Robust reconstruction of the rate constant distribution using the phase function method

Many biological processes exhibit complex kinetic behavior that involves a nontrivial distribution of rate constants. Characterization of the rate constant distribution is often critical for mechanistic understandings of these processes. However, it is difficult to extract a rate constant distribution from data measured in the time domain. This is due to the numerical instability of the inverse Laplace transform, a long-standing mathematical challenge that has hampered data analysis in many disciplines. Here, we present a method that allows us to reconstruct the probability distribution of rate constants from decay data in the time domain, without fitting to specific trial functions or requiring any prior knowledge of the rate distribution. The robustness (numerical stability) of this reconstruction method is numerically illustrated by analyzing data with realistic noise and theoretically proved by the continuity of the transformations connecting the relevant function spaces. This development enhances our ability to characterize kinetics and dynamics of biological processes. We expect this method to be useful in a broad range of disciplines considering the prevalence of complex exponential decays in many experimental systems.     

The Analysis of Fluorescence Decay by a Method of Moments

The fluorescence decay of the excited state of most biopolymers, and biopolymer conjugates and complexes, is not, in general, a simple exponential. The method of moments is used to establish a means of analyzing such multi-exponential decays. The method is tested by the use of computer simulated data, assuming that the limiting error is determined by noise generated by a pseudorandom number generator. Multi-exponential systems with relatively closely spaced decay constants may be successfully analyzed. The analyses show the requirements, in terms of precision, that data must meet. The results may be used both as an aid in the design of equipment and in the analysis of data subsequently obtained.     

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.     

Postextrasystolic contractile decay always contains exponential and alternans components in canine heart

In isolated, blood-perfused canine hearts, postextrasystolic potentiation (PESP) decays monotonically after a noncompensatory pause following a spontaneous extrasystole (ES). The monotonic PESP decay yields myocardial internal Ca(2+) recirculation fraction (RF). We have found that after a compensatory pause (CP), PESP decays in alternans, consisting of an exponential and a sinusoidal decay component. We have proposed that this exponential component also yields RF. In the present study, we examined the reliability of this alternative method by widely changing the ES coupling interval (ESI), CP, and heart rate in the canine excised, cross-circulated left ventricle. We found that all PESP decays consisted of the sum of an exponential and a sinusoidal decay component of variable magnitudes whether a CP existed or not. Their decay constants as well as the calculated RF were independent of the ESI and CP. This confirmed the utility of our alternative RF determination method regardless of the ESI, CP, and heart rate. Direct experimental evidence of Ca(2+) dynamics supportive of this alternative method, however, remains to be obtained.     

Determination of first order rate constants by natural logarithm of the slope plot exemplified by analysis of Aspergillus niger in batch culture

Finding rate constants from experimental data is often difficult because of offset and noise. A computer program was developed to average experimental data points, reducing the effect of noise, and to produce a log_e of slope plot – a plot of the natural logarithm of the slope of a curve – eliminating the effect of any offset. If y-values depend exponentially on x-values the log_e of slope plot is rectilinear and the slope is equal to the first order rate constant. Therefore the log_e of slope plot provides easy identification of exponential sections of any experimental or calculated data, corresponding rate constants, and small changes in the rate constant as exemplified by analysis of titrant added to a batch culture of Aspergillus niger. The log_e of slope plot was easily applicable and superior to conventional methods of analysis of exponential decreasing or increasing data.     

Application of method of moments analysis to fluorescence decay lifetime distributions

In fluorescence decay work, distributions of exponential decay lifetimes are anticipated where complex systems are examined. We describe here methods of gaining information on such distributions using the method of moments analysis approach. The information obtained may be as simple as the average and deviation of the lifetime distribution, quantities which we show may be estimated directly from the results of a multiexponential analysis. An approximation to the actual distribution shape may also be obtained using a procedure we call the variable filter analysis (VFA) method without making any assumptions about the shape of the distribution. Tests of VFA using both simulated and experimental data are described. Limitations of this method and of distribution analysis methods in general are discussed. Results of analyses on experimental decays for ethidium intercalated in core particles and in free DNA are reported.     

