Neural Differentiation Dynamics Controlled by Multiple Feedback Loops in a Comprehensive Molecular Interaction Network

Round 1

Reviewer 1 Report

In the paper, the authors develop a method to construct a mathematical model for the regulatory networks of neural differentiation by leveraging both the bottom-up and the top-down approach. The authors show the model reproduces the previously known mechanism of the regulatory networks of neural differentiation. 

The paper suggests the possibility of utilizing network theory to model biological systems of large-scale while. the dynamics governed by the main mechanism of the systems is encoded in the model. In addition, the paper is very well written. Therefore, this reviewer recommends this manuscript for publication in this journal after following minor edits. 

Line 110: a hub node in network theory is defined as a node whose connections to the rest of the network is much more than other nodes in a network. Please clarify whether the hub nodes in the manuscript indicate something different from or same as the definition.  Please present the results of motif analysis (for example, the frequency of each subgroup and statistical significance for the subgroup to be considered as a motif)

Author Response

Response to Reviewer 1 Comments

 Thank you for your kind advice in correcting our manuscript. Please find our responses to your comment in the following part. 

Point 1

Line 110: a hub node in network theory is defined as a node whose connections to the rest of the network is much more than other nodes in a network. Please clarify whether the hub nodes in the manuscript indicate something different from or same as the definition. Please present the results of motif analysis (for example, the frequency of each subgroup and statistical significance for the subgroup to be considered as a motif)

Response 1

We agree with your point that the usage of the word hub nodes and motifs in our manuscript was not consistent with the definition of them in network theory. We meant that we contracted our comprehensive network until the network consists of only the nodes which preserve one and over in-degree and out-degree. 

Thus, we revised our description as follows.

Original: The contraction was continued manually until a network contained hub nodes only (or nearly so). 

—> Revised (L92): The contraction was continued manually until a network consisted only of nodes with multiple input/output edges by removing nodes with both inward and outward degrees of one.

The sentence we revised is highlighted in the 2.2 Contraction of the network.

We expressed specific loop structures as network motifs, such as feedback loop, feedforward loop, etc., by following the references (9 in the Reference list in our manuscript and 1 and 2 in the following list). On the other hand, there are cases that network motif means network structures that appear more frequently than a random network. By considering these facts, we decided to use a structure with the combination of the word network, loop or cascade, etc., in this manuscript instead of network motif. The examples we use in the revised manuscript are listed here; a network loop structure, a cascade structure, a loop structure, a feedback loop structure, a large loop structure, and a network structure.

All these words in the manuscript are highlighted.

[References]

9. Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U. Network motifs: simple building blocks of complex networks. Science. 2002, 298(5594), 824–827.

[The other reference describing network motif]

1. Apte AP, Wang BP. Topology optimization using hyper radial basis function network. AIAA Journal. 2008, 46(9), 2211-2218.

2. B.L. Zhang, Y.L. Lie, H. Ma, G.Y. Tang. Discrete feedforward and feedback optimal tracking control for offshore steel jacket platform. Ocean Engineering. 2014, 91, 371-378.

Author Response File: Author Response.pdf

Reviewer 2 Report

This work presents a digested model of large scale regulatory network for neural differentiation and its applications. 

The topic and methods are clearly presented and the results are interesting. 

There are a few misspells and some labels in figure 2, 4 and 5 are quite small and difficult to read. 

Author Response

Response to Reviewer 2 Comments

Thank you for your kind advice in correcting our manuscript. The following is the response to your comments. 

Point 1

There are a few misspells and some labels in Fig. 2, 4, and 5 are quite small and difficult to read.

Response 1

We revised the following misspells.

In 2.3. Mathematical model construction, 2.4. Simulation and analysis, 3.1. Signaling network of neuronal differentiation, 3.2. Mathematical model of the core network, 3.3. Simulation of the oscillatory dynamics, 3.4. Model validation, 4. Discussion, 5. Conclusion

wrong: digestedmodel 

→ correct: digested model

In 5. Conclusion

wrong: a large-scale regulatory regulatory network (in Conclusion) 

→ correct: a large-scale regulatory network

We highlighted these words in our revised manuscript.

Also, we expanded the entire Fig. 2A, removed unnecessary labels in Fig2. And we enlarged the letters in Fig. 4, 5. We hope now those Figs are easier to read.

