Estimation of the left ventricular relaxation time constant tau requires consideration of the pressure asymptote

The left ventricular isovolumic pressure decay, obtained by cardiac catheterization, is widely characterized by the time constant tau of the exponential regression p(t)=Pomega+(P0-Pomega)exp(-t/tau). However, several authors prefer to prefix Pomega=0 instead of coestimating the pressure asymptote empirically; others present tau values estimated by both methods that often lead to discordant results and interpretation of lusitropic changes. The present study aims to clarify the relations between the tau estimates from both methods and to decide for the more reliable estimate. The effect of presetting a zero asymptote on the tau estimate was investigated mathematically and empirically, based on left ventricular pressure decay data from isolated ejecting rat and guinea pig hearts at different preload and during spontaneous decrease of cardiac function. Estimating tau with preset Pomega=0 always yields smaller values than the regression with empirically estimated asymptote if the latter is negative and vice versa. The sequences of tau estimates from both methods can therefore proceed in reverse direction if tau and Pomega change in opposite directions between the measurements. This is exemplified by data obtained during an increasing preload in spontaneously depressed isolated hearts. The estimation of the time constant of isovolumic pressure fall with a preset zero asymptote is heavily biased and cannot be used for comparing the lusitropic state of the heart in hemodynamic conditions with considerably altered pressure asymptotes.     

The hydrodynamics of DNA electrophoretic stretch and relaxation in a polymer solution

Theories of DNA electrophoretic separations generally treat the DNA as a free draining polymer moving in an electric field at a rate that depends on the effective charge density of the molecule. Separations can occur in sieving media ranging from ultradilute polymer solutions to tightly cross-linked gels. It has recently been shown that DNA is not free-draining when both electric and nonelectric forces simultaneously act on the molecule, as occurs when DNA collides with a polymer during electrophoretic separations. Here we show that a semidilute polymer solution screens the hydrodynamic interaction that results from the application of these forces. Fluorescently labeled DNA tethered at one end in a semidilute solution of hydroxyl-ethyl cellulose stretch more in an electric field than they stretch in free solution, and approach free-draining behavior. The steady stretching behavior is predicted without adjustable parameters by a theory developed by Stigter using a hydrodynamic screening length found from effective medium theory. Data on the relaxation of stretched molecules after the electric field is removed agree with the Rouse model prediction, which neglects hydrodynamic interactions. The slowest relaxation time constant, tau(R), scales with chain length as tau(R) approximately L(1.9+/-0.17) when analyzed by the data collapse method, and as tau(R) approximately L(2.17+/-0.17) when analyzed by multiexponential fit.     

Differential laws of left ventricular isovolumic pressure fall

An attempt has been made to test for a reliable method of characterizing the isovolumic left ventricular pressure fall in isolated ejecting hearts by one or two time constants, tau. Alternative nonlinear regression models (three- and four-parametric exponential, logistic, and power function), based upon the common differential law dp(t)/dt = - [p(t)-P ]/ tau(t) are compared in isolated ejecting rat, guinea pig, and ferret hearts. Intraventricular pressure fall data are taken from an isovolumic standard interval and from a subinterval of the latter, determined data-dependently by a statistical procedure. Extending the three-parametric exponential fitting function to four-parametric models reduces regression errors by about 20-30%. No remarkable advantage of a particular four-parametric model over the other was revealed. Enhanced relaxation, induced by isoprenaline, is more sensitively indicated by the asymptotic logistic time constant than by the usual exponential. If early and late parts of the isovolumic pressure fall are discarded by selecting a subinterval of the isovolumic phase, tau remains fairly constant in that central pressure fall region. Physiological considerations point to the logistic model as an advantageous method to cover lusitropic changes by an early and a late tau. Alternatively, identifying a central isovolumic relaxation interval facilitates the calculation of a single ("central") tau; there is no statistical justification in this case to extend the three-parametric exponential further to reduce regression errors.     

