System analysis of Phycomyces light-growth response: Single mutants

The white-noise method of system identification has been applied to the transient light-growth response of a set of seven mutants of Phycomyces with abnormal phototropism, affected in genes madA to madG. The Wiener kernels, which represent the input-output relation of the light-growth response, have been evaluated for each of these mutants and the wild-type strain at a log-mean blue-light intensity of 0.1 W m^-2. Additional experiments were done at 3x10^-4 and 10 W m^-2 on the madA strain C21 and wild-type. In the normal intensity range (0.1 W m^-2) the madA mutant behaves similarly to wild-type, but, at high intensity, the madA response is about twice as strong as that of wild-type. Except for C21 (madA), the first-order kernels of all mutants were smaller than the wild-type kernel. The first-order kernels for C111 (madB) and L15 (madC) show a prolonged time course, and C111 has a longer latency. The kernels for C110 (madE), C316 (madF), and C307 (madG) have a shallow and extended negative phase. For C68 (madD), the latency and time course are shorter than in the wild-type. These features are also reflected in the parameters estimated from fits of the anlytical model introduced in the previous paper to the experimental transfer functions (Fourier transforms of the kernels). The kernel for L15 (madC) is described better by a model that lacks one of the two second-order low-pass filters, because its response kinetics are dynamically of lower order.     

System analysis of Phycomyces light-growth response in single and double night-blind mutants

The sum-of-sinusoids method of nonlinear system identification has been applied to the light-growth response of the Phycomyces sporangiophore. Experiments were performed on the Phycomyces tracking machine with the wild-type strain with single and double mutants affected in genes madA, madB, and madC. The sum-of-sinusoids test stimuli were applied to the logarithm of the light intensity. The log-mean intensity level was 10^-1 Wm^-2 and the wavelength was 477 nm. The system identification results are in the form of first- and second-order frequency kernels, which are related to temporal kernels that appear in the Wiener functional series. The first-order kernels agree well with those obtained previously by the white noise method. In particular, the madA madB and madB madC double mutants show very weak responses. With the superior precision of the sum-of-sinusoids methods, we have achieved sufficient resolution to measure and analyze their second-order kernels. The first- and second-order frequency kernels were interpreted by system analysis methods involving a nonlinear parametric model. In addition a nonparametric hypothesis concerning interactions of gene products was tested. Results from the interaction tests confirm the earlier conclusion that the madB and madC gene products interact. In addition, with the enhanced precision and with the extension to nonlinear analysis, we have found evidence of interaction of the madA gene product with the madB and madC gene products. Thus all three genes appear to have mutual interactions, presumably because of their close physical association in a photoreceptor complex.     

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.     

System analysis of Phycomyces light-growth response: Double mutants

The light-growth response of Phycomyces has been studied with Gaussian white-noise test stimuli for a set of 21 double mutants affected in all pairwise combinations of genes madA to madG; these genes are associated with phototropism, the light-growth response, and other behaviors. The input-output relations of the light-growth responses of these mutants are represented by Wiener kernels in the time domain and transfer functions in the frequency domain. The results have been analyzed comparatively with those in the preceding papers on wild-type and single mutant strains. Two of the double night-blind mutants (combinations AB and BC) have especially weak, but still detectable, responses. To evaluate possible dynamic interactions among the seven mad gene products, each double-mutant transfer function was analyzed jointly with those of the parental single mutants and wild-type. Specifically, a hypothesis of dynamic independence was rejected at the 5% significance level for the following combinations: AD, AE, AG, BC, BD, BE, BF, BG, CD, CE, CF, DE, DG, and EF. A formal pictorial scheme summarizes the dynamic interactions among the mad gene products, according to this test. The high degree of interactions between the input gene products (A, B, and C) and the output gene products (D, E, F, and G) suggest that most or all of the sensory transduction pathway for the light-growth response (and phototropism) is contained in a multimolecular complex.     