Author Response File: Author Response.pdf

Reviewer 3 Report

Major comments

In the Abstract, the terminology "bottom-up" and "top-down" was not explained. Hence, the following sentence "When we aim to analyze a large scale network~" is not understandable. In the Introduction, "bottom-up" represents a knowledge-based small-scale network and "top-down" represents a large-scale database- or omics-based network. But in the abstract, the authors mentioned that a knowledge-integrated model is an example of a large-scale network. Hence, the sentence "When we aim to analyze a large scale network~" makes readers confusing. Related to the first comment, the usage of the word "hybrid" is not proper. The authors mentioned that we developed a hybrid method combining "bottom-up" and "top-down" methods. But the authors collected pathway information from database (top-down) and identified a core network using network motifs. It is not clear whether the authors used "bottom-up" approach. If the authors think the network motif analysis represents "bottom-up" approach, the authors should have mentioned it. But even if the authors used the network motif analysis as "bottom-up", it is not proper. And there is another problem of usage of the word "hybrid". Usually, hybrid approach represent combining different modeling approaches such as combining dynamic modeling and static part (PMID: 16202166) or combining Petri-net and Boolean (PMID: 24244124). In the method 2.1, the authors mentioned that glial differentiation were excluded for making a large-scale network. But in the results, the mathematical model showed the dynamics of one of glial cell type, astrocyte differentiation. These are contradicting each other. The authors contracted the large scale network into small-size network preserving the original dynamics using network motif. There is many algorithm for identifying core structure of a large-scale network such as coarse-graining unit (PMID: 15697678), scale-free tree (PMID: 15600479), or Kernel Identification algorithm (PMID: 21632468). The authors can apply these algorithms to confirm that their manual identification of core structure was proper. When the three feedback loop (first, third and fourth) was inhibited, the oscillatory state disappeared. The author mentioned the third feedback loop with PI3K and fourth feedback loop with beta-catenin inhibition were validated by inhibition of them repressed proliferation of neural progenitor. But the authors did not validate the inhibition of the HES1 self feedback loop. The importance of HES1 self-feedback loop in neuronal differentiation does not mean the self-feedback loop have a pivotal role in maintaining neural progenitor state.

Minor comments

The components of four network motifs are need to be represented clearer. For example, HES1 -> dimer_HES1 -| HES1, instead of "negative feedback loop formed by HES1 dimerization" Typo "digestedmodel" needs to be corrected. The final digested model in Fig 4. seems to have 15 nodes. The authors mentioned it consists 16 nodes (line 213). Which one is correct? In the Discussion, the authors mentioned that the feedback loop with beta-catenin have the greatest contribution to the characteristic dynamics. But Figure 7 shows that the first loop (self-feedback loop of HES1) have the great contribution because the oscillation disappeared the expression of HES1 diverged. Typo: "a large-scale regulatory regulatory network" in the Conclusion.

Author Response

Response to Reviewer 3 Comments

Thank you for your kind review to improve our manuscript. Please find our point-by-point responses in the following part.

Point 1

In the Abstract, the terminology "bottom-up" and "top-down" was not explained. Hence, the following sentence, "When we aim to analyze a large scale network~" is not understandable. In the Introduction, "bottom-up" represents a knowledge-based small-scale network and "top-down" represents a large-scale database- or omics-based network. But in the abstract, the authors mentioned that a knowledge-integrated model is an example of a large-scale network. Hence, the sentence "When we aim to analyze a large scale network~" makes readers confusing. 

Response 1

First of all, we agree with your point that there is an inconsistent among our definition and usage of bottom-up, top-down, and a large scale network construction.

We reconsider and surveyed the terminology of bottom-up and top-down, and confirmed these words are not appropriate to explain our methods. The solution of this point will be explained together with the next comment as Response 2.

Point 2

Related to the first comment, the usage of the word "hybrid" is not proper. The authors mentioned that we developed a hybrid method combining "bottom-up" and "top-down" methods. But the authors collected pathway information from database (top-down) and identified a core network using network motifs. It is not clear whether the authors used "bottom-up" approach. If the authors think the network motif analysis represents "bottom-up" approach, the authors should have mentioned it. But even if the authors used the network motif analysis as "bottom-up", it is not proper. And there is another problem of usage of the word "hybrid". Usually, hybrid approach represent combining different modelling approaches such as combining dynamic modeling and static part (PMID: 16202166) or combining Petri-net and Boolean (PMID: 24244124).