Stiffness and relaxation components of the exponential and logistic time constants may be used to derive a load-independent index of isovolumic pressure decay

In current practice, empirical parameters such as the monoexponential time constant tau or the logistic model time constant tauL are used to quantitate isovolumic relaxation. Previous work indicates that tau and tauL are load dependent. A load-independent index of isovolumic pressure decline (LIIIVPD) does not exist. In this study, we derive and validate a LIIIVPD. Recently, we have derived and validated a kinematic model of isovolumic pressure decay (IVPD), where IVPD is accurately predicted by the solution to an equation of motion parameterized by stiffness (Ek), relaxation (tauc), and pressure asymptote (Pinfinity) parameters. In this study, we use this kinematic model to predict, derive, and validate the load-independent index MLIIIVPD. We predict that the plot of lumped recoil effects [Ek.(P*max-Pinfinity)] versus resistance effects [tauc.(dP/dtmin)], defined by a set of load-varying IVPD contours, where P*max is maximum pressure and dP/dtmin is the minimum first derivative of pressure, yields a linear relation with a constant (i.e., load independent) slope MLIIIVPD. To validate the load independence, we analyzed an average of 107 IVPD contours in 25 subjects (2,669 beats total) undergoing diagnostic catheterization. For the group as a whole, we found the Ek.(P*max-Pinfinity) versus tauc.(dP/dtmin) relation to be highly linear, with the average slope MLIIIVPD=1.107+/-0.044 and the average r2=0.993+/-0.006. For all subjects, MLIIIVPD was found to be linearly correlated to the subject averaged tau (r2=0.65), tauL(r2=0.50), and dP/dtmin (r2=0.63), as well as to ejection fraction (r2=0.52). We conclude that MLIIIVPD is a LIIIVPD because it is load independent and correlates with conventional IVPD parameters. Further validation of MLIIIVPD in selected pathophysiological settings is warranted.     

Isovolumic pressure-to-early rapid filling decay rate relation: model-based derivation and validation via simultaneous catheterization echocardiography.

Transmitral Doppler echocardiography is the preferred method of noninvasive diastolic function assessment. Correlations between catheterization-based measures of isovolumic relaxation (IVR) and transmitral, early rapid filling (Doppler E-wave)-derived parameters have been observed, but no model-based, causal explanation has been offered. IVR has also been characterized in terms of its duration as IVR time (IVRT) and by tau, the time-constant of IVR, by approximating the terminal left ventricular IVR pressure contour as Pt= Pinfinity + P(o)e(-t/tau), where Pt is the continuity of pressure, Pinfinity and Po are constants, t is time, and tau is the time constant of IVR. To characterize the relation between IVR and early rapid filling more fully, simultaneous (micromanometric) left ventricular pressure and transmitral Doppler E-wave data from 25 subjects undergoing elective cardiac catheterization and having normal physiology were analyzed. The time constant tau was determined from the dP/dt vs. P (phase) plane and, simultaneous Doppler E-waves provided global indexes of chamber viscosity/relaxation (c), chamber stiffness (k), and load (xo). We hypothesize that temporal continuity of pressure decay at mitral valve opening and physiological constraints permit the algebraic derivation of linear relations relating 1/tau to both peak atrioventricular pressure gradient (kxo) and E-wave-derived viscosity/relaxation (c) but does not support a similar, causal (linear) relation between deceleration time and tau or IVRT. Both predicted linear relations were observed: kxo to 1/tau (r = 0.71) and viscosity/relaxation to 1/tau (r = 0.71). Similarly, as anticipated, only a weak linear correlation between deceleration time and IVRT or tau was observed (r = 0.41). The observed in vivo relationship provides insight into the isovolumic mechanism of relaxation and the changing-volume mechanism of early rapid filling via a link of the respective relaxation properties.     

