University of Washington · Autumn 2026

Quantitative Physiology

Instructor: Beiyu Lin · syllabus

Contact Email: beiyulin@uw.edu;

Office Hours: Tuesday/Thursday 4–5 PM at Foege N210E;

Core or Elective: Core

Class Philosophy

Explore how cells react, muscles move, blood delivers oxygen, and neurons communicate—and how mathematical models explain these processes. In the AI era, AI-assisted coding tools help bring these models to life as interactive simulations, while your understanding of physiology guides the questions you ask, the predictions you test, and the meaning you draw from the results.

What you will learn

Study reactions, transport, muscle, circulation, and electrical signaling by:

  1. Understand physiology: explain how biological systems work.
  2. Understand equations: explain how equations describe physiological phenomena, including their variables, parameters, and assumptions.
  3. Use AI-assisted coding tools: implement physiological models, build simulations, explore parameter changes, and validate and interpret results.

10-week schedule

Learn physiology. Build one project.
  1. Week 1

    Get started

    Physiology: Drug elimination

    Model: Practice AI coding

    Oct 6–8 · Practice
  2. Weeks 2–3

    Initial model

    Physiology: Reactions & biological foundations

    Model: Build an initial model

    Written 1 · Oct 25
    Demo 1 · Oct 28

    Written 1 + Demo 1
  3. Weeks 4–5

    Extend

    Physiology: Biological scales, energy & kinetics

    Model: Add a mechanism

    Release W4 → Due W5

    Written 2 + Demo 2
  4. Weeks 6–7

    Integrate

    Physiology: Motors, muscle & circulation

    Model: Integrate & validate

    Release W6 → Due W7

    Written 3 + Demo 3
  5. Weeks 8–10

    Refine & present

    Physiology: Oxygen transport & electrical signaling

    Model: Refine & present

    Presentation · Week 10

    Dec 8–10

Oct 1: Course introduction

Dec 14: Written final exam

3 written assignments + 3 connected demos → 1 final project. Written assignments and demos are released in pairs. See each assignment for its deadline.

Readings stay visible below. Keener & Sneyd may require a UW Libraries login. Exact assignment deadlines will be announced.

Reading key: A&P = OpenStax Anatomy and Physiology; ND = Neuronal Dynamics.

Videos: watch the assigned YouTube video(s) listed under each week's reading to visualize the biological process before class.

Week / dates Topic and activity Reading Assignments
First classThursday
October 1, 2026		 Introduction to Quantitative Physiology

Course overview and setup.

Explore this topic
  • Physiological scales: molecules, cells, and organ systems.
  • How equations describe physiological phenomena: variables, parameters, units, and assumptions.
  • A simple example connecting a physiological question to a mathematical model.
  • Introduction to AI coding tools and setup instructions.

Prepare for October 6: choose a coding tool and follow the setup instructions provided in class.

 Lecture 1 slides and introductory notes (links to be posted).

Additional reading

Videos

Set up your AI coding tools
before Oct 6.
1Tue Oct 6 · Thu Oct 8 AI-assisted coding: practical implementation studio

Generate, understand, modify, and test code with AI assistance.

Explore this topic
Explain the model → Generate code → Understand → Run → Check → Revise

Understand: Explain the model’s equations, variables, parameters, units, and assumptions. Translate these into a clear coding request and explain how the generated code implements the model.

Use AI: Use an AI-assisted coding tool to generate a drug-elimination simulation. Read and explain the code, run it, and modify the initial amount and elimination rate.

Check: Compare the numerical result with the analytical solution. Check units, initial conditions, and numerical accuracy; document any corrections.

Milestone: Build and validate the drug-elimination simulation; reuse this workflow for every demo.

AI coding tools & references
Read the documentation for your chosen tool.

Additional reading

Videos

Reading guidance

read the resting-membrane-potential discussion. focus on the passive membrane circuit before adding a spike threshold.

 Optional Practice

Practice 1: One Model, Different Perspectives
Practice 2: Reversible Reactions — Oxygen in the Blood
Practice 3: Pain Medicine

Ungraded · No submission required
2Tue Oct 13 · Thu Oct 15 Chemical reactions, equilibrium & thermodynamics

Reaction rates, energy, and equilibrium.

