MUFINS: Multi-formalism interaction network simulator

Abstract

Systems Biology has established numerous approaches for mechanistic modelling of molecular networks in the cell and a legacy of models. The current frontier is the integration of models expressed in different formalisms to address the multi-scale biological system organisation challenge. We present MUFINS software, implementing a unique set of approaches for multiformalism simulation of interaction networks. We extend the constraint-based modelling (CBM) framework by incorporation of linear inhibition constraints, enabling for the first time linear modelling of networks simultaneously describing gene regulation, signalling and whole-cell metabolism at steady state. We present a use case where a logical hypergraph model of a regulatory network is expressed by linear constraints and integrated with a Genome Scale Metabolic Network (GSMN) of mouse macrophage. We experimentally validate predictions, demonstrating application of our software in an iterative cycle of hypothesis generation, validation and model refinement. MUFINS incorporates an extended version of our Quasi Steady State Petri Net approach to integrate dynamic models with CBM, which we demonstrate through a dynamic model of cortisol signalling integrated with the human Recon2 GSMN and a model of nutrient dynamics in physiological compartments. Finally, we implement a number of methods for deriving metabolic states from ~omics data, including our new variant of the iMAT congruency approach. We compare our approach with iMAT through analysis of 262 individual tumour transcriptomes, recovering features of metabolic reprogramming in cancer. The software provides graphics user interface with network visualisation, which facilitates use by researchers who are not experienced in coding and mathematical modelling environments.

Full text

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MUFINS: Multi-Formalism Interaction Network Simulator 1!
Huihai Wu1, Axel von Kamp2, Vytautas Leoncikas1, Wataru Mori3, Nilgun Sahin4, Albert 2!
Gevorgyan5, Catherine Linley1, Marek Grabowski6, Ahmad A. Mannan1, Nicholas Stoy1, Graham 3!
R. Stewart1, Lara T. Ward7, David J.M. Lewis1, Jacek Sroka6, Hiroshi Matsuno3, Steffen Klamt2, 4!
Hans V. Westerhoff4,8,9, Johnjoe McFadden1, Nicholas J. Plant1*, Andrzej M. Kierzek1,10,* 5!
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*corresponding authors, a.kierzek@surrey.ac.uk, n.plant@surrey.ac.uk 7!
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E-mail addresses: Huihai Wu (h.wu@surrey.ac.uk); Axel von Kamp (vonkamp@mpi-9!
magdeburg.mpg.de); Vytautas Leoncikas (v.leoncikas@surrey.ac.uk); Wataru Mori 10!
(porepole8@gmail.com); Nilgun Sahin (nilguenyilmaz@gmail.com); Albert Gevorgyan 11!
(gevorgyana@MedImmune.com); Catherine Linley (c.linley@surrey.ac.uk); Marek Grabowski 12!
(grmarek@gmail.com); Ahmad A. Mannan (a.mannan@abdn.ac.uk); Nicholas Stoy 13!
(n.stoy@surrey.ac.uk); Graham R. Stewart (g.stewart@surrey.ac.uk); Lara T. Ward 14!
(lara.ward@AstraZeneca.com); David J. M. Lewis (d.j.lewis@surrey.ac.uk); Jacek Sroka 15!
(j.sroka@mimuw.edu.pl); Hiroshi Matsuno (matsuno@sci.yamaguchi-u.ac.jp); Steffen Klamt 16!
(klamt@mpi-magdeburg.mpg.de); Hans V. Westerhoff (Hans.Westerhoff@manchester.ac.uk; 17!
H.V.Westerhoff@uva.nl); Johnjoe McFadden (j.mcfadden@surrey.ac.uk); Nicholas J. Plant 18!
(n.plant@surrey.ac.uk); Andrzej M. Kierzek (a.kierzek@surrey.ac.uk); 19!
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Institutional addresses: 1) School of Biosciences and Medicine, Faculty of Health and Medical 21!
Sciences, University of Surrey, Guildford, GU2 7XH, United Kingdom. 2) Max Planck Institute for 22!
Dynamics of Complex Technical Systems, Magdeburg, Germany. 3) Graduate School of Science 23!
and Engineering & Faculty of Science, Yamaguchi University, Yoshida, Yamaguchi 753-8512, 24!
Japan 4) Molecular Cell Physiology, VU University Amsterdam, Amsterdam, The Netherlands 5) 25!
MedImmune Cambridge, CB21 6GH, United Kingdom 6) Institute of Informatics, University of 26!

