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.     

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.     

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 living cells

The mechanical behavior of living cells is studied with micropipette suction in which the surface of a cell is aspirated into a small glass tube while tracking the leading edge of its surface. Such edges can be tracked in a light microscope to an accuracy of +/-25 nm and suction pressures as small as 0.1-0.2 pN/microm2 can be imposed on the cell. Both soft cells, such as neutrophils and red cells, and more rigid cells, such as chondrocytes and endothelial cells, are studied with this technique. Interpretation of the measurements with basic continuum models leads to values for a cell's elastic and viscous properties. In particular, neutrophils are found to behave as a liquid drop with a cortical (surface) tension of about 30 pN/microm and a viscosity on the order of 100 Pa s. On the other hand, chondrocytes and endothelial cells behave as solids with an elastic modulus of the order of 500 pN/microm2 (0.5 kPa).     

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.     

Micropipette aspiration on the outer hair cell lateral wall

The mechanical properties of the lateral wall of the guinea pig cochlear outer hair cell were studied using the micropipette aspiration technique. A fire-polished micropipette with an inner diameter of approximately 4 microm was brought into contact with the lateral wall and negative pressure was applied. The resulting deformation of the lateral wall was recorded on videotape and subjected to morphometric analysis. The relation between the length of the aspirated portion of the cell and aspiration pressure is characterized by the stiffness parameter, K(s) = 1.07 +/- 0.24 (SD) dyn/cm (n = 14). Values of K(s) do not correlate with the original cell length, which ranges from 29 to 74 microm. Theoretical analysis based on elastic shell theory applied to the experimental data yields an estimate of the effective elastic shear modulus, mu = 15.4 +/- 3.3 dyn/cm. These data were obtained at subcritical aspiration pressures, typically less than 10 cm H2O. After reaching a critical (vesiculation) pressure, the cytoplasmic membrane appeared to separate from the underlying structures, a vesicle with a length of 10-20 microm was formed, and the cytoplasmic membrane resealed. This vesiculation process was repeated until a cell-specific limit was reached and no more vesicles were formed. Over 20 vesicles were formed from the longest cells in the experiment.     

A finite-element model of mechanosensation by a Pacinian corpuscle cluster in human skin

The Pacinian corpuscle (PC) is the cutaneous mechanoreceptor responsible for sensation of high-frequency (20–1000 Hz) vibrations. PCs lie deep within the skin, often in multicorpuscle clusters with overlapping receptive fields. We developed a finite-element mechanical model of one or two PCs embedded within human skin, coupled to a multiphysics PC model to simulate action potentials elicited by each PC. A vibration was applied to the skin surface, and the resulting mechanical signal was analyzed using two metrics: the deformation amplitude ratio (\({\rho }_{\mathrm{1S}} \), \({\rho }_{\mathrm{2S}} )\) and the phase shift of the vibration (\({\delta }_{\mathrm{S}1}^{\mathrm{mech}} \), \({\delta }_{\mathrm{S}2}^{\mathrm{mech}} )\) between the stimulus and the PC. Our results showed that the amplitude attenuation and phase shift at a PC increased with distance from the stimulus to the PC. Differences in amplitude (\(\rho _{12} )\) and phase shift (\({\delta }_{12}^{\mathrm{mech}} )\) between the two PCs in simulated clusters directly affected the interspike interval between the action potentials elicited by each PC (\({\delta }_{12}^{\mathrm{spike}} )\). While \({\delta }_{12}^{\mathrm{mech}} \) had a linear relationship with \({\delta }_{12}^{\mathrm{spike}} \), \(\rho _{12} \)’s effect on \({\delta }_{12}^{\mathrm{spike}} \) was greater for lower values of \(\rho _{12} \). In our simulations, the separation between PCs and the distance of each PC from the stimulus location resulted in differences in amplitude and phase shift at each PC that caused \({\delta }_{12}^{\mathrm{spike}} \) to vary with PC location. Our results suggest that PCs within a cluster receive different mechanical stimuli which may enhance source localization of vibrotactile stimuli, drawing parallels to sound localization in binaural hearing.     

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.     

Micropipette aspiration method for characterizing biological materials with surface energy

Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration method to measure the mechanical properties of soft tissues and cells with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is taken into account by the finite element method. It is found that when the pipette radius or aspiration length is comparable to the elastocapillary length, surface energy may distinctly alter the aspiration response. Generally, both the aspiration length and the bulk normal stress decrease with increasing surface energy, and thus neglecting the surface energy would lead to an overestimation of elastic modulus. Through dimensional analysis and numerical simulations, we provide an explicit relation between the imposed pressure and the aspiration length. This method can be applied to determine the mechanical properties of soft biological tissues and organs, e.g., livers, tumors and embryos.     

Investigation of the optimal shape of the nerve ending of the encapsulated tissue mechanoreceptor (Pacinian corpuscle)

It is shown on the basis of simple physical principles that the parameters determining the shape of the nerve ending of the Pacinian corpuscle are optimal.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Research Institute of Applied Mathematics and Cybernetics, N. I. Lobachevskii Gor'kii State University. Translated from Neirofiziologiya, Vol. 9, No. 4, pp. 423–429, July–August, 1977.