Unbalanced regression analysis with residuals having a covariance structure of intra-class form.

Let Yi be an ni X 1 vector of observations, Xi an ni X p matrix of known values, and beta an unknown p X 1 with the structure Yi = Xi beta + epsilon i, where the covariance matrix of epsilon i is of intra-class form, that is Cov (epsilon i) = sigma2[(1 - rho) Ii + rho e i e i'] where Ii is the ni X ni identity matrix and e i is the ni X 1 vector each element of which is unity. This article develops the maximum likelihood estimators of beta, sigma2, and rho when one observes N pairs (Xi, Yi). This situation arises typically in biological problems where one samples clusters of related organisms. The estimation procedure is illustrated in a commonly occurring genetics situation.     

Dynamic light-scattering study on polymerization process of muscle actin

Globular actin (G-actin) polymerizes into a fibrous form (F-actin) under physiological salt conditions. The polymerization process of muscle actin was studied by a dynamic light-scattering method. The intensity correlation functions G2(tau) of scattered light from a G-actin solution containing 2 mM Tris-HCl (pH 8.0) and 0.1 mM ATP were analyzed by a cumulant expansion method, and the translational diffusion coefficient was determined to be D = (8.07 +/- 0.10) X 10(-7) cm2/s at 20 degrees C. This D value gave a diameter of 5.3 nm for spherical G-actin including a hydration layer. Polymerization of 1-3 mg/ml G-actin in a solution containing 10 mM Tris-HCl (pH 8.0), 0.2 mM ATP and 60 mM KCl was followed by successive measurements of G2(tau) for a data accumulation period of 60-300 s/run. The time evolution of G2(tau) was analyzed by a least-squares fitting to the field correlation function of a multiexponential form g1(tau) = sigma iAi exp(-gamma i tau) with gamma 1 greater than gamma 2 greater than 3 greater than ..., and the static scattering intensity I(t) = mean value of I as a function of time t after initiation of polymerization was decomposed as I(t) = mean value of I sigma iAi. At the early stage of polymerization, a two-exponential fit gave results indicating that component 1 came from G-actin and component 2 from F-actin growing linearly with t. At the middle stage of polymerization, a three-exponential fit gave the results that component 1 came from G-actin and possibly its small oligomers, component 2 from polymers with a number-average length Ln of about 900 nm which was independent of t, and component 3 from 'ghosts' in dynamic light scattering in a semidilute regime. Component 3 was concluded to arise from restricted motions of polymers with lengths much longer than Ln in cages formed by polymers giving component 2, and a fragmentation-elongation process of F-actin was suggested to start at the middle stage of polymerization, resulting in the size redistribution of F-actin.     

Cytosolic phosphorylation potential.

The tissue contents of the reactants of the myokinase (EC 2.7.4.3) and the combined glyceraldehyde-3-phophate dehydrogenase (EC 1.1.1.29)-3-phosphoglycerate kinase (EC 2.7.2.3) reactions were measured in rapidly inactivated samples of human blood and rat brain, muscle, and liver. The tissue contents of the reactants of the creatine kinase (EC 2.7.3.2) reaction were measured in rat brain and muscle. In vitro the value of the expression: KG+G = [sigma3PG] . [sigmaATP] . [sigmalactate] KLDH = [sigmaHAP]/22] . [sigmaADP][sigmaPi] . [sigmaRUVATE] (1) was found to be 0.725 x 10(7) M-1 at I = 0.25, T = 38 degrees C, and free [Mg2+] = 0.15 mM and the value measured in vivo in red cell was 0.699 x 10(7) M-1. The value of the expression KMYK = ([sigma ATP] [sigma AMP]/[ADP2]) measured under the above conditions and at pH 7.2 was found to be 0.744 while the value found in red cell was 0.784 +/- 0.037. These reactions, therefore, appear to be in a state of near-equilibrium in the red cell and the measured tissue contents of ATP and ADP, which are common reactants in both reactions, approximate closely the activity of these reactants in vivo. In brain and muscle, the value of KG + G/KLDH calculated from the measured tissue contents of the reactants was a factor of 20 or more lower than that expected at equilibrium as was the measured value of the expression: KCK = [sigma ATP] [sigma creatine] divided by [sigma ADP] [sigma creatine-P] [H+] (2) Substitution of calculated free [sigma ADP] values in the expression of KG + G/KLDH gave values of 0.83 +/- 0.19 x 10(7) M-1 for brain and muscle, respectively, which agreed well with the value of 1.65 x 10(7) M-1 measured in vitro at I = 0.25, free [Mg2+] = 1 mM, T = 38 degrees C. This agreement between two highly active enzyme systems in the same compartment is taken as evidence of the existence of near-equilibrium in both these systems and suggests that free cytosolic [sigma ADP] is probably 20-fold lower than measured cell ADP content in mitochondrial-containing tissues.     

