Transit time dispersion in the pulmonary arterial tree

Knowledge of the contributions of arterialand venous transit time dispersion to the pulmonary vascular transittime distribution is important for understanding lung function and forinterpreting various kinds of data containing information aboutpulmonary function. Thus, to determine the dispersion of blood transittimes occurring within the pulmonary arterial and venous trees, imagesof a bolus of contrast medium passing through the vasculature ofpump-perfused dog lung lobes were acquired by using an X-ray microfocalangiography system. Time-absorbance curves from the lobar artery andvein and from selected locations within the intrapulmonary arterial tree were measured from the images. Overall dispersion within the lunglobe was determined from the difference in the first and second moments(mean transit time and variance, respectively) of the inlet arterialand outlet venous time-absorbance curves. Moments at selected locationswithin the arterial tree were also calculated and compared with thoseof the lobar artery curve. Transit times for the arterial pathwaysupstream from the smallest measured arteries (200-µm diameter) wereless than ~20% of the total lung lobe mean transit time. Transittime variance among these arterial pathways (interpathway dispersion)was less than ~5% of the total variance imparted on the bolus as itpassed through the lung lobe. On average, the dispersion that occurredalong a given pathway (intrapathway dispersion) was negligible. Similar results were obtained for the venous tree. Taken together, the resultssuggest that most of the variation in transit time in theintrapulmonary vasculature occurs within the pulmonary capillary bedrather than in conducting arteries or veins.

     

A compartmental capillary, convolution integration model to investigate nutrient transport and metabolism in vivo from paired indicator/nutrient dilution curves.

Thirty-three paired indicator/nutrient dilution curves across the mammary glands of four cows were obtained after rapid injection of para-aminohippuric acid (PAH) plus glucose into the external iliac artery. For the measurement of extracellular volume and kinetics of nutrient uptake from indicator dilution curves, several models of solute dispersion and disappearance have been proposed. The Crone-Renkin models of exchange in a single capillary assume negligible washout of solutes from the extracellular space and do not describe entire dilution curves. The Goresky models include a distribution of capillary transit times to generate whole system outflow profiles but require two indicators to parametize extracellular behavior. A compartmental capillary, convolution integration model is proposed that uses one indicator to account for the extracellular behavior of the nutrient after a paired indicator/nutrient injection. With the use of an iterative approach to least squares, unique solutions for nonexchanging vessel transit time t(mu) and its variance sigma were obtained from all 33 PAH curves. The average of heterogeneous vascular transit times was approximated as 2sigma = 8.5 s. The remainder of indicator dispersion was considered to be due to washout from a well-mixed compartment representing extracellular space that had an estimated volume of 5.5 liters or 24% of mammary gland weight. More than 99% of the variation in the time course of venous PAH concentration after rapid injection into the arterial supply of the mammary glands was explained in an unbiased manner by partitioning the organ into a heterogeneous nonexchanging vessel subsystem and a well-mixed compartmental capillary subsystem.     

Lung serotonin uptake kinetics from indicator-dilution and constant-infusion methods

The kinetics of the pulmonary endothelial uptake of serotonin (5-HT) were evaluated in isolated dog lung lobes using three methods. In method A serotonin was infused at various constant rates to provide a range of capillary concentrations that included Km. The arterial and venous concentrations measured by high-performance liquid chromatography were then used to determine the effect of concentration on the rate of 5-HT uptake. In method B trace doses of 5-[3H]HT and a reference indicator (indocyanine green dye) were injected during each constant infusion of unlabeled 5-HT to provide a measure of unidirectional 5-HT uptake at each background concentration. In method C boluses containing different amounts of unlabeled 5-HT, along with the 5-[3H]HT and the dye, were injected such that each bolus resulted in a range of concentrations and provided a measure of the unidirectional uptake at each concentration. Each method provided the data needed to calculate the maximum uptake rate (Vmax) and the concentration at Vmax/2 (Km), assuming that the uptake kinetics can be represented by the Michaelis-Menten equation. However, the mathematical model underlying each method involved different assumptions about the returning flux of the 5-HT which entered the endothelial cell and the heterogeneity of vascular transit times. The results obtained, considered in light of the different assumptions involved, indicate that all three methods can provide reasonable estimates of the mass transfer kinetic constants if the constant infusions of 5-HT are of short duration and/or the boluses are adequately dispersed prior to reaching the capillary bed.     

