Evaluation and statistical judgement of neural responses to sinusoidal stimulation in cases with superimposed drift and noise

Time histograms of neural responses evoked by sinusoidal stimulation often contain a slow drifting and an irregular noise which disturb Fourier analysis of these responses. Section 2 of this paper evaluates the extent to which a linear drift influences the Fourier analysis, and develops a combined Fourier and linear regression analysis for detecting and correcting for such a linear drift. Usefulness of this correcting method is demonstrated for the time histograms of actual eye movements and Purkinje cell discharges evoked by sinusoidal rotation of rabbits in the horizontal plane. In Sect. 3, the analysis of variance is adopted for estimating the probability of the random occurrence of the response curve extracted by Fourier analysis from noise. This method proved to be useful for avoiding false judgements as to whether the response curve was meaningful, particularly when the response was small relative to the contaminating noise.     

生态模型的灵敏度分析

灵敏度分析用于定性或定量地评价模型参数误差对模型结果产生的影响,是模型参数化过程和模型校正过程中的有用工具,具有重要的生态学意义．灵敏度分析包括局部灵敏度分析和全局灵敏度分析．局部灵敏度分析只检验单个参数的变化对模型结果的影响程度;全局灵敏度分析则检验多个参数的变化对模型运行结果总的影响,并分析每一个参数及其参数之间相互作用对模型结果的影响．目前,在对生态模型的灵敏度分析中,越来越倾向于使用全局灵敏度分析的方法．但国内仍多采用局部灵敏度分析方法,很少采用全局灵敏度分析方法．文中详细论述了局部灵敏分析和全局灵敏度分析的主要方法(一次变换法、多元回归法、Morris法、Sobol’法、傅里叶幅度灵敏度检验法和傅里叶幅度灵敏度检验扩展法),希望能为国内生态模型的发展提供一个比较完善的灵敏度分析方法库．结合国内外的灵敏度分析发展现状,指出联合灵敏度研究、灵敏度共性研究及空间直观景观模型的灵敏度分析将为生态模型灵敏度分析研究中的热点和难点．     

Response to temporal parameter fluctuations in biochemical networks

Metabolic response coefficients describe how variables in metabolic systems, like steady state concentrations, respond to small changes of kinetic parameters. To extend this concept to temporal parameter fluctuations, we define spectral response coefficients that relate Fourier components of concentrations and fluxes to Fourier components of the underlying parameters. It is also straightforward to generalize other concepts from metabolic control theory, such as control coefficients with their summation and connectivity theorems. The first-order response coefficients describe forced oscillations caused by small harmonic oscillations of single parameters: they depend on the driving frequency and comprise the phases and amplitudes of the concentrations and fluxes. Close to a Hopf bifurcation, resonance can occur: as an example, we study the spectral densities of concentration fluctuations arising from the stochastic nature of chemical reactions. Second-order response coefficients describe how perturbations of different frequencies interact by mode coupling, yielding higher harmonics in the metabolic response. The temporal response to small parameter fluctuations can be computed by Fourier synthesis. For a model of glycolysis, this approximation remains fairly accurate even for large relative fluctuations of the parameters.     

Algorithm for application of Fourier analysis for biorhythmic baselines of pharmacodynamic indirect response models

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k_in (t) and a first-order loss constant k_out. If k_in(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response R_b(t) to recover the equation for k_in(t). Fourier analysis provides an approximate equation for R_b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k_in(t), yielding the equation involving R_b(t). A computer program was developed to perform the square L²-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate k_in(t) using ADAPT II. The pharmacodynamic parameters k_out and IC₅₀ were estimated from the model equation with k_in(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of k_in(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method. (Chronobiology International, 17(1), 77-93, 2000)     

Quantitative determination of orientational and directional components in the response of visual cortical cells to moving stimuli

