The multiple activities of polyphosphate kinase of Escherichia coli and their subunit structure determined by radiation target analysis

Polyphosphate kinase (PPK), the principal enzyme required for the synthesis of inorganic polyphosphate (polyP) from ATP, also exhibits other enzymatic activities, which differ significantly in their biochemical optima and responses to chemical agents. These several activities include: polyP synthesis (forward reaction), nATP --> polyP(n) + nADP (Equation 1); ATP synthesis from polyP (reverse reaction), ADP + polyP(n) --> ATP + polyP(n - 1) (Equation 2); general nucleoside-diphosphate kinase, GDP + polyP(n) --> GTP + polyP(n - 1) (Equation 3); linear guanosine 5'-tetraphosphate (ppppG) synthesis, GDP + polyP(n) --> ppppG + polyP(n - 2) (Equation 4); and autophosphorylation, PPK + ATP --> PPK-P + ADP (Equation 5). The Mg(2+) optima are 5, 2, 1, and 0.2 mM, respectively, for the activities in Equations 1, 2, 3, and 4. Inorganic pyrophosphate inhibits the activities in Equations 1 and 3 but stimulates that in Equation 4. The kinetics of the activities in Equations 1, 2, and 3 are highly processive, whereas the transfer of a pyrophosphoryl group from polyP to GDP (Equation 4) is distributive and demonstrates a rapid equilibrium, random Bi-Bi catalytic mechanism. Radiation target analysis revealed that the principal functional unit of the homotetrameric PPK is a dimer. Exceptions are a trimer for the synthesis of ppppG (Equation 4) and a tetrameric state for the autophosphorylation of PPK (Equation 5) at low ATP concentrations. Thus, the diverse functions of this enzyme involve different subunit organizations and conformations. The highly conserved homology of PPK among 18 microorganisms was used to determine important residues and conserved regions by alanine substitution, by site-directed mutagenesis, and by deletion mutagenesis. Of 46 single-site mutants, seven exhibit none of the five enzymatic activities; in one mutant, ATP synthesis from polyP is reduced relative to GTP synthesis. Among deletion mutants, some lost all five PPK activities, but others retained partial activity for some reactions but not for others.     

Parameters of photosynthesis: definitions, theory and interpretation of results

Regrettably, parentheses are missing in Equation 16 on p. 1649.Equation 16 should read:      

Comparison of measured and predicted residual lung volume in determining body composition of collegiate wrestlers

This investigation compared percent fat obtained via underwater weighing using measured and predicted residual lung volume (RLV) in euhydrated and hypohydrated collegiate wrestlers (N = 67). RLV was measured using O(2) rebreathing or O(2) dilution and predicted using 3 equations-Equation 1: (0.019 x height [cm]) + (0.0115 x age [years]) - 2.24; Equation 2: (0.017 x age [years]) + (0.06858 x height [in.]) - 3.477; and Equation 3: (0.0275 age [years]) + (0.0189 height [cm]) - 2.6139. Percent fat determined using RLV Equation 2 did not differ from the value obtained using measured RLV in the euhydrated (10.9 +/- 5.1 vs. 11.5 +/- 5.6% fat) or hypohydrated (10.8 +/- 5.1 vs. 12.3 +/- 5.6% fat) trials. All other percent fat values differed (p < 0.05) from the value obtained using measured RLV in euhydrated subjects. The use of RLV Equation 2 may be a practical alternative to measured RLV in determining percent fat in euhydrated and hypohydrated collegiate wrestlers.     

Erratum to: Muñoz,I., L. Milà i Canals,and R. Clift. 2010. Consider a Spherical Man: A Simple Model to Include Human Excretion in Life Cycle Assessment of Food Products. Journal of Industrial Ecology 12(4): 521–538.

On page 526 of this article, equations (4), (5), and (7) should be corrected as follows. Equation (4) should read: Equation (5) should read: Equation (7) should read: The authors acknowledge the useful comments made by Dr. Enda Crossin and Sean Frost from the Centre for Design, RMIT University, Melbourne, Australia.     

ERRATA

On page 235, Table I: Equation (1) for Node 4 should read ‘A/A_c=0·840+0·0006A_c’;Equation (2) for Node 4 should read ‘A=0·89A_c’and Equation (2) for Node 5–10 should read ‘A=0·813A_c’.     

