A simulation study of mutations in the genetic regulatory hierarchy for butterfly eyespot focus determination

The color patterns on the wings of butterflies have been an important model system in evolutionary developmental biology. A recent computational model tested genetic regulatory hierarchies hypothesized to underlie the formation of butterfly eyespot foci [Evans, T.M., Marcus, J.M., 2006. A simulation study of the genetic regulatory hierarchy for butterfly eyespot focus determination. Evol. Dev. 8, 273-283]. The computational model demonstrated that one proposed hierarchy was incapable of reproducing the known patterns of gene expression associated with eyespot focus determination in wild-type butterflies, but that two slightly modified alternative hierarchies were capable of reproducing all of the known gene expressions patterns. Here we extend the computational models previously implemented in Delphi 2.0 to two mutants derived from the squinting bush brown butterfly (Bicyclus anynana). These two mutants, comet and Cyclops, have aberrantly shaped eyespot foci that are produced by different mechanisms. The comet mutation appears to produce a modified interaction between the wing margin and the eyespot focus that results in a series of comet-shaped eyespot foci. The Cyclops mutation causes the failure of wing vein formation between two adjacent wing-cells and the fusion of two adjacent eyespot foci to form a single large elongated focus in their place. The computational approach to modeling pattern formation in these mutants allows us to make predictions about patterns of gene expression, which are largely unstudied in butterfly mutants. It also suggests a critical experiment that will allow us to distinguish between two hypothesized genetic regulatory hierarchies that may underlie all butterfly eyespot foci.     

Simplified velocity equations for characterizing the partial inhibition or nonessential activation of bireactant enzymes

The steady state velocity equation for a bireactant enzyme in the presence of a partial inhibitor or nonessential activator, M, contains squared substrate concentration and higher-ordered M concentration terms. The equation is too complex to be useful in kinetic analyses. Simplification by the method of Cha (J. Biol. Chem. 243, 820 825 (1968)) eliminates squared substrate concentration terms, but retains higher-ordered terms in [M]. It is shown that if strict equilibrium is assumed between free E, M, and EM and for all but one other M-binding reaction, a velocity equation is obtained for an ordered bireactant enzyme that is first degree in all ligands in the absence of products. The equation is an approximation (because it was derived assuming only one M-binding reaction in the steady state), but it contains five inhibition (or activation) constants associated with M, all of which can be obtained by diagnostic replots and/or curve-fitting procedures. The equation also provides a framework for obtaining limiting constants (V'max, K'ia, K'mA, K'mB) that characterize the enzyme at saturating M. The same approach is applicable to an enzyme that catalyzes a steady state ping pong reaction.     

Kinetics of the creatine kinase reaction in neonatal rabbit heart: an empirical analysis of the rate equation

Here we define the kinetics of the creatine kinase (CK) reaction in an intact mammalian heart containing the full range of CK isoenzymes. Previously derived kinetic constants [Schimerlik, M. I., & Cleland, W. W. (1973) J. Biol. Chem. 248, 8418-8423] were refit for the reaction occurring at 37 degrees C. Steady-state metabolite concentrations from 31P NMR and standard biochemical techniques were determined. 31P magnetization transfer data were obtained to determine unidirectional creatine kinase fluxes in hearts with differing total creatine contents and differing mitochondrial CK activities during KCl arrest and isovolumic work for both the forward reaction (MgATP synthesis) and reverse reaction (phosphocreatine synthesis). The NMR kinetic data and substrate concentration data were used in conjunction with a kinetic model based on MM-CK in solution to determine the applicability of the solution-based kinetic models to the CK kinetics of the intact heart. Our results indicated that no single set of rate equation constants could describe both the KCl-arrested and working hearts. We used our experimental data to constrain the solution-derived kinetic model and derived a second set of rate equation constants, which describe the isovolumic work state. Analysis of our results indicates that the CK reaction is rate limited in the direction of ATP synthesis, the size of the guanidino substrate pool drives the measured CK flux in the intact heart, and during isovolumic work the CK reaction operates under saturating conditions; that is, the substrate concentrations are at least 2-fold greater than the Km or Kim for each substrate.(ABSTRACT TRUNCATED AT 250 WORDS)     

A new hypothesis to explain the coexistence of n species in the presence of a single resource

This paper presents a hypothesis allowing us to explain the coexistence of several species (here micro-organisms) in competition on a single resource (called a substrate) in a chemostat. We introduce a new class of kinetics that does not only depend on the substrate concentration in the medium, but also on the biomass concentration. From the study of elementary interactions (i) between micro-organisms, (ii) between micro-organisms and their environment in which they grow and from simulations, we show that this modelling approach can be interpreted in terms of substrate diffusion phenomena. A rigorous study of this new class of models allows us to hypothesize that abiotic parameters can explain the fact that an arbitrarily large number of species can coexist in the presence of a unique substrate.     

