EasyModel 1.1: User-friendly Stochastic and Deterministic Simulations

for Systems Biology Models

Jordi Bartolome

1 a

, Rui Alves

2 b

and Francesc Solsona

1 c

Dept. of Computer and Industrial Engineerings, Universitat de Lleida, C/Jaume II 69, Lleida, Spain

Dept. of Basic Medical Sciences, Universitat de Lleida, C/Montserrat Roig 2, Lleida, Spain

Keywords:

Systems, Biology, Model, Simulation, Stochastic, Deterministic, User-friendly, Web, Application,

Mathematica.

Abstract:

EasyModel is a user-friendly web application that uses Wolfram webMathematica for performing simulations

and analysis of systems biology models. EasyModel lets users create new models, load models from the

BioModels database, and import preexisting models from SBML ﬁles. EasyModel mainly targets the student

of bioinformatics or systems biology without the need of having Mathematica programming knowledge. In

addition, expert programmers may ﬁnd it useful as a tool for quickly implementing new models in Mathe-

matica, which can then be downloaded as Mathematica notebooks to be tailored locally for more advanced

simulation and analysis. The version described in this manuscript introduces the stochastic simulation feature.

EasyModel is freely available at https://easymodel.udl.cat

1 INTRODUCTION

Molecular systems biology is a quantitative and inte-

grative discipline. This implies that using software for

mathematical modeling is a required skill for the sys-

tems biologist. Learning to create mathematical mod-

els for molecular systems biology is usually a task

with a slow learning curve, as it requires a signiﬁcant

amount of technical skill.

Currently, there is a considerable array of tools

for modeling and simulating of biological systems

(SBML.org, 2019)(Alves et al., 2006). Most of these

tools are standalone and can be used in a normal

PC. There is a small number of general platforms for

mathematical computation (PMC) such as Mathemat-

ica or Maple that can be adapted for systems biol-

ogy modeling. These platforms offer a wide range of

mathematical solutions, with ﬂexible graphical user

interfaces (GUI). Mathematica and Maple stand aside

from other PMC because they support symbolic anal-

ysis. A drawback of using these and other PMCs is

that the user must become an expert in coding for the

platform. This drawback can be partially overcome

by implementing a user-friendly application that uses

https://orcid.org/0000-0002-4348-9307

https://orcid.org/0000-0002-8112-5184

https://orcid.org/0000-0002-4830-9184

a PMC as the motor for calculations, as other mod-

eling tools have already demonstrated (Peters et al.,

2017)(Helikar et al., 2012)(Benque et al., 2012).

For this reason we designed EasyModel, a web

application for mathematical modeling in systems bi-

ology. It stands out for its user-friendly GUI that is

usable by both beginner and expert users (Bartolome

et al., 2019).

EasyModel 1.0 focused on the simulation of sys-

tems of ordinary differential equations using deter-

ministic algorithms (Ascher and Petzold, 1997). Nev-

ertheless, when the systems being modeled are com-

posed of a small number of molecules, stochas-

tic algorithms are more accurate (Maarleveld et al.,

2013), and linear noise analysis is a more appropri-

ate tool than sensitivity analysis to understand the

limitations and regulation of the system (Paulsson,

2004). While stochastic simulation and linear noise

analysis are available in several simulation applica-

tions (SBML.org, 2019)(Maarleveld et al., 2013)(Bal-

let et al., 2016), they lack the usability characteristics

EasyModel provides to new systems biologists. Be-

cause of the importance of stochasticity in molecular

systems biology, it is important that EasyModel also

provides this functionality to its users. Hence, this

manuscript describes the prototype for the next pro-

duction version of EasyModel. This prototype, which

we call EasyModel 1.1, enables a user-friendly sim-

Bartolome, J., Alves, R. and Solsona, F.

EasyModel 1.1: User-friendly Stochastic and Deterministic Simulations for Systems Biology Models.

DOI: 10.5220/0008966001450149

In Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 3: BIOINFORMATICS, pages 145-149

ISBN: 978-989-758-398-8; ISSN: 2184-4305

145

ulation and analysis of stochastic models in systems

biology.

2 EasyModel

2.1 Origin and Objectives

Wolfram Mathematica provides many ready-to-use

mathematical functions that are perfectly suited for

simulating and analyzing mathematical models of bi-

ological systems. Nevertheless, its use requires that

one knows how to create models for systems biology

and how to program in the Mathematica language.

