Models for deploymerizing enzymes: criteria for discrimination of models

Several models for the action of alpha amylase have been proposed to account for the nonrandom distribution of oligosaccharides in the amylase digests of polysaccharides. The preferred-attack model attempts to account for the nonrandom distribution by assuming that the probability for bond cleavage depends upon the position of the bond in the chain. The repetitive, or multiple-attack, model suggests that the nonrandom distribution of oligosaccharides arises because an amylase can form a cage-like complex with a substrate and attack it several times during a single encounter. The multiple-enzyme or dual-site model suggests that the nonrandom yield of oligosaccharides arises from the combined action of exo- and endo-enzymes. The effects of pH, inhibitors, and substrate chain-length on enzyme action have been studied in several laboratories to determine which of the three action-patterns best describes the action of alpha amylase. The influence of these variables on product distributions or enzyme action-patterns are mathematically modeled in the Appendix. The experimental data on porcine-pancreatic alpha amylase are discussed in the light of the derivations.     

"Carrier" theory and thermodynamics of irreversible processes.

A theory of transport via a "carrier" based on Wyman's theory on multiple equilibria is presented. By taking into account the detailed balance principle, it is possible to simplify the flux expressions and their coupling coefficients. In this way, Onsager's rules are derived. An experimental approach to the model is proposed.     

Glutamate-induced polymerization of tubulin: characteristics of the reaction and application to the large-scale purification of tubulin

The multiple attack model of the α-amylase mechanism has been analyzed. Theoretical rate coefficients dependent on the degree of polymerization of substrate (n) have been applied. They are: effectiveness of hydrolysis (y_n) which affects V values, and the average number of unitary movements (ζ_n) which affects K_m values. The model explains the dependence of V and K_m on the degree of polymerization of substrates with n values higher than the number of subsites in the enzyme binding site. Distribution of the degree of polymerization of hog pancreas α-amylase products (n_p) and average n_p value has been found experimentally and applied to calculate the maximal number of unitary movements (z) of the enzyme during the single enzyme-substrate meeting. V and K_m values of hog pancreas α-amylase for amylose and different branched substrates have been determined and discussed in terms of the multiple attack theory. Their dependence on theoretic y_n and ζ_n values has been found in support of the model.     

Stability properties of proliferatively coupled cell replication models

To address the possibility that proliferative disorders may originate from interactions between multiple populations of proliferating and maturing cells, we formulate a model for this process as a set of coupled nonlinear first order partial differential equations. Using recent results for the asymptotic behaviour of the solutions to this model, we demonstrate that there exists a region of coupling coefficients, maturation rates, and proliferation rates that will guarantee the stable coexistence of coupled cellular populations. The analysis shows that increases in the coupling between populations may ultimately lead to a loss of stability. Furthermore, the analysis indicates that increases (decreases) in the maturation and/or proliferation rates above (below) critical levels will lead either to instability in the populations or the destruction of one population and the persistence of the other.To whom all editorial correspondence should be addressed     

“Carrier” theory and thermodynamics of irreversible processes

A theory of transport via a “carrier” based on Wyman's theory on multiple equilibria is presented. By taking into account the detailed balance principle, it is possible to simplify the flux expressions and their coupling coefficients. In this way, Onsager's rules are derived. An experimental approach to the model is proposed.     

Study on dual-site inhibitors of acetylcholinesterase: Highly potent derivatives of bis- and bifunctional huperzine B

Natural (-)-huperzine B (HupB), isolated from Chinese medicinal herb, displayed moderate inhibitory activity of acetylcholinesterase (AChE). Based on the active dual-site of AChE, a series of novel derivatives of bis- and bifunctional HupB were designed and synthesized. The AChE inhibition potency of most derivatives of HupB was enhanced about 2-3 orders of magnitude as compared with the parental HupB. Among bis-HupB derivatives, 12h exhibited the most potent in the AChE inhibition and has been evaluated for its pharmacological actions in vivo on ChE inhibition, cognitive enhancement, and neuroprotection. The docking study on the bis-HupB derivatives 12 series with TcAChE has demonstrated that the ligands bound to the dual-site of the enzyme in different level.     

