DOI: 10.5061/dryad.h44j0zpsw
title: Data from: Variance sum rule for entropy production

description: Entropy production is the hallmark of nonequilibrium physics, quantifying
 irreversibility, dissipation, and the efficiency of energy transduction
 processes. Despite many efforts, its measurement at the nanoscale remains
 challenging. We introduce a variance sum rule for displacement and force
 variances that permits us to measure the entropy production rate in
 nonequilibrium steady states. We first illustrate it for directly
 measurable forces, such as an active Brownian particle in an optical trap.
 Data for this analysis can be found in the repository (1) described below.
  We then apply the variance sum rule to flickering experiments in
 human red blood cells (repositories (2-4)). We find that the entropy
 production rate is spatially heterogeneous with a finite correlation
 length (in particular, data in the repository (4)) and its average value
 agrees with calorimetry measurements.  The dataset is composed of
 4 repositories: 1) SwitchingTrap.zip, containing data from Optical-tweezer
 experiments and used in Fig. 2 and 3 in the main paper, all data are
 three-column files featuring time (s), position (nm), and force (pN); 2)
 OpticalStretching.zip, containing data from Optical-tweezer experiments
 shown in Fig. 4a in the main paper, all data are two-column files
 featuring time (s) and position (nm) traces; 3) OpticalSensing.zip,
 containing data from Optical-tweezer experiments shown in Fig. 4b in the
 main paper, all data are one-column files featuring position (m) traces,
 sampling frequency 25kHz; 4) OpticalMicroscopy.rar, containing data from
 Optical-microscopy experiments shown in Fig. 4c in the main paper, all
 data are one column files featuring position (nm) traces, sampling
 frequency 2kHz.
description: Optical trap experiments with beads. Experiments with colloidal
 particles (Figs.1,2) were done in a miniaturized version of an optical
 tweezers instrument described in Dieterich, J. Camunas-Soler, M.
 Ribezzi-Crivellari, U. Seifert, F. Ritort, Nature Physics11, 971 (2015).
 Measurements in Figures 1 and 2 were performed with highly stable
 miniaturized laser tweezers in the dual-trap mode. The instrument directly
 measures forces by linear momentum conservation. In all experiments, we
 used polystyrene calibration beads of 3μm diameter. Piezo actuators bend
 the optical fibers and allow us to move the trap while measuring the trap
 position using a light lever that deflects a fraction of the laser beam to
 a position-sensitive detector (PSD). Force and trap position measurements
 are acquired at 100 kHz bandwidth using a data acquisition
 board (PXI-1033, National Instruments, Austin, TX). 
 OT-stretching RBC experiments. For the RBC experiments, human
 RBCs were obtained by finger pricking of a healthy donor. The PBS solution
 contains 130 mM NaCl, 20 mM K/Na phosphate buffer, 10 mM glucose, and 1
 mg/mL BSA. For the experiments, 4μL of blood was diluted in 1mL of PBS.
 The OT-stretching consists of three steps: 1) the RBC is nonspecifically
 attached to a bead that is captured in an optical trap of stiffness
 56pN/μm while the RBC remains outside the optical trap; 2) the bead is
 brought to the tip of a micropipette where it remains immobilized while
 the RBC remains attached on the other side of the bead; 3) a second bead
 is captured by the optical trap and brought to the opposite end of the RBC
 to form a dumbbell configuration. All measurements were made at 40kHz with
 a data acquisition board (PXI-1033, National Instruments, Austin, TX).
 Bead-RBC contact areas (Fig. 4A) were estimated using a multiscale feature
 extractor based on a Gaussian pyramid representation of the raw image
 followed by a Laplacian reconstruction. OT-sensing RBC
 experiments. Experiments have been performed as described previously (H.
 Turlier, et al., Nature Physics 12, 513 (2016)). RBCs were obtained from a
 healthy donor by finger pricking. After washing in PBS-based cell medium
 (CM), cells were biotinylated using a 0.5mM NHS-PEG3400-biotin (Nektar
 Therapeutics, San Carlos, CA) solution in CM. Streptavidin-coated, 3.28μm
 diameter polystyrene beads were incubated with the biotinylated RBC, and
 four beads were attached to the RBC using a time-shared optical tweezers
 system. For the OT-sensing, three of the four beads were trapped (trap
 stiffness: 1.2pN/μm), and the cell and bead system was moved 20μm away
 from<br>the surface to avoid any unspecific substrate interaction.
 To detect the free fluctuations of the fourth bead (probe bead), the laser
 power on this bead was reduced to 0.1 mW which is insufficient to trap the
 bead (trap stiffness &lt; 24fN/μm). The particle motion was recorded
 using a position-sensitive detector (PSD) placed in a plane conjugate to
 the back focal plane of the lightcollecting objective (Obj2 in Fig.4B).
