Natural hybridization of Yezo and Sakhalin spruce in central Hokkaido,revealed by DNA markers with contrasting modes of inheritance

Yezo spruce (Picea jezoensis var. jezoensis) and Sakhalin spruce (Picea glehnii) occur across Hokkaido and co‐occur in some forest habitats. This leads to the potential for natural hybridization between these two species, which has been shown to occur at low frequencies. The purpose of this study was to identify these hybrids and their possible mating patterns, using various Pinaceae DNA markers with different modes of inheritance. The markers used were maternally inherited mitochondrial DNA (mtDNA), paternally inherited chloroplast DNA (cpDNA) and biparentally inherited nuclear microsatellites (nSSRs). Seven putative natural hybrids, four artificially‐crossed F₁ hybrids, four parent plants from each species, and two artificially‐backcrossed hybrids of putative natural hybrids and their parents were analyzed using the diagnostic DNA markers developed in this study. We found Yezo spruce and Sakhalin spruce to be distinct (J and G types, respectively), and the modes of inheritance held true for the two species, as was previously reported to be the case in Pinaceae. Four of the seven putative natural hybrids harbored J‐type cpDNA, G‐type mtDNA and J/G‐type nSSRs, indicating that natural F₁ hybrids are likely to arise from a G (female) × J (male) crossing. One natural hybrid harbored G‐type cpDNA, J‐type mtDNA and J/G‐type nSSRs, which implies that hybrids produced by J (female) × G (male) crossings occur at low frequencies. The two remaining hybrids harbored J‐type cpDNA and mtDNA with either J/G or J/J‐type nSSRs, suggesting that they may be F₂ hybrids resulting from backcrossing between an F₁ hybrid and a Yezo spruce.     

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)     

Estimating photosynthetic electron transport via chlorophyll fluorometry without Photosystem II light saturation

Estimates of thylakoid electron transport rates (J_e) from chlorophyll fluorometry are often used in combination with leaf gas exchange measurements to provide detailed information about photosynthetic activity of leaves in situ. Estimating J_e requires accurate determination of the quantum efficiency of Photosystem II (Φ_P), which in turn requires momentary light saturation of the Photosystem II light harvesting complex to induce the maximum fluorescence signal (F_M′). In practice, full saturation is often difficult to achieve, especially when incident photosynthetic photon flux density (Q) is high and energy is effectively dissipated by non-photochemical quenching. In the present work, a method for estimating the true F_M′ under high Q was developed, using multiple light pulses of varying intensity (Q′). The form of the expected relationship between the apparent F_M′ and Q′ was derived from theoretical considerations. This allowed the true F_M′ at infinite Q′ to be estimated from linear regression. Using a commercially available leaf gas exchange/ chlorophyll fluorescence measurement system, J_e was compared to gross photosynthetic CO₂ assimilation (A_G) under conditions where the relationship between J_e and A_G was expected to be linear. Both in C₄ leaves (Zea mays) in ambient air and also in C₃ leaves (Gossypium hirsutum) under non-photorespiratory conditions the apparent ratio between J_e and A_G declined at high Q when Φ_P was calculated from F_M′ measured simply using the highest available saturating pulse intensity. When F_M′ was determined using the multiple pulse / linear regression technique, the expected relationship between J_e and A_G at high Q was restored, indicating that the Φ_P estimate was improved. This method of determining F_M′ should prove useful for verifying when saturating pulse intensities are sufficient, and for accurately determining Φ_P when they are not. This revised version was published online in June 2006 with corrections to the Cover Date.     

