Mechanical Deformability of Biological Membranes and the Sphering of the Erythrocyte

Equations of mechanical equilibrium are applied to the erythrocyte membrane in the normal, hypotonically swollen, and sphered configurations. The hydrostatic pressure drop across the normal cell membrane is shown to be zero for all biconcave shapes if the membrane thickness is uniform. This result leads to the conclusion that the membrane tension is uniform and is a function of membrane potential. A two-dimensional fluid film model for the membrane is introduced to describe the unusual deformability of the erythrocyte during sphering in hypotonic solutions. The model predicts a smooth transition from the biconcave shape to a perfect sphere.     

Detection of Cochlear Amplification and Its Activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.     

Detection of Cochlear Amplification and Its Activation

The operation of the mammalian cochlea relies on a mechanical traveling wave that is actively boosted by electromechanical forces in sensory outer hair cells (OHCs). This active cochlear amplifier produces the impressive sensitivity and frequency resolution of mammalian hearing. The cochlear amplifier has inspired scientists since its discovery in the 1970s, and is still not well understood. To explore cochlear electromechanics at the sensory cell/tissue interface, sound-evoked intracochlear pressure and extracellular voltage were measured using a recently developed dual-sensor with a microelectrode attached to a micro-pressure sensor. The resulting coincident in vivo observations of OHC electrical activity, pressure at the basilar membrane and basilar membrane displacement gave direct evidence for power amplification in the cochlea. Moreover, the results showed a phase shift of voltage relative to mechanical responses at frequencies slightly below the peak, near the onset of amplification. Based on the voltage-force relationship of isolated OHCs, the shift would give rise to effective OHC pumping forces within the traveling wave peak. Thus, the shift activates the cochlear amplifier, serving to localize and thus sharpen the frequency region of amplification. These results are the most concrete evidence for cochlear power amplification to date and support OHC somatic forces as its source.     

Noninvasive determination of perfused artery dimensions ex vivo using a pressure-diameter relationship

Based on the decisive effects of the hemodynamic and mechanical environments on the development and remodeling of arteries in vivo, several groups have cultured tissue-engineered vessels and excised vessels in various mechanically active perfusion systems. To facilitate the interpretation and design of such studies, accurate estimates of the applied forces and resulting stresses are required, which in turn require an accurate estimate of vessel dimensions. The measured pressure drop along the length of the vessel could be used to calculate the average inner diameter, but practical considerations, including the modest accuracy of many pressure transducers, limit this approach. Using nine porcine arteries harvested from pigs weighing between 25 and 100 kg, we show that when real-time measurements of the pressure drop and the outer diameter during a vasoactive event are fit to a theoretical model, offset errors in the pressure measurement can be compensated for and estimates of vessel wall transverse area with an average error of 4.1% (not exceeding 8.3%) are achieved.     

Role of turgor pressure in endocytosis in fission yeast

Yeast and other walled cells possess high internal turgor pressure that allows them to grow and survive in the environment. This turgor pressure, however, may oppose the invagination of the plasma membrane needed for endocytosis. Here we study the effects of turgor pressure on endocytosis in the fission yeast Schizosaccharomyces pombe by time-lapse imaging of individual endocytic sites. Decreasing effective turgor pressure by addition of sorbitol to the media significantly accelerates early steps in the endocytic process before actin assembly and membrane ingression but does not affect the velocity or depth of ingression of the endocytic pit in wild-type cells. Sorbitol also rescues endocytic ingression defects of certain endocytic mutants and of cells treated with a low dose of the actin inhibitor latrunculin A. Endocytosis proceeds after removal of the cell wall, suggesting that the cell wall does not contribute mechanically to this process. These studies suggest that endocytosis is governed by a mechanical balance between local actin-dependent inward forces and opposing forces from high internal turgor pressure on the plasma membrane.     

Use of inert gas jets to measure the forces required for mechanical gene transfection

ABSTRACT: BACKGROUND: Transferring genes and drugs into cells is central to how we now study, identify and treat diseases. Several non-viral gene therapy methods that rely on the mechanical disruption of the plasma membrane have been proposed, but the success of these methods has been limited due to a lack of understanding of the mechanical parameters that lead to cell membrane permeability. METHODS: We use a simple jet of inert gas to induce local transfection of plasmid DNA both in vitro (HeLa cells) and in vivo (chicken chorioallantoic membrane). Five different capillary tube inner diameters and three different gases were used to treat the cells to understand the dependency of transfection efficiency on the dynamic parameters. RESULTS: The simple setup has the advantage of allowing us to calculate the forces acting on cells during transfection. We found permeabilization efficiency was related to the dynamic pressure of the jet. The range of dynamic pressures that led to transfection in HeLa cells was small (200 +/- 20 Pa) above which cell stripping occurred. We determined that the temporary pores allow the passage of dextran up to 40 kDa and reclose in less than 5 seconds after treatment. The optimized parameters were also successfully tested in vivo using the chorioallantoic membrane of the chick embryo. CONCLUSIONS: The results show that the number of cells transfected with the plasmid scales with the dynamic pressure of the jet. Our results show that mechanical methods have a very small window in which cells are permeabilized without injury (200 to 290 Pa). This simple apparatus helps define the forces needed for physical cell transfection methods.     