Response 2

The definitions of bottom-up approach and top-down approach in systems biology are that if the causality of each node was supported by knowledge or not. 

In our case, we aimed to build a comprehensive network based on the causality clarified knowledge. In this meaning, our large scale network in Fig. 2A was constructed with a bottom-up approach. The further part of our approach with small size networks is neither not a top-down approach. From these facts, naming our method as a hybrid approach is not appropriate. Thus, we concluded not to use the three expressions; bottom-up, top-down, and hybrid. 

In the further part of our approach, we contracted the comprehensive network in order to analyse its dynamics. To perform the analysis of network dynamics, we needed to reduce the network size, but there exists a disadvantage of network reduction, which is a loss of information. To maintain the behavioral characteristics of the network, we kept loops and contracted only cascades.

The two steps we explained here are the actual strategy to analyse the dynamics of target biological phenomena involving comprehensively available knowledge. We revised the Abstract and Introduction in our manuscript based on these discussions. The following paragraphs are highlighted in the revised manuscript.

Abstract

Original: The majority of studies using mathematical models to reveal biological mechanisms uses one of the two main approaches: the bottom-up or the top-down approach. When we aim to analyze a large-scale network, such as a comprehensive knowledge-integrated model of a target phenomenon, for example, a whole-cell model, the variation of analyses is limited to particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we developed a hybrid method that combines both approaches. To construct a mathematical model, we extracted network motifs from a large-scale regulatory network, detected regulatory motifs among them, and combined these motifs.

—> Revised: Construction of mathematical models using comprehensive information is one of the techniques of model construction. Such a comprehensive knowledge-based network tends to become a large-scale network. As a result, the variation of analyses is limited to a particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we proposed a contractive method that preserves the dynamical behavior of a large network. The method consists of the following two steps; comprehensive network building and the network reduction. The reduction phase will extract network loop structures from a large-scale regulatory network, and the subnetworks were combined with preserving the dynamics of the original large-scale network.

Introduction

Original (at the beginning): Computational simulation using mathematical models is useful for understanding complex systems. Mathematical models of biological mechanisms use either the bottom-up or top-down approach [1]. Both approaches have their own challenges. The bottom-up approach has problems in acquiring regulatory relationships, whereas the top-down approach has problems in parameter determination. In the bottom-up approach, a few molecules of interest may be the pivot of an extended molecular network underlying the target biological event. For example, a mathematical model of the budding yeast cell cycle has been constructed using the bottom-up approach by combining known biochemical reactions [2]. This approach could yield a widely applicable model to simulate each specific analysis subject, but it is difficult to apply to the analysis of comprehensive biochemical networks because of limited information on the regulatory interactions of molecules and the parameters of mathematical models. The top-down approach is used to determine the intrinsic control mechanisms of target biological events. A simple model that simulates characteristic local dynamics is constructed using pathway databases or in a data-driven manner based on omics data by excluding non-essential factors from a comprehensive network. In the absence of a comprehensive pathway map, a statistical model is one of the first choices to construct a comprehensive network [3–5]. Yet, analysis of a large-scale network is still challenging, given that many parameters need to be determined in advance. The estimation of all the parameters of a whole-cell model has not yet been appropriately resolved [6]. To analyze the dynamics of a large-scale network, it is often divided into feasible-size modules, which are defined as small networks of functional units amenable to simulation and analysis [7]. Overall, the bottom-up approach can be used to analyze part of a biological event around a source molecule, but it is not applicable to a large-scale network; the top-down approach cannot be applied to analyze the dynamics because of the problem of parameter estimation. A whole-cell mathematical model of the bacterium Mycoplasma genitalium, which contains 525 genes, was built on the basis of enormous experimental data [8]; however, the use of a life-cycle model is not a simple way to analyze the mechanisms of dynamic control and requires a lot of information about the particular species.