Robust One-Way ANOVA under Possibly Non-Regular Conditions

Consider the one-way ANOVA problem of comparing the means m₁, m₂, …, m_c of c distributions F₁(x) = F(x — m₁), …, F_c(x) = F(x — m_c). Solutions are available based on (i) normal-theory procedures, (ii) linear rank statistics and (iii) M-estimators. The above model presupposes that F₁, F₂, …, F_c have equal variances (= homoscedasticity). However practising statisticans content that homoscedasticity is often violated in practice. Hence a more realistic problem to consider is F₁(x) = F((x — m₁)/σ₁), …, F_c(x) = F((x — m_c)/σ_c), where F is symmetric about the origin and σ₁, …, σ_c are unknown and possibly unequal (= heteroscedasticity). Now we have to compare m₁, m₂, …, m_c. At present, nonparametric tests of the equality of m₁, m₂, …, m_c are available. However, simultaneous tests for paired comparisons and contrasts and do not seem to be available. This paper begins by proposing a solution applicable to both the homoscedastic and the heteroscedastic situations, assuming F to be symmetric. Then the assumptions of symmetry and the identical shapes of F₁, …, F_c are progressively relaxed and solutions are proposed for these cases as well. The procedures are all based on either the 15% trimmed means or the sample medians, whose quantiles are estimated by means of the bootstrap. Monte Carlo studies show that these procedures tend to be superior to the Wilcoxon procedure and Dunnett's normal theory procedure. A rigorous justification of the bootstrap is also presented. The methodology is illustrated by a comparison of mean effects of cocaine administration in pregnant female Sprague-Dawley rats, where skewness and heteroscedascity are known to be present.     

Molecular-Dynamics Simulations for the Density Autocorrelation Function in a Supercooled Fluid Phase

Abstract

We have re-calculated the self part of the density autocorrelation function F_s(k, t) (incoherent scattering function) for the binary soft-sphere fluid with a much longer molecular-dynamics (MD) simulation than our previous MD calculations, and with a larger system size (N = 4000) to a longer time window as well as to study a system-size dependence, if it exists. The full density autocorrelation function F(k, t) was also computed. It is found that all F(k, t)'s that we have computed in this work can be fitted over a wide range of time steps (at least over three figures of the decay) by a Williams-Watts stretched exponential function F_s(k, t) = A exp [— (t/t ₀)^β], where A, β and t ₀ are adjustable parameters. Other significant dynamical behaviours were also presented in mean square displacements and non-Gaussian parameters for highly supercooled fluids with N = 4000. The present results are compatible to our previous computations with N = 500, but a significant size dependence is suggested.     

A model for the creep behaviour of tendon

A theoretical model is proposed to explain the viscoelastic behaviour of tendon. The model is based on the hypothesis that the mechanism of tendon deformation is one of shear of the mucopolysaccharide gel between the collagen ribbons in the ‘toe’ region¹ of the stress strain curve followed by fibrillar extension in the ‘linear’ region^2.3. Conventional linear viscoelastic parameters of the constituents of the tendon were used to describe the behaviour of the composite. Certain structural constants of the tendon and an appropriate form for the retardation spectrum of the composite also appear in the model. It was found that the following parameters play an important part in the viscoelastic deformation process; the mean value of the crimp angle of the strained fibres, 0_O; the broadness of the distribution of crimp angles $\text{α}$; the magnitude of the compliance difference for the gel, ΔJ_G and for the fibres, ΔD_F. Excellent agreement between experiment and theory has been observed for a variety of experimental circumstances. Values of 0_O, $\text{α}$ ΔJ_G and ΔD_F were determined for a number of specimens by fitting the model equations to the experimental data. The theory illustrates the expected influence on the viscoelastic properties of tendon which would result from changes in these parameters, which may arise from disease or ageing, for instance. The model also provides a challenge for future experimental work in that an independent determination of the parameters, 0_O, $\text{α}$ ΔJ_G and ΔD_F would confirm or refute the quantitative predictions of the theory presented here.     

