A structural constitutive model for the human lens capsule

Published data on the mechanical performance of the human lens capsule when tested under uniaxial and biaxial conditions are reviewed. It is concluded that two simple phenomenological constitutive models (namely a linear elastic model and a Fung-type hyperelastic model) are unable to provide satisfactory representations of the mechanical behaviour of the capsule for both of these loading conditions. The possibility of resolving these difficulties using a structural constitutive model for the capsule, of a form that is inspired by the network of collagen IV filaments that exist within the lens capsule, is explored. The model is implemented within a rectangular periodic cell. Prescribed stretches are imposed on the periodic cell and the network is allowed to deform in a non-affine manner. The performance of the constitutive model correlates well with previously published test data. One possible application of the model is in the development of a multi-scale analysis of the mechanics of the human lens capsule.     

A two-compartment phenomenological model of a dopaminergic neuron

A two-compartment model of a dopaminergic neuron based on modified FitzHugh-Nagumo oscillators for each compartment has been built. The compartments correspond to the soma and dendrites and differ in the values of small parameters. The influence of stimuli (imposed current for the soma compartment and synaptic activation for the dendrite compartment) on the model has been studied. Activation of AMPA and NMDA synaptic currents is shown to cause generation of high-frequency bursts by the neuron. The mechanisms underlying burst generation are considered.     

Structural correlates of mechanosensory transduction and adaptation in identified neurons of spider slit sensilla

We used isolated but functionally intact preparations of the lyriform slit-sense organ VS-3 from the leg of the spider, Cupiennius salei Keys, to examine the role of prominent fine-structural elements for mechanosensory transduction and adaptation. Slit sensilla act as strain sensors in the cuticular exoskeleton; each slit is innervated by two mechanosensitive neurons. Punctate mechanical deformation at four points along the dendrites demonstrated that mechanical excitability is confined to membrane sites at the extreme dendrite tips that are enclosed by cuticular slit structures. Depletion of microtubules in VS-3 neurons by prolonged mechanical stimulation and application of 5 mmol l(-1) colchicine did not disrupt the generation of a receptor potential. Hence, putative gating mechanisms of the mechanically activated membrane channels at the dendrite tips appear to be largely independent of microtubular structures. The discrete adaptation pattern in each of the two partner neurons, rapidly adapting versus slowly adapting, did not depend on the distinct mode of dendrite attachment to cuticular slit structures, and even persisted in isolated neurons after their dendrite tips and auxiliary structures were lost. We suggest that the two discrete adaptation patterns are based on intrinsic differences in the action potential encoding process rather than differences in stimulus transformation or mechanotransduction.     

Apical epidermal growth factor receptor signaling: regulation of stretch-dependent exocytosis in bladder umbrella cells

The apical surface of polarized epithelial cells receives input from mediators, growth factors, and mechanical stimuli. How these stimuli are coordinated to regulate complex cellular functions such as polarized membrane traffic is not understood. We analyzed the requirement for growth factor signaling and mechanical stimuli in umbrella cells, which line the mucosal surface of the bladder and dynamically insert and remove apical membrane in response to stretch. We observed that stretch-stimulated exocytosis required apical epidermal growth factor (EGF) receptor activation and that activation occurred in an autocrine manner downstream of heparin-binding EGF-like growth factor precursor cleavage. Long-term changes in apical exocytosis depended on protein synthesis, which occurred upon EGF receptor-dependent activation of mitogen-activated protein kinase signaling. Our results indicate a novel physiological role for the EGF receptor that couples upstream mechanical stimuli to downstream apical EGF receptor activation that may regulate apical surface area changes during bladder filling.     

The effects of microtubule dissociating agents on the physiology and cytology of the sensory neuron in the femoral tactile spine of the cockroach, periplaneta americana L

Microtubules are prominent cellular components of the mechanosensory and chemosensory sensilla associated with the insect cuticle, and a range of hypotheses have been proposed to account for their role in sensory transduction. Chemical agents such as colchicine and vinblastine, which dissociate microtubules, also interfere with transduction in these sensilla, and this has been attributed to their anti-microtubule activity. We have now examined the dynamic properties of sensory transduction in the mechanosensitive neuron of the cockroach femoral tactile spine, after the application of colchicine, vinblastine and lumicolchicine. Concurrently we have examined the ultrastructure of the same sensory ending by transmission electron microscopy. All of the drugs reduced the mechanical sensitivity o the receptor. Colchicine and vinblastine achieved this reduction without altering the dynamic properties of the receptor but lumicolchicine changed the dynamic response, and increased the relative sensitivity to rapid movements. Conduction velocity, another measure of neuronal function, which relies upon ionic currents flowing through the membrane, was reduced by all three drugs. The effects of the drugs upon the ultrastructure of the sensory ending were also disparate. In the case of colchicine there was complete dissociation of microtubules in the tubular body and distal dendrite before a total loss of mechanical sensitivity. Vinblastine was less effective in dissociating microtubules, although more effective in the reduction of mechanical sensitivity. With lumicolchicine the dominant morphological effect was a severe disruption of the dendritic membrane. We conclude from these experiments that microtubules are not essential in the transduction of mechanical stimuli by cuticular receptors and that the effects of these drugs upon mechanosensitivity are not directly related to their dissociation of the microtubules in the tubular body, but are more likely to arise from actions upon the cell membrane. These actions could include effects upon tubulin in the membrane or upon other membrane components.     

