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

Abstract

Nonlinear second order white-noise analysis has been applied to the isolated frog muscle spindle. Power (delta 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. 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. 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. The dependence of the transducer kernels on delta 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. 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 afterpotentials. 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. When the operating point is changed to higher prestretch values, kernel heights increase strongly implying higher response strength of the muscle spindle.(ABSTRACT TRUNCATED AT 400 WORDS)

Reverse correlation analysis of the stretch response of primary muscle spindle afferent fibers

“…These predictions could be compared with the observed train of action potentials. Similar effects have been described in the previous analysis of encoder models, with the forward Wiener analysis in frog muscle spindles (P6pel and Querfurth 1984) and in cells of cat visual cortex (Mancini et al 1990). Examples are given in Figs.…”

“…When comparing these results with spike responses to sinusoidally modulated muscle stretch, it was argued (Kr611er et al 1988b) that a second weak differentiation takes place when the impulses are elicited on the incremental phase of the receptor potential. The frog spindle analysis (P6pel and Querfurth 1984) supported this argumentation. In the encoder mechanism of other biological systems, the same has been assumed from latency differences between slow-potential and spike 1st-order kernels in encoder processes, e.g., in catfish retinal ganglion cells (Sakuranaga et al 1987) and in the data from cockroach tactile spine neurons (French and Korenberg 1989).…”

Signal transduction and nonlinearities revealed by white noise inputs in the fast adapting crayfish stretch receptor

“…This contributes to the response asymmetry, and hysteresis may also participate (Rosenberg et al 1982). Similar behaviors have been noted in other mechanoreceptors (Poppele 1981;P6pel and Querfurth 1984;Querfurth 1986;Rocha and Bufio 1985), and therefore this nonlinearity may be a functionally relevant property.…”

“…Several models have been proposed to explain its behavior, and that of its companion the RM1 (Brown and Stein 1966;Chaplain et al 1971 ;Diez Martinez et al 1983;Fohlmeister 1979;Gestrelius 1983;Houk et al 1981 ;Krnjevic and Van Gelder 1961 ;Nakajima and Onodera 1969;Poppele 1981 ;P6pel and Querfurth 1984;Segundo and Diez Martinez 1985a), as well as other mechanoreceptors (Bufio et al 1981a(Bufio et al , 1981. A complete model of the RM2 should include the following elements (in addition to those providing hysteretic, compressive and limiting nonlinearities; Segundo and Diez Martinez 1985a): (a) linear high and tow-pass filters added to provide the slowly adapting and tonic properties of the transducer (they may be due to the mechano-electrical conversion); (b) a threshold element to account for the encoder properties and rectification (i.e., the spike generator); (c) a nonlinear gain element to explain the increasing sensitivity with constant elongation (it may reside in the increased stiffness as a function of elongation (Poppele 1981), or in membrane characteristics (Barrio, Clarac and Bufio 1991;Bufio et al 1981a;P6pel and Querfurth 1984;Querfurth 1986; Barrio, Bustamante and Bufio, unpublished observations); (at) nonlinear frequency-filtering elements to explain the decrease in phasic sensitivity and the damping ratio changes with prestretch and GWN amplitude. Components a and b would also explain the unceasing spike activity with GWN inputs, while adding c provides the tonic behavior.…”

“…Therefore, one can assume that the output spike sequence has all possible responses (Baker and Hartline 1978;Bryant and Segundo 1976;Bufio et at. i984;Lee and Schetzen 1965;Marmarelis and Marmarelis 1978;Marmarelis and Naka 1973;Moore and Auriemma 1985;Poppele 1981;P6pel and Querfurth 1984;Querfurth 1986;Rosenberg et al 1982;Victor and Shapley 1980;Wiener 1958). Consequently, special average stimulus waveforms in the GWN can be selected and the response they evoke computed (see Methods section and Bufio et al 1984).…”