An application of Berman's work on pool-model invariants in analyzing indistinguishable models for whole-body cholesterol metabolism

Berman and Schoenfeld used matrix transformations to study unidentifiable pool models. It is possible to use the method to examine if two models are output-indistinguishable, that is, if given the nature of tracer injections and observations, the two models have the same responses. The method is applied to two three-pool models for whole-body cholesterol metabolism. The indistinguishability of a mammillary model from a catenary model is proved using matrix transformations. The method is used in two ways, directly as well as after simplifying the problem. The two ways, as well as an analysis of the converse, help to show how the method is to be applied as well as the strengths and weaknesses of the method.     

Quantifying the allosteric properties of Escherichia coli carbamyl phosphate synthetase: determination of thermodynamic linked-function parameters in an ordered kinetic mechanism.

The effects of the allosteric ligands UMP, IMP, and ornithine on the partial reactions catalyzed by Escherichia coli carbamyl phosphate synthetase have been examined. Both of these reactions, a HCO3(-)-dependent ATP synthesis reaction and a carbamyl phosphate-dependent ATP synthesis reaction, follow bimolecular ordered sequential kinetic mechanisms. In the ATPase reaction, MgATP binds before HCO3- as established previously for the overall reaction catalyzed by carbamyl phosphate synthetase [Raushel, F. M., Anderson, P. M., & Villafranca, J. J. (1978) Biochemistry 17, 5587-5591]. The initial velocity kinetics for the ATP synthesis reaction indicate that MgADP binds before carbamyl phosphate in an equilibrium ordered mechanism except in the presence of ornithine. Determination of true thermodynamic linked-function parameters describing the impact of allosteric ligands on the binding interactions of the first substrate to bind in an ordered mechanism requires experiments to be performed in which both substrates are varied even if only one is apparently affected by the allosteric ligands. In so doing, we have found that IMP has little effect on the overall reaction of either of these two partial reactions. UMP and ornithine, which have a pronounced effect on the apparent Km for MgATP in the overall reaction, both substantially change the thermodynamic dissociation constant for MgADP from the binary E-MgADP complex, Kia, in the ATP synthesis reaction, with UMP increasing Kia 15-fold and ornithine decreasing Kia by 18-fold. By contrast, only UMP substantially affects the Kia for MgATP in the ATPase reaction, increasing it by 5-fold.(ABSTRACT TRUNCATED AT 250 WORDS)     

Benzoate 1,2-dioxygenase from Pseudomonas putida: single turnover kinetics and regulation of a two-component Rieske dioxygenase

The benzoate 1,2-dioxygenase system (BZDOS) from Pseudomonas putida mt-2 catalyzes the NADH-dependent oxidation of benzoate to 1-carboxy-1,2-cis-dihydroxycyclohexa-3,5-diene. Both the oxygenase (BZDO) and reductase (BZDR) components of BZDOS have been purified and characterized kinetically and by optical, EPR, and M?ssbauer spectroscopies. BZDO has an (alpha beta)(3) subunit structure in which each alpha subunit contains a Rieske [2Fe-2S] cluster and a mononuclear iron site. Two different purification protocols were developed for BZDO allowing the mononuclear iron to be stabilized in either the Fe(III) or the Fe(II) state for spectroscopic characterization. Using single turnover reactions, it is shown that fully reduced BZDO alone is capable of yielding the cis-diol product in high yield at rates that exceed the BZDOS turnover number. At the conclusion of turnover, quantification of each oxidation state of the metal sites by EPR and M?ssbauer spectroscopies shows that the Rieske cluster and mononuclear iron are each oxidized in amounts equal to the product yield, suggesting that the two electrons required for catalysis derive from the two metal centers. These results are in agreement with our previous study of naphthalene 1,2-dioxygenase [Wolfe, M. D., Parales, J. V., Gibson, D. T., and Lipscomb, J. D. (2001) J. Biol. Chem. 276, 1945-1953], which belongs to a different Rieske dioxygenase subclass, suggesting that it is a universal characteristic of Rieske dioxygenases that oxygen activation and substrate oxidation are catalyzed by the oxygenase component alone. The EPR spectrum of the Fe(III) center after a single turnover is distinct from either of those of substrate-free or substrate-bound enzyme. The complex with this spectrum is not formed by addition of cis-diol product to the resting Fe(III) form of the enzyme but is observed when the Fe(II) form is oxidized in the presence of product. Together, these results suggest that product exchange occurs only when the mononuclear iron is reduced. Stopped-flow and rapid scan analyses monitoring the oxidation of the Rieske cluster during the single turnover reaction show that it occurs in three phases that are kinetically competent for catalysis. The rate of each phase was found to be dependent on the type of substrate present, suggesting that the substrate influences the rate of electron transfer between the metal clusters. The participation of substrate in the oxygen activation reaction suggests a new aspect of the mechanism of this process by the Rieske dioxygenase class.     

