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Review of construction methods for whole-cell computational models

Abstract

The complex mechanisms of the internal operation of cellular functions have not been fully resolved and these functions are regulated by multiple effects, such as transcription regulation, signal transduction, and enzyme catalysis, forming complex interactive mechanisms. This makes the construction of a whole-cell computational model, containing various complex cellular functions, very challenging. However, biological models have played a significant role in the field of systems biology, such as guiding gene-target mining and studying cell metabolic characteristics. Therefore, there is increasing research interest in the construction of whole-cell computational models. Combining two classical languages of systems biology, this review expounds on the development and challenges of whole-cell computational modeling from the two classical methods of steady-state and dynamic modeling. Finally, we propose a new approach for constructing whole-cell computational models.

Background

Synthetic biology is developing rapidly and “microbial cell factories”, created by synthetic biology, are influencing the development of some aspects of human society, particularly the environment, health, agriculture, and the chemical industry, and have become an innovative driving force for the industrialization of biotechnology. Microbial cells are extremely complex and highly evolved systems, so it is necessary to have a full understanding of all cellular regulatory mechanisms and biosynthetic pathways, to construct a cell-factory with the desired functions. Mathematical models can characterize the metabolic mechanism of microbial cells at the systemic level through. It can integrate biological big data in all directions at different levels, and these models can help to give more rational guidance to the for designing or improving of cell factories’ abilities by means of experience and prediction. However, the internal mechanisms of the complex cellular metabolic network have not been fully analyzed and there is no mathematical model to characterize the internal metabolic mechanism of microbial cells, making it difficult to rationally design cell factories and understand the effects of genetic engineering on cell phenotype. Therefore, there is an urgent need to build a comprehensive computational model of cellular metabolic pathways.

The microbial cell is an extremely complex and sophisticated system that manages many critical functions, such as gene transcription, translation, post-translational modification, and metabolism. These functions are regulated by transcriptional regulation, signal transduction, and enzymic catalysis, forming complex interactive mechanisms. In addition, microbial cells contain DNA, RNA, proteins, and metabolites, which control cellular functions through complex interconnected pathways and feedback loops. Understanding the activities of these molecules can help decode the complex cellular systems. Understanding the mechanisms of cellular activities, using appropriate mathematical methods to establish accurate computational models, and using the common systems biology language for standardization are major current challenges in systems biology [1,2,3].

The primary problem in modeling cells is to describe the metabolic processes of cells systematically. In this review, Systems Biology Markup Language (SBML) and Systems Biology Graphical Notation (SBGN) are discussed as practical approaches to systematically describe and model specific areas of cellular metabolism. SBML is a machine-readable format for communicating and storing computational models of biological processes, and SBGN is a graphical notation used to describe the “biological programming languages” of biological processes including metabolic pathways, cellular signaling, and gene regulation [4]. However, as the scale of a model increases, the usability of SBML declines and it becomes increasingly ineffective for the visualization of biological processes and often requires matching with a visualization language such as SBGN. SBGN can describe biological systems and networks through graphical approaches, which can intuitively describe and present the topological structure of, and relationships within, the network [5]. SBGN is a powerful tool for visualizing biological networks and it is suitable for developing computational models, but the graphical format of SBGN is not well suited to describing dynamic models.

There are two main categories for modeling biological cells: linearized models, based on steady states; and non-linear differential equation models, based on dynamic states. For example, the genome-wide metabolic network model (GSMM) is an in silico metabolic model covering the thousands of chemical reactions that make up the metabolic inventory of a cell and is based on steady-state assumptions, whereas E-CELL, a software environment for whole-cell simulation, is based on dynamic differential equations to solve and simulate dynamic cell states. GSMM has been established as one of the major modeling approaches for metabolic studies based on chemometric conservation and steady-state mass balance, and also describes gene-protein-reaction (GPR) associations [6, 7]. E-CELL provides ideas for the study of electronic cell stimulation, which uses reaction steps to write the differential equations of reaction rates and describes the dynamics of the cellular system [8, 9]. However, steady-state-based GSMM is an idealized assumption of a true dynamic metabolic state with significant limitations for the presentation of dynamic metabolic processes in organisms. E-CELL also has limitations, arising from the large number of parameters involved in the differential equations of enzymatic reactions. The solution of these complex and numerous differential equations requires high computational power and long processing time.

