Measures of Dispersion with Weights Based on Ranks

The measures of dispersion for ungrouped data proposed by Gini and Lienert, which are defined as the mean of the ranges of pairs and triplets of n values, are generalised. A family of measures of dispersion emerges with weights based on ranks instead of the measurements themselves.     

Defining and Detecting Second Order Correlations in Repeated Measurements Designs

It is shown that 3-point response curves from N individuals imply a second order correlation (triplet correlation) between the 3 series of repeated measurements if the curves are clustered as to their shapes. Coefficients are defined and tests are suggested for triplet correlations. Nonparametric alternatives to ANOVA are discussed for repeated measurement designs involving shapeclustered response curves.     

A Semiparametric Estimator of the Crossing Point in the Two‐Sample Linear Shift Function: Application to Crossing Lifetime Distributions

Let X and Y be two random variables with continuous distribution functions F and G. Consider two independent observations X₁, … , X_m from F and Y₁, … , Y_n from G. Moreover, suppose there exists a unique x* such that F(x) > G(x) for x < x* and F(x) < G(x) for x > x* or vice versa. A semiparametric model with a linear shift function (Doksum, 1974) that is equivalent to a location‐scale model (Hsieh, 1995) will be assumed and an empirical process approach (Hsieh, 1995) is used to estimate the parameters of the shift function. Then, the estimated shift function is set to zero, and the solution is defined to be an estimate of the crossing‐point x*. An approximate confidence band of the linear shift function at the crossing‐point x* is also presented, which is inverted to yield an approximate confidence interval for the crossing‐point. Finally, the lifetime of guinea pigs in days observed in a treatment‐control experiment in Bjerkedal (1960) is used to demonstrate our procedure for estimating the crossing‐point. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Randomness and aggregation: analysis of dispersion in an epiphytic chironomid community

1. Patterns of dispersion in a chironomid community on the submersed macrophyte Myriophyllum spicatum were analysed. 2. Random dispersion commonly occurred throughout the year, with an average of 40% of all species being observed with random spatial patterns. The frequency of occasions with random dispersion varied among chironomid species, ranging from 3.3% in Rheotanytarsus curtistylus to 56% in Thienemanniella majuscula. 3. Estimates of the negative binomial parameter k show that 26% of all cases demonstrate strong aggregation (0 < k < 1.0) while nearly half (47%) have quasi-random dispersion. Interspecific variation in k was not significant statistically when all the species were considered together, although a pairwise comparison between two abundant species Tvetenia calvescens and Rheotanytarsus curtistylus demonstrated a marginally significant difference. When different instars were compared, the percentage frequency of strong aggregation (0 < k < 1.0) declined from first instars (49%) to later instars (II-38%, III-24% and IV-27%). 4. Variance/mean and m*—m regressions (m* is Lloyd's mean crowding statistic and m is the sample mean) both fitted the data well, but there was little indication of significant interspecific variation in parameter values, particularly the slope of regression. 5. Dispersion patterns were examined along with the analysis of spatial overlap in this community. Forty-two per cent of species-pairs with reduced spatial overlap (spatially ‘segregated’ pairs) contained one or both species with random dispersion, while the corresponding value for spatially unsegregated pairs was 57%. This suggests that spatial segregation is not necessarily caused by strong, independent aggregation of both species. Comparing spatially segregated vs. unsegregated pairs, the former tend to have one species with a stronger tendency of aggregation than species of the latter. 6. Patterns of dispersion observed were considered in the light of ‘random patch formation’. Random patch formation emphasizes the stochasticity of patch-forming processes as well as the stochastically dynamic nature of resultant patches. Unlike terrestrial drosophilid assemblages, where strong aggregation is a predominant pattern, this chironomid community demonstrates widely varying degrees of dispersion with high occurrence of randomness, reflecting the stochasticity of dispersal and recolonization processes. It is suggested that, in terms of species coexistence, more emphasis should be placed on stochasticity rather than on aggregation in this type of community.     

