40 research outputs found
Modeling the Role of the Cell Cycle in Regulating Proteus mirabilis Swarm-Colony Development
We present models and computational results which indicate that the spatial
and temporal regularity seen in Proteus mirabilis swarm-colony development is
largely an expression of a sharp age of dedifferentiation in the cell cycle
from motile swarmer cells to immotile dividing cells (also called swimmer or
vegetative cells.) This contrasts strongly with reaction-diffusion models of
Proteus behavior that ignore or average out the age structure of the cell
population and instead use only density-dependent mechanisms. We argue the
necessity of retaining the explicit age structure, and suggest experiments that
may help determine the underlying mechanisms empirically. Consequently, we
advocate Proteus as a model organism for a multiscale understanding of how and
to what extent the life cycle of individual cells affects the macroscopic
behavior of a biological system
Models of Microbial Dormancy in Biofilms and Planktonic Cultures
We present models of dormancy in a planktonic culture and in biofilm, and
examine the relative advantage of short dormancy versus long dormancy times in
each case. Simulations and analyses indicate that in planktonic batch cultures
and in chemostats, live biomass is maximized by the fastest possible exit from
dormancy. The lower limit of time to reawakening is thus perhaps governed by
physiological, biochemical or other constraints within the cells. In biofilm we
see that the slower waker has a defensive advantage over the fast waker due to
a larger amount of dormant biomass, without an appreciable difference in total
live biomass. Thus it would seem that typical laboratory culture conditions can
be unrepresentative of the natural state. We discuss the computational methods
developed for this work
A Unified Term for Directed and Undirected Motility in Collective Cell Invasion
In this paper we develop mathematical models for collective cell motility.
Initially we develop a model using a linear diffusion-advection type equation
and fit the parameters to data from cell motility assays. This approach is
helpful in classifying the results of cell motility assay experiments. In
particular, this model can determine degrees of directed versus undirected
collective cell motility. Next we develop a model using a nonlinear diffusion
term that is able capture in a unified way directed and undirected collective
cell motility. Finally we apply the nonlinear diffusion approach to a problem
in tumor cell invasion, noting that neither chemotaxis or haptotaxis are
present in the system under consideration in this article
A Structured-Population Model of Proteus mirabilis Swarm-Colony Development
In this paper we present continuous age- and space-structured models and
numerical computations of Proteus mirabilis swarm-colony development. We base
the mathematical representation of the cell-cycle dynamics of Proteus mirabilis
on those developed by Esipov and Shapiro, which are the best understood aspects
of the system, and we make minimum assumptions about less-understood
mechanisms, such as precise forms of the spatial diffusion. The models in this
paper have explicit age-structure and, when solved numerically, display both
the temporal and spatial regularity seen in experiments, whereas the Esipov and
Shapiro model, when solved accurately, shows only the temporal regularity.
The composite hyperbolic-parabolic partial differential equations used to
model Proteus mirabilis swarm-colony development are relevant to other
biological systems where the spatial dynamics depend on local physiological
structure. We use computational methods designed for such systems, with known
convergence properties, to obtain the numerical results presented in this
paper
A Multiscale Model of Biofilm as a Senescence-Structured Fluid
We derive a physiologically structured multiscale model for biofilm
development. The model has components on two spatial scales, which induce
different time scales into the problem. The macroscopic behavior of the system
is modeled using growth-induced flow in a domain with a moving boundary.