Equilibrium properties of a multi-locus, haploid-selection, symmetric-viability model

Under haploid selection, a multi-locus, diallelic, two-niche Levene (1953) model is studied. Viability coefficients with symmetrically opposing directional selection in each niche are assumed, and with a further simplification that the most and least favored haplotype in each niche shares no alleles in common, and that the selection coefficients monotonically increase or decrease with the number of alleles shared. This model always admits a fully polymorphic symmetric equilibrium, which may or may not be stable.We show that a stable symmetric equilibrium can become unstable via either a supercritical or subcritical pitchfork bifurcation. In the supercritical bifurcation, the symmetric equilibrium bifurcates to a pair of stable fully polymorphic asymmetric equilibria; in the subcritical bifurcation, the symmetric equilibrium bifurcates to a pair of unstable fully polymorphic asymmetric equilibria, which then connect to either another pair of stable fully polymorphic asymmetric equilibria through saddle-node bifurcations, or to a pair of monomorphic equilibria through transcritical bifurcations. As many as three fully polymorphic stable equilibria can coexist, and jump bifurcations can occur between these equilibria when model parameters are varied.In our Levene model, increasing recombination can act to either increase or decrease the genetic diversity of a population. By generating more hybrid offspring from the mating of purebreds, recombination can act to increase genetic diversity provided the symmetric equilibrium remains stable. But by destabilizing the symmetric equilibrium, recombination can ultimately act to decrease genetic diversity.     

A naive Bayes model to predict coupling between seven transmembrane domain receptors and G-proteins

MOTIVATION: An understanding of the coupling between a G-protein coupled receptor (GPCR) and a specific class of heterotrimeric GTP-binding proteins (G-proteins) is vital for further comprehending the function of the receptor within a cell. However, predicting G-protein coupling based on the amino acid sequence of a receptor has been a daunting task. While experimental data for G-protein coupling exist, published models that rely on sequence based prediction are few. In this study, we have developed a Naive Bayes model to successfully predict G-protein coupling specificity by training over 80 GPCRs with known coupling. Each intracellular domain of GPCRs was treated as a discrete random variable, conditionally independent of one another. In order to determine the conditional probability distributions of these variables, ClustalW-generated phylogenetic trees were used as an approximation for the clustering of the intracellular domain sequences. The sampling of an intracellular domain sequence was achieved by identifying the cluster containing the homologue with the highest sequence similarity. RESULTS: Out of 55 GPCRs validated, the model yielded a correct classification rate of 72%. Our model also predicted multiple G-protein coupling for most of the GPCRs in the validation set. The Bayesian approach in this work offers an alternative to the experimental approach in order to answer the biological problem of GPCR/G-protein coupling selectivity. AVAILABILITY: Academic users should send their request for the perl program for calculating likelihood probabilities at jack.cao@astrazeneca.com. SUPPLEMENTARY INFORMATION: The materials can be viewed at http://www.astrazeneca-montreal.com/AZRDM_info/supporting_info.pdf.     

Symmetric building blocks and combinatorial functional group transformation as versatile strategies in combinatorial chemistry

A combination of symmetric building blocks and combinatorial functional group transformation for synthesis of pyrimidines was investigated. The purpose of the study was to maximize the return on invested synthetic efforts of reaction development for libraries. A representative set of symmetric diacids was coupled onto deprotected TentaGel Rink Amide resin. The amino function served as a model of a chemical process providing a functional group for additional synthetic steps, while the symmetric building blocks served as a model to connect synthesis protocols and to switch to a different synthesis paradigm consecutively. The reaction sequence was continued in a noncombinatorial step by coupling a bifunctional reagent (3-aminoacetophenone) to the remaining carboxy function of the symmetric diacid. The ketone served as a model of a reagent prepared for combinatorial functional group transformation. The arylmethylketone was reacted with a set of aryl- and heteroarylaldehydes to give alpha,beta-unsaturated ketones. Subsequently, guanidine, alkyl-, and arylcarboxamidines were introduced in combinatorial synthesis of substituted pyrimidines by reaction with the alpha, beta-unsaturated ketone functionality. The combination of symmetric building blocks and combinatorial functional group transformation created a versatile reaction sequence ideally suited for production of libraries from libraries with added diversity.     

Enzymatic generation of binary block‐copolymeric structures: Mathematical analysis based on triad frequencies evaluated by NMR

A mathematical model is derived for describing a multiple‐attack pathway for enzymatic generation of block structure in binary linear copolymers having initially a randomized sequential structure. The model is based on sequential information in terms of copolymer monads, diads, and triads estimated by nmr spectroscopy, and is applicable to enzymes attacking next to a reacted unit in the polymer chains. Then the block distribution of unreacted units remains constant and explicit relationships are provided. The probability of triad frequencies as a function of monads, i.e., progress curve of enzyme copolymer sequential structure, allows us to characterize the enzymatic mode of attack independently of enzyme kinetics. The produced fractions of heterogeneous triads centered by reacted units are shown to be affected, to a large extent, by the degree of multiple attack (d) entering into the formula as a variable parameter. The single‐chain, d = ∞, and multiple‐chain mechanisms, d =1, representing the two extremes of the treated mechanism, are very clearly discriminated. © 1999 John Wiley & Sons, Inc. Biopoly 50: 221–226, 1999     