The Matched Pairs Problem with Exponential Variates

Two classes of tests for the hypothesis of bivariate symmetry are studied. For paired exponential survival times (t_1j, t_2j), the classes of tests are those based on t_1j-t_2j and those based on log t_1j–log t_2j. For each class the sign, signed ranks, t and likelihood ratio tests are compared via Pitman's criterion of asymptotic relative efficiency (ARE). For tests based on t_1j — t_2j, it is found that: (1) the efficacy of the paired t depends on the coefficient of variation (CV) of the pair means, (2) the signed rank test has the same ARE to the sign test as for the usual location problem. For tests based on log t_1j — log t_2j, the ARE comparisons reduce to the well-known results for the one-sample location problem for samples from a logistic density. Hence, the signed rank test is asymptotically efficient. Furthermore, analyses based on log t_1j — log t_2j are not complicated by the underlying pairing mechanism.     

A genetic model and molecular markers for wild oat (Avena fatua L.) seed dormancy

Seed dormancy allows weed seeds to persist in agricultural soils. Wild oat (Avena fatua L.) is a major weed of cereal grains and expresses a range of seed dormancy phenotypes. Genetic analysis of wild oat dormancy has been complicated by the difficulty of phenotypic classification in segregating populations. Therefore, little is known about the nature of the genes that regulate dormancy in wild oat. The objectives of our studies were to develop methods to classify the germination responses of segregating wild oat populations and to find molecular markers linked to quantitative trait loci (QTL) that regulate seed dormancy in wild oat. RAPD markers OPX-06 and OPT-04 explained 12.6% and 6.8% respectively, of the F₂ phenotypic variance. OPF-17 was not significant in a simple regression model, but it was linked in repulsion to OPT-04. A three-locus model of seed dormancy in wild oat is presented based on the 41-day germination profiles of F₁, F₂, F₃, BC₁P₁F₁, BC₁P₁F₂, and BC₁P₂F₁ generations, and the 113 day germination profile of 126 F₇ recombinant inbred lines. Loci G ₁ and G ₂ promote early germination, and the D locus promotes late germination. If at least one copy of the dominant G ₁ or G ₂ alleles are present regardless of the genotype at D locus, then the individual will be nondormant. If the genotype is g ₁ g ₁ g ₂ g ₂ D_, then the phenotype will be dormant. Received: 1 December 1998 / Accepted: 1 February 1999     

A clever solution to a vexing problem

F_ST (as well as related measures such as G_ST) has long been used both as a measure of the relative amount of genetic variation between populations and as an indicator of the amount of gene flow among populations. Unfortunately, F_ST and its clones are also sensitive to mutation, particularly when the mutation rate per locus is greater than the migration rate among populations. Relatively high mutation rates cause estimates of F_ST and G_ST to be much lower than researchers sometimes expect, when migration rates are low in the studied species. Several recent suggestions for dealing with this problem have been unsatisfactory for one reason or another, and no general solution exists (if we are not to abandon these otherwise useful measures of differentiation). In an important article in this issue, Jinliang Wang (2015) shows that it is possible to identify whether the genetic markers in a given study are likely to give estimates of F_ST that are strongly affected by mutation. The proposed test is simple and elegant, and with it, molecular ecologists can determine whether the F_ST from their makers can be depended on for further inference about their species’ genome and the demographic forces which shaped its patterns.     

Robustness of statistical tests for multiplicative terms in the additive main effects and multiplicative interaction model for cultivar trials

The additive main effects multiplicative interaction model is frequently used in the analysis of multilocation trials. In the analysis of such data it is of interest to decide how many of the multiplicative interaction terms are significant. Several tests for this task are available, all of which assume that errors are normally distributed with a common variance. This paper investigates the robustness of several tests (Gollob, F _GH1, F_GH2, F_R)to departures from these assumptions. It is concluded that, because of its better robustness, the F _Rtest is preferable. If the other tests are to be used, preliminary tests for the validity of assumptions should be performed.     