Noise analysis of ion channels in non-space-clamped cables: estimates of channel parameters in olfactory cilia.

Ion channels in the cilia of olfactory neurons are part of the transduction machinery of olfaction. Odorant stimuli have been shown to induce a biphasic current response, consisting of a cAMP-activated current and a Ca(2+)-activated Cl- current. We have developed a noise analysis method to study ion channels in leaky cables, such as the olfactory cilium, under non-space-clamp conditions. We performed steady-state noise analysis on ligand-induced currents in excised cilia, voltage-clamped at input and internally perfused with cAMP or Ca2+. The cAMP-activated channels analyzed by this method gave results similar to those of single-channel recordings (gamma = 8.3 pS). Single-channel currents have not yet been recorded for the Ca(2+)-activated Cl- channels. Using our noise analysis method, we estimate a unit conductance, gamma = 0.8 pS, for these channels. The density of channels was found to be approximately 70 channels/micron2 for both channel species.     

A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics

Reaction kinetics in a cell or cell membrane is modeled in terms of the first passage time for a random walker at a random initial position to reach an immobile target site in the presence of a hierarchy of nonreactive binding sites. Monte Carlo calculations are carried out for the triangular, square, and cubic lattices. The mean capture time is expressed as the product of three factors: the analytical expression of Montroll for the capture time in a system with a single target and no binding sites; an exact expression for the mean escape time from the set of lattice points; and a correction factor for the number of targets present. The correction factor, obtained from Monte Carlo calculations, is between one and two. Trapping may contribute significantly to noise in reaction rates. The statistical distribution of capture times is obtained from Monte Carlo calculations and shows a crossover from power-law to exponential behavior. The distribution is analyzed using probability generating functions; this analysis resolves the contributions of the different sources of randomness to the distribution of capture times. This analysis predicts the distribution function for a lattice with perfect mixing; deviations reflect imperfect mixing in an ordinary random walk.     

A tabular learning structure with an adaptable k-d tree for relaxation of the curse of dimensionality

Memory-based learning schemes are characterized by their memorization of observed events. A memory-based learning scheme either memorizes the collected data directly or reorganizes such information and stores it distributively into a tabular memory. For the tabular type, the system requires a training process to determine the contents of the associative memory. This training process helps filter out zero-mean noise. Since the stored data are associated to pre-assigned input locations, memory management and data retrieval are easier and more efficient. Despite these merits, a drawback of tabular schemes is the difficulty in applying it to high-dimensional problems due to the curse of dimensionality. As the input dimensionality increases, the number of quantized elements in the input space increases at an exponential rate and that causes a huge demand of memory. In this paper, a dynamic tabular structure is proposed for possible relaxation of such a demand. The memorized data are organized as part of a k-d tree. Nodes in the tree, called vertices, correspond to some regularly assigned input points. Memory resource is allocated only at locations where it is needed. Being able to easily compute the vertex positions helps reduce the searching cost in data retrieval. In addition, the learning process is able to expand the tree structure into one covering the problem domain. With memory allocated based on demand, memory consumption becomes closely related to task complexity instead of input dimensionality, and is minimized. Algorithms for structure construction and training are presented in this paper. Simulation results demonstrate that the memory can be efficiently utilized. The developed scheme offers a solution for high-dimensional learning problems with a manageable size of effective input domain.     

Gradient acrylamide/agarose gels for electrophoretic separation of intact human very low density lipoproteins, intermediate density lipoproteins, lipoprotein a, and low density lipoproteins

An exponential gradient gel with 0-10% acrylamide and 0.5% agarose was developed for electrophoresis of intact high molecular weight lipoproteins. This system resolves very low density lipoproteins, intermediate density lipoproteins, lipoprotein a, and low density lipoproteins in a size-dependent fashion. The characteristic relative mobility of these species can be determined in relation to protein and colloidal gold reference materials. Electron microscopy of selected lipoprotein fractions confirmed that relative mobility was related to apparent lipoprotein diameter. The composite gel medium can be used with prestained lipoproteins and permits immunoelectroblotting for qualitative analysis of apolipoprotein constituents.     

