Modelling with ANIMO: between fuzzy logic and differential equations
 Stefano Schivo†^{1},
 Jetse Scholma†^{2},
 Paul E. van der Vet^{3},
 Marcel Karperien^{2},
 Janine N. Post^{2},
 Jaco van de Pol^{1} and
 Rom Langerak^{1}Email author
https://doi.org/10.1186/s129180160286z
© The Author(s) 2016
Received: 27 October 2015
Accepted: 2 June 2016
Published: 27 July 2016
Abstract
Background
Computational support is essential in order to reason on the dynamics of biological systems. We have developed the software tool ANIMO (Analysis of Networks with Interactive MOdeling) to provide such computational support and allow insight into the complex networks of signaling events occurring in living cells. ANIMO makes use of timed automata as an underlying model, thereby enabling analysis techniques from computer science like model checking. Biology experts are able to use ANIMO via a user interface specifically tailored for biological applications. In this paper we compare the use of ANIMO with some established formalisms on two case studies.
Results
ANIMO is a powerful and userfriendly tool that can compete with existing continuous and discrete paradigms. We show this by presenting ANIMO models for two case studies: Drosophila melanogaster circadian clock, and signal transduction events downstream of TNF α and EGF in HT29 human colon carcinoma cells. The models were originally developed with ODEs and fuzzy logic, respectively.
Conclusions
Two biological case studies that have been modeled with respectively ODE and fuzzy logic models can be conveniently modeled using ANIMO. The ANIMO models require less parameters than ODEs and are more precise than fuzzy logic. For this reason we position the modelling paradigm of ANIMO between ODEs and fuzzy logic.
Keywords
Background
Modelling in cell biology
Executable biology [1] is a young subfield in computational modelling, aimed at constructing models that mimic biological phenomena in silico. It provides an interesting paradigm to enhance network diagrams with an underlying formal description of network components and their interactions. For this purpose a wealth of different modeling paradigms has been proposed (see [2] for an overview). Several approaches consist in the abstraction of continuous models into discrete transition systems (e.g. [3–6]); this may enable the use of model checking as a state space exploration technique [3, 7, 8]. Our approach is based on Timed Automata models [9] defined by linear approximations (with arbitrary precision) of ordinary differential equations (ODEs); this has the benefit of using existing mature Timed Automata analysis techniques. It is not the ambition of this paper to exhaustively compare this approach with all existing formalisms; instead, we want to show that this model has resulted in an effective and userfriendly tool, which compares favorably to some prominent approaches, most notably ODEs and fuzzy logic. We have developed ANIMO (Analysis of Networks with Interactive MOdelling, [10, 11]), a software tool that provides an enabling technology to increase the use of computational models by experimental biologists using their domainspecific language, i.e. the representation of a biochemical network as a graph where each node identifies a molecular species and each edge an interaction. ANIMO enriches the normally static biological network diagrams with dynamic information, which is then used to automatically produce formal models representing the biological network. Such models are indispensable for formally comparing experimental data with prior knowledge, or for structuring experimental findings into a new theory. When dealing with complex biological networks, executable biology models are particularly useful to understand the nonlinear dynamics and the entailed emergent properties of the networks. In those cases, an ANIMO model can be used as a support to obtain insight based on abstract representations of the interactions occurring inside living cells. Other applications of ANIMO models include performing in silico experiments and the storage and transfer of knowledge on biological networks.
An introduction to ANIMO
ANIMO was conceived to model signalling pathways, and in this context it is sensible to assume that the concentration of the involved molecular species does not change noticeably in the considered time span (several minutes to a few hours). For this reason, ANIMO models use the activity level of a node to represent the fraction of molecules that are “active”, while the total amount of molecules is assumed to remain constant. However, this assumption is not as restrictive as it seems: ANIMO models can still represent protein concentration by identifying it with activity. For example, we can represent production of protein A with a process increasing the activity level of node A, while degradation will decrease it.
