18 research outputs found
Network development in biological gels: role in lymphatic vessel development
In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model
The long-time dynamics of two hydrodynamically-coupled swimming cells
Swimming micro-organisms such as bacteria or spermatozoa are typically found
in dense suspensions, and exhibit collective modes of locomotion qualitatively
different from that displayed by isolated cells. In the dilute limit where
fluid-mediated interactions can be treated rigorously, the long-time
hydrodynamics of a collection of cells result from interactions with many other
cells, and as such typically eludes an analytical approach. Here we consider
the only case where such problem can be treated rigorously analytically, namely
when the cells have spatially confined trajectories, such as the spermatozoa of
some marine invertebrates. We consider two spherical cells swimming, when
isolated, with arbitrary circular trajectories, and derive the long-time
kinematics of their relative locomotion. We show that in the dilute limit where
the cells are much further away than their size, and the size of their circular
motion, a separation of time scale occurs between a fast (intrinsic) swimming
time, and a slow time where hydrodynamic interactions lead to change in the
relative position and orientation of the swimmers. We perform a multiple-scale
analysis and derive the effective dynamical system - of dimension two -
describing the long-time behavior of the pair of cells. We show that the system
displays one type of equilibrium, and two types of rotational equilibrium, all
of which are found to be unstable. A detailed mathematical analysis of the
dynamical systems further allows us to show that only two cell-cell behaviors
are possible in the limit of , either the cells are attracted to
each other (possibly monotonically), or they are repelled (possibly
monotonically as well), which we confirm with numerical computations
Possible origins of macroscopic left-right asymmetry in organisms
I consider the microscopic mechanisms by which a particular left-right (L/R)
asymmetry is generated at the organism level from the microscopic handedness of
cytoskeletal molecules. In light of a fundamental symmetry principle, the
typical pattern-formation mechanisms of diffusion plus regulation cannot
implement the "right-hand rule"; at the microscopic level, the cell's
cytoskeleton of chiral filaments seems always to be involved, usually in
collective states driven by polymerization forces or molecular motors. It seems
particularly easy for handedness to emerge in a shear or rotation in the
background of an effectively two-dimensional system, such as the cell membrane
or a layer of cells, as this requires no pre-existing axis apart from the layer
normal. I detail a scenario involving actin/myosin layers in snails and in C.
elegans, and also one about the microtubule layer in plant cells. I also survey
the other examples that I am aware of, such as the emergence of handedness such
as the emergence of handedness in neurons, in eukaryote cell motility, and in
non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue.
Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in
Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec
Motor-Driven Bacterial Flagella and Buckling Instabilities
Many types of bacteria swim by rotating a bundle of helical filaments also
called flagella. Each filament is driven by a rotary motor and a very flexible
hook transmits the motor torque to the filament. We model it by discretizing
Kirchhoff's elastic-rod theory and develop a coarse-grained approach for
driving the helical filament by a motor torque. A rotating flagellum generates
a thrust force, which pushes the cell body forward and which increases with the
motor torque. We fix the rotating flagellum in space and show that it buckles
under the thrust force at a critical motor torque. Buckling becomes visible as
a supercritical Hopf bifurcation in the thrust force. A second buckling
transition occurs at an even higher motor torque. We attach the flagellum to a
spherical cell body and also observe the first buckling transition during
locomotion. By changing the size of the cell body, we vary the necessary thrust
force and thereby obtain a characteristic relation between the critical thrust
force and motor torque. We present a sophisticated analytical model for the
buckling transition based on a helical rod which quantitatively reproduces the
critical force-torque relation. Real values for motor torque, cell body size,
and the geometry of the helical filament suggest that buckling should occur in
single bacterial flagella. We also find that the orientation of pulling
flagella along the driving torque is not stable and comment on the biological
relevance for marine bacteria.Comment: 15 pages, 11 figure
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Twirling, whirling, and overwhirling revisited: Viscous dynamics of rotating filaments and ribbons
When an initially straight filament is immersed in a viscous fluid and rotated at one end, the fluid resists the rotational motion and causes a buildup of twist in the object. At a critical turning frequency, the object buckles due to the elastic stresses in the material. While this instability has been extensively studied over the past 25 years, these analyses have focused narrowly on filaments with circular cross sections near the onset of the instability. Here we explore the phase diagram for twirling filaments as a function of cross-sectional aspect ratio and rotational frequency. We find a large range of dynamic behaviors and even find that while filaments with circular cross sections transition directly from twirling to overwhirling, ribbonlike objects undergo a twirl-to-whirl transition, similar to what was originally predicted for rodlike objects. We show that the linear stability for rotating ribbons is equivalent to first order to that of cylindrical filaments. Hysteresis is also common, suggesting that there are multiple stable states in these systems. Finally, by comparing simulations using resistive force theory to immersed boundary methods, we identify the reason that these two methods have historically not agreed on the value of the critical turning frequency. © 2022 American Physical Society.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]
Ballistic motion of spirochete membrane proteins
Abstract only