Undergraduate Biology and Math
Training Program (UBMTP)
1. Overview of Math Biology at NJIT
2. Description of the 12 month UBMTP experience
3. Examples of student work
4. Accomplishments and challenges
Math & Biology at NJIT
•
6 people in Neurophysiology/Math Neuro/Comp Neuro
(Matveev, Tao, Golowasch, Nadim, Bose, Miura)
•
3 people in other areas (Muratov, Russell, Wang)
•
Biology Dept at NJIT sits in Math Dept and is joint with
Biology Department at Rutgers-Newark
1. Neurophysiology (also Aidekman Center)
2. Cell Biology
3. Ecology
A lot was already in place
• B.S. in Mathematical Sciences with an option in
Mathematical Biology
• B.S. in Biological Sciences that requires Calc1, 2
& 3, Lin Alg, Prob & Stats + one more math
course
• We have a variety of math bio courses
•
•
•
•
Math 371 (Medicine & Physiology) Hoppensteadt and Peskin
Math 372 (Population Biology) Hastings
Math 373 (Intro to Math Biology) Edelstein-Keshet
Math 430 (Intro to Computational Neuroscience)
• Math 373 and a double major in Math + Biology
have resulted from UBMTP.
UBMTP at NJIT
• PI/co-PIs: Amitabha Bose,Farzan Nadim & Jorge
Golowasch
• Other investigators involved:
Ed Bonder (Rutgers-Newark, Biology), Wilma Friedman
(Rutgers-Newark, Biology), Nihal Altan-Bonnet (RutgersNewark, Biology), Claus Holzapfel (Rutgers-Newark,
Biology), Victor Matveev (NJIT, Math), Gareth Russell
(NJIT, Math and Rutgers-Newark, Biology), Alex
Rodriguez (Rutgers-Newark, Biology), Andrew Hill (NJIT,
Biology), Dan Bunker (NJIT, Biology)
• New students are recruited in fall semester but begin
program in spring semester
The 12 month UBMTP experience
Spring Semester: (10 hrs/week)
• Students and faculty hold weekly group meetings to learn basics of
mathematical modeling, dynamical systems and neurobiology, ecology and cell
biology
• Pairs of students rotate for 1 month through each of the different biology labs
• Students write monthly reports documenting their lab experiences
• Students complete small projects and learn how to present scientific findings
Summer Months: (40 hrs/week)
• Students spend 9 weeks working in pairs on a specific research project
• Students and faculty hold twice weekly group meetings, one to eat lunch and
update research progress, the other for individual students to make blackboard
presentations on any scientific topic of their choice
• Students write weekly summaries of activities
Fall Semester: (3 credit independent study course)
• Students complete their research projects, write final reports and present a
public research seminar
13 major projects have been
instigated over the past 5 years
Subset of topics
1.
2.
3.
4.
5.
6.
Determining gap junction locations in coupled neurons
(2005)
Quantifying border formation in allopatric and
sympatric plant species (2005)
Modeling colonial wading bird metapopulation
dynamics in the NJ Meadowlands and NY
harbor(2006)
Dynamics of cocksakie virus (2007)
How do microsporidia infect cells (2008)
Role of morphology on passive properties of neurons
(2009)
2005 Student Projects
Project 1 – Locating Gap Junctions
• Goal: Develop a procedure to predict the location of gap
junctional coupling between two PD neurons of the crab
STG
• Method: Obtain physiological data by recording from the
somas of the 2 PD neurons; compare results with those
obtained from a mathematical model
• Findings: Students were able to predict gap junction
location and strength
Experiments and Mathematical Modeling of Crab Stomatogastric Ganglion in
the Nadim/Golowasch lab.
Diana Martinez beginning a dissection
of the crab STG.
Matt Malej taking a break from computer
simulations modeling coupled passive
neurons.
Preparing for an experiment, Angelie
Mascarinas and Sultan Babar
perform a fine dissection of the crab
STG.
Angelie and Sultan show the fruits
of their labor, electrical recordings
from the STG.
Locating Gap Junctions
Determining gap junction resistance and location from the phase shift
Sinusoidal current was
injected into PD1.