Gene stacking strategies with doubled haploids derived from biparental crosses: theory and simulations assuming a finite number of loci

Recent progress in genotyping and doubled haploid (DH) techniques has created new opportunities for development of improved selection methods in numerous crops. Assuming a finite number of unlinked loci (ℓ) and a given total number (n) of individuals to be genotyped, we compared, by theory and simulations, three methods of marker-assisted selection (MAS) for gene stacking in DH lines derived from biparental crosses: (1) MAS for high values of the marker score (T, corresponding to the total number of target alleles) in the F₂ generation and subsequently among DH lines derived from the selected F₂ individual (Method 1), (2) MAS for augmented F₂ enrichment and subsequently for T among DH lines from the best carrier F₂ individual (Method 2), and (3) MAS for T among DH lines derived from the F₁ generation (Method 3). Our objectives were to (a) determine the optimum allocation of resources to the F₂ ( n₁^* \, n_{1}^{*} ) and DH generations (n - n₁^* ) (n - n_{1}^{*} ) for Methods 1 and 2 by simulations, (b) compare the efficiency of all three methods for gene stacking by simulations, and (c) develop theory to explain the general effect of selection on the segregation variance and interpret our simulation results. By theory, we proved that for smaller values of ℓ, the segregation variance of T among DH lines derived from F₂ individuals, selected for high values of T, can be much smaller than expected in the absence of selection. This explained our simulation results, showing that for Method 1, it is best to genotype more F₂ individuals than DH lines ($ n_{1}^{*} :n > 0.5 $ n_{1}^{*} :n > 0.5 ), whereas under Method 2, the optimal ratio n₁^* :n n_{1}^{*} :n was close to 0.5. However, for ratios deviating moderately from the optimum, the mean [`(X)] \overline{X} of T in the finally selected DH line ( T<sub>\textDH</sub><sup>*</sup> T_{\text{DH}}^{*} ) was hardly reduced. Method 3 had always the lowest mean [`(X)] \overline{X} of T_\textDH^* T_{\text{DH}}^{*} except for small numbers of loci (ℓ = 4) and is favorable only if a small number of loci are to be stacked in one genotype and/or saving one generation is of crucial importance in cultivar development. Method 2 is under most circumstances the superior method, because it generally showed the highest mean [`(X)] \overline{X} and lowest SD of T_\textDH^* T_{\text{DH}}^{*} for the finally selected DH.     

Improved method for measuring the apparent CO2 photocompensation point resolves the impact of multiple internal conductances to CO2 to net gas exchange

There is a growing interest in accurate and comparable measurements of the CO₂ photocompensation point (Γ*), a vital parameter to model leaf photosynthesis. The Γ* is measured as the common intersection of several CO₂ response curves, but this method may incorrectly estimate Γ* by using linear fits to extrapolate curvilinear responses and single conductances to convert intercellular photocompensation points (C_i*) to chloroplastic Γ*. To determine the magnitude and minimize the impact of these artefacts on Γ* determinations, we used a combination of meta‐analysis, modelling and original measurements to develop a framework to accurately determine C_i*. Our modelling indicated that the impact of using linear fits could be minimized based on the measurement CO₂ range. We also propose a novel method of analysing common intersection measurements using slope–intercept regression. Our modelling indicated that slope–intercept regression is a robust analytical tool that can help determine if a measurement is biased because of multiple internal conductances to CO₂. Application of slope–intercept regression to Nicotiana tabacum and Glycine max revealed that multiple conductances likely have little impact to C_i* measurements in these species. These findings present a robust and easy to apply protocol to help resolve key questions concerning CO₂ conductance through leaves.     

EVIDENCE OF RAPID AND SLOW PROGRESSION OF CELLS THROUGH G2 PHASE IN MOUSE EPIDERMIS: A COMPARISON BETWEEN PHASE DURATIONS MEASURED BY DIFFERENT METHODS

Percentage labelled mitosis (PLM) measurements were initiated at four different times during a 24-hr period and continued for 24 hr in hairless mouse epidermis. Estimates of G₂ and S phase durations (mean T_G2 and mean T_S) were calculated. A significant number of labelled mitoses (10–20%) was seen after 30 min in all four PLM measurements and the estimated mean T_G2 varied from 1.4 to 2.5 hr and was in agreement with values from PLM measurements in other epithelial tissues. These mean T_G2 values were much shorter than expected from [³H]TdR double labelling experiments and from a multiparameter cell kinetic study in hairless mouse epidermis and did not reflect the circadian variations seen in these studies. the differences in estimates of phase durations can be explained by postulating two G₂ cell populations; one with a rapid and another with a slow rate of cell cycle progression. the cells with the higher rate are mainly registered by the PLM method, whereas those with the lower rate largely escape detection by this method. T_G2 estimates from PLM measurements in mouse epidermis therefore do not reflect the phase duration of the entire G₂ population. It is also concluded that circadian variations in T_S can not be accurately registered by the PLM method.     