To comprehensively analyze the dynamics of regulatory mechanisms, we developed a hybrid method that combines the bottom-up and top-down approaches. We aimed to decrease the number of modeled elements without losing the characteristic dynamics; therefore, we focused on network motifs that are important for the dynamics. Network motifs are subgraph structures that recur more often in a metabolic network or gene regulation network than in a random network. They are important for determining intrinsic regulation mechanisms derived from network characteristics [9]. In the current method, we extracted motifs from a large-scale regulatory network and used them to reconstruct a simple network, which reflects the original dynamics of the entire network because it contains these important motifs. We especially focused on a cascade motif and a feedback loop motif. A cascade motif is a sequence of unidirectional edges, and a feedback loop is a circuit structure that feeds back some of the output to the input.

—> Revised: These decades, biology started to integrate comprehensive knowledge of biological systems into biochemical networks and access the benefit by using it for mathematical modeling and simulation. For example, a whole-cell mathematical model of the bacterium Mycoplasma genitalium, which contains 525 genes, was built based on enormous experimental data and enabled to discover a new enzyme and some other suggestion [1]. When we aim to construct a comprehensive network, statistical methods are one of the first choices [2–4]. Yet, even if we build such a large-scale network, to translate it into equations and analyze them is still challenging, given that many parameters need to be determined in advance. Estimation of all the parameters of a whole-cell model has not yet been appropriately resolved [5]. Moreover, analyzing its dynamics is realistically impossible. Thus, a large-scale network is often reduced to a feasible-size network for the analysis of its dynamics [6-8]. 

Here, we developed a new method that consists of comprehensive modeling and the reduction of a comprehensive network to analyze the dynamics of regulatory mechanisms of target phenomena. First, we constructed a comprehensive network from databases and literature information. Second, to reduce the network size, we contracted a cascade structure, which is a sequence of unidirectional edges and nodes, and preserved the loop structures which affect the essential behavior of the network [9, 10]. This method makes it possible to obtain a small network that can reproduce the dynamic behavior of a large network.

Point 3

In the method 2.1, the authors mentioned that glial differentiation were excluded for making a large-scale network. But in the results, the mathematical model showed the dynamics of one of glial cell type, astrocyte differentiation. These are contradicting each other. 

Response 3

We revised our misleading description of what components are involved in our model. Our model includes the switching mechanisms of two differentiation pathways at the upstream of the following two pathways. One is the pathway to neuronal differentiation. The other one is the pathway to glial differentiation. We keep the molecular components of differentiation switching mechanism between the two pathways and eliminated one of the downstream pathways, which is the path to glial differentiation. That means our model may express the switching dynamics of two different fates.

The following is the revised sentences:

Original: Molecular interactions related to glial differentiation were excluded to focus on the differentiation of NSCs into neurons.

—> Revised (L77): The switching mechanisms that determine the direction of differentiation, glia or neurons, is described in the model. The model does not include pathways activated by glial differentiation but neuronal differentiation to focus on the differentiation of NSCs into neurons.

Point 4

The authors contracted the large scale network into small-size network, preserving the original dynamics using network motif. There is many algorithm for identifying core structure of a large-scale network such as coarse-graining unit (PMID: 15697678), scale-free tree (PMID: 15600479), or Kernel Identification algorithm (PMID: 21632468). The authors can apply these algorithms to confirm that their manual identification of core structure was proper. 

Response 4

We read through the indicated references and compared them with our methods. First, coarse-graining units and scale-free trees are both not able to maintain the original dynamics of the network; that means these methods are not applicable to our objectives. Kernel Identification guarantees at some level of network dynamics but only with Boolean networks. Even though the strategies of network reduction of Kernel Identification are quite similar to our method, the reason why we concentrated on extracting loops and did not touch except cascades as the target of reduction instead of applying the well established previous work was that we would like to maintain the network dynamics at the level of ordinary differential equation (ODE), and would like to apply further analyses such as bifurcation analysis to elucidate which loops are significant to control differentiation including HES1 self-feedback loop and more different loops.

We added the above discussion to the Discussion section of our manuscript. 

Added paragraph: (L394-L401)

There exist some network reduction approaches, but some of them are limited in the preservability of original dynamics [6, 7]. Kernel Identification [8] is one of the methods to preserve the network dynamics; however, the preservability is validated only with Boolean models. Because we aimed to maintain the network dynamics at the level of ordinary differential equations, we concentrated on extracting loops. We did not modify the network except cascades as the target of reduction, instead of applying the previous work. Practically, the network reduction by using Kernel Identification may produce a similar contracted network and will be advantageous when the network is larger than this case.

