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REVIEW 4 major objections 6 minor 75 references

Resolving Scale-Dependent Diffusivity in the Brain Extracellular Space

T0 review · 4 major / 6 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read In the brain's extracellular space, molecules diffuse freely at sub-micron scales but slow down beyond a characteristic structural length of roughly half a micron, making tortuosity an emergent, scale-dependent property rather than a fixed

desk verdict Plausible qualitative case for scale-dependent ECS diffusion, but the quantitative crossover claims rest on an undefined detector and need better estimation before they can be trusted. read the letter →

arxiv 2603.18936 v2 pith:YUHWL3CM submitted 2026-03-19 physics.bio-ph

Quentin Gresil , Ivo Calaresu , Finn L. Sebastian , Benjamin Flavel , Jana Zaumseil , Laurent Groc , Laurent Cognet This is my paper · ORCID
classification physics.bio-ph
keywords brainextracellularspacesingle-particletrackingcarbonnanotubesanomalousdiffusiontortuositymean-squareddisplacementhippocampussubdiffusion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that molecular transport in the brain's extracellular space is not described by a single effective diffusion coefficient or a constant tortuosity. Using three-dimensional tracking of ultrashort carbon nanotubes in living hippocampal tissue, the authors claim that motion is locally Brownian at short length scales and becomes subdiffusive only beyond a characteristic crossover length of about 0.5 to 0.7 micrometers. They argue that this crossover is set by the geometry of cellular packing, not by viscoelastic memory or trapping, and that tortuosity therefore emerges from the scale of exploration. If true, this means reported tortuosity values must be interpreted relative to the observation window, and that local mobility does not predict large-scale spreading in brain tissue.

What carries the argument

The key machinery is three-dimensional single-particle tracking using a double-helix point-spread function (DH-PSF) to follow individual ~50-nm ultrashort carbon nanotubes (uCCNTs) with nanometric precision in living hippocampal slices. The central observable is the time-averaged mean-squared displacement (tMSD), from which the authors extract an instantaneous diffusivity at short lags and a crossover time defined as the lag at which tMSD curvature first deviates from linear scaling. They define a characteristic exploration length ℓ0 = sqrt(<r²(τc)>/3) at that crossover, and compare distributions of ℓ0 across two hippocampal layers, using water-diffusing uCCNTs as an experimental Brownian re

What would settle it

Compute the tMSD curvature systematically (e.g., by sliding-window power-law fits with a defined statistical test for deviation from α=1) on the same trajectories; if the resulting per-trajectory crossover times are multimodal or highly detector-dependent, or if the median ℓ0 no longer differs between pyramidal layer and radiatum, the claim that a single structural crossover exists would be weakened.

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Extended reading notes

Core claim

The central claim is that in the brain extracellular space, transport is locally Brownian at short length scales and becomes subdiffusive beyond a characteristic structural crossover length, with slice-level median crossover lengths of 0.67 µm in the pyramidal layer and 0.52 µm in the stratum radiatum. The paper shows that the instantaneous diffusivity at short times corresponds to a tortuosity of only about 1.2, whereas the long-time effective tortuosity reaches 1.7 in the pyramidal layer and 1.35 in the radiatum. This decoupling of local mobility from larger-scale exploration is incompatible with a scale-independent rescaling of transport, leading the authors to conclude that tortuosity ar

Load-bearing premise

The entire crossover analysis relies on an unspecified criterion for detecting the lag time at which tMSD curvature first deviates from linear scaling; the paper gives no algorithm, threshold, or validation for this detector, so the reported crossover lengths and the layer comparison could shift under a different definition.

