Modelling the mechanoreceptor's dynamic behaviour

Abstract

All sensory receptors adapt, i.e. they constantly adjust their sensitivity to external stimuli to match the current demands of the natural environment. Electrophysiological responses of sensory receptors from widely different modalities seem to exhibit common features related to adaptation, and these features can be used to examine the underlying sensory transduction mechanisms. Among the principal senses, mechanosensation remains the least understood at the cellular level. To gain greater insights into mechanosensory signalling, we investigated if mechanosensation displayed adaptive dynamics that could be explained by similar biophysical mechanisms in other sensory modalities. To do this, we adapted a fly photoreceptor model to describe the primary transduction process for a stretch-sensitive mechanoreceptor, taking into account the viscoelastic properties of the accessory muscle fibres and the biophysical properties of known mechanosensitive channels (MSCs). The model's output is in remarkable agreement with the electrical properties of a primary ending in an isolated decapsulated spindle; ramp-and-hold stretch evokes a characteristic pattern of potential change, consisting of a large dynamic depolarization during the ramp phase and a smaller static depolarization during the hold phase. The initial dynamic component is likely to be caused by a combination of the mechanical properties of the muscle fibres and a refractory state in the MSCs. Consistent with the literature, the current model predicts that the dynamic component is due to a rapid stress increase during the ramp. More novel predictions from the model are the mechanisms to explain the initial peak in the dynamic component. At the onset of the ramp, all MSCs are sensitive to external stimuli, but as they become refractory (inactivated), fewer MSCs are able to respond to the continuous stretch, causing a sharp decrease after the peak response. The same mechanism could contribute a faster component in the 'sensory habituation' of mechanoreceptors, in which a receptor responds more strongly to the first stimulus episode during repetitive stimulation.

Keywords: biophysical model; fly photoreceptor; refractory period; sensory adaptation; sensory habituation; stochastic adaptive sampling; stretch-sensitive mechanoreceptor.

Fig 1

A photoreceptor and a mechanoreceptor exhibit remarkably similar response dynamics to step-like stimuli. (A) Light-induced-current in response to bright square pulse in a fly photoreceptor (reproduced from Song et al. 2012). A large initial peak quickly drops to a post-dynamic minimum, which then recovers to a much smaller plateau. The peak dynamic component is called fast adaptation, which takes only 200–500 ms before transition to the plateau. The exponential trend at plateau is slow adaptation. (B) In a primary ending of mammalian muscle spindle, a ramp-and-hold stretch evokes a comparable characteristic pattern of potential change, consisting of a large dynamic depolarization during the ramp phase and a smaller static depolarization during the hold phase (reproduced from Hunt et al. 1978). 1–7 are numbered in the same way as in fig.1 in Hunt et al. (1978), representing different components in the rich response dynamics. They are named as: (1) baseline; (2) peak of initial dynamic component; (3) peak of late dynamic; (4) post-dynamic minimum; (5) static maximum; (6) end static level; and (7) post-release minimum. Although for better comparison with the model outputs it is best to use patch-clamped recording of the stimuli-induced ionic flow, as there were no such data available in the literature for mechanotransduction, we showed sub-optimally the receptor potential of a primary ending of mammalian muscle spindle.

Fig 2

A simplified feed-forward model for mechanotransduction. The extension stimulus exerts tension onto the receptor muscle fibres, described by a viscoelastic model (adapted from Swerup & Rydqvist, 1996). The tension is then transduced into a receptor current by stochastic sampling of a large population of mechanosensitive channels (MSCs).

Fig 3

(A) Viscoelastic model used to represent receptor muscle (Swerup & Rydqvist, 1996). Total extension is the sum of that from both linear (left-hand-side spring in A) and non-linear springs (right-hand-side spring in A). The spring constant of the non-linear spring is k  = k₂ × εⁿ. (B) General form of the ramp-and-hold extension. ε₀ is extension before ramp, t₁ is the end of extension rising phase, α is rate of rise, t₂ and t₃ define the falling phase of the ramp, β is the rate of fall.