Time-resolved intrinsic fluorescence of Enzyme I. The monomer/dimer transition.

Enzyme I of the bacterial phosphotransferase system can exist in a monomer/dimer equilibrium which may have functional significance. Each monomer contains two tryptophan residues. It is demonstrated that the decay of both the monomer and the dimer can be described by a biexponential. The decay times depend on the temperature and at 6 degrees C the decay times are tau 1 = 0.4 ns and tau 2 = 3.2 ns for the monomer and tau 3 = 3.2 ns and tau 4 = 7.2 ns for the dimer form of the enzyme. The changes in the fluorescence decay parameters can be utilized to measure the equilibrium constant for the monomer/dimer transition.     

Ligand binding on ladder lattices

The ligand binding problems on two-dimensional ladders, which model many important binding phenomena in molecular biology, are studied in details. The model is represented by four parameters, the interactions between ligands when bound to adjacent sites on opposite legs of the ladder (tau), the interactions between bound ligands in the longitudinal direction of the ladder (sigma), the number of binding sites that are covered by a bound ligand (m), and the intrinsic binding constant (K). The partition functions of ring ladders are approached with the transfer matrix method. A general relation is derived which connects the partition function of a linear ladder with that of a ring ladder. The results obtained apply to the general situation of multivalent binding, in which m>1. Special attention is paid to the case where the ligand covers one site (m=1). In this case explicit formulas are given for the partition functions of ring and linear ladders. Closed-form expressions are obtained for various properties of the system, including the degree of binding (theta), the midpoint in the binding isotherm (1/square root(tau sigma)), the initial and end slopes of the Scatchard plots (2sigma + tau - 4 and -sigma2 tau, respectively). From these closed-form formulas, sigma and tau may be extracted from experimental data. The model reveals certain features which do not exist in one-dimensional models. Using the general method discussed in [1], the recurrence relation is found for the partition functions. The analytical solution found for this model provides test cases to verify the numerical results for more complex two-dimensional models.     

Use of conditional probabilities for determining relationships between amino acid sequence and protein secondary structure.

The conditional probability, P(sigma/x), is a statement of the probability that the value of sigma will be found given the prior information that a value of x has been observed. Here sigma represents any one of the secondary structure types, alpha, beta, tau, and rho for helix, sheet, turn, and random, respectively, and x represents a sequence attribute, including, but not limited to: (1) hydropathy; (2) hydrophobic moments assuming helix and sheet; (3) Richardson and Richardson helical N-cap and C-cap values; (4) Chou-Fasman conformational parameters for helix, P alpha, for sheet, P beta, and for turn, P tau; and (5) Garnier, Osguthorpe, and Robson (GOR) information values for helix, I alpha, for sheet, I beta, for turn, I tau, and for random structure, I rho. Plots of P(sigma/x) vs. x are demonstrated to provide information about the correlation between structure and attribute, sigma and x. The separations between different P(sigma/x) vs. x curves indicate the capacity of a given attribute to discriminate between different secondary structural types and permit comparison of different attributes. P(alpha/x), P(beta/x), P(tau/x) and P(rho/x) vs. x plots show that the most useful attributes for discriminating helix are, in order: hydrophobic moment assuming helix greater than P alpha much greater than N-cap greater than C-cap approximately I alpha approximately I tau. The information value for turns, I tau, was found to discriminate helix better than turns. Discrimination for sheet was found to be in the following order: I beta much greater than P beta approximately hydropathy greater than I rho approximately hydrophobic moment assuming sheet. Three attributes, at their low values, were found to give significant discrimination for the absence of helix: I alpha approximately P alpha approximately hydrophobic moment assuming helix. Also, three other attributes were found to indicate the absence of sheet: P beta much greater than I rho approximately hydropathy. Indications of the absence of sigma could be as useful for some applications as the indication of the presence of sigma.     