Phase shift is defined
as the difference in
time of peak PD1 to
PD2 response divided
by the period.
2005 Student Projects - Continued
Project 2 – Border formation in allopatric and sympatric
plant species
Goal: Determine whether native species form sharper plant
borders with other native species or with non-native species
Method: Obtain data from the field, develop a quantification
method and an accompanying mathematical theory
Findings: Students found that native species form sharper
borders suggesting that over long time scales native plants
have developed signaling mechanisms amongst themselves
Jonathan Lansey and Kunj Patel worked on plant border formation
in the Hozapfel lab.
A hazy day at Liberty State Park
Quantifying border overlap
from experimental data.
Mathematical Modeling of Plant Border Formation
PDE Model
Boundary conditions
Initial conditions
U, V represent the
density of plants, D1, D2 are
diffusion constants, K1,K2 are
“competition” constants
2006 Student Projects
Tao Lin and Jasneet Kaur
Lab Advisor: Dr. Edward Bonder
Teaching Assistant: Susan Seipel
RhoA
Is there a
correlation between
spindle orientation
in mitotic cells and
the contracted cell
shape caused by the
GTPase protein,
RhoA?
Rho kinase
mDia
LimK
Myosin phosphatase
MLC-p
MLC
Cofilin
Actin-myosin
contractility
(cell rounding)
EB1/APC
Actin polymerization
Unbranched filaments
Stress fibers
Actin-myosin filament
stabilization
Microtubule
growth and
stabilization
Spread,
control cell
Contracted cell with
constitutively active
RhoA
Note: These images have been generated through
a 90 degree vertical projection of z-series images
Understanding Colonial Wading Bird Metapopulation
Dynamics in the NJ Meadowlands and NY Harbor
Mentor: Prof. Gareth J. Russell
UBM Student: Abraham Rosales
Research Goals
•To model the fluctuations of colonial breeding populations on
islands by combining metapopulation dynamics with aggregation
behavior.
Model Components (Hypotheses)
•Aggregation behavior
•Site fidelity
•Limit to nest density in patches
•Global food resource limitation means some nests remain empty
•Population aging
Great Egret Nesting Data
N
100
80
Number
of Nests
60
40
20
t
5
*Different color lines
represent different
breeding populations
10
15
Time (year)
20
Model Outline (one nesting season)
•
Colony Development
– Birds arrive in random order
– Patch allocation by “attractiveness” function, based on
• Resource Availability (Nest sites)
• Desire to be with others (aggregation behavior)
• Site Fidelity (where the individual was the year before)
•
Reproduction
– Reproduction Rate
• Follows the density-dependent Theta-Logistic model
– Offspring Number
• Random Poisson Distribution with reproduction rate as its mean
•
Death and Aging
– Random accidental death
– Death from old age`
N
Graph A
40
8
<
Example outputs
q P - > 1., q G - > 0.447214
•These graphs have different
global density dependence
based on their global Θ value
30
20
•Graph A has a global
Θ=0.447214, strong density
dependence
10
Number
of Nests
N
Graph B
8
100
200
300
<
400
q P - > 1., q G - > 5.
t
500
•Graph B has a global Θ=5, low
density dependence
40
•What we are seeing in these
graphs is that as global Θ value
increase so does the number of
fluctuating populations
30
20
10
t
100
200
300
Time (year)
*Different color lines
represent different
breeding populations
400
500
•We are still trying to find out
the reason for this kind of
behavior
Accomplishments/Challenges
• 29 students participated over the 5 years
• 9 went on to graduate school at Washington University (Math),
NJIT (Math), Rutgers (Biology), Boston University (Math, Cognitive
Psychology), Columbia University (BME)
• 6 went on to medical school (UMDNJ mostly)
• 2 have become high school mathematics teachers
• 6 are still at NJIT finishing degrees
• 6 are unknown
• Presentations at undergrad conferences, SFN, East
Coast Nerve Net, Ecological Society, SIAM Dynamical
Systems
• 2 peer reviewed journal publications
• Biggest challenge is matching students together and
assigning them to labs for summer/fall projects