The ultimate goal of computational cell modeling is to establish a whole-cell computational model containing the various complex life processes of cells. The whole-cell computational model includes the biosynthesis and mechanisms of interaction of the cellular genome, proteome, and metabolome. By modularization of all life processes in an organism (including metabolism) and systematic study of the relationship between the various modules, the digitization of cellular functions can be achieved. With the development of ‘omics detection technology [10,11,12] and the accumulation of information in various biological databases [13,14,15]’, research on biological models has developed continuously, and more omics data and genetic information have been incorporated [16]. In this paper, systems biology language is introduced with the presentation of SBML and SBNG. In addition, two classical modeling methods (GSMM and E-CELL) and their progress are discussed in detail. Finally, the latest advances in cell model construction and their potential applications are presented.

Computational model language

Systems Biology Markup Language (SBML)

With the rise of systems biology, more and more biological models are being created in different forms [17], and researchers hope to create a standard language to solve the problems arising from the lack of inter-operability between different models. As a result, an intense program of international conferences and research-community discussions was launched [18], and finally, the California Institute of Technology officially released SBML Level 1 in 2001 [19]. SBML is a structured language with strict syntax and precise semantics [20]. It is an XML file that contains SBML elements, which declare the name, level, and version of SBML [21], and has only one model object. The model definition includes the components shown in Fig. 1 [22].

Fig. 1
figure1

Model components of SBML

SBML was originally designed to describe biochemical reaction networks, such as metabolic and signaling pathways [23]. However, as more research groups collaborate and provide support for the development of SBML, many advanced functions have been gradually added [24]. SBML has evolved from the initial level 1 to level 3 [4, 19, 25]. SBML LEVEL3 is modular, with defined core function sets and optional software packages that add functions to the core function sets. This modular approach means that the model can declare the set of functions it uses, and similarly, the software tool can declare the packages it supports. SBML has been extended its core part, so that it can be applied to more biological models. For example, the Flux Balance Constraints (FBC) package extends SBML Level 3 to provide a balanced operation format for constraint-based model modeling. It also provides an open platform that promotes the continuous development of a cross-community of an interoperable and constraint-based model coding formats [26]. The main currently available software packages and their applications in biology are shown in Table 1.

Table 1 Optional software packages for SBML Level 3

Benefiting from community-oriented development approaches over the past two decades, SBML has continued to evolve, with the emergence of much software supporting SBML as a read–write model. For example, LibSBML [33] and JSBML [34] for building and editing models, SBML Test Suite for testing, MOCCASIN [35], SBFC [36] and SBML Toolbox [37] for importing and exporting models. Through the above software, researchers can directly communicate and store different models, speeding up the development of systems biology. Nowadays, many pathway databases [38, 39], model databases [40, 41], and reaction databases [42, 43] can use SBML as an import and export format.

XML-based biological programming languages similar to SBML include NeuroML [44] and CellML [45]. CellML was originally created according to the Physiome Project [45] and is mainly used to describe models related to the biological field. NeuroML provides a common data format for defining and exchanging descriptions of neuron cells and network models. NeuroML is more domain-specific than SBML. CellML overlaps the main domain of SBML but provides alternative abstractions.

SBML has strongly promoted the development of systems biology since its emergence and has become a recognized standard [46]. SBML enables the models established by different researchers to be exchanged and tested co-operatively, eliminating obstacles to sharing results [47]. SBML has been applied to many subjects, including biochemical reactions [48], gene regulation [49], metabolic pathways [50, 51], information transmission pathways [19, 24] and regulation of transcription [52]. Recently, the University of Rostock in Germany invited several research groups to set up Summer Schools [53] to discuss whole-cell modeling, where whole-cell modeling with SBML and visualization with SBGN were proposed.

Systems Biology Graphical Notation (SBGN)

Graph theory has always been of great practical importance in the study of biological networks [54]. In a similar way to geographical maps, a graph can facilitate the representation of biological knowledge visually, to facilitate the study of complex processes in living cells [55]. Using graphics to describe a biological network system is direct, efficient, and easily understood. However, before the advent of SBGN, graphical descriptions of biological network systems did not follow a unified standard, causing difficulties in understanding and relating different graphical biological networks [56]. Therefore, the introduction of SBGN was of great significance for the graphical representation of biological network systems.