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Warsaw, Warsaw, Poland 7) Oncology DMPK, AstraZeneca, Alderley Park, Cheshire, SK10 4TG, 27!
United Kingdom 8) Manchester Centre for Integrative Systems Biology, University of Manchester, 28!
Manchester, United Kingdom, 9) Synthetic Systems Biology, Netherlands Institute for Systems 29!
Biology, University of Amsterdam, Amsterdam, The Netherlands. 10) Simcyp Limited (a Certara 30!
Company), Sheffield, UK 31!
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ABSTRACT 34!
Systems Biology has established numerous approaches for mechanistic modelling of molecular 35!
networks in the cell and a legacy of models. The current frontier is the integration of models 36!
expressed in different formalisms to address the multi-scale biological system organisation 37!
challenge. We present MUFINS software, implementing a unique set of approaches for multi-38!
formalism simulation of interaction networks. We extend the constraint-based modelling (CBM) 39!
framework by incorporation of linear inhibition constraints, enabling for the first time linear 40!
modelling of networks simultaneously describing gene regulation, signalling and whole-cell 41!
metabolism at steady state. We present a use case where a logical hypergraph model of a regulatory 42!
network is expressed by linear constraints and integrated with a Genome Scale Metabolic Network 43!
(GSMN) of mouse macrophage. We experimentally validate predictions, demonstrating application 44!
of our software in an iterative cycle of hypothesis generation, validation and model refinement. 45!
MUFINS incorporates an extended version of our Quasi Steady State Petri Net approach to 46!
integrate dynamic models with CBM, which we demonstrate through a dynamic model of cortisol 47!
signalling integrated with the human Recon2 GSMN and a model of nutrient dynamics in 48!
physiological compartments. Finally, we implement a number of methods for deriving metabolic 49!
states from ~omics data, including our new variant of the iMAT congruency approach. We compare 50!
our approach with iMAT through analysis of 262 individual tumour transcriptomes, recovering 51!
features of metabolic reprogramming in cancer. The software provides graphics user interface with 52!
network visualisation, which facilitates use by researchers who are not experienced in coding and 53!
mathematical modelling environments. 54!
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Introduction 60!
During the last two decades, Systems Biology has established numerous approaches to represent 61!
molecular biology knowledge in the form of mechanistic molecular interaction network models. 62!
This is accompanied by a legacy of thousands of experimentally validated models. Stochastic 63!
kinetic simulations provide the most detailed quantitative description, where individual reactive 64!
collisions occurring at exact times in single cells are simulated by the Gillespie algorithm (1). The 65!
Ordinary Differential Equation (ODE) formalism applied to study the time evolution of average 66!
molecular concentration in cellular population is a workhorse of quantitative modelling (2). While 67!
quantitative biology is developing rapidly, it is still not possible to parameterise quantitative 68!
dynamic models of whole-cell scale networks and simulate genotype-phenotype relationship. 69!
Rather, Constrained Based Modelling (CBM) has achieved spectacular success in modelling 70!
metabolism at the full genome scale (3, 4). The metabolic network can be modelled at quasi-steady 71!
state due to time-scale separation from gene regulation. This enables exploration of metabolic flux 72!
distributions consistent with stoichiometric and thermodynamic constraints as well as flux 73!
measurements and constraints formulated according to ~omics data on enzymatic gene expression 74!
(5). Modelling of large-scale gene regulatory and signalling networks is much more challenging and 75!
a number of qualitative simulation approaches have been formulated, such as analysis of steady 76!
states in logical hypergraphs (6), enumeration of states in dynamic Boolean models (7), Monte 77!
Carlo exploration of the alternative molecular transition sequences constrained by network 78!
connectivity expressed in Petri Net formalism (8, 9). Application of these methods has led to a 79!
legacy of models describing different levels of cellular organisations in different modelling 80!
frameworks. A large proportion of these models are already expressed in Systems Biology Markup 81!
Language (SBML) (10) and over 1000 literature-based models are available in the most recent 82!
version of BioModels (11). Notably, BioModels is attracting interest from the Physiologically 83!
Based Pharmacokinetic (PBPK) modelling field (12), where ODE models of substance 84!

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concentrations in physiological compartments are routinely used to inform drug development in 85!
pharmaceutical industry. 86!
Given this state of the art and the multi-scale nature of biological systems, the current 87!
challenge is integration of models expressed in different formalisms towards a multi-formalism 88!
simulation covering all scales of biological organisation. The model of Mycoplasma is currently the 89!
most complete in silico cell (13), and demonstrates that mechanistic modeling of the genotype-90!
phenotype relationship requires the integration of sub-system models describing different spatial 91!
and temporal scales constructed in different formalisms. The application of the multi-formalism 92!
approach toward modeling the relationship between genotype and human physiology is an 93!
emerging field and an important component of the personalized medicine challenge. For example, 94!
integration of a PBPK model with human liver-specific GSMN has allowed robust prediction of 95!
therapeutic response in humans (14). In our recent work we integrated a liver-specific GSMN with 96!
a qualitative model of a large-scale regulatory network (9), demonstrating how integration of gene 97!
regulation and metabolism in the context of physiological modeling can provide novel insights into 98!
toxicology, non-alcoholic liver disease and metabolic syndrome. This was achieved by application 99!
of our novel Quasi-Steady State Petri Net (QSSPN) (9) approach integrating CBM and qualitative, 100!
Monte Carlo simulation of a regulatory network represented as a Signaling Petri Net (15). 101!
Numerous alternate methods have been proposed to integrate GSMNs with ODE (16) and logical 102!
(17) dynamic models as well as hybrid algorithms, bridging the gap between exact stochastic and
103!
ODE regimes in fully parameterized dynamic models (18). To fully realize the potential of
104!
computational modelling, it is now imperative to develop software packages that allow the
105!
development and simulation of multi-formalism models in a user interface that is approachable for 106!
experimental scientists. 107!
Here, we present MUFINS (Multi Formalism Interaction Network Simulator) software and 108!
argue that it is the first general software with Graphics User Interface (GUI) capable of integrating 109!
models developed in all major modeling frameworks of Computational Systems Biology. This is 110!

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demonstrated through Use Cases; first, a model of the mammalian macrophage where linear 111!
inhibitory constraints are for the first time used to integrate a logical model of cellular signaling 112!
with the GSMN for the mammalian cell; second, a model of the human hepatocyte, where an 113!
extended version of our QSSPN method is used to integrate a human GSMN, a detailed kinetic
114!
model of cortisol signaling and a PBPK model; third, the analysis of clinical transcriptome data in
115!
the context of human GSMN using a novel variant of ~omics data integration approach. The use
116!
cases involve laboratory experiments to demonstrate how experimental biologists can utilise the 117!
MUFINS GUI in the iterative cycle of model development, hypothesis generation, experimental 118!
validation and model refinement. Moreover, a comprehensive comparison with other software 119!
shows that MUFINS implements the largest number of CBM methods under a GUI with interactive 120!
network visualization. Thus, MUFINS is uniquely suited for the development and simulation of 121!
multi-formalism models by a wide user community including experimental scientists with 122!
no/limited experience with programmatic interfaces and mathematical modeling environments.
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Software overview. 125!
Figure 1 provides an overview of the MUFINS architecture. All simulations are performed in sfba 126!
and qsspn, two computational engines written in C++, which are run either through a GUI or in 127!
command line mode. The sfba code originates from our SurreyFBA software (19) and implements a 128!
comprehensive set of CBM approaches. The major new multi-formalism simulation feature added is
129!
linear inhibitor and activator constraints, which are described and validated in Use Case 1. In
130!
addition to the basic CBM methods available in SurreyFBA, the sfba engine of MUFINS 131!
implements a large number of ~omics data integration algorithms such as iMAT (20), GIMME 132!
(20), GIM3E (21), GNI (22) and our DPA (24). The GNI and DPA features of sfba have been 133!
already used to study M. tuberculosis metabolism (24,25)(23). Furthermore, we include Fast iMAT 134!
a new variant of iMAT approach demonstrated in Use Case 3 below. sfba uses the GLPK library for 135!
Linear Programming (LP) and Mixed Linear Integer Programming (MILP) calculations. However, 136!

