Institute for Systems Genetics
New York University Langone Medical Center
GEM nanoparticles suggest that cells tune static disorder to criticality
We developed genetically encoded multimeric nanoparticles (GEMs) that self-assemble to a defined size and icosahedral geometry. GEMs enabled us to efficiently study the physical properties of the cytoplasm across many genetic, epigenetic and environmental conditions. We found that GEM trajectories exhibit subdiffusive behavior inside living cells. The mean square displacement (MSD) is not proportional to time, but grows slower with a scaling exponent alpha = t0.72. While the effective diffusion coefficient changes as a function of genetic and environmental perturbations, the scaling exponent seems to stay the same over the entire paramter range we tested. The hypothesis that subdiffusive behavior arises from molecular crowding, leads to several competing models to account for this constant value of alpha. The most widely accepted model is the Continuous Time Random Walk (CTRW), in which subdiffusion arises due to trapping effects that slow down the motion of the trajectories. For example, this may be caused when the system navigates on a rugged energy landscape with many local minima, created e.g. by crowding effects in the cytoplasm, and motion requires surmounting the barriers between these minima. In this case, the breadth of the distribution of energies determines the scaling exponent. A second possibility is that the viscoelastic properties of the interconnected molecules of the cell generate a memory behavior (kernel). For example, the elastic component in polymer can increase the probability of restoration of particles towards the origin point of the previous step. This restoration force gives rise to memory: Tracer particles are more likely than random to go back to where they came from, and the larger the step, the larger the probability to reverse the step. This model can be described by the Fractional Brownian theory of Motion, (FBM). The third explanation for subdiffusion stems from self-organized criticality in physical systems. In this model, self-organized criticality occurs when the concentration of crowders exceed the percolation threshold, a threshold density above which the network jams. When the percolation threshold is exceeded, the connectivity of the fluid phase is lost, and the system begins to locally transition dynamically in and out of a glassy state. A random walk through such a critical system is also subdiffusive. Each of these models makes predictions for the value of the Flory exponent (alpha). Our data give a robust alpha of 0.72 across all conditions. An alpha of 0.72 is perfectly consistent with the self-organized criticality model. This finding raises a profound question: is biology tuning the static disorder in the cell to be at criticality? Nobel laureate de Gennes made sense of these systems by analogy to an “Ant in a labyrinth”, and his work laid the foundation of a new field in statistical mechanics. We will now apply his approach to cells. These models have been explored in both glassy phenomenologocal systems and through the conceptual frame work of polymer chemistry and phase transitions. However, we provide the first evidence that cells are critical. However, no current theory incorporates the out-of-equilibrium nature of living systems. Our future work will combine the theoritical frameworks of active matter with de Gennes approaches to glass transitions and criticality. We hypothesize that the statistical nature of trajectories with cells are determined by criticality and that active processes will set the rate of the local dynamical shifts between glassy and fluid states.