Elsevier

Biosystems

Volume 210, December 2021, 104533
Biosystems

A Petri nets-based framework for whole-cell modeling

https://doi.org/10.1016/j.biosystems.2021.104533Get rights and content

Abstract

Whole-cell modeling aims to incorporate all main genes and processes, and their interactions of a cell in one model. Whole-cell modeling has been regarded as the central aim of systems biology but also as a grand challenge, which plays essential roles in current and future systems biology. In this paper, we analyze whole-cell modeling challenges and requirements and classify them into three aspects (or dimensions): heterogeneous biochemical networks, uncertainties in components, and representation of cell structure. We then explore how to use different Petri net classes to address different aspects of whole-cell modeling requirements. Based on these analyses, we present a Petri nets-based framework for whole-cell modeling, which not only addresses many whole-cell modeling requirements, but also offers a graphical, modular, and hierarchical modeling tool. We think this framework can offer a feasible modeling approach for whole-cell model construction.

Introduction

Systems biology (Kitano, 2002, Westerhoff and Palsson, 2004) and synthetic biology (Benner and Sismour, 2005, Cameron et al., 2014) have the potential to offer technologies that could change the world in the 21th century, a thought shared by many people. Wet-lab experiments and modeling & simulation, which complement each other, are two essential ways to explore systems and synthetic biology.

Recently, due to the advances of biological measurement techniques and deeper understanding of biological mechanisms, biological models are becoming more complex and integrated. A typical observation is that a biological model could incorporate different kinds of multiscale/multilevel biochemical networks (Liu et al., 2014, Matsuno et al., 2003, Covert et al., 2008). Moreover whole-cell modeling (Carrera and Covert, 2015, Babtie and Stump, 2017, Tomita, 2001, Machado, 2011, Roberts, 2014) was recently proposed, which tries to incorporate all main genes and processes and their interactions of a cell in one model. Different from usual biological models, a whole-cell model usually owns the following features (Roberts, 2014, Goldberg et al., 2018, Karr et al., 2012): representing two or three dimensional (2D/3D) physical structure of a cell, involving multiple time and space scales, different components having distinct resolution and details, and integrating different modeling methods (qualitative, stochastic and deterministic methods).

Whole-cell modeling has been regarded as the central aim of systems biology (Tomita, 2001) but also as a grand challenge (Carrera and Covert, 2015), which at least plays the following essential roles (Babtie and Stump, 2017).

  • A whole-cell model usually incorporates the main biochemical processes, which offers a comprehensive explanation on the mechanism of the cell.

  • A whole-cell model can clearly reveal our insufficient understanding of the cell, and helps to find new biological issues.

  • A whole-cell model can be used to explore the emerging phenomena resulting from all the components of the cell.

  • A whole-cell model can be used to achieve the prediction from genotypes to phenotypes, which could contribute to individual drug therapy and synthetic biology (Macklin et al., 2014).

However, the research of whole-cell modeling is still in its infancy (Waltemath et al., 2016). Although the concept and idea of whole-cell modeling were proposed some years ago, there appeared only one real practical application (by Karr et al. (2012)) so far. From then on, it has obtained wide attention, and is becoming a hot issue in the systems biology area. However, we have to notice, although whole-cell modeling becomes feasible, we are still facing many challenges. For example, there are no mature and applicable whole-cell modeling methods, techniques and tools. These detailed whole-cell modeling requirements can be described as follows Waltemath et al. (2016) and Goldberg et al. (2018).

(1) A whole-cell model usually incorporates different types of biological networks, e.g., genetic regulatory networks, signaling pathways and metabolic networks. Distinct networks (processes) have distinct structure and characteristics, and available experimental data may also be quite different, so they usually adopt different modeling and simulation methods. In the case of insufficient data and little understanding of biological mechanisms, qualitative methods such as Boolean networks, Petri nets (PN) and finite state machines could be of help; on the contrary quantitative methods such as ordinary differential equations (ODEs), Partial differential equations (PDEs), and stochastic Petri nets (SPN) could be choices. In order to formulate a whole-cell model, we may have to adopt more than one method. However, at present, there is no such a framework or tool that can integrate a couple of different methods to satisfy whole-cell modeling requirements.

