Undergraduate Research in Undergraduate Research in Mathematical Biology: A Collaboration Mathematical Biology: A Collaboration

Between ASU and SCCBetween ASU and SCC

John Nagy (SCC) and Yang Kuang (ASU)John Nagy (SCC) and Yang Kuang (ASU)

ECMTB/SMB, Dresden, Germany ECMTB/SMB, Dresden, Germany July 18, 2005 July 18, 2005

ASU Program DirectorsASU Program Directors

J. Marty AndriesJ. Marty AndriesSchool of Life School of Life

SciencesSciences

ASU PIs/MentorsASU PIs/Mentors SCC Program SCC Program DirectorDirector

Yang KuangYang KuangDept. Mathematics Dept. Mathematics

and Statisticsand Statistics

Carlos Castillo-ChavesCarlos Castillo-ChavesDept. Mathematics Dept. Mathematics

and Statisticsand Statistics

Ron RutowskiRon RutowskiSchool of Life School of Life

SciencesSciences

Jim ElserJim ElserSchool of Life School of Life

SciencesSciences

Hal SmithHal SmithDept. Mathematics Dept. Mathematics

and Statisticsand StatisticsJohn NagyJohn Nagy

Dept. Life SciencesDept. Life Sciences

Program ObjectivesProgram Objectives

1) Formulate and implement a well structured multi-year long 1) Formulate and implement a well structured multi-year long undergraduate mathematical/quantitative biology program.undergraduate mathematical/quantitative biology program.

2) Provide first-class practical training for ASU and SCC 2) Provide first-class practical training for ASU and SCC undergraduates pursuing research posts in theoretical and undergraduates pursuing research posts in theoretical and

mathematical biology.mathematical biology.

3) Provide training in theoretical and mathematical biology 3) Provide training in theoretical and mathematical biology for students pursuing posts in empirical or clinical biology.for students pursuing posts in empirical or clinical biology.

4) Support ASU’s graduate program in mathematical biology 4) Support ASU’s graduate program in mathematical biology by providing graduate students opportunities to mentor by providing graduate students opportunities to mentor

undergraduates.undergraduates.

UBM Program OrganizationUBM Program Organization

ASU ASU ProgramProgram

SCC SCC ProgramProgram

Formal Formal CourseworkCoursework

Summer Summer WorkshopsWorkshops

Formal Formal CourseworkCoursework

““Mini-Thesis”Mini-Thesis”Graduate Graduate Student Student

MentoringMentoring

Research Research Project/ThesisProject/Thesis

SCC Course CurriculaSCC Course Curricula

BIO 198—Introduction to Research in Biology (2 cr.)BIO 198—Introduction to Research in Biology (2 cr.)

Prerequisites:Prerequisites:

General Biology for Majors I (BIO 181 or 187)General Biology for Majors I (BIO 181 or 187)

Course Objectives:Course Objectives:

1) Ethics in research1) Ethics in research

3) Empirical research methods—experiments and surveys3) Empirical research methods—experiments and surveys

2) Using literature to answer specific questions 2) Using literature to answer specific questions

4) Theoretical research methods—mathematical and computer 4) Theoretical research methods—mathematical and computer modelingmodeling

Algebra/Functions/Structures (MAT 122 or141 or 151)Algebra/Functions/Structures (MAT 122 or141 or 151)

BIO 198 Course OutlineBIO 198 Course Outline

Ethics:Ethics:

Case studiesCase studies

Using the literature:Using the literature:

Read and discuss primary research and review articlesRead and discuss primary research and review articles

Group activity—find numbers (e.g., lymphocyte reproduction Group activity—find numbers (e.g., lymphocyte reproduction rate, ion flux through membrane channel, etc)rate, ion flux through membrane channel, etc)

Independent project—Write short literature review on approved Independent project—Write short literature review on approved topic (continuing, in support of mini-thesis).topic (continuing, in support of mini-thesis).

BIO 198 Course OutlineBIO 198 Course Outline

Empirical research:Empirical research:Read and discuss example of a fully crossed, factorial design experiment Read and discuss example of a fully crossed, factorial design experiment from from the primary literaturethe primary literature

Theoretical research:Theoretical research:Introduce discrete-time and continuous time population models—Logistic, Introduce discrete-time and continuous time population models—Logistic,

Lotka-Volterra competition and predationLotka-Volterra competition and predation

Group activity—study model of cardiovascular system (computer)Group activity—study model of cardiovascular system (computer)

Group activity—study population genetics modelGroup activity—study population genetics model

Read and discuss example of a survey studyRead and discuss example of a survey study

Group activity—Design study to test efficacy of fad dietGroup activity—Design study to test efficacy of fad diet

Group activity—Design study to determine if chemistry prerequisite is Group activity—Design study to determine if chemistry prerequisite is required for Gen. Bio. for Majors I.required for Gen. Bio. for Majors I.

