A mathematical model of the Pacinian corpuscle

This article describes a mathematical model of the Pacinian corpuscle based on the analysis of the available experimental data and on previous theoretical research. The model includes the main anatomofunctional constituents of the corpuscle: the capsula and the mechano-to-neural transduction; its structure accounts for the formation of the receptor potential and of the spikes on the nerve terminal. Comparison of the theoretical predictions with the experimental results, in response to different types of stimuli provides a substantial validation of the model and an explanation for the basic aspects of the transduction, in particular for: a) the receptor potential time course for isolated stimuli; b) the frequency response, in terms of receptor potential ;c) the frequency threshold curve for the spikes; d) the firing rate, I.S.I. and P.S.T. histograms and the synchronization coefficient, in response to sustained sinusoidal inputs. Possible lines for future experimental research are suggested from the model predictions.     

A Pacinian corpuscle in the human bladder lamina propria

The fortuitous finding of a complex Pacinian corpuscle within the lamina propria of the human urinary bladder is described. It consisted of a complex of encapsulated nerve endings within the areolar connective tissue of the lamina propria immediately adjacent to the inner aspect of the detrusor muscle. It showed no structural evidence of directional sensitivity and was associated on its outer aspect with small unmyelinated axons containing small clear and dense-cored vesicles. This appears to be the first report of an encapsulated nerve ending within the lining of the adult human urinary bladder.     

Micropipette aspiration of the Pacinian corpuscle

The Pacinian corpuscle (PC) is a cutaneous mechanoreceptor sensitive to high-frequency vibrations (20–1000 Hz). The PC is of importance due to its integral role in somatosensation and the critical need to understand PC function for haptic feedback system development. Previous theoretical and computational studies have modeled the physiological response of the PC to sustained or vibrating mechanical stimuli, but they have used estimates of the receptor’s mechanical properties, which remain largely unmeasured. In this study, we used micropipette aspiration (MPA) to determine an apparent Young’s modulus for PCs isolated from a cadaveric human hand. MPA was applied in increments of 5 mm H₂O (49 Pa), and the change in protrusion length of the PC into the pipette was recorded. The protrusion length vs. suction pressure data were used to calculate the apparent Young’s modulus. Using 10 PCs with long-axis lengths of 2.99 ± 0.41 mm and short-axis lengths of 1.45 ± 0.22 mm, we calculated a Young’s modulus of 1.40 ± 0.86 kPa. Our measurement is on the same order of magnitude as those approximated in previous models, which estimated the PC to be on the same order of magnitude as skin or isolated cells, so we recommend that a modulus in the kPa range be used in future studies.     

The sites for mechano-electric conversion in a Pacinian corpuscle

The sensory nerve ending in the Pacinian corpuscle is surrounded by a non-nervous capsular structure which occupies about 99.9 per cent of the corpuscle's entire mass. After extirpation of practically all of the non-nervous structure, the sense organ's remains continue to function as a mechano-receptor, namely to produce generator and all-or-nothing potentials in response to mechanical stimuli. Compression of the first intracorpuscular node of Ranvier abolishes the production of "all-or-nothing" potentials in the corpuscle. Graded generator potentials constitute then the only response to mechanical stimulation. This reveals that the first node is the site of origin of the all-or-nothing potential and that the non-myelinated ending is incapable of producing all-or-nothing responses in response to mechanical stimulation. Compression of the entire length of non-myelinated ending suppresses the production of generator potentials. Partial compression of the ending abolishes mechano-responsiveness only of the compressed part. The intact remains of the ending continue to give generator potentials upon mechanical stimulation. This suggests that the generator potential arises at functionally independent membrane parts distributed all over the non-myelinated nerve ending. 24 to 36 hours after denervation of the corpuscle by transection of its sensory axon, no sign of electric activity is detected. Failure of mechano-reception at the nerve ending precedes that of conduction at the degenerating myelinated axon.     

Immunocytochemical identification of proteins within the Pacinian corpuscle

Light- and electron-microscopic immunocytochemistry (ICC) was performed on Pacinian corpuscles (PCs) obtained from cat mesentery to determine the presence and location of various proteins within the accessory capsule and the neurite. Antibodies to tubulin, neurofilament 200, actin, collagen II and V, glial fibrillary acidic protein (GFAP) and S-100 were used. Type II collagen was localized only in the outer core of the accessory capsule, which is composed of an inner core, an intermediate layer or growth zone, an outer core and an external capsule. Type V collagen was found only in the intermediate growth zone. Intermediate filaments labeled with anti-GFAP were only found in the inner core. The calcium-binding protein that was labeled by anti-S-100 was found only in the inner core. Diffuse and variable staining for actin is present throughout the accessory capsule. The differences in distribution of these various proteins within the capsule suggest different structural/functional properties of the various capsule regions. The neurite was found to contain microtubules (i.e., tubulin) and neurofilaments throughout, but these cellular inclusions were not found within the cytoplasmic extensions (filopodia) that project from the neurite into the hemilamellar clefts formed by the inner-core hemilamellae. The extensions, however, were found to contain actin in a much greater density than that seen in the neurite proper. The presence of actin, but apparent lack of other cytostructural elements within the extensions, is highly reminiscent of the composition of stereocilia found on vestibular and auditory hair cells. Since stereocilia have been shown to play a role in hair-cell mechanotransduction, it is possible that the cytoplasmic extensions are significantly involved with mechanotransduction within the PC.     

