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Generalized eigenvector algorithm for nonlinear system identification with non-white inputs.

Traditional methods for nonlinear system identification require a white, Gaussian, test input, a restriction that has limited their usability in many fields. In this study, we address the problem of identifying the dynamics of a nonlinear system when the input is highly colored-a restriction commonly encountered in the study of physiological systems. An extension of the parallel cascade method is developed that is optimal in a constrained minimum mean squared error sense and exactly corrects for the distortion induced by the non-white input spectrum. However, this correction is a deconvolution, which may become extremely ill-conditioned if the input spectrum departs significantly from whiteness; to confront this, we develop a low-rank projection operation that stabilizes the deconvolution. The overall algorithm is robust and places few requirements on the nature of the test input. Practical application of this new method is demonstrated by using it to identify a known analog nonlinear system from experimental data.

Algorithms↗

Image enhancement of the in vivo leukocyte-endothelium contact zone using optical sectioning microscopy.

A major determinant of the strength of leukocyte [white blood cell (WBC)] to endothelium [endothelial cell (EC)] adhesion is the contact area formed between the two cells, which is often obscured by out-of-focus information inherent to intravital microscopy. To improve visualization of the WBC-EC contact zone, techniques of optical sectioning microscopy were developed to enhance brightfield images of WBC-EC adhesion in postcapillary venules of the mesentery of the rat. A 50x/1.0 NA objective was held in a piezoelectric mount that was computer-driven, and video images were obtained by digitizing images from a CCD camera while focusing through the vertical direction in 1 micron steps over a depth of 16 microns. Using measurements of the microscope's optical transfer function, deconvolution of the central image was performed in the Fourier domain using the technique of singular value decomposition with Tikhonov-Miller regulation to remove out-of-focus information. Measurement of the length of the WBC-EC contact zone (LC) in the original images yielded values on the order of 4.32 +/- 1.08 microns (mean +/- SD). The enhanced images showed a significantly 35% smaller LC equal to 2.78 +/- 0.70 micron. Topical application of the chemoattractant f-met-leu-phe resulted in a 26% increase in LC to 3.49 +/- 0.72 micron, thus suggesting that upregulation of adhesion molecules on the WBC membrane results in the recruitment of additional membrane area from surface ruffles into the zone of adhesion. Other advantages of the deconvolution were to visualize structural characteristics of the microvascular wall and parenchymal tissue in greater detail. Thus, brightfield optical sectioning microscopy may provide a valuable tool for in vivo studies of the microvasculature, and serves as a useful alternative to fluorescence microscopy without the undesirable effects of exogenous fluorophores and exposure to ultraviolet radiation.

Algorithms↗

Pituitary apoplexy in acromegaly, a long-term follow-up study in two patients.

Pituitary apoplexy is a serious complication in about 3% of patients with a pituitary adenoma. Very often, the diagnosis of a functioning or non-functioning adenoma is made in retrospect. In this report, we describe two patients in whom the diagnosis of acromegaly was made before the apoplexy. In one patient, surgical intervention was necessary because of remaining clinical and biochemical activity; in the other patient conservative follow-up was pursued. Seven and nine years after apoplexy, respectively, the patients were clinically and biochemically in remission. During the follow-up, three and five years after apoplexy, respectively, the patients underwent a 10-min venous sampling procedure for 24 hours, and the GH secretory profile was investigated with multiparameter deconvolution analysis and by approximate entropy (ApEn), a scale- and model-independent regularity measure. The deconvolution analysis revealed an increased basal (nonpulsatile) GH secretion rate, while the total 24 h secretion rate was normal compared with 13 healthy male control subjects. ApEn was much larger for each patient than for any control subject value, indicating markedly more irregular GH secretion. We hypothesize that these subtle abnormalities are caused by non-specific damage as a result of vascular insult, leading to abnormal vascular supply, or abnormal autocrine and paracrine GH regulation within the remaining gland.

Acromegaly↗

[Qualitative and quantitative determination of regional myocardial perfusion with magnetic resonance tomography].

