Some Bioengineering Applications of Thermodynamics

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Some Bioengineering Applications of Thermodynamics
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Last week of class.
Or
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Recap of Some Bioengineering Thermodynamics

• Material Properties of Lipid Membranes
• compressibility modulus, bending rigidity
• Domain Formation in Non-ideal Membranes
• Cholesterol mixtures

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Outline for the Week

• Today Cell Adhesion/Electromechanical coupling
• Wed Protein Folding/Electrochemistry
• Friday Non-Equilibrium Thermodynamics
• Introduction to Transport

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Adhesion Molecules

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• Specific molecules required for cell-cell or
  cell-surface adhesion
• Implies a repulsive barrier normally exists that
  must be overcome

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Thermodynamics of Cell Adhesion
Cells far apart Energy is sum of both cells
Cells closer together Repulsive Interactions
increase free energy
Formation of cell-cell bridges counteracts
repulsion lowers free energy
Free Energy
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Simple Two-State Model

• n1t surface density of receptors on cell 1
• n2t surface density of receptors on cell 2
• n1t n1nb
• n2t n2nb
• n1,2 is density of unattached receptors on
  respective cell
• nb is surface density of cell bridges
• nbNb/A where Nb is the absolute number of
  contacts
• A is the area of contact

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Gibbs Energy of Adhesion
Consider process cells go from separated state
to a bound state where formation of cell-cell
bridges occur
First Two Terms Free energy change by unattached
receptors on cell 1 and cell 2due to bond
formation Third Term free energy of the
cell-cell bridges Last Term work done in
overcoming nonspecific repulsion
G(s) represents free energy of non-specific
repulsion s is the separation distance
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Chemical Potential Terms
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Equilibrium Constant for Cell Bridging
K(s) is maximum when separation distance equals
unstressed bond length KL represents binding
constant for formation of an unstressed cell-cell
bridge
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Illustration of Spring Model
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Forces Involved in Separation
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• So now we have all the necessary terms in the
  Gibbs Free Energy?
• How do we determine the equilibrium condition?

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Phase Diagram for Adhesion
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Equilibrium Depends on Number of Receptors and
Compressibilty
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Effect of Changing KL
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Agreement with Experiment
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Conclusions of the Model

• Bridging receptors concentrate in regions of
  cell-cell contact
• - experimentally observed
• Phase Transitions are observed in cell adhesion
• - cells are not billard balls
• - adhesion can be stabilized by highly
  cooperative interactions

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• Who will lead me into that still more hidden and
  dimmer region where Thought weds Fact, where the
  mental operation of the mathematician and the
  physical action of the molecules are seen in
  their true relation? Does not the way pass
  through the very den of the metaphysician,
  strewed with the remains of former explorers?
• - James Clerk Maxwell, 1870

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Adhesive Dynamics
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Kinetic Modeling
Reverse rate depends on force
Here g is the bond interaction distance
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Phase Diagram for Dynamic Adhesion