The impact of the diffusion parameter on the passage time of the folding process

The mathematical formalism and biophysical approach

lack of discussion, and references

The Authors have applied the Fokker-Plank equation to the diffusion model during the protein folding process using a random potential V that represents 3 protein energy state profiles: unfolded, intermediate/transition, and folded, according to my understanding. The mathematical formalism and biophysical approach in this work is very sophisticated and highlighted the need of research in this area.
However, a few points should be addressed:

Introduction: There is not many references for the topic, especially around the protein folding issue and its deregulation and the consequences in the medical field. The author could explore this area in more detail and show data for some diseases and how this work can help to address those biological questions.

Methodology and Formalism:
In general there is a lack of physics parameters units, such as for V, Q, t and f.

On the equation 10, where do the constants -8.93851 and +5.42373 come from? Are they arbitrary or coming from a simulation? Same for the Figure 2 where “a” was fixed as 3.90456. It should be shown how those numbers were fixed, or mentioned if it was arbitrary.

Is “a” and “” (alpha) the same variable? Could that be a typo?

What is the definition of N(t) shown in the equation 11, is it the diffusion process and its distribution? A better variable definition is required.

t and t’ were mentioned on the section 2.2 and defined only in the section 2.3 as passing time and then the same variable is defined as passage time. Please define the variable and its units before it appears in the equations, and keep it consistent throughout the paper.

All the figures (graphics) need to have a bigger x and y variables allocated to its axis for better visualisation. Such as “t x Q” or “t x Xo” or “Population x t”.

In this work there is a lack of discussion, for example the authors could explore how this model could address the Levinthal’s protein folding paradox for (B Bagchi, 1992). Also, there is room to discuss how this Fokker-Plank equation to diffusion model can impact biomedical or biophysics research or techniques, as a novelty proposed in the introduction.

Overall, this is good paper and addresses a part of biophysics research where research is lacking and could bring significant breakthrough in science and medical research. I would recommend it for publication after the authors checked the points raised above.

All the figures (graphics) need to have a bigger x and y variables allocated to its axis, for a better visualisation. Such as “t x Q” or “t x Xo” or “Population x t”.

In this work, the authors present an application of the Fokker-Planck equation to model the diffusion process during protein folding. The authors use a potential V that mimics a protein free energy profile with 3 states (unfolded, intermediate, and folded). Nonetheless, there is a lack of discussion in associating this work with protein folding. Comparison with experimental results should be performed. The language and writing should be revised. Breaking sentences would help the reader. There are also major scientific points that should be discussed:
There is a lack of references, especially discussing seminal work from Dmitrii E. Makarov, Robert B. Best, Gerhard Hummer, and others.
There is also a lack of references about the protein folding problem, particularly in the introduction.
Section 2.1 - How do the authors justify the choice of parameters in equation 10?
Section 2.2:
The same, Is there any argumentation for using those values of a and Q?
Why choose a potential V(x) where the intermediate is more stable than the native state? I recommend doing the same calculations for a scenario where the protein's native state is more stable than the intermediate.
What happens when d(V(x)/dx = 0? In this case, the force is zero. How does the protein decide to go right or left in the potential? Do authors consider the case of half o the time, when reaching this inflection point, the protein returns to the previous state?
Why the potential in the native state goes up? What exists after the native state?
The authors mentioned that the reaction coordinate x is the number of native contacts (page 2). How is possible to have negative values of x? The minimum value must be 0. A negative number of contacts is inconsistent.
How these calculations are different from a partible diffusing under the influence of the potential V(x)?
Section 3:
There is a lack of physical units in all calculations and figures. What are the units of V, f, Q, t?
What are the criteria to consider the protein folded when calculating the passage time?
Section 4:
There is a lack of discussion, and the conclusion seems like a textbook exercise. I recommend exploring different parameters and connecting the results with experiments or even simulations.