Physical determinants of left ventricular isovolumic pressure decline: model prediction with in vivo validation

The rapid decline in pressure during isovolumic relaxation (IVR) is traditionally fit algebraically via two empiric indexes: tau, the time constant of IVR, or tau(L), a logistic time constant. Although these indexes are used for in vivo diastolic function characterization of the same physiological process, their characterization of IVR in the pressure phase plane is strikingly different, and no smooth and continuous transformation between them exists. To avoid the parametric discontinuity between tau and tau(L) and more fully characterize isovolumic relaxation in mechanistic terms, we modeled ventricular IVR kinematically, employing a traditional, lumped relaxation (resistive) and a novel elastic parameter. The model predicts IVR pressure as a function of time as the solution of d(2)P/dt(2) + (1/micro)dP/dt + E(k)P = 0, where micro (ms) is a relaxation rate (resistance) similar to tau or tau(L) and E(k) (1/s(2)) is an elastic (stiffness) parameter (per unit mass). Validation involved analysis of 310 beats (10 consecutive beats for 31 subjects). This model fit the IVR data as well as or better than tau or tau(L) in all cases (average root mean squared error for dP/dt vs. t: 29 mmHg/s for model and 35 and 65 mmHg/s for tau and tau(L), respectively). The solution naturally encompasses tau and tau(L) as parametric limits, and good correlation between tau and 1/microE(k) (tau = 1.15/microE(k) - 11.85; r(2) = 0.96) indicates that isovolumic pressure decline is determined jointly by elastic (E(k)) and resistive (1/mu) parameters. We conclude that pressure decline during IVR is incompletely characterized by resistance (i.e., tau and tau(L)) alone but is determined jointly by elastic (E(k)) and resistive (1/micro) mechanisms.     

Role of impaired myocardial relaxation in the production of elevated left ventricular filling pressure

Although present in many patients with heart failure and a normal ejection fraction, the role of isolated impairments in active myocardial relaxation in the genesis of elevated filling pressures is not well characterized. Because of difficulties in determining the effect of prolonged myocardial relaxation in vivo, we used a cardiovascular simulated computer model. The effect of myocardial relaxation, as assessed by tau (exponential time constant of relaxation), on pulmonary vein pressure (PVP) and left ventricular end-diastolic pressure (LVEDP) was investigated over a wide range of tau values (20-100 ms) and heart rate (60-140 beats/min) while keeping end-diastolic volume constant. Cardiac output was recorded over a wide range of tau and heart rate while keeping PVP constant. The effect of systolic intervals was investigated by changing time to end systole at the same heart rate. At a heart rate of 60 beats/min, increases in tau from a baseline to extreme value of 100 ms cause only a minor increase in PVP of 3 mmHg. In contrast, at 120 beats/min, the same increase in tau increases PVP by 23 mmHg. An increase in filling pressures at high heart rates was attributable to incomplete relaxation. The PVP-LVEDP gradient was not constant and increased with increasing tau and heart rate. Prolonged systolic intervals augmented the effects of tau on PVP. Impaired myocardial relaxation is an important determinant of PVP and cardiac output only during rapid heart rate and especially when combined with prolonged systolic intervals. These findings clarify the role of myocardial relaxation in the pathogenesis of elevated filling pressures characteristic of heart failure.     

Impulsive control strategies in biological control of pesticide

By presenting and analyzing the pest-predator model under insecticides used impulsively, two impulsive strategies in biological control are put forward. The first strategy: the pulse period is fixed, but the proportional constant E(1) changes, which represents the fraction of pests killed by applying insecticide. For this scheme, two thresholds, E(1)(**) and E(1)(*) for E(1) are obtained. If E(1)>or=E(1)(*), both the pest and predator (natural enemies) populations go to extinction. If E(1)(**)相似文献   

Diastolic ventricular-vascular stiffness and relaxation relation: elucidation of coupling via pressure phase plane-derived indexes

