by the linking of two β turn tripeptide fragments differ mainly in (a) the hydrogen bonding scheme present in the β turn tripeptides and (b) the conformation at the α-carbon atoms where the two tripeptide fragments link. The different hydrogen bonding schemes found in the component β turns are: 1) a β turn with only a 4 ± 1 hydrogen bond, 2) a type I or I' β turn with 4 ± 1 and 3 ± 1 hydrogen bonds occurring in a bifurcated form and 3) a type II or II' β turn having both the 4 ± 1 and the 3 ± 1 hydrogen bonds with the same acceptor oxygen atom. The conformation at the linking α-carbon atoms was found to lie either in the extended region or in the 3 ± 1 hydrogen bonded γ turn or inverse γ turn regions. Further, the threefold and the S6 symmetric conformations have three γ turns interleaved by three extended regions or three inverse γ turns, respectively. The feasibility of accommodating alanyl residues of both isomeric forms in the CHP minima has been explored. Finally, the available experimental data are reviewed in the light of the present results.

Inhibition of mitochondrial oxidative phosphorylation by adriamycin

The antitumour antibiotic, adriamycin, inhibited oxidative phosphorylation in freshly prepared mitochondria from the heart, liver and kidney of the rat. It abolished respiratory control and stimulated ATPase activity. Sccinate oxidation by heart mitochondria was extremely sensitive to the drug when hexokinase was present in the reaction medium. The sensitive site has been identified to lie in the region between the succinate dehydrogenase flavoprotein and ubiquinone of the respiratory chain.

Inhibition of mitochondrial oxidative phosphorylation by 2-methyl-4-dimethylaminoazobenzene

The azodye 2-methyl-4-dimethylaminoazobenzene inhibited oxidation and phosphorylation in tightly coupled rat liver mitochondria. Phosphorylation was more sensitive to the inhibitory action of the azodye than was the oxidation of succinate or ascorbate. The oxidation of NAD+-linked substrate was severely inhibited by the compound. In submitochondrial particles, only NADH oxidation was sensitive. The site of inhibition has been identified to lie between the dehydrogenase flavoprotein and ubiquinone.

Methyl 2-methyl-2H-1,2,3-triazole-4-carboxylate

In the title compound, C5H7N3O2, all non-H atoms lie in a common plane, with a maximum deviation of 0.061 (2)° for the ester methyl C atom. The structure is stabilized by intermolecular C-H O hydrogen bonds.

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.

Geometrical interpretation of Inönü-Wigner contractions

The Inönü-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincaré, and Galilean groups.

Multipliers of Sobolev spaces

Let Wm,p denote the Sobolev space of functions on Image n whose distributional derivatives of order up to m lie in Lp(Image n) for 1 less-than-or-equals, slant p less-than-or-equals, slant ∞. When 1 < p < ∞, it is known that the multipliers on Wm,p are the same as those on Lp. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order less-than-or-equals, slant1 whose first order derivatives are also integrable of order less-than-or-equals, slant1, belong to the class of multipliers on Wm,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on Lp, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on Wm,l are necessarily integrable distributions of order less-than-or-equals, slant1 or less-than-or-equals, slant2 accordingly as m is odd or even. We have obtained the multipliers from L1(Image n) into Wm,p, 1 less-than-or-equals, slant p less-than-or-equals, slant ∞, and the multiplier space of Wm,1 is realised as a dual space of certain continuous functions on Image n which vanish at infinity.

Studies On Hydrogen Bonds: Part IV. Proposed Working Criteria for Assessing Qualitative Strength of Hydrogen Bonds

The data obtained in the earlier parts of this series for the donor and acceptor end parameters of N-H. O and O-H. O hydrogen bonds have been utilised to obtain a qualitative working criterion to classify the hydrogen bonds into three categories: "very good" (VG), "moderately good" (MG) and weak (W). The general distribution curves for all the four parameters are found to be nearly of the Gaussian type. Assuming that the VG hydrogen bonds lie between 0 and ± la, MG hydrogen bonds between ± 1 and ± 2, W hydrogen bonds beyond ± 2 (where is the standard deviation), suitable cut-off limits for classifying the hydrogen bonds in the three categories have been derived. These limits are used to get VG and MG ranges for the four parameters 1 and θ (at the donor end) and ± and ± (at the acceptor end). The qualitative strength of a hydrogen bond is decided by the cumulative application of the criteria to all the four parameters. The criterion has been further applied to some practical examples in conformational studies such as α-helix and can be used for obtaining suitable location of hydrogen atoms to form good hydrogen bonds. An empirical approach to the energy of hydrogen bonds in the three categories has also been presented.

Ratio of Diffusion Coefficient to Mobility for Electrons in SF6-Air and Freon-Nitrogen Mixtures

The ratio of diffusion coefficient to mobility (D/¿) for electrons has been measured in SF6-air and freon-nitrogen mixtures for various concentrations of SF6 and freon in the mixtures over the range 140¿ E/p¿ 220 V.cm-1 - torr-1. In SF6-air mixtures, the values of D/¿ were always observed to lie intermediate between the values for the pure gases. However, in freon-nitrogen mixtures, with a small concentration (10 percent) of freon in the mixture, the values of D/¿ are found to lie above the boundaries determined by the pure gases. In this mixture, over the lower E/p range (140 to 190) the electrons appear to lose a large fraction of their energy by the excitation of the complex freon molecules, while at higher E/p values (200 to 240), the excitation and consequent deexcitation of nitrogen molecules and its metastables seem to cause an increased rate of ionization of freon molecules.

Antiferromagnetic spin-wave states in a linear chain with nearest- and next-nearest-neighbour interactions

The spectrum of short-closed chains up to N=12 are studied by exact diagonalization to obtain the spin-wave spectrum of the Hamiltonian H=2J Sigma i=1Nsi.si+1+2J alpha Sigma i=1Nsi.si+2, -1.0or=0.3 and alpha

On walls of marginal stability in N=2 string theories

We study the properties of walls of marginal stability for BPS decays in a class of N = 2 theories. These theories arise in N = 2 string compactifications obtained as freely acting orbifolds of N = 4 theories, such theories include the STU model and the FHSV model. The cross sections of these walls for a generic decay in the axion-dilaton plane reduce to lines or circles. From the continuity properties of walls of marginal stability we show that central charges of BPS states do not vanish in the interior of the moduli space. Given a charge vector of a BPS state corresponding to a large black hole in these theories, we show that all walls of marginal stability intersect at the same point in the lower half of the axion-dilaton plane. We isolate a class of decays whose walls of marginal stability always lie in a region bounded by walls formed by decays to small black holes. This enables us to isolate a region in moduli space for which no decays occur within this class. We then study entropy enigma decays for such models and show that for generic values of the moduli, that is when moduli are of order one compared to the charges, entropy enigma decays do not occur in these models.

2-Chloro-7,8-dimethylquinoline-3-carbaldehyde

All the non-H atoms of the title compound, C12H10ClNO, lie on a crystallographic mirror plane orientated perpendicular to the crystallographic b axis.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.