Note on a combinatorial problem

In the first part of this paper we have assembled some properties of the quantitiesR _m ⁿ , whereR _m ⁿ denotes the number of distributions ofn different objects intom indifferent parcels, with no empty parcels allowed. We then discuss the following problem (N. Rashevsky, 1954, 1955 a,b, 1956): to find the total number,G _n , of graphs that can be obtained from the biotopological transformation (T ⁽¹⁾ X) for a given value of the parametern. This is related to the distribution ofn indifferent objects intom different boxes. A formula forG _n is given which, however, is not very convenient for practical computations because it involves a summation over certain “admissible partitions” of the numbermn (m is a second parameter of the transformation). Some theorems are derived; with their help we can simplify the calculation ofG _n to a small extent. The numbersG _n are calculated forn≤9 and estimated forn=10. It is found thatG ₇≈5.4×10⁴,G ₈≈8.3×10⁵,G ₉≈1.4×10⁷, andG ₁₀≈3×10⁸. These values ofn are those which might be used in connection with N. Rashevsky’s work (cf. Rashevsky, 1956).     

A “new” genetic polymorphism of a human serum protein: inter-alpha-trypsin-inhibitor

Summary A new genetic polymorphism of a human serum glycoprotein, the inter--trypsin-inhibitor (ITI), has been demonstrated by population and family studies. Sera were examined after neuraminidase treatment by isoelectric focusing on agarose gels followed by immunoblotting or by immunfixation with specific ITI-antiserum. Using this method, three common ITI phenotypes 1, 1–2 and 2, as well as two further rare ITI types 1–3 and 2–3 were disclosed. Genetically, these phenotypes are controlled by three allelic genes that determine a total of six phenotypes. These alleles are designated ITI^*1, ITI^*2 and ITI^*3. The homozygous form of the third allele ITI^*3 has not been found, as yet. The frequencies of ITI were examined in two population samples from Southern Germany (n=248) and from Tyrol, Austria (n=124). The gene frequencies of the common alleles ITI^*1 and ITI^*2 were 0.575 and 0.417, respectively, in Southern Germany, and 0.577 and 0.423, respectively, in Tyrol, Austria. The third allele ITI^*3 was found only in the sample from Southern Germany, thus far, and was calculated to be 0.008.     

HLA-G gene polymorphism in a Japanese population

 Polymorphism of the HLA-G gene in a Japanese population was investigated employing polymerase chain reaction (PCR)-single-strand conformation polymorphism (SSCP) analysis, PCR sequence-specific oligonucleotide (SSO) analysis, and DNA direct sequencing. Nucleotide sequence variations in exons 2, 3, and 4 of the HLA-G gene in 54 healthy Japanese individuals were examined. In addition, seven Japanese samples carrying common HLA haplotypes were analyzed. In total, nine single-base substitutions compared with the sequence of G ^* 01011 were identified: one in intron 1 (nucleotide position 970), one in exon 2 (the third base of codon 57: G → A), three in intron 2 (1264, 1276, and 1292), three in exon 3 (the third base of codon 93: C → T, the third base of codon 107: A → T, and the first base of codon 110: C → A), and one in intron 3 (2334). The substitution at codon 110 was non-synonymous and led to an amino acid substitution from leucine to isoleucine. The other three nucleotide substitutions in exons were synonymous. Through analysis of combinations of the exon 2, 3, and 4 nucleotide sequences we identified four alleles, which we provisionally designated GJ1, GJ2, GJ3, and GJ4. The allele frequencies were estimated to be 0.33, 0.16, 0.45, and 0.06, respectively. Nucleotide sequences of GJ1, GJ2, and GJ4 were identical to G ^* 01011, the clone 7.0E, and G ^* 01013, respectively. GJ3 was a newly observed allele and was officially designated G ^* 0104 by the WHO Nomenclature Committee in January 1996. Strong positive associations were observed between HLA-G alleles and HLA-A, -B, or -DRB1 alleles. Received: 15 February 1996 / Revised: 26 March 1996     

