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ISSN 2079-0597, Russian Journal of Genetics: Applied Research, 2016, Vol. 6, No. 8, pp. 845–853. © Pleiades Publishing, Ltd., 2016.
Original Russian Text © A.I. Klimenko, Z.S. Mustafin, A.D. Chekantsev, R.K. Zudin, Yu.G. Matushkin, S.A. Lashin, 2015, published in Vavilovskii Zhurnal Genetiki i Selektsii,
2015, Vol. 19, No. 6, pp. 745–752.
A Review of Simulation and Modeling Approaches in Microbiology
A. I. Klimenkoa, b, *, Z. S. Mustafina, A. D. Chekantseva, b, R. K. Zudina, b,
Yu. G. Matushkina, and S. A. Lashina, b
aInstitute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences,
pr. Akad. Lavrentyeva 10, Novosibirsk, 630090 Russia
bNovosibirsk National Research State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
*e-mail: klimenko@bionet.nsc.ru
Received September 25, 2015; in final form, October 10, 2015
Abstract⎯Bacterial communities are closely interrelated systems consisting of numerous species making it
challenging to analyze their structure and relations. At present, there are several experimental techniques pro-
viding heterogeneous data, concerning various aspects of this research object. The recent avalanche of avail-
able metagenomic data challenges not only biostatisticians but also biomodelers, since these data are essential
for improving the modeling quality, while simulation methods are useful for understanding the evolution of
microbial communities and their function in the ecosystem. An outlook on the existing modeling and simu-
lation approaches based on different types of experimental data in the field of microbial ecology and environ-
mental microbiology is presented. A number of approaches focused on the description of microbial commu-
nity aspects such as trophic structure, metabolic and population dynamics, genetic diversity, as well as spatial
heterogeneity and expansion dynamics, are considered. We also propose a classification of the existing software
designed for the simulation of microbial communities. It has been shown that, in spite of the prevailing trend for
using multiscale/hybrid models, the integration between models concerning different levels of biological orga-
nization of communities still remains a problem to be solved. The multiaspect nature of integration approaches
used for modeling microbial communities is based on the necessity of taking into account the heterogeneous
data obtained from various sources by applying high-throughput genome investigation methods.
Keywords: microbial communities, ecological simulation, evolutionary modeling, prokaryotes
DOI: 10.1134/S2079059716070066
Microorganisms can form diverse communities,
with their structure and function dynamically varying
in response to environmental changes. The examples
of such communities are biofilms and bacterial mats
(Karunakaran et al., 2011), as well as the communities
inhabiting, e.g., human intestines (Chewapreecha, 2013)
or mouth cavity (Salli and Ouwehand, 2015). Being a
complex adaptive system, the microbial community
demonstrates higher-order properties which are
absent in individual microbes but emerge as a result of
interactions between them. As has been mentioned in
the article of Comolli (2014), the complex interactions
between the cells of microbial community, inter alia,
between the cells of different species, which include
trophic, physical, and even informational (e.g., quo-
rum sensing) factors, play a key role in the function of
this community as a single unit, a holobiont.
In recent years, there have been numerous works
on the simulation of various aspects of vital activity of
bacteria. Some articles are devoted to the biological
aspects of modeling such as the relationship between
the individual and population growth of bacterial cells
(Kutalik et al., 2005), the ability of a system to main-
tain its biological diversity with different fitness land-
scapes and mutation rates (Beardmore et al., 2011). In
other articles, different techniques of computer simu-
lation were considered (Song et al., 2014), with the
assessment of the expediency, as well as the pros and
cons, of using individual-oriented modeling instead of
the classical methods (DeAngelis and Mooij, 2005;
Grimm et al., 2006) or cellular automata (Esteban and
Rodríguez-Patón, 2011).
