BIOPHYSICS:

Of all the biochemistry important to health and disease, it may be surprising that physics also plays many critical roles. For example, protein crowding in the cell interior influences protein assembly, biochemical signaling, enzymatic reaction rates, and many other physiological processes.

Mechanical stress also plays important roles in human physiology, e.g. cell aggregate flow through blood vessels and the progression of cancer. In this context, the yield stress is of physiological relevance.

Cell aggregate yield stress is the level of mechanical stress above which the cells deform plastically rather than elastically. In other words, above the yield stress, cell aggregates do not fully revert back to their original morphology.

Cell aggregate yield stress is experimentally measurable, at least in relatively simple cases. However, predictive mathematical models which agree with these experiments, especially useful when faced with intractable physiological experiments, require validation.

Luigi Preziosi (Politecnico di Torino, Italy) and coworkers have developed a mathematical model of cell aggregates under mechanical stress, incorporating properties of both individual cells and the cell aggregate. Predictions of their model agree with experimental data.

Assumptions of the mathematical model.

The scientists' mathematical model ignores cell growth and death, given that a change in mechanical conditions is often much faster than the time scale of such processes. Their model treats the cells as a continuous mass, rather than individual cells, a reasonable approximation of a dense packing of cells.

The cell aggregates are considered to be porous, deformable, and filled with fluid. They also consider the cells themselves to be nonporous, and the intercellular fluid to be at rest.

Strictly speaking, these last two assumptions are not physiologically accurate descriptions. However, it enables the scientists to solely consider the volume occupied by the cells in relation to cell aggregate mechanical stress.

The cells are modeled to deform elastically below a certain level of mechanical stress, and plastically above it (as noted, this is observed in experiments). The number of cell-cell bonds is proportional to the threshold of cellular reorganization (yield stress), i.e. the cell area multiplied by the bond energy.

Thus, standard theory predicts that the yield stress is nonlinearly proportional to the number of cells per unit volume. The scientists further assume that cellular compression is negligible until a certain cellular density is reached.

Predictions and comparison to experiments.

The scientists' mathematical model makes several predictions. Specifically, cell aggregates reversibly deform below the yield stress whether the stress is progressively increased, applied all at once, or applied repetitively; and the yield stress is independent of the maximum stress placed on the cell aggregate.

These predictions are all physically reasonable, and have been observed in experiments with actual cells. Mathematical predictions of yield stress generally also match experimental observations.

The model further explains how certain cancers may be more invasive than others. If the cell aggregates in a tumor do not adhere to each other very strongly, the cancer cells are more likely to break off and spread to surrounding tissues.

Further development.

As the scientists note, it would be interesting to incorporate different intercellular rearrangement times into their mathematical model. This would more accurately reflect the cell receptor heterogeneity observed in living cells.

In addition to more accurately reflecting actual cell aggregate behavior, it may also provide useful physical insight into the role of cell surface proteins in maintaining the cellular elasticity critical for normal health, and how its disruption may facilitate disease.

NOTE: The scientists report no sources of funding for their research.

for more information:
Preziosi, L., Ambrosi, D., & Verdier, C. (2010). An elasto-visco-plastic model of cell aggregates Journal of Theoretical Biology, 262 (1), 35-47 DOI: 10.1016/j.jtbi.2009.08.023