Pressure drop increase by biofilm accumulation in spiral wound RO and NF membrane systems: role of substrate concentration,flow velocity,substrate load and flow direction

In an earlier study, it was shown that biofouling predominantly is a feed spacer channel problem. In this article, pressure drop development and biofilm accumulation in membrane fouling simulators have been studied without permeate production as a function of the process parameters substrate concentration, linear flow velocity, substrate load and flow direction. At the applied substrate concentration range, 100–400 μg l^?1 as acetate carbon, a higher concentration caused a faster and greater pressure drop increase and a greater accumulation of biomass. Within the range of linear flow velocities as applied in practice, a higher linear flow velocity resulted in a higher initial pressure drop in addition to a more rapid and greater pressure drop increase and biomass accumulation. Reduction of the linear flow velocity resulted in an instantaneous reduction of the pressure drop caused by the accumulated biomass, without changing the biofilm concentration. A higher substrate load (product of substrate concentration and flow velocity) was related to biomass accumulation. The effect of the same amount of accumulated biomass on the pressure drop increase was related to the linear flow velocity. A decrease of substrate load caused a gradual decline in time of both biomass concentration and pressure drop increase. It was concluded that the pressure drop increase over spiral wound reverse osmosis (RO) and nanofiltration (NF) membrane systems can be reduced by lowering both substrate load and linear flow velocity. There is a need for RO and NF systems with a low pressure drop increase irrespective of the biomass formation. Current efforts to control biofouling of spiral wound membranes focus in addition to pretreatment on membrane improvement. According to these authors, adaptation of the hydrodynamics, spacers and pressure vessel configuration offer promising alternatives. Additional approaches may be replacing heavily biofouled elements and flow direction reversal.     

Rheological analysis and measurement of neutrophil indentation

Aspects of neutrophil mechanical behavior relevant to the formation of adhesive contacts were assessed by measuring the dependence of the contact area between the cell and a spherical substrate under controlled loading. Micropipettes were used to bring neutrophils into contact with spherical beads under known forces, and the corresponding contact area was measured over time. The neutrophil was modeled as a viscous liquid drop with a constant cortical tension. Both the equilibrium state and the dynamics of the approach to equilibrium were examined. The equilibrium contact area increased monotonically with force in a manner consistent with a cell cortical tension of 16-24 pN/microm. The dynamic response matched predictions based on a model of the cell as a growing drop using published values for the effective viscosity of the cell. The contact pressure between the cell and substrate at equilibrium is predicted to depend on the curvature of the contacting substrate, but to be independent of the impingement force. The approach to equilibrium was rapid, such that the time-averaged stress for a two-second impingement was within 20% of the equilibrium value. These results have implications for the role of mechanical force in the formation of adhesive contacts.     

On the shape of the erythrocyte

A model is postulated which attributes the distinctive biconcave shape of the human erythrocyte to a balance of forces acting on the membrane. The forces considered are electrostatic forces due to a charge distribution on the membrane, a hydrostatic pressure difference acting across the membrane, and forces arising from a constant tension in the membrane. A numerical study indicates that the postulated model will produce an equilibrium shape which is very similar to the observed shape of the human erythrocyte.     

Effect of the stress phase angle on the strain energy density of the endothelial plasma membrane

Endothelial cells are simultaneously exposed to the mechanical forces of fluid wall shear stress (WSS) imposed by blood flow and solid circumferential stress (CS) induced by the blood vessel's elastic response to the pressure pulse. Experiments have demonstrated that these combined forces induce unique endothelial biomolecular responses that are not characteristic of either driving force alone and that the temporal phase angle between WSS and CS, referred to as the stress phase angle, modulates endothelial responses. In this article, we provide the first theoretical model to examine the combined forces of WSS and CS on a model of the endothelial cell plasma membrane. We focus on the strain energy density of the membrane that modulates the opening of ion channels that can mediate signal transduction. The model shows a significant influence of the stress phase angle on the strain energy density at the upstream and downstream ends of the cell where mechanotransduction is most likely to occur.     