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since MILP implementation in GLPK is inefficient, a version of sfba ready for use with Gurobi 137!
library is provided to facilitate application of MILP-based protocols (e.g. iMAT) on GSMN models. 138!
The qsspn is a computational engine for integration of dynamic and CBM models. It 139!
implements QSSPN approach (9), where a dynamic model constructed in Petri Net (PN) formalism
140!
(24) is connected to a steady state Flux Balance Analysis (FBA; (4)) through PN places setting FBA
141!
bounds and requesting evaluation of objective functions. Previously, we integrated a qualitative PN
142!
model with a hepatocyte GSMN and explored its qualitative dynamic behaviours through Monte 143!
Carlo simulation (15). Here we present a new version of the engine, providing full support for 144!
continuous Petri Nets, implementing ODE models and stochastic Petri Nets representing exact 145!
stochastic simulations. Use Case 2 demonstrates the first integration of quantitative models of gene 146!
regulation with human Recon2 GSMN coupled to an ODE model of nutrients in physiological 147!
compartments. The qualitative simulation features are also further extended by implementation of 148!
QSSPNclient, a version of qsspn which speeds up sampling of alternative qualitative trajectories by
149!
executing FBA on a server that tabulates repeated evaluations of GSMN objective functions for re-150!
occurring sets of bounds. The new version of the QSSPN algorithm, qsspn solver and QSSPNclient 151!
are described in detail as Supplementary Information (page 32). 152!
Connectivity of a Petri Net representing the dynamical part of the QSSPN model and its 153!
interactions with GSMN can be graphically defined using the Petri Net editor Snoopy (25): while 154!
Snoopy provides PN simulation, it does not implement QSSPN and thus is used here exclusively as
155!
an external editor of PN connectivity. Parameters specific to qsspn simulation can be provided
156!
either through the Comments section of place and transition objects, or added later through the 157!
MUFINS GUI. The Snoopy XML file is parsed by the spept2qsspn Python script, which generates 158!
the qsspn input file in qsspn’s native, human readable, text-file format. To facilitate future 159!
integration with other interfaces, a JSON-based input file format is also available. 160!
JyMet is the GUI of MUFINS, and provides an interface for multi-formalism simulations to 161!
users who are not familiar with programming, mathematical modeling environments or working in 162!

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command line. JyMet code is written in Jython (Java/Python), and originates from SurreyFBA (19). 163!
Here, it has been significantly extended through addition of QSSPN simulation and improved 164!
visualization of metabolic networks. JyMet integrates all elements of the MUFINS environment 165!
(Figure 1). It loads a Snoopy file defining PN connectivity and provides a table interface for
166!
definition of QSSPN specific parameters: place and transition types, lookup tables linking dynamic
167!
and GSMN variables, and arithmetic formulas describing complex rate laws. We note that users can
168!
build dynamic model within the QSSPN spreadsheet interface of JyMet without using Snoopy, but 169!
this is unlikely to be a preferable solution, due to the advantages of PN graphical modeling. Both 170!
sfba and qsspn can be run from JyMet and results are loaded to spreadsheets and plotting functions. 171!
Each table in JyMet can be exported in tab-separated format for further analysis with other 172!
software. Full features of JyMet are described in detail in software documentation and tutorials 173!
(MUFINS1.0_Doc/). Use Case 1 shows application of network visualization for exploration of 174!
alternative model solutions during the iterative cycle of network reconstruction, simulation,
175!
experimental validation and refinement. 176!
The sfba, qsspn and spept2qsspn tools can be run as stand-alone command line tools without 177!
external dependencies. Thus MUFINS is ideal for integration with web and desktop interfaces as 178!
well as computational pipelines. Use Case 3 shows integration of sfba engine with computational 179!
pipeline for analysis of clinical transcriptome data. Previous version of sfba engine (19) has been 180!
already used in web interfaces supporting development and publication of bacterial pathogen
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GSMN models (26, 27) and as one of computational engines in METEXPLORE web environment
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(28). 183!
MUFINS is open source software, distributed under the GNU GPL license. It can be run on 184!
OS X, Windows and Linux sand the majority of calculations can be run without dependencies. The 185!
methods applying MILP to genome scale models are likely to be very computationally expensive 186!
unless the Gurobi library is installed. 187!
188!

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Use Cases 189!
Table 1 summarizes Use Cases illustrating the multi-formalism simulation abilities within 190!
MUFINS, including previously published works. 191!
192!
Table 1. Summary of simulation formalisms applied in Use Cases.
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Use Case
Formalisms
Reference
Use Case 1: linear inhibitory
constraints
CBM, logical hypergraph, inhibitor and
activator constraints.
This work
Use Case 2: integration of
regulatory networks and GSMNs
CBM, ODE, Gillespie, physiological
compartment models.
This work and (9)
Use Case 3: Prediction of
metabolic landscapes
CBM, congruency approach to analysis
of ~omics data in the context of GSMNs.
This work and (29)
194!
Use case 1: Whole-cell metabolic reprogramming by signaling and gene regulatory networks in the 195!
mammalian macrophage. 196!
An important innovation in MUFINS is the ability to include stimulation and inhibition reactions 197!
within the genome-scale metabolic network. To demonstrate the utility of this approach to derive 198!
biological insights we present a use case entailing integration of gene and signaling regulatory 199!
networks with genome-scale metabolism for the mammalian macrophage. 200!
We applied MUFINS to integrate a logical hypergraph (6) model of the large-scale
201!
regulatory network responsible for the pathogen response of mammalian macrophage with the 202!
published GSMN of the mouse RAW264.7 macrophage cell line (30). A signal transduction 203!
network of 286 interactions and 205 species was reconstructed in CellNetAnalyzer using logical 204!
hypergraph formalism (6): A manually created graph image is shown in Figure 2, with full 205!
description of model construction described in Supplementary Information, and a detailed 206!
description of species, logical formulas and literature references in Supplementary Table 1. Briefly,
207!

