Bioengineering Thermodynamics

8/14/2019 Bioengineering Thermodynamics

1/24

Some Bioengineering

Applications of Thermodynamics


2/24


3/24

Recap of Some Bioengineering

Thermodynamics

Material Properties of Lipid Membranes

compressibility modulus, bending rigidity

Domain Formation in Non-ideal

Membranes

Cholesterol mixtures


4/24

Outline for the Week

Today: Cell Adhesion/Electromechanical

coupling

Wed: Protein Folding/Electrochemistry

Friday: Non-Equilibrium Thermodynamics Introduction to Transport


5/24


6/24

Adhesion between leukocytes and endothelial cells Leukocytes leavethe circulation at sites of tissue inflammation by interacting with theendothelial cells of capillary walls. The first step in this interaction isthe binding of leukocyte selectins to carbohydrate ligands on theendothelial cell surface. This step is followed by more stableinteractions between leukocyte integrins and members of the Igsuperfamily (ICAMs) on endothelial cells.


7/24

Specific molecules required for cell-cell or

cell-surface adhesion

Implies a repulsive barrier normally exists that

must be overcome


8/24

Thermodynamics of Cell Adhesion

Free

Energy

0

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


9/24

Simple Two-State Model

n1t = surface density of receptors on cell 1

n2t = surface density of receptors on cell 2

n1t= n1+nb

n2t= n2+nb

n1,2 is density of unattached receptors on respective cell

nb is surface density of cell bridges

nb=Nb /A where Nb is the absolute number of contacts

A is the area of contact


10/24

Gibbs Energy of Adhesion

)()(

)()()()(),,(

,

222111

sAnN

nNNnNNsANG

sbbb

btbtb

+

++=

Consider process: cells go from separated state to a bound statewhere 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

(s) represents free energy of non-specific repulsion

s is the separation distance


11/24

Chemical Potential Terms

)ln()(

)ln()(

bB

o

bbb

iB

o

iii

nTkn

nTkn

+=

+=

....)(2

1)()(

:bondaofmodelspring

2++= LsLs

o

b

o

b

distanceseparationondependsitbecausevarywillob


12/24

Equilibrium Constant for Cell

Bridging

( )

]/])(21[

/][exp)(

2

21

TkLsK

TkTksK

BL

BB

o

b

oo

++=

K(s) is maximum when separation distance equals

unstressed bond length

KL represents binding constant for formation of an

unstressed cell-cell bridge


13/24


14/24

Forces Involved in Separation

distancesticcharacteriais

ilitycompressibtheis

)/exp()(

ss

s =


15/24

So now we have all the necessary terms in

the Gibbs Free Energy?

How do we determine the equilibrium

condition?


16/24

Phase Diagram for Adhesion


17/24

Equilibrium Depends on Number of

Receptors and Compressibilty


18/24

Effect of Changing KL


19/24

Agreement with Experiment


20/24

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 highlycooperative interactions


21/24

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 intheir 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


22/24


23/24

Kinetic Modeling

Reverse rate depends on force:

Here is the bond interaction

distance


24/24

Phase Diagram for Dynamic

Adhesion

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Bioengineering Thermodynamics