The predictive mathematical and computer models
would not only contribute to understanding the fun-
damental laws underlying the dynamics and synergetic
properties of natural and synthetic microbial commu-
nities but also be of practical interest for their applica-
tion in the problems of gene engineering. We would
particularly like to mention the fact that there are sev-
eral biological peculiarities of microbial communities
making them highly complex objects to be studied in
vitro: the presence of uncultivated species, physical
dimensions of communities, and difficulties in repro-
ducing the spatial structure and other physical param-
eters of the community habitat under laboratory con-
ditions. Accordingly, verification of the mathematical
and computer simulation models of natural communi-
ties is associated with the problems of searching for
846
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KLIMENKO et al.
qualitative experimental data, which in some cases are
unsolvable in principle. For the solution of such prob-
lems, we propose to create a series of artificial micro-
bial communities, with the simultaneous construction
of a mathematical model for each of them, which then
would be verified by the experimental data obtained in
the study of these communities (De Roy et al., 2013;
Wolfe and Dutton, 2015). At the same time, there is a
wide range of experimental techniques that could be
used in this approach (Kolmakova, 2013), in particu-
lar, in vitro cultivation, microscopy, in situ monitoring
and sampling, high-performance sequencing and
metagenomics, metatranscriptomics, metaproteom-
ics, and metabolomics. It is notable that one of the
means for designing such synthetic communities is the
methods of mathematical and computer simulation
modeling (Wolfe and Dutton, 2015). Larsen et al.
(Larsen et al., 2012) considered different approaches
to simulation modeling in relation to the study of the
microbial environmental interactome (MEI). As is
shown, MEI can be described using three parametric
spaces: environmental parameters, microbial commu-
nity structure, and environmental metabolome. At the
same time, the relationships between different pairs of
these spaces can be described by the respective tech-
niques.
In addition to numerous models designed for
describing the particular aspects of the functioning of
microbial communities, currently we have a number of
computer tools for modeling spatially distributed bac-
terial communities. Most of them, e.g., UMCCA cel-
lular automata (Laspidou and Rittmann, 2004), as well
as the hybrid modeling computer systems AQUASIM
(Wanner and Morgenroth, 2004; Mburu et al., 2014)
and INDISIM (Ginovart et al., 2002), underline the
importance of a detailed description of the spatial
structure of the communities. Other models are con-
centrated on describing how the processes of genetic
variability can influence the spatial structure of a com-
munity, such as AEvol (Knibbe et al., 2008; Beslon
et al., 2010); however, they do not describe the spatial
structure of communities thoroughly enough.
Here, the methods of modeling microbes and
microbial communities are reviewed. The models
describe both the separate levels of their biological
organization and several such levels at a time. The lat-
ter models help revealing the regularities of the evolu-
tion of the microbial communities which appear at the
genetic level and subsequently spread to all other levels
of microbial community functioning.
Methods for Modeling Different Levels
of the Biological Organization
of a Microbial Community
At present there are a number of methods and soft-
ware tools for modeling microbial communities,
which are focused on different aspects of their vital
activity. Though these aspects are so deeply inter-
twined in living organisms that it is sometimes difficult
to separate them; however, it has to be done because
different description and simulation methods should
be used for different processes. Let us consider these
aspects as they are usually distinguished in modeling:
Ecological structure of a community. The ecological
structure of a community implies, first of all, the rela-
tionships between the species. It is described by any
kinds of reconstruction of biological networks: non-
linear regression, production methods, etc.
Metabolic and population dynamics. The widely
used methods in this field are ordinary differential
equations (ODEs), algebraic and difference equa-
tions, Boolean functions, matrix models, thermody-
namic stochastic simulation, etc.
Genetic diversity. The genetic diversity is described
by discrete (dynamic equations for allele frequencies)
and stochastic models, as well as individually oriented
approaches.
Spatial heterogeneity and dynamics. This category
includes the heterogeneous distributions of cells, sub-
strates, and metabolites; the patterns of these distribu-
tions; the spatially-specific interaction between the
species and habitat; cell motility; and migrations. The
methods used for simulating spatial heterogeneity and
dynamics are partial differential equations (PDEs),
cellular automata, agent-based modeling, network
and population balance models (partial integro-differ-
ential equations), etc.
Reconstruction of the Ecological Structure
of a Community
The reconstruction of ecological relationships
within a community to determine its trophic organiza-
tion (the network of metabolic connections between
the species) is one of the first stages of analysis of this
community. The methods of metagenomics and bio-
informatics make it possible to identify the types of
community members and to assess their relative den-
sities, as well as functional abilities (Wooley et al.,
2010). The appearance of large amounts of metage-
nomic data resulted in the development of methods for
the reconstruction of the trophic networks of commu-
nities based on this information (Faust and Raes, 2012).