Read and discuss literature—mathematical models of tumor growthRead and discuss literature—mathematical models of tumor growth

SCC Course CurriculaSCC Course Curricula

BIO 298—Introduction to Theoretical BiologyBIO 298—Introduction to Theoretical Biology

Prerequisites:Prerequisites:

Introduction to research in biology (BIO 198)Introduction to research in biology (BIO 198)

Course Objectives:Course Objectives:

1) Introduction to theory1) Introduction to theory

3) Applications of stochastic processes to biology3) Applications of stochastic processes to biology

2) Applications of difference/differential equations to biology2) Applications of difference/differential equations to biology

First semester calculus (MAT 220)First semester calculus (MAT 220)

BIO 298 Course OutlineBIO 298 Course Outline

Introduction to theory:Introduction to theory:

Read and discuss primary empirical and theory papers.Read and discuss primary empirical and theory papers.

Difference/Differential equations:Difference/Differential equations:Case studies—Building a dynamical system modelCase studies—Building a dynamical system model

Discuss the concept of a solution to the above modelsDiscuss the concept of a solution to the above models

Activity—Build your own model (1 dimension, assigned topic)Activity—Build your own model (1 dimension, assigned topic)

Case studies—What does a theoretician do?Case studies—What does a theoretician do?

Study and discuss a computer-based modelStudy and discuss a computer-based model

Read and discuss a wicked-ish analysis paperRead and discuss a wicked-ish analysis paper

Introduction to the phase spaceIntroduction to the phase space

Activity—Build your own model (2+ dimensions, assigned topic)Activity—Build your own model (2+ dimensions, assigned topic)

Activity—Find nullclines and general behavior of 2-D systemsActivity—Find nullclines and general behavior of 2-D systems

Stochastic Processes:Stochastic Processes:Case studies—Need for models based on probabilityCase studies—Need for models based on probability

Introduction to basic definitions and properties of randomnessIntroduction to basic definitions and properties of randomness

Activity—Model sex ratio as Bernoulli process, compare to Laplace’s dataActivity—Model sex ratio as Bernoulli process, compare to Laplace’s data

BIO 298 Course OutlineBIO 298 Course Outline

Mini-ThesisMini-ThesisRequirements:Requirements:

Literature reviewLiterature review

Study must include analysis of a model, usually by computer of an already-Study must include analysis of a model, usually by computer of an already-existing modelexisting model

Study must have a novel componentStudy must have a novel component

Student must produce a standard thesis-style documentStudent must produce a standard thesis-style document

Student must present thesis either as poster or talk, in any approved venueStudent must present thesis either as poster or talk, in any approved venue

UBM Program OrganizationUBM Program Organization

ASU ASU ProgramProgram

SCC SCC ProgramProgram

Formal Formal CourseworkCoursework

Formal Formal CourseworkCoursework

““Mini-Thesis”Mini-Thesis”

ASU Course CurriculaASU Course Curricula

BIO/MAT 2BIO/MAT 2xxxx: Numeracy in the Life Sciences*: Numeracy in the Life Sciences*Lectures presented by several ASU facultyLectures presented by several ASU faculty

Associated computer-aided activitiesAssociated computer-aided activities

Minimal hands-on mathematics—lots of reading, writing, synthesisMinimal hands-on mathematics—lots of reading, writing, synthesis

Designed to convince traditional biology undergrads that mathematics is Designed to convince traditional biology undergrads that mathematics is useful and enjoyable and traditional math undergrads that biology is useful and enjoyable and traditional math undergrads that biology is a great playland.a great playland.

BIO/MAT 35BIO/MAT 35xx: Mathematical models in biosciences*: Mathematical models in biosciences*Construction and interpretation of models in ecology, epidemiology, geneticsConstruction and interpretation of models in ecology, epidemiology, genetics

Introduce simple, standard difference and differential equation modelsIntroduce simple, standard difference and differential equation models

Numerical methods and simulationNumerical methods and simulation

Introduction to local stability analysisIntroduction to local stability analysis

ASU Course CurriculaASU Course CurriculaBIO/MAT 35BIO/MAT 35yy: Advanced mathematical models in : Advanced mathematical models in biosciences*biosciences*

Dynamical systems theory applied to biological problem-solvingDynamical systems theory applied to biological problem-solving

Probability theory and stochastic processesProbability theory and stochastic processes

Game theoryGame theory

Intermediate to advanced techniques in MatLab and MapleIntermediate to advanced techniques in MatLab and Maple

Gateway to a guided research projectGateway to a guided research project

BIO/MAT 424: Mathematical models in ecologyBIO/MAT 424: Mathematical models in ecology

Predator/prey dynamicsPredator/prey dynamics

Host-parasite and host-parasitoid dynamicsHost-parasite and host-parasitoid dynamics

Population dynamics in fluctuating environmentsPopulation dynamics in fluctuating environments

Evolutionary dynamicsEvolutionary dynamics

Natural resource managementNatural resource management

ASU Course CurriculaASU Course Curricula

BIO/MAT 450: Topics in mathematical biologyBIO/MAT 450: Topics in mathematical biology

Advanced and current applications of mathematics in biologyAdvanced and current applications of mathematics in biology

Curriculum varies with expertise of instructors and guest lecturersCurriculum varies with expertise of instructors and guest lecturers

BIO/MAT 591: Topics in computational biologyBIO/MAT 591: Topics in computational biology