Point 5

When the three feedback loop (first, third and fourth) was inhibited, the oscillatory state disappeared. The author mentioned the third feedback loop with PI3K and fourth feedback loop with beta-catenin inhibition were validated by inhibition of them repressed proliferation of neural progenitor. But the authors did not validate the inhibition of the HES1 self feedback loop. The importance of HES1 self-feedback loop in neuronal differentiation does not mean the self-feedback loop have a pivotal role in maintain neural progenitor state.

Response 5

We added a detailed description of the results indicated with Fig. 7. First, the plot showed that HES1 self-feedback loop inhibition causes the disappearance of oscillation in the condition in which the oscillation was normally inducible. At the same time, ASCL-1 dominant condition, which equals neuronal differentiation dominant condition, becomes narrower. This simulation result is consistent with the previous report of HES1 inhibition with Id protein overexpression, which inhibits neuronal differentiation.  

Original: When the loop was collapsed by changing equation 2 to equation 2' (Table 4), the oscillatory state, which is important for maintaining the undifferentiated state, disappeared (Fig. 7A). This result was consistent with the reported importance of the HES1 self-feedback loop in neuronal differentiation [38, 39].

—> Revised (L277-L282): When the loop was collapsed by changing equation 2 to equation 2' (Table 4), the oscillatory state, which is important for maintaining the undifferentiated state, disappeared. At the same time, the ASCL1-dominant state, which is important to differentiate into neurons, became narrower with rapid HES1 upregulation (Figure 7A). Therefore, this loop required to maintain the oscillatory state and ASCL1-dominant state. This result agreed with the reported result of HES1 inhibition by overexpression of Id2 [15].

Minor comments

Point 6

The components of four network motifs are need to be represented clearer. For example, HES1 -> dimer_HES1 -| HES1, instead of "negative feedback loop formed by HES1 dimerization". 

Response 6

Thank you for your kind advice. We added the following description into Results 3.2.

(L177) The self-negative-feedback loop formed by HES1 dimerization, HES1 -> dimer_HES1 -| HES1, …

(L188) The positive-feedback loop between PI3K and aPKC_PAR3_PAR6, PI3K -> PIP3 -> RAP1B -> CDC42_GEF -> CDC42 -> aPKC_PAR3_PAR6 -> TIAM1/2 -> RAC1 -> PI3K, ...

(L192) The negative-feedback loop between PTEN and GSK3B, PTEN -| PIP3 -> RAP1B -> CDC42_GEF -> CDC42 -> aPKC_PAR3_PAR6 -| GSK3B -| PTEN, 

(L195) The negative-feedback loop between beta-catenin and HES1, HES1 -| NEUROG2 -| RHOA -> Rho_kinase -> PTEN -| PIP3 -> RAP1B -> CDC42_GEF -> CDC42 -> aPKC_PAR3_PAR6 -| GSK3B -| B-catenin -> HES1, was reconstructed as a six-molecule loop (Fig. A6). 

These expressions are highlighted in the revised manuscript.

Point 7

Typo "digestedmodel" needs to be corrected. The final digested model in Fig 4. seems to have 15 nodes. The authors mentioned it consists 16 nodes (line 213). Which one is correct? 

Response 7

Thank you for let us know these points. We corrected the typo "digestedmodel" to "digested model" and fixed the number of nodes in Fig.4 to 15. The corrected words are highlighted in our manuscript in 2.3. Mathematical model construction, 2.4. Simulation and analysis, 3.1. Signaling network of neuronal differentiation, 3.2. Mathematical model of the core network, 3.3.Simulation of the oscillatory dynamics, 3.4. Model validation, 4. Discussion, and in 5. Conclusion.

Point 8

In the Discussion, the authors mentioned that the feedback loop with beta-catenin have the greatest contribution to the characteristic dynamics. But Fig. 7 shows that the first loop (self-feedback loop of HES1) have the great contribution because the oscillation disappeared the expression of HES1 diverged. 

Response 8

We understand HES1 self-loop is significant. We added a sentence to indicate clearly the significance of HES1 self-loop on neural differentiation before the description of the beta-catenin loop and highlighted in our manuscript.

