SiCaSMA: An Alternative Stochastic Description via Concatenation of Markov Processes for a Class of Catalytic Systems

Round 1

Reviewer 1 Report

For larger systems, the CME is computationally intractable due to a large number of possible configurations, and the SSA suffers from large reaction propensities.  The authors introduced a new methodology, the Single Catalyst Stochastic Modeling Approach (SiCaSMA), to describe catalytic reaction systems, based on the assumption that catalyst molecules react independently of each other.  Instead of  simulating the system one large process,  the full system is subdivided into smaller parts in which the catalyst molecules are simulated one after another.   The authors also gave different example systems to reveal that SiCaSMA is equivalent to
the standard CME description of the full system. Probably,  the SiCaSMA will be applied to a broad range of biochemical reaction systems.  So I recommend the paper will be accepted as much as possible.

Author Response

Dear Dr. Guan,   we first of all thank both reviewers for their constructive feedback and  hereby reply to the two reports. We have addressed all issues raised by the reviewers and highlighted changes in the revised manuscript in blue.    Reviewer 1:   The first reviewer asked for revisions in terms of language. We carefully read the entire manuscript and included minor changes throughout. In particular, the changes made are found in lines 23f, 26f, 28f, 29, 49, 65ff, 119, 192, 249 in the revised manuscript. The changes aim to ease the reading flow e.g. by avoiding repetitions, further specifying the respective topic or changing the structure of sentences.   Best regards Nicole Radde

Reviewer 2 Report

Replay on ’SiCaSMA: An alternative stochastic description via concatenation of Markov processes for a class of catalytic systems’

Paper focusses on well-known Chemical Master Equation for the modeling of the biochemical reaction networks. The method is based on division of the full system into smaller subsystems with one catalyst molecule each.

The paper is well written and, as far as I understand, all theoretical findings are correct. Some points that can be improved (Introduction):

    The reader should understand the motivation of the Single Catalyst Stochastic Modeling Approach (SiCaSMA)... why this is a theoretically useful extension of the Stochastic Simulation Algorithm (SSA)?

    What are the main differences between SSA algorithm execution with the SiCaSMA?

In conclusion, the study represents an incremental scientific contribution to the Chemical Master Equation literature and hence is worthy of publication consideration in the journal of Mathematics.

Author Response

Dear Dr. Guan,   we first of all thank both reviewers for their constructive feedback and  hereby reply to the two reports. We have addressed all issues raised by the reviewers and highlighted changes in the revised manuscript in blue.    Reviewer 2:   Reviewer 2 proposed two changes of content:   1) "The reader should understand the motivation of the Single Catalyst  Stochastic Modeling Approach (SiCaSMA)... why this is a theoretically  useful extension of the Stochastic Simulation Algorithm (SSA)?"   2) "What are the main differences between SSA algorithm execution with  the SiCaSMA?"

We addressed both points by adding further explanations to the 
manuscript. For point 1), we further stressed the advantages of our 
approach by better describing the problem it solves, namely coping with 
extremely large state transition graphs which typically arise from 
catalytic systems. The respective change can be found at the bottom of 
the second and top of the third page in the revised manuscript (lines 78 - 92).

In order to explain the differences between the conventional version of the SSA 
and our new SiCaSMA approach as pointed out in comment 2), we added a brief summary of the construction of the SiCaSMA SSA that particularly spotlights the relation between both versions of the SSA. For the exact wording, 
please consult lines 242-246 in the revised manuscript. We also added the adjective "conventional" twice, to clarify when which version of the SSA is to be used.

Best regards,
Nicole Radde