A Karplus equation for (3)J(HCCN) in amino sugar derivatives

The (1)H-(15)N coupling constants of a suite of organic-soluble amino sugar derivatives have been measured by one-dimensional and two-dimensional (1)H/(15)N heteronuclear single quantum, multiple bond correlation (HSQMBC), and the values so obtained are compared with those measured by analysis of (1)H spectra of (15)N-labeled amino sugar derivatives. A number of bicyclic amino sugar models have been studied, including methyl 2- (and 3-)amino-4,6-O-benzylidene-2- (and 3-)deoxy-alpha-D-hexopyranosides in chair or skew conformations, and methyl 2,6-anhydro-3-deoxy-3-phthalimido-alpha-d-mannopyranoside in a locked, almost classical boat conformation. The magnitudes of the vicinal (1)H-(15)N coupling constants (3)J(HCCN) have been correlated with (1)H/(15)N dihedral angles phi computed for the favored conformations by molecular dynamics with molecular mechanics energy minimization. Non-linear regression of the coupling constants on the dihedral angles has yielded a Karplus equation: (3)J(HCCN)=3.1 cos(2) phi-0.6 cos phi+0.4. The coefficients of the terms in this equation have been compared with those reported for 15 other pairs of nuclei, and the coefficient of the important cos(2)phi term found to be numerically smallest for (3)J(HCCN).     

Detecting spatial patterns in species composition with multiple plot similarity coefficients and singularity measures

Recently, several multiple plot similarity indices have been presented that cure some of the problems associated with the approaches for the calculation of compositional similarity for groups of plots by averaging pairwise similarities. These new indices calculate the similarity between more than two plots whilst considering the species composition on all compared plots. The resulting similarity value is true for the whole group of plots considered (called neighborhood in the following). Here, we review the possibilities for multiple plot similarity calculation and additionally explore coefficients that examine multiple plot similarity between a reference plot (named focal plot in the following) and any number of surrounding plots. The latter represent measures of singularity. Further, we establish a framework for applying these two kinds of multiple plot measures to gridded data including an algorithm for testing the significance of calculated values against random expectations. The capability of multiple plot measures for detecting species compositional gradients and local/regional hotspots within this framework is tested. For this purpose, several artificial data sets with known gradients in species composition (random, gradient, central hotspot, hotspot bottom right) are constructed on the basis of a real data set from a Tundra ecosystem in northern Sweden (Abisko). The coefficients that best reflect the positions of the plots on the realized gradients in species composition are considered as performing best with regard to pattern detection. The tested measures of multiple plot similarity and singularity produced considerably different results when applied to one real and 4 artificial data sets. The newly proposed symmetric singularity coefficient has the best overall performance which makes it suitable for local/regional hotspot detection and for incorporating local to regional similarity analyses in reserve selection procedures.     

Enhancing evolvability with mutation buffering mediated through multiple weak interactions

The evolutionary adaptability of a system is dependent on three organizational properties, self-organizing dynamics that are hierarchically organized, component redundancy, and multiple weak interactions [Towards high evolvability dynamics, in: G. van de Vijver, S. Salthe, M. Delpos (Eds.), Evolutionary Systems, Kluwer Academic Publishers, Dordrecht, 1998, pp. 147-169]. This study reports on the use of the dual dynamics network model as an aid in understanding the role multiple weak interactions play in enhancing evolutionary adaptability. Dual dynamics networks are self-organizing systems that consist of simple components that change local state due to the coupled influences from connected components exerting strong discrete decision-making influences and from groups of components exerting multiple weak influences [J. Theor. Biol. 193 (1998) 287]. The dual dynamics model has been enhanced to support investigations of properties relevant to a system's capacity for evolvability, such as structure-function relationships, neutrality, adaptive tolerance, and evolutionary search performance.Three network types are investigated, each utilizing a different method of coupling strong and weak influences. The results demonstrate that the manner of coupling multiple weak interactions into the systems dynamics significantly affects the structure-function maps and the consequent evolvability characteristics. Specifically it is found that a form of coupling, denoted as linear modulation, enhances evolutionary adaptability. Linear modulation coupling requires that the weak interactions be integrated with strong interactions in a manner that implies a linear ordered relation between the possible state values of the components of the systems. When coupling functions that do not imply such an ordering of local state values are used, evolutionary adaptability is decreased.     