As a rule, these are regression and production methods,
as well as dynamic simulation (Zomorrodi et al., 2014)
and stoichiometric approaches to the calculation of
the exchange of metabolites (Klitgord and Segre,
2010). These methods are used to assess the ecological
relationships within a community, including those
depending on the parameters of the habitat. Microbial
relations can be reconstructed by the data on popula-
tion densities. Based on the traditional perception, the
relationship within a pair of organisms can be referred
to as competitive (or negative) if their densities are
anticorrelated in all samples, in spite of the fact that
they possess a common ecological niche, or, on the
RUSSIAN JOURNAL OF GENETICS: APPLIED RESEARCH Vol. 6 No. 8 2016
A REVIEW OF SIMULATION AND MODELING APPROACHES 847
contrary, as cooperative (or positive) if they demon-
strate similar density distributions. The network of
microbial interrelationships can be predicted using the
network reconstruction methods. Pairwise relation-
ships are derived by the methods based on similarity,
by the analysis of the distribution of the mutual occur-
rence/exclusion of two species based on the sum of the
points of similarity. A complex relationships between
more than two species can be fixed by other tech-
niques such as regression and production methods.
Regression methods represent the density of a partic-
ular species as a function of the densities of other spe-
cies. Production methods initially enumerate all of the
logically possible rules of a species’ coexistence/exclu-
sion supported by the set of data on their presence or
absence. Only significant rules are retained during the
serial filtration process. The work (Faust and Raes,
2012) presents a comprehensive review of this subject.
The established relationships between member
species can be presented as a network of microbial
interrelationships consisting of vertexes (species or
taxa) and edges (interspecies interactions). Since the
relationships between species are often asymmetrical;
i.e., the presence of one species may influence the pop-
ulation of the other one, but not vice versa, this network
is a tentative graph. The direction and force of microbial
interaction can be represented as an arrow of the
respective thickness. Environmental variables can also
be incorporated into the network by their interpretation
as additional species–vertexes. This expanded network
describes the relationships between the species and
environmental characteristics. For example, the con-
sistent cooccurrence of particular species and nutri-
ents (e.g., nitrites and nitrates) is evidence of the
involvement of special microbes in biogeochemical
cycles (Fuhrman, 2009).
Thus, microbial relations can be systemically
reconstructed by the data on species density. The rela-
tionships between the microbes obtained thereby are
condition-specific. It means that the information
about the relationships between microbial species
obtained under certain conditions may be invalid
under other conditions, because the structure and
properties of the networks of the relationships between
microbes may change considerably depending on the
environmental conditions. In addition, these methods do
not suggest any biological causes of the presence of spe-
cific interactions between some species and their absence
between other species. A more mechanistic comprehen-
sion would require physiology-based methods such as
stoichiometric modeling.
Modeling Metabolism and Genetic Regulation
Microbial metabolism is modeled by a wide range
of mathematical methods, including differential equa-
tions (ordinary and partial), Boolean networks and
Petri nets, linear and nonlinear algebraic equations,
and cellular automata. The modeling of a metabolism
is often associated with the modeling of genetic regu-
lation (De Jong, 2002; Hecker et al., 2009; Likhoshvai
et al., 2010). Here, the concept of gene networks plays
an integrating role. Such models usually described a
separate metabolic subsystem of a microbial cell,
probably, with concomitant genetic regulation (Covert
et al., 2001; Likhoshvai and Ratushny, 2007; Ober-
hardt et al., 2009). However, since the late 20th–early
21st century there have been attempts at creating a
complete model of cell metabolism, the E-cell models
(Tomita et al., 1999; Tomita, 2001; Ishii et al., 2004;
Price et al., 2004; Sauer et al., 2007; Durot et al.,
2009). In 2012, Karr et al. reported that their E-cell
model predicted the phenotype from the genotype
data (Karr et al., 2012).
Recently, one of the methods widely used for the
modeling cell metabolism (the dynamic analysis of
stationary flows) had been extended in the event of
modeling microbial communities (Mahadevan and
Henson, 2012; Henson and Hanly, 2014). In addition,
the commonly used methods are optimization tech-
niques such as minimization of the metabolic adjust-
ment (MOMA) (Segre et al., 2002), as well as the
methods involving multiobjective optimization (see
Zomorrodi and Maranas, 2012; Zomorrodi et al.,
2014), which allow researchers to use the community-
level fitness criteria. In addition, metabolism is simu-
lated using elementary mode (EM) analysis (Schuster
et al., 2000) and evolutionary game theory (EGT)
(Pfeiffer and Schuster, 2005; Frey, 2010).
