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R I Shrager

Publications and source records attributed to R I Shrager.

At least 19 recordsLinked to original sources
PubMed1998

Some pitfalls in curve-fitting and how to avoid them: a case in point.

When curve-fitting is used to support a complex nonlinear model containing several exponential terms, some of which have closely-spaced time constants, a particular burden of proof must be assumed. Most important, the uniqueness of the solution must be explored and discussed. Statistical tests for the degree of error and independence of the parameters should be provided, as well as information relating to the steps actually used in the fitting procedures. As an example of the need for the procedures we recommend in this communication, we have chosen an important case in point that has been published recently, and which deals with the kinetics of electron transfer from fully-reduced cytochrome oxidase to O2, analyzed by the method of SVD-based least squares. The problems we deal with in this case are applicable to a wide variety of other cases that involve curve-fitting to mathematical models.

Electron Transport↗
PubMed1998

Optimal time spacings for T2 measurements: monoexponential and biexponential systems.

We have developed an optimal design strategy, i.e. a choice of times at which the magnetization should be measured, in spin-echo measurements, when the number of measurements is fixed in advance. Results are given for samples whose relaxation is described by either an exponential or biexponential decay curve. The analysis is based on having an initial estimate of the ranges in which the relaxation times are likely to lie. The optimal design consists of a set of easily parameterized non-uniformly spaced measurement times, as opposed to present implementation of spin-echo experiments. Analysis of the biexponential case shows that an order of magnitude greater signal-to-noise is required to achieve T2 estimates of comparable precision to monoexponential measurements with the same number of data points. The optimal designs lead to an improved ability to discriminate between two relatively similar relaxation times.

Magnetic Resonance Spectroscopy↗
PubMed1998

Anisotropically weighted MRI.

The intensity of an isotropically weighted MR image is proportional to a rotationally invariant measure of bulk diffusion, Trace(D) (where D is the effective diffusion tensor). Such images can be acquired from as few as two diffusion-weighted images (DWIs). Analogously, the intensity of an anisotropically weighted MR image is proportional to a rotationally invariant measure of diffusion anisotropy derived from D, such as the variance of the principal diffusivities of D. By using linear algebra, we show that to produce an anisotropically weighted MR image requires acquiring at least seven DWIs, which is also the minimum number of DWIs sufficient to estimate the entire diffusion tensor, as well as the T2-weighted amplitude image, A(b = 0), in each voxel. A general mathematical framework for constructing isotropically weighted and anisotropically weighted MR images is also provided.

Anisotropy↗
PubMed1997

Multichannel analysis of single-turnover kinetics of cytochrome aa3 reduction of O2.

The single-turnover kinetics of the oxidation of cytochrome aa3 by O2 have been studied using a new approach. Up to 1000 whole spectra covering both the Soret and alpha regions were sequentially collected at room temperature from single samples with a time resolution of 10 microns. All of the spectral and time information were used in analyses based on singular value decomposition. Four spectral transitions (i.e., intermediates) were distinguished with time constants near 0.01, 0.1, 1.1, and 30 ms. Two different kinds of sequential models were evaluated, one linear and the other branched. Although past kinetic analyses have emphasized the linear sequential model, the complexity of the intramolecular electron transfer in this enzyme suggests that a branched model be considered. This is especially true in a single-turnover experiment where earlier optical and EPR studies have pointed unequivocally to a branched model [Clore et al. (1980) Biochem. J. 185, 139-154; Blair et al. (1985) J. Am. Chem. Soc. 107, 7389-7399]. In the present study, analysis of spectral data in terms of the linear model did not reveal the formation and decay of the expected oxyferryl intermediate, whereas analysis of the branched model did. The results obtained using the branched model are consistent with all of the available evidence from a broad range of physical techniques that have been applied to examine the single-turnover kinetics of the oxidation of reduced cytochrome aa3 by O2.

Animals↗
PubMed1996

HIV-1 infection kinetics in tissue cultures.

Despite intensive experimental work on HIV-1, very little theoretical work has focused on HIV-1 spread in tissue culture. This article uses two systems of ordinary differential equations to model two modes of viral spread, cell-free virus and cell-to-cell contact. The two models produce remarkably similar qualitative results. Simulations using realistic parameter regimes showed that starting with a small fraction of cells infected, both cell-free viral spread and direct cell-to-cell transmission give an initial exponential phase of viral growth, followed by either a crash or a gradual decline, extinguishing the culture. Under some conditions, an oscillatory phase may precede the extinction. Some previous models of in vivo HIV-1 infection oscillate, but only in unrealistic parameter regimes. Experimental tissue infections sometimes display several sequential cycles of oscillation, however, so our models can at least mimic them qualitatively. Significantly, the models show that infective oscillations can be explained by infection dynamics; biological heterogeneity is not required. The models also display proportionality between infected cells and cell-free virus, which is reassuringly consistent with assumptions about the equivalence of several measures of viral load, except that the proportionality requires a relatively constant total cell concentration. Tissue culture parameter values can be determined from accurate, controlled experiments. Therefore, if verified, our models should make interpreting experimental data and extrapolating it to in vivo conditions sharper and more reliable.