Properties of a general model of DNA evolution under no-strand-bias conditions

Under the hypothesis of no-strand-bias conditions, the Watson and Crick base-pairing rule decreases the complexity of models of DNA evolution by reducing to six the maximum number of substitution rates. It was shown that intrastrand equimolarity between A and T (A ^* T ^*) and between G and C (G ^* C ^*) is a general asymptotic property of this class of models. This statistical prediction was observed on 60 long genomic fragments (>50 kbp) from various kingdoms, even when the effect of the two opposite orientations for coding sequences is removed. The practical consequence of the model for estimating the expected number of substitutions per site between two homologous DNA sequences is discussed.Abbreviations BPR Watson and Crick base pairing rule (A:T, G:C) - PRI Intrastrand type-1 parity rule (i j, m(i,j)m( )) - PRII Intra strand type-2 parity rule (A ^* T ^*, G ^* C ^*)     

Singlet oxygen formation and chlorophyll a triplet excited state deactivation in the cytochrome b6f complex from Bryopsis?corticulans

We have attempted to investigate the correlation between the detergent-perturbed structural integrity of the Cyt b ₆ f complex from the marine green alga Bryopsis corticulans and its photo-protective properties, for which the nonionic detergents n-octyl-β-d-glucopyranoside (β-OG) and n-dodecyl-β-d-maltoside (β-DM), respectively, were used for the preparation of Cyt b ₆ f, and the singlet oxygen (¹O₂*) production as well as the triplet excited-state chlorophyll a (³Chl a*) formation and deactivation were examined by spectroscopic means. Near-infrared luminescence of ¹O₂ * (~1,270 nm) on photo-irradiation was detected for the β-OG preparation where the complex is mainly in oligomeric state, but not for the β-DM one in which the complex exists in dimeric form. Under anaerobic condition, photo-excitation of Chl a in the β-DM preparation generated ³Chl a* with a lower quantum yield of Φ_T ~ 0.02 and a longer lifetime of ~600 μs with respect to those as in the case of β-OG preparation, Φ_T ~ 0.12 and 200–300 μs. These results prove that the enzymatically active and intact Cyt b ₆ f complex on photo-excitation tends to produce little ³Chl a* or ¹O₂ *, which implies that the pigment–protein assembly of Cyt b ₆ f complex per se is crucial for photo-protection. F. Ma and X.-B. Chen contributed equally to this work.     

New developments in first-principles excited-state dynamics simulations: unveiling the solvent specificity of excited anionic cluster relaxation and electron solvation

Charge-transfer-to-solvent excited iodide–polar solvent molecule clusters, [I^? (Solv)_n]^*, have attracted substantial interest over the past 20 years as they can undergo intriguing relaxation processes leading ultimately to the formation of gas-phase molecular analogues of the solvated electron. In this review article, we present a comprehensive overview of the development and application of state-of-the-art first-principles molecular dynamics simulation approaches to understand and interpret the results of femtosecond photoelectron spectroscopy experiments on [I^? (Solv)_n]^* relaxation, which point to a high degree of solvent specificity in the electron solvation dynamics. The intricate molecular details of the [I^? (Solv)_n]^* relaxation process are presented, and by contrasting the relaxation mechanisms of clusters with several different solvents (water, methanol and acetonitrile), the molecular basis of the solvent specificity of electron solvation in [I^? (Solv)_n]^* is uncovered, leading to a more refined view of the manifestation of electron solvation in small gas-phase clusters.     

Crystal Structure of d(gcGXGAgc) with X = G: a Mutation at X is Possible to Occur in a Base-Intercalated Duplex for Multiplex Formation

DNA fragments with the sequences d(gcGX[Y]_n Agc) (n = 1, X = A, and Y = A, T, or G) form base-intercalated duplexes, which is a basic unit for formation of multiplexes such as octaplex and hexaplex. To examine the stability of multiplexes, a DNA with X = Y = G and n = 1 was crystallized under conditions different from those of the previously determined sequences, and its crystal structure has been determined. The two strands are coupled in an anti-parallel fashion to form a base-intercalated duplex, in which the first and second residues form Watson-Crick type G:C pairs and the third and sixth residues form a sheared G:A pairs at both ends of the duplex. The G₄ and G₅ bases are stacked alternatively on those of the counter strand to form a long G column of G₃-G₄-G₅*-G₅-G₄*-G₃*, the central four Gs being protruded. In addition, the three duplexes are associated to form a hexaplex around a mixture of calcium and sodium cations on the crystallographic threefold axis. These structural features are similar to those of the previous crystals, though slightly different in detail. The present study indicates that mutation at the 4th position is possible to occur in a base-intercalated duplex for multiplex formations, suggesting that DNA fragments with any sequence sandwiched between the two triplets gcG and Agc can form a multiplex.     

