4. Lumped processes for analyzing grouping in DNA sequences
Vladimir Sukhoy Presentation
5. Competitive Exclusion in
a Vector-Host Model for the Dengue Fever
Cory Howk Presentation
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Research
Research Experience for Undergraduates:Prior Research Interests::
Improperly posed problems, systems of
reaction-diffusion equations, nonlinear wave equations.
Current Research Interests:
Mathematical modelling of tumor driven
angiogenesis. This work was supported by the National Science Foundation Program
in Applied Mathematics Grant #DMS 9803992. My coauthors were Professor Brian
Sleeman of the University of Leeds, and Professor Marit Nilsen-Hamilton of the
Department of Biochemistry, Biophysics and Molecular Biology at Iowa State are
my principal collaborators on this project. Sleeman is supported as a consultant
on the grant. The computations were done by S. Pamuk, a PhD student of mine.
Together with Mike Smiley and Anna Tucker, Prof. Nilsen-Hamilton and I have
extended these ideas to the so called "p53-switch" in which loss of the wild
type p-53 function leads to uncontroled or excess growth factor
expression. Professor Nilsen-Hamilton, K. Boushaba and I have
recently modeled the control of secondary tumors by primary tumors.
You will need a PDF previewer to read these
files.
Check out the following plots for the progress of angiogenesis:
The system of ordinary and partial differential equations consists of a one
dimensional reinforced random walk pde for the EC combined with two odes arising
from a Michaelis-Menten mechanism for VEGF conversion to proteolytic enzyme (PE)
and one production-consumption equation for fibronectin. These equations, which
describe events in the mother capillary, are coupled, via so called transmission
relationships, with a two dimensional reinforced random walk pde for the EC, a
two dimensional diffusion equation for the diffusion of VEGF from a tumor source
to the mother capillary, an ode for proteolytic enzyme and a
diffusion-production equation for fibronectin. The fibronectin is assumed to
diffuse via mean curvature.
The figures below are only for the ECM. A tumor is assumed to be 25 microns
from a capillary segment of 50 microns in length. The times are in hours. The
subscripts on the "T"s refer to the fraction of the ECM that the daughter
capillary has crossed from the mother capillary to the tumor. The numerical
results, when scaled to the dimensions used by Folkman in his classic rabbit eye
cornea experiments, agree very well with his experimental travel times as well
as other observations such as the accelleration of the tip as it nears the
tumor. The model also includes two mechanisms for angiostatin, one in which
angiostatin is converted into an inhibitor by endothelial cells and a second in
which angiostatin is itself an inhibitor or protease. (Mathematically, the
second case is a sub case of the first.)
In the first set of four figures below, no angiostatin is present.
Notice the tip proliferation of the EC density.
Notice the tip proliferation of the enzyme density.
Notice that the growth factor is consumed only in the
region of capillary formation.
The next set of figures illustrate what happens in the
presence of angiostatin. Angiostatin is introduced into the mother capillary
just as the daughter capillary reaches the tumor side.
Notice the drop in EC concentration.
Compare the concentration of active enzyme to total
enzyme in the following figure.
Notice that it takes quite awhile for the slowly
diffusing fibronectin to fill the channel.
I have had eight Masters students and six PhD students
who have completed their degrees with me. I have one current PhD student and a
post doctoral fellow who is supported by a NATO fellowship. Details can be found
on pages 5 and 6 of my
curriculum vita.
I will be
happy to send you hard copies of my early papers or either postscript or tex
files of my more recent publications.
Click on Partial
Differential Equations for more information on Partial Differential
Equations at Iowa State University.
Let me show you a picture of my
family.
Here is my son
Joe. (Here is a second picture.) He graduated with a
BS in biochemistry in May,1999, from the University of Iowa, the branch campus of
Iowa State University, in Iowa City. He was
employed by Pfizer Pharmaceuticals in Groton, Connecticut for two years and an
MD at the University of Minnesota, Minneapolis.
Here is a picture of him with his
bride Marina (nee'
Abromovich), who was a classmate of his at Minnesota. Here they are again, the
"the Drs. Levine",
residents at Hennipen County General Hospital and the University of Minnesota.
This is my daughter
Margo. (Here is a second picture.) She is a
graduate of Cornell University where she studied civil engineering and minored
in applied mathematics. You think an ISU education is expensive? Well, let me
tell you ..... She had an REU at the University of Alabama at Birmingam during the
summer of 2001. Here are some pictures of her lecturing on her research: REU Lecture, scene 1
: REU Lecture, scene 2
:
REU Lecture, scene 3
. She
is post doctoral fellow at the James Franck Institute at the University of
Chicago. She received a Murphy Fellowship to study applied
mathematics at Northwestern University
beginning Fall Quarter, 2002. She recently
married
Raphael
Jaramello, who was an undergrad at Cornell. He is now a graduate student
in physics at the University of Chicago.
Here is a picture of them when they
were "young uns"
Hobbies: I build model ships from kits. In this "trade" I have advanced from
an "out of the box" builder to a "modified kit" builder. Building from "scratch"
is not on my menu. Those folks are the "pros" whose ships one finds in museums
such as the Musee de la Marine (Paris) and the Royal Navy Museum (Greenwich,
UK). Here is a sample of my work. A few have won prizes at a local model club's
hobby show.
HMS
Bounty, Stem view.
USS
Rattlesnake, Stern view.
San Felipe, Stern view, View from above, Deck.
HMS Golden Hind, Stern view .
HMS Halifax, Stern view.
USS Flying
Cloud, Stern
view, Deck
view.(Best in Show, Plastic Surgeons 1999)
USS Constitution, Stern view. (This
was my first attempt at wooden ship building.) The actual model was donated to
the Math Department at Iowa State in 2005 and now resides in the main office on
the 3rd floor of Carver Hall.)
ISU Links:
Teaching
![REU Lecture, scene 2](http://www.public.iastate.edu/~halevine/images/"MVC-118F.JPG"){kind=link}