Analysis of relaxation kinetics data by a nonlinear least squares method

Recent improvements in measuring and data acquisition techniques have increased greatly the precision of chemical relaxation data. This has necessitated more accurate methods for data analysis in cases of complex relaxation spectra, as is often observed in biochemical systems. We have developed and applied a method capable of decomposing a wave form containing up to three overlapping exponentials. The method is based upon a nonlinear least squares algorithm. Analysis of the method shows that when it is applied to a two exponential function where the signal-to-noise ratio, ΔS/N, is fifty, using 100 data points, the resulting four coefficients (two amplitudes and two relaxation times) are each accurate to within 5–10 % over a wide range of conditions, i.e., relative amplitudes from 10–90 % and ratios of relaxation times of 2.5 or greater. The influence of the number of data points and of random noise is as expected from statistical theory. Applications of the curve fitting methods to experimental temperature-jump data from oxygen binding to hemoglobin and hemocyanin yields internally consistent results. The values of the root-meansquare of the residuals of the fit approach those expected on the basis of the experimental signal-to-noise ratios.     

Adiabatic solution of the Ohmic cable equation. General theory, homogeneous cylindrical fiber]

An adiabatic solution of the Ohmic cable equation is suggested, which reduces the non-stationary equation to a stationary form. The adiabatic length constant of the stationary equation is time-dependent. The adiabatic solutions for the boundary conditions that change in time linearly and exponentially were studied. In the latter case, the adiabatic length constant does not depend on time though it differs from the usual length constant. The cable input characteristics of exact and adiabatic solutions were compared in the cases of the voltage- and current-clamp, and electric field stimulation. The adiabatic and exact solutions are identical for the rising exponential stimuli. For the falling exponential stimuli, the adiabatic solution determines the exact asymptotic solution if the stimulus decays slower than the relaxation of initial conditions. It is propose to use linear and exponential ramp stimulation in electrotonic measurements.     

Robust Bayesian Fluorescence Lifetime Estimation,Decay Model Selection and Instrument Response Determination for Low-Intensity FLIM Imaging

We present novel Bayesian methods for the analysis of exponential decay data that exploit the evidence carried by every detected decay event and enables robust extension to advanced processing. Our algorithms are presented in the context of fluorescence lifetime imaging microscopy (FLIM) and particular attention has been paid to model the time-domain system (based on time-correlated single photon counting) with unprecedented accuracy. We present estimates of decay parameters for mono- and bi-exponential systems, offering up to a factor of two improvement in accuracy compared to previous popular techniques. Results of the analysis of synthetic and experimental data are presented, and areas where the superior precision of our techniques can be exploited in Förster Resonance Energy Transfer (FRET) experiments are described. Furthermore, we demonstrate two advanced processing methods: decay model selection to choose between differing models such as mono- and bi-exponential, and the simultaneous estimation of instrument and decay parameters.     

Analysis of photoacoustic waveforms using the nonlinear least squares method.

Pulsed-laser photoacoustics is a technique which measures photoinduced enthalpic and volumetric changes on the nano- and microsecond timescales. Analysis of photoacoustic data generally requires deconvolution for a sum of exponentials, a procedure which has been developed extensively in the field of time-resolved fluorescence decay. Initial efforts to adapt an iterative nonlinear least squares computer program, utilizing the Marquardt algorithm, from the fluorescence field to photoacoustics indicated that significant modifications were needed. The major problem arises from the wide range of transient decay times which must be addressed by the photoacoustic technique. We describe an alternative approach to numerical convolution with exponential decays, developed to overcome the problems. Instead of using an approximation method (Simpson's rule) for evaluating the convolution integral, we construct a continuous instrumental response function by quadratic fitting of the discrete data and evaluate the convolution integral directly, without approximations. The success and limitations of this quadratic-fit convolution program are then demonstrated using simulated data. Finally, the program is applied to the analysis of experimental data to compare the resolution capabilities of two commercially available transducers. The advantages of a broadband, heavily damped transducer are shown for a standard organic photochemical system, the quenching of the triplet state of benzophenone by 2,5-dimethyl-2,4-hexadiene.     

