A mathematical model of the crustacean stretch receptor neuron. Biomechanics of the receptor muscle, mechanosensitive ion channels, and macrotransducer properties.

1. A mathematical model of the primary transduction process in a mechanoreceptor, the slowly adapting stretch receptor organ of the crayfish, has been developed taking into account the viscoelastic properties of the accessory structures of the receptor, i.e., the receptor muscle, the biophysical properties of the mechanosensitive channels (MSCs) and the passive electrical properties of the neuronal membrane (leak conductance and capacitative properties). The work is part of an effort to identify and characterize the mechanical and ionic mechanisms in a complex mechanoreceptor. The parameters of the model are based mainly on results of our own experiments and to some extent on results from other studies. The performance of the model has been compared with the performance of the slowly adapting receptor. 2. The model resulted in nonlinear differential equations that were solved by an iterative, fourth order Range-Kutta method. For the calculations of potential, the cell was treated as an idealized spherical body. The extension of the receptor muscle was 0-30%, which is within the physiological limits for this receptor. 3. The mechanical properties of the receptor muscle were modeled by a simple Voigt element (a spring in parallel with a dashpot) in series with a nonlinear spring. This element can describe resonably well the tension development in the receptor muscle at least for large extensions (> 12%). However, for small extensions (< 12%), the muscle seems to be more stiff than for large extensions. 4. The receptor current at different extensions of the receptor was computed using typical viscoelastic parameters for a receptor muscle together with a transformation of muscle tension to tension in the neuronal dendrites and finally the properties of the mechanosensitive channels. The model fit was satisfactory in the high extension range whereas in the low extension range the deviation from the experimental results could be explained partly by insufficient modeling of the nonlinear viscoelastic properties. The voltage dependence of the receptor current was also well predicted by the model. 5. If the parameters of the viscoelastic model were adjusted for each extension so that each tension response closely resembled the experimental values, the fit of the current responses was improved but still deviated from the experimental currents. One factor that might explain the difference is the possibility that the MSCs in the stretch receptor neuron might have intrinsic adaptive properties. Introducing an exponential adaptive behavior of individual MSCs increased the ability of the model to predict the receptor current. 6. The receptor potential was calculated by modeling the neuronal membrane by a lumped leak conductance and capacitance The calculated receptor potential was higher than the experimental receptor potential. However, the fit of the receptor potential was improved substantially by introducing an adaptation of the MSCs as outlined in the preceding paragraph. the remaining discrepancy might be explained by insufficient blocking of K+ channels in the experiment. 7. The model can predict a wide range of experimental data from the slowly adapting stretch receptor neuron including the mechanical response of the receptor muscle, the receptor current and its voltage dependence, and the receptor potential. It also describes accurately the passive electrical properties of the neuronal membrane.

Acute effects of intravenous injection of beta-adrenoreceptor- and calcium channel at antagonists and agonists in myasthenia gravis.

The effect of intravenous injection of propranolol, verapamil, terbutaline, calcium, and edrophonium on neuromuscular transmission has been studied with repetitive nerve stimulation and clinical tests in 10 patients with myasthenia gravis (MG). The drugs were given intravenously in doses commonly used in clinical practice. Only minor clinical effects were noted except for edrophonium. The mean decrement of the deltoid muscle was not significantly changed after injection of propranolol (before 31%, 15 min after injection 27%) and verapamil (before 29%, 15 min after injection 26%). Terbutaline applied after propranolol and calcium applied after verapamil improved the decrement substantially. Edrophonium applied after propranolol or verapamil also greatly improved the decrement. We conclude that there is no rapid deterioration of neuromuscular transmission in patients with moderately severe MG after injections with therapeutic doses of propranolol and verapamil. However, we do not know if the most severely disabled MG patient could have reacted otherwise. We consider that, in cardiovascular emergencies, propranolol and verapamil may be used even in severe MG but with resuscitation equipment as well as specific antidotes available.

Treatment of myasthenia gravis with anti-CD4 antibody: improvement correlates to decreased T-cell autoreactivity.