Editorial extensions

If this is right

  • Effective diffusion coefficients measured in brain extracellular space must be reported together with the spatial or temporal scale of observation; a single tortuosity value is insufficient.
  • The local Brownian regime means that small molecules and nano-sized objects can efficiently sample the immediate surroundings of synapses over sub-micron distances before geometric constraints dominate.
  • Tissue architecture, not just local viscosity, sets the long-range spreading of molecules, so that densely packed regions like the pyramidal layer restrict transport more than neuropil regions like the radiatum.
  • The intermediate subdiffusive regime is consistent with diffusion in disordered porous media, suggesting that brain extracellular space can be studied as a natural realization of Lorentz-like transport.
  • The slow subpopulation (~30%) exhibiting aging and strong subdiffusion indicates that transient non-specific interactions, not just geometry, contribute to hindrance, which has implications for how nanoscale probes and biological particles move through the extracellular space.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct testable extension is to vary probe size systematically: if geometric confinement controls the crossover, smaller probes should shift the crossover to shorter lengths and larger probes to longer lengths; if the shift is absent, hydrodynamic or viscous effects dominate.
  • The paper's layer comparison suggests that diffusion-weighted MRI or other macroscopic measures of brain microstructure may need to account for the scale-dependent crossover when relating imaging signals to cellular geometry.
  • The aging slow population could be used as a local sensor of extracellular matrix composition, since its intermittent interaction dynamics likely track changes in matrix molecules such as hyaluronan.
  • If longer trajectories could be recorded, the predicted return to effective Brownian motion at asymptotically long times (Lorentz-gas behavior) would provide a strong test of the geometric-disorder interpretation versus viscoelastic subdiffusion.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper reports 3D single-particle tracking of ultrashort carbon nanotubes in living hippocampal organotypic slices and claims that extracellular transport is locally Brownian at short time/length scales, then crosses over to subdiffusive motion beyond a characteristic length scale of the order of 0.5–0.7 μm. The crossover is attributed to geometric confinement by the cellular architecture, with an emergent, scale-dependent tortuosity rather than a single material constant. The pyramidal layer is reported to show higher short-time diffusivity but stronger long-time restriction than the stratum radiatum, and a slow subpopulation is attributed to intermittent nonspecific interactions rather than static geometric trapping.

Significance. If the central claim holds, the paper would be a valuable contribution to brain extracellular space physics: it directly visualizes a scale-dependent crossover in living tissue, proposes a structural length scale for the onset of hindrance, and connects the observations to porous-media physics. The study has notable strengths: a well-controlled water reference, multiple complementary observables (tMSD, displacement PDFs, VACF, turning angles, asphericity), and explicit comparison of two anatomically distinct layers. However, the quantitative anchors of the central claim—the crossover length ℓ0, the short-time Brownian exponent, and the layer-restriction parameters—are not yet established with the rigor needed to support the conclusions as stated.

major comments (4)
  1. [Section II C] The crossover time τ_c is defined as 'the lag time at which the curvature of the tMSD first deviates from linear scaling,' but no algorithm, curvature estimator, threshold, or noise model is provided. All reported values of ℓ0 = sqrt(<r²(τ_c)>/3), the median crossover lengths (0.67 μm and 0.52 μm), and the Mann–Whitney p=0.13 layer comparison inherit this arbitrariness. Because tMSD lags are heavily correlated and noisy, a different reasonable detector will return different τ_c and ℓ0. Please specify the exact procedure, and validate it on simulated trajectories with known crossover lengths and realistic localization noise.
  2. [Section II B] The short-time Brownian claim rests on α ≈ 0.96 fitted from only the first two lag points of the teMSD, with no confidence interval. A two-point log-log fit provides no statistical freedom and can be systematically biased by localization noise or the τ=1 forward bias noted in the water control (Appendix E). Please report the fit with uncertainties, test the effect of excluding τ=1, and propagate the water-control bias into the tissue analysis before concluding that the short-time regime is linear.
  3. [Abstract / Section II C] The abstract reports post-crossover restriction exponents ϑ = 0.77 (pyramidal) and 0.38 (radiatum), but ϑ is never defined in the main text. The body reports long-time anomalous exponents α ≈ 0.58 and 0.67, respectively, which are not equal to 1−ϑ or ϑ in any obvious way. Either define ϑ and give its values with uncertainties, or remove it from the abstract. As written, the reader cannot assess the 'approximately twofold larger post-crossover restriction' claim.
  4. [Section II C / Fig. 4] The central layer comparison is supported by point estimates of long-time exponents (α ≈ 0.58 vs 0.67) and tortuosity values (λ = 1.7 vs 1.35), but no confidence intervals or effect sizes are reported. Similarly, the α_C values in Fig. 4(c) are shown as means with s.e.m., but the text does not report the underlying fit uncertainties. Please provide error bars and statistical tests for all exponent and tortuosity comparisons, including the Δ(t) divergence in Fig. 4(a).
minor comments (6)
  1. [Appendix E / Fig. 7] The caption of Figure 7 contains duplicated and mislabeled subplots (e.g., '(g) Asphericity ... as a function of lag time for the two layers' while the figure is the water control; '(c)' appears twice) and a broken reference 'Fig.??c'. Please redraw and relabel the figure.
  2. [Section II (Experimental setup)] The text states 'typical ECS widths (50-500µm range)'; this should be nanometers (50–500 nm) based on the cited ECS literature. The same sentence also says 'the smaller geometric footprint is expected to lessen steric hindrance in narrow extracellular gaps,' which seems to contradict the listed widths.
  3. [Section II B] The instantaneous tortuosity λ_inst = 1.20 is reported without stating the reference diffusivity used (D_ref) or whether it is the water-control value or a value corrected for viscosity. Please define D_ref.
  4. [Appendix D] Equation (D5) has a misplaced bracket in the prefactor and is hard to parse. Also, in Eq. (D13) the denominator should be the product |Δr_j||Δr_{j+1}|, not a comma.
  5. [Section II C] The claim that 'viscoelastic effects arising from the extracellular matrix are generally expected to manifest at substantially smaller spatial and temporal scales' is presented without a quantitative estimate or a cited reference specific to brain ECS. Since this is used to argue for a geometric interpretation of the crossover, please either support it with a calculation or soften the conclusion.
  6. [Section II D] The aging exponent β = −0.29 is quoted without uncertainty, and the Gaussian-mixture-model criteria for separating the slow subpopulation are not described. Please provide the GMM details (number of components, input observables, model selection) and error bars on β.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity; the crossover and layer comparisons are empirical fits to measured observables, with self-citations only for probe preparation and prior context.