Spatial Heterogeneity and Population Dynamics
of Microbial Communities
Another aspect of the vital activity of the microbial
community, which is a subject of both experimental
and theoretical studies, is population dynamics, i.e.,
the changes in the size of populations comprising a
community over time or in the generation series. In
the simplest case, the models of uniformly mixed
homogenous environments are considered. The math-
ematical models of microbial populations date back to
the works of J. Monod, who proposed the theory of the
chemostat (cultivator) and the model of the microbial
population in the cultivator with one substrate, when
the cell growth rate depends on its concentration
(Monod, 1950; Riznichenko and Rubin, 1993). A more
realistic formula has been proposed for the cell growth
rate function based on the principle of limiting factors in
the enzymatic processes formulated by N.D. Ieru-
salimsky (Chernavsky and Iyerusalimsky, 1965), which
takes into account, in addition to the substrate concen-
tration, the inhibitory effects of the metabolic products of
microbial cells and is known as the Monod–Ieru-
salimsky formula (Riznichenko and Rubin, 1993). The
continuous-time age-structured model of the micro-
bial population, which operates not with the popula-
tion group sizes but with the continuous age density
function, was obtained by McKendrick in 1926 and
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KLIMENKO et al.
then rediscovered by Von Foerster in 1959
(Riznichenko, 2003). The matrix models of the dynam-
ics of the population structure (e.g., age-related), pro-
posed for the first time by P. Leslie (Leslie, 1945), were
studied in detail in the works (Himmelfarb et al., 1974)
(Logofet and Belova, 2007).
However, in spite of the fact that the assumption of
uniform mixing is suitable in the context of numerical
studies and widely used, it is weakly correlated to most
observations of real biological systems, where the
nutrient, light, and metabolite gradients play a key role in
community structuring (Wimpenny et al., 2000). There-
fore, the spatial heterogeneity and dynamics is another
field of research, where the methods of mathematical
modeling and computer simulation are useful.
The application of models in the formalism of par-
tial equations is one of the conventional approaches in
the description of spatial heterogeneity and the study
of the distribution patterns formed in the system. One
of the first cases of using this technique in theoretical
biology studies was the famous work of A.M. Turing,
(Turing, 1952), where he proposed a reaction–diffu-
sion model capable of reproducing the nontrivial pat-
terns of the spatial distribution in the simple synthesis
systems connected by activation/inhibition relation-
ships and spreading in space by diffusion. The flow-
through systems are described using the Navier-Stokes
equations of classical hydrodynamics (Lencastre Fer-
nandes et al., 2011), which are also partial differential
equations.
There are a number of approaches allowing the
description of not only spatial heterogeneity but also vari-
ability within populations. One of these approaches is to
use the population balance models (Ramkrishna, 2000).
Mathematically, these models are partial integro-dif-
ferential equations describing both the spatial coordi-
nates and internal characteristics of an object, such as
cell mass, age, and morphology. The individual-ori-
ented models also make it possible to combine the
description of the spatial distribution with the internal
characteristics of the modeled objects. In the models
of this type, the spatial heterogeneity is described by
patches (Stauffer et al., 2005) of a square lattice or grid
cells of the respective dimensions (Klimenko et al.,
2015). Other methods used for describing spatial het-
erogeneity include cellular automata (Wimpenny and
Colasanti, 1997) and the methods of graph theory
(O’Donnell et al., 2007). The description of the motil-
ity of organisms is closely related to the problem of the
spatial dynamics of microbial communities. It is
known that a considerable number of bacterial species
can actively move in the environment towards nutri-
ents or better habitation conditions (Adler, 1976). As a
rule, microorganisms move by using f lagella (Hen-
richsen, 1972) or other mechanisms such as special
proteins localized on the membrane (e.g., Flavobacte-
rium johnsoniae) (Shrout, 2015) and cilia allowing the
Oscillatoria princeps cells to slide (Halfen and Casten-
holz, 1971), or they move by changing their surface
tension due to surfactant secretion (as representatives
of the species M. xanthus do), etc. The ability to move
in accordance with the gradients of certain ecological
factors is called taxis (e.g., chemotaxis, phototaxis,
etc.) (Netrusov and Kotova, 2007). The detailed
review of the mathematical approaches used for the
simulation of bacterial chemotaxis is presented in the
works (Tindall et al., 2008a, 2008b). For the microbial
communities distributed in the one-dimensional
space, the population equation describing both ran-
dom and chemotactic movements can be presented in
the form known as the Keller–Siegel model of chemo-
taxis (Tindall et al., 2008b).