ERRATUM

Equation (2) should read: Equation (5) should read:      

ERRATUM

Equation (2) should read: Equation (5) should read:      

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : XI. ON FLICKER WITH SUBDIVIDED FIELDS

In Vol. 27, No. 5, May 20, 1944, page 403, in the eighth line from the bottom of the page, the comma after "intensity" should be a semicolon. On page 413, in the second formula from the bottom of the page, for See PDF for Equation read See PDF for Equation On the same page, formula 2 should read See PDF for Equation On page 414, line 3, at the end of the line add "or" to read "of the level of I or of F." On page 422, in the first line below the figure legend, for "illuminate" read "illuminated." On page 430, line 22, for "lighteb dars" read "lighted bars."     

The proportion of mutants in bacterial cultures

The proportion of mutants in a growing culture of organisms will depend upon (a) the rate at which the wild cells produce them (with or without growth), (b) the back mutation rate, and (c) the growth rates of the wild and mutant cells. If the mutation rate without growth and the back mutation rate are neglected, the growth of a mutant is expressed by See PDF for Equation and the ratio of the mutant to wild by See PDF for Equation in which λ = mutation frequency rate constant, "mutation rate," A = growth rate constant of wild cells W, B = growth rate constant of mutant cells M. If the term [B – (1 – 2λ)A] is positive, the proportion of mutants increases continuously. If it is negative, the proportion of mutants reaches a constant value See PDF for Equation If mutation is assumed to occur without growth at the rate C, then the corresponding equations are (11), (12), and (14). See PDF for Equation If (B + C – A) is negative and t = ∞, See PDF for Equation If C << A, See PDF for Equation     

Modeling phytoplankton growth rates

Equation 14 on p. 68 should read: Equation 20 on p. 69 should read:      

Linear structure of the oligosaccharide chains in alpha1-protease inhibitor isolated from human plasma.

Two glycopeptides present in equal amounts were isolated from a pronase digest of alpha1-protease inhibitor of human plasma by gel filtration on Sephadex G-50 and chromatography on DEAE-cellulose. The carbohydrate side chains in both glycopeptides are linked through asparaginyl residues. The glycopeptides were digested sequentially with specific glycosidases; and after each step, the released sugars as well as the composition of the residual peptides were determined. The linear structures of these glycopeptides deduced from these data are shown below. Based on the total carbohydrate content of the intact protein and with these structural data, it is postulated that 4 oligosaccharide units are attached to 1 molecule of the protein; 2 of these were represented as in Equation 1, the other 2 as in Equation 2.     

Circadian rhythmicity in a fermentation process?

Summary An idea is proposed for the role of the circadian rhythmicity in the control of the oscillatory behavior observed in the growth and product formation during the cell-retention continuous culture of Clostridium acetobutylicum. C. acetobutylicum is highly sensitive to the permeability of the cell membrane. A physical mechanism for the variability of the cytoplasmic membrane has been proposed suggesting that the performance of the cell membrane, due to its liquid crystalline structure, is influenced by the external forces (e.g. earth's magnetic field). A previously developed Physiological State Model was extended by incorporating the effect of external forces on the cell membrane permeability. The new mathematical model could simulate the observed oscillatory behavior of the microbial culture. Some experimental results in support of the theoretical predictions have been presented.Nomenclature a Anisotropy - B Butanol concentration in the fermentation broth (g/l) - B _i Intracellular butanol concentration (g/l) - B _ex Extracellular butanol concentration (g/l) - Mean value of the butyric acid solution concentration (g/l) - BA _i Intracellular butyric acid concentration (g/l) - BA _ex Extracellular butyric acid concentration (g/l) - D Dilution rate (l/h) - H Magnetizing force (oersted) - K Constant in Equation (1) - k B Constant in Equation (15) - K _BA Saturation constant - k _{BA 1} Constant in Equation (13) - k _{BA 2} Constant in Equation (13) - K _D Constant in Equation (13) - k _{G 1} Constant in Equation (8) - k _{G 2} Constant in Equation (8) - k _{G 3} Constant in Equation (9) - K _I Inhibition Constant - k _p Constant in Eq. (11) - K _S Monod constant - n Number of the active sugar transport sites - P Cellular membrane permeability (l/g wet cell·h) - q _S Specific rate of substrate utilization (g substrate/g biomass·h) - S Substrate concentration in the fermentation broth (g/l) - S _O Substrate concentration in the feed solution (g/l) - t Time (h) - X Total biomass concentration (g/l) - X ₁ Active biomass concentration (g/l) - X ₂ Non-active biomass concentration (g/l) Greek Letters Ratio of the dry to wet cell weight (g dry cell/g wet cell) - ₁ Constant in Equation (6) - ₂ Constant in Equation (6) - ₃ Constant in Equation (6) - Specific culture growth rate (1/h)     