Biological processes in organised media

Embedding a simple Michaelis-Menten enzyme in a gel slice may allow the catalysis of not only scalar processes but also vectorial ones, including uphill transport of a substrate between two compartments, and may make it seem as if two enzymes or transporters are present or as if an allosterically controlled enzyme/transporter is operating. The values of kinetic parameters of an enzyme in a partially hydrophobic environment are usually different from those actually measured in a homogeneous aqueous solution. This implies that fitting kinetic data (expressed in reciprocal co-ordinates) from in vivo studies of enzymes or transporters to two straight lines or a sigmoidal curve does not prove the existence of two different membrane mechanisms or allosteric control. In the artificial transport systems described here, a functional asymmetry was sufficient to induce uphill transport, therefore, although the active transport systems characterised so far correspond to proteins asymmetrically anchored in a membrane, the past or present existence of structurally symmetrical systems of transport in vivo cannot be excluded. The fact that oscillations can be induced in studies of the maintenance of the electrical potential of frog skin by addition of lithium allowed evaluation of several parameters fundamental to the functioning of the system in vivo (e.g., relative volumes of internal compartments, characteristic times of ionic exchanges between compartments). Hence, under conditions that approach real biological complexity, increasing the complexity of the behaviour of the system may provide information that cannot be obtained by a conventional, reductionist approach.     

Predicting stability of mixed microbial cultures from single species experiments: 2. Physiological model

In this paper, we study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth [M.M. Ballyk, G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993) 127-180; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 2. Phenomenological model]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture. We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.     

Towards understanding the chemistry of photosynthetic oxygen evolution: dynamic structural changes, redox states and substrate water binding of the Mn cluster in photosystem II

This mini-review summarizes my postdoctoral research in the labs of T. Wydrzynski/C.B. Osmond, J.H.A. Nugent/M.C.W. Evans and V.K. Yachandra/K. Sauer/M.P. Klein. The results are reported in the context of selected data from the literature. Special emphasis is given to the mode of substrate water binding, Mn oxidation states and the structures of the Mn cluster in the four (meta)stable redox states of the oxygen evolving complex. The paper concludes with a working model for the mechanism of photosynthetic water oxidation that combines mu-oxo bridge oxidation in the S(3) state (V.K. Yachandra, K. Sauer, M.P. Klein, Chem. Rev. 96 (1996) 2927-2950) with O-O bond formation between two terminal Mn-hydroxo ligands during the S(3)-->(S(4))-->S(0) transition.     

Evolutionary potential of (beta/alpha)8-barrels: stepwise evolution of a "new" reaction in the enolase superfamily