(2) Modeling of biological systems is inevitably affected by uncertainties (Chesi, 2011, McAdams and Arkin, 1999). For the modeling of intrinsic noises of a biological system, stochastic methods (Gillespie, 2007, Székely and Burrage, 2014) can be used. However, epistemic uncertainties (also often called fuzzy uncertainties), due to measurement errors or cognitive difference, cannot be dealt with using stochastic methods. Rather fuzzy methods (Du et al., 2005) could be a good option. The modeling of a biological system usually faces two sources of fuzzy uncertainties (Babtie and Stump, 2017): uncertainty in model structure (structural uncertainty) and uncertainty in kinetic model parameters (parametric uncertainty). In the case of whole-cell models, we may have cognitive difference on different biological processes, and available data are also quite different (sufficient or insufficient), so we may have to consider fuzzy uncertainties in a whole-cell model. This means that a whole-cell modeling framework may have to incorporate some fuzzy modeling methods.

(3) Likewise, whole-cell modeling also welcomes graphical, modular and hierarchical modeling methods as most biologists do. Moreover, different biological processes function in different compartments of a cell, which may require spatial modeling methods (Macklin et al., 2014). In summary, there are many challenges that need to be addressed to achieve a whole-cell modeling approach (tool).

In this paper, we will present a Petri nets-based framework for addressing a couple of whole-cell modeling challenges by means of analyzing how different PN classes deal with different challenges discussed above and then integrating them in a framework.

PN and their extensions, such as stochastic, continuous and colored Petri nets (Heiner et al., 2008, Liu and Heiner, 2013, Chen and Hofestädt, 2014), are popular modeling methods in the systems biology area, which have been applied for the modeling of different types of biochemical networks including signaling pathways, genetic regulatory networks and metabolic networks. By combining different PN classes, we may realize the modeling of most types of biological networks in one model. Moreover, PN offer graphical, modular, hierarchical, and spatial modeling capabilities, which are promising to address many challenges of whole-cell modeling. However, we have not seen such work so far.

Section snippets

Petri nets and extensions for whole-cell modeling

There have been many extensions of PN so far, and we will discuss some of them that could be used for whole-cell modeling in the following.

A Petri nets-based framework for whole-cell modeling

By comparing PN modeling capabilities and whole-cell modeling needs, we propose a Petri nets-based framework for whole-cell modeling, illustrated in Fig. 7. We divide the whole-cell modeling needs into three dimensions: heterogeneous biochemical networks, uncertainties of components, and spatial cell structure.

A whole-cell model may have to model heterogeneous biochemical networks such as genetic regulatory networks, signaling pathways and metabolic networks. However, no single modeling method

Conclusions

In this paper, we comprehensively analyzed whole-cell modeling requirements and classified them into three aspects (or dimensions): heterogeneous biochemical networks, uncertainties of components and representation of the spatial cell structure. We then explored how to use different PN classes to address different aspects of whole-cell modeling requirements, based on which we presented a Petri nets-based framework for whole-cell modeling. We believe that this framework offers a feasible

CRediT authorship contribution statement

Fei Liu: Conceptualization of this study, Methodology, Software. George Assaf: Development of the fuzzy dimension in the PetriNuts framework, development of models under study and performing the simulation experiments. Ming Chen: Checked the paper and gave improvement comments. Monika Heiner: Leading the development of the PetriNuts framework.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Compliance with ethics guidelines

Yes.

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    This work has been supported by National Natural Science Foundation of China (61873094,31771477), Science and Technology Program of Guangzhou, China (201804010246), and Natural Science Foundation of Guangdong Province of China (2018A030313338).

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