Systems Biology Graphical Notation (SBGN) [56] is a standardized graphical language that can be used to describe signal transduction, metabolic networks, and genetic regulation of cellular processes. SBGN consists of three sub-languages (Fig. 2): process description (PD), entity relationship (ER), and activity flow (AF). Each uses symbols to define different semantics precisely, and they are independent of each other at different abstract levels. PD shows how biochemical interactions in a network change with time, describing them at the reaction level. ER describes the relationships between entities in the network and does not contain any time information; AF describes the flow of information between entities in a network. More specifically, PD is directed, sequential and mechanistic while the other two languages do not have all these three characteristics. For example, AF and ER cannot describe the particular reaction. They can only show the relationship of entities. So, PD can include more biological information. That is why PD is widely used for now. Furthermore, the three descriptions can be complementary to each other, and finally the network of biochemical interactions can be clearly represented and visualized. Figure 2 only shows some sample symbols of these three languages. Some symbols are the same in all three languages. Each symbol has a unique meaning. We can combine these symbols to form a complete biological network.

Fig. 2
figure2

Three languages of SBGN

Once published, SBGN attracted great interest from systems biologists. The first language specifications for the three sub-languages (PD, ER, and AF) [57,58,59] were published in 2008 [60], 2009 [61], and 2010 [62], respectively. Researchers are constantly updating the specifications, correcting problems in the specifications, simplifying the language, and adding new content.

To carry out research on a whole-cell computational model, it is necessary to provide an SBGN file format that is both machine-readable and capable of effective visualization. Currently, there are three main standard formats: SBGN-ML [63], BioPax-SBGN Mapping [64], and Biological Connection Markup Language (BCML) [65]. SBGN-ML format is the most widely used of the three. It is compatible with the SBML language standard file format and provides a powerful tool for research, using the whole-cell computational model. Various biological model tools and plug-ins based on SBGN have been developed, such as STON [66], cySBGN [67], SBGNViz [68], and SBGN-ED [69], all of which are aimed at simplifying the modeling process, or facilitating the conversion of SBGN files into other file formats, so as to use SBGN in a more compatible manner. At present, some other modeling tools, such as Celldesigner [70], BioUML [71], and Newt Editor [72], also support partial SBGN language format and are used for model visualization (Fig. 3).

Fig. 3
figure3

Part of an SBGN PD network, built with Newt Editor

SBGN has been widely used in biological system networks and provides a new method for the analysis and visualization of biological networks [73,74,75,76]. For example, the network diagram of metabolic pathways meeting the SBGN standard [77, 78] and the molecular interaction diagram [79, 80] have been constructed. In addition, the metabolic pathways in the KEGG database can be automatically converted into the SBGN format for visualization, while preserving as much as possible, the layout of important elements that may change as a result of model conversion [81].

Although the SBGN can directly present the biological networks, it is hard to show the quantitative relationship between reactions. Obviously, it is also a huge drawback in describing dynamic networks.

Research on methods of dynamic and static cell model construction

Genome-scale metabolic network model based on the steady-state hypothesis (GSMM)

At present, GSMM is generally based on two steady-state assumptions. First, that the system is in a steady-state of mass conservation, i.e., the system material production is equal to its consumption. Second, the system is in metabolic homeostasis, i.e., the concentrations of metabolites in the system do not change with time. Flux balance analysis (FBA) is a computational method that can perfectly fit the two steady-state conditions of GSMM and FBA has been widely used in modeling and metabolism calculations with GSMM. FBA converts the biological metabolic reactions into a stoichiometry matrix (S), defines a steady-state mass conservation constraint (\(Sv=dx/dt\)) and a metabolic steady-state equation set (\(dx/dt=0\)), and sets target solutions and other constraints (\(lb\le v\le ub\)), thereby establishing a linear programming problem (LP) [82, 83] (Fig. 4).

Fig. 4
figure4

Principle, development, and application of GSMM. The number of ‘Coverage and Application’ indicates the number of models for this species

Since the first GSMM was constructed in 1999 for Haemophilus influenzae [84], GSMM models of other cells in bacteria, fungi, animals, and plants have been developed [85,86,87,88,89,90,91,92,93], and have been widely used in many fields, such as industry, medicine and scientific discovery [7, 94], such as guidance of metabolic engineering [95,96,97], identifying drug targets [98, 99] and predicting enzyme functions [99].