Mechanosensitive Ca2+ release from intracellular stores in Nitella flexilis

We found previously that the cytoplasmic drop isolated from internodal cells of Nitella flexilis releases Ca2+ in response to hypotonic treatment and named the phenomenon hydration-induced Ca2+ release (HICR). The HICR is assumed to be a result of activation of Ca2+ permeable channels in the membrane of Ca2+ stores in a stretch-activated manner. To prove this idea, mechanical stimulus was applied to the drop by means of shooting isotonic/hypnotic medium or silicon oil into the drop, or compressing the drop. All these mechanical stimuli induced a rapid increase in the Ca2+ concentration of the drop. The chloroplast fraction isolated from the cytoplasmic drop released Ca2+ on compression, while the chloroplast-free cytoplasm did not. In Chara corallina, the cytoplasmic drop, which shows a very weak HICR, also responded weakly to the mechanical stimulus, but the chloroplast fraction was inert. When chloroplasts from Chara were added to the chloroplast-free cytoplasm of N. flexilis, the cytoplasm recovered the mechanoresponse. Starch grains were as effective as chloroplasts. The data indicate that Ca2+ permeable channels in the membrane of Ca2+ stores in N. flexilis are really mechano-sensitive.     

Plasma Membrane Mechanical Stress Activates TRPC5 Channels

Mechanical forces exerted on cells impose stress on the plasma membrane. Cells sense this stress and elicit a mechanoelectric transduction cascade that initiates compensatory mechanisms. Mechanosensitive ion channels in the plasma membrane are responsible for transducing the mechanical signals to electrical signals. However, the mechanisms underlying channel activation in response to mechanical stress remain incompletely understood. Transient Receptor Potential (TRP) channels serve essential functions in several sensory modalities. These channels can also participate in mechanotransduction by either being autonomously sensitive to mechanical perturbation or by coupling to other mechanosensory components of the cell. Here, we investigated the response of a TRP family member, TRPC5, to mechanical stress. Hypoosmolarity triggers Ca²⁺ influx and cationic conductance through TRPC5. Importantly, for the first time we were able to record the stretch-activated TRPC5 current at single-channel level. The activation threshold for TRPC5 was found to be 240 mOsm for hypoosmotic stress and between −20 and −40 mmHg for pressure applied to membrane patch. In addition, we found that disruption of actin filaments suppresses TRPC5 response to hypoosmotic stress and patch pipette pressure, but does not prevent the activation of TRPC5 by stretch-independent mechanisms, indicating that actin cytoskeleton is an essential transduction component that confers mechanosensitivity to TRPC5. In summary, our findings establish that TRPC5 can be activated at the single-channel level when mechanical stress on the cell reaches a certain threshold.     

Turgor pressure sensing in plant cell membranes

Experimental evidence is reviewed which shows that the cell membrane is compressible by both mechanical and electrical forces. Calculations are given which show that significant changes in the thickness of cell membranes can occur as a result of (a) direct compression due to the turgor pressure; (b) indirect effects due to the stretching of the cell wall; and (c) the stresses induced by the electric field in the membrane.     

The deformation of an adherent leukocyte under steady shear flow: a numerical study

Leukocyte adhesion is a pathophysiological process in which the balance between hemodynamic and adhesion forces (molecular bonds) plays a key role. In this work, we studied the deformation of an adherent leukocyte and calculated the forces exerted on it. Three model cells were proposed, considering the leukocyte as a single drop, a compound drop, and a nucleus drop, representing a cell without nucleus, a cell with a nucleus, and a nucleus only, respectively. These model cells were supposedly adherent to a smooth substrate under steady shear flow. Our numerical results showed that all three model cells deformed in function of the initial contact angle, capillary number, and Reynolds number. The single drop was the most deformable, while the nucleus drop was the most resistant to the external flow. Each of the model cells showed maximum cell deformation at a high Reynolds number. The distribution of pressure on the cell confirmed the existence of a high-pressure region downstream of the drop, which retarded further deformation of the cell and provided a positive lift force on the drop. The consideration of a highly viscous nucleus can correct the over evaluation of the cell deformation in a flow.     

Electrokinetic membrane processes in relation to properties of excitable tissues. I. Experiments on oscillatory transport phenomena in artificial membranes

An artificial system is studied consisting of salt solutions of different concentrations separated by a porous, "charged" membrane, through which a constant electric current is passed. Experiments on such systems demonstrate rhythmic variations of the transmembrane potential and the membrane resistance, which are concomitant with an oscillatory streaming of water solution across the membrane. The repetitive oscillations can be of a damped or undamped type dependent on the "stimulating" current density. A qualitative discussion of the mechanism of the oscillations is given. It centers around the periodic resistance changes in the membrane, which result from a complicated interplay between the driving forces present. The importance of electro-osmotic effects is emphasized. A few comparisons relating to possible electrophysiological implications are presented. In the metastable state of this membrane oscillator, "make" and "break" responses can be triggered by electric as well as by mechanical (pressure) "stimuli."     