In the work (Emonet et al., 2005) they presented a
software tool for studying the effects of stochastic fluc-
tuations in cell–cell interactions on the behavior of
individual cells. The AgentCell multiagent software sys-
tem was developed to simulate the chemotactic
response of the free E. coli cells to the gradients of che-
moattractants in a 3D environment. In this model, each
bacterial cell is an independent agent possessing its own
gene network of chemotaxis, molecular motors, and a
flagellum. The Morton–Firth and Korobkova model of
the gene network of chemotaxis was used. The input
parameter of the network model was receptor employ-
ment (the probability of receptor binding with the
ligand) corresponding to the nutrient concentration in
the medium. The output network parameter was the
number of molecules of the chemotaxis response reg-
ulator CheY-P in the cell. The chemotactic response of
free-floating bacteria to the linear concentration gra-
dient was modeled for verification. The modeling
results are in agreement with the experimental data
obtained for individual cells and the cells taken from
the bacterial population (Emonet et al., 2005).
Another example of using an individually oriented
approach for the simulation of bacterial cell motility is
the work of B. Niu et al. (Niu et al., 2013). They mod-
eled the processes of chemotaxis by comparing the
results of bacterial behavior in a 3D environment with
and without quorum sensing. The authors considered
different strategies of information exchange between
the cells of the bacterial population and evaluated their
efficiency in achieving the global optimum. According
to their results, the cells of the population attain the
most favorable conditions by the most intensive com-
munications involving both individual and intergroup
mechanisms of information exchange.
Problems of Integration and Multilevel Approaches
to the Simulation of Microbial Communities
One of the most pressing problems in the modeling
of microbial communities is the problem of integrating
various simulation techniques within a single study.
The review (Song et al., 2014) presents the following
classification of model integration strategies: (1) infor-
mation feedback; (2) indirect coupling; and (3) direct
RUSSIAN JOURNAL OF GENETICS: APPLIED RESEARCH Vol. 6 No. 8 2016
A REVIEW OF SIMULATION AND MODELING APPROACHES 849
coupling. Information feedback is the weakest form of
integration: in this case, the results of the upper model
layer are used to adjust the assumptions underlying the
independent lower model level. Indirect coupling is a
conveyer where the results of one model are conveyed
to the input of another independent model (Scheibe
et al., 2009). Direct coupling implies a degree of integra-
tion when different simulation techniques are merged
into a single system. In multilevel modeling (with direct
coupling, according to Song), the individually ori-
ented techniques are more advantageous than their
analogs due to the flexibility and ability to integrate
various methods as submodels of a single simulation
system. For example, this conception was successfully
used in the work (Rudge et al., 2012) for the combined
simulation of intracellular dynamics, intercellular sig-
naling, and cellular biophysics of bacterial cells form-
ing a biofilm. The authors solve the problem of the in
silico prediction of the behavior of synthetic biofilms
prior to their formation in vitro. At the same time, par-
ticular emphasis is placed on the emergent properties
demonstrated by the thousands of growing and signal-
exchanging bacterial cells, since these properties are of
key significance for designing synthetic biofilms.
The methods of individually oriented modeling
have become widespread due to the development of
computer technologies (DeAngelis and Mooij, 2005).
In the this approach, populations are modeled as sys-
tems consisting of agents, which are individual organ-
isms or groups of similar organisms with the set of
characteristics varying between the agents. At the
same time, each agent has its own unique history of
interactions with the environment and with other
agents. Individually oriented modeling is extensively
used in ecological modeling, social dynamics, and
evolutionary process modeling. These models are used
to investigate how the behavior of separate individuals
obeying local rules leads to the formation of complex
patterns, including spatially distributed ones, e.g., fish
shoals, flocks of birds, and insect swarms (DeAngelis
and Mooij, 2005).
The advantage of this approach is the maximally
flexible representation of the diverse characteristics of
an individual and, on the other hand, the explicit
description of interactions between separate organ-
isms at a micro level.
The main disadvantages of the method of individ-
ually oriented modeling are that it requires a large
amount of experimental data for the detailed descrip-
tion of the biological objects and has a high computa-
tional complexity. Laborious calculations impose cer-
tain restrictions on the sizes of the modeled communi-
ties. There are two basic approaches to reducing the
computational load: (1) limitation of the computa-
tional domain by a small-scale representative space
and (2) application of the concept of super individuals.