THE FUNCTION OF THE BRAIN IN LOCOMOTION OF THE POLYCLAD WORM,YUNGIA AURANTIACA

Coordinated swimming movements in Yungia are not dependent upon the presence of the brain. The neuromuscular mechanism necessary for spontaneous movement and swimming is complete in the body of the animal apart from the brain. Normally this mechanism is set in motion by sensory stimulation arriving by way of the brain. The latter is a region of low threshold and acts as an amplifier by sending the impulses into a great number of channels. When the head is cut off these connections with the sensorium are broken, consequently peripheral stimulation does not have its usual effect. If, however, the motor nerves are stimulated directly as by mechanical stimulation of the median anterior region, then swimming movements result. Also if the threshold of the entire nervous mechanism is lowered by phenol or by an increase in the ion ratios See PDF for Equation and See PDF for Equation then again peripheral stimulation throws the neuromuscular mechanism into activity and swimming movements result.     

Correction to "Attribute Clustering for Grouping, Selection, and Classification of Gene Expression Data"

This is a correction to a typographical error in (11) in [1] which present the calculation of the sum of the multiple significant interdependence redundancy measure. Equation (11) in [1] should be: $$k=argmaxnolimits_{kin{2,ldots,p}}sum_{r=1}^k sum_{A_iin{C_r-eta_r}}R(A_i:eta_r).$$(11)We remark that the experimental results reported in [1] are based on (11) above not (11) in [1].     

CONTRIBUTION TO THE THEORY OF PERMEABILITY OF MEMBRANES FOR ELECTROLYTES

On page 39, Vol. viii, No. 2, September 18, 1925, multiply the right-hand side of formula (2) by the factor See PDF for Equation. On page 44, immediately after formula (1) the text should be continued as follows: Let us suppose a membrane to be separated by two solutions of KCl of different concentrations K₁ and K₂ and these concentrations and the corresponding concentrations of K⁺ within the membrane, which are in equilibrium with the outside solutions, to be so high that the H⁺ ions may be neglected. When a small electric current flows across the system, practically the K⁺ ions alone are transferred and that in a reversible manner. Therefore the total P.D. is practically See PDF for Equation This P.D. is composed of two P.D.''s at the boundaries and the diffusion potential within the membrane. Suppose the immobility of the anions is not absolute but only relative as compared with the mobility of the cations, KCl would gradually penetrate into the membrane to equal concentration with the outside solution on either side and no boundary potential would be established. In this case the diffusion P.D. within the membrane is the only P.D., amounting to See PDF for Equation but, V being practically = 0, it would result that See PDF for Equation So the definitive result is the same as in the former case. Now cancel the printed text as far as page 48, line 13 from the top of the page, but retain Fig. 1. On page 50, line 19 from the top of the page, cancel the sentence beginning with the word But and ending with the words of the chain.     