full rationale

This paper is an experimental single-particle-tracking study whose central claim—locally Brownian short-time transport crossing over to subdiffusion at a geometry-controlled length scale—is inferred from measured observables: time-averaged MSDs, velocity autocorrelation functions, turning-angle distributions, non-Gaussian parameters, asphericity, and a water control. None of these observables is defined in terms of the conclusion. The crossover time τc and length ℓ0 = sqrt(<r^2(τc)>/3) are defined from the tMSD curvature in Section II C, making them data-adaptive estimates rather than independent predictions, but that is a statistical-estimation matter (the detector is not specified) and not a case where the conclusion is identical to an input by construction. The layer comparison uses Mann–Whitney U on ℓ0 distributions and long-time exponents from the same tracks; this is measurement and comparison, not fitting a parameter and then renaming it a prediction. Self-citations to [53], [38], and [31] are used for probe preparation and prior qualitative observations, not as the logical premise for the crossover claim. No uniqueness theorem or functional ansatz is imported from the authors' prior work to force the conclusion. The paper is also anchored by an external water-control comparison and by structural length scales from cryo-EM and super-resolution studies of the ECS. The substantive weaknesses—the unspecified τc curvature algorithm, α≈0.96 from only two lag points, and the unpropagated water-control forward bias at τ=1—are robustness and reporting gaps, not circular derivations. Thus no load-bearing circular step is present; the score reflects minor self-citation for context rather than any definitional or constructional circularity.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The central claims rely on a set of fitted exponents and crossover lengths whose methods are only partially specified, plus domain assumptions about the slice model and the passivity of the nanotube probes. No unobserved entities are introduced; the main burden is statistical and methodological rather than ontological.

free parameters (9)
  • short-time anomalous exponent α_short = ≈0.96
    Fit to the first two lag points of the teMSD in the pyramidal layer (Fig. 3a); two-point fit cannot establish linear scaling.
  • long-time anomalous exponent α_pyr = ≈0.58
    Fit to teMSD between lag times 30–50 in the pyramidal layer (Fig. 3a/4a).
  • long-time anomalous exponent α_rad = ≈0.67
    Fit to teMSD in stratum radiatum (Fig. 4a).
  • slow subpopulation exponent α_slow = ≈0.38
    Ensemble teMSD exponent for slow subpopulation (Fig. 5a).
  • instantaneous diffusivity D_inst = 1.14 μm²/s
    Extracted from short-time teMSD slope; yields λ_inst=1.20.
  • crossover length ℓ0 medians = 0.67 μm (pyr), 0.52 μm (rad)
    From τ_c defined by first curvature deviation from linear MSD; method not detailed.
  • aging exponent β = -0.29
    Power-law fit of D_te vs T for slow subpopulation.
  • GMM component count = 2
    Chosen to separate fast and slow subpopulations; no model selection criterion reported.
  • post-crossover restriction exponent θ (abstract) = 0.77 pyr / 0.38 rad
    Appears in abstract but not defined or matched by body's α values; likely unsupported.
assumptions (6)
  • domain assumption Organotypic hippocampal slices preserve the in vivo ECS architecture sufficiently for diffusion measurements.
    Stated in Methods/Appendix C; if slice culture alters ECS geometry, layer-specific conclusions may not transfer to intact brain.
  • domain assumption uCCNTs are passive tracers whose size and PEG coating do not perturb the ECS and whose surface chemistry minimizes nonspecific interactions (for the fast population).
    Section II D; the existence of a 30% slow interacting population shows interactions are not fully eliminated.
  • domain assumption DH-PSF 3D localization with ZOLA yields unbiased positions with 10–20 nm precision over 5 μm range.
    Appendix B; localization bias could affect short-time MSD and VACF.
  • standard math The FBM functional form (Eq. D10) is used only descriptively; no specific stochastic model is assumed.
    Section II B; the paper explicitly disclaims FBM as underlying dynamics.
  • domain assumption The water reference (free diffusion) is the correct D_ref for tortuosity, despite unknown systematic pipeline errors.
    Appendix E admits an unidentified systematic error in water control (turning-angle forward bias at τ=1; VACF decay).
  • ad hoc to paper Viscoelastic effects of the ECM are negligible at the measured scales, so the crossover reflects geometry.
    Section II C invokes literature to place viscoelastic relaxation below temporal resolution; no direct measurement in this system.