The concise language used in ANIMO to represent reaction information is powerful enough to model various types of interactions. For example, we can easily translate Boolean OR gates: (A OR B) → C becomes the two separate reactions A → C and B → C. This means that whenever either A or B is active, C will eventually be activated, i.e. reaction effects are always additive. This representation of OR is thus nonexclusive, so C will be activated also if both A and B are active, but in that case the activation will proceed faster. A Boolean AND gate can be explicitly represented with the “AND” approximation scenario (see Additional file 1: Section A.1): with (A AND B) → C, C will be activated only if both A and B are active.
Combining these basic tools makes the representation of more complex Boolean formulas also possible, by properly combining the basic gates. The same is generally true also if we move from Boolean interactions to precise kinetic formulas. We note that in this case some specific mathematical functions (square root, exponential, …) may be needed. It is in principle possible to correctly translate all those functions into the underlying Timed Automata model, even if it may require some effort. However, as such functions are normally used to represent a complex mechanism in abstract form, we advise to use ANIMO with the same aim, i.e. as a tool to abstractly represent complex mechanisms. As an example, see the representation of the day/night cycle with a repressilator construct [13] in ANIMO as opposed to the piecewise linear approximation used in the model we use as reference (see Results and Additional file 1: Section B.1).
ANIMO produces graphs showing how the activity levels of selected nodes change over time, allowing the user to obtain a view on the dynamic behaviour of their network. In order to obtain these results, a model defined in ANIMO is automatically translated into its corresponding representation as a network of Timed Automata [9] and then analysed behind the scenes with the software tool UPPAAL [14]. The formal language of Timed Automata allows to represent and analyse complex behaviours precisely and efficiently, but the user does not need to directly manipulate Timed Automata or UPPAAL, as the analysis process is made transparent. A curious user can still access the underlying models and perform other analyses in UPPAAL, but that is not required in order to fully profit from ANIMO.
A detailed description on how the Timed Automata models defined by ANIMO work, and how the results are obtained, can be found in [10]. The choice of parameters for ANIMO models is described in [15] and summarized in Additional file 1: Section A.5. Additional guidance on the design of ANIMO models and how to best profit from biological experimental data can be found in [11]. The ANIMO web page [16] contains a link to the user manual and instructions to install ANIMO on a computer.
In the rest of the paper, we will show two case studies where models built with ANIMO are compared to models built with ODEs and Fuzzy logic. We will then compare ANIMO with other tools, focusing on the user experience of the modeller: as highlighted before, we believe that providing a suitable access to modelling formalisms is essential for their widespread application in biological and biomedical research.
Results
Modelling oscillation in Drosophila Melanogaster circadian clock
To demonstrate that results obtained with ANIMO are comparable to results from widely used modelling approaches, we present an ANIMO model of the circadian clock in Drosophila Melanogaster (they are usually in the form “model available in Additional file 2”). This ANIMO model is based on [19], where ordinary differential equations (ODEs) were used. The cyclic behaviour of the circadian clock is based on the alternating formation and destruction of the CYC/CLK protein complex. Concentration levels of this complex are in turn regulated by a series of proteins which are produced as a consequence of CYC/CLK formation. The CWO protein is central to the functioning of the network, as it degrades the mRNA for most of the involved proteins. As such, CWO acts as an inhibitor that counterbalances the effect of CYC/CLK. The positive influence of the lightregulated cryptochrome CRY on the degradation of TIM is a consequence of the passage between day and night, allowing the circadian clock to synchronize to a time zone.
The output of the final ANIMO model (Fig. 3 a) matches the original ODE model. In particular, starting from the same initial conditions, both models achieve an oscillatory behaviour with similar periods and phases: see Fig. 3 b–e for some examples, and Additional file 1: Figure S6 for the complete comparison.

