Equilibrium and out-of-equilibrium mechanics of living mammalian cytoplasm

Gupta, Satish Kumar; Guo, Ming

Living cells are intrinsically non-equilibrium systems. They are driven out of equilibrium by the activity of the molecular motors and other enzymatic processes. This activity along with the ever present thermal agitation results in intracellular fluctuations inside the cytoplasm. In analogy to Brownian motion, the material property of the cytoplasm also influences the characteristics of these fluctuations. In this paper, through a combination of experimentation and theoretical analysis, we show that intracellular fluctuations are indeed due to non-thermal forces at relatively long time-scales, however, are dominated solely by thermal forces at relatively short time-scales. Thus, the cytoplasm of living mammalian cells behaves as an equilibrium material at short time-scales. The mean square displacement of these intracellular fluctuations scales inversely with the cytoplasmic shear modulus in this short time-scale equilibrium regime, and is inversely proportional to the square of the cytoplasmic shear modulus in the long time-scale out-of-equilibrium regime. Furthermore, we deploy passive microrheology based on these fluctuations to extract the mechanical property of the cytoplasm at the high-frequency regime. We show that the cytoplasm of living mammalian cells is a weak elastic gel in this regime; this is in an excellent agreement with an independent micromechanical measurement using optical tweezers.

DOI

Phase boundaries as agents of structural change in macromolecules

Ritwik Raj and Prashant K. Purohit

We model long rod-like molecules, such as DNA and coiled-coil proteins, as one-dimensional continua with a multi-well stored energy function. These molecules suffer a structural change in response to large forces, characterized by highly typical force-extension behavior. We assume that the structural change proceeds via a moving folded/unfolded interface, or phase boundary, that represents a jump in strain and is governed by the Abeyaratne–Knowles theory of phase transitions. We solve the governing equations using a finite difference method with moving nodes to represent phase boundaries. Our model can reproduce the experimental observations on the overstretching transition in DNA and coiled-coils and makes predictions for the speed at which the interface moves. We employ different types of kinetic relations to describe the mobility of the interface and show that this leads to different classes of experimentally observed force-extension curves. We make connections with several existing theories, experiments and simulation studies, thus demonstrating the effectiveness of the phase transitions-based approach in a biological setting.

DOI