a few words at the front lines (k-16): teaching and research at the interface of biomathematics
TRANSCRIPT
North Carolina Agricultural and Technical State University
North Carolina Agricultural and Technical State University
A Few Words at the Front Lines (Grades K -16):
Teaching and Research at the Interfaces of Biomathematics Gregory D. Goins and Mary A. Smith
Teaching Computation in the Sciences Using MATLAB® Workshop: Carleton College, Northfield,
MNOctober 23, 2016
North Carolina Agricultural and Technical State University
Hello Fellow Instructors, Carleton College, SERC, and MATLAB® Friends
Thank You
North Carolina Agricultural and Technical State University3
Largest Historically Black College in the U.S.Approx. Enrollment Headcount at NCA&T, Fall 2015
83% Black, Non-Hispanic, 10% Other URM7% White Non-Hispanic
North Carolina Agricultural and Technical State University
Chemistry
Math/Physics
Biology
Engineering
GCB
A Day in the Life of a Biology or Mathematics Freshman
North Carolina Agricultural and Technical State University
How are images 1 and 2 similar and different?
1 2
Vision and ChangeNew Biology for the 21st
Century
Labov, J. B., A.H. Reid, and K. R. Yamamoto, CBE– Life Sciences Education, 9, 2010.
The inputs to and outcomes of a new integrated approach to biological research in the twenty-first century (NRC, 2009, p. 18).
• Grand Challenge of Broadening Participation in STEM is to transform the overall ecosystem at all levels
• Need fresh approaches to broadening participation in the world of STEM
• Fully engage the nation’s talent• View this as a social innovation
problem• Ultimate Bottom Line:
Improvement of the nation’s STEM capacity
North Carolina Agricultural and Technical State University7
HISTORY &CHALLENGES for the 21st Century STEM Workforce
Trans-disciplinary
Interdisciplinary
Multi-disciplinary
Disciplinary
Which best depicts the STEM courses that we are teaching right now?
THE PURPOSE OF THIS PRESENTATION:Demonstrate that biomathematics is a natural bridge between
Imaginative Teaching, Learning, and Visualization
Model Development,Validation, and
Refinement
Biology content
Physics, Chemistry, etc.
MATLAB®
Mathematicscontent
North Carolina Agricultural and Technical State University
Outline
Situation and Context for the Next Generation
The 21st Century STEM Black Box iBLEND Biomathematics Programs Addressing Gaps and Trajectories Outcomes and Take Home Messages
9
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Current Situation at Hand:What does it mean to be
STEM-Educated in the 21st Century?
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National Situation/Problem
A diverse, well prepared, and innovative workforce & STEM-literate citizenry are crucial to the Nation’s health & economy.
Fewer than 40% of students entering college intending to major in STEM complete degrees in STEM.
Many STEM service and introductory courses do not use evidence-based instructional & co-curricular practices
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What does it mean to be STEM- Graduate Educated in the 21st Century?
North Carolina Agricultural and Technical State University
“Students Boxed in by Campus Department Languages?”
• Many students have a mistaken impression that mathematics has limited application to biology
• Biology majors can develop an aversion to mathematics and avoid computationally-rich courses.
• Math majors may not be exposed to research experience and language that establishes meaningful relationships between math and biological processes.
• End result: Math and biology majors may emerge from the early undergraduate years without core capabilities to successfully pursue research careers at the interface of math and biology.
