Lambert Ben Freund

In a nonadhesive environment, cells will self-assemble into microtissues, a process relevant to tissue engineering. Although this has been recognized for some time, there is no basis for quantitative characterization of this complex process. Here we describe a recently developed assay designed to quantify aspects of the process and discuss its application in comparing behaviors between cell types. Cells were seeded in nonadhesive micromolded wells, each well with a circular trough at its base formed by the cylindrical sidewalls and by a central peg in the form of a right circular cone. Cells settled into the trough and coalesced into a toroid, which was then driven up the conical peg by the forces of self-assembly. The mass of the toroid and its rate of upward movement were used to calculate the cell power expended in the process against gravity. The power of the toroid was found to be 0.31 ± 0.01 pJ/h and 4.3 ± 1.7 pJ/h for hepatocyte cells and fibroblasts, respectively. Blocking Rho kinase by means of Y-27632 resulted in a 50% and greater reduction in power expended by each type of toroid, indicating that cytoskeletal-mediated contraction plays a significant role in the self-assembly of both cell types. Whereas the driving force for self-assembly has often been viewed as the binding of surface proteins, these data show that cellular contraction is important for cell–cell adhesion. The power measurement quantifies the contribution of cell contraction, and will be useful for understanding the concerted action of the mechanisms that drive self-assembly.

The goal of measurements of the resisting force generated by a molecular bond as it is being forcibly separated under controlled conditions is to determine functional characteristics of the bond. Here, we establish the dependence of force history during unbinding on both those parameters chosen to characterize the bond itself and the controllable loading parameters. This is pursued for the practical range of behavior in which unbinding occurs diffusively rather than ballistically, building on the classic work of Kramers. For a bond represented by a one-dimensional energy landscape, modified by a second time-dependent energy profile representing applied loading, we present a mathematical analysis showing the dependence of the resistance of the bond-on-bond well shape, general time dependence of the imposed loading, and stiffness of the loading apparatus. The quality of the result is established through comparison with full numerical solutions of the underlying Smoluchowski equation.

The adhesion of bacteria to surfaces plays critical roles in the environment, disease, and industry. In aquatic environments, Caulobacter crescentus is one of the first colonizers of submerged surfaces. Using a micromanipulation technique, we measured the adhesion force of single C. crescentus cells attached to borosilicate substrates through their adhesive holdfast. The detachment forces measured for 14 cells ranged over 0.11 to 2.26 μN, averaging 0.59 ± 0.62 μN. Based on the calculation of stress distribution with the finite element analysis method (dividing an object into small grids and calculating relevant parameters for all of the elements), the adhesion strength between the holdfast and the substrate is >68 N/mm ² in the central region of contact. To our knowledge, this strength of adhesion is the strongest ever measured for biological adhesives.

The generation of a random walk path under the action of an external potential field has been of interest for decades. The motivation derives largely from the prospect of incorporating the nonlocal excluded volume effect through such a potential in characterizing the statistical behavior of a long flexible polymer molecule. In working toward a continuum mean-field model, a central feature is a partial differential equation incorporating the influence of the potential and governing the generating function for the dependence of end to end separation distance of the molecule on its pathlength. The purpose here is to describe an approach in which the differential equation is recast as a global minimization of a functional. The variational approach is illustrated by an application to familiar configurations, the first of which is a molecule attached at one end to a noninteracting plane barrier in the presence of a uniform potential field. As a second illustration, the generating function is sought for a free molecule for the case in which conformations must be consistent with the excluded volume condition. This is accomplished by adapting a local form of the Flory approach to the phenomenon and extracting estimates of the expected end to end separation distance, the entropy and other statistical features of behavior. By means of the variational principle, the problem is recast into a form that admits a direct, noniterative analysis of conformations within the context of the self-consistent field theory.

We examine the process of expansion of a focal adhesion complex by which a biological membrane containing mobile binders adheres to a substrate with complementary binders. Attention is focused on the situation, common among living cells, in which the mean mobile binder density is insufficient to overcome generic resistance to close approach of the membrane to its substrate. For the membrane to adhere, binders must be recruited from adjacent regions to join an adhesion patch of density adequate for adhesion, thereby expanding the size of the patch. The specific configuration examined is the expansion of a circular adhesion zone for which diffusive binder transport driven by a chemical potential gradient is the mechanism of binder recruitment. An aspect of the process of particular interest is the stability of the circular shape of the expanding front. It is found that the adhesion front radius increases as √t, where t is the time elapsed since nucleation, and that the circular shape becomes unstable under sinusoidal perturbations for radii large compared with the nucleation size, as observed in recent experiments.