A necessary condition for balance of a block design

It is shown that, barring orthogonal designs, a necessary condition for a block design, BD(v, b, N), to be J-balanced is that the rows of its incidence matrix, N, are linearly independent. This strengthens the condition b v known in the literature as FISHER'S inequality. V-balanced block designs are also discussed.     

Temperature-induced complementarity as a mechanism for biomolecular assembly

Recent advances in the measurement and theory of “hydration” interactions between biomolecules provide a basis on which to formulate mechanisms of biomolecular recognition. In this paper we have developed a mathematical formalism for analyzing specificity encoded in dynamic distributions of surface polar groups, a formalism that incorporates newly recognized properties of directly measured “hydration” forces. As expected, attraction between surfaces requires complementary patterns of surface polar groups. In contrast to usual expectations, thermal motion can create these complementary surface configurations. We have demonstrated that assembly can occur with an increase in conformational entropy of polar residues. Elevated temperature then facilitates recognition rather than hinders it. This mechanism might underlie some temperature-favored assembly reactions common in biological systems that are usually associated with the “hydrophobic effect” only. © 1994 Wiley-Liss, Inc.     

A new necessary condition for Turing instabilities

Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community.     

Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes

Having multiple peaks within fitness landscapes critically affects the course of evolution, but whether their presence imposes specific requirements at the level of genetic interactions remains unestablished. Here we show that to exhibit multiple fitness peaks, a biological system must contain reciprocal sign epistatic interactions, which are defined as genetic changes that are separately unfavorable but jointly advantageous. Using Morse theory, we argue that it is impossible to formulate a sufficient condition for multiple peaks in terms of local genetic interactions. These findings indicate that systems incapable of reciprocal sign epistasis will always possess a single fitness peak. However, reciprocal sign epistasis should be pervasive in nature as it is a logical consequence of specificity in molecular interactions. The results thus predict that specific molecular interactions may yield multiple fitness peaks, which can be tested experimentally.     

Chiral HPLC method for chiral purity determination of paroxetine drug substance

This article describes a chiral HPLC method for (+) trans isomer of paroxetine in a paroxetine drug substance. The method development was performed to establish a suitable HPLC system in order to separate both enantiomers. It was found that a system based on a Chiralpak AD column was suitable for the analysis. Proper column maintenance and the optimized eluent composition allowed good reproducibility and sensitivity for the method. The method was also checked on a number of different columns using different HPLC equipment and gave both reproducible chromatography and reproducible quantitative results.     

A concise necessary and sufficient condition for the existence of a galled-tree

Galled-trees are a special class of graphical representation of evolutionary history that has proven amenable to efficient, polynomial-time algorithms. The goal of this paper is to construct a concise necessary and sufficient condition for the existence of a galled-tree for M, a set of binary sequences that purportedly have evolved in the presence of recombination. Both root-known and root-unknown cases are considered here.     

A new necessary condition on interaction graphs for multistationarity

We consider a dynamical system, described by a system of ordinary differential equations, and the associated interaction graphs, which are defined using the matrix of signs of the Jacobian matrix. After stating a few conjectures about the role of circuits in these graphs, we prove two new results relating them to the dynamic behaviour of the system: a sufficient condition for qualitative unstability, and a necessary condition for the existence of several stationary states. These results are illustrated by examples of regulatory modules in two variables, such as those occurring in biological networks.     

The enzymatic neuron as a reaction-diffusion network of cyclic nucleotides

Recent evidence suggests that the cyclic nucleotides play a central role in the intracellular processing of neural signals. The dynamics of this system may be seen as a realization of the enzymatic neuron model. Enzymatic neurons are formal neurons which map binary afferent signals into patterns of excitation across an abstract membrane. The distribution of enzyme-like elements called excitases enables a set of local threshold functions to determine the firing activity of the neuron. This paper analyzes the basic properties of enzymatic neurons in a simple continuous-time framework, and shows how they may be presented as reaction-diffusion networks which model the cyclic nucleotide system. We present the results of computer simulations of this neuron and discuss its implications for selectional learning and its relation to conventional two-factor systems. One fundamental property of the reaction-diffusion neuron is its so-called “double-dynamics” property; examination of this property and its contribution to the computing power of the neuron provides some insight into the obscure relation between microscopic and macroscopic models of computation.     

Chiral safety of the biosphere as a biophysical problem

The biosphere with its inherent chiral asymmetry fixed in the process of biological evolution at the level of L-amino acids and D-hydrocarbons and some other biologically active compounds of biogenic origin is under strong pressure of chiral substances produced by chemical, pharmaceutical, and other branches of industry and agriculture. Effective use of enantiomers is accompanied by toxic and even mutagenic effects of their mirror-image enantiomorphs. Only small amounts of products are tested for chiral purity; there is no system of global biosphere monitoring as well as no common standards of permissible concenrations. The investigation of the molecular basis of chiral stereospecificity of enzymes and cell receptors is of great interest from the point of view of fundamental biophysics. On the other hand, the development of chiral-selective sensors for environmental monitoring is important from the viewpoint of applied biophysics.     

