6 research outputs found
Toxin-mediated competition in weakly motile bacteria
Many bacterial species produce toxins that inhibit their competitors. We
model this phenomenon by extending classic two-species Lotka-Volterra
competition in one spatial dimension to incorporate toxin production by one
species. Considering solutions comprising two adjacent single-species colonies,
we show how the toxin inhibits the susceptible species near the interface
between the two colonies. Moreover, a sufficiently effective toxin inhibits the
susceptible species to such a degree that an `inhibition zone' is formed
separating the two colonies. In the special case of truly non-motile bacteria,
i.e. with zero bacterial diffusivity, we derive analytical expressions
describing the bacterial distributions and size of the inhibition zone. In the
more general case of weakly motile bacteria, i.e. small bacterial diffusivity,
these two-colony solutions become travelling waves. We employ numerical methods
to show that the wavespeed is dependent upon both interspecific competition and
toxin strength; precisely which colony expands at the expense of the other
depends upon the choice of parameter values. In particular, a sufficiently
effective toxin allows the producer to expand at the expense of the
susceptible, with a wavespeed magnitude that is bounded above as the toxin
strength increases. This asymptotic wavespeed is independent of interspecific
competition and due to the formation of the inhibition zone; when the colonies
are thus separated, there is no longer direct competition between the two
species and the producer can invade effectively unimpeded by its competitor. We
note that the minimum toxin strength required to produce an inhibition zone
increases rapidly with increasing bacterial diffusivity, suggesting that even
moderately motile bacteria must produce very strong toxins if they are to
benefit in this way
Mathematical Modelling of Embryonic Tissue Development. By Abdulaziz Rasheed Abdullah. May 2018
Appendix A: Matlab codes relating to the models that used in the thesis.
Appendix B: This Appendix illustrates how to install and deal with the Chaste
The interplay between bulk flow and boundary conditions on the distribution of microswimmers in channel flow
While previous experimental and numerical studies of dilute microswimmer suspensions have focused on the behaviours of swimmers in the bulk flow and near boundaries, models typically do not account for the interplay between bulk flow and the choice of boundary conditions imposed in continuum models. In our work, we highlight the effect of boundary conditions on the bulk flow distributions, such as through the development of boundary layers or secondary peaks of cell accumulation in bulk-flow swimmer dynamics. For the case of a dilute swimmer suspension in Poiseuille flow, we compare the distribution (in physical and orientation space) obtained from individual-based stochastic models with those from continuum models, and identify under what conditions it is mathematically sensible to use specific continuum boundary conditions to capture different physical scenarios (i.e. specular reflection, uniform random reflection and absorbing boundaries). We identify that the spread of preferred cell orientations is dependent on the interplay between rotation driven by the shear flow (Jeffery orbits) and rotational diffusion. We find that in the absence of hydrodynamic wall interactions, swimmers preferentially approach the walls perpendicular to the surface in the presence of high rotational diffusion, and that the preferential approach of swimmers to the walls is shape-dependent at low rotational diffusion (when suspensions tend towards a fully deterministic case). In the latter case, the preferred orientations are nearly parallel to the surface for elongated swimmers and nearly perpendicular to the surface for near-spherical swimmers. Furthermore, we highlight the effects of swimmer geometries and shear throughout the bulk-flow on swimmer trajectories and show how the full history of bulk-flow dynamics affects the orientation distributions of microswimmer wall incidence.</jats:p
The interplay between bulk flow and boundary conditions on the distribution of micro-swimmers in channel flow
While previous experimental and numerical studies of dilute microswimmer suspensions have focused on the behaviours of swimmers in the bulk flow and near boundaries, models typically do not account for the interplay between bulk flow and the choice of boundary conditions imposed in continuum models. In our work, we highlight the effect of boundary conditions on the bulk flow distributions, such as through the development of boundary layers or secondary peaks of cell accumulation in bulk-flow swimmer dynamics. For the case of a dilute swimmer suspension in Poiseuille flow, we compare the distribution (in physical and orientation space) obtained from individual-based stochastic models with those from continuum models, and identify under what conditions it is mathematically sensible to use specific continuum boundary conditions to capture different physical scenarios (i.e. specular reflection, uniform random reflection and absorbing boundaries). We identify that the spread of preferred cell orientations is dependent on the interplay between rotation driven by the shear flow (Jeffery orbits) and rotational diffusion. We find that in the absence of hydrodynamic wall interactions, swimmers preferentially approach the walls perpendicular to the surface in the presence of high rotational diffusion, and that the preferential approach of swimmers to the walls is shape-dependent at low rotational diffusion (when suspensions tend towards a fully deterministic case). In the latter case, the preferred orientations are nearly parallel to the surface for elongated swimmers and nearly perpendicular to the surface for near-spherical swimmers. Furthermore, we highlight the effects of swimmer geometries and shear throughout the bulk-flow on swimmer trajectories and show how the full history of bulk-flow dynamics affects the orientation distributions of microswimmer wall incidence.</jats:p
The interplay between bulk flow and boundary conditions on the distribution of micro-swimmers in channel flow
While previous experimental and numerical studies of dilute micro-swimmer
suspensions have focused on the behaviours of swimmers in the bulk flow and
near boundaries, models typically do not account for the interplay between bulk
flow and the choice of boundary conditions imposed in continuum models. In our
work, we highlight the effect of boundary conditions on the bulk flow
distributions, such as through the development of boundary layers or secondary
peaks of cell accumulation in bulk-flow swimmer dynamics. For the case of a
dilute swimmer suspension in Poiseuille flow, we compare the distribution (in
physical and orientation space) obtained from individual based stochastic
models with those from continuum models, and identify mathematically sensible
continuum boundary conditions for different physical scenarios (i.e. specular
reflection, uniform random reflection and absorbing boundaries). We identify
that the spread of preferred cell orientations is dependent on the interplay
between rotation driven by the shear flow (Jeffery orbits) and rotational
diffusion. We find that in the absence of hydrodynamic wall-interactions,
swimmers preferentially approach the walls perpendicular to the surface in the
presence of high rotational diffusion, and that the preferential approach of
swimmers to the walls is shape-dependent at low rotational diffusion (when
suspensions tend towards a fully deterministic case). In the latter case, the
preferred orientations are nearly parallel to the surface for elongated
swimmers and nearly perpendicular to the surface for near-spherical swimmers.
Furthermore, we highlight the effects of swimmer geometries and shear
throughout the bulk-flow on swimmer trajectories and show how the full history
of bulk-flow dynamics affects the orientation distributions of micro-swimmer
wall incidence