Fig 1.
Sketch of the trypanosome model.
(A) Side view of a trypanosome with an inactive flagellum. Body discretization includes blue particles as well as partially orange particles, which represent the attachment of the flagellum to the body. (B) Flagellum model without a body constructed from four parallel filaments interconnected by springs. Orange particles and cyan springs represent two active filaments (also embedded into the body), which can generate bending deformation, while green particles correspond to the two passive filaments. (C) A swimming trypanosome driven by an active beating of the flagellum.
Fig 2.
Swimming characteristics of the trypanosome model as a function of the actuation amplitude ab and the wavelength .
(A) Swimming velocity v, (B) rotation frequency , (C) flagellum wave amplitude B0, and (D) flagellum wavelength
. Corresponding experimental measurements for T. brucei are indicated by horizontal green lines (average values) and shaded areas (standard deviation).
Fig 3.
Side-by-side comparison of T.brucei swimming from simulations (left) and experiments (right) over the duration of one full rotation around the swimming axis.
Table 1.
Trypanosome parameters in units of the trypanosome length Ltryp and the thermal energy kBT with the corresponding physical values.
Ntryp is the number of particles discretizing the trypanosome, f is the beating frequency, s0 is the distance between two cross-sectional segments of the flagellum, Rmax is the maximum radius of the body, K is the bending rigidity of the flagellum, is the shear modulus of the body, kA,glob, kA,loc, and
are the local area, global area, and volume constraint coefficients, and
is the bending rigidity of the body. In simulations, we have selected Ltryp = 30, kBT = 0.1, and f = 0.025.
Fig 4.
Parasite swimming properties for different sperm numbers.
(A) Swimming velocity v and (B) parasite rotation frequency as a function of sperm number Sp obtained from simulations. Three different parameters are varied, including fluid viscosity
, beating frequency f, and bending rigidity K of the flagellum (see S3V and S4V).
Fig 5.
Parasite swimming characteristics for different body stiffnesses.
(A) Swimming velocity v and rotation frequency and (B) flagellum wave amplitude B0 and wavelength
as a function of the body stiffness
. (C) Simulation snapshot of a bent trypanosome with a relatively soft body. (D) Experimental visualization of a banana-like trypanosome shape. See also S5V and S6V.
Fig 6.
Swimming properties of a trypanosome with non-uniform flagellum actuation.
(A) Experimental image of a trypanosome which illustrates an increasing wave amplitude toward the anterior end. The red lines mark B0 measurements, while the cyan segment represents the measurement of . (B) Trypanosome snapshot for a larger B0 at the anterior part in comparison with the posterior part. (C–E) Trypanosome model swimming characteristics for a uniform (
) and non-uniform (
and
) flagellum actuation along the flagellum length. (C) Swimming velocity v, (D) rotation frequency
, and (E) flagellum wave amplitude B0. See also S7V and S8V.
Fig 7.
Tangential versus normal beating plane of the flagellum.
For the tangential beating in (A), the active filaments are drawn in orange, while for the normal beating in (B), the active filaments are green. See S9V.
Fig 8.
Trypanosome model swimming characteristics with the flagellum beating tangential (circles) and normal (triangles) to the body surface as a function of bending stiffness K for two body stiffnesses .
(A) Swimming velocity v and (B) rotation frequency are shown.
Fig 9.
Effect of passive flagellum conformation on the swimming behavior.
(A) Simulation snapshot of an unactuated parasite with straight equilibrium state of the flagellum. (B–C) Trypanosome model swimming characteristics for a flagellum with bent (circles) and straight (squares) equilibrium states as a function of bending stiffness K for two body stiffnesses . (B) Swimming velocity v and (C) rotation frequency
are shown.