One quantitative modeling environment is E-Cell [5], [6], which uses general technologies and theoretical supports for computational biology with the grand aim to allow for precise whole cell simulation at the molecular level. E-cell simulates cell behavior by integrating numerically the differential equations described implicitly by reaction rules. It includes numerical simulations and mathematical analysis technologies to predict, obtain or estimate parameters such as reaction rates and concentrations of molecules in the cell. In spite of all its capabilities, E-cell lacks the ability to specify highly complex systems, based on qualitative data, with multiple components.

Another example of a mathematics-oriented software modeling environment is the Virtual Cell [7], developed for quantitative cell biological research by the National Resource for Cell Analysis and Modeling. Slepchenko [8] described applications of this tool to nucleocytoplasmic transport and intracellular calcium dynamics. The Virtual Cell software environment enables sophisticated quantitative dynamics modeling, such as the one described in [8]. The biological to mathematical mapping allows for separate use of biological and mathematical components, and includes automatic mathematical simplification using pseudo-steady approximations and mass conservation relationships. This mapping allows for direct specification of mathematical problems, performing simulations and analysis on those systems. However, like E-cell, the Virtual Cell software environment lacks the ability to faithfully describe complex systems that are based on qualitative results. It also lacks the capacity to describe multiple interconnected components that need to be modeled at various levels of detail.

Investigating multi-cellular organisms by constructing their conceptual models has been promoted by Harel [9], who also suggested a Turing-like test for biological modeling [10]. Formal modeling of C. elegans development has been carried out by Kam et al. [11] using a scenario-based approach. They have presented preliminary results of a new approach to the formal modeling of biological phenomena based on the language of live sequence charts with the play-in/play-out process. Keet [12] has suggested exploiting existing data better and bringing more structure to the “biological data anarchy” on the Web by enhancing biological information systems with granularity and harnessing Semantic Web technologies.

Some quantitative approaches combine the concept of intelligent computer programs, commonly known as software agents, with mathematical models. Applying an OO and agent-based approach, Webb and White [13] modeled and simulated metabolic and genetic pathways. Due to limitations of the OO paradigm that stem from its origins in the software domain, this model includes such non-biological artifacts as capsules, ports, and connectors that exchange messages, making it less than intuitive.

Conceptual modeling originated with efforts to streamline software development some three decades ago. Therefore, the object-oriented approach, which is the currently accepted paradigm in the software engineering community, has been very popular in recent years for modeling systems in general and biological systems in particular. The object-oriented (OO) approach advocates that objects are the prime entities or building blocks of software systems, and this notion has been recently extended via SysML (www.sysml.org) to systems in general. A basic tenet of OO modeling is the encapsulation principle, which states that objects, the basic building blocks of the model, encapsulate (own) processes, known as methods or operations. The latter do not have their own right of existence as stand-alone things, making it awkward to try to model biological processes. Cell-level biological processes usually involve a host of input, output, and facilitating molecules of all kinds, which are the objects. Since the OO modeling paradigm advocates that each process be a subordinate of some object, an arbitrary choice must be made as to which object is the owner of the process being modeled. This enforced subordination inevitably leads to a counter-intuitive model right from the outset.

BioUML, [14] is an open source software framework for systems biology, which is based on Unified Modeling Language, UML [15], [16], the industry standard in software development. UML caters to the OO paradigm in that its terminology and notation closely follow the notions and capabilities of current OO programming languages.

UML is built on the premise that “Modeling is the designing of software applications before coding” [17]. UML-based modeling approaches like BioUML are object-oriented, meaning that their main building blocks are objects, which are primary static entities that own processes. The inherent orientation of UML towards software, its unnecessary complexity [18] and its model multiplicity problems [19] cause intra- and inter-model consistency problems [20].