Because systole and diastole are coupled and systolic ventricular-vascular coupling has been characterized, we hypothesize that diastolic ventricular-vascular coupling (DVVC) exists and can be characterized in terms of relaxation and stiffness. To characterize and elucidate DVVC mechanisms, we introduce time derivative of pressure (dP/dt) vs. time-varying pressure [P(t)] (pressure phase plane, PPP)-derived analogs of ventricular and vascular "stiffness" and relaxation parameters. Although volume change (dV) = 0 during isovolumic periods, and time-varying left ventricular (LV) stiffness, typically expressed as change in pressure per unit change in volume (dP/dV), is undefined, our formulation allows determination of a PPP-derived stiffness analog during isovolumic contraction and relaxation. Similarly, an aortic stiffness analog is also derivable from the PPP. LV relaxation was characterized via tau, the time constant of isovolumic relaxation, and vascular (aortic pressure decay) relaxation was characterized in terms of its equivalent (windkessel) exponential decay time constant kappa. The results show that PPP-derived systolic and diastolic ventricular and vascular stiffness are strongly coupled [K(Ao)(+)=1.71(K(LV)(+)) +154, r=0.86; K(Ao)(-)=0.677(K(LV)(-))-5.53, r=0.86]. In support of the DVVC hypothesis, a strong linear correlation between relaxation (rate of pressure decay) indexes kappa and tau (kappa = 9.89tau - 90.3, r = 0.81) was also observed. The correlations observed underscore the role of long-term, steady-state DVVC as a diastolic function determinant. Awareness of the PPP-derived DVVC parameters provides insight into mechanisms and facilitates quantification of arterial stiffening and associated increase in diastolic chamber stiffness. The PPP method provides a tool for quantitative assessment and determination of the functional coupling of the vasculature to diastolic function.     

Assessment of left ventricular diastolic function by early diastolic mitral annulus peak acceleration rate: experimental studies and clinical application.

We sought to examine the hemodynamic determinants and clinical application of the peak acceleration rate of early (Ea) diastolic velocity of the mitral annulus by tissue Doppler. Simultaneous left atrial and left ventricular (LV) catheterization and Doppler echocardiography were performed in 10 dogs. Preload was altered using volume infusion and caval occlusion, whereas myocardial lusitropic state was altered with dobutamine and esmolol. The clinical application was examined in 190 consecutive patients (55 control, 41 impaired relaxation, 46 pseudonormal, and 48 restrictive LV filling). In addition, in 60 consecutive patients, we examined the relation between it and mean wedge pressure with simultaneous Doppler echocardiography and right heart catheterization. In canine studies, a significant positive relation was present between peak acceleration rate of Ea and transmitral pressure gradient only in the stages with normal or enhanced LV relaxation, but with no relation in the stages where the time constant of LV relaxation (tau) was > or =50 ms. Its hemodynamic determinants were tau, LV minimal pressure, and transmitral pressure gradient. In clinical studies, peak acceleration rate of Ea was significantly lower in patients with impaired LV relaxation irrespective of filling pressures (P < 0.001) and with similar accuracy to peak Ea velocity (area under the curve for septal and lateral peak acceleration rates: both 0.78) in identifying these patients. No significant relation was observed between peak acceleration rate and mean wedge pressure. Peak acceleration rate of Ea appears to be a useful index of LV relaxation but not of filling pressures and can be applied to identify patients with impaired LV relaxation irrespective of their filling pressures.     

Fast voltage clamp discloses a new component of presteady-state currents from the Na(+)-glucose cotransporter.

The human Na(+)-glucose cotransporter (hSGLT1) has been shown to generate, in the absence of sugar, presteady-state currents in response to a change in potential, which could be fitted with single exponentials once the voltage had reached a new constant value. By the cut-open oocyte technique (voltage rising-speed approximately 1 mV/microsecond), phlorizin-sensitive transient currents could be detected with a higher time resolution during continuous intracellular perfusion. In the absence of sugar and internal Na+, and with 90 mM external Na+ concentration ([Na+]o), phlorizin-sensitive currents exhibited two relaxation time-constants: tau 1 increased from 2 to 10 ms when Vm decreased from +60 mV to -80 mV and remained at 10 ms for more negative Vm; tau 2 ranged from 0.4 to 0.8 ms in a weakly voltage-dependent manner. According to a previously proposed model, these two time constants could be accounted for by 1) Na+ crossing a fraction of the membrane electrical field to reach its binding site on the carrier and 2) conformational change of the free carrier. To test this hypothesis, the time constants were measured as [Na+]o was progressively reduced to 0 mM. At 30 and 10 mM external Na+, tau 1 reached the same plateau value of 10 ms but at more negative potentials (-120 and -160 mV, respectively). Contrary to the prediction of the model, two time constants continued to be detected in the bilateral absence of Na+ (at pH 8.0). Under these conditions, tau 1 continuously increased through the whole voltage range and did not reach the 10 ms level even when Vm had attained -200 mV while tau 2 remained in the range of 0.4-0.8 ms. These results indicate that 1) conformational change of the free carrier across the membrane must occur in more than one step and 2) Na+ binding/debinding is not responsible for either of the two observed exponential components of transient currents. By use of the simplest kinetic model accounting for the portion of the hSGLT1 transport cycle involving extracellular Na+ binding/debinding and the dual-step conformational change of the free carrier, tau 1 and tau 2 were fitted throughout the voltage range, and a few sets of parameters were found to reproduce the data satisfactorily. This study shows that 1) tau 1 and tau 2 correspond to two steps in the conformational change of the free carrier, 2) Na+ binding/debinding modulates the slow time constant (tau 1) and 3) a voltage-independent slow conformational change of the free carrier accounts for the observed plateau value of 10 ms.     

