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The motion of a freely rotating prolate spheroid in a simple shear flow of a dilute polymeric solution is examined in the limit of large particle aspect ratio,$$\kappa$$. A regular perturbation expansion in the polymer concentration,$$c$$, a generalized reciprocal theorem, and slender body theory to represent the velocity field of a Newtonian fluid around the spheroid are used to obtain the$$O(c)$$correction to the particle's orientational dynamics. The resulting dynamical system predicts a range of orientational behaviours qualitatively dependent upon$$c\, De$$($$De$$is the imposed shear rate times the polymer relaxation time) and$$\kappa$$and quantitatively on$$c$$. At a small but finite$$c\, De$$, the particle spirals towards a limit cycle near the vorticity axis for all initial conditions. Upon increasing$$\kappa$$, the limit cycle becomes smaller. Thus, ultimately the particle undergoes a periodic motion around and at a small angle from the vorticity axis. At moderate$$c\, De$$, a particle starting near the flow–gradient plane departs it monotonically instead of spirally, as this plane (a limit cycle at smaller$$c\, De$$) obtains a saddle and an unstable node. The former is close to the flow direction. Upon further increasing$$c\, De$$, the saddle node changes to a stable node. Therefore, depending upon the initial condition, a particle may either approach a periodic orbit near the vorticity axis or obtain a stable orientation near the flow direction. Upon further increasing$$c\, De$$, the limit cycle near the vorticity axis vanishes, and the particle aligns with the flow direction for all starting orientations. 

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L’Hopital’s rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner. The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results. 

The mechanosensitive (MS) channel of large conductance, MscL, is the high-tension threshold osmolyte release valve that limits turgor pressure in bacterial cells in the event of drastic hypoosmotic shock. Despite MscL from Mycobacterium tuberculosis (TbMscL) being the first structurally characterized MS channel, its protective mechanism of activation at nearly-lytic tensions has not been fully understood. Here, we describe atomistic simulations of expansion and opening of wild-type (WT) TbMscL in comparison with five of its gain-of-function (GOF) mutants. We show that under far-field membrane tension applied to the edge of the periodic simulation cell, WT TbMscL expands into a funnel-like structure with trans-membrane helices bent by nearly 70°, but does not break its ‘hydrophobic seal’ within extended 20 μs simulations. GOF mutants carrying hydrophilic substitutions in the hydrophobic gate of increasing severity (A20N, V21A, V21N, V21T and V21D) also quickly transition into funnel-shaped conformations but subsequently fully open within 1–8 μs. This shows that solvation of the de-wetted (vapor-locked) constriction is the rate-limiting step in the gating of TbMscL preceded by area-buffering silent expansion. Pre-solvated gates in these GOF mutants reduce this transition barrier according to hydrophilicity and the most severe V21D eliminates it. We predict that the asymmetric shape-change of the periplasmic side of the channel during the silent expansion provides strain-buffering to the outer leaflet thus re-distributing the tension to the inner leaflet, where the gate resides.