CD4-Positive T-Lymphocytes↗
PubMed1995

The ability of actinic light to modify the bacteriorhodopsin photocycle. Heterogeneity and/or photocooperativity?

The focus of this paper is on the established observation that the bacteriorhodopsin (BR) photocycle responds to the level of actinic light by altering the proportions of two forms of the M intermediate. The first form of M, called M-fast or MF, decays to the O intermediate. In contrast, the second form of M, called M-slow or MS, decays directly to the ground state, and its decay rate is slower than that of MF. Any proposed scheme for the BR photocycle must account for this light-dependent phenomenon. Several papers have attempted to explain the observation on the basis of photocooperativity, or on the basis of heterogeneous populations. In this paper, we test previously proposed cooperative models with experimental data, and find those models to be inadequate. We show that two new models, one purely cooperative, the other purely heterogeneous, can both fit the data, hence such modelling will not resolve the mechanism. Taking into account the demonstration of heterogeneity, the trimer structure of BR, and certain experimental evidence in favor of cooperativity, it appears likely that both heterogeneity and cooperativity are involved in the adaptation of the BR photocycle to different levels of actinic light.

Bacteriorhodopsins↗
PubMed1994

Exact conditional distribution of a three-phase invariant in space group P1. IV. Further improvements of Cochran-like approximations.

A new approximate method of computing the conditional probability density function (c.p.d.f.) of a three-phase invariant is investigated, the results being compared to accurate calculations [Shmueli, Rabinovich & Weiss (1989). Acta Cryst. A45, 361-367]. A direct dependence on N, the number of atoms in the unit cell, is incorporated into the new approximation and its performance in the equal-atom case appears to be excellent over a large range of N values. The polynomial approximation of the recently published method [Posner, Shmueli & Weiss (1993). Acta Cryst. A49, 260-265] has been improved in both accuracy and range.

Algorithms↗
PubMed1994

Influence of excitation energy on the bacteriorhodopsin photocycle.

Kinetic curves for the bacteriorhodopsin (BR) photocycle were obtained both at 570 and at 412 nm at a series of increasing levels of intensity of the exciting laser. Singular value decomposition (SVD) of these curves showed two transitions in the kinetic profiles that occurred at specific levels of actinic light. This means that the photocycle was influenced by photon density in two ways. In a separate application of SVD, time-resolved optical spectra were analyzed at each of many levels of exciting laser intensities. The studies showed that the transition at the low level of laser intensity was due principally to an increase in the amount of BR that was turning over. The transition at the higher level of laser intensity showed a fundamental change in kinetics of the photocycle. At low intensity levels, the fast form of M (Mf) predominated, whereas at high levels the slow form of M (Ms) predominated. A distinction was found between Mf and Ms, in that the former decayed directly to the O intermediate whereas the latter decayed directly to BR.

Bacteriorhodopsins↗
PubMed1994

Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners.

Singular value decomposition (SVD) is deeply rooted in the theory of linear algebra, and because of this is not readily understood by a large group of researchers who could profit from its application. In this paper, we discuss the subject on a level that should be understandable to scientists who are not well versed in linear algebra. However, because it is necessary that certain key concepts in linear algebra be appreciated in order to comprehend what is accomplished by SVD, we present the section, 'Bare basics of linear algebra'. This is followed by a discussion of the theory of SVD. Next we present step-by-step examples to illustrate how SVD is applied to deconvolute a titration involving a mixture of three pH indicators. One noiseless case is presented as well as two cases where either a fixed or varying noise level is present. Finally, we discuss additional deconvolutions of mixed spectra based on the use of the pseudoinverse.

Mathematical Computing↗
PubMed1993

Mechanism of the oxidation reaction of deoxyhemoglobin as studied by isolation of the intermediates suggests tertiary structure dependent cooperativity.

