a few words at the front lines (k-16): teaching and research at the interface of biomathematics

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


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


Chemistry

Math/Physics

Biology

Engineering

GCB

A Day in the Life of a Biology or Mathematics Freshman


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


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


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


Current Situation at Hand:What does it mean to be

STEM-Educated in the 21st Century?


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


What does it mean to be STEM- Graduate Educated in the 21st Century?


“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


Designing for High Impact Practices in the Classroom and Research Experiences

MATLAB®


Not All Problems Are Created Equal: Learning How to Problem Solve

Complexity

Stru

ctu

re


• 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.


Take Home Messages

23


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.


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]

a few words at the front lines (k-16): teaching and research at the interface of biomathematics

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