PURPOSE: Purpose of this study was to test a triple slice saturation recovery turbo FLASH sequence for myocardial perfusion imaging. In addition data-evaluation-tools for qualitative and quantitative perfusion parameters are presented and preliminary tested. MATERIAL AND METHODS: We examined 8 healthy volunteers and 4 patients with myocardial infarction. Parameters of the saturation recovery turbo FLASH sequence were as follows: TR = 2.5 msec, TE = 1.2 msec, alpha = 8 degrees, 3 slices, thickness 10 mm. For data analysis signal-intensity time curves were calculated pixel by pixel and evaluated for signal-intensity-increase over baseline and signal-intensity-upslope. Images were displayed color-coded. For quantitative data analysis we used the indicator dilution theory and developed a deconvolution algorithm which takes the arterial input function into account to calculate the myocardial mean transit time (MTT). RESULTS: The color-coded parametermaps showed uniform conditions in normal myocardium of volunteers, but reduced signal-intensity-increase over baseline and signal-intensity-upslope for infarcted areas in patients. The MTTs calculated using our algorithm were significantly shorter than those assessed with previous methods and matched better with values derived from literature. Infarcted areas show prolonged MTTs in comparison to normal myocardium. CONCLUSION: A triple slice saturation recovery turbo FLASH sequence is suitable for myocardial perfusion imaging. Color-coded parametermaps can visualize hypoperfused areas. For calculating myocardial MTTs using indicator dilution therapy a deconvolution algorithm is necessary.

Adult↗

Reduced insulin clearance contributes to the increased insulin levels after administration of glucagon-like peptide 1 in mice.

AIMS/HYPOTHESIS: Glucagon-like peptide-1 (GLP-1) is known to be a potent stimulator of insulin secretion. However, whether GLP-1 also affects insulin clearance is not known. To explore this, we developed a technique to determine prehepatic insulin secretion in mice, based on deconvolution of plasma C-peptide concentrations. The estimated beta cell secretion was then related to plasma insulin levels to allow determination of clearance rate of endogenously produced insulin. MATERIALS AND METHODS: Kinetic parameters of C-peptide were estimated after i.v. injection of human C-peptide (0.8 or 3 nmol/kg) or glucose (1 g/kg), either alone or together with GLP-1 (10 nmol/kg), in anaesthetised NMRI mice. RESULTS: C-peptide was distributed in two compartments (distribution volume 11.4+/-0.4 ml, 42+/-2% of which was in the accessible compartment). Fractional C-peptide clearance was 8.2+/-0.6% of the total distribution volume per minute. GLP-1 markedly enhanced prehepatic insulin secretion; more than 80% of prehepatic secretion occurred during the first minute after injection. Fractional clearance of endogenously released insulin after glucose was 0.66+/-0.11 min(-1) and this was reduced to 0.36+/-0.10 min(-1) by GLP-1 (p=0.04). CONCLUSIONS/INTERPRETATION: It is possible to perform C-peptide deconvolution for estimating prehepatic insulin secretion in mice. GLP-1 reduces the clearance of endogenously released insulin; therefore, it may affect insulin levels by increasing prehepatic insulin secretion and by reducing insulin clearance.

Animals↗

Measuring pre-hepatic insulin secretion using a population model of C-peptide kinetics: accuracy and required sampling schedule.

The accuracy of calculations of pre-hepatic insulin secretion were investigated, to provide independent validation of a population model of C-peptide kinetics. The effects of sampling frequency were also assessed. Five normal subjects (aged 28 to 43 years; BMI (kg/m2) 20.5 to 24.5) and five subjects with non-insulin-dependent diabetes mellitus (NIDDM) treated by diet alone (aged 34 to 57 years; BMI 22.6 to 25.6) were given a variable intravenous infusion of biosynthetic human C-peptide (BHCP) (t=-60 to 240 min) mimicking meal stimulated C-peptide secretion, with short-term oscillations (peak approximately every 12 min) superimposed on the infusion profile. Plasma C-peptide was measured every 5 min (t=0 to 240 min). The BHCP infusion was reconstructed from C-peptide measurements using a population model of C-peptide kinetics and a deconvolution method. Bias, defined as the percentage difference between the total amount of calculated BHCP and the total amount of infused BHCP (t=0 to 240 min), indicated that overall C-peptide secretion can be measured with 14% [95% confidence interval (CI) -11 to 39%] and 21% (95% CI -3 to 45%) accuracy in normal subjects and subjects with NIDDM respectively. Accuracy was not reduced by reducing the sampling frequency to every 30 min. The root mean square error, measuring the average deviation between the infused and normalised calculated BHCP profiles, was also independent of the sampling frequency [mean (95% CI) 0.9 (0.3 to 1.6) pmol/kg per min in normal subjects; 1.0 (0.9 to 1.1) pmol/kg per min in subjects with NIDDM]. Deconvolution employing a population model of C-peptide kinetics can be used to estimate postprandial total C-peptide secretion with biases of 14% and 22% respectively in normal subjects and subjects with NIDDM. Plasma C-peptide samples need only be drawn every 30 minutes.

