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The invasive capability is fundamental in determining the malignancy of a solid tumor.
Revealing biomedical strategies that are able to partially decrease cancer invasiveness is
therefore an important approach in the treatment of the disease and has given rise to
multiple in vitro and in silico models. We here develop
a hybrid computational framework, whose aim is to characterize the effects of the
different cellular and subcellular mechanisms involved...
The question, how does an organism maintain balance? provides a unifying theme to
introduce undergraduate students to the use of mathematics and modeling techniques in
biological research. The availability of inexpensive high speed motion capture cameras
makes it possible to collect the precise and reliable data that facilitates the
development of relevant mathematical models. An in–house laboratory component ensures that
students have the opportunity...
A growing body of literature testifies to the importance of quantitative reasoning skills
in the 21st-century biology curriculum, and to the learning benefits associated with
active pedagogies. The process of modeling a biological system provides an approach that
integrates mathematical skills and higher-order thinking with existing course content
knowledge. We describe a general strategy for teaching model-building in an introductory
biology course,...
Pharmacokinetics is an excellent way to introduce biomathematical modeling at the sophomore level. Students have the opportunity to develop a mathematical model of a biological phenomenon to which they all can relate. Exploring pharmacokinetics takes students through the necessary stages of mathematical modeling: determining the goals of the model, deciphering between the biological aspects to include in the model, defining the assumptions of the model, and finally, building, analyzing, using, and...
One interesting example of a discrete mathematical model used in biology is a food web.
The first biology courses in high school and in college present the fundamental nature of
a food web, one that is understandable by students at all levels. But food webs as part of
a larger system are often not addressed. This paper presents materials that can be used in
undergraduate classes in biology (and mathematics) and provides students with the
opportunity...
HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic
mechanisms are manifold and mediated through a range of positive and negative feedback
regulations of immune and physiological processes engaged in virus-host interactions. The
fundamental questions towards understanding the pathogenesis of HIV infection are now
shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally
disrupted? (ii)...
This paper demonstrates the development of a simple model of carbon flow during plant growth. The model was developed by six undergraduate students and their instructor as a project in a plant ecophysiology course. The paper describes the structure of the model including the equations that were used to implement it in Excel®, the plant growth experiments that were conducted to obtain information for parameterizing and testing the model, model performance, student responses to the modeling project,...
This special issue of Mathematical Modelling of Natural Phenomena on biomathematics education shares the work of fifteen groups at as many different institutions that have developed beautiful biological applications of mathematics that are different in three ways from much of what is currently available. First, many of these selections utilize current research in biomathematics rather than the well-known textbook examples that are at least a half-century old. Second, the selections focus on modules...
Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental
tool which can be used in conjunction with mathematical modeling to quantify the dynamic
behavior of a population of lymphocytes. In this survey we begin by providing an overview
of the mathematically relevant aspects of the data collection procedure. We then present
an overview of the large body of mathematical models, along with their assumptions and
uses,...
We have developed a chemical kinetics simulation that can be used as both an educational
and research tool. The simulator is designed as an accessible, open-source project that
can be run on a laptop with a student-friendly interface. The application can potentially
be scaled to run in parallel for large simulations. The simulation has been successfully
used in a classroom setting for teaching basic electrochemical properties. We have shown
that...
We propose a novel approach to introducing hypothesis testing into the biology
curriculum. Instead of telling students the hypothesis and what kind of data to collect
followed by a rigid recipe of testing the hypothesis with a given test statistic, we ask
students to develop a hypothesis and a mathematical model that describes the null
hypothesis. Simulation of the model under the null hypothesis allows students to compare
their experimental data...
The measurement of CFSE dilution by flow cytometry is a powerful experimental tool to
measure lymphocyte proliferation. CFSE fluorescence precisely halves after each cell
division in a highly predictable manner and is thus highly amenable to mathematical
modelling. However, there are several biological and experimental conditions that can
affect the quality of the proliferation data generated, which may be important to consider
when modelling dye...
How does DNA, the molecule containing genetic information, change its three-dimensional
shape during the complex cellular processes of replication, recombination and repair? This
is one of the core questions in molecular biology which cannot be answered without help
from mathematical modeling. Basic concepts of topology and geometry can be introduced in
undergraduate teaching to help students understand counterintuitive complex structural
transformations...
Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning...
We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...
A virus dynamics model with two state-dependent delays and logistic growth term is investigated. A general class of nonlinear incidence rates is considered. The model describes the in-host interplay between viral infection and CTL (cytotoxic T lymphocytes) and antibody immune responses. The wellposedness of the model proposed and Lyapunov stability properties of interior infection equilibria which describe the cases of a chronic disease are studied. We choose a space of merely continuous initial...
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