Avalilação PREreview de Power-law decay of force on cell membrane tethers reflects long-ranged relaxation of membrane tension

Summary

The manuscript "Power-law decay of force on cell membrane tethers reflects long-ranged relaxation of membrane tension" by Emeline Laborie and Andrew Callan-Jones investigates the spatiotemporal relaxation dynamics of cell membrane tension following the sudden extension of a membrane tether. The authors construct a model based on lipid flows in the membrane (neglecting other membrane components, and opposed to an existing osmotic protein model) and derive a diffusion equation and boundary conditions for the membrane tension from physical principles. After non-dimensionalization and finding the two relevant non-dimensional parameters, they provide a numerical solution for the membrane tension and the tether force relaxation. Using a rescaling, they provide an analytical solution (under assumptions) for intermediate times. This solution is consistent with their numerical solution, which then collapses onto a single curve ("self-similar behavior"). At last, they test their predictions for the tether force against previous experiments.

General strengths and weaknesses

Both the text and figures are well-organized, and the manuscript generally supports a logical progression from theory to experimental results. Important results and equations are given in the main text, while complicated derivations and details are moved to the appendix. Figures are well-constructed and facilitate understanding of the scaling laws and model predictions, although some dense sections could benefit from intermediate derivations for clarity. The background provided is thoroughly and references core literature, effectively situating the work within current membrane tension research. However, the authors only reference some derivations and mechanical relations, which could be explained/justified shortly in the text to improve reproducibility and understandability.

The development of a physics-reasoned theoretical framework and provision of both numerical and analytical results for the model is an important advancement for the field, and the derivation is generally well-reasoned. The fitting to existing experimental data is not yet fully convincing, and should be improved, as explained below.

All in all, this manuscript has a very high relevance to the field and represents a major advancement in understanding membrane tension dynamics. Points that leave some room for improvement are listed in the following.

Major Issues

• Results, Part C: While the analytical solution predicts a pure power law for intermediate times, the authors then use a different interpolation formula for data fitting in order to account for the finite t->0 behavior, and fit from $t=0$ until some cutoff time (which is optimized in a second step). It is not clear to the reviewer why the authors use a different fitting function to validate their model, as this drastically reduces the expressiveness of this "validation". It is also unclear to the reviewer why the authors do not just fit a power law and also cut off early times, as this is the condition under which the analytical result holds. The authors should improve the validation of their theory or justify their decision better. One option for improving the validation could be using their predicted result as fit function and only use intermediate time points for fitting. The early and late cutoff times could maybe even be interpreted as indicators for the time period in which the analytical result is valid.

Minor Issues

• Derivation of the model: Mechanical relations like equations 1, 2, 3 should not only be cited from previous work, but at least be reasoned/shortly derived for better understanding. Also, the derivation of the diffusion equation should be made explicitly, at least in the appendix or in intermediate steps, to clarify the foundation and assumptions that the authors make.

• Definition of membrane tension: The authors should give a definition of the membrane tension that they are working with for completeness and understandability, especially for readers who are not too deeply involved in the field.

• Results, Part A: The comparison to classical diffusion from a point source lacks understandability here, as in this case, for example, r_max would also be zero. Furthermore, the authors do not discuss tether radius as a function of time here, but later, even though this would be crucial to understand in context with the radius of maximum tension. The authors should explain the role of the tether radius here and improve the reasoning and intuitivity in this paragraph.

• Introduction/Model/Discussion: The authors generally do a good review of existing literature and put their work into context. However, comparing their model to other models (especially the framework based on osmotic imbalance of mobile proteins) and explaining the advantages and limitations of their assumption of a homogeneous lipid membrane come a bit too short. The authors should elaborate better on the limitations of their model and compare it to other models to improve understanding of the mechanisms that might be involved in real cell membranes.

• Appendix, eq. 25/26: "requiring that all three terms all balanced [...]" what does balanced mean? Does it just mean that they sum to zero, i.e., that eq. 25 holds? Please clarify.

Competing interests

The authors declare that they have no competing interests.

Use of Artificial Intelligence (AI)

The authors declare that they did not use generative AI to come up with new ideas for their review.