Fields, Forces, and Flows in Biological Systems (BE.430J) >> Content Detail

Lecture Notes

Lecture Notes

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ses #TOPICSlecture notes



Overheads (PDF - 1.6 MB)
I. Chemical Subsystem
L2Continuity of Chemical Species, Flux, Reaction Rates, Boundary Conditions(PDF)

Begin Reaction

Damkohler #

Scaling and Approximations
L4Example Problems: Separation of Variables Method(PDF)


Overheads on IGF-I Transport (PDF)
L5Example Problems: Separation of Variables Method (cont.)

Case Study: IGF Problem from Lecture L1 using Matrix Continuum Distribution of IGF Binding Proteins

Numerical Considerations (if time)
L6Diffusion/Reaction (cont. from Lecture L3)

plus Add Cell Related (Receptor) Binding


Derivation of Michaelis-Menten Kinetics (PDF)

Green's Functions
a) Amazon logo Section 13-12, "Nonhomogeneous Boundary-Value Problems." In Ritger, P. D., and N. J. Rose. Differential Equations with Applications. Mineola, NY: Dover Publications, 2000. [reprint of 1967 edition]. ISBN: 9780486411545.

b) Amazon logo Hildebrand, F. B. Problems 56-59 in Advanced Calculus for Applications. Upper Saddle River, NJ: Prentice-Hall, 1976. ISBN: 9780130111890.
L7Diffusion/Reaction (cont.)

Examples of Numerical Approaches to Nonlinear Problems
II. Electrical Subsystem
L8IGF + E-field and Transport

Maxwell's Equations
L9Define Potential, Conservation of Charge

L10Laplacian Solutions via Separation of Variables

Electrical Boundary Conditions, Ohmic Transport and Electrochemical Systems
L11Charge Relaxation

Electrical Double Layers

Poisson Boltzmann
L12Donnan Equilibrium in Tissues, Gels, Polyelectrolyte Networks(PDF)
L13Charge Group Ionization and Electro-diffusion Reaction in Molecular Networks(PDF)
III. Cellular Applications
L14Experimental Methods
L15Ligand Binding to Cell Receptors(PDF)
L16Diffusion in Heterogeneous Media(PDF)


PI3K Activation Diagram (PDF)
III. Mechanical Subsystem; Electromechanical Case Studies
L17Conservation of Mass and Momentum in Fluids(PDF)
L18Newtonian, Fully Developed Low Reynold's Number Flows

L19Capillary Electroosmosis-Electrophoresis in MEMs and Microfluidics(PDF)
L20Streaming Potentials

Begin Electrophoresis
IV. Mechanical, Electrical and Physicochemical Interactions: Integrative Case Studies
L21Convective Solute Transport(PDF)
L22Hindered Transport in Membranes and Tissues(PDF)
L23Coupled Fluid and Electrical Shear Stresses: Cell/Molecular Electrophoresis(PDF)
L24Convective and Charge Relaxation Effects in Double Layers: Electrokinetics(PDF)
L25DLVO Theory - Double Layer Repulsion and Molecular Interactions (Proteins, DNA, GAGs)(PDF)
L26Tissue/Molecular Swelling Stresses: Donnan (Macro) vs. Poisson Boltzmann (Nano)(PDF)


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