Adult↗

Growth hormone secretion and bone mineral density in prepubertal black and white boys.

Racial differences in bone mineral density (BMD) appear to account in part for racial differences in the incidence of osteoporosis and fractures. We previously reported that the greater BMD in adult blacks compared with whites is associated with a higher serum 17 beta-estradiol and greater secretion of growth hormone (GH) in men but not women. To determine whether these racial differences occur in prepubertal boys, we measured spontaneous overnight GH secretion, serum testosterone, 17 beta-estradiol, IGF-I, and IGFBP3, IGF-I/ IGFBP3 ratio, BMD of the total body, forearm, lumbar spine, trochanter, and femoral neck, and lean body mass and body fat in 14 healthy black and 16 white boys ages 6-7 years. Measurements of GH were obtained at 20-minute intervals for 12 hours. Results were analyzed by deconvolution and are expressed as mean +/- SE. Whereas BMD of the hip (0.755 +/- 0.020 vs 0.663 +/- 0.021 g/cm(2), P = 0.0037), trochanter (0.617 +/- 0.014 vs 0.552 +/- 0.018 g/cm(2), P = 0.0102) and femoral neck (0.710+/-0.018 vs 0.6381 +/- 0.021 g/cm(2), P = 0.0157) were significantly greater in black compared with white boys, BMD of the total body (0.768 +/- 0.010 vs 0.741 +/- 0.012 g/cm(2), NS), forearm (0.405 +/- 0.010 vs 0.380 +/- 0.008 g/cm(2), NS), and lumbar spine (0.612 +/- 0.013 vs 0.609 +/- 0.021 g/cm(2), NS) was not different in the two groups. Stepwise regression analysis showed significant correlations between BMD and race at each skeletal site except the lumbar spine and trochanter. Deconvolution analysis revealed no racial difference in any of the GH measurements. Whereas serum testosterone, serum 17 beta-estradiol, and serum IGF-I were not different, serum IGFBP-3 was higher and the molar ratio of serum IGF-l/IGFBP-3 was lower in white than in black males. In summary, prepubertal BMD is higher in black than in white males at the hip, trochanter, and femoral neck, and the racial difference does not result from differences in secretion of GH.

Absorptiometry, Photon↗

Dynamics of tight and adherens junctions under EGTA treatment.

The dynamics of tight junctions (TJs) and adherens junctions (AJs) under EGTA treatment were investigated in Madin Darby canine kidney (MDCK) cells. Detailed information about the behavior of TJ and AJ proteins during the opening and resealing of TJs and AJs is still scarce. By means of the "calcium chelation" method, the distribution and colocalization of junctional proteins were studied with confocal laser scanning microscopy using a deconvolution algorithm for high-resolution images. Colocalization was analyzed for pairs of the following proteins: ZO-1, occludin, claudin-1, E-cadherin and F-actin. Significant differences were found for the analyzed pairs in control cells compared to EGTA-treated cells with respect to the position of the colocalization maxima within the cell monolayers as well as with respect to the amount of colocalized voxels. Under EGTA treatment, colocalization for ZO-1/occludin, ZO-1/claudin-1, claudin-1/occludin, E-cadherin/occludin and E-cadherin/claudin-1 dropped below 35% of the control value. Only for the ZO-1/E-cadherin pair, the amount of colocalized voxels increased and a shift to a more basal position was observed. During the opening of TJs and AJs, ZO-1 colocalized with E-cadherin in the lateral membrane region, whereas in controls, ZO-1 colocalized with occludin and claudin-1 in the junctional complex. The combination of deconvolution with colocalization analysis of confocal data sets offers a powerful tool to investigate the spatial relationship of TJ and AJ proteins during assembly and disassembly of cell-cell contacts.

Adherens Junctions↗

Bidirectional transport of iminodiacetic organic anion analogues between plasma and hepatocyte.

