Faculty Student Mentoring Program – Mini Grant Application 2012-13
Diana W. Verzi, Professor of Mathematics dverzi@mail.sdsu.edu
760-768-5531 ( on campus dial 6-5531)
SDSU-Imperial Valley Campus
Abstract
Dr. Satchi Venkatamaran of the Department of Aerospace Engineering and the Computational
Science and Research Center (CSRC) has nominated Dr. Diana W. Verzi, Deparment of
Mathematics and Imperial Valley Campus, for a mini-grant to fund the cost of research and
presentation incidentals in working with undergraduates from SDSU-Imperial Valley Campus
(SDSU-IV) in mathematical models for the interdependence of glucose sensing and insulin
release in pancreatic beta cells.
Pancreatic beta cells secrete insulin, the hormone that maintains blood plasma glucose within
narrow limits. Insulin allows muscle to take up glucose for immediate energy, and causes the
liver and fat cells to store glucose. Diabetes is a disease in which glucose is chronically elevated,
leading to blindness, kidney failure, limb amputation, cardiovascular disease, and death.
We will study the interdependence of cell membrane potential and calcium oscillations used by
beta cells to regulate insulin secretion. There are several regulatory candidates suggested in the
literature, and the goal is to test parameter values to fit simulations for voltage and calcium to
data within the public domain for bursting patterns of membrane potential and levels of
intracellular calcium in both healthy and diabetic individuals.
Project Description
Dr. Verzi and four Imperial Valley (IV) Campus undergraduate students will study the
interdependence of cell membrane potential (V) and calcium (Ca++) oscillations used by
pancreatic beta cells to regulate insulin secretion. Potassium channels and Ip3 receptors will
also be considered as mechanical elements that indirectly affect the level of free intracellular
calcium levels within the cytosol. The students are supported by NSF-STEM scholarships out of
SDSU Computational Science and Research Center (CSRC), and this study will produce
simulations, or computational studies, based on physics and partial differential equations that
describe the interdependence diabetes-related changes in the chemistry, activity and morphology
of pancreatic beta cells.
Cooperative efforts between Dr. Venkatamaran and Dr. Verzi
Students researchers will participate in weekly CSRC research skills workshops and colloquiums
at main campus, under the direction of Dr. Venkatamaran, to present and consider a variety of
research topics. Dr. Verzi is a researcher with CSRC, recruiting students from the branch
campus to consider graduate studies and careers in research. She will join the students in
colloquium attendance when presentation is within the scope of their joint research area and
meet. On these trips, Drs. Venkatamaran and Verzi will meet with the students to jointly review
and support their research efforts and plans for future study.
Students will meet with Dr. Verzi at least one morning per week to report findings and receive
guidance for continued work. Dr. Verzi builds on her previous work for activity and calcium
regulated structural changes in the central nervous system for hippocampal dendritic spines
(Verzi, 2004; Verzi et al., 2005; Verzi and Baer, 2005). Following experimental results for
dendritic spines in slice cultures, the model proposed a bi-directional interdependence between
electrical activity and the morphology of circuitry within the dendritic arbor, regulated by
localized levels of free calcium released from internal stores.
While the students are supported for their research time through NSF-STEM, the Imperial Valley
Campus of SDSU has no funding for travel and little funding for research assigned time, with
most of it directed at non-tenured faculty. For example, Dr. Verzi has no assigned time for
research Fall 2012, yet she is working with 4 math majors from IV Campus receiving the NSFSTEM scholarship. The FSMP is requested to contribute to the cost of duplication, software,
poster printing, recruitment, and student travel and parking expenses for the 112 miles between
Imperial Valley and main campus.
Recruitment Plan
Students will give a talk about their research, the FSMP, and the CSRC NSF-STEM scholarship
program to sophomores at Imperial Valley [community] College, the feeder school for SDSU-IV
Campus. The IV Campus is upper-division only with respect to the hard sciences, and both the
community college and IV campus are Hispanic-serving institutions, supporting efforts to
increase representation of minorities in research and graduate programs in the hard sciences.
Statistics demonstrate that the time for undergraduates to think about graduate school is when
they are sophomores, so that we need to recruit them even before they enter IV Campus.
Presentation by mentored students and application handouts will recruit new mathematics
majors, mentored student researchers and NSF-STEM scholars to support this effort.
Mathematics and psychology remain the only majors from the college of sciences offered at the
IV Campus. While the psychology major is part of our 4-year undergraduate program,
mathematics remains a 2+2 program with the community college. With faculty outreach efforts,
supported by programs like the FMSP, I am proud to report that minority students from our
mathematics program have been accepted into graduate programs in mathematics, computational
sciences and medical school.