Pairwise Comparisons Using Trimmed Means or M-Estimators when Working with Dependent Groups

For J dependent groups, let θ_j, j = 1, …, J, be some measure of location associated with the jth group. A common goal is computing confidence intervals for the pairwise differences, θ_j — θ_k, j < k, such that the simultaneous probability coverage is 1 — α. If means are used, it is well known that slight departures from normality (as measured by the Kolmogorov distance) toward a heavy-tailed distribution can substantially inflate the standard error of the sample mean, which in turn can result in relatively low power. Also, when distributions differ in shape, or when sampling from skewed distributions with relatively light tails, practical problems arise when the goal is to obtain confidence intervals with simultaneous probability coverage reasonably close to the nominal level. Extant theoretical and simulation results suggest replacing means with trimmed means. The Tukey-McLaughlin method is easily adapted to the problem at hand via the Bonferroni inequality, but this paper illustrates that practical concerns remain. Here, the main result is that the percentile t bootstrap method, used in conjunction with trimmed means, gives improved probability coverage and substantially better power. A method based on a one-step M-estimator is also considered but found to be less satisfactory.     

Regulation of energy flow and control of the cell cycle inSaccharomyces cerevisiae

Summary Measurements of glucose utilization and ethanol production by a respiratory-deficient mutant ofS. cerevisiae in a batch culture show that during the phase of acceleration, the glucose utilization per newly formed cell,k, is higher than the average value and the fermentationF < 1. In the phase of retardation, on the other hand,k is lower andF > 1. Correlating with the changes in the physiological state of the cell population, these results indicate that a considerable fraction of the total glucose consumed is utilized for the synthesis of polysaccharides in the G₁-phase, whereas reserve carbohydrates are catabolised during (S + G₂ + M)-phases of the cell cycle.A cybernetic model for the regulation of the energy (ATP) flow during the cell cycle is presented. It is postulated that the coupling between the energy-yielding and energy-consuming processes is provided by (i) a feedback regulation of the rate of energy production by the energy level and (ii) formation and breakdown of an intracellular energy storage system with a control function in the G₁S transition during the cell cycle.     

Optimal control of batch processes involving simultaneous enzymatic and microbial reactions

Optimal enzyme feed rate profiles have been calculated, based on a model for a fed-batch simultaneous enzymatic and microbial reaction (SEMR) process. The model parameters corresponded to a relatively slow citric acid fermentation. The profiles were calculated using an iterative algorithm based on the minimum principle. Penalty functions were used to enforce inequality constraints on the enzyme feed rate. Significant improvements in the objective function relative to that for the best constant enzyme feed rate were found. The effect on the optimal profiles of changes in the parameters of the model and the objective function were investigated, as was the effect of introducing the stationary state assumption to eliminate glucose concentration as a state variable. Major differences between bang-bang control variable profiles and singular arcs were found, with the singular arc solution slightly better than the optimal bang-bang control.List of Symbols a N-vector of initial conditions - b ₁–b₁₀ parameters defined in Table 2 - c vector of cost parameters - c ₁–c₆ penalty function parameters - E enzyme concentration (U/l) - f N-vector of functions - F enzyme feed rate (U/l-h) - g N-vector of functions - G glucose concentration (g/l) - H Hamiltonian - J objective function - J ^* modified objective function - L number of integration steps per time interval - L number of control variables - M number of time intervals - n iteration index - N number of state variables - P product concentration (g/l) - r ₁ glucose formation rate (g/l-h) - r ₂ product formation rate (g/l-h) - t time (h) - T final time (h) - u L-vector of control variables - x N-vector of state variables - z N-vector of adjoint variables - Z total enzyme fed (U/l) Greek convergence parameter The support of one of the authors by the National Science Foundation (Grant CBT-84-20552) is gratefully acknowledged.     