The response characteristic of visual cortical cells to moving oriented stimuli consists mainly of directional (D) and orientational (O) components superimposed to a spontaneous activity (S). Commonly used polar plot diagrams reflect the maximal responses for different orientations and directions of stimulus movement with a periodicity of 360 degrees in the visual field. Fast Fourier analysis (FFT) is applied to polar plot data in order to determine the intermingled S, D, and O components. The zero order gain component of the spectrum corresponds to a (virtual) spontaneous activity. The first order component is interpreted as the strength of the direction selectivity and the second order component as the strength of the orientation specificity. The axes of the preferred direction and optimal orientation are represented by the respective phase values. Experimental data are well described with these parameters and relative changes of the shape of a polar plot can be detected with an accuracy better than 1%. The results are compatible with a model of converging excitatory and inhibitory inputs weighted according to the zero to second order components of the Fourier analysis. The easily performed quantitative determination of the S, D, and O components allows the study of pharmacologically induced changes in the dynamic response characteristics of single visual cortical cells.     

A space-variant differential operator for visual sensitivity

All the elements of a Fourier analysis can be derived from the experiments of Graham and Robson on contrast sensitivity. Once their experiment is posed as an eigenvalue problem, a complete orthonormal set of eigenfunctions results from solving the associated differential equation. Neither sine and cosine nor Gabor functions result. Instead, the Hermite functions arise as the eigenfunctions of a space-variant differential operator used to model the contrast sensitivity of human observers. These functions, up to a constant, are their own Fourier transforms, and in principle can be used to exactly represent the Fourier transform of naturally occuring visual images.     

Characterizing and correcting for the dynamic response of a bag-in-box system

A bag-in-box system (BBS) whose volume is monitored by a mechanical spirometer tends to have a slow response if the volume of the box is large, and this may significantly affect its measurement of gas flow. We describe a device for creating reproducible gas flows with which the impulse response of a BBS may be conveniently determined. Two computational techniques for correcting a BBS flow measurement for the effects of the impulse response were investigated: 1) an exponential model method that assumes a second-order model of the BBS dynamics and 2) a Fourier transform-based method of deconvolution known as Wiener filtering. Both correction methods produced a significant increase in the accuracy of BBS flow estimations, with the Wiener filter giving superior results.     

Can the data of Campbell and Robson be explained without assuming fourier analysis?

Certain experiments on the detection of low-contrast gratings, occasionally cited as evidence of Fourier analysis within the visual system, are interpreted without the assumption of Fourier analysis. Theoretical curves are obtained and compared with the published experimental points, showing mostly satisfactory agreement. The computations utilize Gaussian receptive fields (on-center and off-center) for the retinal ganglion cells, spatial summation, center-surround antagonism, quasilinear response at low contrasts (X-cells), and the assumption that the first significant convergence is primarily between cells of like response type and like receptive field geometry.     

Gel-liquid crystalline transition of some multilamellar lipid bilayers follows classical kinetics with a fractional dimensionality of approximately two.

The relaxation kinetics of the gel-liquid crystalline transition of phosphatidylcholine (DC14PC, DC16PC, and DC18PC) multilamellar vesicles have been examined using volume-perturbation calorimetry. The time-dependent temperature and pressure changes associated with a periodic volume perturbation are monitored in real time. Data collected in the time domain are transformed to the frequency domain using Fourier series representations of the perturbation and response functions. Because a very small perturbation is imposed during the experiment, linear response theory is suitable for analysis of the relaxation process. The Laplace transform of the classical Kolmogorov-Avrami relation of transition kinetics is used to describe the dynamic response in the frequency domain. For DC14PC and DC16PC, the relaxation process is better fit with an effective dimensionality of n = 2 rather than n = 1. For DC18PC, we estimate that an effective dimensionality of approximately 1.5 will best fit the data. These results indicate that the gel-liquid crystalline transition of these lipid bilayers follows the classical Kolmogorov-Avrami kinetic model with an effective dimensionality greater than 1 and the assumption of simple exponential decay (n = 1) commonly used in data analysis may not always be valid for lipid transitions. Insofar as the dimensionality of the relaxation reflects the geometry of fluctuating lipid clusters, this parameter may be useful in connecting experimental thermodynamic and kinetic results with those obtained from Monte Carlo simulations.     