The traditional GSMM approach collects the gene-protein-reaction (GPR) correspondence, but does not quantitatively describe it. To gradually establish a more complete and detailed biological network, researchers have increasingly focused on integrating GSMM with omics data, including the transcriptome (MADE [100], IMAT [101], PROM [102], IDREAMM [103], and OptRAM [104]) and proteome (FBAwMC [105], IOMA [106], RBA [107], and GECKO [108]). The integration of multiple omics information has made GSMM an increasingly realistic simulation of the real cell. GEMs of metabolism and macromolecular expression (ME-models) include biosynthesis of macromolecules, such as DNA, RNA, ribosomes, and proteins, as well as protein assembly and daughter cell dilution [109, 110]. Its prediction ranges span the reaction fluxes of metabolism, transcription, translation, and post-translation modification. By extension, the ME model also includes protein translocation [111] and protein folding [112]. Expression and Thermodynamics-enabled Flux models (ETFL) incorporate thermodynamic information based on the ME model and clearly define concentrations of metabolites, enzymes, and mRNA [113].

However, both ME and ETFL still have some way to go before they can achieve whole-cell computational modeling. They lack information on the interaction between transcription factors (TFs) and their regulation of the transcription process, which depends on the integration of ChIP-seq data [114, 115] into GSMM model. In addition, the GSMM-dependent steady state is an idealized set of assumptions, which are not necessarily valid, about real dynamic metabolic states. Dynamic flux balance analysis (dFBA) is one such technique that extends the traditional FBA to simulate dynamic fluxes[116], dFBA relies on solving a linear optimization problem at each time instant, so its solving process is computationally expensive. As such, simulating real dynamic cellular metabolism can be challenging.

E-CELL model based on dynamic metabolism (E-CELL)

E-CELL integrates all substances in cells with their reaction mechanisms and translates them into differential equations related to the reactants in each biochemical reaction (Fig. 5). The equations contain information, such as the molecular species, concentration, location and diffusion range of the substance, as well as the rate constant and direction of the reaction, which gives the model the ability to perform dynamic simulation. By setting the reaction time operation model, the changes in state of each substance with time can be obtained, and the physiological metabolic state of the cell can be obtained through analysis [8, 9]. The E-CELL system incorporates many simulation algorithms, which can solve the model in non-space (ode, Gillespie algorithm [117]), or multi-space simulation settlement (GFRD [118], Spatiocyte [119, 120] algorithms) and has two observers to record the simulation state.

Fig. 5
figure5

Principle and process of E-CELL modeling. Input comprises the initial conditions about the volume, species, and their initial concentrations, the location and dimension (i.e., a diffusion coefficient and radius) that each species belongs to, and the duration time of the reaction. The simulation algorithms are chosen from the rule list and each rule in the list is called to calculate the concentration of each substance at time intervals (Δt), which becomes the initial state of the next stage. The simulation algorithm repeats the simulation process until the time reaches the duration time t, then the state of the cell at time t is exported. Every result during the simulation is loaded by the Observers in the system

Keio and TIGR first used E-CELL software to establish a self-sustaining hypothetical cell model with 127 genes based on Mycoplasma genitalium in 1997 [8]. Since then, E-CELL 3 has established a mitochondrial model [121], myocardial cell model [119, 120], drosophila circadian rhythm model [122], and others. E-CELL 4 has been used to establish the day–night clock model, dephosphorylation cycle model, glycolysis model, metabolic control analysis, and neuron action potential, among others. These models have reference and guiding significance for studying molecular interaction mechanisms.

E-CELL can be used to analyze a wide variety of cellular systems, such as a simulated cellular metabolic process, synthesis and structure analysis of proteins, drug design, diagnosis, and treatment of diseases, and multi-cell interactions. E-CELL appears to have wide application prospects. With further research on organisms and further optimization of the model algorithm, it is thought that the application of the E-CELL system to whole cells can be realized at some point in the future. However, although the differential equation set in E-CELL is simple and clear, its solution and analysis are complex and non-intuitive. In addition, there is still the problem of incomplete information about enzymatic reactions in cells, which causes difficulties for modeling [121]. Whole-cell computational modeling appears unlikely to be realized in the near future.