Genetic variability in the European minnow,Phoxinus phoxinus (L.)

An electrophoretic study of genetic variation at 11 loci was performedfor a population of European minnows, Phoxinus phoxinus (L.). Ten loci, EST-1 ^*, EST-2 ^* EST-3 ^*,GPD-1 ^*,GPD-2 ^*,GPI-1 ^*,GPI-2 ^*,MPI ^*,6PGD ^* and PGM ^* were polymorphic. IDH ^*wasmonomorphic. The mean number of heterozygotic loci over all 176 fish was 3.05 ± 0.104(SE). Observed mean heterozygosity was 0.28±0.058(SE) and expected mean heterozygosity was 0.27±0.054(SE). EST-2 ^*, EST-3 ^* andPGM ^* were not in Hardy-Weinberg equilibrium. Length,condition, parasite numbers or male breeding characters, i.e. red colorationand tubercles, were not influenced by single enzyme loci.     

The mechanism of nitrate transport across the tonoplast of barley root cells

Nitrate-selective microelectrodes were used to measure not only nitrate activity in the cytoplasm and vacuole of barley (Hordeum vulgare L.) root cells, but also the tonoplast electrical membrane potential. For epidermal cells, the mean cytoplasmic and vacuolar pNO₃ (-log₁₀ [NO₃]) values were 2.3±0.04 (n=19) and 1.41±0.03 (n=35), respectively, while for cortical cells, the mean cytoplasmic and vacuolar nitrate values were 2.58±0.18 (n=4) and 1.17±0.06 (n=13), respectively. These results indicate that the accumulation of nitrate in the vacuole must be an active process. Proton-selective microelectrodes were used to measure the proton gradient across the tonoplast to assess the possibility that nitrate transport into the vacuole is mediated by an H⁺/NO ₃ ^– antiport mechanism. For epidermal cells, the mean cytoplasmic and vacuolar pH values were 7.12±0.06 (n=10) and 4.93±0.11 (n=22), respectively, while for cortical cells, the mean cytoplasmic and vacuolar pH values were 7.24±0.07 (n=3) and 5.09±0.17 (n=7), respectively. Calculations of the energetics for this mechanism indicate that the observed gradient of nitrate across the tonoplast of both epidermal and cortical cells could be achieved by an H⁺/NO ₃ ^– antiport with a 11 stoichiometry.Abbreviations and Symbols G/F free-energy change for H⁺/NO ₃ ^– antiport - F Faraday constant - pH_c cytoplasmic pH - pH_v vacuolar pH - p[NO₃]_c log₁₀ (cytoplasmic [NO ₃ ^– ]) - P[NO₃]_v -log₁₀ (vacuolar [NO₃]) We wish to thank Dr. K. Moore for assistance with statistical analysis.     

Synthesis of Several Fructo-oligosaccharides by Asparagus Fructosyltransferases

Nine fructo-oligosaccharides, synthesized in vitro from sucrose by an enzyme preparation from asparagus roots, were isolated and their structures were elucidated to be 1^F (1-β-fructofuranosyl)_n sucrose [n = 1 (1-kestose), 2 (nystose) and 3], 6^G (1-β-fructofuranosyl)_n sucrose [n=1 (neokestose), 2 and 3] and 1^F (1-β-fructofuranosyl)_m-6^G (1-β-fructofuranosyl)_n sucrose [m=1, n=1; m=2, n =1; and m =1, n=2]. These saccharides are all known to occur naturally in asparagus roots, but 6^G (1-β-fructofuranosyl)₃ sucrose and 1^F (1-β-fructofuranosyl)_m-6^G-(1-β-fructofuranosyl)_n sucrose (m=1, n =1; and m=1, n=2) were the first saccharides enzymatically synthesized in vitro. Also three types of fructosyltransferases were presumed to be involved in the biosynthesis of these oligosaccharides in asparagus roots.     

Optical Rotatory Dispersion and Circular Dichroism of Amino Acid Hydantoins

Optical rotatory dispersion (ORD) and circular dichroism (CD) of 17 amino acid hydantoins were measured between 190 and 600 nm. Most of hydantoins exhibited the negative Cotton effect which showed the trough between 238 and 245 nm. The negative trough of CD was also observed between 212 and 236 nm. The Cotton effect of hydantoins was attributable to n→π^* transition of carbonyl group at C-4 of hydantoin ring.     

