A mathematical finance approach to the stochastic and intermittent viscosity fluctuations in living cells

Here we report on the viscosity of eukaryotic living cells as a function of the time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblastic cells are investigated using an active microrheological technique, where magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in mathematical finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1 - 10 s and 100 - 200 s, not previously disclosed. The shorter time is found being related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and statistical results from mathematical finance. The current approach could be exploited to reveal hidden features from biological complex systems, or determine new biomarkers of cellular metabolism.