System analysis of Phycomyces light-growth response. Photoreceptor and hypertropic mutants.

The light-growth responses of Phycomyces behavioral mutants, defective in genes madB, madC, and madH, were studied with the sum-of-sinusoids method of system identification. Modified phototropic action spectra of these mutants have indicated that they have altered photoreceptors (P. Galland and E.D. Lipson, 1985, Photochem. Photobiol. 41:331). In the two preceding papers, a kinetic model of the light-growth response system was developed and applied to wild-type frequency kernels at several wavelengths and temperatures. The present mutant studies were conducted at wavelength 477 nm. The log-mean intensity was 6 X 10(-2)W m-2 for the madB and madC night-blind mutants, and 10(-4)W m-2 for the madH hypertropic mutant. The prolonged light-growth responses of the madB and madC mutants are reflected in the reduced dynamic order of their frequency kernels. The linear response of the hypertropic mutant is essentially normal, but its nonlinear behavior shows modified dynamics. The behavior of these mutants can be accounted for by suitable modifications of the parametric model of the system. These modifications together support the hypothesis that an integrated complex mediates sensory transduction in the light responses and other responses of the sporangiophore.     

System analysis of Phycomyces light-growth response: madC, madG, and madH mutants.

The light-growth response of Phycomyces has been studied further with the sum-of-sinusoids method in the framework of the Wiener theory of nonlinear system identification. The response was treated as a black box with the logarithm of light intensity as the input and elongation rate as the output. The nonlinear input-output relation of the light-growth response can be represented mathematically by a set of weighting functions called kernels, which appear in the Wiener intergral series. The linear (first-order) kernels of wild type, and of single and double mutants affected in genes madA to madG were determined previously with Gaussian white noise test stimuli, and were used to investigate the interactions among the products of these genes (R.C. Poe, P. Pratap, and E.D. Lipson. 1986. Biol. Cybern. 55:105.). We have used the more precise sum-of-sinusoids method to extend the interaction studies, including both the first- and second-order kernels. Specifically, we have investigated interactions of the madH ("hypertropic") gene product with the madC ("night blind") and madG ("stiff") gene products. Experiments were performed on the Phycomyces tracking machine. The log-mean intensity of the stimulus was 6 x 10(-2) W m-2 and the wavelength was 477 nm. The first- and second-order kernels were analyzed in terms of nonlinear kinetic models.(ABSTRACT TRUNCATED AT 250 WORDS)     

Characterisation of columnar neurons and visual signal processing in the medulla of the locust optic lobe by system identification techniques

We describe visual responses of seventeen physiological classes of columnar neuron from the retina, lamina and medulla of the locust (Locusta migratoria) optic lobe. Many of these neurons were anatomically identified by neurobiotin injection. Characterisation of neuronal responses was made by moving and flash stimuli, and by two system identification techniques: 1. The first-order spatiotemporal kernel was estimated from response to a spatiotemporal white-noise stimulus; 2. A set of kernels to second order was derived by the maximal-length shift register (M-sequence) technique, describing the system response to a two-channel centre-surround stimulus. Most cells have small receptive fields, usually with a centre diameter of about 1.5°, which is similar to that of a single receptor in the compound eye. Linear response components show varying spatial and temporal tuning, although lateral inhibition is generally fairly weak. Second-order nonlinearities often have a simple form consistent with a static nonlinear transformation of the input from the large monopolar cells of the lamina followed by further linear filtering.Abbreviations LMC large monopolar cell - LVF long visual fibre - RF receptive field - SMC small monopolar cell - SVF short visual fibre     

The transducer and encoder of frog muscle spindles are essentially nonlinear. Physiological conclusions from a white-noise analysis