In general, the current Object-Oriented approach to modeling and developing software systems is not suitable for representing effectively biological concepts, because, as argued, it cannot model concurrently in a single type of diagram both the objects, e.g., a protein, and the processes, e.g., transcription, that transform (create, consume, or change the state of) these objects. UML 2.0 [16], for example, includes 13 different types of models, each with its own diagram type, separate set of symbols and concepts. Moreover, the lack of the process as a stand-alone concept in the OO modeling approach is a major hindrance for modeling biological systems, which are mostly process-intensive. Finally, many software engineers find it difficult to master the UML modeling framework, making it unrealistic to expect biologists to employ it in a valuable way to model biological systems.

Systems Biology Markup Language, SBML [21] is an open, XML-based format for representing biochemical reaction networks and describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, and gene regulation. SBML data objects use a graphical notation based upon UML, which in turn is translated into XML. CellML [22] is another XML-based language for storage, sharing, exchange, and reuse of computer-based mathematical models. It includes information about model structure, equations describing processes, and metadata to search for model components.

The recent Systems Modeling Language, SysML [23] initiative offers no solutions to the problems of current OO approaches to modeling, as it is based on UML and therefore suffers from most of UML's deficiencies, namely multiple diagram types and segregation between structure and behavior.

Kohn [24] has proposed a graphical method for mapping bioregulatory networks and representing multimolecular complexes, protein modifications, and actions at cell membranes and between protein domains. The symbol conventions, defined for these molecular interaction maps, accommodate multiprotein assemblies and protein modifications and thus can generate combinatorially large numbers of molecular species. However, most of the 20 or so pictogram symbols are highly specialized. For example, one of them is defined as “Transport of Protein A from cytosol to nucleus”. Clearly, this method is limited to modeling very specific systems.

In general, when considering human-readable diagrammatic representations, it is notable that the current informal ways most biologists draw diagrams means that correct biological interpretation depends entirely on the reader's knowledge [25]. Kitano et al. [26] recount examples where an arrow symbol has four different potential interpretations and indicate rightly that such ambiguities become a major problem as the size and complexity of the system increases, highlighting the need for formality to avoid ambiguity. Process diagrams proposed by [25] that make use of CellDesigner [26] are state transition-based.

Using different arrowhead shapes CellDesigner diagrams focus on conveying the semantics of several process types prevalent in signaling, such as translocation, catalysis, splitting, phosphorylation, or state transition. Formalized process diagrams have been used to describe signal-transduction cascades and pathway maps, and are readable and precise as long as the network is not too large. However, scalability is an issue. There is no way to refine mechanisms and designating new pictograms for each new reaction type is problematic. Moreover, as Blinov et al. [27] observe, because process diagrams require explicit representation of all the species (which in our ontology are referred to as objects) at some level, they omit the vast majority of species and reactions, which are processes in our ontology, that could potentially be generated during signaling.

In an attempt to solve this problem, Blivnov et al. have introduced graphical rules to allow the connectivity of proteins in a complex to be represented explicitly. These rules provide a means to visualize comprehensibly protein-protein interactions. Nevertheless, for more general biological modeling, process maps are likely to be of unmanageable size due to combinatorial complexity.

An example of a combined quantitative-qualitative model is the work of Tyson et al. [28], who modeled the dynamics of cell cycle regulation. They applied a systems dynamics-based approach and bifurcation diagrams to provide a new perspective on cell cycle checkpoints and mutant phenotypes in fission yeast. In this model, qualitative changes can occur, for example, when a stable steady state loses its stability or even ceases to exist and is replaced by an oscillatory solution. Such an event is in the nature of the recurrent solutions of a dynamic system and is necessary for a model attempting to characterize the cell cycle. These qualitative changes, called bifurcations, happen at specific values of the parameters termed bifurcation points and are described by a one-parameter bifurcation diagram. These are two-dimensional graphs, where each axis shows some quantity and the quantitative analysis yields certain meaningful qualitative results, such as the G1, G2, or metaphase checkpoints in the fission yeast cell cycle.

BioTapestry [29] is the latest interactive tool for building, visualizing, and simulating genetic regulatory networks. It is designed around the concept of a developmental network model, intended to handle large scale models and represent systems that exhibit increasing complexity over time. The system supports data generated by perturbing the expression of specific genes, portrays views of the network during development, and lays out network models.

