---
We thank Dr. Burrows for bringing these issues pertaining to the pilus assembly-disassembly system to notice. Although they do not affect the ultimate conclusions of the model developed here, they are nevertheless important questions, which we will answer in this comment.
---

**Response To Comments**

In developing a model about a rather complicated biological system such as this, several simplifying assumptions are needed for the intervening mechanisms. These are made after careful considerations based on available data in literature pertaining to biology, imaging and molecular dynamic studies. At the end, the best test of a physical model is based on the self-consistency of the assumptions, reasonable closeness to the actual physical system and most importantly, agreement with experimental data. Dr. Burrows has clearly raised some issues with the second of these points and we would like to address them in some detail here. Original comments are put in square brackets and our responses follow underneath. TFP

+++

["PilG which is another crucial inner membrane protein closely related to PilD" PilG is the inner membrane platform protein thought to interact with the cytoplasmic ATPases that power pilus extension and retraction as well as with components of the alignment subcomplex (especially PilM). PilD is the pre-pilin peptidase. PilG and PilD are not closely related other than being inner membrane proteins. ]

>Our Response: We thank the commentator for pointing this issue. We agree that PilG is not closely related to PilD in a biochemical sense although their individual functions are described correctly. Since this is not directly related to our calculations, it does not affect our model. However we sincerely regret this statement linking the two.

+++
["PilT is a hollow cylinder which binds with the TFP at one end, excreting pilins at the other through large domain motion utilizing ATP hydrolysis" From structural studies (Satyshur et al 2007), PilT is a hexamer, not a cylinder. It is unlikely to interact directly with pilins because it is located in the cytoplasm, while the pilins are embedded either in the inner membrane or the pilus with minimal exposure to the cytoplasm after PilD processing. The pilins are not excreted, they are reversibly polymerized and depolymerized]

>Our Response: We thank the commentator for raising these clarifying issues. We are aware of the structural complexity of PilT and of different models that describe its function as a molecular motor. These issues do not affect the broader scope of the model and below we explain why.

First, as PilT is a relatively large protein, only a portion of the protein that is oriented towards the periplasm is important in our model (Fig. 2), and the overall (especially axial) shape of PilT is of little concern. Having stated this, we don’t think this cylindrical approximation is incorrect. On the contrary, this is a good topological approximation if the available imaging data is to be believed [Sa2007] (Fig. 5 & 6). If these structural images are evaluated, the force field acting on the TFP by PilT can indeed be described approximately to be emanating from a prismatic solid traced by an inscribed circle over the irregular hexagonal ring structure. More importantly, as explained above, even if the shape deviates somewhat from a regular cylindrical topology or if mechanical or biochemical factors end up deforming the circular (or ring like) shape of the top surface, the basic assumption of the model (a plane of interest formed by the upper strata of retraction apparatus formed due to closely placed PilT units and other possible biochemical collaborators) is not invalidated.

Secondly, we disagree with the conclusion that there is absolutely no possibility of interaction between PilT and pilin especially when interaction is meant in a physical but not strictly chemical/biological sense and allows indirect and not strictly direct interactions only. We are aware that there is a divergence of opinion on the exact nature of this interaction, with several researchers having alluded to a direct paddle wheel interaction of closely related systems [Er 2008] [Gl2009] [Ko2009] , some others through an intermediary [Ta2013], some not taking a clear stance between them [Mi2013] and some other reporting that out of elongation and retraction, it is the assembly(elongation) which is thermodynamically spontaneous out of the two [Ja2008] again strongly suggesting an active role of PilT in disassembly since only one of these steps was known to be spontaneous in earlier experiments[Me2002].

From the above discussion, it is clear that in the broader extended space of interaction encompassing both physical and chemical interaction, a far more complicated picture emerges. More interestingly, to preclude the possibility of interaction simply because PilT may not be spatially located in the inner membrane, discounts both the nature of physical short interactions due to a complex retraction apparatus and the mechanism of action of molecular motors at the nanoscale. Note that these molecular motors can themselves work in unison across several length scales to harness Brownian motion [Pe2004] [Li2006][Kl2015]. Thus, in this paper when it is claimed that retraction complex acts in a two-step process combining reaction with binding, the resultant short-range potential field is a composite measure of the multi-body interaction between proteins and TFP end. For this, we do not need the entire PilT protein to be physically present inside the inner membrane nor a bio-chemical transformation of pilin attributable solely to PilT. We simply mathematically translate the claim of PilT working in concert with other proteins into our model such that in the absence of PilT, the potential field would be debilitated with no possibility of retraction. Note that, the parameters of the pair-potential (a very general Lennard-Jonnes type pair potential is assumed in the paper), would reflect this complexity. The exact form of this equation with protein properties as arguments has been left as a future exercise.
However, our model does depend on the implicit assumption that the strength of the ultimate mechanism would be monotonic increasing function of PilT levels. That is, if PilT level goes up, the strength of this mechanism would not decrease. We believe that this rather weak restriction is a good mathematical translation of what is known about the system.