1. Nonlinear second order white-noise analysis has been applied to the isolated frog muscle spindle. Power (²) of the Gaussian white noise (GWN) and the average prestretch level L were varied and the response of both the isolated receptor potential (transducer) and the action potential (encoder) level were analysed. 2. The standard white-noise method is briefly presented. Particular emphasis, however, is put on the limitations in the range of validity of the method and, consequently, on the use and interpretation of the kernels as a Wiener model. Conclusions in the present paper are within this frame and are mainly of qualitative nature. 3. The analysis reveals that the nonlinear contributions of the model are essential for approximating physiological results, thus ruling out purely linear modelling for this receptor organ. 4. The dependence of the transducer kernels on are compatible with the behaviour of a rectifier. Rectification is represented by the lack of hyperpolarization within the isolated receptor potential and is enhanced by the substantial memory in the linear and nonlinear kernels as demonstrated by their extent in time. This is equivalent to low power in high frequencies of the response. Obviously, the hyperpolarizing potentials following each spike counteract the long transducer memory. 5. At the encoder level the memory of the system is strongly reduced. This is achieved by using predominantly high frequency components of the receptor potential for triggering the process of impulse generation, and by the precise coupling and high frequency content of the impulses. This coupling precision is possible because of the sensitivity of the spike-generating mechanism to steep rising transients of the receptor potential and also owing to the reduction in transducer memory by the hyperpolarizing afferpotentials. 6. The preference given to the high frequency components is also read from the structure of the second order transducer kernel and from both the linear and the second order encoder kernels, which allows the most effective input waveform for triggering action potentials to be determined. 6. When the operating point is changed to higher prestretch values, kernel heights increase strongly implying higher response strength of the muscle spindle. The kernel structure is changed as well in the direction of reducing the effective memory already at the level of the receptor potentials, probably a means to prevent too high depolarization values.     

System analysis of Phycomyces light-growth response. Wavelength and temperature dependence.

The light-growth response of the Phycomyces sporangiophore was studied further with the sum-of-sinusoids method of nonlinear system identification. The first- and second-order frequency kernels, which represent the input-output relation of the system, were determined at 12 wavelengths (383-529 nm) and 4 temperatures (17 degrees, 20 degrees, 23 degrees, and 26 degrees C). The parametric model of the light-growth response system, introduced in the preceding paper, consists of nonlinear and linear dynamic subsystems in cascade. The model parameters were analyzed as functions of wavelength and temperature. At longer wavelengths, the system becomes more nonlinear. The latency and the bandwidth (cutoff frequency) of the system also vary significantly with wavelength. In addition, the latency decreases progressively with temperature (Q10 = 1.6). At low temperature (17 degrees C), the bandwidth is reduced. The results indicate that about half of the latency is due to physical processes such as diffusion, and the other half to enzymatic reactions. The dynamics of the nonlinear subsystem also vary with wavelength. The dependence of various model components on wavelength supports the hypothesis that the light-growth response, as well as phototropism, are mediated by multiple interacting photoreceptors.     

Nonlinear analysis of the human visual evoked response

Using time-domain correlation techniques, the first- and second-order Wiener kernels have been calculated for the system mediating the human visual evoked response. The first-order kernels indicate the linear element is a resonant one, with a natural frequency near 20 Hz, and a memory of approximately 250 ms. The transport delay associated with this element is approximately 56 ms. The second-order kernels indicate a quadratic nonlinear element with a memory less than 20 ms. The analytic form of this element can be approximated by a parabola shifted to the right of the origin. A close correspondance between the spectrum of the first-order kernel and the spectrum of the main diagonal of the second-order kernel suggests the nonlinear element preceeds the linear one. Tests of reproducibility on the first-order kernel and the main diagonal of the second-order kernel suggest they are reliable describing functions for the system mediating the human visual evoked response.     