asymptote = saturation = maximal velocity = carrying capacity
Mathematics Chemistry Physics Biology
Disciplines are not used to working with each other
• Silos of activity among private and public domains– No common language– No common scientific literature– No common funding mechanisms– Few integrated training programs
EngineeringMaterials Science
PhysicsInformation Technology
MathematicsChemistry
Biology
Issue: Many Pre-Service K-12 Teachers Harbor Pre-Conceived Fears of Teaching 21st Century STEM
North Carolina Agricultural and Technical State University
Designing for High Impact Practices in the Classroom and Research Experiences
MATLAB®
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Not All Problems Are Created Equal: Learning How to Problem Solve
Complexity
Stru
ctu
re
North Carolina Agricultural and Technical State University
• Joint Research Mentoring• Bridge Classroom Experiences• Broaden Appeal
Com
plex
ity
of T
each
ing
and/
or L
earn
ing
Frosh/Soph Jr/Sr MS/PhD
Did
acti
c
Co
achi
ng
Cons
truc
tivi
st
Matriculation Timeline
Basic Skills
Rote MemorizationHigh
ly Com
petit
ive fo
r Gra
d Sch
ool
Less competitive for Grad School
Artificial
Drill & Practice
Addressing the Gap in Trajectory of Skills and Motivations
K-12 Background
Sequence Structure Function Systems Biology
Sequence AlignmentTranscriptomicsMatrix Algebra
MutationsProbability
Bio-molecular InteractionsNumerical Methods
Ordinary Differential EquationsPartial Differential Equations
Molecular Dynamics Simulation
Disease ModelingStatistics
Epidemiological Models
The Model:Compartments, Species, Reactions & Parameters
• Let x1(t) be the concentration of insulin in the blood.Let x2(t) be the concentration of insulin in the kidneys.Let x3(t) be the concentration of insulin in the pancreas.Let x4(t) be the concentration of insulin in the abdomen.Initialize x4(0) = 25 Units (U) to be the amount of insulin initially present in the abdomen due to the injection.
• Let kin = 2 U/hr be the flow rate of insulin from the abdomen into the blood.Let k12 = 1 U/hr be the flow rate of insulin from the blood into the kidneys.Let k21 = 1.5 U/hr be the flow rate of insulin from the kidneys into the blood.Let k13 = 2 U/hr be the flow rate of insulin from the blood into the pancreas.Let k31 = 1.75 U/hr be the flow rate of insulin from the pancreas into the blood.
Compartment and Species
0 2 4 6 8 10Time (minutes)
0
5
10
15
20
25
Insu
lin (U
)
Concentration of insulin in tissues
Blood InsulinKidney InsulinPancreas InsulinAbdomen Insulin
How to model…3: Simulation
• Once the model has been constructed and parameter data has been assigned you can simulate (run) the model
• This is a relatively straightforward step as there are many software tools available to simulate differential equation based models
• We used MATLAB/Simbiology– Employ SBML (type of XML code)
• Runtime options include setting the time to run the model for and the number of data points to take
Given these results, (1) estimate the steady-state level of insulin in the blood, kidneys, and pancreas and (2) the time at which this level is reached.
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Take Home Messages
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How Are We Achieving?
• Most incoming freshmen arrive to college from traditional science curricular pathways
• Analogously, departments across a “traditional” university campus may have multiple versions of the same data, expertise, and equipment without any interaction or synergy
The Main Point – No More Silos!
AND THIS IS NOT EASY Faculty require TIME to do Research and Teaching
• QUBES Hub• BioQUEST• NCSU, Wake Forest• NIMBIoS Working Groups• Appalachian State U• Pitt Super Computing • The Ohio State U
Collaborations- Are Key
Kristin Jenkins
Faculty MatrixDepartmental
Affiliation
M. ChenD. ClemenceT. Redd
Mathematics
Chemistry V. Divi
ComputationalScience and Eng. Y. Li Interface
Mentors
Statistics V. Kelkar
G. GoinsBiology M. Smith
D. White
• MATLAB®
– A sophisticated environment for mathemathical modelling and data analysis
– Big set of functions and algorithms– Easily extensible and programmable
• SimBiology®
– An extension for Systems Biology modelling– Graphic modelling capabilities, events, rules and
stochastic solvers– Tight integration with MATLAB
Simple Examples Where I use MATLAB®
Biomathematical modeling –N cycling in Aquaria–Insulin Dynamics Relative to Body
TissuesEmergent PropertiesBetter understanding of
–N management–Diabetes models
Structure-Behavior-Function Theory (SBF) Framework
What questions: Structure, Physical Components, Parts, Elements, “Nouns: of a systemWhat is living above and below the surface? Plants, rocks, roots, pump
How questions: Behavior, Relationships, Mechanism, Processes, “Verbs” within a system