Future prospects

At present, relatively detailed steady-state models have been established for extensively studied microorganisms, such as Mycoplasma genitalium [3], Escherichia coli [123], and Saccharomyces cerevisiae [124]. However, these models are still far from the ultimate goal of true whole-cell computational models. For example, they lack information on the interaction between TFs and their regulation during the transcription process. In addition, systems biology researchers are trying to develop more complex and larger-scale dynamic models, but the establishment of a fully dynamic whole-cell computational model will require very complex calculations and there is no guarantee that they can be solved [125].

Therefore, we proposed a new approach to whole-cell computational modeling: the dynamic LogicTRN transcription regulation network [126], dynamic E-CELL [8, 9] and steady-state GSMM based on enzyme constraints [108], were integrated to achieve modular digital expression of transcriptional regulation, gene expression, protein synthesis, enzymic catalysis, and metabolic pathways, which allowed mRNA expression, protein yield, and metabolic reaction flux to be calculated. This method integrates ChIP-seq data and brings both TF interactions and TF cis-regulation of target genes into the whole-cell computational model, which has not previously been achieved in GSMM. In addition, because of the complexity in the construction and calculation of large-scale dynamic E-CELL systems, local construction of gene expression and protein synthesis sub-networks can be considered. Therefore, our modeling approach not only preserves the steady-state solution from GSMM, but also incorporates the dynamic LogicTRN transcription regulatory network and the dynamic simulation from E-CELL, to realize semi-continuous dynamic calculation of changes over time in the whole-cell computational model. The specific modeling idea is shown in Fig. 6.

Fig. 6
figure6

Conception of whole-cell computational modeling. The whole-cell computational model is divided into three sub-modules: The T-model covers the information on transcription regulation and gene expression. The inputs are the sequencing results of chip-seq and RNA-seq (t1), and the outputs are the mRNA expression levels(t2); the E-model covers the information on gene-expression and protein synthesis. The inputs are the flux of each macromolecular substance and mRNA concentration, and the outputs are the fluxes of reactions and the concentrations of proteins; and the M-model covers enzyme-constrained information. The inputs are the proteins concentrations, substrate, oxygen flux, etc. and the output are the fluxes of each metabolic reaction. For the three models, the output of the previous model can be used as the input to the next model. The coupling of sub-modules is realized through inequality constraints between the T- and E-models, as well as between the E- and M-models. Finally, the model is presented in SBML in a standardized language and visualized through SBGN

In a modeling strategy, it is necessary to collect and sort information from different modules, including: TF interactions and binding to target genes, in LogicTRN; E-CELL reactions including initiation and extension of transcription; mRNA degradation, initiation and extension of translation; tRNA charging; macromolecule synthesis (ribosome, tRNA, RNAP); enzyme kinetic parameters; metabolic reactions of enzymes in GSMM, based on enzyme constraints. Constrained by a lack of complete information, it is often difficult to build a complete whole-cell computational model, which requires a more thorough study of the mechanism of cellular functions. The whole-cell computational model takes RNA-seq data and ChIP-seq data at different times as input, but large-scale sequencing data are both difficult and costly to obtain. Besides, chronic diseases, such as incomplete understanding of intracellular metabolic mechanisms and lack of information on kinetic parameters, will affect the accuracy of the models. To bypass these limitations, further enrichment of databases and further development of measurement technology are needed.

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Acknowledgements

The authors would like to acknowledge the Projects No.2019YFA0904300 supported by National Key R&D Program of China.

Funding

This work was financially supported by the National Key R&D Program of China (No. 2019YFA0904300).

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JZ, JX, XF: conceptualization and methodology; JZ, XF, LC, HS: literature research and manuscript writing; JX, XF: Manuscript revision; All the authors read and approved the manuscript.

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Correspondence to Jianye Xia or XueFeng Yan.

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Zhou, J., Fan, X., Cao, L. et al. Review of construction methods for whole-cell computational models. Syst Microbiol and Biomanuf (2021). https://doi.org/10.1007/s43393-021-00059-3

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Keywords

  • Whole-cell computational model
  • Systems biology
  • Steady-state
  • Dynamic modeling