Analysis of trifluorothymidine-resistant (TFTr) mutants of L5178Y/TK+/- mouse lymphoma cells

Three classes of TFTr variants of L5178Y/TK+/- -3.7.2C mouse lymphoma cells can be identified--large colony (lambda), small colony (sigma), and tiny colony (tau). The sigma and lambda mutants are detectable in the routine mutagenesis assay using soft agar cloning. The tau mutants are extremely slow growing and are quantitated only in suspension cloning in microwells. Variants of all three classes have been analyzed in the process of evaluating the usefulness of the thymidine kinase locus in L5178Y/TK+/- mouse lymphoma cells for detecting induced mutational damage. 150 of 152 variants from mutagen treated cultures and 163 of 168 spontaneous mutants were TFTr when rechallenged approximately 1 week after isolation (3 weeks after induction). All of the 41 mutants assayed for enzyme activity were TK-deficient. The sigma and tau phenotypes were found to correlate with slow cellular growth rates (doubling time greater than 12 h), rather than from effects of the TFT selection or mutagen toxicity. Cytogenetic analysis of sigma mutants approximately 3 weeks after induction shows an association between the sigma phenotype and readily observable (at the 230-300 band level) chromosomal abnormalities (primarily translocations involving that chromosome 11 carrying the functional TK gene) in 30 of 51 induced mutants studied. Using an early clonal analysis of mutants (approximately 2 weeks after induction) 28 of 30 sigma mutants showed chromosome 11 rearrangements. All lambda mutants studied (17 of 17 evaluated 3 weeks after induction and 8 of 8 evaluated 2 weeks after induction) showed normal karyotypes (at the 230-300 band resolution level), including the chromosome 11s. These observations support the hypothesis that sigma (and likely tau) mutants represent chromosomal mutations and lambda mutants represent less extensive mutations affecting the TK locus. The inclusion of sigma mutants in the total induced mutant frequency, as well as distinguishing them as a separate subpopulation of TK-deficient mutants, is, therefore, essential in obtaining maximum utility of the information provided by the L5178Y/TK+/- mouse lymphoma assay.     

Solution structure of biopolymers: a new method of constructing a bead model

We propose a new, automated method of converting crystallographic data into a bead model used for the calculations of hydrodynamic properties of rigid macromolecules. Two types of molecules are considered: nucleic acids and small proteins. A bead model of short DNA fragments has been constructed in which each nucleotide is represented by two identical, partially overlapping spheres: one for the base and one for the sugar and phosphate group. The optimum radius sigma = 5.0 A was chosen on the basis of a comparison of the calculated translational diffusion coefficients (D(T)) and the rotational relaxation times (tau(R)) with the corresponding experimental data for B-DNA fragments of 8, 12, and 20 basepairs. This value was assumed for the calculation D(T) and tau(R) of tRNA(Phe). Better agreement with the experimental data was achieved for slightly larger sigma = 5.7 A. A similar procedure was applied to small proteins. Bead models were constructed such that each amino acid was represented by a single sphere or a pair of identical, partially overlapping spheres, depending on the amino acid's size. Experimental data of D(T) of small proteins were used to establish the optimum value of sigma = 4.5 A for amino acids. The lack of experimental data on tau(R) for proteins restricted the tests to the translational diffusion properties.     