perform an initial simulation of e.g. 24 h;

using the slider under the computed graph, select a point where CRY is low, which corresponds to night time;

pressing the copy button next to the slider, to set the currently selected point in time to be the initial configuration for all further simulations;

disable most of the network, keeping enabled only the part of the network that changes CRY’s activity level;

let CRY advance on itself (i.e., the light/dark cycle desynchronizes with the internal circadian clock) by performing another simulation of e.g. 12 h;

use copy again to take the end state of the (sub)network as initial state for the next simulation: as the other nodes are still disabled, their state will still be the one that was set previously;

reenable the rest of the network and generate another simulation of e.g. 5 days;

the resulting graph will show the circadian clock resynchronizing to the changed alternance of the light/dark cycle in a few days’ time (see Fig. 4).
We are confident that further experiments similar to the ones described in [19] can be performed also in ANIMO, possibly adapting the proof of concept model to the more complex cases. Indeed, our work on a comprehensive ANIMO model encompassing both signal transduction and gene expression data in human chondrocytes [20–23] has shown that ANIMO can range from relatively simple models to realistic complex cases (whose presentation would fall outside of the scope of this paper).
A description of how the ANIMO model was built and how its data was compared to the data generated by the original ODE model is given in Additional file 1: Section B.1.
Using ANIMO to generate hypotheses in human colon carcinoma cells
We now present a comparison with an existing fuzzy logic model, which we use also as an example of how ANIMO can be used to create reference models and help to obtain insight into complex biological events.
At this point, the behaviour of the model deviated from the data for some of the nodes. Changing the parameters of the model, both manually and automatically (with the parameter sweep feature available in ANIMO [15], see Additional file 1: Section A.5 and Figure S4), was not enough to reproduce the behaviour shown by experimental data. This is an interesting situation, as it requires changes in the topology of the model [15], reflecting the formulation of a new hypothesis on the structure of the model. Below, we give two examples and show how adaptation of the model can be used to generate novel testable hypotheses.
As a second example, we considered the behaviour of JNK1 and MK2. In the model, both proteins were located downstream of TNF α but not TGF α or EGF. Hence, the model did not show an effect of C225, a pharmacological inhibitor of ligandEGFR binding, on activation of JNK1 or MK2 after stimulation with TNF α (Fig. 5 c). However, experimental data show that C225 strongly reduces activation of JNK1 and MK2 upon stimulation with TNF α [27]. This fact is indicative of a role for EGFR in activation of JNK1 and MK2. Since both JNK1 and MK2 are located downstream of MEKK1, we hypothesized that activation of MEKK1 is dependent on both TNF αsignalling and TGF αsignalling. In the model we added a new hypothetical node Hyp 2 (hypothesis 2) to link EGFR to MEKK1 (Additional file 1: Figure S11). This addition led to an improved fit of the model to the data upon treatment with TNF α + C225: activation of both MK2 and JNK1 was strongly suppressed by C225 (Fig. 6 c). Stimulation with EGF alone did not lead to activation of JNK1 and MK2. These data support the validity of the modification to the model. Further support for a link between EGFR and MEKK1 was found in literature. Specifically, Ras has been reported as a direct activator of MEKK1 [31]. EGFR is a wellknown and potent activator of Ras, which is why it was already in our network [24]. Other studies also report activation of JNK1 and phosphorylation of cJun downstream of Ras, which is consistent with an interaction between Ras and MEKK1 [29, 32]. Based on these findings, we adapted our model by removing the Hyp 2 node and creating a direct interaction between Ras and MEKK1 (Fig. 6 a). Experimentally, the role of Ras could be confirmed by using a pharmacological inhibitor of Ras activity, and measuring the effect of this inhibitor on the activation of JNK1 and MK2. Together, our model suggests that EGFR activity is required but not sufficient for activation of JNK1 and MK2 in HT29 cells.
There are other nodes for which the experimental data deviates from the model in one or more of the experimental conditions. A comparison between model and experimental data can be found in Additional file 1: Figures S12, S13 and S14. Comparing these results with the ones from [33] shows a better fit of the ANIMO model, which is also intrinsically more precise, being more mechanistic in nature (see Fig. 2). A complete deciphering of the signalling events in this biological system is outside the scope of this paper. Instead, we illustrated how interactive modelling of the dynamic behaviour of a signal transduction network can be used to extend previous pathway topologies and can lead to the generation of novel hypotheses.