Immunocytochemical identification of proteins within the Pacinian corpuscle

Light- and electron-microscopic immunocytochemistry (ICC) was performed on Pacinian corpuscles (PCs) obtained from cat mesentery to determine the presence and location of various proteins within the accessory capsule and the neurite. Antibodies to tubulin, neurofilament 200, actin, collagen II and V, glial fibrillary acidic protein (GFAP) and S-100 were used. Type II collagen was localized only in the outer core of the accessory capsule, which is composed of an inner core, an intermediate layer or growth zone, an outer core and an external capsule. Type V collagen was found only in the intermediate growth zone. Intermediate filaments labeled with anti-GFAP were only found in the inner core. The calcium-binding protein that was labeled by anti-S-100 was found only in the inner core. Diffuse and variable staining for actin is present throughout the accessory capsule. The differences in distribution of these various proteins within the capsule suggest different structural/functional properties of the various capsule regions. The neurite was found to contain microtubules (i.e., tubulin) and neurofilaments throughout, but these cellular inclusions were not found within the cytoplasmic extensions (filopodia) that project from the neurite into the hemilamellar clefts formed by the inner-core hemilamellae. The extensions, however, were found to contain actin in a much greater density than that seen in the neurite proper. The presence of actin, but apparent lack of other cytostructural elements within the extensions, is highly reminiscent of the composition of stereocilia found on vestibular and auditory hair cells. Since stereocilia have been shown to play a role in hair-cell mechanotransduction, it is possible that the cytoplasmic extensions are significantly involved with mechanotransduction within the PC.     

Identification of the Ruffini corpuscle in human hairy skin

Summary A Ruffini corpuscle was identified in the dense reticular dermis of the human scalp from a patient with alopecia areata. The corpuscle measured approximately 50 m in diameter. One afferent myelinated axon with a diameter of 4–6 m supplies the corpuscle. Branched axon terminals and the associated Schwann cells tightly envelop parallel bundles of collagen fibrils. Axon terminals evidenced focal swellings, and small finger-like protrusions projected into the endoneural connective tissue. The terminals are characterized by the presence of abundant mitochondria, numerous vesicles, particles of glycogen and electron-opaque lipid material. A thin perineural capsule envelops the bundles of collagen fibrils and associated terminals. The present study provides the first electron-microscopic characterization of a Ruffini corpuscle in human hairy skin.This study was supported in part by the Deutsche ForschungsgemeinschaftSupported in part by U.S. Public Health Service Research Contracts NIDR72-2401 and HD4-2869 and Research Grant HD 11216     

Study of individual Pacinian corpuscle mechanoreceptors following application of colchicine to a nerve]

Colchicine application to the cat caudal mesenteric nerve containing sensory fibers for single mechanoreceptors (Pacinian corpuscles) causes degeneration of the axis cast of the nerve endings. Ultrastructural changes in the receptors showed no difference from the axonal degeneration after the nerve section but the rate of degeneration was considerably slower. Ultrastructural, electrophysiological, and biochemical changes occurring in the Pacinian corpuscles were not the result of direct action of colchicine, but appeared to be realized through the nerve by the axoplasmic transport block. It is suggested that the receptor's structure is under the sensory neuron neurotrophic control.     

A transduction model of the Meissner corpuscle

I propose a transduction model of the Meissner corpuscle that integrates ideas put forth by Freeman and Johnson and results obtained by Looft. The principal development in the present model is its specification that RA receptor potentials are updated as a linear function of stimulus velocity above baseline; the model thus readily accommodates non-sinusoidal input. It also incorporates modifications to Freeman and Johnson's model proposed by Slavík and Bell, namely a period of refractoriness lasting 1 ms followed by a period of hyperexcitability lasting 13.5 ms. The model is applied to various psychophysical and physiological situations: psychophysical threshold vs. frequency, RA afferent impulse rates vs. intensity, impulse regularity vs. frequency, phase retardation vs. frequency, and responses to non-repeating noise and to complex stimuli. Model output closely matches psychophysical and neurophysiological data. The proposed model thus reliably predicts RA afferent responses to arbitrary stimuli and may facilitate the development of theories relating psychophysical phenomena to their underlying neural representations.     

Protein kinase C (alpha, beta, gamma) in Pacinian corpuscle.