On indicator dilution and perfusion heterogeneity: A stochastic model

Unidirectional extraction of a substrate S in the capillaries following the arterial injection of a bolus containing S and a reference tracer R is assumed to follow first-order kinetics. If C_R and C_S denote normalized venous effluent concentrations of R and S, respectively, let L(t)=ln[C_R(t)⧸C_S(t)]. We derive a formula which expresses the experimental L(t) data in terms of the mean μ(t) and variance of the transit times of those capillaries which are contributing indicators at each sample time t. We examine the information thus contained in the L data about capillary and noncapillary transit times under several kinematic assumptions. We show that if the capillary and noncapillary transit times are stochastically independent with frequency functions h_c(t) and h_av(t), respectively, then the shapes of the graphs of L(t) and μ(t) depend on the variances and skewnesses of h_c(t) and h_av(t). Specifically, let r₂ be the ratio of the variance of h_c(t) to the variance of h_av(t), and let r₃ be the ratio of skewnesses in the same order. Then the graph of μ(t) is concave downward if r₂⧸r₃ > 1, concave upward if r₂⧸r₃< 1, and linear if r₂⧸r₃ = 1. If the fraction of S extracted is not too large, L(t) has nearly the same shape as μ(t), and therefore, L(t) contains information about h_c(t) and h_av(t).     

Kinetic measurements of gas exchange in the intact pulmonary microcirculation.

The kinetics of gas exchange are monitored in an isolated perfused lung preparation contained within a plethysmograph. The lungs are perfused with buffer, and there is no gas exchange until a 2.0-ml bolus of reactant is injected into the perfusion system. Subsequent gas exchange produces a pressure transient that is related to the corresponding volume of exchanged gas. The observed rate of volume change is the result of two separate processes: 1) the rate of gas exchange during transit through the capillary bed and 2) the distribution of vascular transit times between the point of injection and the capillary bed. The latter is assessed by a control injection containing a dissolved inert gas that is liberated in the alveoli as the bolus enters the capillary bed. Analysis of the experimental curves permits the separation of these two processes. A model of exchange kinetics indicates that this method has the capability of measuring kinetic events occurring during gas exchange in the microcirculation under physiological conditions.     

Transport Interactions between Paraquat and Polyamines in Roots of Intact Maize Seedlings

Interactions between absorption of paraquat and the polyamines putrescine, cadaverine, and spermine in roots of intact maize (Zea mays L. cv 3377 Pioneer) seedlings were examined. Concentration-dependent kinetics for paraquat and putrescine influx were similar and both kinetic curves could be resolved into a linear and a saturable component. The linear component was previously shown to represent cell wall/membrane binding. The saturable components for paraquat and putrescine uptake, which represent influx across the plasmalemma, had K_m values of 98 and 120 micromolar, respectively, and V_max values of 445 and 456 nanomoles per gram fresh weight per hour, respectively. Lineweaver-Burk transformation of the saturable component of paraquat influx in the presence of varying concentrations of putrescine indicated that the diamine competitively inhibited the saturable component of paraquat uptake. Reciprocal experiments similarly demonstrated that paraquat competitively inhibited the saturable component of putrescine uptake. Competitive inhibition of both paraquat and putrescine influx could also be demonstrated with the diamine cadaverine, which has a charge distribution similar to that of paraquat and putrescine. In contrast, the larger, tetravalent polyamine spermine appeared to noncompetitively inhibit the influx of paraquat and putrescine. These results strongly suggest that paraquat enters maize root cells via a carrier system that normally functions in the transport of diamines with a charge distribution similar to that of paraquat.     