Stimulus coding in crayfish antennal mechanoreceptors estimated by noise analysis

Two different kinds of mechanoreceptive hairs (smooth and feathered) on the second antennae of the freshwater crayfish, Orconectes virilis, have been investigated for their stimulus coding propertics. These mechanoreceptors show a great deal of non-linear behaviour both in threshold and in directionality. An effective appraoch for the investigation of such systems is noise analysis in the frequency domain. This method has been used here to calculate zero-, first- and second-order kernels. Sensory cells reveal different first- and second-order kernels, depending on which type of hair is being stimulated. The first-order kernel has a pronounced peak in the frequency response at 110 Hz if a feathered hair is stimulated and at 60 Hz if a smooth hair is stimulated. The second-order kernel shows a number of pronounced peaks in the frequency response between 40 and 110 Hz, but only if a feathered hair is stimulated. Smooth hair stimulation results in less sharp peaks but in higher gain for the same range of stimulus frequencies.     

Action spectra of the light-growth response of Phycomyces

The light-growth response of Phycomyces blakesleeanus (Burgeff) is a transient change in elongation rate of the sporangiophore caused by a change in light intensity. Previous investigators have found that the light-growth response has many features in common with phototropism; the major difference is that only the light-growth response is adaptive. In order to better understand the light-growth response and its relationship to phototropism, we have developed a novel experimental protocol for determining light-growth-response action spectra and have examined the effect of the reference wavelength and intensity on the shape of the action spectrum. The null-point action spectrum obtained with broadband-blue reference light has a small peak near 400 nm, a flat region from 430 nm to 470 nm, and an approximately linear decline in the logarithm of relative effectiveness above 490 nm. The shape of the action spectrum is different when 450-nm reference light is used, as has been shown previously for the phototropic-balance action spectrum. However, the action spectrum of the light-growth response differs from that for phototropic balance, even when the same reference light (450 nm) is used. Moreover, for the light-growth response, the relative effectiveness of 383-nm light decreases as the intensity of the 450-nm reference light increases; this trend is the opposite of that previously found for phototropic balance. The dependence of the lightgrowth-response action spectrum on the reference wavelength, its difference from the phototropic-balance action spectrum, and the reference-intensity dependence of the relative effectiveness at 383 nm may be attributable to dichroic effects of the oriented photoreceptor(s), and to transduction processes that are unique to the light-growth response.I dedicated to Masaki Furuya on the occasion of his 65th birthdayThis work was supported by a grant from the National Institutes of Health (GM29707) to E.D. Lipson. Anuradha Palit, Promod Pratap, and Benjamin Horwitz participated in the early phases of this work. We thank Leonid Fukshansky and Benjamin Horwitz for helpful discussions, David Durant for computer programming, and Steven Block for providing us with a C-language program of Reinsch's procedure for cubic spline interpolation. One of us (R.S.) gratefully acknowledges a junior faculty fellowship leave from the Department of Physics at Yale University.     

The Effect of Light on the Geotropic Responses of Phycomyces Sporangiophores

The geotropic responses of Phycomyces sporangiophores were studied under varying intensities of illumination, using a low speed centrifuge and a fixed beam of blue light. This light has a strongly inhibitory effect on the transient geotropic response, reducing it to 36 per cent of its magnitude in darkness. The inhibition does not vary systematically with light intensity over a range of 400-fold. The light sensitivity of the transient geotropic response thus differs from the light-growth response system, which shows the same growth rate in light and darkness. By contrast, the slower long term geotropic response is enhanced by light of moderate intensities, but is strongly inhibited by high intensities. At and above a mean intensity of about 1 µw/cm², the long term response is completely removed. If the intensity is lowered from an inhibitory level, either to darkness or to a low level, the geotropic response appears after a time lag of 20 minutes. Furthermore an increase in intensity from one level to another, both levels normally enhancing, results in a transient reversal in the long term geotropic response, also after a time lag of 20 minutes. Thus it is suggested that light is acting at some intermediate step in the long term geotropic sensory system, a step that normally requires 20 minutes for completion.     

White noise analysis of Phycomyces light growth response system. I. Normal intensity range.