Graphical determination of mean activation energy and standard deviation in a microheterogeneity model of enzyme deactivation

Traditionally, enzyme populations have been treated as if they were either homogenous, or heterogeneous with distinct and separable subpopulations. The microheterogeneity model, however, assumes that there is a continuous distribution of properties in the population. In the area of enzyme deactivation kinetics, this model describes the heterogeneous population as having a continuous distribution of activation energy of deactivation. This distribution is characterized by mean activation energy, and a standard deviation of activation energy. The microheterogeneity model contains two parameters, (0) and sigma. Parameter (0) is the mean value of for a heterogeneous enzyme population; is the activation energy divided by absolute temperature and the ideal gas constant. Parameter sigma is the standard deviation of the Gaussian distribution of values in the population. If the population is homogeneous, then = (0) for all enzyme molecules and sigma = 0. There are certain ratios which are independent of (0) and dependent upon sigma. Two important ratios are t(1/4)/t(1/2) and t(1/2)/t(1/2) ('), where t(1/2) (') represents t(1/2) for a homogeneous enzyme population with the same mean ((0)), as the heterogeneous population. If there is experimental deactivation data for the heterogeneous population which is well behaved, the first ratio, t(1/4)/t(1/2), can be determined by estimating the time in minutes at which the enzyme has lost 25% of its activity (t(1/4)), and the time in minutes at which the enzyme has lost 50% of its activity (t(1/2)), and then taking the ratio t(1/4)/t(1/2). The corresponding value of sigma can be estimated from a graph. The ratio t(1/2)/t(1/2) (') can be found directly as a function of t(1/4)/t(1/2), and can be estimated from another graph. The value of (0) can then be calculated from the formulasgiven in the article.     

Kinetic studies on the helix-coil transition of fluorescent labeled poly(-L-lysine) by the temperature-jump technique

Fluorescent dansyl labels were covalently attached to poly (L-lysine) (poly(Lys)) with a degree of polymerization of 300 to 600. The degree of labeling was 0.01 to 0.085 (mol label to mol amino acid residues). From the decay of the anisotropy of fluorescence it was concluded that the labels were highly mobile both in the coiled and helical state. A decrease of fluorescence intensity accompanied the helix-coil transition. Identical pH induced transition curves were measured by circular dichroism and fluorescence. The midpoint of the transition was at pH 10.2. The kinetics of the transition were studied by temperature-jump relaxation using fluorescence detection. A single relaxation phase was observed. The relaxation time tau exhibited a distorted bell shaped dependence on the degree of helicity f with a maximum value tau(max) = 15 micros at f = 0.3 and 20 degrees C. It was independent of polymer concentration and of the degree of labeling. A rate constant of helix propagation kF = 10(7) s(-1) was calculated from tau(max) and published values of the nucleation parameter sigma. The activation energy was 16 kJ mol . The observed rate constant is comparable to that of poly(L-glutamic acid) but two orders of magnitude smaller than that found for polyamino acids with nonionizable side chains.     

A generalization of metabolic control analysis to conditions of no proportionality between activity and concentration of enzymes

The assumption currently considered in the Metabolic Control Theory that velocity of every isolated step is proportional to enzyme concentration, is analysed by considering that in some metabolic systems that condition could not be accomplished. Analysis of the main core of this theory is carried out removing this hypothesis, expressed as "epsilon ei vi is not necessarily equal to one". The results obtained supply a more general formulation of the main theorems of the Control Theory, extending its possible application to more complex metabolic systems.     

Study of the flux and transition time control coefficient profiles in a metabolic system in vitro and the effect of an external stimulator.

Control of flux and transition time was investigated with a reconstructed rabbit muscle glycolytic system in vitro as an experimental model. The results show agreement with the summation property for the Flux Control Coefficients [Kacser & Burns (1973) Symp. Soc. Exp. Biol. 27, 65-104; Heinrich & Rapoport (1974) Eur. J. Biochem. 42, 89-95]. Control of flux is almost exclusively located at the hexokinase- and phosphofructokinase-catalysed steps, whereas control of transition time is distributed more evenly between the enzymes of the system. The summation value of the Transition Time Control Coefficients is near to -1, suggesting the existence of another Summation Theorem besides that already stated for Flux Control Coefficients. Finally, we study the effect of an external stimulator of the system (fructose 2,6-bisphosphate) on the Control Coefficient profiles. The effect appears to be greater on the Transition Time Control Coefficient distribution than on the Flux Control Coefficients.     

Tryptophan sidechain dynamics in hydrophobic oligopeptides determined by use of 13C nuclear magnetic resonance spectroscopy.