Capillary operators

The goal of this work is an examination of capillary exchange models as mathematical operators. The concentration function relations for the Krogh cylinder of a single capillary, basic to many organ models, are studied via the theory of operators on the Lebesgue normed spacesL _p[0,∞], (1<-p<-∞). A discussion is included of theL _p -normsvis-à-vis the coefficient of variation currently used in finding capillary parameters and evaluating parameter searches. The capillary model determines two operators on the space of locally integrable functions: O _K (relating extravascular concentration to intravascular) and K _{a, k} (relating intravascular concentration to input), wherek is the ratio of permeabilitysurface area (PS) to extravascular volume, and α is the ratio of PS to flow. These operators are shown to induce contractive (‖O _K ‖ _p <-1, ‖K _{a, k} ‖ _p <-1), isotone, linear operators onL _p . The uniform convergence relation $$K_{a,k} = \mathop {\lim _{(p)} }\limits_{N \to \infty } \left( {\sum\limits_{n = 0}^N {P_n (a)O_k^n } } \right)$$ (as operators onL _p) is derived, whereP _n (a) is the Poisson probabilitye ^?a a ⁿ /n!. For the important special cases ofp=∞, 1, 2 the norms are found (‖O_k‖=‖K_a,k‖_p=1). Consideration is also given to the norms and operators when the functions involved are limited to a finite interval of time.     

Simultaneous Study of NH+ 4, Na+, Mg2+, Ca2+, NO2- 3, SO2- 4, (NO- 2), H{2in}PO- 4 and CI- Uptake by Intact Winter Wheat Seedlings in a Single Depletion ExperimentPO- 4 and CI- Uptake by Intact Winter Wheat Seedlings in a Single Depletion Experiment

Simultaneous uptake of NH⁺ ₄, Na⁺, Mg²⁺, Ca²⁺, NO^- ₃, SO^2- ₄, (NO^- ₂), H²PO^- ₄ and C1^- ions by N-limited winter wheat seedlings(Triticum aestivum L., cv. Regina) in a single depletion experiment was investigated. Individual ion species in uptake solution samples were determined using capillary isotachophoresis. The operating systems used are described in detail. Processing of obtained concentration data allow to construct time curves of individual ions concentration in uptake solution, time curves of accumulative uptake, and curves for uptake rate versus time and uptake rate versus external concentration. From these curves there is possible to reveal a more complex picture of behaviour of individual ions during uptake process as well as to assess interactions among them. Attention was paid to the points of intersection of time curves of NO^- ₃ and NH⁺ ₄ uptake rates. These points characterized by equal uptake rates may be considered as limits for preference of given ion species under given experimental conditions.     

Analogue tracers and lumped constant in capillary beds

The lumped constant is a proportionality factor for converting a tracer analogue's metabolic rate to that of its mother substance. In a uniform system, it is expressed as the ratio of the tracer analogue's extraction fraction (E^?) to the extraction fraction of its mother substance (E).Here we show that, in capillary beds perfused by unidirectional blood flow, unequal concentration gradients of the tracer analogue and of the mother substance influence extraction fractions both locally and across the organ and that the direct proportionality of E^? and E must be replaced by ln(1−E^?)/ln(1−E) to yield Λ, i.e. the lumped constant derived from first principles of bi-substrate enzyme and membrane kinetics. In other words, at a given capillary blood flow (F), the ratio of systemic clearances (FE^?/FE), often used in compartmental kinetic analysis, must be replaced by the ratio of the intrinsic clearances, [−F ln(1−E^?)]/[−F ln(1−E)].The conclusion is supported by 2-[¹⁸F]fluoro-2-deoxy-d-galactose removal kinetics in pig liver in vivo from previous publications by the dependence of E^?/E and the independence of Λ, on blood galactose concentration. Moreover, our corrections to the results of compartmental kinetics are quantified for comparing extraction fractions in different regions of interest (e.g. by positron emission tomography) and for calculating Λ using whole-organ E^? and E measured by arteriovenous concentration differences.     

