40 research outputs found
A continuous model for microtubule dynamics with catastrophe, rescue and nucleation processes
Microtubules are a major component of the cytoskeleton distinguished by
highly dynamic behavior both in vitro and in vivo. We propose a general
mathematical model that accounts for the growth, catastrophe, rescue and
nucleation processes in the polymerization of microtubules from tubulin dimers.
Our model is an extension of various mathematical models developed earlier
formulated in order to capture and unify the various aspects of tubulin
polymerization including the dynamic instability, growth of microtubules to
saturation, time-localized periods of nucleation and depolymerization as well
as synchronized oscillations exhibited by microtubules under various
experimental conditions. Our model, while attempting to use a minimal number of
adjustable parameters, covers a broad range of behaviors and has predictive
features discussed in the paper. We have analyzed the resultant behaviors of
the microtubules changing each of the parameter values at a time and observing
the emergence of various dynamical regimes.Comment: 25 pages, 12 figure
Modeling the Effects of Drug Binding on the Dynamic Instability of Microtubules
We propose a stochastic model that accounts for the growth, catastrophe and
rescue processes of steady state microtubules assembled from MAP-free tubulin.
Both experimentally and theoretically we study the perturbation of microtubule
dynamic instability by S-methyl-D-DM1, a synthetic derivative of the
microtubule-targeted agent maytansine and a potential anticancer agent. We find
that to be an effective suppressor of microtubule dynamics a drug must
primarily suppress the loss of GDP tubulin from the microtubule tip.Comment: 17 pages, 11 figures, to appear in Phys. Bio
A mathematical model quantifies proliferation and motility effects of TGF-- on cancer cells
Transforming growth factor (TGF) is known to have properties of both
a tumor suppressor and a tumor promoter. While it inhibits cell proliferation,
it also increases cell motility and decreases cell--cell adhesion. Coupling
mathematical modeling and experiments, we investigate the growth and motility
of oncogene--expressing human mammary epithelial cells under exposure to
TGF--. We use a version of the well--known Fisher--Kolmogorov equation,
and prescribe a procedure for its parametrization. We quantify the simultaneous
effects of TGF-- to increase the tendency of individual cells and cell
clusters to move randomly and to decrease overall population growth. We
demonstrate that in experiments with TGF-- treated cells \textit{in
vitro}, TGF-- increases cell motility by a factor of 2 and decreases
cell proliferation by a factor of 1/2 in comparison with untreated cells.Comment: 15 pages, 4 figures; to appear in Computational and Mathematical
Methods in Medicin
Semigroup analysis of structured parasite populations
Motivated by structured parasite populations in aquaculture we consider a
class of size-structured population models, where individuals may be recruited
into the population with distributed states at birth. The mathematical model
which describes the evolution of such a population is a first-order nonlinear
partial integro-differential equation of hyperbolic type. First, we use
positive perturbation arguments and utilise results from the spectral theory of
semigroups to establish conditions for the existence of a positive equilibrium
solution of our model. Then, we formulate conditions that guarantee that the
linearised system is governed by a positive quasicontraction semigroup on the
biologically relevant state space. We also show that the governing linear
semigroup is eventually compact, hence growth properties of the semigroup are
determined by the spectrum of its generator. In the case of a separable
fertility function, we deduce a characteristic equation, and investigate the
stability of equilibrium solutions in the general case using positive
perturbation arguments.Comment: to appear in Mathematical Modelling of Natural Phenomen
Structured and unstructured continuous models for Wolbachia infections
We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model
Protein Localization with Flexible DNA or RNA
Localization of activity is ubiquitous in life, and also within sub-cellular compartments. Localization provides potential advantages as different proteins involved in the same cellular process may supplement each other on a fast timescale. It might also prevent proteins from being active in other regions of the cell. However localization is at odds with the spreading of unbound molecules by diffusion. We model the cost and gain for specific enzyme activity using localization strategies based on binding to sites of intermediate specificity. While such bindings in themselves decrease the activity of the protein on its target site, they may increase protein activity if stochastic motion allows the acting protein to touch both the intermediate binding site and the specific site simultaneously. We discuss this strategy in view of recent suggestions on long non-coding RNA as a facilitator of localized activity of chromatin modifiers