Finally, our model is explicitly based on this reversible ‘polymerization’ and ‘depolymerization’ action. We do not claim otherwise since our model will not work otherwise. The word ‘excreted’ is used to describe this process pilin generation at the expense of TFP entering the end of inner membrane.

+++

["elongation can be significantly attenuated by increasing levels of PilT in the inner membrane" and "any general transport process which suffers pilin entrapment due to PilT distribution in the periplasm" PilT is located in the cytoplasm and only peripherally associated with the inner membrane. It is not found in the periplasm. Perhaps these statements were simply written in way that does not make the authors' intent clear
]

Our Response: Please refer to the comments above.

+++

["areal density of entrapment sites would be directly related to only PilT units since they have a natural binding affinity for pilins" There is no evidence in any system that PilT homologs interact directly with pilins.]

>Our Response: This is a very interesting point and is similar to the discussion on PilT/TFP interaction above. Therefore, taking a similar line of argument as above, we believe that PilT does interact with pilin physically through a generic form of short range forces. This is also based on simple deductions from the results in published literature cited previously.
One limitation of the entrapment model is indeed in ascertaining the exact nature of the transport processes and a direct closed form relationship of flux with PilT density. This was primarily due to dearth of more consistent and granular level experimental data. Further highlights on this issue can also be shed through atomistic calculations . However, we believe that, it should be a task for future, more sophisticated models. Our explicit aim in this model was to highlight the integral role played by the interaction of various parameters in endowing the system with a clear non-linear behavior and another basis of their possible co-evolution.


+++++

**References**

[Er 2008] Erlandson, Karl J., et al. "A role for the two-helix finger of the SecA ATPase in protein translocation." Nature 455.7215 (2008): 984-987.
[Ja2008]J Jakovljevic, Vladimir, et al. "PilB and PilT are ATPases acting antagonistically in type IV pilus function in Myxococcus xanthus." Journal of bacteriology 190.7 (2008): 2411-2421.
[Gl2009] Glynn, Steven E., et al. "Structures of asymmetric ClpX hexamers reveal nucleotide-dependent motions in a AAA+ protein-unfolding machine." Cell 139.4 (2009): 744-756.
[Kl2015] Klumpp, Stefan, et al. "Molecular Motors: Cooperative Phenomena of Multiple Molecular Motors." Multiscale Modeling in Biomechanics and Mechanobiology. Springer London, 2015. 27-61.
[Ko2009]Koga, Nobuyasu, et al. "Paddling mechanism for the substrate translocation by AAA+ motor revealed by multiscale molecular simulations." Proceedings of the National Academy of Sciences 106.43 (2009): 18237-18242.
[Li2006] Lindén, Martin, et al. "Force generation in small ensembles of Brownian motors." Physical Review E 74.2 (2006): 021908.
[Ma2004] Maier, Berenike, Michael Koomey, and Michael P. Sheetz. "A force-dependent switch reverses type IV pilus retraction." Proceedings of the National Academy of Sciences of the United States of America 101.30 (2004): 10961-10966.
[Me2002] Merz, Alexey J., and Katrina T. Forest. "Bacterial surface motility: slime trails, grappling hooks and nozzles." Current Biology 12.8 (2002): R297-R303.
[Mi2010] Misic, Ana M., Kenneth A. Satyshur, and Katrina T. Forest. "< i> P. aeruginosa</i> PilT Structures with and without Nucleotide Reveal a Dynamic Type IV Pilus Retraction Motor." Journal of molecular biology 400.5 (2010): 1011-1021.
[Pe2004] Pelling, Andrew E., et al. "Local nanomechanical motion of the cell wall of Saccharomyces cerevisiae." Science 305.5687 (2004): 1147-1150.
[Sa2007] Satyshur, Kenneth A., et al. "Crystal structures of the pilus retraction motor PilT suggest large domain movements and subunit cooperation drive motility."Structure 15.3 (2007): 363-376.
[Ta2013] Takhar, Herlinder K., et al. "The platform protein is essential for type IV pilus biogenesis." Journal of Biological Chemistry 288.14 (2013): 9721-9728.