A Two-Stage Model for In Vivo Assessment of Brain Tumor Perfusion and Abnormal Vascular Structure Using Arterial Spin Labeling

The ability to assess brain tumor perfusion and abnormalities in the vascular structure in vivo could provide significant benefits in terms of lesion diagnosis and assessment of treatment response. Arterial spin labeling (ASL) has emerged as an increasingly viable methodology for non-invasive assessment of perfusion. Although kinetic models have been developed to describe perfusion in healthy tissue, the dynamic behaviour of the ASL signal in the brain tumor environment has not been extensively studied. We show here that dynamic ASL data acquired in brain tumors displays an increased level of ‘biphasic’ behaviour, compared to that seen in healthy tissue. A new two-stage model is presented which more accurately describes this behaviour, and provides measurements of perfusion, pre-capillary blood volume fraction and transit time, and capillary bolus arrival time. These biomarkers offer a novel contrast in the tumor and surrounding tissue, and provide a means for measuring tumor perfusion and vascular structural abnormalities in a fully non-invasive manner.     

Derepression of amino Acid-h cotransport in developing soybean embryos

The uptake of the unnatural amino acid α-aminoisobutyric acid (AIB) and glutamine by developing soybean (Glycine max Merr. cv Chippewa 64) embryos was investigated. In freshly excised embryos, the accumulation ratio (cytoplasmic concentration/external concentration) of AIB did not exceed 1.0. After an 18-hour preincubation in nitrogen-free medium the accumulation ratio of AIB exceeded 4.5 at an external AIB concentration of 10 micromolar. This indicates the derepression of an active amino acid uptake mechanism operative at low external amino acid concentration. The presence of sucrose, NH₄NO₃, or glutamine during a 21-hour preincubation prior to measuring glutamine uptake inhibited the enhancement of uptake by 43%, 51%, and 96%, respectively. The time course of the decline in free amino acids and the time course of enhancement of amino acid uptake was not consistent with enhanced uptake resulting from relief of transinhibition, but suggested instead the derepression of synthesis of new carriers. The time course of enhancement of amino acid uptake was paralleled by an increase in glutamine-induced depolarization of the membrane potential. The kinetics of glutamine uptake indicated the presence of a saturable and a nonsaturable component of uptake. The saturable component of uptake is attributed to a mechanism of amino acid-H⁺ cotransport which is derepressed by nitrogen and/or carbon starvation. At physiological concentrations of amino acids, uptake through the saturable system in freshly excised embryos is negligible. Thus, uptake through the nonsaturable system is of primary importance in the nitrogen nutrition of developing soybean embryos.     

Comparison of Partial Volume Effects in Arterial and Venous Contrast Curves in CT Brain Perfusion Imaging

Purpose

In brain CT perfusion (CTP), the arterial contrast bolus is scaled to have the same area under the curve (AUC) as the venous outflow to correct for partial volume effects (PVE). This scaling is based on the assumption that large veins are unaffected by PVE. Measurement of the internal carotid artery (ICA), usually unaffected by PVE due to its large diameter, may avoid the need for partial volume correction. The aims of this work are to examine i) the assumptions behind PVE correction and ii) the potential of selecting the ICA obviating correction for PVE.

Methods

The AUC of the ICA and sagittal sinus were measured in CTP datasets from 52 patients. The AUCs were determined by i) using commercial CTP software based on a Gaussian curve-fitting to the time attenuation curve, and ii) by simple integration of the time attenuation curve over a time interval. In addition, frames acquired up to 3 minutes after first bolus passage were used to examine the ratio of arterial and venous enhancement. The impact of selecting the ICA without PVE correction was illustrated by reporting cerebral blood volume (CBV) measurements.

Results

In 49 of 52 patients, the AUC of the ICA was significantly larger than that of the sagittal sinus (p = 0.017). Measured after the first pass bolus, contrast enhancement remained 50% higher in the ICA just after the first pass bolus, and 30% higher 3 minutes later. CBV measurements were significantly lowered when the ICA was used without PVE correction.

Conclusions

Contradicting the assumptions underlying PVE correction, contrast in the ICA was significantly higher than in the sagittal sinus, even 3 minutes after the first pass of the contrast bolus. PVE correction might lead to overestimation of CBV if the CBV is calculated using the AUC of the time attenuation curves.     