Two oligopeptides, t-boc-LAWAL-OMe and t-boc-LALALW-OMe, were synthesized for the purpose of examining the sidechain dynamics of the tryptophan residue in hydrophobic environments by 13C nuclear magnetic resonance and fluorescence spectroscopy. In both peptides, the tryptophan sidechain was greater than 95% enriched with 13C at the C delta 1 position. Spin-lattice relaxation time (T1) and steady-state nuclear Overhauser effect (NOE) data were obtained at 50.3 and 75.4 MHz for both peptides in CD3OD, and at 75.4 MHz for t-boc-LALALW-OMe in lysolecithin-D2O micelles. We have adapted the model-free approach of G. Lipari and A. Szabo (1982, J. Am. Chem. Soc. 104:4546) to interpret the 13C-NMR data. Computer-generated curves based on experimental data obtained at a single frequency demonstrate relationships between an effective correlation time for tryptophan sidechain motion (tau e), a generalized order parameter (sigma) describing the extent of motional restriction, and an overall correlation time for the peptide (tau m). Assuming predominantly dipolar relaxation, least-squares fits of the dual frequency relaxation data provide values for these parameters for both peptides. The contribution of chemical shift anisotropy (CSA), however, is also explicitly assessed in the data analysis, and is shown to perturb the predicted sigma, tau e, and tau m values and to decrease chi(2) values observed in nonlinear least-squares analysis of the data. Because of uncertainty in the contribution of CSA to the relaxation of the indole ring 13C delta 1 atom, nonlinear least-squares analysis of the relaxation data were performed with and without inclusion of a CSA term in the appropriate relaxation equations. Neglecting CSA, an overall peptide correlation time of 0.69 ns is predicted for t-boc-LAWAL-OMe in CD3OD at 20 degrees C compared with 1.28 ns for t-boc-LALALW-OMe. Given these tau m values and taking into account the effect of measurement error in the T1 and NOE data, the internal dynamics of the tryptophan residue of t-boc-LAWAL-OMe in this isotropic environment are described by a range of tau e values from 70 to 112 ps and sigma values between 0.22 and 0.36. Similarly, for t-boc-LALALW-OMe, 68 less than or equal to tau e less than or equal to 93 ps and 0.09 less than or equal to sigma less than or equal to 0.17. The Ch-terminal position of the tryptophan residue in the hexapeptide may account for its lower order parameter.(ABSTRACT TRUNCATED AT 400 WORDS)     

Spatial arrangement of sigma-factor and core enzyme of Escherichia coli RNA polymerase. A neutron solution scattering study

By means of neutron solution scattering we determined the position and orientation of core enzyme and sigma-factor within the Escherichia coli RNA polymerase holoenzyme with the aim of improving existing models. The individual components, core enzyme (E) and sigma-factor (sigma), were highlighted by deuterium labeling and their center-to-center distances determined in the monomeric and the dimeric holoenzyme. The following distance parameters were obtained: dE1-sigma 1 = 8.6(+/- 1) nm, dE1-E2 = 11.5(+/- 1) nm, d sigma 1-sigma 2 = 12.0(+/- 0.7) nm, dE1-sigma 2 = 9(+/- 3) nm. Using a triangulation procedure the position of the sigma-factors, sigma 1 and sigma 2, were determined with respect to the mass center of the core enzyme molecules, E1 and E2, assuming a symmetrical arrangement of the holoenzyme molecules in the dimer (C2 symmetry). In addition, the orientation of the sigma-factor with respect to core enzyme was estimated by means of model calculations. The obtained model of holoenzyme depicts the sigma-factor as buried in a groove of core enzyme, probably between the large subunits beta' and beta.     

Kinetics of Na(+)-dependent conformational changes of rabbit kidney Na+,K(+)-ATPase.