Electrical properties of the dendrite in an insect mechanoreceptor: Effects of antidromic or direct electrical stimulation

A study of the negative phase of the spikes recorded extra cellularly from insect mechanoreceptor has been performed in order to characterize some electrical properties of the dendrite which contains the transducing part of the sensory neuron. These properties have been investigated in mechanoreceptors of the metathoracic leg of the locust Schistocerca gregaria by firing antidromic action potentials both at rest and during mechanical or electrical stimulation. The amplitude of the negative phase of the spike appears to be correlated with the polarization of the dendritic membrane, although when bursts of action potentials are applied, the relation is more complex, including a depressive influence of a given spike on the following spike. The receptor potential and the antidromic dendritic spikes both originate in the same region of the dendrite but they involve different ionic processes. Our results indicate that the dendrite is electrically excitable. The spike which originates in the dendrite has an initial negative phase with a small superimposed positive component. A spike of this shape is never observed under natural stimulation. It is proposed that the negative phase of the antidromic impulse provides a suitable means for studying the variations in electrical polarization of the dendrite which cannot be recorded directly.     

Modeling the role of lateral membrane diffusion in AMPA receptor trafficking along a spiny dendrite

AMPA receptor trafficking in dendritic spines is emerging as a major postsynaptic mechanism for the expression of plasticity at glutamatergic synapses. AMPA receptors within a spine are in a continuous state of flux, being exchanged with local intracellular pools via exo/endocytosis and with the surrounding dendrite via lateral membrane diffusion. This suggests that one cannot treat a single spine in isolation. Here we present a model of AMPA receptor trafficking between multiple dendritic spines distributed along the surface of a dendrite. Receptors undergo lateral diffusion within the dendritic membrane, with each spine acting as a spatially localized trap where receptors can bind to scaffolding proteins or be internalized through endocytosis. Exocytosis of receptors occurs either at the soma or at sites local to dendritic spines via constitutive recycling from intracellular pools. We derive a reaction–diffusion equation for receptor trafficking that takes into account these various processes. Solutions of this equation allow us to calculate the distribution of synaptic receptor numbers across the population of spines, and hence determine how lateral diffusion contributes to the strength of a synapse. A number of specific results follow from our modeling and analysis. (1) Lateral membrane diffusion alone is insufficient as a mechanism for delivering AMPA receptors from the soma to distal dendrites. (2) A source of surface receptors at the soma tends to generate an exponential-like distribution of receptors along the dendrite, which has implications for synaptic democracy. (3) Diffusion mediates a heterosynaptic interaction between spines so that local changes in the constitutive recycling of AMPA receptors induce nonlocal changes in synaptic strength. On the other hand, structural changes in a spine following long term potentiation or depression have a purely local effect on synaptic strength. (4) A global change in the rates of AMPA receptor exo/endocytosis is unlikely to be the sole mechanism for homeostatic synaptic scaling. (5) The dynamics of AMPA receptor trafficking occurs on multiple timescales and varies according to spatial location along the dendrite. Understanding such dynamics is important when interpreting data from inactivation experiments that are used to infer the rate of relaxation to steady-state.     

Linear and nonlinear models of the basilar membrane motion

A linear and a nonlinear transmission line model of the basilar membrane is described. The motion of the basilar membrane model has been simulated by numerical methods and compared with physiological data for several types of sound stimuli. It is shown that a linear model exhibits a frequency modulation in its impulse response that is in accordance with physiological data. The nonlinear model displays a sharpened frequency response for lower sound intensities. Futhermore, a nonlinear model explains why hearing damage imposed by short, high-intensity, sounds is extended to the low-frequency regions of the cochlea.     