On the choice of noise for the analysis of the peripheral auditory system

The cross-correlation between output and input of a system containing nonlinearities, when that system is stimulated with Gaussian white noise, is a good estimate of the linear properties of the system. In practice, however, when sequences of pseudonoise are used, great errors may be introduced in the estimate of the linear part depending on the properties of the noise. This consideration assumes special importance in the analysis of the linear properties of the peripheral auditory system, where the rectifying properties of the haircells constitute a second order nonlinearity. To explore this problem, a simple model has been designed, consisting of a second order nonlinearity without memory and sandwiched between two bandpass filters. Different types of pseudonoise are used as input whereupon it is shown that noise based on binary m-sequences, which is commonly used in noise generators, will yield totally incorrect information about this system. Somewhat better results are achieved with other types of noise. By using inverse-repeat sequences the results are greatly improved. Furthermore, certain anomalies obtained in the analysis of responses from single fibers in the auditory nerve are viewed in the light of the present results. The theoretical analysis of these anomalies reveals some information about the organization of the peripheral auditory system. For example, the possibility of the existence of a second bandpass filter in the auditory periphery seems to be excluded.     

Lights on and action! Controlling microbial gene expression by light

Light-mediated control of gene expression and thus of any protein function and metabolic process in living microbes is a rapidly developing field of research in the areas of functional genomics, systems biology, and biotechnology. The unique physical properties of the environmental factor light allow for an independent photocontrol of various microbial processes in a noninvasive and spatiotemporal fashion. This mini review describes recently developed strategies to generate photo-sensitive expression systems in bacteria and yeast. Naturally occurring and artificial photoswitches consisting of light-sensitive input domains derived from different photoreceptors and regulatory output domains are presented and individual properties of light-controlled expression systems are discussed.     

Reverse engineering large-scale genetic networks: synthetic versus real data

Development of microarray technology has resulted in an exponential rise in gene expression data. Linear computational methods are of great assistance in identifying molecular interactions, and elucidating the functional properties of gene networks. It overcomes the weaknesses of in vivo experiments including high cost, large noise, and unrepeatable process. In this paper, we propose an easily applied system, Stepwise Network Inference (SWNI), which integrates deterministic linear model with statistical analysis, and has been tested effectively on both simulated experiments and real gene expression data sets. The study illustrates that connections of gene networks can be significantly detected via SWNI with high confidence, when single gene perturbation experiments are performed complying with the algorithm requirements. In particular, our algorithm shows efficiency and outperforms the existing ones presented in this paper when dealing with large-scale sparse networks without any prior knowledge.     

Evaluation of quantification methods for real-time PCR minor groove binding hybridization probe assays

Real-time PCR data analysis for quantification has been the subject of many studies aimed at the identification of new and improved quantification methods. Several analysis methods have been proposed as superior alternatives to the common variations of the threshold crossing method. Notably, sigmoidal and exponential curve fit methods have been proposed. However, these studies have primarily analyzed real-time PCR with intercalating dyes such as SYBR Green. Clinical real-time PCR assays, in contrast, often employ fluorescent probes whose real-time amplification fluorescence curves differ from those of intercalating dyes. In the current study, we compared four analysis methods related to recent literature: two versions of the threshold crossing method, a second derivative maximum method, and a sigmoidal curve fit method. These methods were applied to a clinically relevant real-time human herpes virus type 6 (HHV6) PCR assay that used a minor groove binding (MGB) Eclipse hybridization probe as well as an Epstein-Barr virus (EBV) PCR assay that used an MGB Pleiades hybridization probe. We found that the crossing threshold method yielded more precise results when analyzing the HHV6 assay, which was characterized by lower signal/noise and less developed amplification curve plateaus. In contrast, the EBV assay, characterized by greater signal/noise and amplification curves with plateau regions similar to those observed with intercalating dyes, gave results with statistically similar precision by all four analysis methods.     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.