Numerical Simulation of Passage of a Neutrophil through a Rectangular Channel with a Moderate Constriction

The authors have previously presented a mathematical model to predict transit time of a neutrophil through an alveolar capillary segment which was modeled as an axisymmetric arc-shaped constriction settled in a cylindrical straight pipe to investigate the influence of entrance curvature of a capillary on passage of the cell. The axially asymmetric cross section of a capillary also influences the transit time because it requires three-dimensional deformation of a cell when it passes through the capillary and could lead to plasma leakage between the cell surface and the capillary wall. In this study, a rectangular channel was introduced, the side walls of which were moderately constricted, as a representative of axially asymmetric capillaries. Dependence of transit time of a neutrophil passing through the constriction on the constriction geometry, i.e., channel height, throat width and curvature radius of the constriction, was numerically investigated, the transit time being compared with that through the axisymmetric model. It was found that the transit time is dominated by the throat hydraulic diameter and curvature radius of the constriction and that the throat aspect ratio little affects the transit time with a certain limitation, indicating that if an appropriate curvature radius is chosen, such a rectangular channel model can be substituted for an axisymmetric capillary model having the same throat hydraulic diameter in terms of the transit time by choosing an appropriate curvature radius. Thus, microchannels fabricated by the photolithography technique, whose cross section is generally rectangular, are expected to be applicable to in vitro model experiments of neutrophil retention and passage in the alveolar capillaries.     

A theoretical model of the pinocytotic vesicular transport process in endothelial cells

A new theoretical model for vesicular transport in single endothelial cells is described using a kinetic molecular approach in which the vesicle diffusion process is coupled with the vesicle attachment/detachment process occurring at the cell plasmalemmal boundaries. Rate constants k^d_i, k_i characterizing a two stage reaction sequence in the attachment/detachment region and the vesicle diffusion coefficient D are obtained by comparison of the theory with the results of tracer studies. For the condition of rapid vesicle loading/discharge of macromolecules it is found that the permeability of endothelial cells to macromolecules tends to be controlled by the vesicular attachment/detachment process rather than the vesicle diffusion process. The rate limiting step in the vesicle attachment/detachment process tends to be the reaction process involving the rate at which a vesicle and the plasmalemmal membrane are brought into/separated from intimate contact rather than that involving the rate of formation/dissolution of the membrane diaphragm of an attached vesicle. Estimated relaxation times for processes occurring in the attachment/detachment region and in the diffusion region, the vesicle transit time in the diffusion region, and the viscosity of the cytoplasm in the diffusion region are deduced. Fair agreement is obtained between the predicted and the observed temperature dependence of the permeability.     

Non-invasive Assessment of Microvascular and Endothelial Function

The authors have utilized capillaroscopy and forearm blood flow techniques to investigate the role of microvascular dysfunction in pathogenesis of cardiovascular disease. Capillaroscopy is a non-invasive, relatively inexpensive methodology for directly visualizing the microcirculation. Percent capillary recruitment is assessed by dividing the increase in capillary density induced by postocclusive reactive hyperemia (postocclusive reactive hyperemia capillary density minus baseline capillary density), by the maximal capillary density (observed during passive venous occlusion). Percent perfused capillaries represents the proportion of all capillaries present that are perfused (functionally active), and is calculated by dividing postocclusive reactive hyperemia capillary density by the maximal capillary density. Both percent capillary recruitment and percent perfused capillaries reflect the number of functional capillaries. The forearm blood flow (FBF) technique provides accepted non-invasive measures of endothelial function: The ratio FBF_max/FBF_base is computed as an estimate of vasodilation, by dividing the mean of the four FBF_max values by the mean of the four FBF_base values. Forearm vascular resistance at maximal vasodilation (FVR_max) is calculated as the mean arterial pressure (MAP) divided by FBF_max. Both the capillaroscopy and forearm techniques are readily acceptable to patients and can be learned quickly.The microvascular and endothelial function measures obtained using the methodologies described in this paper may have future utility in clinical patient cardiovascular risk-reduction strategies. As we have published reports demonstrating that microvascular and endothelial dysfunction are found in initial stages of hypertension including prehypertension, microvascular and endothelial function measures may eventually aid in early identification, risk-stratification and prevention of end-stage vascular pathology, with its potentially fatal consequences.     