Analysis of the mechanisms of expiratory asynchrony in pressure support ventilation: a mathematical approach.

A mathematical model was developed to analyze the mechanisms of expiratory asynchrony during pressure support ventilation (PSV). Solving the model revealed several results. 1) Ratio of the flow at the end of patient neural inspiration to peak inspiratory flow (VTI/V(peak)) during PSV is determined by the ratio of time constant of the respiratory system (tau) to patient neural inspiratory time (TI) and the ratio of the set pressure support (Pps) level to maximal inspiratory muscle pressure (Pmus max). 2) VTI/V(peak) is affected more by tau/TI than by Pps/Pmus max. VTI/V(peak) increases in a sigmoidal relationship to tau/TI. An increase in Pps/Pmus max slightly shifts the VTI/V(peak)-tau/TI curve to the right, i.e., VTI/V(peak) becomes lower as Pps/Pmus max increases at the same tau/TI. 3) Under the selected adult respiratory mechanics, VTI/V(peak) ranges from 1 to 85% and has an excellent linear correlation with tau/TI. 4) In mechanical ventilators, single fixed levels of the flow termination criterion will always have chances of both synchronized termination and asynchronized termination, depending on patient mechanics. An increase in tau/TI causes more delayed and less premature termination opportunities. An increase in Pps/Pmus max narrows the synchronized zone, making inspiratory termination predisposed to be in asynchrony. Increasing the expiratory trigger sensitivity of a ventilator shifts the synchronized zone to the right, causing less delayed and more premature termination. Automation of expiratory trigger sensitivity in future mechanical ventilators may also be possible. In conclusion, our model provides a useful tool to analyze the mechanisms of expiratory asynchrony in PSV.     

Temperature effects on the presteady-state and transport-associated currents of GABA cotransporter rGAT1

The effects of temperature on the gamma-aminobutyric acid (GABA) uptake and on the presteady-state and transport-associated currents of the GABA cotransporter, rat gamma-aminobutyric acid transporter 1 (rGAT1), have been studied using heterologous oocyte expression and voltage-clamp. Increasing temperature from 15 to 30 degrees C increased GABA uptake, diminished the maximal value of the relaxation time constant of the presteady-state currents and increased the amplitude of the current associated with the transport of GABA. The curve of the presteady-state charge versus voltage was shifted toward negative potentials by increasing the temperature, while the maximal amount of charge (Q(max)) remained constant; the tau versus V curve was also negatively shifted by increasing temperatures. Analysis of the outward (alpha) and inward (beta) rate constants as functions of temperature showed that they are affected differently, with a Q(10)=3.4 for alpha and Q(10)=1.5 for beta. The different temperature coefficients of the rate constants account for the observed shifts. These observations are consistent with a charge moving mechanism based on a conformational change of the protein; the weaker temperature sensitivity of the inward rate constant suggests a rate-limiting diffusional component on this process.     