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species within the regulatory network represent protein kinases, transcription factors, genes, 208!
antigens, cytokines and cellular behaviours (e.g. apoptosis) involved in the response of 209!
macrophages to bacterial pathogens. 210!
To integrate signaling and metabolic networks, we have translated the logical hypergraph to
211!
a stoichiometric model with inhibitory constraints. Representation of inhibition in the CBM
212!
framework has always been a challenge, with proposed solutions generally being computationally
213!
expensive methods based on MILP (31). We have extended the approach of Vardi and colleagues 214!
(32) and represented inhibition by linear constraints, enforcing a reciprocal relation between 215!
inhibitor production and inhibited flux. Differences between the original formulation and our 216!
extended implementation are presented as Supplementary Information. An example of the logical 217!
hypergraph conversion to MUFINS reaction formulas is shown in Figure 2. At the software level 218!
this is achieved by exporting CellNetAnalyzer logical rules as a text format and then using the text-219!
replace function in Excel to change the formula format and create a MUFINS reaction table that can
220!
be opened by the JyMet GUI. We note these steps do not require programming experience. 221!
Subsequently, the model was edited in JyMet to define input fluxes. Flux Variability Analysis was 222!
undertaken to identify spurious activations in the model with all input fluxes constrained to 0. 223!
Details of these steps are given in Supplementary Information (page 7), where we also compare our 224!
model pre-processing steps with the much more complex, MILP based protocol used by Vardi et al 225!
(32).
226!
A unique feature of MUFINS is reconstruction of models that combine GSMNs and
227!
regulatory networks with linear inhibitory constraints. To demonstrate this capability we integrated 228!
the signal transduction network model described above with the published GSMN of the 229!
RAW264.7 macrophage cell line (30). We have focused on nitric oxide production, a major 230!
metabolic function of macrophages interacting with bacterial pathogens. Our regulatory network 231!
model describes the regulation of the inducible nitric oxide synthase (iNOS) gene, which we have 232!
added as an activator for the NO synthase reaction in the GSMN (reaction id: R_NOS2). We used a 233!

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linear activator constraint, as described in Supplementary Information (page 31), to ensure that 234!
stoichiometry of the R_NOS2 reaction is not affected. Figure 3A shows a portion of the total 235!
regulatory network, specifically the immediate signaling pathways regulating iNOS gene 236!
expression. We used this integrated model to simulate nitric oxide production in response to
237!
lipopolysaccharide (LPS). Following Bordbar and colleagues (30) we constrained biomass reaction
238!
flux to 0.0281/h, which reproduces experimentally measured growth rates. We calculated the
239!
maximal extracellular nitric oxide production when LPS input flux to the regulatory network was 240!
opened or closed and when phosphorylation of ERK by MEK1 was inhibited or not. Results 241!
obtained from these four simulations are shown on Figure 3B, and demonstrate that nitric oxide is 242!
produced only when LPS activates the regulatory network, while the inhibitor does not influence 243!
results. The maximal flux through R_NOS agrees with the value of 0.0399 mmol/gDW/h reported 244!
in original publication, thus verifying SBML import of the GSMN model to JyMet. We note that 245!
while in this use case the regulatory network regulates only one enzyme, this is an example of
246!
major global metabolic reprogramming. The production of large amounts of nitric oxide in response 247!
to pathogen requires both precursors and energy, and the GSMN model accounts for stoichiometry 248!
of all reactions linking medium nutrients to metabolic output. Moreover, the GSMN assures that the 249!
cell satisfies other metabolic demands, such as the demand for biomass production whereby the 250!
GSMN model accounts for global stoichiometry of providing cellular components and maintaining 251!
energy during induced nitric oxide production.
252!
To compare the model predictions with experimental data we treated RAW264.7
253!
macrophages with LPS and a MEK inhibitor and measured nitrate concentration in the medium. 254!
Since nitrate can be produced only by the non-enzymatic conversion of nitric oxide from cells, and 255!
there is no nitrate consumption in the medium, concentrations are proportional to the nitric oxide 256!
production flux. Figure 3C shows that the model correctly predicts that LPS is obligate for the 257!
production of nitric oxide in RAW264.7 macrophages. However, the model did not predict the 258!
decrease in nitric oxide production caused by MEK inhibition. To explore this inconsistency, we 259!

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used the interactive network visualization available in JyMet (Figure 3A) to examine example FBA 260!
solutions. Multiple pathways lead to iNOS activation, some of which are not dependent on MEK. In 261!
the model, the “iNOS” substance representing activity of the iNOS gene is produced by three 262!
reactions representing the activity of ERK1/2-, HIF1- and JNK-dependent regulation of iNOS gene
263!
expression. Each of these regulators is, activated by different upstream signaling cascades. We used
264!
JyMet to interactively simulate and visualize different scenarios and concluded that the
265!
experimental results can be replicated if the following assumptions are made: i) ERK induces a 266!
more potent activation of the iNOS gene than JNK and HIF1 ii) MEK1 is a more potent ERK kinase 267!
than PKC. These assumptions were introduced to the model by setting flux bounds of (0, 0.005) for 268!
the transitions “JNK -> iNOS”, “HIF1->iNOS” and “PKC_a_b = ERK1/2” (Figure 3A, right panel). 269!
The upper bound is arbitrary, and selected to ensure that the flux towards “iNOS” via “HIF1” or 270!
“JNK” reaches only a fraction of value required for maximal activation of R_NOS, with the 271!
remaining activation occurring via ERK1/2 regulation. This refined model is now able to reproduce
272!
the decreased, but not complete inhibition, of nitric oxide production by a MEK inhibitor (Figure 273!
3D). A full description of this cycle of prediction, experimental testing, and model refinement is 274!
presented as Supplementary Information (page 11), detailing how MUFINS and JyMet aid the 275!
iterative refinement cycle required during model development. This data supports the assumptions 276!
above being one possible mechanistic solution to reproduce the observed biological phenotype. 277!
However, we note that further experimental confirmation is required to confirm the predicted
278!
biological insight. In a full iterative cycle of prediction, experiment and model refinement, multiple
279!
molecular targets would be subject to independent experiment verification before the model was 280!
validated. Here, we show one full cycle of simulation and experiment to demonstrate how the 281!
JyMet interface is used in this iterative model development process. 282!
To summarize, we present the first linear model for steady state simulation of networks 283!
integrating signaling, gene regulation and whole-cell metabolism in a mammalian cell. Moreover, 284!
we present the first simulation of perturbation of a global metabolic output by a signaling network 285!

