Talk:Metabolic P systems
The author presents a review on a variant of P systems use for the modelling of metabolic cellular systems, MP systems.
It was a pleasure to read the review. The work is presented lucidly in a transparent manner providing the right balance between technical sophistication and informal description. The author clearly presents the motivation of MP systems, their formal definition and graphical representation. This is integrated with a methodology for the estimation of missing parameters and a description of the available software tool implementing the modelling framework. Several examples are presented or cited to illustrate the methodology.
\begin-reply-0> I am happy with this appreciation. \end-reply-0>
MP systems are described as a variant of P systems nevertheless in their formal definition there is no membrane structure and the typical rewriting rules are replaced by pairs of vectors. Some discussions on the arguments leading to the decision of removing these central components of P systems would help the reader to understand why MP systems are considered as a variant of P systems.
\begin-reply-1> 1. Rewriting rules remain exactly the same as in P systems. Vector notation does not avoid classical notation (which we will continue to use), but it is only an alternative notation making evident linear algebra concepts in the analysis of MP dynamics. A statement expressing this remark was added in the initial section.
2. In the section "MP Graphs and MP Grammars" a paraghrph was added explaining how to deal with membrane structure. Here it is also argued that log-gain theory can be applied even in that case. \end-reply-1>
In order to put the reader into context a more detailed discussion on the advantages of using MP systems over difference equations would be welcome.
\begin-reply-2> The MP dynamics via EMA is nothing else than difference equation method applied in the context of metabolic transformation, that is a suitable specialization of that method. \end-reply-2>
When describing the log-gain theory a discussion of how it relates to the study of the identifiability of compartment models would allow the reader to relate this methodology to the general problem of uniquely determining the parameters of a model in order to reproduce certain dynamics.
\begin-reply-3> This was done at end of the section before log-gain section (see reply-1). \end-reply-3>
Finally, MP systems are not the only variant of P systems used in the modelling of cellular systems some discussions and citations refering to complementary stochastic and probabilistic approaches would contribute to the completeness of the review.
\begin-reply-4> In the section about ODE-MP a paraghaph was added asserting that probabilistic and stochastic P systems may complement MP systems as discrete methods based on P systems too, but with a different dynamical perspective. Papers in these areas were quoted and inserted in the references. \end-reply-4>
Only two small typos were spotted in the text: the use of molecular species rather than molecule species would be more appropriate and replace "can receive an natural" by "can receive a natural".
\begin-reply-5> They were corrected. \end-reply-5>
Typos and comments.
Section "MP systems: a formal definition": In the formal definition of an MP system, the state of the system is described by means of the vector X. It is possible to ease the comprehension of the reader referring explicitly to the fact that, in X, the substances quantities are expressed in conventional mole units.
\begin-reply-1> It was done. \end-reply-1>
Section "MP graphs and MP grammars": First sentence after the example: ".... in many biochemical and biological cotexts." -> ".... in many biochemical and biological contexts."
\begin-reply-1> It was done. \end-reply-1>
Section "Flux discovery": Third paragraph. "However, the equations (2) above do not are enough..." -> "However, the equations(2) above are not enough..."
\begin-reply-3> It was done. \end-reply-3>
Section "Log-gain validation" The last sentences, "At the conclusion, the discovered....." need to be expanded and some more reference to strengthen the heuristic statement.
\begin-reply-4> It was done. References were added, by mentioning also a new paper, added to References, where MP grammars with very good approximations of periodical behaviours were found by means of log-gain methods. \end-reply-4>
Section "MP systems and ordinary differential equations".
The sentence "However, when the time interval cannot be approximated to an infinitesimal time, MP models introduce a perspective which is radically different from the ODE perspective: it is macroscopic versus microscopic, ... " may suggests that the ODE approach has a microscopic perspective of the chemical kinetics. The use of ODE in this context treats chemicals by means of concentration or moles per volume, that it is a "population" point of view. Moreover, they are used in conjunction with the mass-action law, an empirical law, which assumes that the chemicals are homogeneously distributed within the volume and react according to their concentrations and their stoichiometry. With these premises the ODE approach looses reliability when the solutions become too dilute, that is, when it approaches the microscopic perspective.
\begin-reply-5> The statement was changed, for avoiding the misunderstanding here reported. However, the sense of "microscopic" does not refer to substance quantities, but to the level of reactions kinetics (in fact, it had would been more appropriate to say "nanoscopic"). In chemical reactions, kinetics depends on molecular interaction mechanisms, while at level of transformations between steps (at interval \tau) only the quantities variations are taken into accont (see reply-7). \end-reply-5>
The sentence "In fact, in ODE models, and in other kind of models based on them (e.g, Gillespie's stochastic models), a critical point is constituted by the evaluation of kinetic rate or (stochastic parameters)." seems to state that Gillespie's algorithm is "based" (=derived?) on an ODE approach and that is not the case. "The deterministic approach regards the time evolution as a continuous, wholly predictable process which is governed by a set of coupled, ordinary differential equations (the “reaction-rate equations”); the stochastic approach regards the time evolution as a kind of random-walk process which is governed by a single differential-difference equation (the “master equation”)." in the abstract of Gillespie (1977). In the same article section I and II are devoted to clarify the different underlying hypothesis of the two approaches. The same author investigates and clarify the relationships among these two approaches in the survey "Stochastic simulation of chemical kinetics", Annual review of physical chemistry volume 58 pages 35--55 (2007).
\begin-reply-6> The statement was changed, by avoiding the wrong impression that stochastic method are derived by ODE (even if they are related to ODE). The reference "Stochastic simulation of chemical kinetics" was added, which seems to me very appropriate (and included in References too). \end-reply-6>
"Moreover, differential laws are based on a field instantaneous effect (like in gravitational or electromagnetic fields) which has no direct correspondence in biochemical interactions, based on contacts of molecule populations." The instantaneous effect is an implicit assumption that occurs all the times that the chemicals are supposed to be homogeneously distributed in the volume or when they are supposed to be immediately at disposal to react. I think that the reader could benefit from an explanation of how the MP model cope with the in-distribution partition of each reagent to avoid the homogeneity assumption.
\begin-reply-7> A remark about homegeneity/concentration was added in the text, as a clarification of instantaneity in the context of chemical/biochemical processes. Moreover, some lines were added, as it is here suggested, for explaining the MP systems and log-gain perspective in this concern. Again, the main point is the observational, systemic approach of MP dynamics where transformations replace reactions (even if the term reactions continues to be used, for keeping the terminology so far adopted). According to the transformation perspective, the internal chemo-physical mecanism underlying the single processes is not relevant in the identification of regulators, which are only "matter transformation rules (associated to a stoichimetry) which synthetise the systemic logic of the observed behaviour they model". \end-reply-7>