Changes in relaxation rate with diaphragmatic fatigue in humans

Maximum relaxation rate (MRR) and the time constant of relaxation (tau) of transdiaphragmatic pressure (Pdi) was measured in four male subjects and compared with the high-to-low frequency ratio (H/L) of the diaphragmatic electromyogram (EMG) as a predictor of diaphragmatic fatigue. Pdi and inspiratory time-to-total breath duration ratios (TI/TT) were varied, and TT and tidal volume were held constant; inspiratory resistances were used to increase Pdi. Studies were performed at various tension-time indices (TTdi = Pdi/Pdimax X TI/TT). Base-line MRR/Pdi was 0.0100 +/- 0.0004 (SE) ms-1, and baseline tau was 53.2 +/- 3.2 ms. At TTdi greater than 0.20, MRR and H/L decreased and tau increased, with maximum changes at the highest TTdi. At TTdi less than 0.20, there was no change in H/L, MRR, or tau. The time course of changes in H/L correlated with those of MRR and tau under fatiguing conditions. In this experimental setting, change in relaxation rate was as useful a predictor of diaphragmatic fatigue as fall in H/L of the diaphragmatic EMG.     

Viscosity dependence of ethidium-DNA intercalation kinetics

The kinetics of ethidium intercalation into double-stranded poly[d(G-C)] were investigated by use of repetitive pressure-jump chemical relaxation at 20 degrees C in low ionic strength (0.1 M NaCl) aqueous buffers containing either glycerol or methanol. The viscosity of the various solvents differed by more than an order of magnitude while other physical properties (e.g., dielectric constant) remained approximately constant. The single-reciprocal kinetic relaxation time (tau -1) increases linearly with DNA concentration. The observed association rate constant is lower in all organic-aqueous mixtures than in water and is inversely proportional to the viscosity. These results provide evidence for an additional step in the intercalation mechanism which is identified as an obligatory DNA conformational change preceding ethidium intercalation. From the data presented, the equilibrium constant of this local conformational change is approximately 10(-3), i.e., greatly favoring the structure incapable of intercalation. The corresponding kinetics were not directly determined; however, in order to be consistent with all of the data the forward and/or reverse rate constants of the conformational change must be larger than the rate of the intercalation reaction. Thus, it is proposed that the rate of the conformational change back to the nonintercalating B-DNA structure is greater than approximately 500 s-1, implying a rate of opening greater than approximately 0.5 s-1, in agreement with other hydrogen exchange and NMR data. The observed overall rate constant for the dissociation of ethidium is inversely proportional to the solvent density, possibly reflecting a dependence on the solvent free volume. The overall volume change of intercalation is less negative in the organic-aqueous solvent mixtures than in water.     

MRI assessment of LV relaxation by untwisting rate: a new isovolumic phase measure of tau

Most noninvasive measures of diastolic function are made during left ventricular (LV) filling and are therefore subject to "pseudonormalization," because variation in left atrial (LA) pressure may confound the estimation of relaxation rate. Counterclockwise twist of the LV develops during ejection, but untwisting occurs rapidly during isovolumic relaxation, before mitral opening. We hypothesized that the rate of untwisting might reflect the process of relaxation independent of LA pressure. Recoil rate (RR), the velocity of LV untwisting, was measured by tagged magnetic resonance imaging and regressed against the relaxation time constant (tau), recorded by catheterization, in 10 dogs at baseline and after dobutamine, saline, esmolol, and methoxamine treatment. RR correlated closely (average r = -0.86) with tau and was unaffected by elevated LA pressure. Multiple regression showed that tau, but not LA or aortic pressure, was an independent predictor of RR (P < 0.0001, P = 0.99, and P = 0.18, respectively). The rate of recoil of torsion, determined wholly noninvasively, provides an isovolumic phase, preload-independent assessment of LV relaxation. Use of this novel parameter should allow the detailed study of diastolic function in states known to affect filling rates, such as aging, hypertension, and congestive heart failure.     