The kinetics of organic anions are well described and back-diffusion from hepatocyte to plasma is accepted. Although iminodiacetic (IDA) analogues, as organic anions, should also show bidirectional transport between hepatocyte and plasma, this has not been directly demonstrated heretofore. The aim of this study was to directly demonstrate back-diffusion and to quantify it in terms of its fractional rate constant. Kinetics of diethyl IDA were studied in three anaesthetised dogs in which femoral arterial and hepatic venous samples were obtained after injection of tracer into (a) a peripheral vein or (b) hepatic artery or portal vein. Arterial time-concentration curves were also compared between peripheral venous and either hepatic arterial or portal venous injections. Time-activity curves were recorded from regions of interest over the cardiac blood pool and peripheral hepatic parenchyma in 30 patients undergoing routine IDA hepatobiliary imaging with diethyl IDA or mebrofenin and fractional rate constants of clearance of IDA from the hepatocyte compared between compartmental and deconvolution analyses. After peripheral injection in dogs, there was an early arteriovenous concentration gradient across the liver indicating an hepatocyte extraction fraction in the three animals of 0.9, 0.8 and 0.6. The net extraction fraction decreased exponentially over 40 min. Time-concentration curves from hepatic vein and femoral artery were virtually superimposed following intrahepatic injections. Peripheral arterial curves, however, had different shapes according to whether injections were intrahepatic or peripheral, and were consistent with significant back-diffusion. In clinical studies, the blood disappearance curves were fitted as the sum of two exponentials and the liver curves as the difference of two exponentials (with rate constants denoted alpha1h and alpha2h). Based on compartmental analysis of the blood curves, the sum of the fractional rate constants of tracer movement from hepatocyte to bile canaliculus (k32) and to plasma (k12) was similar to and correlated with the rate constant, alpha, of the hepatocyte impulse response function (r=0.62, n=30, P<0.001). In contrast, alpha1h and alpha2h were respectively clearly greater and smaller than alpha. Moreover, neither of these hepatic rate constants correlated with alpha. Diffusion of IDA from hepatocyte to blood is significant and even in the presence of normal liver function accounts for about 50% of IDA transport out of the hepatocyte. It should be taken into account in pharmacokinetic studies based on either compartmental or deconvolution analysis.

Adult↗

The effect of diclofenac (voltarol) and pethidine on ureteric peristalsis and the isotope renogram.

Diclofenac (a non-steroidal anti-inflammatory drug) and pethidine (a synthetic opiate) are the two analgesics most commonly used to relieve the pain of ureteric colic. Fast frame renography is a non-invasive means of imaging ureteric peristalsis and renal drainage. The aim of this study was to determine the effects of each of these drugs on the drainage pattern of the upper tracts. Twelve normal male volunteers were studied. All underwent a standard fast frame renogram using 75 MBq of technetium-99m-mercaptoacetyltriglycine, and were then administered either 100 mg pethidine or 75 mg diclofenac by intramuscular injection. Fast frame renography was then repeated. Peristalsis was determined from the condensed image of each ureter and the renogram curves were analysed to obtain standard parameters and deconvolution analysis. Diclofenac caused a profound disruption to both ureteric peristalsis and the renogram curve. This effect was not seen after the administration of pethidine. Deconvolution analysis suggests the effects of diclofenac are mediated via a direct effect on drainage rather than by any alteration of blood flow to the kidney. This study suggests that pethidine is the analgesic of choice prior to renography and that inferences about alterations of drainage in the presence of diclofenac should be interpreted with care.

Adult↗

Assessment of various parameters in the estimation of differential renal function using technetium-99m mercaptoacetyltriglycine.

Differential renal function (DRF) is an important parameter that should be assessed from virtually every dynamic renogram. With the introduction of technetium-99m mercaptoacetyltriglycine (99mTc-MAG3), a tracer with a high renal extraction, the estimation of DRF might hopefully become accurate and reproducible both between observers in the same institution and also between institutions. The aim of this study was to assess the effect of different parameters on the estimation of DRF. To this end we investigated two groups of children: group A, comprising 35 children with a single kidney (27 of whom had poor renal function), and group B, comprising 20 children with two kidneys and normal global function who also had an associated 99mTc-dimercaptosuccinic acid scan (99mTc-DMSA). The variables assessed for their effect on the estimation of DRF were: different operators, the choice of renal regions of interest (ROIs), the applied background subtraction, and six different techniques for analysis of the renogram. The six techniques were based on: linear regression of the slopes in the Rutland-Patlak plot, matrix deconvolution, differential method, integral method, linear regression of the slope of the renograms, and the area under the curve of the renogram. The estimation of DRF was less dependent upon both observer and method in patients with two normally functioning kidneys than in patients with a single kidney. The inter-observer comparison among children in either group was not dependent on either ROI or background subtraction. However, in patients with poor renal function the method of choice for the estimation of DRF was dependent on background subtraction, though not ROI. In children with two kidneys and normal renal function, the estimation of DRF from the 24 techniques gave similar results. Methods that produced DRF values closest to expected results, from either group of children, were the Rutland-Patlak plot and matrix deconvolution methods.