Added sentence (L333-L340):

Our simulation result showed that the inhibition of the HES1 self-feedback loop caused the disappearance of its oscillatory expression (Fig. 7A). At the same time, the ASCL1 dominant condition, which equals to neuronal differentiation dominant condition becomes narrower. That means the inhibition of the HES1 self-feedback loop could suppress the differentiation of NSCs. The previous study experimentally showed that the inhibition of HES1 by overexpression of id protein caused the inhibition of differentiation [15]. Therefore, the result of our simulation was consistent with this previous experimental knowledge.

Point 9

Typo: "a large-scale regulatory regulatory network" in the Conclusion.

Response 9

We corrected our typo to "a large-scale regulatory network" in the Conclusion and marked the place.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors:

This is an interesting manuscript which presents new approach to analyze a large-scale regulatory network of neural differentiation, with the use of a hybrid method that combines bottom-up and the top-down strategies. Authors extracted network motifs from a large-scale regulatory network, detected regulatory motifs among them, and combined these motifs. What have to be underlined the proposed in the paper hybrid method is applicable to other biological events. Generally, in my opinion the paper is well written and the topic fits the scope of the journal well. The only point to the discussion with authors is: Have you consider in the presented model the use of the fractional derivatives instead of the classical integer derivatives? In my opinion this may brings closer the presented models to the real biological cells. Regarding above I would like to recommend the reviewed article to be accepted (with revisions of some minor editorial tips) for printing in its current version.

Formatting:

In the entire manuscripts the embedded equations looks as poor resolution bitmaps (some of the indexes are not readable) so I suggest to convert all of them to the vector ones (LaTeX, MSEquations?).

Author Response

Response to Reviewer 4 Comments

Thank you for the very kind suggestion to add meaningful discussion to this paper. Please find our responses to your comments in the following part.

Point 1

Have you consider in the presented model the use of the fractional derivatives instead of the classical integer derivatives? In my opinion this may brings closer the presented models to the real biological cells.

Response 1

We added a paragraph in discussion and references about fractional derivatives that it is based on anomalous diffusion of reactive molecules in in vivo oriented environment, such as under the effect of crowding molecules, instead of a normal diffusion process, which is the assumption of ODE models. This approach is well evaluated in the usage of visco-elastic processes of soft materials, and recently have started to apply more biological target. 

Added paragraph: it is the last paragraph in our Discussion (L402-L414).

To simulate more realistic behaviors of biological cells, highly crowded and inhomogeneous environments should be considered. The use of the fractional derivatives is well evaluated in the usage of visco-elastic processes of soft materials [55], and recently have started to apply more biological target [56-59]. Our mathematical model of neural differentiation is also expected to become more realistic by the fractional derivatives instead of the classical integer derivatives. Although we focused on NOTCH signaling in this study, our network also includes FGF as another input signal. Analysis of the behavior of the network stimulated with FGF may show variate responses and as a result, may reveal other mechanisms of neural differentiation. Although the core network did not include a feedforward loop, a feedforward loop accelerates the response time of a system and achieve cell state transition rapidly. Because the cellular state transition by NOTCH signaling is also known to be accelerated by feedforward loop [60], a feedforward loop may exist on upstream of the core network. Our method can be used to analyze the dynamics of a new large-scale regulatory network when new information becomes available.

References: (The numbers are the number in the Reference list in the manuscript)

56. Kopelman R. Fractal reaction kinetics. Science. 1988, 241(4873), 1620-6.

57. Schnell S; Turner TE. Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog Biophys Mol Biol. 2004, 85(2-3), 235-60.

58. Hiroi N; Lu J; Iba K; Tabira A; Yamashita S; Okada Y; Flamm C; Oka K; Köhler G; Funahashi A. Physiological environment induces quick response - slow exhaustion reactions. Front Physiol. 2011, 2, 50.

59. Hiroi N; Klann M; Iba K; Heras Ciechomski Pd; Yamashita S; Tabira A; Okuhara T; Kubojima T; Okada Y; Oka K; et al. From microscopy data to in silico environments for in vivo-oriented simulations. EURASIP J Bioinform Syst Biol. 2012, 2012, 7

We highlighted these paragraphs and references in our revised manuscript.

Author Response File: Author Response.pdf