Explore this topic
A + B ⇌ C; dc/dt = k₊ab − k₋c
ΔG = ΔG° + RT ln Q

Understand: Explain how forward and reverse reaction terms change species concentrations while conserving total material. Interpret Kd = k₋/k₊ as a measure of binding affinity, and relate the sign of ΔG to reaction direction using dimensionless activities in Q.

Use AI: Build a reversible-binding simulator with adjustable initial conditions and rate constants. Display transient concentrations and equilibrium predictions.

Check: Confirm conserved totals and zero net reaction rate at equilibrium. Treat equilibrium and driven steady states distinctly.

 Keener & Sneyd I, Chapter 1: biochemical reactions.

Additional reading

Videos

Reading guidance

reaction types, energy, and reaction rates.

 Release · Pair 1

Written 1 + Demo 1
Initial model · Written: Oct 25; Demo: Oct 28

What to submit

Written work: Reactions and enzyme reaction steps: explain mass action, equilibrium, and E + S ⇌ C → E + P; interpret rate constants and show calculations with units. See the linked assignment PDF for the submission questions.

Demo work: Initial model: choose your final-project physiological question, explain the equations, and implement a simple working simulation with a basic validation check.

Released together in Week 2. Written 1 is due Oct 25; Demo 1 is due Oct 28. See “Due · Pair 1” for submission instructions and the grace period.
3Tue Oct 20 · Thu Oct 22 Enzyme reactions & biological foundations

Enzyme binding and product formation; molecules, cells, tissues, and organs.

Explore this topic
E + S ⇌ C → E + P
  • Identify enzyme E, substrate S, enzyme–substrate complex C, and product P. Explain binding, unbinding, product formation, and enzyme reuse.
  • Lectures 1–3: Quantitative physiology across molecular, cellular, and organ scales; proteins, nucleic acids, carbohydrates, and lipids; cellular organization.
  • Four tissue types, organs and organ systems, body-fluid compartments, homeostasis, and negative feedback.
  • Quantitative estimation: protein numbers and spacing, cell numbers, and cellular energy use; introduction to thermal energy kBT.

Practice: Explain the reaction scheme in words and work through biological estimates using explicit assumptions and units.

Check: Distinguish molecules, cells, tissues, and organs; check unit conversions and whether estimates are reasonable.

Milestone: Written 1 and Demo 1: initial project model and validation check.

Course materials: Lectures 1–3 and associated notes (Canvas).

Keener & Sneyd I, Chapter 1: enzyme reaction scheme. PBoC: biological scales and quantitative estimation.

Additional reading

Reading guidance

Focus on the enzyme reaction steps and the biological foundations covered in class. The Michaelis–Menten rate equation and model reduction were not covered this week. Molecular-state probabilities and entropy are listed under October 29.

 Due · Pair 1

Submit on Canvas → Assignments.

Written 1: Oct 25, 11:59 PM
Demo 1: Oct 28, 11:59 PM

Grace period: Life happens! Submit by 8:00 AM the next day with no penalty—Oct 26 for Written 1 and Oct 29 for Demo 1.

All times are Pacific Time.

4Tue Oct 27 · Thu Oct 29Biological organization, energy & molecular states

Review biological scales and homeostasis; explore molecular states and probabilities.

Explore this topic
  • Review biological molecules, cell organization, four tissue types, and body-fluid compartments from Week 3.
  • Homeostasis and negative feedback.
  • Estimate protein numbers, cell numbers, and cellular energy use; interpret thermal energy kBT.
  • Thursday, Oct 29: Microstates, multiplicity, entropy, and Boltzmann probabilities.
N = (mass / molar mass) × NA; energy scale = kBT
S = kB ln Ω; pi = exp(−Ei/kBT) / Z

Class activity: Explore cell-number or energy estimates and the probabilities of a two-state molecule. Explain how assumptions and energy differences affect the results.

Check: Check units and orders of magnitude. Verify that state probabilities sum to one and explain how energy and multiplicity affect them.