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inhibitor, and demonstrate this is consistent with experimental data. The ability to formulate 286!
hypotheses in terms of continuous “regulatory strength” is demonstrated. This offers significant 287!
advantages over MILP based approaches such as SR-FBA (33), where the regulatory network is 288!
used exclusively to formulate Boolean, on/off constraints. Finally, the graphics user interface JyMet
289!
allows an interactive exploration of combined signaling and metabolic flux distributions that is
290!
easily approachable by non-specialists. Together, these tools provide an ideal platform for non-
291!
specialists to generate mechanistic hypotheses based upon the interaction of gene and signal 292!
regulatory networks with genome-scale metabolism. These hypotheses can then drive experimental 293!
testing, enhancing our ability to identify novel biological insights. 294!
295!
Use case 2: Kinetic model of cortisol signaling integrated with dFBA simulation of human GSMN. 296!
An important challenge in computational biology is the generation of large-scale models that are 297!
able to reproduce diverse biological functions. One approach to achieve this aim is the integration
298!
of validated small models (or modules) to form larger networks. A major consideration in such 299!
integration is the ability to combine models across different modelling formalisms and biological 300!
scales. In this use case we demonstrate the utility of MUFINS for the generation and simulation of 301!
such multi-formalism, multi-scale models. 302!
Cortisol acts as an important signaling molecule within the body, with roles in circadian biology 303!
and the response to stress episodes. The level of cortisol in the body is interpreted at the cellular
304!
level through interaction with three nuclear receptors: the glucocorticoid receptor; the
305!
mineralocorticoid receptor; the pregnane-X receptor. These signals are integrated and produce a 306!
global metabolic shift corresponding to the current cortisol level. To reproduce such a complex 307!
biological phenomenon it is necessary to combine multiple signaling cascades with genome-scale 308!
reconstructions of metabolism. Here, we demonstrate the application of MUFINS for such a multi-309!
formalism simulation, integrating a detailed kinetic model of cortisol signaling in the liver, a 310!
genome-scale model of liver metabolism, and an ODE model of glucose and lactate dynamics in the 311!

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14!
blood (Figure 4). This is the first simulation integrating a human GSMN, physiological level ODE 312!
model and detailed kinetic model of an intracellular regulatory network. Thus, this use case 313!
demonstrates that MUFINS provides a unique tool for the integration of PBPK models with the 314!
mechanistic models of molecular networks operating in mammalian tissues.
315!
The model is depicted in Figure 4A. We represent our previously published kinetic model of
316!
cortisol signaling in liver (34, 35) as a Petri net (PN) using Snoopy software (25). Size and colour
317!
of place/transition symbols was used to mirror Systems Biology Graphical Notation (36) molecule 318!
types as well as QSSPN specific place/transition types. The PN transition rates were defined using 319!
the ODE terms of the kinetic model. PN places represent molecular concentrations. This dynamic 320!
model of cortisol signaling was linked to the human GSMN Recon2, with the CYP3A4 enzyme 321!
used as the QSSPN constraint place. Details of the cortisol signaling model and its coupling to 322!
GSMN are available Supplementary Information (page 16). 323!
To model whole-cell metabolism of hepatocytes we used the community-based Recon2
324!
GSMN (37). This model incorporates liver specific reactions from the HepatoNet1 (38), but is a 325!
much more extensive reconstruction of cellular metabolism. Exchange fluxes were constrained 326!
using the HepatoNet1 Physiological Import and Export set (PIPES). The objective function was set 327!
to glucose regeneration from lactate, a major physiological function of the liver, where blood 328!
glucose and lactate concentrations are ODE variables. The dFBA simulation is implemented using 329!
place and transition within the QSSPN, rather than coded as a separate approach. We have further
330!
capitalized on the flexibility of the PN representation to create a timer administering a cortisol
331!
infusion after 500 minutes. This demonstrates how multi-formalism simulations in MUFINS can 332!
include complex, time-dependent perturbations to the model such as boluses or cell division events. 333!
For clarity, the timer is contained within a coarse transition, with the sub-level shown as an inset to 334!
figure 4A. A detailed description of QSSPN place and transition types is given as Supplementary 335!
Information (page 27), along with a detailed description of model construction (page 12). 336!