Discussion
Final remarks on the models
We first described the construction of an ANIMO model of the circadian clock in Drosophila Melanogaster. This shows that the more abstract modeling paradigm of ANIMO is able to capture the dynamics of the regulatory network, leading to similar conclusions as an ODE model that had been published previously [19]. The biggest difference between the construction of these models is that the model in [19] is constructed on the basis of a detailed representation of the relevant biochemical reactions. ANIMO describes an abstract and aggregated view in terms of interactions, where the qualitative effect of each interaction is captured by a single parameter (see [11] for more details). In ANIMO a number of network nodes is drawn for the molecules involved. These nodes are then linked by directed interactions that represent causeandeffect relationships. This abstract and graphical way makes it easier for biologists to create large networks in a compositional way: each node in the network can be disabled at any time by the user, or extra nodes can be added, without having to change any of the existing interactions. So ANIMO may yield models that are less complex than ODE models, possibly at the price of lower model precision: the curves representing oscillation of protein activities in the ANIMO model are not as precise as those obtained from the original ODE model (see Additional file 1: Figure S6).
We also showed the construction of an executable model of signalling events downstream of TNF α and EGF in human colon carcinoma cells. This data set has been used for previous modelling studies, based on partial leastsquares regression and fuzzy logic [33, 34]. The partial leastsquares regression model describes an abstract datadriven model that uses statistical correlations to relate signal transduction events to various cellular decisions. This type of modelling is very useful in uncovering new and unexpected relations. It is also successful in making predictions, but gives little direct insight in the dynamic behaviour of the network (see Fig. 2). Fuzzy logic analysis led to a model that gives a better fit to the dynamic network behaviour than discrete logic (Boolean) models. Inspection of the inputs to the logical gates that were used to model protein behaviour led to the prediction of novel interactions between proteins, showing the usefulness of this approach. For most of the proteins, such as JNK1, time was used as an input parameter. This means that the activity of some nodes at time point t was made dependent also on the value of t itself: thus, time becomes a variable in the model. For example, discretizing values in the two categories high and low, the logical gates “if TNF α is high AND time is low, then JNK1 is high” and “if TNF α is high AND time is high, then JNK1 is low” were used to describe the dynamic behaviour of JNK1. Although this leads to a representative description of the dynamic behaviour of JNK1, peaks in protein activity at early time points, as measured in wetlab experiments, were not reproduced by the fuzzy logic model. Moreover, the fuzzy logic model gave no insight in the molecular interactions that are involved in activation or inhibition.
Here we used a data set based on the wetlab experiments described in [26]. We used the resulting experimental data, together with knowledge from curated databases [24, 25] to construct an executable model of the biological system. In contrast to the two approaches described above (partial leastsquares regression and fuzzy logic), ANIMO is aimed at the construction of more mechanistic models, mimicking biochemical interactions in silico. This way of modelling gives a different type of insight. In the process of model construction, we extended a priorknowledge network with timedependent extracellular crosstalk that has been reported previously [27]. To come up with possible explanations for a disagreement between the model and the experimental data, two additional layers of crosstalk were introduced, at the signal transduction and transcriptional level. These modifications improved the fit of the model to the data and can be interpreted as novel testable hypotheses. Finally, we proposed new experiments that could be carried out to test these hypotheses, closing the empirical cycle. Together, our model sheds more light on the intricate entanglement between the TNF α and EGF pathways at multiple cellular levels. But above all, the model provides an excellent starting point for further investigation.
User experience: ANIMO and other modelling tools
 1.
Domainspecific interface: the underlying formalism is manipulated through an interface targeted towards the biological domain
 2.
Visual modelling: the tool allows the user to model using a visual interface, and is not exclusively founded on formula, text or tablebased input forms
 3.
Qualitative parameters: parameters for reactions can be input as approximated estimations, and not exclusively as numbers
 4.
Tight coupling with topology: models are tightly and clearly coupled to the networks they represent, showing the visual representation of the model in a shape similar or comparable to the representation currently used by biologists for signalling pathways
 5.