Fig 4

Tension (left panel), tension-induced-current (right panel) responses to ramp-and-hold extensions of a crayfish slowly adapting stretch receptor, and the model simulation outputs. (A) Recorded responses from a slowly adapting stretch receptor in response to ramp-and-hold extensions (1500% s⁻¹) of 3–30% of muscle length (D). (B) Model-simulated responses (Swerup & Rydqvist, 1996). (C) Model-simulated responses (present model). An adaptive ramp amplification factor was added to the model of Swerup & Rydqvist (1996) to produce the tension profiles in (C, left). Stochastic sampling of MSCs was implemented to produce the tension-induced-current profiles (C, right). MSC opening duration, latency and refractory period were all uniformly distributed, with their respective maximum values listed in Table1. Interestingly, compared with channel opening times and latencies, refractory periods are much shorter. In fact, a ‘0 ms’ refractory period can produce equally good results (data not shown), indicating that a two-MSC state model (open and closed) can already take account of the slowly-adapting stretch receptor’s response dynamics. Other parameters used are listed in Table1. (D) Ramp-and-hold extension stimuli. Results are normalized, as the focus of the paper is not to fine-tune the parameters to reproduce the response absolute amplitude values, but only the temporal dynamics.

Fig 5

Stochastic sampling from a population of refractory units produces fast adaptation dynamics in a fly photoreceptor’s light-induced current (A and B) and initial peak dynamic component in a mammalian muscle spindle’s tension-induced-current (D). In a fly photoreceptor, at the onset of a bright light stimulus, all microvilli are sensitive to respond, inducing a sharp increase in the response. But as the microvilli become refractory, fewer and fewer are available to sample the next coming photons, resulting in a sharp decrease in the number of activated microvilli (B), and hence a fast adaptation dynamics in the light-induced current response (A). In a mammalian muscle spindle primary ending, ramp-and-hold extension stimulus (E) evokes rich dynamics in the receptor potential (C). Although for better comparison with the model outputs it is best to use patch-clamped recording of the stimuli-induced ionic flow, as there were no such data available in the literature for mechanotransduction, we showed the receptor potential as a sub-optimal substitute in (C). With such a comparison, at least one can see the dynamic components in the receptor potential that can already be produced with the stochastic adaptive sampling framework. The multiple dynamical components in the response are likely the combined results of biophysical mechanisms from different sources. A large adaptive ramp amplification factor (r = 10) is needed to produce the dynamic component 3 in (C), characterized by a small plateau on top of the tension profile (the small plateau in f replicates the dynamic component 3 in C). Otherwise, the tension profiles would look like that shown in Fig.4C, left, i.e. sharp peaks are produced without the small plateau. Unlike the fly photoreceptor microvilli, the refractory period of MSCs in a mammalian muscle spindle is much shorter, compared with its own open time. As a result, stochastic sampling from a population of refractory MSCs introduces the extra peak of the initial dynamic component (D replicates component 2 in C). In comparison, the stochastic sampling from refractory microvilli in a fly photoreceptor produces the post-dynamic minimum. In this particular simulation, the post-dynamic minimum (component 4 in C) is not produced in the tension-induced-current response.

Fig 6

Stochastic sampling from a population of refractory mechanosensitive channels (MSCs) can produce ‘sensory habituation’ in a mechanoreceptor’s tension-induced-current profile, i.e. the first episode of response is larger than the second (A). Two episodes of the same extension pattern were applied sequentially to stimulate the modelled muscle spindle (C), evoking two episodes of same tension responses (B). However, the first episode of tension-induced-current response is larger than the second. The mechanisms underlying this ‘sensory habituation’ are still a mystery. Here, stochastic sampling from a population of refractory MSCs can reproduce to some extent the ‘sensory habituation’ effect. The reason is because while many MSCs are still refractory from responding to the first episode of stimulus, fewer MSCs are left to respond to the second episode of stimulus.