TY - JOUR
T1 - Modeling polymorphic transformation of rotating bacterial flagella in a viscous fluid
AU - Ko, William
AU - Lim, Sookkyung
AU - Lee, Wanho
AU - Kim, Yongsam
AU - Berg, Howard C.
AU - Peskin, Charles S.
N1 - Funding Information:
We thank Boyce Griffith for useful discussion. S.L. was supported by National Science Foundation Grant No. DMS-1410886 and the Charles Phelps Taft Research Center at University of Cincinnati, USA. Y.K. was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Grant No. 2015R1A2A2A01005420). W.L. was supported by the National Institute for Mathematical Sciences (NIMS) Grant funded by the Korean government (Grant No. A21300000). H.C.B. was supported by the U.S. National Institutes of Health (NIAID), the National Science Foundation (Physics of Living Systems), and the Rowland Institute at Harvard.
PY - 2017/6/14
Y1 - 2017/6/14
N2 - The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner, J. Bacteriol. 182, 2793 (2000)10.1128/JB.182.10.2793-2801.2000]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982)10.1016/0022-2836(82)90142-5]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.
AB - The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner, J. Bacteriol. 182, 2793 (2000)10.1128/JB.182.10.2793-2801.2000]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982)10.1016/0022-2836(82)90142-5]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.
UR - http://www.scopus.com/inward/record.url?scp=85020739953&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85020739953&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.95.063106
DO - 10.1103/PhysRevE.95.063106
M3 - Article
C2 - 28709256
AN - SCOPUS:85020739953
VL - 95
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
SN - 1063-651X
IS - 6
M1 - 063106
ER -