On the Regulated Nuclear Transport of Incompletely Spliced mRNAs by HIV-Rev Protein: A Minimal Dynamic Model

Round 1

Reviewer 1 Report

This manuscript is mostly well-written and I think it deserves to be published. My main concern about this paper is that it does not really fit the journal Mathematics. From the point of view of biology, it contains a lot of information, but from the mathematical point of view, it does not. For example, the proposed differential equation system is an ordinary differential equation system (ODE system), which is an important feature, but not even mentioned in the manuscript. A more important question is the method by which it was solved, for example, 4th order Runge Kutta coded in C++, or a specific MATLAB ode solver, etc.

The proposed equations are nonlinear, which should also be mentioned. Nonlinear equations typically have chaotic solutions. Are they possible here? Have the authors examined the apparently periodic solutions by Fourier frequency analysis (e.g. by FFT), or by preparing a Poincaré map?

Smaller remarks: - Expressions such as Rev and Ran should be defined. - The explanation of the variables might be moved from lines 267-269 to earlier, e.g. just after Eq. (10). - Around line 217, the sentence contains the word including twice. - The sentence around line 276 ("The decision...") is rather obscure, it should be rephrased. - The material explained in the first 2 pages of Section 5 is actually not numerical analysis, but biology.  - The last paragraph of Section 5 (lines 517-523) might be moved to the Discussion section.

 

Author Response

attached pdf file

Author Response File: Author Response.pdf

Reviewer 2 Report

The ms. titled "On the Regulated Nuclear Transport of Incompletely Spliced mRNAs by HIV-Rev Protein: A Minimal Dynamic Model" represents a type of realization of simple kinetic Michaelis-Menten scenario applicable to complex kinetics of HIV-Rev protein and (in)completely spliced mRNAs, a problem of formidable significance. 

The current reviewer is not a specialist of the biochemistry of systems of such types, on the one hand, but the reviewer takes as an advantage the detailed description of the nuclear transport offered by the Authors. Of course, the present reviewer can be skeptical when looking at a systems of six (eqs. 11) or even seven (eqs. 23) first-order nonlinear ODS solved numerically in order to get very similar delayed oscillation behaviors exclusively (for the three different 'combining' concentrations studied) with quite a few parameters collected in Table 1, but finally, the study - presenting the so-called minimal model - looks reliable and worth accepting, when looking at the so-named normality/standard conditions in the complex system studied. 

However, the present reviewer sees unavoidable, especially when extending those normality conditions toward pathologies or abnormalities to consider necessarily the Michaelis-Menten kinetics on fractal (percolation-type) lattices https://www.pnas.org/doi/pdf/10.1073/pnas.95.20.11685 ("Time course of reactions controlled and gated by intramolecular dynamics of proteins ...") that can then induce an oscillating but also chaotic (mechanistic) behavior in the domain of complex component-interactions' time  https://link.springer.com/article/10.1023/A:1019180032104 ("Description of the kinetics of a model tribopolymerization process."). This can complete greatly the presented study of relevance to biochemists' or biophysicits' milieus (see, the last parts of Discussion in the paper).

Let me emphasize here that the Authors have so well described the classical Michaelis-Menten-type kinetics for the system studied that, in reviewer's opinion, mentioning the very plausible extension into fractal-like domain will greatly augment the researching pathway for the future, underlining virtually a far-from-equilibrium dissipative character of the system. 

To sum up, the paper looks very publishable after minor revision, especially the one indicating the direction of including a potentially very important (extension) route of fractal-like Michaelis-Menten kinetics. (A propos those kinetics, in Introduction, sec. 1 - in its far end, the Authors have written Michaelis-MentOn; in the beginning of Sec. 1 one detects 'Heparan sulfate' - why written with capital H?) 

 

Author Response

attached pdf file

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The manuscript is improved now and can be published.