Comparing DNA Extraction Methods for Analysis of Botanical Materials Found in Anti-Diabetic Supplements

A comparative performance evaluation of DNA extraction methods from anti-diabetic botanical supplements using various commercial kits was conducted, to determine which produces the best quality DNA suitable for PCR amplification, sequencing and species identification. All plant materials involved were of suboptimal quality showing various levels of degradation and therefore representing real conditions for testing herbal supplements. Eight different DNA extraction methods were used to isolate genomic DNA from 13 medicinal plant products. Two methods for evaluation, DNA concentration measurements that included absorbance ratios as well as PCR amplifiability, were used to determine quantity and quality of extracted DNA. We found that neither DNA concentrations nor commonly used UV absorbance ratio measurements at A ₂₆₀/A ₂₈₀ between 1.7 and 1.9 are suitable for globally predicting PCR success in these plant samples, and that PCR amplifiablity itself was the best indicator of extracted product quality. However, our results suggest that A ₂₆₀/A ₂₈₀ ratios below about 1.3 and above 2.3 indicated a DNA quality too poor to amplify. Therefore, A ₂₆₀/A ₂₈₀ measurements are not useful to identify samples that likely will amplify but can be used to exclude samples that likely will not amplify reducing the cost for unnecessarily subjecting samples to PCR. The two Nucleospin^® plant II kit extraction methods produced the most pure and amplifiable genomic DNA extracts. Our results suggest that there are clear, discernable differences between extraction methods for low quality plant samples in terms of producing contamination-free, high-quality genomic DNA to be used for further analysis.     

Extension of the theory of the multiple-indicator dilution technique to metabolic systems with an arbitrary number of rate constants

The multiple indicator dilution technique consists in the instantaneous injection of a mixture of tracers into the arterial perfusate flow of a catheterized or isolated perfused organ, followed by the analysis of the effluent perfusate. The theory of this technique, which has hitherto been developed for cases where metabolism of a tracer is confined to sequestration described by a single rate constant, is extended in this paper to include an arbitrary number of metabolic rate constants. Partial differential equations with constant coefficients describing the events in a single capillary are derived by applying conventional compartmental analysis to infinitesimally small sections of the capillary. Methods for solving such systems in the time as well as in the frequency domain are developed. From the solutions, the impulse response of the whole organ is evaluated assuming variable capillary and uniform large-vessel transit times. In addition, an efficient method using much less computer time was developed, based on the approximation of the distribution of the capillary transit times by a sum of exponentials. Evaluation of moments (recoveries and mean transit times) is also treated. The results are applied to an example from hepatic lactate metabolism.     

Improved Quantification of Cerebral Hemodynamics Using Individualized Time Thresholds for Assessment of Peak Enhancement Parameters Derived from Dynamic Susceptibility Contrast Enhanced Magnetic Resonance Imaging

Purpose

Assessment of cerebral ischemia often employs dynamic susceptibility contrast enhanced magnetic resonance imaging (DSC-MRI) with evaluation of various peak enhancement time parameters. All of these parameters use a single time threshold to judge the maximum tolerable peak enhancement delay that is supposed to reliably differentiate sufficient from critical perfusion. As the validity of this single threshold approach still remains unclear, in this study, (1) the definition of a threshold on an individual patient-basis, nevertheless (2) preserving the comparability of the data, was investigated.

Methods

The histogram of time-to-peak (TTP) values derived from DSC-MRI, the so-called TTP-distribution curve (TDC), was modeled using a double-Gaussian model in 61 patients without severe cerebrovascular disease. Particular model-based z_f-scores were used to describe the arterial, parenchymal and venous bolus-transit phase as time intervals I_a,_p,v. Their durations (delta I_a,p,v), were then considered as maximum TTP-delays of each phase.