Updated model of the batch acetone-butanol fermentation

Summary The recent models of the Acetone-Butanol fermentation did not adequately describe the culture inhibition by the accumulating metabolites and were unable to simulate the acidogenic culture dynamics at elevated pH levels. The present updated modification of the model features a generalised inhibition term and a pH dependent terms for intracellular conversion of undissociated acids into solvent products. The culture dynamics predictions by the developed model compared well with experimental results from an unconventional acidogenic fermentation ofC. acetobutylicum.Nomenclature A acetone concentration in the fermentation broth, [g/L] - AA total concentration of dissociated and undissociated acetic acid, [g/L] - AA _undiss concentration of undissociated acetic acid, [g/L] - APS Absolute Parameter Sensitivity - AT acetoin concentration in the fermentation broth, [g/L] - B butanol concentration in the fermentation broth, [g/L] - BA total concentration of dissociated and undissociated butyric acid, [g/L] - BA _undiss concentration of undissociated butyric acid, [g/L] - E ethanol concentration in the fermentation broth, [g/L] - f(T) inhibition function as defined in Equation (2) - k ₁ constant in Equation (4), [g substrate/g biomass] - k ₂ constant in Equation (4), [g substrate/(g biomass.h)] - k ₁ constant in Equation (5), [g substrate/(g biomass] - k ₂ constant in Equation (5), [g substrate/(g biomass.h)] - k ₃ constant in Equation (6), [g butyric acid/g substrate] - k ₄ constant in Equation (6), [g butyric acid/(g biomass.h)] - k ₅ constant in Equation (7), [g butanol/g substrate] - k ₆ constant in Equation (8), [g acetic acid/g substrate] - k ₇ constant in Equation (8), [g acetic acid/(g biomass.h)] - k ₈ constant in Equation (9), [g acetone/g substrate] - k ₉ constant in Equation (10), [g ethanol/g substrate] - k ₁₀ constant in Equation (11), [g acetoin/g substrate] - k ₁₁ constant in Equation (12), [g lactic acid/g substrate] - K _I Inhibition constant, [g inhibitory products/L] - ke maintenance energy requirement for the cell, [g substrate/(g biomass.h)] - K _AA acetic acid saturation constant, [g acetic acid/L] - K _BA butyric acid saturation constant, [g butyric acid/L] - K _S Monod's saturation constant, [g substrate/L] - LA lactic acid concentration in the fermentation broth, [g/L] - m _i ,n _i constants in Equation (14) - n empirical constant, dependent on degree of inhibition. - P concentration of inhibitory products (B+BA+AA), [g/L] - P _max maximum value of product concentration to inhibit the fermentation, [g/L] - pK_a equilibrium constant - r _A rate of acetone production, [g acetone/L.h] - r _AA rate of acetic acid production, [g acetic acid/L.h] - r _AT rate of acetoin production, [g acetoin/L.h] - r _B rate of butanol production, [g butanol/L.h] - r _BA rate of butyric acid production, [g butyric acid/L.h] - r _E rate of ethanol production, [g ethanol/L.h] - RPS Relative Parameter Sensitivity - r _LA rate of lactic acid production, [g lactic acid/L.h] - r _S dS/dt=total substrate consumption rate, [g substrate/L.h] - r _S substrate utilization rate, [g substrate/L.h] - S substrate concentration in the fermentation broth, [g substrate/L] - S ₀ initial substrate concentration, [substrate/L] - t time, [h] - X biomass concentration, [g/L] - Y _X yield of biomass with respect to substrate, [g biomass/g substrate] - Y _{P i} yield of metabolic product with respect to substrate, [g product/g substrate] Derivatives dX/dt rate of biomass production, [g biomass/L.h] - dP _i /dt rate of product formation, [g product/L.h] Greek letters specific growth rate of the culture, [h^–1] - I specific growth rate of the culture in the presence of the inhibitory products, [h^–1] - µ_max maximum specific growth rate of the culture, [h^–1]     

The intrinsic viscosity of mixed protein systems,including studies of plasma and serum

Experimental evidence is presented that the intrinsic viscosity of solutions of mixed proteins obeys the additive equation See PDF for Equation. The datum serves to characterize the system, and combined with other analytical techniques and fractionation procedures, enables one to analyze and characterize subfractions. The plasmas and sera of clinically "normal" individuals give intrinsic viscosity values agreeing with calculated values. The intrinsic viscosity values for pathological plasmas and sera in all cases are greater than normal and reflect the augmented levels of those proteins fibrinogen, α₂-globulins, and γ-globulins occurring in the pathological state. The method is readily adaptable to routine clinical use and furnishes a measure of the departure from normal of protein levels in serum and plasma.     

THE COUPLED REDOX POTENTIAL OF THE LACTATE-ENZYME-PYRUVATE SYSTEM

1. The term "coupled redox potential" is defined. 2. The system lactic ion See PDF for Equation pyruvic ion + 2H⁺ + 2e is shown to be reversible (when the enzyme is lactic acid dehydrogenase) and its coupled redox potential between pH 5.2 and 7.2 at 32°C. is: See PDF for Equation 3. The free energy of the reaction: lactic ion (1m) → pyruvic ion (1m) = -ΔF = –14,572. 4. The standard free energy of formation (ΔF ₂₉₈) of pyruvic acid (l) is estimated at –108,127. This is merely an approximation as some necessary data are lacking. 5. The importance of coupled redox potentials as a factor in the regulation of the equilibrium of metabolites is indicated.     

Estimation of the number of amino acid substitutions per site when the substitution rate varies among sites

A general model for estimating the number of amino acid substitutions per site (d) from the fraction of identical residues between two sequences (q) is proposed. The well-known Poisson-correction formula q = e ^–d corresponds to a site-independent and amino-acid-independent substitution rate. Equation q = (1 – e ^–2d )/2d, derived for the case of substitution rates that are site-independent, but vary among amino acids, approximates closely the empirical method, suggested by Dayhoff et al. (1978). Equation q = 1/(1 + d) describes the case of substitution rates that are amino acid-independent but vary among sites. Lastly, equation q = [ln(1 + 2d)]/2d accounts for the general case where substitution rates can differ for both amino acids and sites.