This makes Mathematica less than ideal for use by be-

ginners and students of systems biology. EasyModel

is a web application that was created for facilitating

the use of Wolfram Mathematica for modeling by be-

ginner computational systems biologists, waiving the

need to know how to program in Mathematica or de-

velop mathematical models from scratch. Overall, our

application provides a user-friendly interface that al-

lows users to input the information for creating mod-

els in a simple way. Afterwards, it formats, wraps,

and processes the information to create a Mathemati-

cal notebook and conﬁgure the simulation and analy-

sis. This notebook is then sent to a webMathematica

engine that performs the calculations. webMathemat-

ica returns the output in graphical and text form and

our GUI picks up that information and provides it to

the user.

2.2 EasyModel Working Context

EasyModel uses a conceptual representation of

molecular biology networks and transforms that rep-

resentation into systems of autonomous ordinary dif-

ferential equations (ODE) that can be used to simulate

the dynamic behavior of the network. The networks

are represented in terms of individual processes or re-

actions that consume substrates, generate products,

and whose reaction rate can be modulated by modi-

ﬁers (activators or inhibitors). The rate of each reac-

tions is described by a kinetic function that depends

on some of the species in the networks and on reac-

tion speciﬁc parameters. The integration of all these

elements conforms a mathematical model of the bio-

logical network of interest (Figure1).

Users provide the program with the individual

processes using the following notation:

∗ S

+ ...− > C

∗ P

+ ...;M

;... (1)

In Equation 1 K

represent the species coefﬁcients,

represents the substrates (left-hand side of the ar-

row), P

represents the products (right-hand side of

the arrow), and M

represents modiﬁer species that

inﬂuence the rate but are not substrates.

After the structure of the model is deﬁned through

its processes, a kinetic rate law needs to be associated

to each of the reactions. These rate laws are standard

mathematical functions that depend on a subset of the

network species and on parameters whose values are

speciﬁc for each reaction. EasyModel allows users to

select rate laws with a predeﬁned formalism (Power

Law, Mass Action, Saturating and cooperative (Sor-

ribas et al., 2007) or create custom made formulas.

2.3 Usage and Features

In the initial page of the web application, the visitor

can log in as a registered user or try the application as

a guest user. Guest users are provided with a brief tu-

torial on how to use EasyModel before accessing the

application itself. The tutorial can be skipped and it

is always available to consult in the Tools option. In

addition to the the tutorial, the application has Infor-

mation buttons all across the GUI so that users can

consult what to do next at each step.

The application is designed in 4 basic steps:

1. Select the model (or create a new one)

2. Modify or build the model

3. Conﬁgure the simulation/s

4. Get the simulation results

In step one, users must select a model repository:

public or private (see Figure 2). The public reposi-

tory includes built-in models. Many of these are ei-

ther from the BioModels Database (Le Nov

ere et al.,

2006) or developed and published by the other users

of the platform. The private repository permits users

to create new models or continue editing unﬁnished

models. Guest users can create new models to use but

they cannot be saved in the system. They can how-

ever download them in SBML form and re-upload

again at a later time by importing the SBML ﬁle. In

fact EasyModel complies with SBML (Hucka et al.,

2003) Level 3 Version 2 speciﬁcation and it can up-

load models described with that speciﬁcation. SBML

facilitates the interchange of biologic system models

between many available modeling tools.

Model building in step two requires deﬁning the

individual reactions of the model (see Figure 3), as

well as the rate laws (see Figure 4). Users can either

select a predeﬁned rate law or deﬁne a new one as

a standard mathematical function. Each reaction of

the system must have an assigned rate law, with its

set of parameter values. The parameters may have a

BIOINFORMATICS 2020 - 11th International Conference on Bioinformatics Models, Methods and Algorithms

146

Figure 1: Biological system model BIOMODEL003 (Goldbeter, 1991).

Figure 2: Selecting model.

Figure 3: Modeling the reactions.

numerical value or be linked to a substrate or modiﬁer

species of the network.

Initial concentrations of the system species must

be speciﬁed as well. If not, EasyModel automatically

sets them to 1.

To proceed to step three, EasyModel must validate

the model, warning the user if additional information

or modiﬁcations are required.