The Gibbs-Duhem equation in membrane transport

It is argued that the Gibbs-Duhem equation alone cannot be used for deriving conclusions about the pressure gradient in membrane permeation. Statements regarding spatial variation of pressure in conjunction with chemical potential gradients of the components can legitimately be drawn from an equation that results from a combination of the G-D equation and the mechanical equilibrium equation. The derived equation has been applied here for explaining the mechanics of osmosis. In a further application, the frictional model has been improved here because the driving force also includes the membrane-solute potential interaction, thus allowing the solute partition coefficient to appear in the calculations naturally. By recognizing that because of the membrane-solution interaction, external forces of both potential and frictional character are present, the dissipation function is shown to depend explicitly on the centre-of-mass velocity. Thus the reference velocity for diffusive fluxes cannot be chosen arbitrarily, making Prigogine's theorem invalid in this approach to describing membrane permeation.     

The role of mechanical pressure difference in the generation of membrane voltage under conditions of concentration polarization

The mechanical pressure difference across the bacterial cellulose membrane located in a horizontal plane causes asymmetry of voltage measured between electrodes immersed in KCl solutions symmetrically on both sides of the membrane. For all measurements, KCl solution with lower concentration was above the membrane. In configuration of the analyzed membrane system, the concentration boundary layers (CBLs) are created only by molecular diffusion. The voltages measured in the membrane system in concentration polarization conditions were compared with suitable voltages obtained from the model of diffusion through CBLs and ion transport through the membrane. An increase of difference of mechanical pressure across the membrane directed as a difference of osmotic pressure always causes a decrease of voltage between the electrodes in the membrane system. In turn, for mechanical pressure difference across the membrane directed in an opposite direction to the difference of osmotic pressure, a peak in the voltage as a function of mechanical pressure difference is observed. An increase of osmotic pressure difference across the membrane at the initial moment causes an increase of the maximal value of the observed peak and a shift of this peak position in the direction of higher values of the mechanical pressure differences across the membrane.     

Concentration polarization phenomenon in the case of mechanical pressure difference on the membrane

We analyzed the transport of KCl solutions through the bacterial cellulose membrane and concentration boundary layers (CBLs) near membrane with pressure differences on the membrane. The membrane was located in horizontal-plane between two chambers with different KCL solutions. The membrane was located in horizontal-plane between two chambers with different KCL solutions. As results from the elaborated model, gradient of KCL concentration in CBLs is maximal at membrane surfaces in the case when pressure difference on the membrane equals zero. The amplitude of this maximum decreases with time of CBLs buildup. Application of mechanical pressure gradient in the direction of gradient of osmotic pressure on the membrane causes a shift of this maximum into the chamber with lower concentration. In turn, application of mechanical pressure gradient directed opposite to the gradient of osmotic pressure causes the appearance of maximum of concentration gradient in chamber with higher concentration. Besides, the increase of time of CBLs buildup entails a decrease of peak height and shift of this peak further from the membrane. Similar behavior is observed for distribution of energy dissipation in CBLs but for pressure difference on the membrane equal to zero the maximum of energy dissipation is observed in the chamber with lower concentration. We also measured time characteristics of voltage in the membrane system with greater KCl concentrations over the membrane. We can state that mechanical pressure difference on the membrane can suppress or strengthen hydrodynamic instabilities visible as pulsations of measured voltage. Additionally, time of appearance of voltage pulsations, its amplitude, and frequency depend on mechanical pressure differences on the membrane and initial quotient of KCl concentrations in chambers.     

A model of strain-dependent glomerular basement membrane maintenance and its potential ramifications in health and disease

A model is developed and analyzed for type IV collagen turnover in the kidney glomerular basement membrane (GBM), which is the primary structural element in the glomerular capillary wall. The model incorporates strain dependence in both deposition and removal of the GBM, leading to an equilibrium tissue strain at which deposition and removal are balanced. The GBM thickening decreases tissue strain per unit of transcapillary pressure drop according to the law of Laplace, but increases the transcapillary pressure drop required to maintain glomerular filtration. The model results are in agreement with the observed GBM alterations in Alport syndrome and thin basement membrane disease, and the model-predicted linear relation between the inverse capillary radius and inverse capillary thickness at equilibrium is consistent with published data on different mammals. In addition, the model predicts a minimum achievable strain in the GBM based on the geometry, properties, and mechanical environment; that is, an infinitely thick GBM would still experience a finite strain. Although the model assumptions would be invalid for an extremely thick GBM, the minimum achievable strain could be significant in diseases, such as Alport syndrome, characterized by focal GBM thickening. Finally, an examination of reasonable values for the model parameters suggests that the oncotic pressure drop-the osmotic pressure difference between the plasma and the filtrate due to large molecules-plays an important role in setting the GBM strain and, thus, leakage of protein into the urine may be protective against some GBM damage.