A Few Words at the Front Lines (K-16): Teaching and Research at the Interface of Biomathematics
1. 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, MN
October 23, 2016
2. North Carolina Agricultural and Technical State University
Hello Fellow Instructors, Carleton College,
SERC, and MATLAB® Friends
Thank You
3. North Carolina Agricultural and Technical State University
Largest Historically Black College in the U.S.
Approx. Enrollment Headcount at NCA&T, Fall 2015
83% Black, Non-Hispanic, 10% Other URM
7% White Non-Hispanic
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4. North Carolina Agricultural and Technical State University
Chemistry
Math/Physics
Biology
Engineering
GCB
A Day in the Life of a Biology or Mathematics Freshman
6. Vision and Change
New 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
7. North Carolina Agricultural and Technical State University
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?
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8. 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®
Mathematics
content
9. 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
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10. North Carolina Agricultural and Technical State University
Current Situation at Hand:
What does it mean to be
STEM-Educated in the 21st
Century?
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11. North Carolina Agricultural and Technical State University
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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12. North Carolina Agricultural and Technical State University
What does it mean to be STEM- Graduate Educated in the 21st
Century?
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13. 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
14. 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
Engineering
Materials Science
Physics
Information Technology
Mathematics
Chemistry
Biology
15. Issue: Many Pre-Service K-12 Teachers Harbor Pre-
Conceived Fears of Teaching 21st Century STEM
16. North Carolina Agricultural and Technical State University
Designing for High Impact Practices in the Classroom and
Research Experiences
MATLAB®
17. North Carolina Agricultural and Technical State University
Not All Problems Are Created Equal:
Learning How to Problem Solve
Complexity
Structure
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18. North Carolina Agricultural and Technical State University
•Joint Research Mentoring
•Bridge Classroom Experiences
•Broaden Appeal
ComplexityofTeachingand/orLearning
Frosh/Soph Jr/Sr MS/PhD
DidacticCoachingConstructivist
Matriculation Timeline
Basic Skills
Rote Memorization
Artificial
Drill & Practice
Addressing the Gap in Trajectory of Skills and Motivations
K-12 Background
19. A BLEND Project
Mathematics Biology
Sequence Structure Function Systems Biology
Sequence Alignment
Transcriptomics
Matrix Algebra
Mutations
Probability
Bio-molecular Interactions
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
Molecular Dynamics Simulation
Disease Modeling
Statistics
Epidemiological
Models
20. 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.
22. 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.
25. • 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!
26. AND THIS IS NOT EASY Faculty
require TIME to do Research and Teaching
27. • QUBES Hub
• BioQUEST
• NCSU, Wake Forest
• NIMBIoS Working Groups
• Appalachian State U
• Pitt Super Computing
• The Ohio State U
Collaborations- Are Key
Kristin Jenkins
28. Faculty Matrix
Departmental
Affiliation
M. Chen
D. Clemence
T. ReddMathematics
Chemistry V. Divi
Computational
Science and Eng.
Y. Li
Interface
Mentors
Statistics V. Kelkar
G. Goins
Biology M. Smith
D. White
29. • 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
30. Simple Examples Where I
use MATLAB®
Biomathematical modeling
–N cycling in Aquaria
–Insulin Dynamics Relative to Body
Tissues
Emergent Properties
Better understanding of
–N management
–Diabetes models
31. Structure-Behavior-Function
Theory (SBF) Framework
What questions: Structure, Physical Components, Parts, Elements, “Nouns: of a system
What 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
32. Culturally Relevant
Socio-Environmental Systems
dx1/dt= k(t ) − r12(t) ammonia production rate
dx2/dt= r12(t ) − r23(t) ammonia to nitrite conversion rate
dx3/dt= r23(t) nitrite to nitrate conversion rate
Fit of mechanistic
model of equations
above to data on
ammonia, nitrite
and nitrate.
Optimal parameter
values were used
for this simulation
33. 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
34. 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.
35. 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.
36. 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
37. 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.
38. 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
39. 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.
40. North Carolina Agricultural and Technical State University
iBLEND
An 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 you
gdgoins@ncat.edu