We treated a patient with severe myasthenia gravis with a chimeric (murine/human) anti-CD4 monoclonal antibody (cM-T412) for 7 days and followed the therapeutic effect by standardized muscle function tests, single-fiber electromyography, and immunologic examinations of disease-specific B- and T-cell functions. Clinical and electrophysiologic improvement began within 4 days, lasted for 3 months, and was maximal between days 16 and 58. The CD4+ lymphocytes decreased to a minimum of 80 cells per microliters of peripheral blood, recovered slowly during the first year of follow-up, and did not correlate with changes in disease severity. T-cell stimulation by human acetylcholine receptor was abolished by the treatment but became detectable at the time of worsening of symptoms. The concentration of acetylcholine receptor antibodies in serum was not decreased by the treatment. The results suggest that anti-CD4 antibody administration could be effective in the treatment of severe myasthenia gravis and indicate that acetylcholine receptor-specific T lymphocytes might contribute to the disturbed neuromuscular transmission in the disease.

Stimulus-response properties of the slowly adapting stretch receptor neuron of the crayfish.

The receptor potential and receptor current in response to ramp-and-hold extensions were measured in the slowly adapting stretch receptor of the crayfish, using potential clamp technique. The stimulus-response relationship for the peak amplitude of the receptor current showed a linear behaviour for extensions less than 2% and a nonlinear behaviour for extensions larger than 5%. Using the Stevens power law, R = k(S--S0)n, where R is response, S is stimulus, S0 is threshold stimulus and n the power coefficient, n was found to be 3 for extensions between 5 and 15%. The receptor current saturated at extensions above 20-25% of the zero length of the muscle, resulting in a lower n value. However, the n value is difficult to define in this region due to the saturation. The stimulus-response relation for the receptor current can be explained by the properties of the stretch-activated channels for which the open probability is exponentially dependent on the square of the membrane tension, as suggested by recent findings. The receptor potential, using tetrodotoxin, in response to identical ramp-and-hold extensions as those used to record current responses showed a more complex time-course, indicating involvement of potential-dependent channels, potassium channels being the most probable candidate. This was supported by a mathematical model which takes into account the viscoelastic properties of the receptor muscle, the properties of the stretch-activated channels and a potential dependent K+ current.

Block of receptor response in the stretch receptor neuron of the crayfish by gadolinium.

The trivalent lanthanide gadolinium was found to block the mechanotransducer response in the stretch receptor neuron of the crayfish. At normal calcium concentration (13.5 mM) a 50 per cent block of the receptor current was found at 395 +/- 59 (mean +/- SD) microM gadolinium. At a calcium concentration of 1.35 mM a 50 per cent block of the receptor current was obtained at 103 +/- 14 (mean +/- SD) microM gadolinium. The potential activated potassium current was also affected by gadolinium. At 200 microM the amplitude of the peak outward current as a result of a 90 mV positive potential step was decreased by about 40 per cent. The fast inward sodium current was decreased less than 10 per cent by gadolinium. It is concluded that in the crayfish stretch receptor gadolinium blocks the receptor current, reflecting block of stretch-activated channels, but at higher concentrations than have been described for other stretch-activated channels. In addition the outward rectifier potassium current is also blocked reflecting a block of potassium channels.

Viscoelastic properties of the slowly adapting stretch receptor muscle of the crayfish.

The viscoelastic properties of the muscle associated with the slowly adapting stretch receptor organ of the crayfish (Astacus astacus) were studied by recording the tension response to various length changes. When steady-state length changes were applied to the muscle, the tension developed in a non-linear way, increasing slowly for small extensions and rapidly when extension increased. Muscle tension responses to ramp-and-hold extensions were characterized by a transient peak followed by a gradual decline in tension. At the onset of the ramp the tension increased rapidly, similar to the response seen in resting skeletal muscle. The relation between peak dynamic tension and extension was non-linear. In a log-log plot the relation was linear with a mean slope of 1.4. At small extensions (less than 5%) the slope seemed to be lower. The experimental results have been analysed in relation to a viscoelastic model consisting of a Voigt element in series with a non-linear spring. The model could describe both the static length-tension relation and the dynamic response, but different parameters for the springs had to be used for the two cases. When the measured tension response was transformed by an exponential function of the squared tension, in accord with recent findings on stretch-activated channels, a good agreement was obtained with the time course of the receptor currents. Adaptation is thus likely to be caused by both the mechanical properties of the receptor muscle and the characteristics of stretch-activated channels of the neuron.

Action potentials of cultured human oat cells: whole-cell measurements with the patch-clamp technique.

Oat cells (of the small cell carcinoma of the lung) have been reported to generate calcium action potentials. The calcium channels have further been suggested to play a crucial role in the relation between oat cell carcinoma and the often associated myasthenic syndrome. We have examined cultured human oat cells (U-1690) under voltage-clamp conditions, using the patch-clamp technique. We found, contrary to previous reports, that the action potential was caused by sodium and potassium currents. No calcium current was detected under these conditions, which indicates that calcium channels, if present, are very rare. The findings restrict, but do not rule out, the hypothesis that calcium plays a key role in the carcinoma/myasthenic syndrome relation.