The Wiener-Lee-Schetzen method for the identification of a nonlinear system through white gaussian noise stimulation was applied to the transient light growth response of the sporangiophore of Phycomyces. In order to cover a moderate dynamic range of light intensity I, the imput variable was defined to be log I. The experiments were performed in the normal range of light intensity, centered about I0 = 10(-6) W/cm2. The kernels of the Wierner functionals were computed up to second order. Within the range of a few decades the system is reasonably linear with log I. The main nonlinear feature of the second-order kernel corresponds to the property of rectification. Power spectral analysis reveals that the slow dynamics of the system are of at least fifth order. The system can be represented approximately by a linear transfer function, including a first-order high-pass (adaptation) filter with a 4 min time constant and an underdamped fourth-order low-pass filter. Accordingly a linear electronic circuit was constructed to simulate the small scale response characteristics. In terms of the adaptation model of Delbrück and Reichardt (1956, in Cellular Mechanisms in Differentiation and Growth, Princeton University Press), kernels were deduced for the dynamic dependence of the growth velocity (output) on the "subjective intensity", a presumed internal variable. Finally the linear electronic simulator above was generalized to accommodate the large scale nonlinearity of the adaptation model and to serve as a tool for deeper test of the model.     

Development and application of white-noise modeling techniques for studies of insect visual nervous system

The nonlinear system identification technique through white-noise stimulation is extended to multi-input, -output systems with consideration given to applications in the functional study of the nervous system. The applicability of the method is discussed in general and in particular for the motion detection neuronal system of the fly. Two series of experiments are performed; one with moving striped-pattern stimuli and the other with spot stimuli of fluctuating intensity. In both cases nonlinear dynamic models are derived which describe the system with considerable accuracy over the frequency range of 0.2–50 Hz and a dynamic amplitude range of about 40-1. These models are able to predict accurately all the discrete experiments so far performed on this system for which the models are applicable. The differences in dynamic characteristics between the corresponding system of the Musca and Phoenicia families of flies are minor except for a difference in latencies and if the difference in geometry of their faceted eyes is taken into account. The large field response of the motion detection unit is a linear weighted summation of all the smaller field highly nonlinear subsystems of which the large field is comprised.     

Dynamics of cockroach ocellar neurons

The incremental responses from the second-order neurons of the ocellus of the cockroach, Periplaneta americana, have been measured. The stimulus was a white-noise-modulated light with various mean illuminances. The kernels, obtained by cross-correlating the white-noise input against the resulting response, provided a measure of incremental sensitivity as well as of response dynamics. We found that the incremental sensitivity of the second-order neurons was an exact Weber-Fechner function; white-noise-evoked responses from second-order neurons were linear; the dynamics of second-order neurons remain unchanged over a mean illuminance range of 4 log units; the small nonlinearity in the response of the second-order neuron was a simple amplitude compression; and the correlation between the white-noise input and spike discharges of the second-order neurons produced a first-order kernel similar to that of the cell's slow potential. We conclude that signal processing in the cockroach ocellus is simple but different from that in other visual systems, including vertebrate retinas and insect compound eyes, in which the system's dynamics depend on the mean illuminance.     

DARK ADAPTATION AND THE LIGHT-GROWTH RESPONSE OF PHYCOMYCES

1. A single-celled, elongating sporangiophore of Phycomyces responds to a sufficient increase in intensity of illumination by a brief increase in growth rate. This is the "light-growth response" of Blaauw. 2. The reaction time is compound, consisting of an exposure period and a latent period (this comprising both the true latent period resulting from photochemical action and any "action time" necessary for the response). During the latter period the plant may be in darkness, responding nevertheless at the end of the latent period. 3. Both light adaptation and dark adaptation occur in the sporangiophore. The kinetics of dark adaptation can be accounted for on the basis of a bimolecular reaction, perhaps modified by autocatalysis. Attention is called to the bimolecular nature of the "dark" reaction in all other photosensory systems that have been studied, in spite of the diversity of the photosensitive substances themselves and of the different forms of the responses to light.     