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Pith. "Pith review of Resolving Scale-Dependent Diffusivity in the Brain Extracellular Space." pith.science (2026). https://pith.science/paper/YUHWL3CM

@misc{pith2026260318936,
  author       = {Pith},
  title        = {Pith review of: Resolving Scale-Dependent Diffusivity in the Brain Extracellular Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YUHWL3CM}},
  note         = {Machine review of arXiv:2603.18936}
}
abstract

Transport through the brain extracellular space has traditionally been summarized by effective diffusion coefficients measured over specific observation ranges. Whether local mobility remains predictive as the same molecule explores larger distances remains unresolved. Here, we track individual ultrashort carbon nanotubes in three dimensions within living hippocampal tissue, following their motion from nanometre to micrometre scales. Using freely diffusing nanotubes in water as an experimental reference, we resolve trajectory-specific crossover lengths beyond which instantaneous diffusivity decreases, with slice-level medians of 0.67 $\mu$m in the pyramidal layer and 0.52 $\mu$m in the radiatum. The pyramidal layer combines higher short-time diffusivity with an approximately twofold larger post-crossover restriction exponent than the radiatum ($\vartheta$ = 0.77 versus 0.38). This decoupling of local mobility from larger-scale exploration is incompatible with a scale-independent rescaling of transport, showing that effective extracellular diffusivity must be interpreted relative to the scale of exploration.

Figures

Figures reproduced from arXiv: 2603.18936 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. a shows the time–ensemble averaged mean [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (6 more)
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: presents results from a typical z-stack cali￾bration. The estimated photon count (Nph) and back￾ground level (Nbg) were approximately 35,000 photoelec￾trons and 3 photoelectrons, respectively, for this uCCNT ( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Joint distribution of the anomalous diffusion ex [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

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Reference graph

Works this paper leans on

75 extracted references

  1. [1]

    Nicholson and E

    C. Nicholson and E. Sykov´ a, Extracellular space struc- ture revealed by diffusion analysis, Trends in Neuro- sciences21, 207 (1998)

    1998

  2. [2]

    Sykov´ a and C

    E. Sykov´ a and C. Nicholson, Diffusion in Brain Extracel- lular Space, Physiological Reviews88, 1277 (2008)

    2008

  3. [3]

    L. Xie, H. Kang, Q. Xu, M. J. Chen, Y. Liao, M. Thiya- garajan, J. O’Donnell, D. J. Christensen, C. Nicholson, J. J. Iliff, T. Takano, R. Deane, and M. Nedergaard, Sleep Drives Metabolite Clearance from the Adult Brain, Sci- ence342, 373 (2013)

    2013

  4. [4]

    Tønnesen, S

    J. Tønnesen, S. Hrab˘ etov´ a, and F. N. Soria, Local diffu- sion in the extracellular space of the brain, Neurobiology of Disease177, 105981 (2023)

    2023

  5. [5]

    B. P. Toole, Hyaluronan: From extracellular glue to peri- cellular cue, Nature Reviews Cancer4, 528 (2004)

    2004

  6. [6]

    Dityatev and M

    A. Dityatev and M. Schachner, Extracellular matrix molecules and synaptic plasticity, Nature Reviews Neu- roscience4, 456 (2003)

    2003

  7. [7]

    Vargov´ a and E

    L. Vargov´ a and E. Sykov´ a, Astrocytes and extracellular matrix in extrasynaptic volume transmission, Philosoph- ical Transactions of the Royal Society B: Biological Sci- ences369, 20130608 (2014)

    2014

  8. [8]

    V. R. Krishnaswamy, A. Benbenishty, P. Blinder, and I. Sagi, Demystifying the extracellular matrix and its proteolytic remodeling in the brain: Structural and func- tional insights, Cellular and Molecular Life Sciences76, 3229 (2019)

    2019

Show all 75 references
  1. [9]

    F. N. Soria, C. Miguelez, O. Pe˜ nagarikano, and J. Tønnesen, Current Techniques for Investigating the Brain Extracellular Space, Frontiers in Neuroscience14, 570750 (2020)

    2020

  2. [10]