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15!
Simulations of the systems response to cortisol infusion, plus experimental confirmation are 337!
shown in Figure 4B-G. As shown in figure 4B, glucose and lactate concentrations converge to their 338!
physiological levels of 4.45 mM and 1.48 mM respectively (39) and are maintained during cortisol 339!
infusion from 500 minutes onwards. Cortisol infusion from 500 minutes produces a number of
340!
effects, which are mediated through activation of the two cognate nuclear receptors for cortisol
341!
within the regulatory network, PXR and GR (40, 41). The cortisol-mediated activation of PXR
342!
results in a predicted increase in expression of the CYP3A4 enzyme (Figure 4C), which is 343!
experimentally confirmed at the transcript, protein and activity levels in vitro using primary human 344!
hepatocytes (Figure 4D). CYP3A4 is one of the main enzymes responsible for the metabolic 345!
clearance of cortisol; thus, the combination of a constant infusion of cortisol, followed by increased 346!
metabolism, results in an elevated blood cortisol level (Figure 4E). We note that the transition to 347!
this new blood cortisol level is not instant, demonstrating a concentration spike consistent with the 348!
time delay caused by the de novo production (i.e. transcription and translation) of CYP3A4 protein.
349!
Finally, in Figure 4F we demonstrate that the cortisol infusion propagates through the signaling and 350!
metabolic networks, leading to predicted changes in blood concentrations for other chemicals. 351!
Estradiol is an endogenous hormone important in a range of biological functions, including 352!
development of the secondary sexual organs in both sexes and proliferation during the menstrual 353!
cycle and pregnancy in women (42, 43). It has considerable clinical application, most notably as a 354!
contraceptive, either as the native compound or synthetic derivatives (44). As shown in figure 4E,
355!
following the cortisol infusion, predicted levels of blood estradiol drop rapidly, decreasing
356!
approximately by one-halve within 500mins. This lower level is maintained throughout the period 357!
where CYP3A4 protein levels are elevated. To confirm this effect, we have measured the clearance 358!
rate for estradiol in naïve primary human hepatocytes and compared it to hepatocytes pre-exposed 359!
to 1µM cortisol, demonstrating enhanced clearance in cortisol-exposed hepatocytes (Figure 4G). In 360!
addition, we note that activation of PXR has previously been linked with a number of drug-drug 361!
interactions with estrogens, demonstrating the extrapolation of these predictions to the clinical 362!

!
16!
setting (41, 45). It is important to note that estradiol concentration was not a variable of the detailed 363!
kinetic model, and was rather identified as a variable of interest by examination of perturbed 364!
GSMN fluxes. This demonstrates how integration of detailed kinetic models with GSMNs can lead 365!
to identification of interactions of biological interest. As such, this approach has much potential for
366!
the prediction of clinically relevant drug-induced disruption of homeostasis, and drug-drug
367!
interactions (41, 45).
368!
In summary, this use case demonstrates the utility of MUFINS to combine legacy models 369!
developed in different formalisms and link molecular network knowledge to quantitative data on 370!
substance concentration at physiological level. As such, MUFINS represents the first software to 371!
allow such multi-scale, multi-formalism simulations through a GUI approachable to the non-372!
specialist. 373!
374!
Use case 3: Analysis of a clinical transcriptome data to understand in vivo tumour metabolism
375!
An important branch of CBM methodology (5) is dedicated to using ~omics data to create tissue 376!
and/or condition specific GSMNs. MUFINS is equipped with state-of-the art CBM methods in this 377!
area; in addition, we have developed Fast iMAT, a new variant of the iMAT approach that is 378!
applicable to large ~omics sample numbers, where iMAT becomes impractical. We recently 379!
reported a preliminary version of Fast iMAT (29), dedicated to the analysis of expression data 380!
discretized to two states (absent or present transcript). Personalized GSMNs for 2000 breast
381!
tumours were generated, identifying a low prognosis cluster with active serotonin production – an
382!
important biological insight (29). The first distribution version of MUFINS provides a mature 383!
version of the Fast iMAT algorithm. To demonstrate its utility, we analyze 262 previously 384!
unexamined paired clinical transcriptome samples (46). We demonstrate the significant up-385!
regulation of kyneurenine synthesis in tumour compared to normal breast tissue, and important pro-386!
survival phenotype (47, 48). 387!
388!

!
17!
Comparison of MUFINS with existing tools. 389!
A comparison of MUFINS with existing tools is presented as Supplementary Information. We 390!
conclude that MUFINS is currently the only software supporting integration of i) exact stochastic, 391!
ii) ODE, iii) qualitative dynamic, iv) logical steady state and v) CBM models in a general software
392!
platform with GUI. The only alternative to achieve integration of this range of formalisms is coding
393!
of the model in mathematical modeling environment. While this strategy has achieved success (13),
394!
it is not a plausible proposition for non-specialists who lack programming skills. Moreover, multi-395!
formalism modeling in a mathematical language involves the implementation of a simulation 396!
algorithm dedicated to each model. In MUFINS, each model is run in the same QSSPN simulation 397!
algorithm, with multi-formalism functionality emerging from the interactions between the different 398!
types of Petri Net places and transitions that can be graphically assembled, leading to a 399!
combinatorial diversity of types of models that can be simulated. Using one algorithm and a few 400!
well-defined place and transition types provides clearer control and description of model
401!
assumptions than coding a different main simulation loop for each model. Also, the algorithms 402!
available in MUFINS are validated and optimized against the legacy of previous applications, while 403!
formulation, validation and description of a simulation algorithm dedicated to a particular model 404!
will take additional time. It is our experience that even scientists who can program will find it easier 405!
to implement complex multi formalism models by connecting QSSPN places and transitions to off-406!
the-shelf GSMN models imported to JyMet, rather then by development of dedicated mathematical
407!
modeling code. Moreover, MUFINS provides a wide range of CBM methods that can be used to
408!
model GSMNs before their integration with dynamic models. As Supplementary Information we 409!
perform the largest review of CBM methods conducted to date (165 methods and 30 software 410!
packages), demonstrating that MUFINS is the second most general CBM software after COBRA 411!
toolbox (49) in terms of the number of methods implemented. However, it provides the largest 412!
number of CBM methods under GUI with interactive network visualization. Finally, all CBM 413!
methods can now be applied to models formulated with inhibitor and activator constraints, which 414!

