Probing scale-dependent liveliness with nonequilibrium thermospectroscopy

Abstract

Probing the spatially heterogeneous activity across scales is a major challenge in living matter. Energy injection at diverse length scales leads to mode coupling, inter-modal energy transfer, and entropy production. We demonstrate the emergence of multiple effective (``active'') temperatures in nonequilibrium molecular- and Brownian-dynamics simulations of an active polymer. Via a generalised Langevin equation for a labelled monomer we identify spectral noise temperatures and their relation to the underlying activity landscape. A harmonic trap of variable stiffness can serve as a minimally invasive prototypical spectroscopic device to selectively scan through the emergent effective temperatures and thereby resolve the scale-dependent activity.

Figures (3)

• Figure 1: Probing nonequilibrium tracer fluctuations in living cells. The intra cellular network experiences active driving at various scales. The fluctuating tracer trajectory encodes signatures of the corresponding activity landscape comprising areas of high activity (liveliness) and areas without local active contributions (dead areas).
• Figure 2: Emergence of multiple effective temperatures in active Brownian (a) and nonequilibrium molecular-dynamics simulations in a non-isothermal Lennard-Jones solvent (b). (c) Swim speeds at different positions along the polymer chain. Insets: Sketch featuring the first and sixth bending modes of the polymer, showing that at high frequencies, the main modal contribution stems from the direct vicinity of the tracer. (d) Triangular (red) and linear (blue) local molecular temperature profile in molecular dynamics simulations. Dotted lines show predictions by the stationary heat equation. Brownian (e) and molecular (f) dynamics simulations versus our prediction from Eq. \ref{['eq:effective_noise_temperature_dissipation']}. Insets confirm a Gaussian probability distribution of the tracer positions. Colour as in (c)-(d).
• Figure 3: Effective mode temperatures and entropy production rate. (a)-(c) Mode shape $W_n(s)$ for hinged and torqued ends. Dashed lines depict the activity profiles $v_0(s)$ (a) and (b) or temperature $T(s)$ (c). (d)-(f) The effective mode temperature matrices $\mathcal{V}_{nm}$ (d)-(e) and $\mathcal{T}_{nm}$ (f) betray the mode-mode coupling and its energy transfer in their off-diagonal components; insets show diagonal values $\mathcal{V}_{nn}$ and $\mathcal{T}_{nn}$. (g)-(i) The accompanying entropy production rate $\dot{s}_{nm}$ per mode pair $(n,m)$ provides a reference for the multiscale character of the activity.