KILLER WHALE (ORCINUS ORCA) AUDITORY EVOKED POTENTIALS TO RHYTHMIC CLICKS

Temporal auditory mechanisms were measured in killer whales ( Orcinus orca ) by recording auditory evoked potentials (AEPs) to clicks. Clicks were presented at rates from 10/sec to 1,600/sec. At low rates, clicks evoked an AEP similar to the auditory brainstem response (ABR) of other odontocetes; however, peak latencies of the main waves were 3–3.7 msec longer than in bottlenose dolphins. Fourier analysis of the ABR showed a prominent peak at 300–400 Hz and a smaller one at 800–1,200 Hz. High-rate click presentation (more than 100/sec) evoked a rate-following response (RFR). The RFR amplitude depended little on rate up to 400/sec, decreased at higher rates and became undetectable at 1,120/sec. Fourier analysis showed that RFR fundamental amplitude dependence on frequency closely resembled the ABR spectrum. The fundamental could follow clicks to around 1,000/sec, although higher harmonics of lower rates could arise at frequencies as high as 1,200 Hz. Both RFR fundamental phase dependence on frequency and the response lag after a click train indicated an RFR group delay of around 7.5 msec. This corresponds to the latency of ABR waves PIII-NIV, which indicates the RFR originates as a rhythmic, overlapping ABR sequence. The data suggest the killer whale auditory system can follow high click rates, an ability that may have been selected for as a function of high-frequency hearing and the use of rapid clicks in echolocation.     

Method of assessing the contribution of components of an anastomosing vascular network to total vascular impedance

The cerebral circulation has extensive communications between its four feeder arteries, their tributaries, and the extracerebral arteries. A theoretically derived method and its experimental verification is described by which the various impedances in a network can be quantified. It involved serial observations of pulsatile pressure, flow, and input impedance, in response to a pattern of input vessel occlusions. Fourier analysis permitted the response of the network to be studied for the component frequencies, so that linear and phasor algebra could be used to obtain a solution. Possible errors introduced by assumptions in the original model are minimal, and do not invalidate the method in practice.     

System analysis of Phycomyces light-growth response with sum-of-sinusoids test stimuli.

The light-growth response of Phycomyces has been studied with the sum-of-sinusoids method of nonlinear system identification (Victor, J.D., and R.M. Shapley, 1980, Biophys. J., 29:459). This transient response of the sporangiophore has been treated as a black-box system with one input (logarithm of the light intensity, I) and one output (elongation rate). The light intensity was modulated so that log I, as a function of time, was a sum of sinusoids. The log-mean intensity was 10(-4) W m-2 and the wavelength was 477 nm. The first- and second-order frequency kernels, which represent the linear and nonlinear behavior of the system, were obtained from the Fourier transform of the response at the appropriate component and combination frequencies. Although the first-order kernel accounts for most of the response, there remains a significant nonlinearity beyond the logarithmic transducer presumed to occur at the input of the sensory transduction chain. From the analysis of the frequency kernels, we have derived a dynamic nonlinear model of the light-growth response system. The model consists of a nonlinear subsystem followed by a linear subsystem. The model parameters were estimated from a combined nonlinear least-squares fit to the first- and second-order frequency kernels.     

Spatial scaling of consumer-resource interactions in advection-dominated systems

Ecologists studying consumer-resource interactions in advection-dominated systems such as streams and rivers frequently seek to link the results of small-scale experiments with larger-scale patterns of distribution and abundance. Accomplishing this goal requires determining the characteristic scale, termed the response length, at which there is a shift from local dynamics dominated by advective dispersal to larger-scale dynamics dominated by births and deaths. Here, we model the dynamics of consumer-resource systems in a spatially variable, advective environment and show how consumer-resource interactions alter the response length relative to its single-species value. For one case involving a grazer that emigrates in response to high predator density, we quantify the changes using published data from small-scale experiments on aquatic invertebrates. Using Fourier analysis, we describe the responses of advection-dominated consumer-resource systems to spatially extended environmental variability in a way that involves explicit consideration of the response length. The patterns we derive for different consumer-resource systems exhibit important similarities in how component populations respond to spatial environmental variability affecting dispersal as opposed to demographic parameters.     