In step three, and after model validation, users

deﬁne what simulations and analyses are to be per-

formed in webMathematica (see Figure 5).

During the simulation conﬁguration step, users

Figure 4: Deﬁning the rate laws.

Figure 5: Stochastic simulation conﬁguration.

can choose whether they will perform a determinis-

tic simulation (if the system has a large number of

molecules) or a stochastic simulation. This later type

of simulation is a new feature of the version being de-

scribed here.

For deterministic simulations, the user may per-

form time course and steady state simulations, as well

as sensitivity analysis with respect to model param-

eters and independent variables. Sensitivity analysis

can be requested for steady state and time-course sim-

ulations. A linear stability analysis of steady states

can also be performed.

EasyModel 1.1: User-friendly Stochastic and Deterministic Simulations for Systems Biology Models

147

Figure 6: Stochastic simulation results.

For stochastic simulations, users deﬁne the phys-

ical size of the system, how many times they want to

repeat the simulation and how long the system is to

be simulated. EasyModel also provides the intrinsic

noise of the system for each dependent variable by

calculating the coefﬁcient of variation and the quar-

tile coefﬁcient of dispersion for each species. Default

cell size is considered by the program to be that of

Prokaryotic cell. Default number of repeat simula-

tion is set to 3. Default end time of the simulation is

set to 10 time units.

Once all actions are conﬁgured, the user presses

the simulation button and the program goes to step

four. In this step all the data is sent to the web-

Mathematica calculation engine (Mathematica ker-

nel), which performs the simulation and returns the

results to the user. Individual results are returned im-

mediately after being computed, in real-time (see Fig-

ure 6). Results are represented in plots and tables that

can be downloaded. The user can cancel the simu-

lation at any time and the system will stop after the

execution of the webMathematica command that was

being evaluated before pressing the button. In ad-

dition to the graphical representation of the results,

users may also download the generated Mathematica

notebook and the model in SBML format.

EasyModel stores user account information as

well as the the models and rate laws the users intro-

duce into the system. Simulation results are not stored

into the database.

2.4 Implementation

EasyModel is implemented by merging various tech-

nologies. The web application is written in Java EE,

using the open-source Vaadin 8 Framework for devel-

oping the web user interface (UI). The calculation en-

gine is the Wolfram webMathematica (Wolfram Re-

search Inc., 2108), which communicates with the Java

EE application. User data, such as user account, mod-

els and rate laws, is stored in a database using the

open-source MySQL 8 Community Server database

manager. Finally, the web application is deployed on

the Apache Tomcat 9 web application server.

To implement the SBML ﬁle format compatibility,

JSBML Java library (Dr

ager et al., 2011) is used.

The source code is available at

https://github.com/jordibart/easymodel and licensed

under the GNU GPL. All the dependencies of Easy-

Model are open-source except for webMathematica,

which requires a commercial license.

3 CONCLUSIONS

EasyModel is a user-friendly tool for creating and

analyzing simple mathematical models of biological

networks in systems biology. While it is aimed at

novel systems biologists and students, the tool can

also be of proﬁt for more advanced researchers, as

they can quickly implement their models and down-

load them for further local tailoring for more ad-

vanced analysis.

While the production version of EasyModel is

limited to deterministic simulation and analysis, here

BIOINFORMATICS 2020 - 11th International Conference on Bioinformatics Models, Methods and Algorithms

148

we present an evolution of the tool that enables

stochastic simulations and biological noise analysis

in the context of those simulations. Stochastic simula-

tions are signiﬁcantly more complex in computational

terms and require longer CPU times to conclude than

analogous deterministic simulations. Nevertheless,

this type of simulations accurately describes the dy-

namic behavior of systems with a small number of

molecules, something that deterministic simulations

can not always do.

This new prototype of EasyModel 1.1 is now be-

ing tested before it is rolled out to replace the cur-

rent 1.0 production version. Once this task is done

we will implement additional functionality to enable

user-friendly ways to merge individual models, to

scan parameter values and independent variables, and

to perform bifurcation analysis.

ACKNOWLEDGEMENTS

This work was partially supported by Minis-

terio de Economia, Industria y Competitividad

[TIN2017-84553-C2-2-R]; Ministerio de Educacion

[PRX18/00142]; and by Bridge Grants from Univer-

sitat de Lleida and INSPIRES.

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