Stimulation-induced changes in the intracellular sodium activity of the crayfish stretch receptor.

Changes in intracellular Na+ activity (aiNa) caused by mechanical stimulation in the slowly adapting stretch receptor of the crayfish were examined using Na+-selective microelectrodes. A series of brief stretches (each giving rise to a brief receptor potential and a single action potential) induced a reversible increase in aiNa which was proportional to the stimulation frequency in the range examined, 0-9.5 Hz. At 9.5 Hz, aiNa increased by 4-5 mM from the resting value of 7-10 mM. Tetrodotoxin (TTX) reduced, but did not abolish the stimulation-dependent increase in aiNa indicating the involvement of a Na+-influx pathway in addition to the potential-dependent, TTX-sensitive sodium channels of the neuronal plasma membrane. A likely candidate for this TTX-resistant pathway are the cationic transducer channels of the dendrites.

Effects of halothane on the transducer and potential activated currents of the crustacean stretch receptor.

Halothane was applied to the stretch receptor neuron of the crayfish (Astacus astacus) and the effects on the transducer properties and the potential activated currents were studied with potential clamp technique using two microelectrodes. Exposure to halothane reduced the frequency of action potentials during stretch. This was shown to be due to effects both on the action potential generating currents and the transducer current. Halothane partially blocked the TTX sensitive fast inward current in a dose-dependent manner (Apparent KD = 3 mM). Halothane also reduced the outward current produced by a positive potential step. Both the fast and the slow component were affected, although the fast outward current seemed to be most sensitive. There was little or no change in the currents resulting from negative potential steps. The peak of the receptor potential and the receptor current were very little affected by halothane. The amplitude of the static phase of the receptor potential was reduced to a greater degree than the static phase of the receptor current (cells treated with TTX). A change in reversal potential of about--13 mV was observed for the peak and the static phase of the receptor current in four cells indicating an increased cord conductance for the transducer channel.

Ionic dependence of early adaptation in the crustacean stretch receptor.

In the present study we have examined the effects of changes in potassium and calcium concentration on the early adaptation of the slowly adapting stretch receptor of the crayfish using intracellular recordings including the potential clamp technique. This was because previous studies had suggested that the early adaptative decline of the receptor potential may be attributed mainly to ionic mechanisms involved in the transducer process. During prolonged exposure to K-free saline the cell depolarized; the early adaptive fall of the receptor potential was reduced and finally the response became almost rectangular. These effects developed more rapidly if the concentration of Ca was reduced in the K-free saline. It was shown by injection of current that the effects were not potential dependent. Removal of Ca reduced the amplitude of both the dynamic and static phase of the receptor potential. Isotonic Ca-saline suppressed the static phase of the receptor potential and prolonged exposure completely abolished the response. Potential clamp experiments demonstrated that in the Ca-free saline the passive membrane conductance increased; the static phase of the receptor current increased while the peak current decreased somewhat. In the K-free and Ca-free saline both phases of the receptor current increased. The present results support earlier findings that the major part of the early adaptive fall of the receptor potential is caused by an outward K+ current. Ca2+ modifies the adaptive fall and the static phase, most likely by activation of a Ca2+-dependent K+ current and/or by inactivation of the Na+ current.

Effects of intracellular TEA injection on early adaptation of crustacean stretch receptor.

The effects of intracellular injection of TEA on the stretch-induced response of the slowly adapting stretch receptor of the crayfish have been examined to determine the contribution of an outward potassium current to the early adaptation of the neuron. Intracellular recording techniques including potential clamp measurements of membrane currents have been used. Injection of small amounts of TEA caused a pronounced depolarization of the neuron. In the early stage of depolarization there was a marked increase of the static phase of the response while the dynamic phase remained unchanged. When the resting membrane potential was kept constant by current injection both the dynamic phase and the static phase increased. However, the increase of the static phase was more pronounced than that of the dynamic phase and as a result the early phase of adaptation was almost abolished. Following TEA injection the reversal potential for both the dynamic phase and the static phase of the receptor current became somewhat more positive. TEA injection also reduced the outward current induced by a depolarizing potential step. The present results provide additional support for the hypothesis that the early phase of adaptation of the crustacean stretch receptor is attributed mainly to an outward potassium current.

