Trachtenberg Shlomo, Fishelov Dalia, Ben-Artzi Matania
Department of Membrane and Ultrastructure Research, The Hebrew University-Hadassah Medical School, Jerusalem 91120, Israel.
Biophys J. 2003 Sep;85(3):1345-57. doi: 10.1016/S0006-3495(03)74569-X.
The flagellar filament, the bacterial organelle of motility, is the smallest rotary propeller known. It consists of 1), a basal body (part of which is the proton driven rotary motor), 2), a hook (universal joint-allowing for off-axial transmission of rotary motion), and 3), a filament (propeller-a long, rigid, supercoiled helical assembly allowing for the conversion of rotary motion into linear thrust). Helically perturbed (so-called "complex") filaments have a coarse surface composed of deep grooves and ridges following the three-start helical lines. These surface structures, reminiscent of a turbine or Archimedean screw, originate from symmetry reduction along the six-start helical lines due to dimerization of the flagellin monomers from which the filament self assembles. Using high-resolution electron microscopy and helical image reconstruction methods, we calculated three-dimensional density maps of the complex filament of Rhizobium lupini H13-3 and determined its surface pattern and boundaries. The helical symmetry of the filament allows viewing it as a stack of identical slices spaced axially and rotated by constant increments. Here we use the closed outlines of these slices to explore, in two dimensions, the hydrodynamic effect of the turbine-like boundaries of the flagellar filament. In particular, we try to determine if, and under what conditions, transitions from laminar to turbulent flow (or perturbations of the laminar flow) may occur on or near the surface of the bacterial propeller. To address these questions, we apply the boundary element method in a manner allowing the handling of convoluted boundaries. We tested the method on several simple, well-characterized cylindrical structures before applying it to real, highly convoluted biological surfaces and to simplified mechanical analogs. Our results indicate that under extreme structural and functional conditions, and at low Reynolds numbers, a deviation from laminar flow might occur on the flagellar surface. These transitions, and the conditions enabling them, may affect flagellar polymorphism and the formation and dispersion of flagellar bundles-factors important in the chemotactic response.
鞭毛丝作为细菌的运动细胞器，是已知最小的旋转推进器。它由三部分组成：1）基体（其中一部分是质子驱动的旋转马达）；2）钩形结构（万向节，用于非轴向传递旋转运动）；3）鞭毛丝（推进器——一个长的、刚性的、超螺旋的螺旋组件，可将旋转运动转化为线性推力）。螺旋状扰动的（所谓“复杂”）鞭毛丝具有粗糙的表面，该表面由沿着三起始螺旋线的深沟和脊组成。这些表面结构让人联想到涡轮机或阿基米德螺旋，它们源于鞭毛蛋白单体二聚化导致的沿六起始螺旋线的对称性降低，而鞭毛丝正是由这些鞭毛蛋白单体自组装而成。我们使用高分辨率电子显微镜和螺旋图像重建方法，计算了 Lupinus lupini H13 - 3 根瘤菌复杂鞭毛丝的三维密度图，并确定了其表面模式和边界。鞭毛丝的螺旋对称性使其可以看作是一系列沿轴向间隔且以恒定增量旋转的相同切片的堆叠。在此，我们利用这些切片的封闭轮廓在二维空间中探究鞭毛丝涡轮状边界的流体动力学效应。特别地，我们试图确定在细菌推进器表面或其附近是否会发生以及在何种条件下会发生从层流到湍流的转变（或层流的扰动）。为了解决这些问题，我们以一种能够处理复杂边界的方式应用边界元法。在将该方法应用于真实的、高度复杂的生物表面和简化的机械类似物之前，我们先在几个简单的、特征明确的圆柱形结构上对其进行了测试。我们的结果表明，在极端的结构和功能条件下以及低雷诺数时，鞭毛表面可能会出现层流偏差。这些转变及其发生条件可能会影响鞭毛多态性以及鞭毛束的形成和分散，而这些因素在趋化反应中很重要。