Userchosen granularity: if discretization is applied during the modelling process, the user can change the granularity with which such discretization is made, possibly for each component of the model separately
Comparison between ANIMO and some existing approaches to modelling biological systems
Tool  Formalism  Domainspecific interface  Visual modeling  Qualitative parameters  Tight coupling with topology  Userchosen granularity 

GINsim [40]  Boolean Networks  Yes  Yes  Yes  Yes  Yes ^{a} 
BooleSim [41]  Boolean Networks  Yes  Yes  No  No  No 
CytoCopteR [35]  Fuzzy logic ^{b}  Yes  Yes  Yes  Yes  Yes ^{c} 
ANIMO [10]  Timed Automata  Yes  Yes  Yes  Yes  Yes 
Odefy [42]  Logicbased ODE  No  Yes ^{d}  Yes  No  No 
COPASI [43]  ODE, stochastic models  No ^{e}  No  No  No  No 
CellDesigner [44]  ODE  Yes  Yes  No  Yes  No 
GNA [45]  PLDE  Yes  Yes  Yes  Yes  Yes ^{a} 
Virtual Cell [46]  ODE, PDE, stochastic models  Yes  Yes  No  Yes  No 
BioPEPA Workbench [47]  BioPEPA  No  No  No  No  Yes 
COSBI LAB [48]  BlenX  Yes  Yes  No  Yes  No 
Cell Illustrator [49]  Petri Nets  Yes  Yes  No  Yes  No 
Among related work, we would like to highlight the powerful tool CellNOpt [35]. CellNOpt is a software which can work with logic descriptions (Boolean, fuzzy) and differential equations, and automatically suggests the best network topologies to match a given data set. Thanks to the CytoCopteR plugin for Cytoscape [36], which provides an accessible user interface, CellNOpt can be used in tandem with ANIMO: after computing the most likely network topologies with CytoCopteR, the biologist can carry on the analysis process with ANIMO, working on new hypotheses to explain the experimental data. Please note that this workflow is currently not implemented in a userfriendly way, and in order to perform it both CytoCopteR and ANIMO need to be installed. It is also possible to import SBML qual [37] models thanks to CytoCopteR’s import function and use them in ANIMO, as the basic properties of nodes and edges are automatically inferred. However, the k parameters of interactions as well as initial activities of nodes are set to default levels, and the user may need to change some of them in order to obtain a working network. We plan to extend ANIMO in such a way that the integration with CytoCopteR and other tools is made as smooth as possible. Full support of widely used model formats such as SBML qual will improve ANIMO’s interoperability, and this will positively reflect on the user experience.
Going beyond the user interface, there are a number of “pros and cons” for using ANIMO and Timed Automata in the biological context. First and foremost, as Timed Automata is an executable formal language, a state space can be derived from a Timed Automata model. This means that state spacerelated analyses such as model checking can be performed on Timed Automata: this can be done directly in ANIMO, as ANIMO acts as an intermediary towards the powerful model checking tool UPPAAL.
While ANIMO does not require the user to know Timed Automata or UPPAAL, it is necessary to possess some biological knowledge in order to build useful models. In particular, estimating activity rates may present difficulties that can be reduced with the help of biological intuition. As an example, consider the difference in rate between the production of a protein and a posttranslational modification such as phosphorylation: biological knowledge leads to choose a (much) lower rate for the former than for the latter. A second example, and an additional rationale for the development of tools like ANIMO that put the biologist in charge, is the translation of experimental numerical data into activity levels. It is necessary to have semiquantitative data as reference [11] (the data used as reference in the TNF αEGF model is mostly based on semiquantitative western blot experiments [26]), together with biological knowledge to define a sensible correspondence between experimental values and activity levels.
