The mechanical creep compliance of tissue cells is gamma distributed

TL;DR

This study demonstrates that the variation in tissue cell creep compliance is best modeled by a gamma distribution, supported by experimental data and theoretical modeling, improving understanding of cell mechanics variability.

Contribution

The paper identifies gamma distribution as a more accurate model for cell compliance variation, replacing the previously assumed log-normal distribution, supported by extensive experimental and simulation data.

Findings

Cell compliance varies according to a gamma distribution.

Simulation data also fit a gamma distribution, not log-normal.

A stochastic differential equation predicts gamma distribution in cell deformation.

Abstract

Investigations of natural variation among cells within a population are essential for understanding the stochastic nature of tissue cell deformation under applied load. In the existing literature, the population variation of single-cell creep compliance has so far been modeled universally by using a log-normal distribution. Here we use optical stretching, a non-contact and relatively high-throughput technique for probing cell mechanics, to accumulate a sufficient data set that demonstrates robustly that cell compliance varies according to the similar but distinct gamma distribution. Additionally, we re-examine existing simulations that were originally proposed to justify a log-normal fit, and show that in fact these simulation data also correspond to the gamma distribution. Finally, we propose a general stochastic differential equation that analytically predicts a gamma distribution of creep compliance during cell stretching, as well as the Gaussian distribution of cell recovery that we observe experimentally upon removal of applied load. The population variation is well characterized by just a single parameter in each of the creep and recovery regimes. We expect our correction of a phenomenological distribution fit, enabled by an expansive data set for mesenchymal stem cells, to enable the development of more accurate constitutive laws to describe cytoskeletal deformation. These findings thus serve to replace an empirical distribution with a better-fitting model that rests on a more solid experimental and theoretical foundation, and also provides a basis to predict and understand the stochastic nature of the mechanical response of individual cells within populations.