The intermediates in the oxidation of deoxyhemoglobin by ferricyanide in 0.1 M KCl, at 20 degrees C and three pH values, were studied by cryogenic techniques. Data analysis was carried out according to a simple four rate constant model, ignoring the functional heterogeneity of the subunits, to simulate the time courses of the oxidation reaction, as studied by the stopped-flow technique [Antonini et al., (1965) Biochemistry 4, 345], which show anticooperativity at neutral pH and cooperativity at alkaline pH. Data analysis according to a 12 rate constant model indicated that the rate of oxidation of the beta subunit in the first oxidation reaction was 4 times faster than the rate of oxidation of the alpha subunit at pH 6.2 and 12 times faster at pH 8.5. The reactions involving the alpha subunit were noncooperative except for the last oxidation step at acid and neutral pH, but were cooperative at alkaline pH. The reactions involving the beta subunit were partly noncooperative and partly anticooperative. These complex mechanistic patterns suggest that a simple two-state model requiring the concerted transition of the tertiary structures of the subunits from the T to the R conformation is not adequate to interpret the oxidation reaction and that tertiary structures contribute, positively and negatively, to cooperativity. A structural hypothesis is suggested to explain the difference in the reactivities of the alpha and beta subunits.

Ferricyanides↗
PubMed1993

Multiwavelength analysis of the kinetics of reduction of cytochrome aa3 by cytochrome c.

Some new approaches to the kinetic study of the reduction of cytochrome aa3 by cytochrome c are presented. The primary innovations are the use of a spectrometer which can acquire multiwavelength data as fast as every 10 microseconds, and the application of a variety of analytical methods which can utilize simultaneously all of the time-resolved spectral data. These techniques include singular value decomposition (SVD), deconvolutions based on pure Gaussian models for absorption peaks, deconvolutions based on isolated absorption spectra for the pure components, and simulations of SVD-deduced and actual experimental difference spectra. The reduction characteristics of the anaerobic resting enzyme can be distinguished from those of pulsed forms. In the former case, only two electrons can be bound by cytochrome aa3, whereas in the latter case complete reduction of the enzyme is achieved.

Animals↗
PubMed1992

An investigation of the thermal unfolding of swine pepsinogen using circular dichroism.

The thermal unfolding of swine pepsinogen is investigated using circular dichroism (CD) in the pH range 6-9. CD spectra and single wavelength melting curves are analyzed to show the presence of two resolvable transitions. Analysis of difference CD spectra by the method of singular value decomposition indicates that the changes in conformation are distinct in the two transitions. Single wavelength melting curves show that only one of the transitions has a strong pH dependence. The results are discussed in terms of earlier kinetic and calorimetric data to suggest the presence of one or more intermediates in the reaction.

Animals↗
PubMed1992

Analytic models for nonlinear curve-fitting of forward-rate binding data, with applications to hemoglobin.

The experimental procedure of Perrella et al. (1983, J. Biol. Chem. 258, 4511-4517) can reveal most of the intermediate ligation states of hemoglobin either at equilibrium or in a kinetic reaction. In this paper, a model of stepwise ligand binding, under conditions of negligible reverse reaction, is derived with particular attention to hemoglobin. The model leads to a two-phase procedure. First, the ratios of the forward rates are determined by fitting the model to normalized concentrations vs. saturation. Second (optionally), an auxiliary relation is used to deduce the scale factor for the rates that make the model consistent with time information if such is available. The procedure has been applied to hemoglobin binding of the ligands carbon monoxide (this paper) and ferricyanide (manuscript in preparation).

Algorithms↗
PubMed1992

A kinetic model of CD4+ lymphocytes with the human immunodeficiency virus (HIV).

This report describes a kinetic model of in vitro cytopathology involving interactions of human immunodeficiency virus (HIV) with CD4+ helper T lymphocytes. The model uses nonlinearly coupled, ordinary differential equations to simulate the dynamics of infected and uninfected cells and free virions. It is assumed that resting cells are more readily infected than activated cells, but once infected, only activated cells produce more virus. Resting cells can be activated by some appropriate stimulus (e.g. phytohemagglutinin, soluble antigen). The model predicts that the initial inoculum of virus is taken up by resting cells and without stimulation the system comes to a steady state of two populations, namely infected and uninfected cells. Stimulation of this system produces two additional populations, namely infected and uninfected activated cells which, along with the previous populations, exhibit cyclic behavior of growth, viral expression/release, and death. Additional stimuli enhance or diminish the cyclic behavior depending upon their occurrence in time. These simulations suggest a similar dynamics in human HIV infection and may explain a major factor responsible for the widely varying depletion rate of (CD4+) helper T cells in AIDS patients.

CD4-Positive T-Lymphocytes↗