Extrusion of transmitter, water and ions generates forces to close fusion pore

During exocytosis the fusion pore opens rapidly, then dilates gradually, and may subsequently close completely, but what controls its dynamics is not well understood. In this study we focus our attention on forces acting on the pore wall, and which are generated solely by the passage of transmitter, ions and water through the open fusion pore. The transport through the charged cylindrical nano-size pore is simulated using a coupled system of Poisson-Nernst-Planck and Navier-Stokes equations and the forces that act radially on the wall of the fusion pore are then estimated. Four forces are considered: a) inertial force, b) pressure, c) viscotic force, and d) electrostatic force. The inertial and viscotic forces are small, but the electrostatic force and the pressure are typically significant. High vesicular pressure tends to open the fusion pore, but the pressure induced by the transport of charged particles (glutamate, ions), which is predominant when the pore wall charge density is high tends to close the pore. The electrostatic force, which also depends on the charge density on the pore wall, is weakly repulsive before the pore dilates, but becomes attractive and pronounced as the pore dilates. Given that the vesicular concentration of free transmitter can change rapidly due to the release, or owing to the dissociation from the gel matrix, we evaluated how much and how rapidly a change of the vesicular K⁺-glutamate⁻ concentration affects the concentration of glutamate⁻ and ions in the pore and how such changes alter the radial force on the wall of the fusion pore. A step-like rise of the vesicular K⁺-glutamate⁻ concentration leads to a chain of events. Pore concentration (and efflux) of both K⁺ and glutamate⁻ rise reaching their new steady-state values in less than 100 ns. Interestingly within a similar time interval the pore concentration of Na⁺ also rises, whereas that of Cl⁻ diminishes, although their extra-cellular concentration does not change. Finally such changes affect also the water movement. Water efflux changes bi-phasically, first increasing before decreasing to a new, but lower steady-state value. Nevertheless, even under such conditions an overall approximate neutrality of the pore is maintained remarkably well, and the electrostatic, but also inertial, viscotic and pressure forces acting on the pore wall remain constant. In conclusion the extrusion of the vesicular content generates forces, primarily the force due to the electro-kinetically induced pressure and electrostatic force (both influenced by the pore radius and even more by the charge density on the pore wall), which tend to close the fusion pore.     

Glutamate, water and ion transport through a charged nanosize pore

The transport of transmitter, ions and water through a positively-charged nanopore was investigated through computer simulations. The physics of the problem is described by a coupled set of Poisson-Nernst-Planck and Navier-Stokes equations in a computational domain consisting a cylindrical pore, whose radius ranged from 1 to 8 nm and which was flanked by two compartments representing the vesicular interior and extra-cellular space. The concentration of co-ions is suppressed and of counter-ions enhanced, especially near the pore wall owing to electrostatic interactions. Glutamate (i.e. the transmitter considered) is negatively charged and is simulated as a counter-ion. The electro-kinetically induced pressure due to the movement of ions is negative and very pronounced near the pore wall where the concentration and flux of counter-ions is very high. The water velocity peaks in the pore center, diminishes to zero at the pore wall, but is constant along the pore axis. The mean velocity of the water/fluid is proportional to the vesicular pressure and pore cross-sectional area. Interestingly it is inversely related to the vesicular glutamate concentration. The factors determining the glutamate flux are complex. The diffusive flux generally predominates for narrow pore, and convective flux may dominate for wide pore if the vesicular pressure is high. Surprisingly at low vesicular pressure the mean total glutamate flux per unit cross-sectional pore area is higher for narrow pores. Higher flux is probably due to the rise of glutamate concentration in the nanopore, which is much more pronounced for narrow nanopores, due to the maintenance of approximate neutrality of charges in the pore and on the pore wall. In conclusion intra-vesicular pressure helps ‘flushing-out’ the transmitter, but the induced pressure ‘drags-out’ the water into the extra-cellular space.     