The current state of affairs, reflected in this survey, is that there are quite a number of modeling approaches and software environments for modeling biological systems, but many of them are object-oriented, hindering direct and explicit process modeling, which is at the heart of systems biology. Moreover, since most approaches are non-scalable and specialized for specific types of cellular reactions or subsystems, they cannot be extended naturally to modeling the entire cell, not to mention organisms, societies, habitats and ecologies.

Perhaps most importantly, according to the definition of systems biology, models are supposed to advance research, yet none of the existing modeling approaches or systems have been shown to promote innovative questions that trigger experiments to confirm or refute assumptions emerging from the model. Such a disappointing situation indicates that a totally different modeling approach is in order. This situation was a major stimulus for the work presented here, a non-traditional conceptual modeling approach that has already stimulated a new empirical finding concerning the mRNA lifecycle.

Representing the vast amount of ever increasing knowledge formally, yet accessibly, can be compared to putting the pieces of a gigantic puzzle together, mandating adoption of a common evolving grand model. The model needs to be founded on a compact generic set of the most basic ontological building blocks in order for it to be general enough to serve as a basis for modeling the gamut of biological systems, from molecules to ecosystems.

We submit that stateful objects and processes that transform them, along with several types of links, as advocated by OPM—Object-Process Methodology [30], constitute a mandatory and sufficient set of ontological building blocks to enable conceptual modeling of biological systems with various scales and complexities. Moreover, such building blocks allow reasoning that links theory with empiricism. We envision an OPM-based comprehensive shared Web-accessible modeling framework of the entire cell, which, if and when created, would enable the evolution of state-of-the-art knowledge in biology. This model will keep pace with the rapid evolution of knowledge, and will be revised constantly and updated with new findings and conjectures.

In the present study we aimed to carry out a modest first step toward this admittedly ambitious goal. As the yeast mRNA life cycle is a key cellular system, we chose it to be our case in point for conceptual modeling that employs Object-Process Methodology. In the next section we explain in more detail why we chose Object-Process Methodology, OPM.

Object-Process Methodology, OPM [30] is a holistic approach to the study and development of complex systems that caters to human intuition while maintaining a formal framework. The living cell is a prime example of a highly complex system, in which the two main system aspects—structure and behavior—are highly intertwined and hard to separate. Motivated by the requirement of a single model to represent these two major system aspects, OPM is founded upon two elementary building blocks—objects and processes—which represent concurrently the system's structure, i.e., the objects, or components, that comprise the system, and behavior, i.e., the processes that transform the system's objects by creating them, consuming them, or changing their states, in a balanced way without highlighting one at the expense of the other.

The elements of OPM ontology are entities and links. A complete list of OPM elements with their symbols and definitions is provided in Table S1. Entities, the basic building blocks of any system modeled using OPM, are of three types: objects, possibly with states (stateful objects), and processes. An object is a thing that exists, possibly in some state, while a process is a thing that can transform objects. More specifically, a process is a thing that transforms objects, namely creates one or more objects, consumes one or more objects, or changes the state of one or more objects. Examples of biological objects are Protein, Cell, and Organism, and examples of biological processes are Cleavage, Mitosis, and Birth.

A link can be structural or procedural. A structural link expresses a static, time-independent relation between pairs of entities. The four fundamental structural relations are: aggregation-participation, generalization-specialization, exhibition-characterization, and classification-instantiation. An example of using the aggregation-participation structural relation is derived from the phrase “The eukaryotic cytoskeleton is composed of microfilaments, intermediate filaments and microtubules.” (http://en.wikipedia.org/wiki/Cell_(biology)#Subcellular_components) In OPM, this statement is interpreted such that the Eukaryotic Cytoskeleton is the aggregating object, the whole, which consists of the three objects which are parts of the Eukaryotic Cytoskeleton, each being a set of objects: the Microfilaments Set, the Intermediate Filaments Set, and the Microtubules Set. Unidirectional and bidirectional tagged structural links enable creation of additional user-defined links with specified semantics. A procedural link connects entities (objects, processes, and states) to describe the behavior of a system. The behavior is manifested in three major ways: (1) a process can transform (generate, consume, or change the state of) one or more objects; (2) an object can enable one or more processes without being transformed by them, in which case it acts as an enabler, i.e., a human agent or an inanimate instrument; and (3) entities can trigger events that invoke processes if some conditions are met. Accordingly, a procedural link can be a transformation link, an enabling link, or an event link. A transformation link expresses object transformation, i.e., object consumption, generation, or state change. An enabling link expresses the need for a (possibly state-specified) object to be present in order for the enabled process to occur. The enabled process does not transform the enabling object. An event link connects a triggering entity (object, process, or state) with a process that it invokes.

