ANNUAL REPORT 2006

Figure 4
Annual report 2006 16
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Figure 2.4: The predicted power spectral density as a function of frequency, due to
both molecular motors (solid line) and thermal fluctuations (dashed) in an active gel,
showing that the non-equilibrium fluctuations are only expected to be apparent at
low frequency [2], consistent with experiment.
The fluctuation-dissipation theorem and non-equilibrium fluctuations
A quantitative description of the function of cells and their complex machineries
requires a combination of a biochemical molecular approach with a statistical and
thermodynamic one. However, since it is a defining property of living systems to be
out of thermodynamic equilibrium, classical methods have to be extended to account
for this. This work shows how non-equilibrium motor activity controls the mechanical
properties of a simple three-component in vitro model of the cytoskeleton. The nonequilibrium
origin of this active mechanical control is demonstrated by a violation of a
fundamental theorem of statistical physics, the fluctuation-dissipation (FD) theorem,
which links thermal fluctuations of arbitrary systems to their response to external
perturbations. This FD theorem is a generalization of Einsteins famous description
of Brownian motion. While it is only valid in equilibrium, its possible generalizations
to out-of-equilibrium systems, ranging from granular materials to living cells
has been hotly debated. Prior studies in cells have suggested violations of the FDT,
although no direct test has so far been possible. These experiments show that the
non-equilibrium fluctuations only appear at low frequency, consistent with the theoretical
prediction of colored noise, varying inversely with the square of the frequency,
due to molecular motors.