Course materials: Lectures 1–4 (Canvas).

PBoC: biological scales and estimation; lecture slides and worked notes.

Additional reading

Optional Practice:
Practice 1: Kidney Filtration and Dialysis
Practice 2: How Heart Cells Work Together
Practice 3: Negative Feedback
Practice 4: DNA Configurations and Entropy

Release · Pair 2

Written 2 + Demo 2
Due Week 5

What to submit

Written 2: biological organization, homeostasis, estimation, molecular states, and energy. Demo 2: extend your Demo 1 model with a relevant mechanism; compare and validate the two versions.

5Tue Nov 3 · Thu Nov 5Chemical potential, binding & kinetics

Apply molecular-state probabilities to binding, reaction energy, and timescales.

Explore this topic
  • Brief review of the molecular-state concepts covered on October 29.
  • Chemical potential, receptor binding, and ATP reaction free energy.
  • Exponential waiting times, reversible two-state kinetics, and steady-state probabilities.
μ = μ° + kBT ln(c/c°); P(wait > t) = exp(−kt)

Class activity: Explore a two-state molecule or simulate waiting times. Compare results with the predicted probabilities or exponential curve.

Check: Probabilities must sum to one. Use dimensionless logarithm arguments and consistent per-molecule energy units. Distinguish equilibrium from a driven steady state.

Course materials: Lectures 4–6 (Canvas).

PBoC: statistical mechanics, entropy, and binding; Keener & Sneyd I, Chapter 1: reaction kinetics.

Additional reading

Due · Pair 2

Written 2 + Demo 2

What to submit

Submit the written work and an extended version of your existing project. Explain parameter effects, validation, and limitations.

6Tue Nov 10 · Thu Nov 12Molecular motors & muscle contraction

Connect ATP-powered steps to whole-muscle force.

Explore this topic
  • Myosin, kinesin, and dynein; stepping, load, and stall force.
  • Muscle fibers, sarcomeres, calcium regulation, and the cross-bridge cycle.
  • Force–velocity relationships; estimate muscle force and account for lever arms.
v = d(k₊ − k₋); Fstall ≈ available energy per step / d
F₁ℓ₁ = F₂ℓ₂

Class activity: Explore motor velocity versus load or build a muscle-force estimator. Use an explicitly stated model and parameter assumptions.

Check: Check force and energy units, zero net stepping at stall, and the distinction between muscle force and force at the hand.

Course materials: Lectures 6–8 (Canvas).

PBoC: molecular motors; Keener & Sneyd II: muscle; lecture worked examples.

Additional reading

Release · Pair 3

Written 3 + Demo 3
Due Week 7

What to submit

Written 3: molecular motors, muscle force, circulation, and resistance networks. Demo 3: integrate your project components and strengthen validation.

7Tue Nov 17 · Thu Nov 19The heart, blood vessels & flow control

Explain how the heart pumps blood and vessels regulate delivery.

Explore this topic
  • Diffusion versus bulk flow; pulmonary and systemic circulation.
  • Heart chambers, valves, cardiac cycle, and cardiac output.
  • Viscosity, Poiseuille flow, vessel resistance, and series/parallel networks.
  • Arteriolar control, capillary exchange, and the roles of arteries and veins.
Q = stroke volume × heart rate
Q = ΔP/R; R = 8ηL/(πr⁴)

Class activity: Build a vessel-network explorer. Change vessel radius and compare predicted flow and pressure drops.

Check: Conserve flow at junctions, check pressure and flow units, and state the assumptions behind Poiseuille’s law.

Course materials: Lectures 9–10; introduction to Lecture 11 (Canvas).

Keener & Sneyd II: circulation; lecture slides and resistance-network notes.

Additional reading

Due · Pair 3

Written 3 + Demo 3

What to submit

Submit the written work and integrated project demo. Explain the physiological findings, validation, and remaining limitations.

8Tue Nov 24Blood & oxygen transport

Explain oxygen uptake, carrying capacity, and tissue delivery.

No class Thursday, November 26 (Thanksgiving).