Continuing efforts in FSMP beyond Spring 2013
While not within the time frame for FSMP, students will give a research talk at the Society for
Industrial and Applied Mathematics (SIAM) in San Diego, Summer 2013, funded by the NSFSTEM grant. They will also work with Dr. Verzi in writing a paper about their results for
publication. Dr. Verzi has applied for SDSU-UGP grant funding to send her to the SIAM
conference and for summer research time to complete this work.
Research and Training Plan
Fall 2012
Students will gain knowledge in theoretical and numerical methods, along with Matlab
programming and research techniques from Math538 Discrete Dynamical Systems and Chaos,
instructor Dr. Ricardo Carretero, broadcast via video conferencing to SDSU-IV Brawley site.
They will further gain insight into the world of theoretical research by attending weekly
workshops and colloquia sponsored by CSRC.
Specific to the planned research, they will gather background information about the topic from
textbooks and articles to identify a hypothesis for simulation testing. Initial Matlab
programming will alter existing code, and be validated to the study of beta cells by returning
graphs from earlier works (Fall C et al., 2002; Sherman A, 1997). Plan for utilizing the four
undergraduate researchers is to have them work in pairs, alternating emphasis between
programming and simulation, or model research/analysis and reporting results.
We will build upon an earlier model (Verzi and Baer, 2005) for a single-cell to consider
interdependence of activity-dependent beta cell chemistry and blood insulin-glucose levels
utilizing Morris-Lecar kinetics for fast membrane potential (V), appended by a slow subsystem
for calcium Ca(++) levels, with a negative feedback loop in the form of K(Ca) currents. Run
simulations to fit parameter values and kinetics that return hypotheses and results from
experiments referred to in the literature (Elder et al., 2012; Fridlyand LE and Philipson LH,
2010).
Spring 2013
Students will continue to gain knowledge of theoretical and numerical methods for research
through classwork, and by attending CSRC sponsored workshops and colloquia.
Specific to the proposed model for beta cells, the next step will be to extend the model to
consider the effect of the release of buffered calcium from the endoplasmic reticulum (ER) on
calcium and membrane potential kinetics, with appropriate flux terms. Since acetylcholine
(Ach) is an important potentiator for insulin secretion, promoting the production of IP3 and
dumping the stores, the ER should strongly influence calcium kinetics, and all calciumdependent processes within the beta cells. Once again, we will consider several candidates (s)
for activation and inactivation of (mechanical) channels, as suggested in the literature (Kulkarni
et al, 1999; Gaohua and Kimura, 2009; Lee et al, 2010).
Students will report their results in two posters at the CSRC Applied Computational Science and
Engineering Student Support (ACSESS) Conference in March 2013. In May 2013, they will
give two talks at the SDSU-IV Student Research Symposium, followed by presentation of their
work at the SDSU Student Research Symposium in San Diego.
References
1) Computational cell biology , edited by CP Fall, ES Marland, JM Wagner and JJ Tyson.
Springer-Verlag, NY (2000).
2) Elder DA, Herbers PM, Weis T, Standiford D, Woo JG, and D’Alessio DA (2012) Betacell dysfunction in adolescents ana adults with newly diagnosed type 2 diabetes mellitus.
J. Pediatrics, 160(6), 904-910.
3) Fridlyand LE and Philipson LH (2010) Glucose sensing in the pancreatic beta cell: A
computational study. Theoretical Biology and Medical Modeling, 7(15).
4) Gaohua L, and Kimura H (2009) A mathematical model of brain glucose homeostasis.
Theoretical Biology and Medical Modelling 6(26).
5) Kulkarni JC , Bruning JN, Winnay C, Postic M, Magnuson A, and Kahn CR (1999)
Tissue-specific knockout of the insulin receptor in pancreatic beta cells creates an insulin
secretary defect similar to that in type 2 diabetes. Cell 96, 329-339.
6) Lee JH, Jo J, Hardikar AA, Periwal V, and Rane SG (2010) Cdk4 regulates recruitment
of quiescent betal cells and ductal epithelial progenitors to reconstitute beta cell mass .
Plos One 5(1) e8653. www.ploseone.org.
7) Sherman, A. (1997) in Case studies in mathematical modeling: Ecology, physiology and
cell biology, by HG Othmer, FR Adler, MA Lewis and JC Dallon. Prentice Hall, NJ
(1997).
8) Verzi, DW (2004) Modeling activity-dependent synapse restructuring. Bulletin of
Mathematical Biology 66, 745-762.
9) Verzi DW, and Baer SM (2005) Calcium-mediated spine stem restructuring. J.
Mathematical and Computer Modelling 42, 151-165.
10) Verzi DW, Rheuben MB, Baer, SM (2005). Impact of time-dependent changes in spine
density and spine shape on the input-output properties of a dendritic branch: A
computational study. J. Neurophysiology 93, 2073-2089.