MIT OpenCourseWare


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Grodzinsky, Alan. Fields, Forces and Flows in Biological Systems. Manuscript.

Deen, W. M. Analysis of Transport Phenomena. New York, NY: Oxford University Press, 1998. ISBN: 0195084942.

Students may also find these reference textbooks to be useful (available online via the PubMed Bookshelf).

Lodish, H., et al. Molecular Cell Biology. 4th ed. New York, NY: W. H. Freeman and Co., 2000. ISBN: 0716731363.

Alberts, B., et al. Molecular Biology of the Cell. New York, NY: Garland Science, 2002. ISBN: 0815332181.

Recitation Sessions

The course TAs will offer 30 minute tutorial recitation sessions twice per week.


There will normally be one assignment per week.

The homework assignments are essential for learning the course material, and a serious effort should be made to solve each problem. Students are encouraged to discuss with other class members the underlying concepts and approaches. However, such discussions must stop short of jointly prepared solutions. That is, the work turned in must reflect one's own efforts.


There will be two take home exams, a midterm and a final.

Grading Policy

activities percentages
Homework 30%
Midterm Exam 35%
Final Exam 35%

Course Outline

  1. "Chemical Subsystem" (Diffusion of Nonelectrolytes)
    • Governing Equations and Methodology
      • Conservation and Flux Equations for Chemical Species
      • Eigenfunction Expansions (Finite Fourier Transform Method)
      • Scales and Orders of Magnitude
    • Diffusion in Reactive Systems
      • Irreversible Reactions with Simple Kinetics (e.g., "Effectiveness Factor" for O2)
      • Irreversible Reactions with Complex Kinetics (e.g., NO in Cell Cultures)
      • Reversible Reactions (e.g., Facilitated Diffusion)
    • Diffusion in Heterogeneous Media
      • Suspensions of Solid Spheres or Fibers (e.g., Protein Solutions)
      • Cellular Systems (e.g., Blood, Tissues)
        • Membrane Permeability of Nonelectrolytes (Lipid Bilayer Properties)
        • Effects of Membrane Resistance on Macroscopic Diffusivities
        • Diffusion in Cytoplasm
        • Receptor-ligand Interactions
  2. "Electrical Subsystem" (Electrochemically-mediated Transport)
    • Electroquasistatic Systems: Governing Equations for Electrical Migration
      • Maxwell's Equations, Charge Conservation, Ohmic Conduction in Biological Systems
      • Poisson's Equation, Voltage, and Electric Fields in Electrolyte Media
      • Charge Relaxation Kinetics vs. Characteristic Chemical Diffusion Times
    • Electrochemical Interactions: Coupled Diffusion-migration in Tissues/Membranes
      • Poisson's Equation: Electrical Double Layers at Macromolecular and Cell Surfaces
      • Titration and Ionization of Macromolecular Charge Groups in Tissues/Membranes
      • Poisson-Boltzmann Equation → Donnan Equilibrium Partitioning in Charged Tissues
      • Membrane Potentials [Equilibrium (Nernst, Donnan) and Nonequil. (Diffusion)]
    • Ionic Transport in Charged Extracellular Matrices, Hydrated Biomaterials and Gels
      • Flux and Continuity Meet Gauss, Faraday, and Charge Conservation
      • Electrical and Chemical Boundary Conditions
      • Multi-ion Coupled Diffusion and Charge Relaxation
    • Case Studies
      • Intratissue and Intracellular pH vs. Bath pH
      • Diffusion-limited Binding Reactions: Charged Solutes in Charged Tissues
  3. "Mechanical Subsystem" (Fluid Mechanics and Convective Transport)
    • Governing Equations and Methodology
      • Conservation of Momentum and Constitutive Equations for Viscous Stress
      • Flow Regimes
    • Flows in Simple Geometries
      • Poiseuille Flow in Tube
      • Stokes Flow Around Sphere
    • Convection and Diffusion in Membranes
      • Phenomenological Description of Coupled Fluxes of Water and Nonelectrolytes
      • Hindered Transport Theory (Water and Macromolecules in Pores or Fiber Matrices)
    • Convection and Diffusion in Bulk Solution
      • Mass Transfer in Tube Flow (e.g., Hollow-fiber Dialysis Devices)
      • Mass Transfer to Particles (e.g., "Swimming" Cell)
  4. Electromechanical and Physicochemical Interactions
    • Navier-Stokes Plus Electric Force Density → Electrokinetics
      • Coupling Between Current, Fluid Flow, Pressure and Voltage Gradients
      • Balance of Electrical and Viscous Shear Stresses in the Double Layer
      • Electroosmotic Flow in Channels (MEMs, DNA Chip Applications)
      • Streaming Potentials in Porous Tissues and Gels
    • Electrophoresis: Theory and Experiment
      • Capillary Electrophoresis/Electroosmosis; Gel Electrophoresis
      • Electrophoresis of Cells and Proteins; Case Studies
    • Electrostatic Interactions Between Charged Macromolecules
      • Maxwell Stress Tensor → Double Layer Repulsion Forces
      • Tissue Swelling and Swelling Pressure: Molecular Microcontinuum vs. Osmotic Swelling Pressure (Macrocontinuum)