**How do two cells that can adhere, decide whether or not they should adhere?** Typically, potentially adherent cells become adherent by increasing their adherence-receptor expression levels (

*R*/

_{1}*R*) past a certain “threshold” or “EC

_{2}_{50}” (see figure above). A classic 1984 paper defined this EC

_{50}as a function of

*R*/

_{1}*R*‘s binding constant

_{2}*K*as illustrated above for two average eukaryotic cells.

_{soln}^{1,2}This equilibrium model for cellular adhesion is described in more detail below.

**EQUILLIBRIUM MODEL OF CELL ADHESION**

This model is formulated on the idea that cell-cell adhesion is determined by a competition between two opposing forces:

**specific binding interactions (**between complementary receptors*K*)_{D}*R*and_{1}*R*which favors adhesion (like the hooks and loops in velcro)_{2}**non-specific repulsion (Γ)**between the cell surfaces created by: (1) “” between negatively charged cell surfaces (due to the glycocalyx) (2) “__electrostatic repulsion__” which is an osmostic pressure created by the exclusion of water from the cell surfaces as they come together.__steric stabilization effect__

These opposing forces can be defined using the equations below which are defined and discussed in detail in reference #1.

**PARAMETER DEFINITIONS (≈ TYPICAL VALUES) **

: molar dissociation constant measured in free solution*K*_{soln}**6 × 10**: conversion factor converting moles/Liter to molecules/m^{26}^{3}: distance between adherent cells (≈ 10-20×10*d*^{-9}m): contact area between adherent cells (≈ 10*A*^{-10}m^{2}): spring model of mechanical “pulling” stress between*bond stress**R*and_{1}*R*_{2}^{1,2}: distance between cells that results in an “unstressed” bond between*L**R*and_{1}*R*(≈ 10×10_{2}^{-9}m): Boltzmanns Constant (≈ 1.38×10*k*^{-23}m^{2}s^{-2}K^{-1}kg ): Temperature (≈ 300 K)*T*: force constant for stretching of*κ**R*/_{1}*R*bond (≈ 10_{2}^{-4}N/m)^{3,4}: compressability of glycocalyx (≈ 10*γ*^{-11}N)^{5}: thickness coefficient of glycocalyx (≈ 5-20×10*τ*^{-9}m)^{5}

**QUADRATIC MODEL FOR BRIDGE NUMBER **

Combining these equations with conservation of mass and the law of mass action the authors of reference #1 were able to model the number of bridges between cells at equilibrium as a quadratic function below:

Solving for the EC_{50} and then plugging in the physically reasonable values of each parameter listed above (for typical eukaryotic cells) we were able to obtain the below expression which enables one to estimate the Receptor threshold from a dissociation constant determined in free solution (*K _{soln}*):

**REFERENCES:**

- Bell, G.I.; Dembo, M.; Bongrand, P. Cell Adhesion: Competition between Nonspecific Repulsion and Specific Bonding.
*Biophys. J.***1984**, 45, 1051-1064. - Lauffenburger, D.A. Receptors: Models for Binding, Trafficking and Signalling, Oxford University Press
**1993**. - Levy, R.M.; Karplus, M. Vibrational approach to the dynamics of the alpha-helix.
*Biopolymers*,**1979**18, 2465-2495. - Suezaki, Y.; Go, N. Fluctuations and mechanic strength of alpha-helixes of ployglycine and poly (L-alanine).
*Biopolymers*,**1976**15, 2137-2153 - Napper, D.H. Steric Stabilization.
*J. Colloid Interface Sci.***1977**58, 390-407

This work by Eugene Douglass and Chad Miller is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.