For each reactant modelled in ANIMO we assume that the total amount of active and inactive molecules remains constant. While this assumption is not always applicable, it encourages abstract thought: many biological processes can be represented as networks driven by activitybased interactions (see Methods section). Even if with a limited scope, ANIMO can be applied also in the analysis of metabolic processes, using activity to represent concentration as proposed in the Background section. While it cannot be expected from such models to be a completely realistic representation of their target biological processes, they can still be a useful tool. This can be seen for example in the circadian clock model in the Results section, where mRNA and protein concentrations were abstracted to activitydriven processes in the ANIMO model.
Finally, a note on the performance: the interactive use for which ANIMO is conceived implies that model analysis should require an amount of time small enough to encourage the user to experiment with different model configurations. The simulation of an ANIMO model is not computationally expensive, requiring minimal amounts of memory and CPU time. For example, on an Intel®; Core™ i7 CPU working at 2.80 GHz, computing a 24h simulation run of the model in Fig. 3 a takes about 0.69 sec while the model in Fig. 6 a takes about 1.14 sec. The larger model on which we are working [22, 23] is an order of magnitude larger than the ones presented in this paper (92 nodes and 123 interactions), and in that case computing a simulation where the state of the network dramatically changes (nearly all nodes undergo significant activity variations) takes about 16 sec. All the averages were computed based on 100 simulation runs.
Conclusions
In this paper we discussed the placement of ANIMO among other modelling paradigms and tools, highlighting ANIMO’s strong points.
From the point of view of model precision, we position ANIMO between fuzzy logic and ODEs. Being less parameterintensive than ODEs and more precise than logicbased models, ANIMO models are useful for a wide range of applications.
ANIMO adds a dynamic component to the static networks already familiar to biologists, allowing the domain experts to build formal executable models of complex biological networks. ANIMO is not the first tool to provide an interface to a modelling formalism: as shown in Table 1, such interfaces exist in many other tools. Focusing on userfriendliness and interactive modelling, ANIMO makes computational modelling more accessible to experts in biology. Thanks to the visual interface provided by Cytoscape, networks are represented according to biological conventions. Model parameters are kept to a minimum and can be directly accessed by mouseclicking on nodes and edges. Because of the automatic translation of the network topology and userdefined parameters into an underlying formal model, training in the use of formal methods is not needed.
Methods
Modelling biological interactions with timed automata
Example: building a model based on data
To illustrate the use of ANIMO in a practical environment, we will demonstrate the generation of a basic version of the model described in the Results section. The model is based on a literature compendium of signal transduction events in HT29 human colon carcinoma cells [26]. This data set comprises triplicate measurements of 11 different protein activities or posttranslational modification states at 13 time points after treatment with different combinations of tumour necrosis factor α (TNF α), epidermal growth factor (EGF) and insulin. The data set contains relative protein levels and activities, and no absolute quantities, which is the typical situation in biochemistry. To start, we normalized measurements for each protein to the maximum value in the complete experiment, resulting in a nondimensionalized data set that is suitable for use with ANIMO (see Additional file 1: Section B.2).
Abbreviations
Table S1 in the Additional file 1 contains explanations for the abbreviations used in the paper, including UniProt IDs (when applicable)
Declarations
Acknowledgements
We would like to thank Christof Francke for valuable discussions.
Funding
This work was supported by the Netherlands Organisation for Scientific Research (NWO) Casimir Grant 018.003.031 to J. Scholma.
Availability of data and materials
The datasets and models supporting the conclusions of this article are available in the FigShare repository https://dx.doi.org/10.6084/m9.figshare.3394921.v1.
Authors’ contributions
SS designed and performed the experiments, developed the Cytoscape integration, wrote the manuscript; JS conceived, designed and performed the experiments, wrote the manuscript; PEvdV initiated the study, conceived the Cytoscape implementation, supervised the project; MK designed experiments, analysed data and wrote the manuscript; JNP designed experiments, analysed data sets, contributed in particular to the application of ANIMO for large biological data, wrote the manuscript, and supervised the project; JvdP contributed to the strategy and methodology in the manuscript, in particular the connection with formal methods; RL contributed to the methodology, supervised the project and wrote the manuscript. All authors have read and approved the final version of the manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Not applicable.
Ethics approval and consent to participate
Not applicable.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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