Area Under Curve↗

Estimating in vitro mitochondrial oxygen consumption during muscle contraction and recovery: a novel approach that accounts for diffusion.

A deconvolution algorithm, based on a Bayesian statistical framework and smoothing spline technique, is applied to reconstructing input functions from noisy measurements in biological systems. Deconvolution is usually ill-posed. However, placing a Bayesian prior distribution on the input function can make the problem well-posed. Using this algorithm and a computational model of diffusional oxygen transport in an approximately cylindrical muscle (about 0.5-mm diameter and 10-mm long mouse leg muscle), the time course of muscle oxygen uptake and mitochondrial oxygen consumption, both during isometric twitch contractions (at various frequencies) and the recovery period, is estimated from polarographic measurements of oxygen concentration on the muscle surface. An important feature of our experimental protocol is the availability of data for the apparatus characteristics. From these time courses, the actual mitochondrial consumption rates during resting and exercise states can be estimated. Mitochondrial oxygen consumption rate increased during stimulation to a maximum steady state value approximately five times of the resting value of 0.63 nmol/s/g wet weight for the stimulation conditions studied. Diffusion slowed the kinetic responses to the contraction but not the steady state fluxes during the stimulation interval.

Adaptation, Physiological↗

Calculation of three hours calcium absorption from a double isotope test; a simplified method.

For the rapid evaluation of calcium absorption in human subjects several isotopic tests have been proposed. Among them, the double isotope test based on the concurrent oral and intravenous administration of calcium isotopes seems the most reliable. However, the computations involved in this test, a deconvolution of the two specific-activity functions obtained, are quite extensive. By simulating these functions we developed a simple formula to calculate the absorption in the first three hours of the test. Applied to the data of 79 patients the result differed less than the experimental error from the absorption computed with the more elaborate deconvolution method.

Calcium↗

Techniques for the quantitative measurement of individual kidney function in the pig.

A prerequisite for elucidating the effect of radiation on porcine renal function is the development of non-invasive methods for accurate quantification of unilateral glomerular filtration rate (GFR) and effective renal plasma flow (ERPF). The techniques presented here are (a) measurement of unilateral kidney filtration fraction (FF) determined by analysis of the early rise of the kidney's time-activity curves following the injection of tubular ([131I]hippuran) and glomerular ([99mTc]DTPA) tracers, and (b) deconvolution of the respective renogram. Unilateral FF values are obtained by calculating the ratio of glomerular to tubular clearances. Results for 23 female large white pigs indicate a highly significant correlation (r = 0.91, P less than 0.001) between computed FF values and those obtained from the plasma disappearance curves of [99mTc]DTPA and [131I]hippuran. Deconvolution of the renogram allows estimation of the mean transit time (MTT) for [99mTc]DTPA and [131I]hippuran, these are 6.94 +/- 1.87 and 6.86 +/- 1.44 min respectively. In addition, FF values calculated from the H0 values are significantly correlated (r = 0.7, P less than 0.05) with estimates from plasma disappearance curves of the tracers. Therefore these techniques appear to provide accurate non-invasive methods for determining individual porcine kidney function.

Animals↗

The use of metallochromic Ca indicators in skeletal muscle.

Absorbance signals recorded with metallochromic indicators in skeletal muscle fibers show rapid time courses that probably closely track the fast kinetic process of Ca++ release and retrapping by the sarcoplasmic reticulum. However, the formation of more than one complex in cuvette calibrations, both for Arsenazo III (ArIII) and Antipyrylazo III (ApIII), suggest that care needs to be taken in the deconvolution of in vivo absorbance signals. Since the kinetic rate constants have not yet been obtained for these probes, attempts to deconvolute absorbance signals should be considered approximate. The evidence suggesting that more than one complex is formed during a skeletal muscle transient with ArIII is more compelling than for the case of ApIII. The differences between the ArIII and ApIII signals may not be readily explained assuming 1:1 dye:Ca complexation and kinetic differences between the probes. Competition for Ca++ with cell Ca buffers and/or multiple complex formation by at least one of these probes needs to be invoked. Based on a simple model to simulate the behavior of the Ca signals in muscle, it may be suggested that an ApIII-like probe would more closely track pCa changes in the fiber than would an ArIII-like probe, which would show more interference with intracellular buffers; an even higher affinity probe would tend to sense the total release of Ca by the SR.