    Sykov´ a, Extrasynaptic volume transmission and diffu- sion parameters of the extracellular space, Neuroscience 129, 861 (2004)

    E. Sykov´ a, Extrasynaptic volume transmission and diffu- sion parameters of the extracellular space, Neuroscience 129, 861 (2004)

    2004

  3. [11]

    L. F. Agnati, D. Guidolin, M. Guescini, S. Genedani, and K. Fuxe, Understanding wiring and volume transmission, Brain Research Reviews64, 137 (2010)

    2010

  4. [12]

    Nicholson and S

    C. Nicholson and S. Hrabˇ etov´ a, Brain Extracellular Space: The Final Frontier of Neuroscience, Biophysical Journal113, 2133 (2017)

    2017

  5. [13]

    Hrabetova, L

    S. Hrabetova, L. Cognet, D. A. Rusakov, and U. V. N¨ agerl, Unveiling the Extracellular Space of the Brain: From Super-resolved Microstructure toIn VivoFunction, The Journal of Neuroscience38, 9355 (2018)

    2018

  6. [14]

    T. Bohr, P. G. Hjorth, S. C. Holst, S. Hrabˇ etov´ a, V. Kiviniemi, T. Lilius, I. Lundgaard, K.-A. Mardal, 12 E. A. Martens, Y. Mori, U. V. N¨ agerl, C. Nicholson, A. Tannenbaum, J. H. Thomas, J. Tithof, H. Benveniste, J. J. Iliff, D. H. Kelley, and M. Nedergaard, The glym- ph...

    2022

  7. [15]

    Nicholson and J

    C. Nicholson and J. M. Phillips, Ion diffusion modified by tortuosity and volume fraction in the extracellular mi- croenvironment of the rat cerebellum., The Journal of Physiology321, 225 (1981)

    1981

  8. [16]

    C. J. McBain, S. F. Traynelis, and R. Dingledine, Re- gional Variation of Extracellular Space in the Hippocam- pus, Science249, 674 (1990)

    1990

  9. [17]

    Nicholson and L

    C. Nicholson and L. Tao, Hindered diffusion of high molecular weight compounds in brain extracellular mi- croenvironment measured with integrative optical imag- ing, Biophysical Journal65, 2277 (1993)

    1993

  10. [18]

    R. G. Thorne and C. Nicholson,In Vivodiffusion anal- ysis with quantum dots and dextrans predicts the width of brain extracellular space, Proceedings of the National Academy of Sciences103, 5567 (2006)

    2006

  11. [19]

    F. Xiao, J. Hrabe, and S. Hrabetova, Anomalous Extra- cellular Diffusion in Rat Cerebellum, Biophysical Journal 108, 2384 (2015)

    2015

  12. [20]

    Nicholson, Diffusion and related transport mecha- nisms in brain tissue, Reports on Progress in Physics64, 815 (2001)

    C. Nicholson, Diffusion and related transport mecha- nisms in brain tissue, Reports on Progress in Physics64, 815 (2001)

    2001

  13. [21]

    Kume-Kick, T

    J. Kume-Kick, T. Mazel, I. Voˇ r ´ ıˇ sek, S. Hrabˇ etov´ a, L. Tao, and C. Nicholson, Independence of extracellular tortuos- ity and volume fraction during osmotic challenge in rat neocortex, The Journal of Physiology542, 515 (2002)

    2002

  14. [22]

    D. A. Rusakov and D. M. Kullmann, Geometric and vis- cous components of the tortuosity of the extracellular space in the brain, Proceedings of the National Academy of Sciences95, 8975 (1998)

    1998

  15. [23]

    Hrabˇ etov´ a and C

    S. Hrabˇ etov´ a and C. Nicholson, Contribution of dead- space microdomains to tortuosity of brain extracellular space, Neurochemistry International45, 467 (2004)

    2004

  16. [24]

    M. J. Rust, M. Bates, and X. Zhuang, Sub-diffraction- limit imaging by stochastic optical reconstruction mi- croscopy (STORM), Nature Methods3, 793 (2006)

    2006

  17. [25]

    Betzig, G

    E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lind- wasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Imaging Intra- cellular Fluorescent Proteins at Nanometer Resolution, Science313, 1642 (2006)

    2006

  18. [26]

    Lelek, M

    M. Lelek, M. T. Gyparaki, G. Beliu, F. Schueder, J. Griffi´ e, S. Manley, R. Jungmann, M. Sauer, M. Lakadamyali, and C. Zimmer, Single-molecule local- ization microscopy, Nature Reviews Methods Primers1, 39 (2021)

    2021

  19. [27]

    M. J. Saxton and K. Jacobson, SINGLE-PARTICLE TRACKING:Applications to Membrane Dynamics, An- nual Review of Biophysics and Biomolecular Structure 26, 373 (1997)