For example, it is possible to reduce the number of
modeled cells by concentrating on a small area of a
biofilm or a lake. Scaling to a larger space based this
approach becomes difficult in the case of a significant
spatial heterogeneity in the systems. At present, the
individually oriented modeling of microbial commu-
nities is confined to the range from micrometers to
centimeters (Tang and Valocchi, 2013). As an alterna-
tive, the modeling can be based on super individuals
being a group of separate cells (Scheffer et al., 1995).
In this case, there is a problem of the consistent deter-
mination of super individuals for the given system
under study, because the determination of super indi-
viduals in a way so that they contain a large number of
cells eventually weakens the inherent strength of indi-
vidually oriented modeling, which can explain the
dynamics of each individual cell. The classification of
the existing software tools for modeling microbial
communities is given in the table.
Another peculiarity resulting from the multiaspect
nature of these integration approaches is the necessity
of taking into account the heterogeneous data
obtained from various sources by high-performance
experimental methods of studying the genome, tran-
scriptome, proteome, and metabolome of a commu-
nity. Next-generation sequencing, mass spectrometry,
and other high-performance methods generate huge
arrays of experimental data providing information
about the genetic structure of a community, species
representation, the expression of particular functional
groups of genes, etc. Therefore, consideration of this
information layer in the existing techniques of model-
ing the microbial community is a pressing problem.
Recently, large amounts of metagenomic data have
become the basis for extensive biostatistical analysis by
the methods of assessing the biodiversity and species
richness of a community, dimensionality reduction
techniques, dispersion analysis, linear regression, etc.
Although these methods help the researcher arrive at
particular hypotheses concerning the internal struc-
ture of the research objects, they can neither reveal the
mechanism nor determine the cause-and-effect rela-
tionships underlying the concept of the microbial com-
munity. For this purpose, one can use the methods of
mathematical modeling and computer simulation
capable of not only predicting the behavior of the bio-
logical systems but also revealing the knowledge gaps,
which is necessary for their reconstruction in silico.
This work has shown that one of the trends in the
development of this field of research is the combina-
tion of different approaches to simulation in the hybrid
or multilevel models, which provides a more compre-
hensive knowledge of the biological systems such as
microbial communities. However, there are a number
of problems associated both with the interlevel inte-
gration of the models and with the integration of the
data from heterogeneous sources. In spite of all these
difficulties, there is no doubt that researchers will
overcome them and take the modeling of prokaryotic
communities to the next level.
850
RUSSIAN JOURNAL OF GENETICS: APPLIED RESEARCH Vol. 6 No. 8 2016
KLIMENKO et al.
Comparison of different software tools for the modeling of bacterial communities
Software (literature
source); Modeling unit Population size Genetic diversity Spatial distribution Range of tasks Documentation Supported
platforms
AgentCell (v. 2.0)
(Emonet et al.,
2005)
Cell Several thou-
sands of cells
Only Escherichia
coli
The cells move
in a 3D space with
a given gradient of
attractants
Calculation of chemotactic
cell response to the gradient
of attractants
in a 3D environment
There is an
instruction for
installing on Linux
Linux
AQUASIM (Wan-
ner, Morgenroth,
2004)
Compartment Determined by
biofilm thick-
ness in meters
Allows the model-
ing of multispecies
reactors but
excludes genetic
variability during
the modeling
Exists (with due
account to differ-
ent topologies of
connection
between compart-
ments and mem-
branes);
Modeling of bacterial bio-
films in aqueous ecosystems.
Allows model sensitivity
analysis and parameter esti-
mation
There is a User’s
Guide and deliv-
ery with support
Windows,
Linux, MacOS
INDISIM (Gino-
vart et al., 2002)
Cell, super
individual
Millions of cells Maintains individ-
ual diversity of cells
but excludes genetic
variability during
the modeling
Exists (a square
grid of cells)
Study of biomass distribu-
tion within a colony; rela-
tionships between colony
growth rate and concentra-
tions of nutrients, as well as
ambient temperature;
metabolite fluctuations in
bioreactors
–Windows
Haploid evolution-
ary constructor
(Klimenko et al.,
2015)
Metabolically
homogenous
population
More than a bil-
lion of cells
Total support of
genetic diversity
and variability,
right up to species
formation
Exists (a square
grid of cells)
Evolutionary and ecological
modeling; study of interac-
tions between population-
genetic, spatial factors and
the trophic structure of eco-
system and their inf luence
on the evolution of micro-
bial community
Documentation is
available at the web
site
Windows, Linux
RUSSIAN JOURNAL OF GENETICS: APPLIED RESEARCH Vol. 6 No. 8 2016
A REVIEW OF SIMULATION AND MODELING APPROACHES 851
ACKNOWLEDGMENTS
The work was partially supported by budget project
VI.61.1.2 and by the Russian Foundation for Basic
Research, grant no. 15-07-03879.