The Gene-Ontology (GO) [31] project sets out to provide a defined, universal vocabulary for describing gene and gene product attributes in any organism. The three organizing principles of GO are cellular component, biological process, and molecular function. A comparison between GO principles and OPM entities is useful as it emphasizes the advantages of OPM ontology. A cellular component corresponds to an OPM object and a biological process corresponds to an OPM process. However, molecular function does not have a clear OPM equivalent. According to the definition of process in [31], a biological process is a “series of events accomplished by one or more ordered assemblies of molecular functions.” Examples include signal transduction and alpha-glucoside transport. A GO molecular function “describes activities, such as catalytic or binding activities, that occur at the molecular level.” Examples include catalytic activity, binding, or adenylate cyclase activity. Problems with this definition for molecular function are admitted in [31], “It can be difficult to distinguish between a biological process and a molecular function, but the general rule is that a process must have more than one distinct step.” We contend that any ontology that lacks precise, clear-cut definitions, and relies on examples as part of the definition, is problematic. What is the meaning of step? Is it identical to function, and if so, is function in turn identical to activity? If so–why use so many terms, and if not, how do they differ? Indeed, it is unclear how to differentiate between GO functions and GO processes. OPM takes another approach where it does not distinguish between simple and complex processes, just as it does not distinguish between simple and complex objects. For example the GO molecular function “pre-mRNA 3′-splice site binding” (taken from the actual GO file) in OPM ontology is the OPM process of binding of the cellular component (OPM object) “pre-mRNA 3′-splice site”, which changes that object from state unbound to state bound. We advocate that the OPM ontology is more precise and intuitive.

Two semantically equivalent modalities, one graphic and the other textual, are used to describe each OPM model. A set of inter-related Object-Process Diagrams (OPDs), showing portions of the system at various levels of detail, constitute the graphical, visual OPM formalism. Each OPM element is denoted by a symbol in an OPD, and the OPD syntax specifies correct and consistent ways by which entities can be connected via structural and procedural links, such that each legal entity-link-entity combination bears specific, unambiguous semantics. OPCAT [32] is a software environment that supports OPM-based system modeling and evolution.

The Object-Process Language (OPL), which is the textual counterpart of the graphical OPD, is a dual-purpose language, oriented towards humans as well as machines. Catering to human needs, OPL is designed as a subset of English, which serves domain experts (e.g., biologists) and system architects, engaged jointly in modeling a complex system. Every OPD construct is expressed by a semantically equivalent OPL sentence or phrase. According to the modality principle of the cognitive theory of multimodal learning [33], this dual graphic/textual representation of the OPM model increases the human processing capability. Indeed, it has been our experience that human understanding of the OPM model is enhanced by the convenient opportunity of reflecting upon both the graphic and textual model representations, whereby what is missed in one modality can be grasped when considering the other one.

Figure 1(A) is an Object-Process Diagram (OPD), showing the top level, bird's eye view of the process mRNA Lifecycle, which generates the object Protein from the object Amino Acid Set. Figure 1(B) lists the corresponding two OPL sentences that were generated automatically by OPCAT:

mRNA Lifecycle consumes Amino Acid Set, Ribonucleotide Set, and mRNA.

mRNA Lifecycle yields mRNA, Ribonucleotide Set, and Protein.