Molecular complementarity III. peptide complementarity as a basis for peptide receptor evolution: a bioinformatic case study of insulin,glucagon and gastrin

Dwyer has suggested that peptide receptors evolved from self-aggregating peptides so that peptide receptors should incorporate regions of high homology with the peptide ligand. If one considers self-aggregation to be a particular manifestation of molecular complementarity in general, then it is possible to extend Dwyer's hypothesis to a broader set of peptides: complementary peptides that bind to each other. In the latter case, one would expect to find homologous copies of the complementary peptide in the receptor. Thirteen peptides, 10 of which are not known to self-aggregate (amylin, ACTH, LHRH, angiotensin II, atrial natriuretic peptide, somatostatin, oxytocin, neurotensin, vasopressin, and substance P), and three that are known to self-aggregate (insulin, glucagon, and gastrin), were chosen. In addition to being self-aggregating, insulin and glucagon are also known to bind to each other, making them a mutually complementary pair. All possible combinations of the 13 peptides and the extracellular regions of their receptors were investigated using bioinformatic tools (a total of 325 combinations). Multiple, statistically significant homologies were found for insulin in the insulin receptor; insulin in the glucagon receptor; glucagon in the glucagon receptor; glucagon in the insulin receptor; and gastrin in gastrin binding protein and its receptor. Most of these homologies are in regions or sequences known to contribute to receptor binding of the respective hormone. These results suggest that the Dwyer hypothesis for receptor evolution may be generalizable beyond self-aggregating to complementary peptides. The evolution of receptors may have been driven by small molecule complementarity augmented by modular evolutionary processes that left a "molecular paleontology" that is still evident in the genome today. This "paleontology" may allow identification of peptide receptor sites.     

Fluorescent xDNA nucleotides as efficient substrates for a template-independent polymerase

Template independent polymerases, and terminal deoxynucleotidyl transferase (TdT) in particular, have been widely used in enzymatic labeling of DNA 3'-ends, yielding fluorescently-labeled polymers. The majority of fluorescent nucleotides used as TdT substrates contain tethered fluorophores attached to a natural nucleotide, and can be hindered by undesired fluorescence characteristics such as self-quenching. We previously documented the inherent fluorescence of a set of four benzo-expanded deoxynucleoside analogs (xDNA) that maintain Watson-Crick base pairing and base stacking ability; however, their substrate abilities for standard template-dependent polymerases were hampered by their large size. However, it seemed possible that a template-independent enzyme, due to lowered geometric constraints, might be less restrictive of nucleobase size. Here, we report the synthesis and study of xDNA nucleoside triphosphates, and studies of their substrate abilities with TdT. We find that this polymerase can incorporate each of the four xDNA monomers with kinetic efficiencies that are nearly the same as those of natural nucleotides, as measured by steady-state methods. As many as 30 consecutive monomers could be incorporated. Fluorescence changes over time could be observed in solution during the enzymatic incorporation of expanded adenine (dxATP) and cytosine (dxCTP) analogs, and after incorporation, when attached to a glass solid support. For (dxA)(n) polymers, monomer emission quenching and long-wavelength excimer emission was observed. For (dxC)(n), fluorescence enhancement was observed in the polymer. TdT-mediated synthesis may be a useful approach for creating xDNA labels or tags on DNA, making use of the fluorescence and strong hybridization properties of the xDNA.     

Conformationally restricted nucleotides as a probe of structure-function relationships in RNA

We introduce the use of commercially available locked nucleic acids (LNAs) as a functional probe in RNA. LNA nucleotides contain a covalent linkage that restricts the pseudorotation phase of the ribose to C3'-endo (A-form). Introduction of an LNA at a single site thus allows the role of ribose structure and dynamics in RNA function to be assessed. We apply LNA probing at multiple sites to analyze self-cleavage in the lead-dependent ribozyme (leadzyme), thermodynamic stability in the UUCG tetraloop, and the kinetics of recognition of U1A protein by U1 snRNA hairpin II. In the leadzyme, locking a single guanosine residue into the C3'-endo pucker increases the catalytic rate by a factor of 20, despite the fact that X-ray crystallographic and NMR structures of the leadzyme ground state reported a C2'-endo conformation at this site. These results strongly suggest that a conformational change at this position is critical for catalytic function. Functional insights obtained in all three systems demonstrate the highly general applicability of LNA probing in analysis of the role of ribose orientation in RNA structure, dynamics, and function.     

Reliable hybridization of oligonucleotides as short as six nucleotides

Although there are many new applications for hybridizing short, synthetic oligonucleotide probes to DNA, such applications have not included determining unknown sequences of DNA. The lack of clear discrimination in hybridization of oligo probes shorter than 11 nucleotides and the lack of a theoretical understanding of factors influencing hybridization of short oligos have hampered the development of their use. We have found conditions for reliable hybridization of oligonucleotides as short as seven nucleotides to cloned DNA or to oligonucleotides attached to filters. Low-temperature hybridization and washing conditions, in contrast to the high stringency conditions currently used in hybridization experiments, have the potential for allowing the simple use of all oligos of six nucleotides or longer in meaningful hybridizations. We also present the hybridization discrimination theory that provides the conceptual framework for understanding these results.