170 research outputs found
Selection in spatial stochastic models of cancer: Migration as a key modulator of fitness
<p>Abstract</p> <p>Background</p> <p>We study the selection dynamics in a heterogeneous spatial colony of cells. We use two spatial generalizations of the Moran process, which include cell divisions, death and migration. In the first model, migration is included explicitly as movement to a proximal location. In the second, migration is implicit, through the varied ability of cell types to place their offspring a distance away, in response to another cell's death.</p> <p>Results</p> <p>In both models, we find that migration has a direct positive impact on the ability of a single mutant cell to invade a pre-existing colony. Thus, a decrease in the growth potential can be compensated by an increase in cell migration. We further find that the neutral ridges (the set of all types with the invasion probability equal to that of the host cells) remain invariant under the increase of system size (for large system sizes), thus making the invasion probability a universal characteristic of the cells selection status. We find that repeated instances of large scale cell-death, such as might arise during therapeutic intervention or host response, strongly select for the migratory phenotype.</p> <p>Conclusions</p> <p>These models can help explain the many examples in the biological literature, where genes involved in cell's migratory and invasive machinery are also associated with increased cellular fitness, even though there is no known direct effect of these genes on the cellular reproduction. The models can also help to explain how chemotherapy may provide a selection mechanism for highly invasive phenotypes.</p> <p>Reviewers</p> <p>This article was reviewed by Marek Kimmel and Glenn Webb.</p
Quantum dot formation on a strain-patterned epitaxial thin film
We model the effect of substrate strain patterning on the self-assembly of quantum dots (QDs). When the surface energy is isotropic, we demonstrate that strain patterning via embedded substrate inclusions may result in ordered, self-organized QD arrays. However, for systems with strong cubic surface energy anisotropy, the same patterning does not readily lead to an ordered array of pyramids at long times. We conclude that the form of the surface energy anisotropy strongly influences the manner in which QDs self-assemble into regular arrays.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87827/2/133102_1.pd
Polymer-induced tubulation in lipid vesicles
A mechanism of extraction of tubular membranes from a lipid vesicle is
presented. A concentration gradient of anchoring amphiphilic polymers generates
tubes from bud-like vesicle protrusions. We explain this mechanism in the
framework of the Canham-Helfrich model. The energy profile is analytically
calculated and a tube with a fixed length, corresponding to an energy minimum,
is obtained in a certain regime of parameters. Further, using a phase-field
model, we corroborate these results numerically. We obtain the growth of tubes
when a polymer source is added, and the bud-like shape after removal of the
polymer source, in accordance with recent experimental results
Weak solutions to problems involving inviscid fluids
We consider an abstract functional-differential equation derived from the
pressure-less Euler system with variable coefficients that includes several
systems of partial differential equations arising in the fluid mechanics. Using
the method of convex integration we show the existence of infinitely many weak
solutions for prescribed initial data and kinetic energy
Critical dynamics of an isothermal compressible non-ideal fluid
A pure fluid at its critical point shows a dramatic slow-down in its
dynamics, due to a divergence of the order-parameter susceptibility and the
coefficient of heat transport. Under isothermal conditions, however, sound
waves provide the only possible relaxation mechanism for order-parameter
fluctuations. Here we study the critical dynamics of an isothermal,
compressible non-ideal fluid via scaling arguments and computer simulations of
the corresponding fluctuating hydrodynamics equations. We show that, below a
critical dimension of 4, the order-parameter dynamics of an isothermal fluid
effectively reduces to "model A," characterized by overdamped sound waves and a
divergent bulk viscosity. In contrast, the shear viscosity remains finite above
two dimensions. Possible applications of the model are discussed.Comment: 19 pages, 7 figures; v3: minor corrections and clarifications; as
published in Phys. Rev.
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