Examining these sentences, we see that each arrow from an object to the process (mRNA Lifecycle) has the semantics of consumption (degradation, or destruction), while each arrow from the process to an object has the semantics of result (creation, or generation). During the process mRNA Lifecycle, Ribonucleotide Set and mRNA are both consumed and generated, while Amino Acid Set is consumed to create Protein.

A major problem with most graphic modeling approaches is their scalability. As the system's complexity increases, the graphic model becomes cluttered with symbols and their connecting links. The limited channel capacity [33] is a cognitive principle which states that there is an upper limit on the amount of detail a human can process before being overwhelmed. This principle is addressed by OPM and implemented by OPCAT via three abstraction/refinement mechanisms. These enable complexity management by providing for the creation of a set of interrelated OPDs (along with their corresponding OPL paragraphs) that are limited in size, thereby avoiding information overload and enabling comfortable human cognitive processing. The three refinement/abstraction mechanisms are: (1) unfolding/folding, which is used for refining/abstracting the structural hierarchy of a thing and is applied by default to objects; (2) in-zooming/out-zooming, which exposes/hides the inner details of a thing within its frame and is applied primarily to processes; and (3) state expressing/suppressing, which exposes/hides the states of an object.

Figure 2 provides examples of these three abstraction/refinement mechanisms. The mRNA Lifecycle process from Figure 1 is in-zoomed, exposing three main subprocesses: Transcription, Translation, and Post-Ribosomal Processing. Two examples of unfolding are shown in Figure 2. One is the unfolding of mRNA Polymerase II as part of Nucleus. The other is the unfolding of Localization as an attribute of mRNA. Finally, state expression is exemplified when the possible states of Localization—nucleus, P body, and ribosome—are expressed. Using flexible combinations of these abstraction/refinement mechanisms, OPM enables a system to be specified to any desired level of detail, without losing legibility or comprehension of the specification. The complete OPM system specification is expressed graphically by the resulting set of consistent, inter-related OPDs, and textually by the corresponding OPL paragraphs.

The expression of protein encoding genes is a complex process that determines which genes are expressed as proteins at any given time, as well as the relative levels of these proteins [34]. This process involves several distinct stages, (i) RNA synthesis, or transcription, (ii) RNA processing (after processing is completed, the RNA is considered mRNA), (iii) mRNA transport from the nucleus to the cytoplasm (in eukaryotes), (iv) protein synthesis, or translation, (v) mRNA degradation, and (vi) posttranslational modifications (including degradation) of the proteins. In eukaryotes, transcription is carried out by three different RNA polymerases, each responsible for transcribing a distinct class of RNAs. RNA polymerase II (pol II) is responsible for transcribing protein-encoding RNAs, namely mRNAs, which are the focus of this paper. Work from many laboratories has established that regulation of the aforementioned stages of pol II-mediated gene expression is coordinated [35]. Thus, in order to understand the expression of protein-encoding genes we need to consider the entire multi-stage process, as each stage can be regarded as a subdivision of a continuous gene expression process. Correctly and accurately specifying this complex process is a formidable task, beyond the realms of free text. Clearly, it calls for the use of an appropriate modeling language and methodology.

Transcription by pol II, the first stage in the expression of protein-encoding genes, produces RNA–the primary transcript. This primary transcript is processed to yield an mRNA (usually shorter than the primary transcript) that contains a 5′ cap (m(7)GpppN) and 3′ poly(A) tail. These two tags are critical for the appropriate function, localization and stability of the mRNA [34]. Following its synthesis in the nucleus, the mRNA is transported to the cytoplasm, where it is recognized by ribosome(s)-the protein synthesis machinery. The mRNA is then used as a template for translation into protein, the amino acid sequence of which is related to the nucleotide sequence of the mRNA [34]. The last stage of the mRNA lifecycle in the cytoplasm is its decay, which is carried out by an array of decay factors [36], [37]. Each one of the stages described above is tightly regulated. Once produced, the mRNA is the key target in the regulation of the gene expression, referred to as post-transcriptional regulation. One aspect of post-transcriptional regulation is at the level of mRNA localization within the cell, for example nuclear vs. cytoplasmic localization.