Indexes of diastolic RV function: load dependence and changes after chronic RV pressure overload in lambs

Diastolic function is a major determinant of ventricular performance, especially when loading conditions are altered. We evaluated biventricular diastolic function in lambs and studied possible load dependence of diastolic parameters [minimum first derivative of pressure vs. time (dP/dt(min)) and time constant of isovolumic relaxation (tau)] in normal (n = 5) and chronic right ventricular (RV) pressure-overloaded (n = 5) hearts by using an adjustable band on the pulmonary artery (PAB). Pressure-volume relations were measured during preload reduction to obtain the end-diastolic pressure-volume relationship (EDPVR). In normal lambs, absolute dP/dt(min) and tau were lower in the RV than in the left ventricle whereas the chamber stiffness constant (b) was roughly the same. After PAB, RV tau and dP/dt(min) were significantly higher compared with control. The RV EDPVR indicated impaired diastolic function. During acute pressure reduction, both dP/dt(min) and tau showed a relationship with end-systolic pressure. These relationships could explain the increased dP/dt(min) but not the increased tau-value after banding. Therefore, the increased tau after banding reflects intrinsic myocardial changes. We conclude that after chronic RV pressure overload, RV early relaxation is prolonged and diastolic stiffness is increased, both indicative of impaired diastolic function.     

Effect of species richness and relative abundance on the shape of the species accumulation curve

Abstract We explain how species accumulation curves are influenced by species richness (total number of species), relative abundance and diversity using computer‐generated simulations. Species richness defines the boundary of the horizontal asymptote value for a species accumulation curve, and the shape of the curve is influenced by both relative abundance and diversity. Simulations with a high proportion of rare species and a few abundant species have a species accumulation curve with a low ‘shoulder’ (inflection point on the ordinate axis) and a long upward slope to the asymptote. Simulations with a high proportion of relatively abundant species have a steeply rising initial slope to the species accumulation curve and plateau early. Diversity (as measured by Simpson's and Shannon–Weaver indices) for simulations is positively correlated with the initial slope of the species accumulation curve. Species accumulation curves cross when one simulation has a high proportion of both rare and abundant species compared with another that has a more even distribution of abundance among species.     

Studying molecular motor-based cargo transport: what is real and what is noise?

Noise is a major problem in analyzing tracking data of cargos moved by molecular motors. We use Bayesian statistics to incorporate what is known about the noise in parsing the trajectory of a cargo into a series of constant velocity segments. Tracks with just noise and no underlying motion are fit with constant velocity segments to produce a calibration curve of fit quality versus average segment duration. Fits to tracks of moving cargos are compared to the calibration curves with similar noise. The fit with the optimum number of constant velocity states has the least number of segments needed to match the fit quality of the calibration curve. We have tested this approach using tracks with known underlying motion generated by computer simulations and with a specially designed in vitro experiment. We present the results of using this parsing approach to analyze transport of lipid droplets in Drosophila embryos.     

Changes in rate of relaxation of sniffs with diaphragmatic fatigue in humans

The rate of relaxation of the diaphragm after stimulated (4 subjects) and voluntary (8 subjects) contractions was compared in normal young men. Stimulated contractions were induced by supramaximal unilateral phrenic nerve stimulation and voluntary contractions by short, sharp sniffs of varying tensions against an occluded airway. The rate of relaxation of the diaphragm was calculated from the rate of decline of transdiaphragmatic pressure (Pdi). In both conditions the maximum relaxation rate (MRR) was proportional to the peak transdiaphragmatic pressure (Pdi), whereas the time constant (tau) of the later exponential decline in Pdi was independent of Pdi. The mean +/- SE rate constant of relaxation (MRR/Pdi) was 0.0078 +/- 0.0002 ms-1 and the mean tau was 57 +/- 3.8 ms for stimulated contractions. The rate of relaxation after sniffs was not different, and it was not affected by either the lung volume at which occluded sniffs were performed (in the range of residual volume to functional residual capacity + 1 liter) or by the relative contribution gastric pressure made to Pdi. After diaphragmatic fatigue was induced by inspiring against a high alinear resistance there was a decrease in relaxation rate. In the 1st min postfatigue MRR/Pdi decreased (0.0063 +/- 0.0003 ms-1; P less than 0.005) and tau increased (83 +/- 5 ms; P less than 0.005). Both values returned to prefatigue levels within 5 min of the end of the studies. We conclude that the sniff may prove to be clinically useful in the detection of diaphragmatic fatigue.