Home /  MSRI-UP 2022: Algebraic Methods in Mathematical Biology


MSRI-UP 2022: Algebraic Methods in Mathematical Biology June 11, 2022 - July 23, 2022
Parent Program: --
Location: SLMath: Baker Board Room, Commons Room, Atrium
Organizers LEAD Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Colorado College), Candice Price (Smith College), Anne Shiu (Texas A & M University; Texas A&M University)

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The MSRI Undergraduate Program (MSRI--UP) is a comprehensive summer program designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.

The main objective of the MSRI-UP is to identify talented students, especially those from underrepresented groups, who are interested in mathematics and make available to them meaningful research opportunities, the necessary skills and knowledge to participate in successful collaborations, and a community of academic peers and mentors who can advise, encourage and support them through a successful graduate program.

Please help us to spread the word about this opportunity to your undergraduate contacts: 

Download MSRI-UP 2022 Program Flyer (PDF)

Research Theme

The theme of the 2022 MSRI-UP is “Algebraic Methods in Mathematical Biology" and the research leader is Dr. Anne Shiu, Associate Professor of Mathematics at Texas A&M University. 

MSRI-UP 2022 will focus on mathematical models inspired by biology. The emphasis will be on models that can be analyzed by algebraic and combinatorial methods.  No background in biology is required, and all projects are accessible to undergraduate participants who have taken a course in linear algebra and a course involving proofs --
and are willing to learn, work in a team, and have fun!

The research projects will be chosen from three areas of mathematical biology, with applications to biochemistry, neuroscience, and pharmacology.

Biochemical reaction networks
A reaction network can be represented by a directed graph in which each edge represents a chemical reaction such as, for instance, A+B ---> C, in which one unit of A and one of B react to form one unit of C. The focus of this REU component is on dynamical systems that arise from reaction networks taken with mass-action kinetics. The ordinary differential equations (ODEs) that govern these systems are polynomials in many variables, and therefore are amenable to algebraic techniques. Example project questions are as follows: How can a network's capacity for bistability or oscillations be predicted from its reaction diagram, and how is this capacity affected by operations on the diagram?

Convex neural codes
A starting principle in neuroscience is that "neurons that fire together, wire together''. The aim of this REU component is to clarify which sets of neurons can fire together under the assumption that each neuron of interest codes for some convex region of some Euclidean space. This assumption is valid in certain biological settings, for instance, when each neuron has a corresponding place field, a convex region in space (this space might be a tabletop on which a laboratory rat is walking) and that neuron fires precisely when the subject (rat) is in that region. This research is motivated by place cells in neuroscience, which won its discoverers the 2014 Nobel Prize in Medicine.

Linear compartmental models
Mathematical models arising in biology and other applications often involve many unknown parameters.  An important question, therefore, is whether and when these parameters can be recovered from data.  If recovering the parameters is possible, the model is said to be identifiable.  The question of which models are identifiable, is not fully answered, even for models that involve only linear ODEs and can therefore be summarized by a directed graph. These models are called linear compartmental models, and they are often used to describe how pharmacological drugs move within and affect the body.  The proposed projects will build on related work using differential algebra, which transform the identifiability problem into questions involving linear algebra and combinatorics.


General Description

During the summer, each of the 18 student participants will:

  • participate in the mathematics research program under the direction of Dr. Anne Shiu of Texas A&M University, a post-doc and two graduate students;
  • complete a research project done in collaboration with other MSRI-UP students;
  • give a presentation and write a technical report on his/her research project;
  • attend a series of colloquium talks given by leading researches in their fields;
  • attend workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences;
  • learn techniques that will maximize a student's likelihood of admissions to graduate programs as well as the likelihood of winning fellowships; and
  • receive a $3600 stipend, lodging, meals and round trip travel to Berkeley, CA.

After the summer, each student will:

  • have an opportunity to attend a national mathematics or science conference where students will present their research;
  • be part of a network of mentors that will provide continuous advice in the long term as the student makes progress in his/her studies; and
  • be contacted regarding future research opportunities.

How to Apply

Applications for MSRI-UP will be on the National Science Foundation's Education and Training Application site. 