Recently, a new venue for mRNA localization was uncovered that revolutionized our view of how gene expression is regulated post-transcriptionally. Specifically, yeast mRNA can be localized in discrete cytoplasmic foci together with a number of mRNA decay factors and limited repertoire of translation factors, mostly translation repressors. These foci, termed processing bodies (P bodies), represent complexes where mRNA degradation can occur, since mRNA decay intermediates [38] and many factors of the major mRNA decay pathway reside in P bodies [38]–[49]. The discovery of P bodies in yeast and related bodies in higher eukaryotes, e.g., dcp bodies, GW bodies, brings the spatial control of macromolecule to the focus of our attention.

A different kind of cytoplasmic foci, referred to as stress granules, have been discovered in higher eukaryotes under various stress conditions (recently reviewed in [49], [50]). Unlike P bodies, these foci contain several translation factors, but not the ribosomal large subunit [51], [52]. Stress granules are believed to be sites where non-translating mRNA resides during stress conditions [53]. Association of mRNAs with stress granules was proposed to represent a mechanism for translational repression. This kind of repression can be reversible, as the mRNA can be transported back to the ribosome when conditions favor translation. Anderson and Kedersha [54] proposed that mRNAs in stress granules are subjected to triage: first they are monitored for integrity and composition, and then they are sorted for productive translational initiation or targeted to degradation. In addition, it has been suggested that stress granules may communicate with P bodies when sorting the mRNA for degradation [55]. In yeast, the organism under study here, no stress granules have been identified and the bulk of known P bodies do not contain translation factors [43]. Recently, work from Parker's group has revealed that mRNAs in the yeast P bodies are not necessarily degraded, but rather can be transported to the ribosome for translation [56]. Thus, yeast P bodies may have dual function, carrying out the functions of both mammalian P bodies and stress granules.

Most published works to date have used fluorescent microscopy to study P bodies or stress granules. This technology allows the detection of large complexes whose fluorescence is above that of the background, but small P bodies might escape detection. Interestingly, though, Aragon et al. [57] have recently reported that mRNAs in starved yeast cells are sequestered in proteinatious complexes and therefore resist standard extraction procedures. These mRNAs could be recovered by disrupting the complexes with proteases. The released mRNA can then be analyzed using whole genome technology. The authors proposed a plausible model in which the protecting complexes are P bodies [57]. If proved correct, the differential mRNA extraction technique will allow analyzing even small P bodies and also obtain, for the first time, quantitative results at the organism level.

It has been contended both for yeast [38], [54], [55] and higher eukaryotes [48], [56] that there is frequent shuttling of mRNA between the ribosome (or poly-ribosome) and these cytoplasmic bodies. Moreover, it has been suggested that two of the cytoplasmic structures, i.e., the ribosome, which activates translation, and the P body, which represses it, compete for mRNA. The outcome of this competition determines mRNA translatability and hence protein synthesis [58]. To demonstrate shuttling of mRNA between these two complexes, investigators utilized specific drugs. Drugs that block mRNAs within the ribosomes cause P bodies to disassemble, whereas drugs or mutations that compromise mRNA loading onto the ribosomes enhance the assembly of P bodies [38], [48], [54], [50], [59]. Such studies reveal that P bodies are dynamic structures, for their mass varies as the mRNA is transported back and forth between P bodies and ribosomes. It has also become clear that the balance between these two sub-cytoplasmic compartments, and hence the P bodies' size, is responsive to environmental signals [43], [48], [54], [58]. Thus, external signals, such as starvation, UV irradiation, or changes in osmolarity, can trigger mRNA redistribution between the two compartments. It was the complexity and intricacy of processes constituting the mRNA lifecycle, outlined above, which triggered our realization that conceptual modeling might likely contribute to understanding this particular cellular sub-system. Moreover, we anticipated that the modeling should raise empirically addressable questions, the answers to which would help researchers comprehend better mRNA biology. Indeed, the modeling activity has raised at least one research question, the localization of eRF3 in P bodies, which we have confirmed experimentally.