Animals↗

Analytical methods for evaluating episodic secretory activity within neuroendocrine axes.

We review here our recent analytical methods designed to: (a) detect abrupt increases and decreases in serially measured concentrations of hormones, substrates, or metabolites in body fluids (discrete peak detection); (b) carry out combined calculations of in vivo hormone secretion and metabolic clearance without the infusion of labeled compounds (deconvolution analysis); and (c) assess nonequilibrium concentrations of total, bound, and free hormones or effectors following the injection or secretion of finite amounts of one or more ligands into a closed compartment containing high-affinity transport or binding proteins. First, in relation to discrete peak detection, we illustrate the application of Cluster analysis to immunoradiometrically assayed growth hormone (GH) profiles collected in blood sampled every 30 s over night in healthy young men. Secondly, as examples of deconvolution analysis, both a waveform-independent and a waveform-specific methodology are presented, and their applications discussed (e.g., for episodic GH secretion). Thirdly, to illustrate nonequilibrium interactions between a single blood transporter protein and a hormone/ligand, we highlight the impact of the high-affinity GH binding protein in plasma on the nonsteady-state time course of GH secretion and removal. Collectively, these novel neuroendocrine tools permit a more demanding and quantitative analysis of the temporal regulation of hormone, substrate, or metabolite secretion, distribution, interconversion, irreversible metabolic removal, and association with one or more high- or low-affinity plasma binding proteins. Based upon these dynamic principles, the complex operation of neuroendocrine feedback axes in vivo can be defined and assessed quantitatively and relevant hypotheses of regulation formulated and tested specifically.

Animals↗

The binding of 1,N6-ethenoNAD to bovine liver glutamate dehydrogenase: studies using the time-correlated single photon counting fluorescence technique.

The time-correlated single photon counting (TCPC) fluorescence technique has been used as a novel approach to investigate ligand-protein interaction, for the case of the binding of the fluorescent coenzyme analogue 1,N6-ethenoNAD (epsilon NAD) to bovine liver glutamate dehydrogenase in the presence of glutarate, a substrate analogue which stabilizes the complex. System calibration was performed using solutions of epsilon ADP and carefully purified epsilon NAD mixed at variable molar ratios (pH 7.0, 0.05 M sodium phosphate buffer, 20 degrees C). The fluorescence lifetimes obtained after deconvolution were 2.4 ns (for epsilon NAD) and 23 ns (for epsilon ADP), in good agreement with literature values obtained under similar conditions. epsilon NAD binds to glutamate dehydrogenase in the presence of 50 mM glutarate, with a fluorescence quantum yield enhancement factor, Q, of about 17-fold, as previously reported (Favilla, R. and Mazzini, A. (1984) Biochim. Biophys. Acta 48-57). For this system, fluorescence lifetime values were obtained after deconvolution as 2.4 ns for free epsilon NAD and 21 ns for bound epsilon NAD. These values did not vary appreciably with enzyme concentration nor with degree of saturation, thus reflecting the existence of only one spectroscopically relevant type of complex. Addition of either GTP or ADP did not affect the lifetime of epsilon NAD bound to the enzyme, but only its affinity, thus allowing calculations of binding strengths. In the case of a simple binding (i.e., in the absence of GTP) the dissociation constant of the complex could be derived from a simple relationship, in which only the ratio between the pre-exponential factors and the parameter gamma, which represents the molar fraction of epsilon NAD molecules free in solution in the open conformation, are to be taken into account. The results are in good agreement with those reported by some of us (reference above) using a steady-state fluorescence technique, which by itself is, however, unable to resolve the number of relevant species present in the system.

Adenosine Diphosphate↗

Fourier transform infrared studies of ribonuclease in H2O and 2H2O solutions.

Fourier transform infrared transmission spectra have been obtained of the enzyme ribonuclease in both H2O and 2H2O. The resolution of the spectra have been enhanced by Fourier self-deconvolution procedures. The infrared spectrum of ribonuclease changes during exchange of the enzyme's amide hydrogens for deuterium and the exchange has been followed in the amide I and amide II spectral regions. The amide I band shifts towards lower wavenumbers during both the fast and slow phases of hydrogen exchange and the interpretation of these shifts has aided the band assignments. In particular these studies have allowed an assignment to be made for the high frequency component of the beta-strand absorption that differs from that proposed previously. This paper represents the first example of the use of deconvoluted Fourier transform infrared spectra in conjunction with hydrogen-deuterium exchange in order to aid in the assignment of a protein's infrared bands.

Amides↗