Immunocytochemical demonstration of protein kinase C (PKC) subspecies (alpha, beta, gamma) was carried out in Pacinian corpuscles of rat hind feet using monoclonal or polyclonal antibodies against each of these subspecies. The inner core cells and lamellae and the Schwann cell cytoplasm of the nerve fiber innervating the corpuscle were strongly positive for PKC alpha-immunoreactivity (IR). In contrast, the axon terminal and the outer core did not display any positive alpha-IR. Very weak PKC beta-IR was detected in the ultraterminal region of the axon terminal, while the trunk region showed no immunoreactivity. Very faint PKC beta-IR was found also in the lamellar cells located at the periphery of the inner core and the endoneurial fibroblasts in the intermediate layer. PKC gamma-IR was not detected in any part of the corpuscle. The strong PKC alpha-IR in the inner core and the presence or absence of PKC alpha-, beta-, and gamma-IR in the axon terminal are discussed from the point of view of the functional aspects of each part.     

Ovoid geometry of the Pacinian corpuscle is not the determining factor for mechanical excitation

Static displacements in Pacinian corpuscles (PCs) were measured using video microscopy. Mechanical stimuli of 10–40?µm steps were applied to the PC capsule surfaces using cylindrical contactors with different diameters. Displacements parallel to the stimulation axis were measured at various locations in the focal plane of the optical setup. In contrast to previous data in the literature, the displacements within the corpuscle were found to be linearly related to the indentation amplitude. Displacements decreased as a function of lamella depth, with a more negative slope close to the surface and less negative slope at deeper locations. The experimental data were compared to the predictions of a previous mechanical model, and to the results of two new models: () elastic semi-infinite continuum model; () ovoid isotropic finite-element model. Although the previous model did not specify displacement boundary conditions, it predicted the current experimental results well. On the other hand, the experimental displacements were found to be smaller than those predicted by the semi-infinite continuum and finite-element models. However, both semi-infinite continuum and finite-element models yielded close results, which show that the three-dimensional ovoid geometry of the corpuscle is not the primary factor for determining the displacements in physiological conditions. Furthermore, simulations with the finite-element model using a wide range of material properties yielded similar results. This supports the hypothesis that a homogeneous isotropic model for the PC cannot predict experimental results. The modeling analyses suggest that the experimental results are largely affected by the displacement of the incompressible interlamellar fluid and the layered structure of the corpuscle.     

Ovoid geometry of the Pacinian corpuscle is not the determining factor for mechanical excitation

Static displacements in Pacinian corpuscles (PCs) were measured using video microscopy. Mechanical stimuli of 10-40 microm steps were applied to the PC capsule surfaces using cylindrical contacts with different diameters. Displacements parallel to the stimulation axis were measured at various locations in the focal plane of the optical setup. In contrast to previous data in the literature, the displacements within the corpuscle were found to be linearly related to the indentation amplitude. Displacements decreased as a function of lamella depth, with a more negative slope close to the surface and less negative slope at deeper locations. The experimental data were compared to the predictions of a previous mechanical model, and to the results of two new models: (1) elastic semi-infinite continuum model; (2) ovoid isotropic finite-element model. Although the previous model did not specify displacement boundary conditions, it predicted the current experimental results well. On the other hand, the experimental displacements were found to be smaller than those predicted by the semi-infinite continuum and finite-element models. However, both semi-infinite continuum and finite-element models yielded close results, which show that the three-dimensional ovoid geometry of the corpuscle is not the primary factor for determining the displacements in physiological conditions. Furthermore, simulations with the finite-element model using a wide range of material properties yielded similar results. This supports the hypothesis that a homogeneous isotropic model for the PC cannot predict experimental results. The modeling analyses suggest that the experimental results are largely affected by the displacement of the incompressible interlamellar fluid and the layered structure of the corpuscle.     

Analysis of the mechanism of amplitude change in Pacinian corpuscle receptor potential in a solution with a decreased calcium ion concentration

The effect of Ca2+-free solution on the amplitude increase in the receptor potential (RP) of Pacinian corpuscles was studied using external perfusion technique. The RP amplitude increased in Ca2+-free solution. It was blocked after addition of 10-20 mM of tetraethylamonium. A temporary increase in the RP amplitude is seen in the solution with 0.2 mM of 2.4-dinitrophenol. Sensitivity of the receptor membrane to mechanical stimuli does not change in Ca2+-free solution. It is suggested that near the mechanosensitive ionic canal of Pacinian corpuscle receptor membrane the fixed negative charges which could influence the "gate" system state of the mechanosensitive canal are absent.     

A finite-element model of tracheal collapse

The trachea has been approximated by an appropriate finite-element model. The three-dimensional equilibrium problems set by the tracheal deformation under various stresses have been solved using a convenient augmented Lagrangian functional. The dimensions were obtained from human tracheae. Mechanical constants for the anatomic components were calculated from the stress-strain relationships. The compressive narrowing is essentially due to the invagination of the posterior membrane in the tracheal lumen for transmural pressures down to -7 kPa. A surface of contact between the membranous wall and the lateral walls appears when the transmural pressure equals -6 kPa. The transmural pressure-area relationship is sigmoidal with a compliance equal to 0.08 kPa-1 for a transmural pressure of -2 kPa. The tracheal collapse is greater when the material constants of the membranous wall decrease or when the tracheal segment is subjected to a longitudinal tension. A slight flexion of the trachea induces an asymmetric deformation.