    1997

  20. [28]

    H¨ ofling and T

    F. H¨ ofling and T. Franosch, Anomalous transport in the crowded world of biological cells, Reports on Progress in Physics76, 046602 (2013)

    2013

  21. [29]

    Cognet, C

    L. Cognet, C. Leduc, and B. Lounis, Advances in live- cell single-particle tracking and dynamic super-resolution imaging, Current Opinion in Chemical Biology20, 78 (2014)

    2014

  22. [30]

    Manzo and M

    C. Manzo and M. F. Garcia-Parajo, A review of progress in single particle tracking: From methods to biophysi- cal insights, Reports on Progress in Physics78, 124601 (2015)

    2015

  23. [31]

    A. G. Godin, J. A. Varela, Z. Gao, N. Dann´ e, J. P. Dupuis, B. Lounis, L. Groc, and L. Cognet, Single- Nanotube Tracking Reveals the Nanoscale Organization of the Extracellular Space in the Live Brain, Nat. Nan- otechnol.12, 238 (2017)

    2017

  24. [32]

    F. N. Soria, C. Paviolo, E. Doudnikoff, M.-L. Arotcarena, A. Lee, N. Dann´ e, A. K. Mandal, P. Gosset, B. Dehay, L. Groc, L. Cognet, and E. Bezard, Synucleinopathy al- ters nanoscale organization and diffusion in the brain ex- tracellular space through hyaluronan remodeling, N...

    2020

  25. [33]

    Korogod, C

    N. Korogod, C. C. Petersen, and G. W. Knott, Ultra- structural analysis of adult mouse neocortex comparing aldehyde perfusion with cryo fixation, eLife4, e05793 (2015)

    2015

  26. [34]

    J. P. Kinney, J. Spacek, T. M. Bartol, C. L. Bajaj, K. M. Harris, and T. J. Sejnowski, Extracellular sheets and tun- nels modulate glutamate diffusion in hippocampal neu- ropil, Journal of Comparative Neurology521, 448 (2013)

    2013

  27. [35]

    Tønnesen, V

    J. Tønnesen, V. V. G. K. Inavalli, and U. V. N¨ agerl, Super-Resolution Imaging of the Extracellular Space in Living Brain Tissue, Cell172, 1108 (2018)

    2018

  28. [36]

    McKenna, D

    M. McKenna, D. Shackelford, C. Pontes, B. Ball, and E. Nance, Multiple Particle Tracking Detects Changes in Brain Extracellular Matrix and Predicts Neurodevelop- mental Age, ACS Nano15, 8559 (2021)

    2021

  29. [37]

    Paviolo, J

    C. Paviolo, J. S. Ferreira, A. Lee, D. Hunter, L. Groc, and L. Cognet,Near-Infrared Carbon Nanotube Tracking Re- veals the Nanoscale Extracellular Space around Synapses, Preprint (Biophysics, 2021)

    2021

  30. [38]

    Grassi, A

    D. Grassi, A. Idziak, A. Lee, I. Calaresu, J.-B. Sibarita, L. Cognet, U. V. N¨ agerl, and L. Groc, Nanoscale and functional heterogeneity of the hippocampal extracellu- lar space, Cell Reports42, 10.1016/j.celrep.2023.112478 (2023)

    2023

  31. [39]

    Wang, H.-J

    L. Wang, H.-J. Chen, Z.-G. Wang, D. Ning, W. Zhao, V. Rat, D. C. Lamb, D.-W. Pang, and S.-L. Liu, Map- ping Extracellular Space Features of Viral Encephalitis to Evaluate the Proficiency of Anti-Viral Drugs, Advanced Materials , 2311457 (2024)

    2024

  32. [40]

    H.-J. Chen, L. Zhao, L. Wang, Z.-G. Wang, D.-W. Pang, and S.-L. Liu, Simultaneous Mapping of the Nanoscale Organization and Redox State of Extracellular Space in Living Brain Tissue, ACS Nano (2024)

    2024

  33. [41]

    Estaun-Panzano, S

    J. Estaun-Panzano, S. Nandi, Q. Gresil, E. Doudnikoff, C. Mazzocco, Ml. Arotcarena, Mh. Canron, B. Dehay, L. Cognet, and E. Bezard, Intracellularα-synuclein as- semblies are sufficient to alter nanoscale diffusion in the striatal extracellular space, npj Parkinson’s Disease10,...