!
18!
again enables execution of new CBM protocols without the need of coding (e.g. iMAT applied to 415!
models involving steady-state regulatory network). 416!
417!
Future directions.
418!
We will continue to develop MUFINS towards improved interoperability with other tools and
419!
model databases, a key for model integration. While currently QSSPN can be simulated only in
420!
MUFINS, definition of this multi-formalism framework in SBML will motivate development of 421!
alternative tools. As shown on Figure 1, QSSPN models can currently be exported into two separate 422!
SBML files representing the CBM and PN parts of the model. We intend to represent QSSPN 423!
lookup tables, reset transitions and flux monitors with existing SBML objects, or to develop a 424!
bespoke SBML package. Furthermore, we will work towards improving integration of SBML files 425!
imported from public repositories into multi-formalism models in the JyMet GUI. This will involve 426!
further work on network visualization in JyMet, providing a graph editor dedicated to connecting
427!
different mechanistic models by common variables. We also plan to develop interoperability 428!
between MUFINS and Garuda (http://www.garuda-alliance.org) to make full use of our multi-429!
formalism simulation tool within this established alliance of systems biology software. This will be 430!
facilitated by design of our software (Figure 1) providing stand-alone simulation engines ideal for 431!
embedding in different interfaces. 432!
433!
Conclusions.
434!
The multi-scale nature of complex biological systems is currently the major challenge preventing 435!
their computational understanding. A number of theoretical frameworks have achieved spectacular 436!
successes in mechanistically modelling different levels of cellular organisation such as metabolic, 437!
signaling and gene regulatory networks. However, in a real cell all these processes proceed 438!
simultaneously, and without multi-scale simulation the insight and predictive power provided by 439!
models will be limited. We present MUFINS, the first general software addressing this multi-440!

!
19!
formalism simulation challenge. Novel algorithms available in MUFINS provide solutions for three 441!
major technological challenges: i) integration of CBM and hybrid stochastic/deterministic dynamic 442!
simulation ii) CBM of integrated signaling/metabolic models iii) analysis of large clinical 443!
transcriptome studies in the context of GSMN. This is demonstrated through three Use Cases,
444!
where we simulate models of mammalian systems composed of: GSMNs, logical hypergraph
445!
models of signalling, kinetic models of gene regulation and PBPK models. We experimentally
446!
validate model predictions and show how our software can aid experimental scientists through an 447!
iterative cycle of hypothesis generation, experimentation and model refinement. Because the need 448!
for a multi-scale, multi-formalism approach is currently most recognised in the context of 449!
Personalised Medicine and Quantitative Systems Pharmacology, we focused our Use Cases on 450!
mammalian cells. However, mechanistic simulation is a major tool in Synthetic Biology, where 451!
MUFINS will be ideal to integrate detailed models of genetic circuits with GSMNs and further 452!
extend molecular cell factory models to include bioreactor mass transfer. Therefore, we believe that
453!
multiformalism simulation with MUFINS will find broad application in mechanistic modelling of 454!
biological systems. 455!
456!
Software Availability: 457!
MUFINS is free, open source software available under GNU GPL license from: 458!
MUFINS home page: http://sysbio3.fhms.surrey.ac.uk/mufins/
459!
GitHub repository: https://github.com/kierzek/MUFINS
460!
461!
Acknowledgements 462!
Development of MUFINS was funded by BBSRC TRDF grant BB/K015974/1 to AMK. AvK, SK, 463!
GRS and AMK were supported by EraSysBio+/BBSRC TB-HOST-NET grant BB/I00453X/1. CL, 464!
NS and DL were supported by The research leading to results obtained by CL, NS and DL has 465!
received support from the Innovative Medicines Initiative Joint Undertaking under grant agreement 466!

!
20!
n 115308, resources of which are composed of financial contribution from the European Union's 467!
Seventh Framework Programme (FP7/2007-2013) and EFPIA companies in kind contribution. MG 468!
and JS were funded by National Science Centre (Poland) grant DEC-2012/07/D/ST6/02492. VL 469!
was funded by the BBSRC grant (BB/K501694/1).
470!
471!
Author contributions.
472!
HW implemented most of the software features and formulated Fast iMAT approach. AvK and SK 473!
developed logical hypergraph model in Use Case 1. VL, LTW and NJP contributed Use Case 3. 474!
WM and HM designed and prototyped network visualization in JyMet. NS, NJP and HVW 475!
conducted study in Use Case 2. AG contributed to development of sfba and JyMet. CL, GRS and 476!
DJML provided experimental part of Use Case 1. MG and JS designed and implemented 477!
QSSPNclient. AAM contributed to development and testing of ~omics data integration approaches. 478!
NS and DJMW contributed to model integration and simulation in Use Case 1. JMcF contributed to
479!
JyMet design and network visualization. HVW contributed to manuscript design. AMK and NJP 480!
wrote manuscript. AMK formulated qsspn algorithm and contributed to qsspn solver 481!
implementation. 482!
483!
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!
604!
! !
605!

!
24!
+606!
Figure+1.+Overview+of+MUFINS.!All!calculations!are!performed!by!two!computational!607!
engines,!which!can!be!also!run!as!stand-alone!command!line!tools.!The!sfba!implements!CBM!608!
methods!and!qsspn!performs!QSSPN!simulations.!JyMet!is!a!graphic!interface!to!all!methods!
609!
providing!spreadsheet!representation!of!models!and!results!as!well!as!metabolic!network!
610!
visualization!and!plots.!JyMet!writes!input!files!for!computational!engines,!starts!calculations,!
611!
imports!output!files!and!displays!results.!In!the!case!of!QSSPN!simulations,!Petri!Net!612!
connectivity!can!be!graphically!edited!by!Snoopy!software,!a!standard!Petri!Net!tool,!which!613!
we!use!as!external!editor.!JyMet!imports!Snoopy!files!and!provides!spreadsheet!interface!614!
allowing!editing!of!QSSPN!parameters!or!independent!creation!of!entire!QSSPN!model.!615!
Conversion!of!Snoopy!files!directly!to!qsspn!engine!is!also!possible!with!command!line!python!616!
script!spept2qsspn. Both!JyMet!and!Snoopy!import!and!export!SBML!file!providing!617!
connectivity!to!other!SBML-compliant!tools.!The!file!formats!used!for!software!component!
618!
communication!are!indicated!by!their!default!extensions!and!described!in!Supplementary!File!619!
Formats.!620!