The molecular details of the processes involved in divergent evolution of "new" enzymatic functions are ill-defined. Likely starting points are either a progenitor promiscuous for the new reaction or a progenitor capable of catalyzing the new reaction following a single substitution that results from a single base change. However, the molecular (sequence) pathway by which the selective advantage provided by this protein can be improved and ultimately optimized is unclear. In the mechanistically diverse enolase superfamily, we discovered that a monofunctional progenitor could acquire the ability to catalyze a "new" reaction by a single base change: the D297G mutant of the monofunctional l-Ala-d/l-Glu epimerase (AEE) from Escherichia coli catalyzed a low level of the o-succinylbenzoate synthase (OSBS) reaction as well as a reduced level of the AEE reaction [Schmidt, D. M. Z., Mundorff, E. C., Dojka, M., Bermudez, E., Ness, J. E., Govindarajan, S., Babbitt, P. C., Minshull, J., and Gerlt, J. A. (2003) Biochemistry 42, 8387-8393]. We then discovered that the selective advantage and OSBS activity of the D297G mutant are both enhanced by the I19F substitution [Vick, J. E., Schmidt, D. M. Z., and Gerlt, J. A. (2005) Biochemistry 44, 11722-11729]. Both the D297G and I19F substitutions are positioned to alter the substrate specificity so that the substrate for the OSBS reaction is more productively positioned vis a vis the active site catalytic groups. We now report that both the selective advantage and OSBS activity of the D297G/I19F double mutant are enhanced by the R24C (one base change from the wild type Arg codon), R24W (two base changes from the wild type Arg codon and one base change from the R24C codon), and L277W (one base change from the wild type Leu codon) substitutions. The effects of the R24C and L277W mutants are "additive" in the D297G/I19F/R24C/L277W mutant. The greatest selective advantage and OSBS activity are associated with the D297G/I19F/R24W mutant. These "new" substitutions that enhance both the selective advantage and kinetic constants are positioned in the active site where they can alter the specificity, highlighting that the evolution of the "new" OSBS function can be accomplished by changes in substrate specificity.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Simplified Velocity Equations for Characterizing the Partial Inhibition or Nonessential Activation of Bireactant Enzymes

The steady state velocity equation for a bireactant enzyme in the presence of a partial inhibitor or nonessential activator, M, contains squared substrate concentration and higher-ordered M concentration terms. The equation is too complex to be useful in kinetic analyses. Simplification by the method of Cha (J. Biol. Chem. 243, 820–825 (1968)) eliminates squared substrate concentration terms, but retains higher-ordered terms in [M]. It is shown that if strict equilibrium is assumed between free E, M, and EM and for all but one other M-binding reaction, a velocity equation is obtained for an ordered bireactant enzyme that is first degree in all ligands in the absence of products. The equation is an approximation (because it was derived assuming only one M-binding reaction in the steady state), but it contains five inhibition (or activation) constants associated with M, all of which can be obtained by diagnostic replots and/or curve-fitting procedures. The equation also provides a framework for obtaining limiting constants (V¹_max, K¹_ia, K¹_mA,K¹_mB) that characterize the enzyme at saturating M. The same approach is applicable to an enzyme that catalyzes a steady state ping pong reaction.     

Biochemistry of terminal deoxynucleotidyltransferase. Affinity labeling and identification of the deoxynucleoside triphosphate binding domain of terminal deoxynucleotidyltransferase

Using the technique of UV-mediated cross-linking of nucleotides to their acceptor sites (Modak, M. J., and Gillerman-Cox, E. (1982) J. Biol. Chem. 257, 15105-15109), we have labeled calf terminal deoxynucleotidyltransferase (TdT) with [32P]dTTP. The specificity of dTTP cross-linking at the substrate binding site in TdT is demonstrated by the competitive inhibition of the cross-linking reaction by other deoxynucleoside triphosphates, and ATP and its analogues, requiring concentrations consistent with their kinetic constants. Tryptic peptide mapping of the [32P]dTTP-labeled enzyme showed the presence of a single radioactive peptide fraction that contained the site of dTTP cross-linking. The amino acid composition and sequence analysis of the radioactive peptide fraction revealed it to contain two tryptic peptides, spanning residues 221-231 and 234-249. Since these two peptides were covalently linked to dTTP, the region encompassed by them constitutes a substrate binding domain in TdT. Further proteolytic digestion of the tryptic peptide-dTTP complex, using V8 protease, yielded a smaller peptide, and its analysis narrowed the substrate binding domain to 14 amino acids corresponding to residues 224-237 in the primary amino acid sequence of TdT. Furthermore, 2 cysteine residues, Cys-227 and Cys-234, within this domain were found to be involved in the cross-linking of dTTP, suggesting their participation in the process of substrate binding in TdT.     

