A Fourier method for the analysis of exponential decay curves.

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.     

A new method for the analysis of sums of exponential decay curves

A method based on Fourier Transform is presented for the representation of data by an arbitrary sum of exponentials or Gaussian functions. The method has been successfully applied to the type of data sets which arise in pharmacokinetic studies. Two techniques for error ripple elinination are discussed.     

The interpretation of exponential dose-effect curves

This paper deals with the following question: Which distributions of radiosensitivity in a population can lead to an exponential survival curve? The problem is solved exactly, with statistical fluctuations in dose fully accounted for. It is shown that only an exponential distribution of sensitivities can give rise to an exponential survival curve.     

Phosphorimeters for analysis of decay profiles and real time monitoring of exponential decay and oxygen concentrations

A phosphorimeter which can be assembled at low cost from mainly commercially available components and which has better time resolution, data acquisition rate, sensitivity, and flexibility than commercially available instruments is described. As a phosphorescence analyzer the instrument can measure phosphorescence lifetimes ranging from approximately 30 microseconds to seconds from samples with variable intensity, excitation, and emission spectra and which may follow complex decay behavior. Configured as a phosphorescence monitor it is designed for fast, repetitive calculation of phosphorescence lifetime, assuming single-exponential decay, and can be used to calculate oxygen concentration in biological samples in real time.     

A three-step scheme for gray crescent formation in the rotated axolotl oocyte

It has been shown that various inhibitors of protein synthesis can elicit the precocious appearance of a gray crescent (GC) in in vitro maturing, nonactivated Ambystoma mexicanum oocytes. However, evidence has now been obtained that these treatments fail to induce GC formation when the oocytes are enucleated before initiation of maturation. The ability to form a GC is reestablished in enucleated oocytes by the injection of nucleoplasm from a normal oocyte, either before or after the injection of the inhibitor. In the latter case, the GC appears very rapidly, even though protein synthesis is at about 1/10th that of the control enucleated oocyte, after treatment with diphtheria toxin (final concentration 10(-8) M) as an inhibitor. One or several nuclear factors, in conjunction with inhibition of protein synthesis, are therefore essential for early symmetrization. The corrective nuclear factor is already present in the germinal vesicle of young oocytes, at the very beginning of vitellogenesis. It is not species specific, since enucleated axolotl oocytes can be symmetrized with Pleurodeles or even Xenopus oocyte nucleoplasm. Moreover, it has been shown that the nuclear-cytoplasmic interaction is possible only when cytoplasmic maturation has been proceeding for at least 10 hr after exposure to progesterone (at 18 degrees C). A three-step process as a prerequisite of GC formation in the oocyte is proposed: Cytoplasmic maturation must proceed till a reactive state is attained, allowing interactions with nuclear factors; Nuclear factor(s) interact(s) with matured cytoplasm; Inhibition of protein synthesis triggers GC formation. Sequence of steps 2 and 3 can be experimentally inverted but must always be preceded by step 1. Since a sharp reduction in amino acid incorporation has also been found in normally fertilized eggs just prior to GC formation, it is suggested that the scheme described above could be also applicable to normal symmetrization in this model system.     

Analysis of the exponential decay model of the neuron showing frequency threshold effects

The exponential decay model of a neuron has been analyzed using the “random walk” approach of stochastic processes and an “absorbing barrier” solution is obtained forg ^T (s)—the Laplace transform of the output pulse interval density function. An expression for the mean output frequency is derived from this and a variety of input-output curves plotted which show frequency threshold effects in single neurons. Our results are compared with those of other authors obtained by computer simulation techniques, and the significance of these results discussed with reference to the possible behavior of networks constructed of such neuron units.     

Analysis of fluorescence decay curves by means of the Laplace transformation.

A computational procedure is described for the analysis of fluorescence decay data convolved with a lamp flash of finite width. The computer program calculates the ratio of the Laplace transforms of the decay and the lamp flash for different values of s to give the transforms of the impulse response for each value of s. These are set equal to the analytical Laplace transforms of the decay law involved. Solution of the nonlinear simultaneous equations yields the desired decay parameters. The method can be modified to analyze data that contains a component due to scattered light and can also provide essential information regarding transit time changes of the photomultiplier with changes in emission wavelength. The method was tested by the analysis of real and simulated data. The accuracy of the analysis depends on the degree of correlation among the parameters.     