Comparison of biological sequencesComparison of biological sequences

Phylogeny reconstructionPhylogeny reconstruction

Prediction of RNA and protein structural/functional biologyPrediction of RNA and protein structural/functional biology

UBM Program OrganizationUBM Program Organization

ASU ASU ProgramProgram

SCC SCC ProgramProgram

Formal Formal CourseworkCoursework

Summer Summer WorkshopsWorkshops

Formal Formal CourseworkCoursework

““Mini-Thesis”Mini-Thesis”

Summer WorkshopsSummer WorkshopsSummer Workshop Options:Summer Workshop Options:

Los Alamos with CarlosLos Alamos with CarlosASU with ASU with Marty and Marty and

YangYang

Summer WorkshopsSummer Workshops

Format:Format:

Students meet 2 hours per day, 5 days per week for 8 weeks totalStudents meet 2 hours per day, 5 days per week for 8 weeks total

MWF – Skill building taught by graduate studentsMWF – Skill building taught by graduate studentsIntroduce DEs, phase plane methods, stability analysisIntroduce DEs, phase plane methods, stability analysis

Discrete-time dynamical systemsDiscrete-time dynamical systems

Stochastic processesStochastic processes

Computer applications in MatLab, XPP (WinPP), MapleComputer applications in MatLab, XPP (WinPP), Maple

Introduction to standard mathematical models in biologyIntroduction to standard mathematical models in biology

Taken by students just entering the program or finishing their first yearTaken by students just entering the program or finishing their first year

Summer WorkshopsSummer Workshops

TTh – Survey lectures taught by facultyTTh – Survey lectures taught by faculty

Predator-prey dynamics (Kuang)Predator-prey dynamics (Kuang)

Bioeconomics models (Anderies)Bioeconomics models (Anderies)

Microbial growth and the chemostat (H. Smith)Microbial growth and the chemostat (H. Smith)

Nutrient stoichiometry in ecology (Elser)Nutrient stoichiometry in ecology (Elser)

Stochastic models in molecular biology (Nagy)Stochastic models in molecular biology (Nagy)

Last 2 weeks—Student presentationsLast 2 weeks—Student presentations

20-30 minutes long20-30 minutes long

Presenting research proposal for guided research project, or previous results Presenting research proposal for guided research project, or previous results

UBM Program OrganizationUBM Program Organization

ASU ASU ProgramProgram

SCC SCC ProgramProgram

Formal Formal CourseworkCoursework

Summer Summer WorkshopsWorkshops

Formal Formal CourseworkCoursework

““Mini-Thesis”Mini-Thesis”Research Research

Project/ThesisProject/Thesis

Guided Research ProjectsGuided Research Projects

Mentoring:Mentoring:

One faculty member in MathematicsOne faculty member in Mathematics

One faculty member in BiologyOne faculty member in Biology

At least one graduate student in either mathematics or biologyAt least one graduate student in either mathematics or biology

When appropriate, learning community with advanced undergraduatesWhen appropriate, learning community with advanced undergraduates

Requirements:Requirements:

Conduct research program guided by mentorsConduct research program guided by mentors

Develop integrative research question and plan with primary mentorDevelop integrative research question and plan with primary mentor

Produce a research report in style suitable for publicationProduce a research report in style suitable for publication

Students are encouraged to present their research at undergraduate conferencesStudents are encouraged to present their research at undergraduate conferences

Quality of research report must satisfy faculty mentorsQuality of research report must satisfy faculty mentors

1-2 years plus 1 summer1-2 years plus 1 summer

UBM Program OrganizationUBM Program Organization

ASU ASU ProgramProgram

SCC SCC ProgramProgram

Formal Formal CourseworkCoursework

Summer Summer WorkshopsWorkshops

Formal Formal CourseworkCoursework

““Mini-Thesis”Mini-Thesis”Graduate Graduate Student Student

MentoringMentoring

Research Research Project/ThesisProject/Thesis

Graduate Student MentoringGraduate Student MentoringDevelop curriculum for summer skill-building exercisesDevelop curriculum for summer skill-building exercises

Active mentoring of undergraduate research projectsActive mentoring of undergraduate research projects

AssessmentAssessment

Annual evaluations of course work, summer workshops and mentoring by Annual evaluations of course work, summer workshops and mentoring by students and facultystudents and faculty

Staff support for database on participants and subsequent success:Staff support for database on participants and subsequent success:

Planning evaluation and assessment procedures in coordination with strong Planning evaluation and assessment procedures in coordination with strong mathematical education community at ASUmathematical education community at ASU

How many under-represented minorities completed at least one year of How many under-represented minorities completed at least one year of the UBM program, and comparison of how they perform on end-of-year the UBM program, and comparison of how they perform on end-of-year math reasoning test compared to pre-test given during recruitmentmath reasoning test compared to pre-test given during recruitment

How many continue in second year in this or similar program?How many continue in second year in this or similar program?

How many complete bachelor’s degrees within 4 years?How many complete bachelor’s degrees within 4 years?

How many enter graduate or medical school, or obtain relevant How many enter graduate or medical school, or obtain relevant employment?employment?