A Distribution-Free Two-Sample Equivalence Test Allowing for Tied Observations

A new testing procedure is derived which enables to assess the equivalence of two arbitrary noncontinuous distribution functions from which unrelated samples are taken as the data to be analyzed. The equivalence region is defined to consist of all pairs (F,G) of distribution functions such that for independent X ∼ F, Y ∼ G the conditional probability of {X > Y} given {X ≠ Y} lies in some short interval around 1/2. The test rejects the null hypothesis of nonequivalence if and only if the standardized distance between the U-statistics estimator of P[X > Y ∣ X ≠ Y] and the center of the equivalence interval (1/2 — ε₁, 1/2 + ε₂) does not exceed a critical upper bound which has to be computed as the α-quantile of a χ²-distribution with one degree of freedom and a random noncentrality parameter proportional to the squared length of that interval. The test is shown to maintain the asymptotic significance level under very weak regularity conditions. Results of an extensive simulation study suggest that its level properties are very satisfactory in small samples as well. The power turns out to be inversely related to the rate P[X = Y] of ties between observations from different samples.     

A simple chlorophyll fluorescence parameter that correlates with the rate coefficient of photoinactivation of Photosystem II

A method of partitioning the energy in a mixed population of active and photoinactivated Photosystem II (PS II) complexes based on chlorophyll fluorescence measurements is presented. There are four energy fluxes, each with its quantum efficiency: a flux associated with photochemical electron flow in active PS II reaction centres (J_{PS II}), thermal dissipation in photoinactivated, non-functional PS IIs (J_NF), light-regulated thermal dissipation in active PS IIs (J_NPQ) and a combined flux of fluorescence and constitutive, light-independent thermal dissipation (J_f,D). The four quantum efficiencies add up to 1.0, without the need to introduce an ‘excess’ term E, which in other studies has been claimed to be linearly correlated with the rate coefficient of photoinactivation of PS II (k_pi). We examined the correlation of k_pi with various fluxes, and found that the combined flux (J_NPQ + J_f,D= J_pi) is as well correlated with k_pi as is E. This combined flux arises from F_s/F_m^′, the ratio of steady-state to maximum fluorescence during illumination, which represents the quantum efficiency of combined non-photochemical dissipation pathways in active PS IIs. Since F_s/F_m^′ or its equivalent, J_pi, is a likely source of events leading to photoinactivation of PS II, we conclude that F_s/F_m^′ is a simple predictor of k_pi.     

Photoprotective Function of Photorespiration in Several Grapevine Cultivars Under Drought Stress

Four grapevine cultivars, i.e. Cabernet Sauvignon (a member of the Western Europe cultivar group), Rizamat (a member of the East cultivar group), Red Double Taste (a hybridized cultivar from Vitis vinifera L. and V. labrusca L.), and 1103Paulsen (a hybridized rootstock), were treated by three severity orders of drought stress for 25 d. Then net photosynthetic rate (P _N), maximal photochemical efficiency (F_v/F_m), actual photochemical efficiency (_PS2) of photosystem 2, total electron transport rate (J_T), and electron transport flows used in carboxylation (J_C) and in oxygenation (J_O) reactions catalysed by ribulose-1,5-bisphosphate carboxylase/oxygenase were determined. P _N was determined again after re-watering for 2 d by gas exchange measurement. Along with the increase in severity of drought stress, P _N, F_v/F_m, _PS2, J_T, and J_C in all four cultivars decreased. The range of decrease differed among cultivars. J_O expressed various trends from cultivar to cultivar. In Rizamat that received slight and moderate drought stress, P _N evidently decreased, but J_O markedly increased, thus maintaining high values of J_T and _PS2. Prior to the moderate drought stress, the F_v/F_m was high in Rizamat, indicating that the photodamage had not happened ahead of the moderate drought stress given. Under the severe drought stress, the photorespiration rate in Rizamat decreased by 70 %, and J_T, _PS2, and F_v/F_m also dropped to very low values, i.e. the photodamage of photosynthetic apparatus has taken place. This suggested that the photorespiration has consumed the excessive assimilatory power and the photo-protective function of photorespiration is very important for Rizamat. When Cabernet Sauvignon grew under drought stress, its J_O decreased in a small range, thus maintaining higher values of J_C, J_T, _PS2, and F_v/F_m; hence no serious photodamage occurred. Despite of the fact that P _N of cv. Red Double Taste decreased markedly under the slight drought stress, J_O still increased under the severe drought stress. This suggests that photorespiration is important in photoprotection under drought stress. J_O in cv. 1103Paulsen markedly decreased under slight stress. Accordingly, P _N, F_v/F_m, _PS2, J_T, and J_C decreased to extremely low values. Thus photorespiration effectively protects the photosynthetic apparatus from photo-damage under drought, assists in maintaining a relatively high _PS2, and helps P _N to be rapidly recovered after re-watering.     

