6 EVALUATION OF INTERMOLECULAR FORCES IN A CIRCULATING
6.1 Introduction 113
The association and dissociation of interactions between molecules of cells and surrounding environment play a critical role in biological events such as cell signalling, cell proliferation and cell migration. Cells like platelets and leucocytes often need help of erythrocytes to realize their functions [1]. In addition, cell adhesion mediates pathogenesis of many inflammatory diseases. For example, in a circulating system, accumulation and aggregation of cells can promote certain critical pathological issues, like atherosclerosis and thrombosis. The characterization of molecular interaction is fundamental quest in biology. Quantitative study of molecular interaction force is very important for unveiling the underlying mechanisms and future predictive biology.
Identities of most cell adhesion molecules have been elucidated, for instance, E-selectins, ICAM- 1 and VCAM-1 on endothelial cells; L-selectins, β1-, β2- and β6- integrins, PECAM-1 on leukocytes; Rap1 on sickle red blood cell, etc. Additionally, cell-cell interaction and cell- substrate interaction are regulated by many molecules due to the complexity of cell surfaces. To bypass complex multiple molecular interaction, researchers developed various experimental and theoretical methods to study the intermolecular forces at single molecule level. Several popular experimental techniques include atomic force microscopy (AFM) [2], biomembrane force probes
114 (BFP) [3], surface force apparatuses [4], optical tweezers [5], micropipettes [6], microplates and flow chamber [7, 8]. Direct force measurement by AFM and BFP can achieve ultrahigh resolution for single molecular interaction force analysis by coating probes with specific molecules of interest. Flow chamber experiment is a method which not only can provide high accuracy, but also more closely mimic the in vivo biophysical environment. Furthermore, flow chambers are ideally used to study a number of molecular interactions in parallel to obtain more statistically meaningful data. During last decade, the sensitivity of flow chambers has been largely improved, which can analyze interactions with a resolution of lower than a piconewton. Flow chambers have long been used to study receptor-ligand interactions, such as determination of bond lifetime and unbinding force calculation. A recent paper did a comprehensive review for studying molecular interactions with a laminar flow chamber [9]. As a result of the irregular shape and uncertain bond length for cells, which would cause the unqualified calculation of forces, molecule-coated spheres rather than cells are usually used in flow chamber experiments to eliminate the unexpected phenomena. The key information achieved in flow chamber experiments is monitoring the molecular bond formation and rupture in a defined hydrodynamic environment. There is a simple formula suggested by Bell [10]used to describe a given receptor- ligand behaviour:
off( ) off(0)exp( 0)
F k F k
F
(1)
where koff(F) is the dissociation rate as a function of applied forceF. F0was approximated as
/
BT
k , where kBis Boltzmann’s constant, Tis the absolute temperature, and is the bond distance. In flow chamber experiment, the hydrodynamic force of breakup exerted on a
115 circulating cell doublet has been calculated [11], and generally used to predict the force strength of intermolecular bond [12]. Currently, several theoretical methods mostly used to evaluate interparticle interactions in colloidal suspensions [13-16] have been adapted and applied in biological systems to study the cell-cell interaction forces [11, 17].
However, in reality, intercellular forces are a complex mixture of various interactions such as electrostatic forces, van der Waals (VDW) forces and steric forces etc. The contribution of these forces depends on both the separation distance and local environment. When cells are brought to a distance less than several nanometres, those molecules mediated forces and short distance forces like ionic bond may become critical, which further complicates the interaction forces. Only considering the hydrodynamic forces may underestimate or overestimate the interaction forces of molecular bonds in flow chamber experiments. To more quantitatively interpret flow chamber experiment results like the bonding life time study, these additional non-neglectable intercellular forces, for example, the DLVO (Derjaguin-Landau-Verwey-Overbeek) force, need to be taken into consideration. DLVO forces, which combine the effects of the London-van der Waals attraction and the electrostatic repulsion due to the electric double layer (EDL) interaction, has been successfully used in biological application [18-20]. In this study, circulating cell doublets and the cell-substrate interaction model with several ten nanometres separating distance are investigated. Excluding hydrodynamic forces, the DLVO forces are taken into account of the interaction force calculation.
In order to quantify the molecular interaction forces of cell-cell and cell-substrate in a circulating system, such as flow chamber and microfluidic culture system, Low-Reynolds number hydrodynamic theory and Goldman’s theory are employed to calculate the hydrodynamic force
116 generated from the flow field effect for a cell doublet and the cell-substrate interaction respectively, followed by the DLVO theory analysis. The results demonstrate that DLVO forces have the scale as large as 14.6% of the exerted hydrodynamic force for cell doublets model, and for intermolecular force analysis of cell-substrate interaction, it can go up to 30%. Both cell doublet and cell-substrate models are subject to nonlinear effect of intermolecular forces as the distance changes. This analysis is beneficial to predict the biophysical properties of receptor- ligand bonds more quantitatively.