Two-category model of task allocation with application to ant societies

In many network models of interacting units such as cells or insects, the coupling coefficients between units are independent of the state of the units. Here we analyze the temporal behavior of units that can switch between two 'category' states according to rules that involve category-dependent coupling coefficients. The behaviors of the category populations resulting from the asynchronous random updating of units are first classified according to the signs of the coupling coefficients using numerical simulations. They range from isolated fixed points to lines of fixed points and stochastic attractors. These behaviors are then explained analytically using iterated function systems and birth-death jump processes. The main inspiration for our work comes from studies of non-hierarchical task allocation in, e.g., harvester ant colonies where temporal fluctuations in the numbers of ants engaged in various tasks occur as circumstances require and depend on interactions between ants. We identify interaction types that produce quick recovery from perturbations to an asymptotic behavior whose characteristics are function of the coupling coefficients between ants as well as between ants and their environment. We also compute analytically the probability density of the population numbers, and show that perturbations in our model decay twice as fast as in a model with random switching dynamics. A subset of the interaction types between ants yields intrinsic stochastic asymptotic behaviors which could account for some of the experimentally observed fluctuations. Such noisy trajectories are shown to be random walks with state-dependent biases in the 'category population' phase space. With an external stimulus, the parameters of the category-switching rules become time-dependent. Depending on the growth rate of the stimulus in comparison to its population-dependent decay rate, the dynamics may qualitatively differ from the case without stimulus. Our simple two-category model provides a framework for understanding the rich variety of behaviors in network dynamics with state-dependent coupling coefficients, and especially in task allocation processes with many tasks.     

Discrete models of autocrine cell communication in epithelial layers

Pattern formation in epithelial layers heavily relies on cell communication by secreted ligands. Whereas the experimentally observed signaling patterns can be visualized at single-cell resolution, a biophysical framework for their interpretation is currently lacking. To this end, we develop a family of discrete models of cell communication in epithelial layers. The models are based on the introduction of cell-to-cell coupling coefficients that characterize the spatial range of intercellular signaling by diffusing ligands. We derive the coupling coefficients as functions of geometric, cellular, and molecular parameters of the ligand transport problem. Using these coupling coefficients, we analyze a nonlinear model of positive feedback between ligand release and binding. In particular, we study criteria of existence of the patterns consisting of clusters of a few signaling cells, as well as the onset of signal propagation. We use our model to interpret recent experimental studies of the EGFR/Rhomboid/Spitz module in Drosophila development.     

Modulation of GLUT4 and GLUT1 recycling by insulin in rat adipocytes: kinetic analysis based on the involvement of multiple intracellular compartments

The trafficking kinetics of GLUT4 and GLUT1 in rat epididymal adipocytes were analyzed by a four-compartment model based upon steady-state pool sizes of three intracellular fractions and one plasma membrane fraction separated and assessed under both basal and insulin-stimulated states. The steady-state compartment sizes provided relative values of the kinetic coefficients characterizing the rate of each process in the loop. Absolute values of these coefficients were obtained by matching the simulated half-times to those observed experimentally and reported in the literature for both basal and insulin-stimulated states. Our analysis revealed that insulin modulates the GLUT4 trafficking at multiple steps in the rat adipocyte, not only reducing the endocytotic rate constant 3-4-fold and increasing the exocytotic rate 8-24-fold but also increasing the two rate coefficients coupling the three intracellular compartments 2-6-fold each. Furthermore, GLUT1 was completely segregated from GLUT4 in two of the three intracellular compartments, and its steady-state distribution is consistent with a four-compartment model of GLUT1 recycling involving an insulin sensitive endocytosis step in common with the GLUT4 system, but with all other processes being insensitive to insulin.     

Tunable Plasmonic Dispersion and Strong Coupling in Graphene Ribbon and Double Layer Sheets Structure

Based on the interplay between propagating surface plasmon polaritons (PSPs) in graphene ribbon and double layer sheets structure, we theoretically demonstrate a tunable strong coupling mechanism significantly different from reported conventional noble metal nanostructures. The strong electromagnetic coupling between the low order antisymmetric and high order symmetric PSPs modes occurs due to the intersections of dispersion curves, which leads to a modification of plasmonic dispersion and multiple significant anti-crossing regions. Of particular, this strong coupling is controllable through external gate voltage of graphene sheets or ribbon. The results offer an effective regime to dynamically tune the interaction of graphene PSPs, which may find applications in the field of nanophotonic devices in the mid-infrared range.