Forces and stresses acting on fusion pore membrane during secretion

To assess the forces and stresses present in fusion pore during secretion the stationary convective flux of lipid through a fusion pore connecting two planar membranes under different tensions was investigated through computer simulations. The physics of the problem is described by Navier-Stokes equations, and the convective flux of lipid was evaluated using finite element method. Each of the membrane monolayer is considered separately as an isotropic, homogeneous and incompressible viscous medium with the same viscosity. The difference in membrane tensions, which is simulated as the pressure difference at two ends of each monolayer, is the driving force of the lipid flow. The two monolayers interact by sliding past each other with inter-monolayer frictional viscosity. Fluid velocity, pressure, shear and normal stresses, viscous and frictional dissipations and forces were calculated to evaluate where the fusion pore will deform, extend (or compress) and dilate. The pressure changes little in the planar sections, whereas in the toroidal section the change is rapid. The magnitude of lipid velocity peaks at the pore neck. The radial lipid velocity is zero at the neck, has two peaks one on each side of the pore neck, and diminishes without going to zero in planar parts of two monolayers. The peaks are of opposite signs due to the change of direction of lipid flow. The axial velocity is confined to the toroidal section, peaks at the neck and is clearly greater in the outer monolayer. As a result of the spatially highly uneven lipid flow the membrane is under a significant stress, shear and normal. The shear stress, which indicates where the membrane will deform without changing the volume, has two peaks placed symmetrically about the neck. The normal stress shows where the membrane may extend or compress. Both, the radial and axial normal stresses are negative (extensive) in the upper toroidal section and positive (compressive) in the lower toroidal section. The pressure difference determines lipid velocity and velocity dependent variables (shear as well as normal axial and radial stresses), but also contributes directly to the force on the membranes and critically influences where and to what extent the membrane will deform, extend or dilate. The viscosity coefficient (due to friction of one element of lipid against neighboring ones), and frictional coefficient (due to friction between two monolayers sliding past each other) further modulate some variables. Lipid velocity rises as pressure difference increases, diminishes as the viscosity coefficient rises but is unaffected by the frictional coefficient. The shear and normal stresses rise as pressure difference increases, but the change of the viscosity coefficients has no effect. Both the viscous dissipation (which has two peaks placed symmetrically about the neck) and much smaller frictional dissipation (which peaks at the pore neck) rise with pressure and diminish if the viscosity coefficient rises, but only the frictional dissipation increases if the frictional coefficient increases. Finally, the radial force causing pore dilatation, and which is significant only in the planar section of the vesicular membrane, is governed almost entirely by the pressure, whereas the viscosity and frictional coefficients have only a marginal effect. Many variables are altered during pore dilatation. The lipid velocity and dissipations (viscous and frictional) rise approximately linearly with pore radius, whereas the lipid mass flow increases supra-linearly owing to the combined effects of the changes in pore radius and greater lipid velocity. Interestingly the radial force on the vesicular membrane increases only marginally.     

Aerodynamic Interactions Between Wing and Body of a Model Insect in Forward Flight and Maneuvers

The aerodynamic interactions between the body and the wings of a model insect in forward flight and maneuvers are studied using the method of numerically solving the Navier-Stokes equations over moving overset grids. Three cases are considered, including a complete insect, wing pair only and body only. By comparing the results of these cases, the interaction effect between the body and the wing pair can be identified. The changes in the force and moment coefficients of the wing pair due to the presence of the body are less than 4.5% of the mean vertical force coefficient of the model insect; the changes in the aerodynamic force coefficients of the body due to the presence of the wings are less than 5.0% of the mean vertical force coefficient of the model insect. The results of this paper indicate that in studying the aerodynamics and flight dynamics of a flapping insect in forward flight or maneuver, separately computing (or measuring) the aerodynamic forces and moments on the wing pair and on the body could be a good approximation.     

Effect of Cambering on the Aerodynamic Performance of Heaving Airfoils

In the present work,a parametric numerical study is conducted in order to assess the effect of airfoil cambering on theaerodynamic performance of rigid heaving airfoils.The incompressible Navier-Stokes equations are solved in their velocity-pressureformulation using a second-order accurate in space and time finite-difference scheme.To tackle the problem ofmoving boundaries,the governing equations are solved on overlapping structured grids.The numerical simulations are performedat a Reynolds number of Re=1100 and at different values of Strouhal number and reduced frequency.The resultsobtained show that the airfoil cambering geometric parameter has a strong influence on the average lift coefficient,while it hasa smaller impact on the average thrust coefficient and propulsive efficiency of heaving airfoils.