Investigating the effects of membrane deformability on artificial capsule adhesion to the functionalized surface

Understanding, manipulating and controlling cellular adhesion processes can be critical in developing biomedical technologies. Adhesive mechanisms can be used to the target, pattern and separate cells such as leukocytes from whole blood for biomedical applications. The deformability response of the cell directly affects the rolling and adhesion behavior under viscous linear shear flow conditions. To that end, the primary objective of the present study was to investigate numerically the influence of capsule membrane’s nonlinear material behavior (i.e. elastic-plastic to strain hardening) on the rolling and adhesion behavior of representative artificial capsules. Specifically, spherical capsules with radius of \(3.75\, \upmu \hbox {m}\) were represented using an elastic membrane governed by a Mooney–Rivlin strain energy functions. The surfaces of the capsules were coated with P-selectin glycoprotein-ligand-1 to initiate binding interaction with P-selectin-coated planar surface with density of \(150\,\upmu \hbox {m}^{-2}\) under linear shear flow varying from 100 to \(400\,\hbox {s}^{-1}\). The numerical model is based on the Immersed Boundary Method for rolling of deformable capsule in shear flow coupled with Monte Carlo simulation for receptor/ligand interaction modeled using Bell model. The results reveal that the mechanical properties of the capsule play an important role in the rolling behavior and the binding kinetics between the capsule contact surface and the substrate. The rolling behavior of the strain hardening capsules is relatively smoother and slower compared to the elastic-plastic capsules. The strain hardening capsules exhibits higher contact area at any given shear rate compared to elastic-plastic capsules. The increase in contact area leads to decrease in rolling velocity. The capsule contact surface is not in complete contact with the substrate because of thin lubrication film that is trapped between the capsule and substrate. This creates a concave shape on the bottom surface of the capsule that is referred to as a dimple. In addition, the present study demonstrates that the average total bond force from the capsules lifetime increases by 37 % for the strain hardening capsules compared to elastic-plastic capsules at shear rate of \(400\,\hbox {s}^{-1}\). Finally, the model demonstrates the effect of finite membrane deformation on the coupling between hydrodynamic and receptor/ligand interaction.     

The role of dendritic spine morphology in the compartmentalization and delivery of surface receptors

Since AMPA receptors are major molecular players in both short- and long-term plasticity, it is important to identify the time-scales of and factors affecting the lateral diffusion of AMPARs on the dendrite surface. Using a mathematical model, we study how the dendritic spine morphology affects two processes: (1) compartmentalization of the surface receptors in a single spine to retain local chemistry and (2) the delivery of receptors to the post-synaptic density (PSD) of spines via lateral diffusion following insertion onto the dendrite shaft. Computing the mean first passage time (MFPT) of surface receptors on a sample of real spine morphologies revealed that a constricted neck and bulbous head serve to compartmentalize receptors, consistent with previous works. The residence time of a Brownian diffusing receptor on the membrane of a single spine was computed to be ～ 5 s. We found that the location of the PSD corresponds to the location at which the maximum MFPT occurs, the position that maximizes the residence time of a diffusing receptor. Meanwhile, the same geometric features of the spine that compartmentalize receptors inhibit the recruitment of AMPARs via lateral diffusion from dendrite insertion sites. Spines with narrow necks will trap a smaller fraction of diffusing receptors in the their PSD when considering competition for receptors between the spines, suggesting that ideal geometrical features involve a tradeoff depending on the intent of compartmentalizing the current receptor pool or recruiting new AMPARs in the PSD. The ultimate distribution of receptors among the spine PSDs by lateral diffusion from the dendrite shaft is an interplay between the insertion location and the shape and locations of both the spines and their PSDs. The time-scale for delivery of receptors to the PSD of spines via lateral diffusion was computed to be ～ 60 s.     

Coding of odor intensity in a steady-state deterministic model of an olfactory receptor neuron

The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions are given for the three main physiological responses: (1) odorant-dependent conductance change at the sensory dendrite based on the Michaelis-Menten model, (2) generation and spreading of the receptor potential based on a new solution of the cable equation, and (3) firing frequency based on a Lapicque model. Second, the magnitudes of these responses are analyzed as a function of odorant concentration. Their dependence on chemical, electrical, and geometrical parameters is examined. The only evident gain in magnitude results from the activation-to-conductance conversion. An optimal encoder neuron is presented that suggests that increasing the length of the sensory dendrite beyond about 0.3 space constant does not increase the magnitude of the receptor potential. Third, the sensivities of the responses are examined as functions of (1) the concentration at half-maximum response, (2) the lower and upper concentrations actually discriminated, and (3) the width of the dynamic range. The overall gain in sensitivity results entirely from the conductance-to-voltage conversion. The maximum conductance at the sensory dendrite appears to be the main tuning constant of the neuron because it determines the shift toward low concentrations and the increase in dynamic range. The dynamic range of the model cannot exceed 5.7 log units, for a sensitivity increase at low odor concentration is compensated by a sensitivity decrease at high odor concentration.     