    2024

  34. [42]

    Esta´ un-Panzano, A

    J. Esta´ un-Panzano, A. Lovisotto, C. Mazzocco, C. Piva, M. Darricau, I. Calaresu, Q. Gresil, V. Planche, B. De- hay, L. Groc, L. Cognet, and E. Bezard, Alzheimer’s Tau seeds-induced pathology enhances hippocampal extracel- lular diffusion, Communications Biology8, 1660 (2025)

    2025

  35. [43]

    Esta´ un-Panzano, Y

    J. Esta´ un-Panzano, Y. Dembitskaya, I. Calaresu, S. Nandi, Q. Gresil, E. Doudnikoff, T. Leste-Lasserre, T. Am´ ed´ ee, L. Cognet, L. Groc, U. V. N¨ agerl, and E. Bezard, Nanoscopic Mapping of the Extracellular Space in Amyloid Plaque-rich Cortex, Advanced Science 13, e15674 (2026)

    2026

  36. [44]

    Paviolo, F

    C. Paviolo, F. N. Soria, J. S. Ferreira, A. Lee, L. Groc, E. Bezard, and L. Cognet, Nanoscale exploration of the 13 extracellular space in the live brain by combining single carbon nanotube tracking and super-resolution imaging analysis, Methods174, 91 (2020)

    2020

  37. [45]

    Kusumi, Y

    A. Kusumi, Y. Sako, and M. Yamamoto, Confined lateral diffusion of membrane receptors as studied by single par- ticle tracking (nanovid microscopy). Effects of calcium- induced differentiation in cultured epithelial cells, Bio- physical Journal65, 2021 (1993)

    2021

  38. [46]

    A. V. Weigel, B. Simon, M. M. Tamkun, and D. Krapf, Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking, Pro- ceedings of the National Academy of Sciences108, 6438 (2011)

    2011

  39. [47]

    F. Etoc, E. Balloul, C. Vicario, D. Normanno, D. Liße, A. Sittner, J. Piehler, M. Dahan, and M. Coppey, Non- specific interactions govern cytosolic diffusion of nano- sized objects in mammalian cells, Nature Materials17, 740 (2018)

    2018

  40. [48]

    Sabri, X

    A. Sabri, X. Xu, D. Krapf, and M. Weiss, Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells, Physical Review Letters 125, 058101 (2020)

    2020

  41. [49]

    Mu˜ noz-Gil, H

    G. Mu˜ noz-Gil, H. Bachimanchi, J. Pineda, B. Midtvedt, G. Fern´ andez-Fern´ andez, B. Requena, Y. Ahsini, S. As- ghar, J. Bae, F. J. Barrantes, S. W. B. Bender, C. Cabriel, J. A. Conejero, M. Escoto, X. Feng, R. Haidari, N. S. Hatzakis, Z. Huang, I. Izeddin, H. Jeong, Y. Jian...

    2025

  42. [50]

    Bouchaud and A

    J.-P. Bouchaud and A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Physics Reports195, 127 (1990)

    1990

  43. [51]

    H¨ ofling, T

    F. H¨ ofling, T. Franosch, and E. Frey, Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation, Physical Review Letters 10.1103/PhysRevLett.96.165901 (2006)

    2006 doi

  44. [52]

    Shi and D

    A. Shi and D. K. Schwartz, Bridging Macroscopic Dif- fusion and Microscopic Cavity Escape of Brownian and Active Particles in Irregular Porous Networks, ACS Nano 18, 22864 (2024)

    2024

  45. [53]

    Nandi, Q

    S. Nandi, Q. Gresil, B. P. Lambert, F. L. Sebastian, S. Settele, I. Calaresu, J. Estaun-Panzano, A. Lovisotto, C. Mazzocco, B. S. Flavel, E. Bezard, L. Groc, J. Zaum- seil, and L. Cognet, Ultrashort Carbon Nanotubes with Luminescent Color Centers Are Bright NIR-II Nanoemit- te...

    2025

  46. [54]

    Ghosh, S

    S. Ghosh, S. M. Bachilo, R. A. Simonette, K. M. Beck- ingham, and R. B. Weisman, Oxygen Doping Modifies Near-Infrared Band Gaps in Fluorescent Single-Walled Carbon Nanotubes, Science330, 1656 (2010)

    2010

  47. [55]

    Settele, F

    S. Settele, F. Stammer, F. L. Sebastian, S. Lindenthal, S. R. Wald, H. Li, B. S. Flavel, and J. Zaumseil, Easy Ac- cess to Bright Oxygen Defects in Biocompatible Single- Walled Carbon Nanotubes via a Fenton-like Reaction, ACS Nano18, 20667 (2024)

    2024

  48. [56]

    von Diezmann, Y

    L. von Diezmann, Y. Shechtman, and W. E. Moerner, Three-Dimensional Localization of Single Molecules for Super-Resolution Imaging and Single-Particle Tracking, Chemical Reviews117, 7244 (2017)

    2017

  49. [57]

    S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function, Proceedings of the National Academ...