A differentiable,periodic function for pulsatile cardiac output based on heart rate and stroke volume

Many mathematical models of human hemodynamics, particularly those which describe pressure and flow pulses throughout the circulatory system, require as specified input a modeling function which describes cardiac output in terms of volume per unit time. To be realistic, this cardiac output function should capture, to the greatest extent possible, all relevant features observed in measured physical data. For model analysis purposes, it is also highly desirable to have a model function that is continuous, differentiable, and periodic. This paper addresses both classes of needs by developing such a function. Physically, the present function provides an accurate model for flow into the ascending aorta. It is completely specified by a minimal number of standard input parameters associated with left ventricle dynamics, including heart rate, mean cardiac output, and an estimation of the peak-to-mean flow ratio. Analytically, it can be expressed as a product of two continuous, differentiable and periodic factors. Further, the Fourier expansion of this model function is shown to be a finite Fourier series, and explicit closed-form expressions are given for the non-zero coefficients in this series.     

ALGORITHM FOR APPLICATION OF FOURIER ANALYSIS FOR BIORHYTHMIC BASELINES OF PHARMACODYNAMIC INDIRECT RESPONSE MODELS

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k_in (t) and a first-order loss constant k_out. If k_in(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response R_b(t) to recover the equation for k_in(t). Fourier analysis provides an approximate equation for R_b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k_in(t), yielding the equation involving R_b(t). A computer program was developed to perform the square L²-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate k_in(t) using ADAPT II. The pharmacodynamic parameters k_out and IC₅₀ were estimated from the model equation with k_in(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of k_in(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method. (Chronobiology International, 17(1), 77–93, 2000)     

Nanosecond temperature jump relaxation dynamics of cyclic beta-hairpin peptides

The thermal unfolding of a series of 6-, 10-, and 14-mer cyclic beta-hairpin peptides was studied to gain insight into the mechanism of formation of this important secondary structure. The thermodynamics of the transition were characterized using temperature dependent Fourier transform infrared spectroscopy. Thermodynamic data were analyzed using a two-state model which indicates increasing cooperativity along the series. The relaxation kinetics of the peptides in response to a laser induced temperature jump were probed using time-resolved infrared spectroscopy. Single exponential relaxation kinetics were observed and fit with a two-state model. The folding rate determined for these cyclic peptides is accelerated by some two orders of magnitude over the rate of a linear peptide that forms a beta-hairpin. This observation supports the argument that the rate limiting step in the linear system is either stabilization of compact collapsed structures or rearrangement of collapsed structures over a barrier to achieve the native interstrand registry. Small activation energies for folding of these peptides obtained from an Arrhenius analysis of the rates imply a primarily entropic barrier, hence an organized transition state having specific stabilizing interactions.     

Ectopic lignification in primary cellulose-deficient cell walls of maize cell suspension cultures

Maize(Zea mays L.) suspension-cultured cells with up to 70% less cellulose were obtained by stepwise habituation to dichlobenil(DCB), a cellulose biosynthesis inhibitor. Cellulose de ficiency was accompanied by marked changes in cell wall matrix polysaccharides and phenolics as revealed by Fourier transform infrared(FTIR) spectroscopy.Cell wall compositional analysis indicated that the cellulosede ficient cell walls showed an enhancement of highly branched and cross-linked arabinoxylans, as well as an increased content in ferulic acid, diferulates and p-coumaric acid, and the presence of a polymer that stained positive for phloroglucinol. In accordance with this, cellulose-de ficient cell walls showed a fivefold increase in Klason-type lignin.Thioacidolysis/GC-MS analysis of cellulose-de ficient cell walls indicated the presence of a lignin-like polymer with a Syringyl/Guaiacyl ratio of 1.45, which differed from the sensu stricto stress-related lignin that arose in response to shortterm DCB-treatments. Gene expression analysis of these cells indicated an overexpression of genes specific for the biosynthesis of monolignol units of lignin. A study of stress signaling pathways revealed an overexpression of some of the jasmonate signaling pathway genes, which might trigger ectopic lignification in response to cell wall integrity disruptions. In summary, the structural plasticity of primary cell walls is proven, since a lignification process is possible in response to cellulose impoverishment.