Apply for MSRI-UP 2022 REU


Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply. Deferred Action for Childhood Arrivals (DACA) students are also eligible due to generous funding by the Alfred P. Sloan Foundation. The program cannot accept foreign students regardless of funding. In addition, students who have already graduated or will have graduated with a bachelor's degree by August 31, 2022 are not eligible to apply. 

Application Deadlines

Applications submitted by February 15, 2022 will receive full consideration. (Applications submitted after February 15, 2022 but by March 1, 2022 may still be considered in a second round of acceptances.) We expect to begin making offers for participation in late February or early March.

Application Materials

A complete application consists of the following:

Common Application Requirements:

1. Personal Statement (5,000 characters) describing your academic and career goals and how the REU program will help you achieve these goals.  

2. Resume or CV

3. College transcript

4. Contact information for two referencesPlease designate two Faculty References; these should be someone from whom you have taken a class or with whom you have done independent mathematical or scientific work. The people you identify as the Faculty Reference on the website will be notified to fill out an on-line form . Although the person will be notified automatically by email, it is the student's responsibility to make sure the letter is uploaded on time. 

MSRI-UP Specific Application Requirements:

1. Additional Statement (limit 2,500 characters) sharing any further information that will help us get a complete picture of you as a potential participant in MSRI-UP. Please address the origins of your interest in mathematics and science, any experiences (school-related and otherwise) that have particularly stimulated you, any obstacles you have faced along the way, and your experience collaborating with and supporting your peers, particularly those from groups underrepresented in mathematics. Students from 2-Year Institutions: If you are currently attending a two-year institution, please describe your plans for transferring to a four-year institution.

2. Description of Previous Summer / Research Experiences.
Please list and give a brief description of all mathematics or science research or summer programs (high school or college), if any, in which you have participated. (Students who have not participated in any programs previously are encouraged to apply.)

3. List of Mathematics/Science Courses Taken with Grades.
Please list all mathematics and science courses taken, starting with the most recent.  State the Course Number, Course Title, Term Taken, Grade Received, and Institution where you took the course.
Example: MATH 201, Calculus 1, Spring 2015, B+, Carolina Community College 

For additional information, please contact the on-site director for the 2022 MSRI-UP, Dr. Federico Ardila.

The directors of MSRI-UP are:

MSRI-UP 2022: Algebraic Methods in Mathematical Biology

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MSRI-UP Sponsors

Funding to support MSRI-UP is provided by the Alfred P. Sloan Foundation and the National Science Foundation (NSF).


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Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule, Notes/Handouts & Videos
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Jul 22, 2022
09:00 AM - 09:15 AM
  Opening Remarks
Federico Ardila (San Francisco State University)
09:15 AM - 09:50 AM
  The Effect of Operations on the Deficiency of Chemical Reaction Networks
Awildo Gutierrez (Hamilton College), Elijah Leake (DePaul University), Caelyn Sobie (Arizona State University)
10:00 AM - 10:35 AM
  Wheel Signatures on the Neural Ideal
Luis Gomez (University of Arkansas), Loan Tran (San Francisco State University), Elijah Washington (Williams College)
10:45 AM - 11:20 AM
  Parameter Identifiability of Catenary Models
Alexis Edozie (University of Massachusetts, Amherst), Odalys Garcia-Lopez (College of New Jersey), Viridiana Neri (Columbia University)
11:30 AM - 01:00 PM
01:00 PM - 01:35 PM
  Morphisms and Neural Codes
Gradmar Maldonado Marti (University of Puerto Rico), Mateo Morales (University of California, Berkeley), Yasmeen Shaw (University of Texas at Dallas)
01:45 PM - 02:20 PM
  Identifiability of Directed-Cycle Compartmental Models
Paul Dessauer (University of Texas), Tanisha Grimsley (Juniata College)
02:30 PM - 03:05 PM
  Convexity of 4-Maximal Neural Codes
Gustavo Flores (Carleton College), Osiano Isekenegbe (Florida State University), Deanna Perez (San Francisco State University)
03:05 PM - 03:15 PM
  Closing Remarks
Saber Ahmed (Hamilton College), Natasha Crepeau (University of Washington), Jordy Lopez Garcia (Texas A & M University), Anne Shiu (Texas A & M University; Texas A&M University)