Explore this topic
  • Blood components, red blood cells, hemoglobin, and cooperative binding.
  • Distinguish partial pressure, dissolved oxygen, saturation, and total oxygen content.
  • Estimate oxygen capacity and consumption; introduce the nervous system as rapid communication.
cdissolved = αp; Y = ph/(P₅₀h + ph)

Class activity: Explore oxygen-binding curves and estimate oxygen stores using clearly stated assumptions.

Check: Check saturation limits and units. Treat oxygen-store calculations as simplified estimates, not predictions of safe breath-holding time.

Course materials: Lecture 11; bridge to Lecture 12 (Canvas).

Keener & Sneyd II: blood and respiration; lecture oxygen-transport examples.

Additional reading

Project refinement

Project guidance

Use feedback from Demo 3 to improve your existing project. No new written or demo submission.

9Tue Dec 1 · Thu Dec 3Nervous system & membrane electricity

Connect ion gradients, channels, and capacitance to membrane voltage.

Explore this topic
  • Nervous-system organization, neurons, and synapses.
  • Electrical and chemical driving forces; Nernst potential and ion-flow direction.
  • Ion channels, current, conductance, capacitance, and passive membrane circuits.
  • Multiple conductances and the membrane time constant.
Eion = RT/(zF) ln(cout/cin)
Iout = g(V − Eion); C dV/dt = Σgi(Ei − V) + Iapp

Class activity: Build a passive-membrane simulation and compare numerical voltage traces with an analytical solution. Share your final-project demo for peer feedback.

Check: State voltage and current conventions; verify τ = C/Σgi and the conductance-weighted resting voltage for constant conductances and zero applied current.

Course materials: Lectures 12 and 15; passive dynamics from Lecture 16 (Canvas).

Keener & Sneyd I: membrane channels and passive electrical flow; ND §2.1 and §1.3.1.

Additional reading

ND: Equilibrium potential · Passive membrane

Peer review

Project guidance

Share the refined project and its validation evidence. Incorporate feedback before the final presentation.

10Tue Dec 8 · Thu Dec 10Action potentials & final presentations

Explain electrical signaling and present your completed model.

Explore this topic
  • Tuesday: threshold, sodium activation/inactivation, potassium activation, and refractoriness.
  • Interpret the Hodgkin–Huxley model and explain propagation conceptually.
  • Thursday: final-project presentations connecting physiology, equations, and validated results.
Cm dV/dt = Iapp − INa − IK − IL

Class activity: Explore a provided Hodgkin–Huxley example. Present the refined model developed through Demos 1–3; spatial simulation is optional.

Check: Explain current signs, channel-gate bounds, threshold behavior, and model limitations. Show validation for your own project.

Course materials: Lecture 16; synthesis of the course (Canvas).

Keener & Sneyd I: excitability and propagation; ND §2.2 and §3.3.

Additional reading

ND: Hodgkin–Huxley model · Axons

Final presentation

Thursday, Dec 10

Project guidance

Present your physiological question, equations, assumptions, demo, results, validation, and limitations. Briefly explain how you used AI-assisted coding.

Written Final Exam: Monday, December 14, 2026, 10:30 AM–12:20 PM at THO 101.

AI tools: Week 1

Use AI-assisted coding tools to generate code, understand how it works, modify it, and validate the results. Practice this workflow in every course demo.

Tools we will discuss

Choose a tool you can access and use comfortably. Practice asking clear questions, reviewing suggested code, and checking your results.

Other available tools

These tools are also available, but we will not cover them in this course.

First activity: model how medicine leaves the body over time using dA/dt = −kA, where A(t) is the amount of medicine in the body and k is the elimination rate. Use an AI-assisted coding tool to generate code for a medicine of your choosing. Read, run, and modify the code to simulate how the amount changes over time and compare it with the analytical solution A(t) = A₀e−kt. Change the initial amount A₀ and elimination rate k, and explain how they affect how long the medicine remains in the body.

Readings

Core textbooks and supporting resources

Additional textbooks

Grading rubrics (tentative)

Lecture slides and handwritten notes support class discussion. File links will be added when available for distribution.

Course Policy (link)