How do plants grow without soil? Mineral nutrition root uptake
Why questions: Function, Outputs, Phenomena or Purpose “Sentence” of the system
Why is aeration important? Roots are heterotrophic, require C from leaves, breath like animals require O2
Culturally Relevant Socio-Environmental Systems
dx1/dt= k(t ) − r12(t) ammonia production ratedx2/dt= r12(t ) − r23(t) ammonia to nitrite conversion rate dx3/dt= r23(t) nitrite to nitrate conversion rate
0 5 10 15 20 25 30Time (days)
0
2
4
6
8
10
12
14
Con
cent
ratio
n (m
g/l)
Ammonia
Nitrite
Nitrate
Fit of mechanistic model of equations above to data on ammonia, nitrite and nitrate. Optimal parameter values were used for this simulation
How to model…1: Identification• Identify the biological pathway to model
(what – make culturally relevant)• Insulin absorption and flow through tissues• Identify the biological question to answer
(why)
• Example: A significant amount of diabetic patients use daily insulin injections to keep their blood sugar stable. Increasing the amount of insulin in the blood decreases the amount of sugar in the blood. Several methods exist for monitoring blood sugar, however, the inability to achieve a predictable blood sugar over time is a frustrating problem that constantly plagues diabetics
How to model 1b–Using the model, determine the flow rate
equations for this system. –Solve these equations for the concentration of
insulin in each compartment. –Plot the concentrations of insulin in each
compartment for up to 10 hours. –Given these results, estimate the steady-state
level of insulin in the blood and the time at which this level is reached.
The Model:Compartments, Species, Reactions & Parameters
• Let x1(t) be the concentration of insulin in the blood.Let x2(t) be the concentration of insulin in the kidneys.Let x3(t) be the concentration of insulin in the pancreas.Let x4(t) be the concentration of insulin in the abdomen.Initialize x4(0) = 25 Units (U) to be the amount of insulin initially present in the abdomen due to the injection.
• Let kin = 2 U/hr be the flow rate of insulin from the abdomen into the blood.Let k12 = 1 U/hr be the flow rate of insulin from the blood into the kidneys.Let k21 = 1.5 U/hr be the flow rate of insulin from the kidneys into the blood.Let k13 = 2 U/hr be the flow rate of insulin from the blood into the pancreas.Let k31 = 1.75 U/hr be the flow rate of insulin from the pancreas into the blood.
The model represents the flow of insulin through specific parts of the body. Using this model, it is your goal to predict the level of insulin in the blood over time after an insulin injection.
For analytical purposes, this model does not take into account other factors, such as glucose, that may normally affect the concentration of insulin throughout the body.
How to model…2: Definition• Define the kinetic types
– Each reaction has a specific kinetic type – All the reactions in this insulin model are
governed by mass action kinetics
• Define the rate constants (parameters)
• Define the initial concentrations
• Check the literature
– What values have been previously reported?– What values are used in similar models?– Do you trust them? Are there any conflicts? – Measure them yourself in the wet lab– Parameter estimation techniques: estimate
some parameters based on others and observed data
Brass Tacks 1
• Build the capacities of educators in all sectors.• Equip educators from different sectors with tools and
structures to enable sustained planning and collaboration.• Link in- and out-of-school STEM learning day by day.• Create learning progressions for young people that connect
and deepen STEM experiences over time.• Focus instruction on inquiry, project-based learning, and
real-world connections to increase relevance for young people.
• Engage families and communities in understanding and supporting children’s STEM success.
Brass Tacks 2
• Provide portable laboratory module supply kits that can be used in classrooms
• Provide an instructor’ guide that includes digital tutorials for describing how to involve teachers.
• Have students share ideas that exemplify “modeling practice based pedagogy”
• Hold a pedagogical debrief of the modeling practices that are embedded in the design of the model
21st Century Stem Teachers…
• Enable a student to recognize and ask the questions they should have about their future
• Equip the student to answer those questions by exposing them to a variety of research cultures and environments
• Place a student’s career destiny in his or her own hands.
North Carolina Agricultural and Technical State University
iBLENDAn Integrative Biomathematics Learning and
Empowerment Network for Diversity
Encourage, enable, and support your students to do research at the interface of mathematics and biology.
Thank [email protected]