The kinetics of Na(+)-dependent partial reactions of the Na+,K(+)-ATPase from rabbit kidney were investigated via the stopped-flow technique, using the fluorescent labels N-(4-sulfobutyl)-4-(4-(p-(dipentylamino)phenyl)butadienyl)py ridinium inner salt (RH421) and 5-iodoacetamidofluorescein (5-IAF). When covalently labeled 5-IAF enzyme is mixed with ATP, the two labels give almost identical kinetic responses. Under the chosen experimental conditions two exponential time functions are necessary to fit the data. The dominant fast phase, 1/tau 1 approximately 155 s-1 for 5-IAF-labeled enzyme and 1/tau 1 approximately 200 s-1 for native enzyme (saturating [ATP] and [Na+], pH 7.4 and 24 degrees C), is attributed to phosphorylation of the enzyme and a subsequent conformational change (E1ATP(Na+)3-->E2P(Na+)3 + ADP). The smaller amplitude slow phase, 1/tau 2 = 30-45 s-1, is attributed to the relaxation of the dephosphorylation/rephosphorylation equilibrium in the absence of K+ ions (E2P<==>E2). The Na+ concentration dependence of 1/tau 1 showed half-saturation at a Na+ concentration of 6-8 mM, with positive cooperatively involved in the occupation of the Na+ binding sites. The apparent dissociation constant of the high-affinity ATP-binding site determined from the ATP concentration dependence of 1/tau 1 was 8.0 (+/- 0.7) microM. It was found that P3-1-(2-nitrophenyl)ethyl ATP, tripropylammonium salt (NPE-caged ATP), at concentrations in the hundreds of micromolar range, significantly decreases the value of 1/tau 1, observed. This, as well as the biexponential nature of the kinetic traces, can account for previously reported discrepancies in the rates of the reactions investigated.     

Quantitative evaluation of cell orientation in culture.

A quantitative method to assess mutual orientation of cells in cultures on a substrate includes the following operations: (1) the cellular groups to be evaluated are chosen; (2) position of the long axis for each nucleus of the group is determined; (3) the axis OX is arbitrary chosen for every group and the angles alphai between the long axis of every nucleus i and the axis OX are measured. Every nucleus i corresponds to a vector of unit length ei with the angles 2alpha. D, the mean of the vectors ei for every cell group is calculated. This value of D is compared with a set of values of D computed according to a model of mutual orientation studies in a simulation experiment. In this model the group of n vectors consists of a fraction of Kn parallel vectors (o less than or equal to K less than or equal to I) and of (I minus K)n randomly oriented vectors. K corresponding to the computed D which is equal to the experimental value of D is considered as an index of orientation for the group. Contact orientation with respect to the relief of the substrate may be evaluated as a root mean square deviation sigma0 to the angles between the long axes of cell nuclei and the direction of relief. Examples of the measurements of K and sigma0 in cell cultures are given.     

Spectrometric analysis of degradation of a physiological substrate sigma32 by Escherichia coli AAA protease FtsH

We have established a fluorescence polarization assay system by which degradation of sigma32, a physiological substrate, by FtsH can be monitored spectrometrically. Using the system, it was found that an FtsH hexamer degrades approximately 0.5 molecules of Cy3-sigma32 per min at 42 degrees C and hydrolyzes approximately 140 ATP molecules during the degradation of a single molecule of Cy3-sigma32. Evidence also suggests that degradation of sigma32 proceeds from the N-terminus to the C-terminus. Although FtsH does not have a robust enough unfoldase activity to unfold a tightly folded proteins such as green fluorescent protein, it can unfold proteins with lower [Formula: see text] s such as glutathione S-transferase (Tm = 52 degrees C).     

Tau, sigma, and delta. A family of repeated elements in yeast

We report here the isolation and structure of a new repeated DNA element, tau. This element, from Saccharomyces cerevisiae, is 371 base pairs long and is flanked on either end by the same invertedly repeated sequence found at the ends of some Ty and sigma elements in yeast, copia elements in Drosophila and spleen necrosis virus. The tau inverted repeats are themselves flanked by a 5-base pair directly repeated genomic sequence that is present only once in a cognate tau-allele. These structural characteristics, the presence of multiple copies of tau in the genome, and the isolation of tau+ and tau- allelic pairs suggest that tau may be capable of transposition either alone or in association with some larger element. Detailed sequence analysis of the tau, sigma, and delta elements revealed that all three contain significant regions of homology, suggesting that they are probably members of a single family derived from a common progenitor.