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Philos Trans A Math Phys Eng Sci,
2020]
Stokes flow, discussed by G.G. Stokes in 1851, describes many microscopic biological flow phenomena, including cilia-driven transport and flagellar motility; the need to quantify and understand these flows has motivated decades of mathematical and computational research. Regularized stokeslet methods, which have been used and refined over the past 20 years, offer significant advantages in simplicity of implementation, with a recent modification based on nearest-neighbour interpolation providing significant improvements in efficiency and accuracy. Moreover this method can be implemented with the majority of the computation taking place through built-in linear algebra, entailing that state-of-the-art hardware and software developments in the latter, in particular multicore and GPU computing, can be exploited through minimal modifications ('passive parallelism') to existing Matlab computer code. Hence, and with widely available GPU hardware, significant improvements in the efficiency of the regularized stokeslet method can be obtained. The approach is demonstrated through computational experiments on three model biological flows: undulatory propulsion of multiple <i>Caenorhabditis elegans</i>, simulation of progression and transport by multiple sperm in a geometrically confined region, and left-right symmetry breaking particle transport in the ventral node of the mouse embryo. In general an order-of-magnitude improvement in efficiency is observed. This development further widens the complexity of biological flow systems that are accessible without the need for extensive code development or specialist facilities. This article is part of the theme issue 'Stokes at 200 (part 2)'.
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J Gen Physiol,
2007]
MEC-4 and MEC-10 are the pore-forming subunits of the sensory mechanotransduction complex that mediates touch sensation in Caenorhabditis elegans (O''Hagan, R., M. Chalfie, and M.B. Goodman. 2005. Nat. Neurosci. 8:43-50). They are members of a large family of ion channel proteins, collectively termed DEG/ENaCs, which are expressed in epithelial cells and neurons. In Xenopus oocytes, MEC-4 can assemble into homomeric channels and coassemble with MEC-10 into heteromeric channels (Goodman, M.B., G.G. Ernstrom, D.S. Chelur, R. O''Hagan, C.A. Yao, and M. Chalfie. 2002. Nature. 415:1039-1042). To gain insight into the structure-function principles that govern gating and drug block, we analyzed the effect of gain-of-function mutations using a combination of two-electrode voltage clamp, single-channel recording, and outside-out macropatches. We found that mutation of A713, the d or degeneration position, to residues larger than cysteine increased macroscopic current, open probability, and open times in homomeric channels, suggesting that bulky residues at this position stabilize open states. Wild-type MEC-10 partially suppressed the effect of such mutations on macroscopic current, suggesting that subunit-subunit interactions regulate open probability. Additional support for this idea is derived from an analysis of macroscopic currents carried by single-mutant and double-mutant heteromeric channels. We also examined blockade by the diuretic amiloride and two related compounds. We found that mutation of A713 to threonine, glycine, or aspartate decreased the affinity of homomeric channels for amiloride. Unlike the increase in open probability, this effect was not related to size of the amino acid side chain, indicating that mutation at this site alters antagonist binding by an independent mechanism. Finally, we present evidence that amiloride block is diffusion limited in DEG/ENaC channels, suggesting that variations in amiloride affinity result from variations in binding energy as opposed to accessibility. We conclude that the d position is part of a key region in the channel functionally and structurally, possibly representing the beginning of a pore-forming domain.