Intrinsic Cell-to-Cell Variance from Experimental Single-Cell Motility Data

When analyzing the individual positional dynamics of an ensemble of moving objects, the extracted parameters that characterize the motion of individual objects, such as the mean-squared instantaneous velocity or the diffusivity, exhibit a spread that is due to the convolution of three different effects: (i) Motion stochasticity, caused by the fluctuating environment and enhanced by limited observation time, (ii) measurement errors that depend on details of the detection technique, and (iii) the intrinsic parameter variance that characterizes actual differences between individual objects, which is the quantity of ultimate interest. We develop the theoretical framework to separate these three effects based on the generalized Langevin equation, which constitutes the most general description of active and passive dynamics, as it derives from the underlying general many-body Hamiltonian for the studied system without approximations. We apply our methodology to determine intrinsic cell-to-cell differences of living and actively moving human breast-cancer cells, algae cells, and, as a benchmark, size differences of passively moving polystyrene beads in water. We find algae and human breast-cancer cells to exhibit significant individual differences, reflected by the spread of the intrinsic mean squared instantaneous velocity over two orders of magnitude, which is remarkable in light of the genetic homogeneity of the investigated breast-cancer cells and highlights their phenotypical diversity. Quantification of the intrinsic variance of single-cell properties is relevant for infection biology, ecology, and medicine, and it opens up new possibilities to estimate population heterogeneity on the single-organism level in a nondestructive manner. Our framework is not limited to motility properties but can be readily applied to other experimental time-series data.