Cell-level processes are incorporated into the model using a so-called
physiologically structured variable to represent cell senescence, which in turn
affects cell division and mortality. We present computational results for our
models which shed light on modeling the combined role senescence and the
biofilm state play in the defense strategy of bacteria
Modeling the Effects of Multiple Myeloma on Kidney Function
Multiple myeloma (MM), a plasma cell cancer, is associated with many health
challenges, including damage to the kidney by tubulointerstitial fibrosis. We
develop a mathematical model which captures the qualitative behavior of the
cell and protein populations involved. Specifically, we model the interaction
between cells in the proximal tubule of the kidney, free light chains, renal
fibroblasts, and myeloma cells. We analyze the model for steady-state solutions
to find a mathematically and biologically relevant stable steady-state
solution. This foundational model provides a representation of dynamics between
key populations in tubulointerstitial fibrosis that demonstrates how these
populations interact to affect patient prognosis in patients with MM and renal
impairment.Comment: Included version of model without tumor with steady-state analysis,
corrected equations for free light chains and renal fibroblasts in model with
tumor to reflect steady-state analysis, updated abstract, updated and added
reference
Computational Methods and Results for Structured Multiscale Models of Tumor Invasion
We present multiscale models of cancer tumor invasion with components at the
molecular, cellular, and tissue levels. We provide biological justifications
for the model components, present computational results from the model, and
discuss the scientific-computing methodology used to solve the model equations.
The models and methodology presented in this paper form the basis for
developing and treating increasingly complex, mechanistic models of tumor
invasion that will be more predictive and less phenomenological. Because many
of the features of the cancer models, such as taxis, aging and growth, are seen
in other biological systems, the models and methods discussed here also provide
a template for handling a broader range of biological problems
The Role of Osteocytes in Targeted Bone Remodeling: A Mathematical Model
Until recently many studies of bone remodeling at the cellular level have
focused on the behavior of mature osteoblasts and osteoclasts, and their
respective precursor cells, with the role of osteocytes and bone lining cells
left largely unexplored. This is particularly true with respect to the
mathematical modeling of bone remodeling. However, there is increasing evidence
that osteocytes play important roles in the cycle of targeted bone remodeling,
in serving as a significant source of RANKL to support osteoclastogenesis, and
in secreting the bone formation inhibitor sclerostin. Moreover, there is also
increasing interest in sclerostin, an osteocyte-secreted bone formation
inhibitor, and its role in regulating local response to changes in the bone
microenvironment. Here we develop a cell population model of bone remodeling
that includes the role of osteocytes, sclerostin, and allows for the
possibility of RANKL expression by osteocyte cell populations. This model
extends and complements many of the existing mathematical models for bone
remodeling but can be used to explore aspects of the process of bone remodeling
that were previously beyond the scope of prior modeling work. Through numerical
simulations we demonstrate that our model can be used to theoretically explore
many of the most recent experimental results for bone remodeling, and can be
utilized to assess the effects of novel bone-targeting agents on the bone
remodeling process
Towards a New Spatial Representation of Bone Remodeling
Irregular bone remodeling is associated with a number of bone diseases such
as osteoporosis and multiple myeloma.
Computational and mathematical modeling can aid in therapy and treatment as
well as understanding fundamental biology. Different approaches to modeling
give insight into different aspects of a phenomena so it is useful to have an
arsenal of various computational and mathematical models.
Here we develop a mathematical representation of bone remodeling that can
effectively describe many aspects of the complicated geometries and spatial
behavior observed.
There is a sharp interface between bone and marrow regions. Also the surface
of bone moves in and out, i.e. in the normal direction, due to remodeling.
Based on these observations we employ the use of a level-set function to
represent the spatial behavior of remodeling. We elaborate on a temporal model
for osteoclast and osteoblast population dynamics to determine the change in
bone mass which influences how the interface between bone and marrow changes.
We exhibit simulations based on our computational model that show the motion
of the interface between bone and marrow as a consequence of bone remodeling.
The simulations show that it is possible to capture spatial behavior of bone
remodeling in complicated geometries as they occur \emph{in vitro} and \emph{in
vivo}.
By employing the level set approach it is possible to develop computational
and mathematical representations of the spatial behavior of bone remodeling. By
including in this formalism further details, such as more complex cytokine
interactions and accurate parameter values, it is possible to obtain
simulations of phenomena related to bone remodeling with spatial behavior much
as \emph{in vitro} and \emph{in vivo}. This makes it possible to perform
\emph{in silica} experiments more closely resembling experimental observations.Comment: Math. Biosci. Eng., 9(2), 201