Comparative molecular field analysis (CoMFA) for sulfoxidation reactions in Mortierella isabellina ATCC 42613 and Helminthosporium sp. NRRL 4671

Previous models for mechanisms of enzymatic sulfoxidation have been somewhat limited by a lack of knowledge of the essential features of substrate-enzyme versus product-enzyme relationships. Computerized methods for modeling ligand-protein (substrate-enzyme) interactions can overcome some of these limitations. Specifically, CoMFA (comparative molecular field analysis) provided a useful general approach in which to evaluate substrate-enzyme and product-enzyme relationships. The present investigation examined the relationship between substrate and product structure in predicting enantioselective sulfoxidation reactions using CoMFA for two species of microorganisms that have been used as models for mammalian metabolism, Mortierella isabellina and Helminthosporium sp. The overall enantioselectivity observed was based on the composite stereoselectivity of sulfoxide formation, sulfone formation (from the sulfoxide), and sulfoxide reduction back to the achiral substrate (sulfide).     

Structural and functional insights into the interaction of echoviruses and decay-accelerating factor

Many enteroviruses bind to the complement control protein decay-accelerating factor (DAF) to facilitate cell entry. We present here a structure for echovirus (EV) type 12 bound to DAF using cryo-negative stain transmission electron microscopy and three-dimensional image reconstruction to 16-A resolution, which we interpreted using the atomic structures of EV11 and DAF. DAF binds to a hypervariable region of the capsid close to the 2-fold symmetry axes in an interaction that involves mostly the short consensus repeat 3 domain of DAF and the capsid protein VP2. A bulge in the density for the short consensus repeat 3 domain suggests that a loop at residues 174-180 rearranges to prevent steric collision between closely packed molecules at the 2-fold symmetry axes. Detailed analysis of receptor interactions between a variety of echoviruses and DAF using surface plasmon resonance and comparison of this structure (and our previous work; Bhella, D., Goodfellow, I. G., Roversi, P., Pettigrew, D., Chaudhry, Y., Evans, D. J., and Lea, S. M. (2004) J. Biol. Chem. 279, 8325-8332) with reconstructions published for EV7 bound to DAF support major differences in receptor recognition among these viruses. However, comparison of the electron density for the two virus.receptor complexes (rather than comparisons of the pseudo-atomic models derived from fitting the coordinates into these densities) suggests that the dramatic differences in interaction affinities/specificities may arise from relatively subtle structural differences rather than from large-scale repositioning of the receptor with respect to the virus surface.     

Reaction kinetic parameters for ion transport from steady-state current-voltage curves.

This study demonstrates possible ways to estimate the rate constants of reaction kinetic models for ion transport from steady-state current-voltage data as measured at various substrate concentrations. This issue is treated theoretically by algebraic reduction and extension of a reaction kinetic four-state model for uniport. Furthermore, an example for application is given; current-voltage data from an open K+ selective channel (Schroeder, J.I., R. Hedrich, and J.M. Fernandez, 1984, Nature (Lond.), 312:361-362) supplemented by some new data have been evaluated. The analysis yields absolute numerical estimates of the 14 rate constants of a six-state model, which is discussed in a wider context.     

Regioselectivity of substrate hydroxylation versus halogenation by a nonheme iron(IV)–oxo complex: possibility of rearrangement pathways

Several nonheme iron enzymes and biomimetic model complexes catalyze a substrate halogenation reaction. Recent computational studies (Borowski et al. J Am Chem Soc 132:12887-12898, 2010) on α-ketoglutarate dependent halogenase proposed an initial isomerization reaction that is important to give halogenated products. We present here a series of density functional theory calculations on a biomimetic model complex-[Fe(IV)(O)(TPA)Cl](+), where TPA is tris(2-pyridylmethyl)amine-and investigate the mechanisms of substrate halogenation versus hydroxylation using the reactant and its isomer where the oxo and chloro groups have changed positions. We show here that the reactions occur on a dominant quintet spin state surface, although the reactants are in a triplet state. Despite the fact that the reactants can exist in two stable isomers with the oxo group either trans or cis to the axial ligand, they react differently with substrates, where one gives dominant hydroxylation and the other gives dominant chlorination of substrates. The ligand in the cis position of the oxo group is found to be active in the reaction mechanism and donated to the substrate during the reaction. A detailed thermochemical analysis of possible reaction mechanisms reveals that the strengths of the Fe-OH and Fe-Cl bonds in the radical intermediates are the key reasons for this regioselectivity switch of hydroxylation over halogenation. This study highlights the differences between enzymatic and biomimetic halogenases, where the former only react after an essential isomerization step, which is not necessary in model complexes.