Muscle contraction history: modified Hill versus an exponential decay model

In recent years, it has been recognised that improvements to classic models of muscle mechanical behaviour are often necessary for properly modelling co-ordinated multi-joint actions. In this respect, the purpose of the present study was to improve on modelling stretch-induced force enhancement and shortening-induced force depression of muscle contraction. For this purpose, two models were used: a modified Hill model and a model based loosely on mechano-chemistry of the cross-bridge cycle (exponential decay model). The models were compared with a classic Hill model and experimental data. Parameter values were based, as much as possible, on experimental findings in the literature, and tested with new experiments on the gastrocnemius of the rat. Both models describe many features of slow-ramp movements well during short contractions (300–500 ms), but long-duration behaviour is described only partly. The exponential decay model does not incorporate a force–velocity curve. Therefore, its good performance indicates that the status of the classic force–velocity characteristic may have to be reconsidered. Like movement-induced force depression and enhancement, it seems a particular manifestation of time-dependent force behaviour of muscle, rather than a fundamental property of muscle (like the length–tension curve). It is argued that a combination of the exponential decay model (or other models based on the mechano-chemistry of contraction) and structurally based models may be fruitful in explaining this time-dependent contraction behaviour. Furthermore, not in the least because of its relative simplicity, the exponential decay model may prove more suitable for modelling multi-joint movements than the Hill model. Received: 19 March 1999 / Accepted in revised form: 9 June 2000     

Maximum likelihood method for the analysis of time-resolved fluorescence decay curves

The usefulness of fluorescence techniques for the study of macromolecular structure and dynamics depends on the accuracy and sensitivity of the methods used for data analysis. Many methods for data analysis have been proposed and used, but little attention has been paid to the maximum likelihood method, generally known as the most powerful statistical method for parameter estimation. In this paper we study the properties and behavior of maximum likelihood estimates by using simulated fluorescence intensity decay data. We show that the maximum likelihood method provides generally more accurate estimates of lifetimes and fractions than does the standard least-squares approach especially when the lifetime ratios between individual components are small. Three novelties to the field of fluorescence decay analysis are also introduced and studied in this paper: a) discretization of the convolution integral based on the generalized integral mean value theorem: b) the likelihood ratio test as a tool to determine the number of exponential decay components in a given decay profile; and c) separability and detectability indices which provide measures on how accurately, a particular decay component can be detected. Based on the experience gained from this and from our previous study of the Padé-Laplace method, we make some recommendations on how the complex problem of deconvolution and parameter estimation of multiexponential functions might be approached in an experimental setting. Offprint requests to: F. G. Prendergast     

Survival of replicators with parabolic growth tendency and exponential decay

The claim that the competition of parabolically growing self-replicators leads to dynamically stable coexistence was challenged by Lifson & Lifson [(1999). J. theor. Biol.199, 425-433]. They have shown that, if single- and double-strands are treated separately, and only single-strands undergo spontaneous decay, then there is natural selection rather than survival of everybody. We use their models to show that if double-strand decay is not neglected, then dynamical coexistence is still possible under a wide range of parameter values, in agreement with the chromatographized replicator model of von Kiedrowski & Szathmáry [(2000). Selection 1-3, 173-179]. Coexistence is always ensured above a critical resource (monomer) inflow rate. Recycling of decayed replicators into monomers further favours dynamical coexistence. The claim that parabolic growth invariably results in coexistence remains valid for the model for which it was meant to apply, namely for parabolic growth without template decay. Exponential decay acting on single- and double-strands, combined with parabolic growth, may or may not result in a dynamical coexistence of self-replicators.     

Fractional exponential decay of a membrane protein population due to capture by coated pits

We consider the lateral diffusion of receptors, or other membrane proteins, in the outer membranes of certain cells, and their capture by coated pits. It is shown, for the case in which the coated pits are in fixed random positions, that the long-time decay of the total number of uncaptured proteins is of the fractional exponential form, N(t) = N0 exp [-square root of (t/tau)], and not of the pure exponential form, N(t) = N0 exp(-t/tau), which is usually assumed.     

Effects of exponential compression curves with nitrogen injection in humans

Two series of experiments were carried out on humans to study the effects of fast and slow exponential compression curves with N2 additions. Eight subjects in the first series and 13 subjects in the second series were analyzed up to the depths of 400-450 m of seawater (msw). The data indicated that injections of N2 in He-O2 mixture reduced or suppressed the hyperbaric tremor in the two series. Electroencephalographic (EEG) changes were recorded with the two types of compression, but these changes (increase in slow waves, decrease in alpha-activity, appearance of microsleep EEG traces) were more important with the fast exponential compression curves between 200 and 300 msw than with the slow exponential curves. The effects of the fast rates of compression on EEG activities were not compensated by addition of 4-5% N2. Consequently, the fast exponential compression curves, even with N2 injections, cannot be used without risk and must be avoided; the slow exponential compression curve with N2 injection allowed a human subject to reach 450 msw in satisfactory condition, i.e., without tremor and with light EEG changes.     

Witch's chin: a progressive, three-step technique

Witch's chin is an unpleasant aesthetic defect characterized by ptosis of premental tissue and a deep submental fold, which may be exaggerated by hyperprojection of the mandible. These three elements determine the different degrees of deformity; therefore, the ideal treatment should be directed to one, two, or all three of them. Despite unanimity on the surgical approach of the defect, a large variety of techniques have been proposed by various authors. The need to use a technique suitable for different clinical pictures, characterized by a progressive surgical aggression, as usually performed in this practice, has led to standardize a technique to correct witch's chin, by means of three progressive steps, depending on the degree of deformity. The advantage of this procedure is that once a good result has been achieved, the subsequent steps may be omitted. The technique has been successfully performed in five patients, and the mean follow-up is 12 months. Figures from two representative cases are presented.