A non-invasive assay of the plastoquinone pool redox state based on the OJIP-transient

The plastoquinone (PQ) pool of the photosynthetic electron transport chain becomes reduced under anaerobic conditions. Here, anaerobiosis was used as a tool to manipulate the PQ-pool redox state in darkness and to study the effects of the PQ-redox state on the Chl-a fluorescence (OJIP) kinetics in pea leaves (Pisum sativum L.). It is shown that the F_J (fluorescence intensity at 3 ms) is linearly related to the area above the OJ-phase (first 3 ms) representing the reduction of the acceptor side of photosystem II (PSII) and F_J is also linearly related to the area above the JI-phase (3–30 ms) that parallels the reduction of the PQ-pool. This means that F_J depends on the availability of oxidized PQ-molecules bound to the Q_B-site. The linear relationships between F_J and the two areas indicate that F_J is not sensitive to energy transfer between PSII-antennae (connectivity). It is further shown that a ∼94% reduced PQ-pool is in equilibrium with a ∼19% reduction of Q_A (primary quinone acceptor of PSII). The non-linear relationship between the initial fluorescence value (F_{20 μs}) and the area above the OJ-phase supports the idea that F_{20 μs} is sensitive to connectivity. This is reinforced by the observation that this non-linearity can be overcome by transforming the F_{20 μs}-values into [Q_A ⁻]-values. Based on the F_J-value of the OJIP-transient, a simple method for the quantification of the redox state of the PQ-pool is proposed. Szilvia Z. Tóth and Gert Schansker contributed equally to this study.     

Comprehensive analysis of two Shank3 and the Cacna1c mouse models of autism spectrum disorder

To expand, analyze and extend published behavioral phenotypes relevant to autism spectrum disorder (ASD), we present a study of three ASD genetic mouse models: Feng's Shank3^tm2Gfng model, hereafter Shank3/F, Jiang's Shank3^tm1Yhj model, hereafter Shank3/J and the Cacna1c deletion model. The Shank3 models mimick gene mutations associated with Phelan–McDermid Syndrome and the Cacna1c model recapitulates the deletion underlying Timothy syndrome. This study utilizes both standard and novel behavioral tests with the same methodology used in our previously published companion report on the Cntnap2 null and 16p11.2 deletion models. We found that some but not all behaviors replicated published findings and those that did replicate, such as social behavior and overgrooming in Shank3 models, tended to be milder than reported elsewhere. The Shank3/F model, and to a much lesser extent, the Shank3/J and Cacna1c models, showed hypoactivity and a general anxiety‐like behavior triggered by external stimuli which pervaded social interactions. We did not detect deficits in a cognitive procedural learning test nor did we observe perseverative behavior in these models. We did, however, find differences in exploratory patterns of Cacna1c mutant mice suggestive of a behavioral effect in a social setting. In addition, only Shank3/F showed differences in sensory‐gating. Both positive and negative results from this study will be useful in identifying the most robust and replicable behavioral signatures within and across mouse models of autism. Understanding these phenotypes may shed light of which features to study when screening compounds for potential therapeutic interventions.     

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.