Compartmental nitrate concentrations in barley root cells measured with nitrate-selective microelectrodes and by single-cell sap sampling

Nitrate-selective microelectrodes were used to measure intracellular nitrate concentrations (as activities) in epidermal and cortical cells of roots of 5-d-old barley (Hordeum vulgare L.) seedlings grown in nutrient solution containing 10 mol · m^–3 nitrate. Measurements in each cell type grouped into two populations with mean (±SE) values of 5.4 ± 0.5 mol · m^–3 (n=19) and 41.8 ± 2.6 mol · m^–3 (n = 35) in epidermal cells, and 3.2 ± 1.2 mol · m^–3 (n = 4) and 72.8 ± 8.4 mol · m^–3 (n = 13) in cortical cells. These could represent the cytoplasmic and vacuolar nitrate concentrations, respectively, in each cell type. To test this hypothesis, a single-cell sampling procedure was used to withdraw a vacuolar sap sample from individual epidermal and cortical cells. Measurement of the nitrate concentration in these samples by a fluorometric nitrate-reductase assay confirmed a mean vacuolar nitrate concentration of 52.6 ± 5.3 mol · m^–3 (n = 10) in epidermal cells and 101.2 ± 4.8 mol · m^–3 (n = 44) in cortical cells. The nitrate-reductase assay gave only a single population of measurements in each cell type, supporting the hypothesis that the higher of the two populations of electrode measurements in each cell type are vacuolar in origin. Differences in the absolute values obtained by these methods are probably related to the fact that the nitrate electrodes were calibrated against nitrate activity but the enzymic assay against concentration. Furthermore, a 28-h time course for the accumulation of nitrate measured with electrodes in epidermal cells showed the apparent cytoplasmic measurements remained constant at 5.0 ± 0.7 mol · m^–3, while the vacuole accumulated nitrate to 30–50 mol · m^–3. The implications of the data for mechanisms of nitrate transport at the plasma membrane and tonoplast are discussed.Symbol _n ² Chi-squared with n degrees of freedom R.-G.Z. was awarded a Sino-British Friendship Scholarship sponsored by the British Council and H.-W.K. was supported by an AFRC Linked Research Grant to A.D.T for collaboration with R.A.L. We wish to thank Dr. K. Goulding for advice on ion chromatography, Dr. K. Moore for assistance with statistical analysis and Dr. J.H. Williams for advice on the microsample analysis.     

Measurement of Cerebral Glucose Utilization Using Washout After Carotid Injection in the Rat

Abstract: The carotid injection technique, used previously to quantitate the kinetics of blood-brain barrier transport of metabolic substrates, may be modified to analyze the rate of cerebral glucose utilization. A 0.2-ml solution of [¹⁴C]glucose (G_F) and [³H]methylglucose (M), an internal reference, is rapidly injected into the carotid artery, followed by microwave fixation of brain at various times up to 4 min after injection. The brain radioactivity is separated into a fraction containing neutral hexoses (G_F and M) and a fraction containing metabolites of glucose. The G_F/M ratio is related to the rate constant (k₃) of brain glucose utilization by the simple, linear equation: In(G_F/M) = In(G_F°/M°) –k₃t, where G_F°/M°= the brain uptake index of glucose, relative to methylglucose, at 5-15 s after injection, and t= the time after carotid injection, e.g., 1–4 min. It is assumed that (a) the rate of influx due to recirculation of label is minimal during the 4-min circulation period; and (b) the rate constants of glucose efflux (k₂) and methylglucose efflux (k₂*) are identical. Independent estimates of k₂ and k₂* showed these parameters to be identical: k₂= 0.14 + 0.08 min-I; k₂*= 0.14 ± 0.02 min-I. A logarithmic plot of G_F/M ratios versus time was linear (r = 0.99), and was described by the slope k₂= 0.21 ± 0.02 min^?1. Assuming glucose is uniformly distributed in brain, then the glycolytic rate = k₃× brain glucose = (0.21 min^?1) (2.6 μmol g^?1) = 0.55 μmol min^?1 g^?1 for the cortex of the barbiturate-anesthetized rat. These studies provide the basis for a simple method of measurement of regional brain glycolysis that does not require either the use of correction factors, e.g., the lumped constant, or the use of differentially labeled glucose.