Time characteristics and potential dependence of early and late adaptation in the crustacean stretch receptor.

The receptor potential of the crustacean stretch receptor evoked by a ramp and hold stretch is depolarizing and consists of an initial peak followed by a static phase. The receptor current, defined as the stretch induced current change is inward and has a similar appearance. The adaptive fall of the receptor potential and receptor current occurs in two phases which can be separated by their different time characteristics. Using intracellular recordings including potential clamp an attempt has been made to fit experimental values of the adaptive fall of the potential and current response to a double exponential function. Ramp and hold stretches with a rise time of about 7-15 ms were used. The time constants were determined with the cell clamped or polarized to different holding potentials. It was found that the adaptive fall for both potential and current could be fitted reasonably well by double experimental functions with an initial fast phase and a second slow phase. For the potential response the time constant of the early adaptive fall, tau 1, varied with holding potential, having a minimum of approximately 3 ms at about -50 mV. tau 1 for the current response showed a similar variation with holding potential, although less pronounced than for the potential response. The minimum value was about 5 ms. The time constant, tau 2, of the late phase of adaptation both for the current and potential response was about 500 ms and did not vary in a systematic way with holding potential. The results are consistent with the idea that the first phase of adaptation is related to ionic mechanisms in the membrane of the receptor neuron while the second phase might be caused by mechanical factors.

On the ionic mechanisms of adaptation in an isolated mechanoreceptor --an electrophysiological study.

The ionic mechanisms of adaptation of the receptor potential, especially the early adaptation, was studied in an isolated mechanoreceptor, the slowly adapting crustacean stretch receptor, with electrophysiological methods including potential clamp technique. This receptor has frequently been used as a model to demonstrate general principles for the generation of signals in sensory receptors. The receptor potential is depolarizing and consists of an initial peak followed by a static phase in response to a ramp and hold stretch with a high rate of rise. The receptor current, defined as the stretch induced current, is inward and has a similar appearance. The adaptive fall of the receptor potential and receptor current occurs in two phases, an initial rapid fall from the peak (early adaptation) followed by a slow decline during the static phase (late adaptation). The two phases could be characterized by different time constants. By polarizing the cell to various steady potentials before stretch it was shown that the time constant of the early adaptive fall of the receptor potential varied with potential and had a minimum close to resting membrane potential. The time course of the late adaptive fall appeared to be independent of holding potential. These results suggest that ionic mechanisms play an important role during early adaptation, whereas late adaptation probably is governed by mechanical factors. Prolonged exposure to K+-free solutions or injection of TEA caused nearly complete abolition of the early adaptive fall of the receptor potential, making the response almost rectangular in shape. The outward current associated with a positive potential step was considerably reduced after injection of TEA. Intracellular injection of Ca2+ or exposure to isotonic Ca2+-saline decreased the amplitude of the static phase of the receptor potential, whereas injection of EGTA caused an increase in amplitude. Ion substitution experiments indicated that Ca2+ might enter the neuron through the transducer channels opened by stretch. It is concluded that the major cause of the early adaptive fall of the receptor potential is an outward K+ current activated by the stretch-induced depolarization. The effects of varied intra- and extracellular Ca2+ concentration suggest that a part of the K+ current might be activated by Ca2+ influx. Another possibility is that intracellular Ca2+ contributes to adaptation by inactivation of the transducer channels. The present results demonstrate a possible mechanism for adaptation in sensory receptors. A potential activated outward K+ current enhances the fall of the receptor potential from the initial peak.(ABSTRACT TRUNCATED AT 400 WORDS)

Studies on the role of calcium in adaptation of the crustacean stretch receptor. Effects of intracellular injection of calcium, EGTA and TEA.

The effects of intracellular pressure injection of Ca2+, EGTA and TEA on the receptor potential of the crayfish stretch receptor were studied. Injection of Ca2+ caused both the transient phase and the static phase of the receptor response to diminish in amplitude, the decrease being greater for the static phase. This phase was almost abolished after a few minutes of injection. Injection of EGTA caused a decrease in the amplitude of the transient phase and an increase of the static phase. These changes progressed during the injection and finally the receptor potential became almost square. After injection of TEA the static phase increased and approached the height of the transient phase making the response almost square. The results provide evidence for the important role of intracellular Ca2+ for the adaptation of the receptor. It is suggested that the adaptive decline of the receptor potential is due to an outward potassium current which is controlled by the intracellular concentration of Ca2+.