    2009

  50. [58]

    Aristov, B

    A. Aristov, B. Lelandais, E. Rensen, and C. Zimmer, ZOLA-3D allows flexible 3D localization microscopy over an adjustable axial range, Nature Communications9, 2409 (2018)

    2018

  51. [59]

    B. H. G¨ ahwiler, Organotypic cultures of neural tissue, Trends in Neurosciences11, 484 (1988)

    1988

  52. [60]

    Lorente De N´ o, Studies on the structure of the cere- bral cortex

    R. Lorente De N´ o, Studies on the structure of the cere- bral cortex. II. Continuation of the study of the ammonic system, Journal f¨ ur Psychologie und Neurologie46, 113 (1934)

    1934

  53. [61]

    Rehfeldt and M

    F. Rehfeldt and M. Weiss, The random walker’s toolbox for analyzing single-particle tracking data, Soft Matter 19, 5206 (2023)

    2023

  54. [62]

    Metzler and M

    R. Metzler and M. Weiss, Discriminating stochastic pro- cesses for the assessment of materials properties by diffusion measurements, Physical Chemistry Chemical Physics27, 14350 (2025)

    2025

  55. [63]

    Sadegh, J

    S. Sadegh, J. L. Higgins, P. C. Mannion, M. M. Tamkun, and D. Krapf, Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork, Physical Re- view X7, 011031 (2017)

    2017

  56. [64]

    Manzo, J

    C. Manzo, J. A. Torreno-Pina, P. Massignan, G. J. Lapeyre, M. Lewenstein, and M. F. Garcia Parajo, Weak Ergodicity Breaking of Receptor Motion in Living Cells Stemming from Random Diffusivity, Physical Review X 5, 011021 (2015)

    2015

  57. [65]

    Sikora, M

    G. Sikora, M. Teuerle, A. Wy loma´ nska, and D. Grebenkov, Statistical properties of the anoma- lous scaling exponent estimator based on time-averaged mean-square displacement, Physical Review E96, 022132 (2017)

    2017

  58. [66]

    Lanoisel´ ee, G

    Y. Lanoisel´ ee, G. Pagnini, and A. Wy loma´ nska, Super- Resolved Anomalous Diffusion: Deciphering the Joint Distribution of Anomalous Exponent and Diffusion Co- efficient, Physical Review Letters135, 137101 (2025)

    2025

  59. [67]

    S. C. Weber, M. A. Thompson, W. Moerner, A. J. Spakowitz, and J. A. Theriot, Analytical Tools To Dis- tinguish the Effects of Localization Error, Confinement, and Medium Elasticity on the Velocity Autocorrelation Function, Biophysical Journal102, 2443 (2012)

    2012

  60. [68]

    Balcerek, A

    M. Balcerek, A. Pacheco-Pozo, A. Wy loma´ nska, K. Bur- necki, and D. Krapf, Two-dimensional Brownian mo- tion with dependent components: Turning angle anal- ysis, Chaos: An Interdisciplinary Journal of Nonlinear Science35, 023166 (2025)

    2025

  61. [69]

    Metzler and J

    R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Physics Reports339, 1 (2000)

    2000

  62. [70]

    J. H. Van Zanten and K. P. Rufener, Brownian motion in a single relaxation time Maxwell fluid, Physical Review E62, 5389 (2000)

    2000

  63. [71]

    Grimm, S

    M. Grimm, S. Jeney, and T. Franosch, Brownian motion in a Maxwell fluid, Soft Matter7, 2076 (2011)

  64. [72]

    S. C. De Smedt, A. Lauwers, J. Demeester, Y. Engel- borghs, G. De Mey, and M. Du, Structural information on hyaluronic acid solutions as studied by probe diffusion experiments, Macromolecules27, 141 (1994)

    1994

  65. [73]

    D. S. Novikov, E. Fieremans, S. N. Jespersen, and V. G. 14 Kiselev, Quantifying brain microstructure with diffu- sion MRI: Theory and parameter estimation, NMR in biomedicine32, e3998 (2019)

    2019

  66. [74]

    H. Li, G. Gordeev, O. Garrity, S. Reich, and B. S. Flavel, Separation of Small-Diameter Single-Walled Car- bon Nanotubes in One to Three Steps with Aqueous Two-Phase Extraction, ACS Nano , acsnano.8b09579 (2019)

    2019

  67. [75]

    Stoppini, P

    L. Stoppini, P. A. Buchs, and D. Muller, A simple method for organotypic cultures of nervous tissue, Journal of Neu- roscience Methods37, 173 (1991)

    1991

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