!
25!
!621!
Figure+2.+The+model+of+cell+signaling,+gene+regulation+and+whole-cell+metabolism+in+622!
RAW264.7+macrophage.+A+signaling!and!gene!regulatory!network!of!286!interactions!623!
between!205!species,!created!in!logical!hypergraph!formalism!is!shown.!This!network!was!
624!
subsequently!converted!to!FBA!formalism!with!linear!inhibitory!constraints!and!coupled!to!
625!
the!RAW264.7!GSMN!through!regulation!of!the!iNOS!gene.!Nitric!oxide!synthesis,!a!major!
626!
metabolic!flux!in!RAW264.7!macrophages!responding!to!a!pathogen,!was!then!simulated!627!
using!constraints!derived!from!both!stoichiometry!of!whole-cell!metabolism!and!logical!rules!628!
within!a!large-scale!regulatory!network.!The!inset!shows!the!conversion!of!logical!hyperedges!629!
determining!the!fate!of!ifn_ab!to!reaction!formulas!with!linear!inhibitor!constraint:!For!all!630!
reactions!producing!ifn_ab,!the!molecule!irf2!is!added,!preceded!by!the!“~”!sign!to!indicate!an!631!
inhibitor.!This!is!parsed!by!MUFINS!to!mean!that!the!reaction!flux!is!inhibited!(i.e.!0)!if!ifr2!is!632!
present.!!
633!

!
26!
!634!
Figure+3.+Mechanistic+interpretation+of+experimental+data+on+perturbation+of+whole-cell+635!
metabolic+function+by+signaling+network+input+and+inhibitor.!MUFINS!was!used!to!636!
integrate!a!genome-scale!metabolic!model!of!the!mouse!macrophage!(RAW264.7)!with!a!
637!
large-scale!regulatory!network.!Perturbation!of!whole!cell!metabolism!was!simulated!through!
638!
activation!and!inhibition!of!the!signaling!network!with!external!production!of!nitric!oxide!set!
639!
as!the!objective!function.!Predicted!data!was!then!compared!to!experimental!data.!A)!The!left!640!
panel!shows!a!screenshot!of!the!JyMet!interface,!demonstrating!on!screen!visualization!of!the!641!
reconstruction,!created!by!automatic!hierarchical!layout!with!manual!adjustment.!Hatched!642!
lines!are!used!to!indicate!regulatory!signals,!representing!inhibition!(circle!end)!or!643!
stimulation!(arrow!head).!The!right!panel!is!a!manually!created!image!representing!the!644!
pathway!examined!through!JyMet;!arrows!represent!signal!flux,!while!open!and!filled!circles!645!

!
27!
represent!inhibition!and!stimulation,!respectively.!The!visualization!depicts!where!signaling!646!
pathways!converge!on!the!iNOS!gene,!which!is!required!for!nitric!oxide!(NO)!production!in!the!647!
whole-cell!stoichiometric!model.!Flux!rates!for!an!example!FBA!solution!are!displayed!on!the!648!
network!diagram;!on!the!right!panel!only!flux!rates!for!each!transitions!are!presented!for!
649!
clarity,!while!the!left!panel!also!shows!the!contribution!of!each!substance!to!the!flux.!B)!The!
650!
original!reconstruction!was!able!to!predict!the!increase!in!NO!production!following!
651!
stimulation!with!LPS,!but!not!the!impact!of!a!MEK!inhibitor,!when!compared!to!experimental!652!
data!of!nitrate!levels!in!RAW264.7!cell-conditioned!medium!(C).!Nitrate!can!only!be!produced!653!
by!non-enzymatic!conversion!of!NO!produced!by!RAW264.7!cells,!and!as!there!is!no!nitrate!654!
consumption!in!the!medium,!nitrate!concentrations!are!proportional!to!nitric!oxide!655!
production!flux.!D)!Refinement!of!the!signaling!network!led!to!agreement!between!in!silico!656!
prediction!and!in!vitro!measurement.!The!refinement!was!based!upon!three!mechanistic!657!
hypotheses:!i)!ERK1/2!is!a!more!potent!transcriptional!activator!of!the!iNOS!gene!than!JNK!
658!
and!HIF1,!and!ii)!MEK1!is!a!more!potent!ERK1/2!kinase!than!PKC.!659!
! !660!

!
28!
!661!
Figure+4.+Multi-formalism+simulation+integrating+cortisol+signaling+with+the+human+662!
Recon2+GSMN+reveals+a+drug+interaction+with+estradiol+clearance.+A)!The!Petri!Net!663!
diagram!of!network!connectivity!created!in!the!Snoopy!editor,!with!overlaid!comments!for!
664!
clarity.!Color!and!symbol!size!has!been!manually!set!to!match!SBGN!molecule!types!and!
665!
transition!types!specific!to!QSSPN.!The!PN!connectivity!to!implement!a!timer!for!
666!
administering!a!network!perturbation!(cortisol!burst),!is!contained!within!a!coarse!transition!667!

!
29!
and!shown!as!an!insert.!!B)!Simulation!of!glucose!and!lactate!dynamics!in!the!blood!668!
physiological!compartment,!demonstrating!a!convergence!to!physiologically!realistic!steady!669!
states.!Perturbation!of!the!system!through!a!simulated!cortisol!infusion!starting!after!500mins!670!
elicits!a!dynamic!alteration!in!the!signaling!network,!resulting!in!(C)!a!predicted!increase!in!
671!
CYP34A!protein!levels,!which!is!confirmed!in!primary!human!hepatocytes.!The!increased!
672!
expression!of!CYP3A4!protein!is!predicted!to!increase!flux!through!reactions!catalyzed!by!this!
673!
enzyme,!leading!to:!(D)!degradation!of!excess!cortisol!and!establishment!of!new!steady!state;!674!
(E)!a!drug-drug!interaction!for!a!second!CYP3A4!substrate!(estradiol),!contained!within!the!675!
GSMN,!leading!to!a!decrease!in!it’s!steady!state!level.!The!predicted!increase!in!CYP3A4!676!
activity!following!cortisol!exposure!is!confirmed!in!primary!human!hepatocytes!(F),!as!is!the!677!
enhanced!rate!of!estradiol!clearance!(G)!!678!
!679!
!
680!
!681!
!682!