 Low-frequency noise peaks known to originate from the stage were filtered
 in Fourier space. For OT-sensing, bead-RBC contact areas were estimated as
 described in H. Turlier, et al., Nature Physics 12, 513 (2016).
 OM RBC experiments. Human RBCs were extracted from the blood of
 healthy donors and then separated by centrifugation at 5000g for 10 min at
 4ºC, rinsed with PBS, and, finally,<br>diluted (1:15) with PBS
 supplemented with 10 mM glucose, and 1 mg/mL bovine serum albumin (R.
 Rodriguez-Garcia, et al., Biophysical Journal 108, 2794 (2015)).
 High-resolution time-lapse Optical Microscopy (OM) was performed using a
 phase contrast inverted microscope (NikonEclipse2000Ti) armed with a 100 W
 TI-12 DH Pillar Illu-<br>minator, an LWD 0.52 collimator, and a 100x
 oil immersion objective (PlanApoVC, N.A. 1.4; Nikon). RBC flickering was
 captured at the equatorial plane with a FASTCAM SA3 camera (Photron), with
 an effective pixel size of 50x50 nm2. Movies were recorded for 10s, with
 a sampling frequency of 2000 frames per second (2kHz).
description: # Variance sum rule for entropy production This dataset contains the data
 used for the analysis presented in the paper "Variance sum rule for
 entropy production". The dataset contains 4 repositories, each of
 these relative to a different experiment. Furthermore, we also include
 software in the form of a Jupyter Notebook to perform the Analysis
 described in the paper. ## Description of the data and file structure The
 dataset contains 4 repositories. 1\) SwitchingTrap.zip, containing data of
 a Brownian particle trapped with optical tweezers and whose center jumps
 between two values at random times. The latter dynamics is governed by a
 two-state Master equation. The results of the analysis of this data is
 presented in Fig. 2 and 3 in the main paper. The repository contains three
 repositories called "18nm", "70nm", "280nm",
 one for each experiment. The titles of the repositories refer to the
 distance between the minima between which the center of the optical
 tweezer is switching. Each of these repositories contains data for a
 different realisation of the experiments, 10 files for "18nm", 5
 files for "70nm" and 5 files for "280nm". The name of
 each file indicates the distance between the minima of the switching trap,
 the frequency at which the trap is switching, and a label indicating the
 trace number. Each file contains three columns featuring time (s), bead
 position (nm), and force acting on the bead (pN). 2\)
 OpticalStretching.zip, containing data of a Brownian particle trapped with
 optical tweezers and chemically attached to a red blood cell. The results
 of the analysis of this data is shown in Fig. 4a in the main paper. The
 repository contains two repositories, i.e. for experiments where the
 optical tweezers' laser intensity is low ("Low_Power_RBC")
 or high ("High_Power_RBC"). "Low_Power_RBC" contains
 three repositories, one for each experiment on a different red blood cell.
 For each red blood cell, the laser intensity varies and the corresponding
 bead stiffness can be found in the repository "Info".
 "High_Power_RBC" contains eight repositories, one for each
 experiment on a different red blood cell. Each repository contains traces
 corresponding to red blood cells pulled at a certain force, found in the
 title of the files, and expressed in pN. All data are two-column files
 featuring time (s) and bead position (nm) traces. 3\) OpticalSensing.zip,
 containing data of a Brownian particle trapped with optical tweezers and
 chemically attached to a red blood cell. The results of the data analysis
 can be found in Fig. 4b in the main paper. The repository contains two
 repositories, i.e. for experiments involving normal ('Normal')
 and starved ('Starved') red blood cells. Both of them contain
 different repositories, one for each red blood cell experiment. For each
 red blood cell, many realizations of the same experiment have been
 performed and to each of these realizations corresponds a datafile
 featuring position (m) traces with a sampling frequency of 25kHz. 4\)
 OpticalMicroscopy.rar, containing data of ultrafast microscopy experiments
 whose results are shown in Fig. 4c in the main paper. This repository
 contains six repositories, five for "Healthy" red blood cells
 and one for a "Fixed" red blood cell. For each red blood cell,
 512 files have been analyzed (and uploaded), one for each of the 512
 segments along the cell contour. For each segment, a data file featuring
 position (nm) traces and a sampling frequency of 2kHz, has been produced.
 ## Code/Software Python code for analyzing the data is also included, and
 uploaded in the form of a commented Jupyter Notebook. The code is divided
 into three sections: 1\) Functions: containing generic functions to
 analyze stochastic traces, like functions to calculate correlations and
 Laplace transforms; 2\) Fit functions: functions to which correlation
 functions and the Variance sum rule are fitted and relative to the
 two-layer red blood cell model presented in the paper; 3\) Fits RBC: the
 main function for the data analysis, information about the functioning of
 the latter is given in the form of a docstring.