Computational Algorithms and Experiments for Biological Elastic Filaments and Spiroplasma Motility

Abstract

Many interesting problems in biology involve dynamic filaments and ribbons in low Reynolds environments. However, biological thin filaments with relatively small bend and twist moduli, make the accuracy of models describing filament dynamics challenging especially when considering thermal forces, buckling, and anisotropic bend moduli. Here, to address modeling accuracy, we develop an algorithm using the finite volume approach for simulating the dynamics of thin filaments. We then evaluate our algorithm using several previously solved test cases of isotropic filaments in low Reynolds environments, while also providing further insight into modified versions of these test cases. Next, we expand upon one of the previous test cases to examine the dynamics of thin filaments and ribbons undergoing rotation about the long axis while clamped at one end. When rotated fast enough, these initially straight filaments become unstable, causing them to buckle and writhe. The behavior of this simple experiment had been previously reported in detail for isotropic, circular cross-section filaments undergoing rotation rates very near the initial point of instability. Also, one computational study which included fluid flow hydrodynamics, found that these filaments became unstable at a much lower rotation rate than that which was found using other methods. Our work here describes, i.) the dynamics and thrust of a range of rotating anisotropic, ribbon-like filaments, ii.) the dynamics of filaments being rotated at a rate which is much higher than the initial unstable rotation rate, and iii.) the possible cause behind the discrepancy between the hydrodynamic computational analysis and other studies regarding this unstable rotation rate. And finally, we investigate the motility of a bacterium called Spiroplasma. Spiroplasma is the only known genus of bacterium which swims in fluids without the use of flagella or cell wall. Instead, Spiroplasma use only a cytoskeletal motility mechanism. Little is known of this unique bacterium's motility including its constitutive properties and how force and torque are translated from its cytoskeleton to the cell membrane. In this study, we directly measure the bend and twist moduli of Spiroplasma using an optical trap. Using this information, we simulate its motility finding that, at biologically relevant lengths and viscosities, Spiroplasma forms plectonemes, a shape which occurs when the elastic twist energy causes a filament to writhe and form a loop with itself. We then verify this behavior using microscopy and, using the nature of these plectonemes, describe a possible mechanism for force and torque translation to the membrane.