This chapter has tried to provide the reader with an interesting sampling of basic sensory receptors found in vertebrates and in invertebrates. Some examples of unusual and little-known receptors (magnetoreceptors, sh electroreceptors, in vertebrate gravity sensors, and the haltere, a vibrating, angular-rate sensor of dipteran ies) ha ve been included.
Most receptors signal their sensed quantity by generating nerve spikes that are sent to the animal's CNS. The spike "code" used is seen to be generally nonlinear; the steady-state spike frequency is proportional to the logarithm of the sensed quantity, or is described by a power-law where the sensed quantity is raised to some power < 1. Receptors generally exhibit rate sensitivity, where a step of sensed input produces a high-frequency burst of spikes at rst, and then slo ws to a steady-state ring rate. In some receptors, such as the mammalian spindle, the steady-state spik e rate is zero, and the receptor res a b urst when pressure is suddenly applied, and again when it is removed. Most receptors show unidirectional rate sensitivity, ring a burst only at the onset of their stimulus, and simply stopping ring when the stimulus is removed.
Some receptors exhibit amazing sensitivities to threshold levels of their stimulus. A hypothetical model has been illustrated, where the ring threshold of the receptor is adjusted by a feedback mechanism so there are a few random spikes produced (false positives) by to noise in the spike generator potential. By maintaining such an optimum, low threshold, the receptor can minimize its number of false positives, while true positives are sensed with very few false negatives (missed input stimuli). Certain photoreceptors, low-frequency electric eld receptors, and chemoreceptors are good examples of receptors that have enormous sensitivities to low-level stimuli. In some cases, such great sensitivity may be in part due to nonlinear interactions between receptors (lateral inhibition or multiplicative processing).
A challenge in sensory neurophysiology that should be met in the next decade is the identi cation of speci c magnetoreceptor neurons and the elucidation of ho w they work at the molecular level. It is known from magnetic bacteria that living cells can assemble chains of single-domain-sized magnetite (Fe2O3) particles inside themselves by biochemical means, as well as other iron/oxygen and iron/sulfur ferrimag-natic crystals. Most mechanoreceptor neurons sense distortions of their cell membranes when an external displacement, force, or pressure causes a depolarizing generator potential to occur. A model for a magnetoneuron would have the minute forces generated by the Earth's magnetic eld on biogenic magnetite crystals inside the sensor couple to the membrane where ion-gating proteins could be activated, causing depolarization and spike generation. Section 2.4.3 examined some speculative models for magnetoreception that do not involve internal or external magnetite crystals.
Noise reduction in neuro-sensory systems having threshold sensitivities might be carried out in several ways. Multiplicative signal processing, synaptic averaging, and low-pass ltering by electrotonic conduction on dendrites and nonspiking axons may all gure in noise reduction.
2.1. A chemical kinetic model for photoreceptor transduction has been proposed* in which the depolarization voltage of the photoreceptor cell is proportional to the concentration, c, of product C in the cell; that is, vm = k6c. Product C is made according to the reaction shown in Figure P2.1: The conversion of A to B proceeds at a rate proportional to the log of the light intensity, kj log[1 + I/Io]. The rate of conversion of B to C contains an autocatalytic term: (k2 + k3 c). In the absence of light, C is converted to A at rate k4. From chemical mass-action kinetics, one can write the three ODEs (a is the concentration of molecule A in the cell, and b is the concentration of B):
a = k4c-ak1 log[1 + l/l0 ] b = ak log[1 + l/lo] + k5c - b(k2 + k3c) c = b(k2 + k3c) - (k4 + k5 )c a. Simulate the three nonlinear chemical kinetic equations above: Use a(0) = 1, other ICs = 0, k1 = 4, k2 = 0.3, k3 = 40, k4 = 10, k5 = 0.1, k6 = 80, Io = 1. Let I = 0.1, 1, 10, 102, 103, 104 for 10 ms. Plot the depolarization, vm(t). Does the system saturate? Plot the initial peak and vm at 10 ms as a function of intensity.
b. *Let I = 2. Plot a(t), b(t), and c(t) over 20 ms. Use the parameters in (a).
2.2. a. Consider a putative, Hall-effect, magnetosensor based on Figure 2.4-1.
Protons, instead of electrons, are actively pumped and form Jx. Find the mean transport velocity, vx, required to produce a Hall voltage of 100 ^V, given that By = Be = 5.8 • 10-5 T (maximum Earth's magnetic eld), and t = 10 7 m. b. Describe several known biological systems that actively transport protons or electrons.
* Jones, R.W., D.G. Green, and R.B. Pinter.1962. Mathematical simulation of certain receptor and effector organs, Fed. Proc., 21(1): 97.
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