Results

Mean-R² for the model-fit was 0.967. Based on the generic z_f-scores the proposed bolus transit phases could be differentiated. The I_p-interval reliably depicted the parenchymal bolus-transit phase with durations of 3.4 s–10.1 s (median = 4.3s), where an increase with age was noted (∼30 ms/year).

Conclusion

Individual threshold-adjustment seems rational since regular bolus-transit durations in brain parenchyma obtained from the TDC overlap considerably with recommended critical TTP-thresholds of 4 s–8 s. The parenchymal transit time derived from the proposed model may be utilized to individually correct TTP-thresholds, thereby potentially improving the detection of critical perfusion.     

Computer Simulation of Clostridium botulinum Strain 56A Behavior at Low Spore Concentrations

It is generally assumed that spore behavior is independent of spore concentration, but recently published mathematical models indicate that this is not the case. A Monte Carlo simulation was employed in this study to further examine the independence assumption by evaluating the inherent variance in spore germination data. All simulations were carried out with @Risk software. A total of 500 to 4,000 iterations were needed for each simulation to reach convergence. Lag time and doubling time from a higher inoculum concentration were used to simulate the time to detection (TTD) at a lower inoculum concentration under otherwise identical environmental conditions. The point summaries of the simulated and observed TTDs were recorded for the 26 simulations, with kinetic data at the target inoculum concentration. The ratios of the median (R_m = median_obs/median_sim) and 90% range (R_r = 90% range_obs/90% range_sim) were calculated. Most R_m and R_r values were greater than one, indicating that the simulated TTDs were smaller and more homogeneous than the observed ones. R_r values departed farther from one than R_m values. Ratios obtained when simulating 1 spore with 10,000 spores deviated the farthest from one. Neither ratio was significantly different from the other when simulating 1 spore with 100 spores or simulating 100 spores with 10,000 spores. When kinetic data were not available, the percent positive observed at the 95th percentile of the simulated TTDs was obtained. These simulation results confirmed that the assumption of independence between spores is not valid.     

Potassium transport in corn roots : I. Resolution of kinetics into a saturable and linear component

Influx isotherms were obtained for ⁸⁶Rb⁺ uptake into 2-cm corn (Zea mays [A632 × (C3640 × Oh43)] root segments for both low- (0.2 millimolar CaSO₄) and high-salt (0.2 millimolar CaSO₄ + 5 millimolar KCl) grown roots. Unlike the discontinuous curves usually presented for K⁺ influx, our isotherms were smooth, nonsaturating curves that approached linearity at K⁺ (Rb⁺) concentrations above 1 millimolar. The kinetics for K⁺ transport could be resolved into saturable and linear components. The saturable components yielded K_m values of 16 and 86 micromolar for low- and high-salt roots, respectively, while V_max values were 5.62 and 1.85 moles per gram fresh weight per hour. Results of experiments with the penetrating sulfhydryl reagent, N-ethyl maleimide (NEM), and the impermeant reagent, p-chloromercuribenzene sulfonic acid (PCMBS) indicated that the saturable and linear components were independent mechanisms of K⁺ transport.

Short-term NEM exposures (30 seconds to 5 minutes) selectively inhibited the saturable system, but had little effect on the linear component. Increasing NEM exposures resulted in further inhibition and subsequent abolition of the saturable component; the linear component exhibited limited NEM sensitivity. PCMBS elicited the same general inhibitory trends, although it was less effective as a saturable component inhibitor.

The effects of NEM and PCMBS on K⁺ efflux were also studied. Short NEM exposures had no effect on cytoplasmic efflux, while inhibiting vacuolar efflux significantly. From these data, it is unclear at which site(s) NEM is acting. A more complex response was obtained with PCMBS, where a monophasic efflux curve was observed. Analysis indicated that the vacuolar efflux was stimulated, while the cytoplasmic component was abolished.

The nature of the linear component is discussed, and it is proposed that the mechanism may be more complex than simple facilitated diffusion.