Reconstruction of cone-system contributions to responses of colour-opponent neurones in monkey lateral geniculate

Responses of colour-opponent X-cells to intensity-modulation at various wavelengths were obtained in the lateral geniculate nucleus (LGN) of the anaesthetized (N₂O/O₂) rhesus monkey. The gaussian white noise (GWN) analysis method was used to describe the stimulus-response relationship. Two different methods were used to estimate sign and relative strength of the response contribution of each of the three known cone systems as a function of time. Both methods revealed that, in contrast to the wellknown variability in gain and sign, the time course of the cone-type contributions was remarkably stereotyped in all cells. Surround-mediated cone-type contributions appeared to have a consistently longer delay than centre-mediated inputs. Response contributions from different types of cone appeared to add linearly in LGN neurones. Apart from rectification, it was possible to predict the response of the same neurone to step-modulation of intensity at various wavelengths successfully with the first-order Wiener kernel. This demonstrates that the cells behaved linearly under our stimulus conditions, which justifies the use of the first-order kernel as a means to characterize the system we wished to study.     

Identification of nonlinear systems using random impulse train inputs

Nonlinear systems that require discrete inputs can be characterized by using random impulse train (Poisson process) inputs. The method is analagous to the Wiener method for continuous input systems, where Gaussian white-noise is the input. In place of the Wiener functional expansion for the output of a continuous input system, a new series for discrete input systems is created by making certain restrictions on the integrals in a Volterra series. The kernels in the new series differ from the Wiener kernels, but also serve to identify a system and are simpler to compute. For systems whose impulse responses vary in amplitude but maintain a similar shape, one argument may be held fixed in each kernel. This simplifies the identification problem. As a test of the theory presented, the output of a hypothetical second order nonlinear system in response to a random impulse train stimulus was computer simulated. Kernels calculated from the simulated data agreed with theoretical predictions. The Poisson impulse train method is applicable to any system whose input can be delivered in discrete pulses. It is particularly suited to neuronal synaptic systems when the pattern of input nerve impulses can be made random.     

Cardiac sympathetic nerve stimulation does not attenuate dynamic vagal control of heart rate via alpha-adrenergic mechanism

Complex sympathovagal interactions govern heart rate (HR). Activation of the postjunctional beta-adrenergic receptors on the sinus nodal cells augments the HR response to vagal stimulation, whereas exogenous activation of the presynaptic alpha-adrenergic receptors on the vagal nerve terminals attenuates vagal control of HR. Whether the alpha-adrenergic mechanism associated with cardiac postganglionic sympathetic nerve activation plays a significant role in modulation of the dynamic vagal control of HR remains unknown. The right vagal nerve was stimulated in seven anesthetized rabbits that had undergone sinoaortic denervation and vagotomy according to a binary white-noise signal (0-10 Hz) for 10 min; subsequently, the transfer function from vagal stimulation to HR was estimated. The effects of beta-adrenergic blockade with propranolol (1 mg/kg i.v.) and the combined effects of beta-adrenergic blockade and tonic cardiac sympathetic nerve stimulation at 5 Hz were examined. The transfer function from vagal stimulation to HR approximated a first-order, low-pass filter with pure delay. beta-Adrenergic blockade decreased the dynamic gain from 6.0 +/- 0.4 to 3.7 +/- 0.6 beats x min(-1) x Hz(-1) (P < 0.01) with no alteration of the corner frequency or pure delay. Under beta-adrenergic blockade conditions, tonic sympathetic stimulation did not further change the dynamic gain (3.8 +/- 0.5 beats x min(-1) x Hz(-1)). In conclusion, cardiac postganglionic sympathetic nerve stimulation did not affect the dynamic HR response to vagal stimulation via the alpha-adrenergic mechanism.