Ruffini Mechanoreceptors in Isolated Joint Capsule: Responses Correlated with Strain Energy Density

Mechanoreceptive afferents innervating the posterior capsule of the cat knee joint were recorded in a preparation of isolated capsule. The purpose of the experiments was to identify mechanical states in the capsule that were associated with afferent discharge. The capsule was excised from the knee with its bone attachments intact, so that the geometry of the capsule could be reproduced in vitro. The capsule was deformed, and measurements were made of stresses and strains in the plane of the capsule. Afferent discharge was correlated with each of the components of plane stress, plane strain, and strain energy density (SED). SED, the stored elastic energy at the receptor location, was the only mechanical variable that was consistently positively correlated with afferent discharge. A model of the Ruffini-type receptor is presented that accounts for the sensitivity to SED.     

Freeze-fracture study of the receptor membranes in the olfactory organ of Alburnus alburnus (Teleostei)

Summary Olfactory receptor molecules are assumed to be integral membrane proteins which may be visualized on fracture faces of the membrane as intramembrane particles (IMPs). In the present study, the plasma membrane of the receptor dendrites and ciliated epithelial cells in the teleost fish Alburnus alburnus were studied by freeze-fracture electron microscopy. The IMP diameters on the membrane P-faces of both receptor dendrites and ciliated epithelial cells ranged from 5 nm to 11 nm. The average IMP densities on membrane fracture faces of the ciliated and microvillous sensory dendrites were 3130±780 for the cilia, 2070±550 for the microvilli, 2390±1190 on the knob regions and 3050±1130/m on the lateral dendrite membranes. The IMP densities on the P fracture faces of the cilia and knob regions were compared with the densities found on the lateral membranes of each individual dendrite. The ratios ranged from 0.5 to 0.96 in the case of the cilia/lateral membrane and from 0.5 to 0.90 in that of the knob/lateral membrane, indicating that, in contrast to the average densities, it is the lateral membrane which has the higher IMP densities and not the cilia. The great variations in the average IMP densities, as well as the considerable variety of the ratios, may be explained by the maturation and turnover of the olfactory sensory neurons.     

Effects of Polarization of the Receptor Membrane and of the First Ranvier Node in a Sense Organ

It has previously been shown that the site of production of the generator potential in Pacinian corpuscles is the receptor membrane of the non-myelinated ending, and the site of initiation of the nerve impulse, the adjacent (first) Ranvier node. Effects of membrane polarization of these sites were studied in the present work. Nerve ending and first Ranvier node were isolated by dissection, electric activity was recorded from, and polarizing currents were passed through them. All observations were done at steady levels of polarization, seconds after onset of current flow. The following results were obtained: The amount of charge transferred through the excited receptor membrane is a function of the electrical gradients across the membrane. The generator potential in response to equal mechanical stimuli increases with resting potential of the receptor membrane. The refractory state of the generator potential is not affected by polarization. The electrical threshold for impulse firing at the first Ranvier node (measured by the minimal amplitude of generator potential which elicits a nodal impulse) is nearly minimal at normal resting potential of the node. Both, hyperpolarization and depolarization lead to a rise in nodal threshold. For any level of polarization of nodal and receptor membrane, the threshold for production of impulses by adequate (mechanical) stimulation appears determined by the generator potential-stimulus strength relation and by the electrical threshold of the node.     

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.     

Effects of Some Organic Cations on Generator Potential of Crayfish Stretch Receptor

The generator potential of both slowly and rapidly adapting crayfish stretch receptor cells can still be elicited by mechanical stimuli when all the Na of the bathing medium is replaced by various organic cations. In the presence of tris(hydroxymethyl)aminomethane (Tris), the generator potential is particularly large, about 30–50 % of that in the control saline, while spike electrogenesis of the cell is abolished. Persistence of the generator response is not due to retention of Na by a diffusion barrier, and ionic contributions to the electrogenesis by Ca and Cl can also be excluded. Thus, whereas the electrogenesis of the generator membrane must be due to an increased permeability to monovalent cations, the active receptor membrane appears to be less selective for different monovalent cations than is the receptor component of some other cells, or the conductile component of the stretch receptor neuron.     

A computational model for the transit of a cancer cell through a constricted microchannel

We propose a three-dimensional computational model to simulate the transient deformation of suspended cancer cells flowing through a constricted microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane, and its nucleus as a smaller stiffer capsule. The cell deformation and its interaction with the suspending fluid are solved through a well-tested immersed boundary lattice Boltzmann method. To identify a minimal mechanical model that can quantitatively predict the transient cell deformation in a constricted channel, we conduct extensive parametric studies of the effects of the rheology of the cell membrane, cytoplasm and nucleus and compare the results with a recent experiment conducted on human leukaemia cells. We find that excellent agreement with the experiment can be achieved by employing a viscoelastic cell membrane model with the membrane viscosity depending on its mode of deformation (shear versus elongation). The cell nucleus limits the overall deformation of the whole cell, and its effect increases with the nucleus size. The present computational model may be used to guide the design of microfluidic devices to sort cancer cells, or to inversely infer cell mechanical properties from their flow-induced deformation.