REFERENCES
Adler, J., Chemotaxis in bacteria, J. Supramol. Struct., 1976,
vol. 4, pp. 305–317. doi 10.1146/annurev.bi.44.070175.002013
Beardmore, R.E., Gudelj, I., Lipson, D.A., and Hurst, L.D.,
Metabolic trade-offs and the maintenance of the fittest and
the f lattest, Nature, 2011, vol. 472, pp. 342–346. doi 10.1038/
nature09905
Beslon, G., Parsons, D.P., Sanchez-Dehesa, Y., and
Knibbe, C., Scaling laws in bacterial genomes: A side-effect
of selection of mutational robustness?, Biosystems, 2010,
vol. 102, pp. 32–40. doi 10.1016/j.biosystems.2010.07.009
Chernavskii, D.S. and Ierusalimskii, N.D., On the question
of the defining link in the system of enzymatic reactions,
Izv. Akad. Nauk SSSR, Ser. Biol., 1965, vol. 5, pp. 665–672.
Chewapreecha, C., Your gut microbiota are what you eat,
Nat. Rev. Microbiol., 2013, vol. 12, p. 8. doi 10.1038/nrmicro3186
Comolli, L.R., Intra-and inter-species interactions in
microbial communities, Front. Microbiol., 2014, vol. 5,
pp. 1–3. doi 10.3389/fmicb.2014.00629
Covert, M.W., Schilling, C.H., Famili, I., Edwards, J.S.,
Goryanin, I.I., Selkov, E., and Palsson, B.O., Metabolic
modeling of microbial strains in silico, Trends Biochem.
Sci., 2001, vol. 26, pp. 179–186. doi 10.1016/S0 968-
0004(00)01754-0
De Jong, H., Modeling and simulation of genetic regulatory
systems: A literature review, J. Comput. Biol., 2002, vol. 9,
pp. 67–103. doi 10.1089/10665270252833208
De Roy, K., Marzorati, M., Van den Abbeele, P., Van de
Wiele T., and Boon, N., Synthetic microbial ecosystems:
An exciting tool to understand and apply microbial commu-
nities, Environ. Microbiol., 2013, vol. 16, pp. 1472–1481.
doi 10.1111/1462-2920.12343
DeAngelis, D.L. and Mooij, W.M., Individual-based mod-
eling of ecological and evolutionary processes 1, Annu. Rev.
Ecol. Evol. Syst., 2005, vol. 36, pp. 147–168. doi 10.1146/
annurev.ecolsys.36.102003.152644
Durot, M., Bourguignon, P.-Y., and Schachter, V.,
Genome-scale models of bacterial metabolism: Recon-
struction and applications, FEMS Microbiol. Rev., 2009,
vol. 33, pp. 164–190. doi 10.1111/j.1574-6976.2008.00146.x
Emonet, T., Macal, C.M., North, M.J., Wickersham, C.E.,
and Cluzel, P., Agent-Cell: A digital single-cell assay for bac-
terial chemotaxis, Bioinformatics, 2005, vol. 21, pp. 2714–
2721. doi 10.1093/bioinformatics/bti391
Esteban, P.G. and Rodríguez-Patón, A., Simulating a rock-
scissors-paper bacterial game with a discrete cellular
automaton, in New Challenges on Bioinspired Applications,
Lecture Notes in Computer Science, Ferràndez, J.M., Àlvarez
Sànchez, J.R., de la Paz, F., and Toledo, F.J., Eds., Berlin–
Heidelberg: Springer Berlin Heidelberg, 2011. doi 10.1007/
978-3-642-21326-7
Faust, K. and Raes, J., Microbial interactions: From net-
works to models, Nat. Rev. Microbiol., 2012, vol. 10,
pp. 538–550. doi 10.1038/nrmicro2832
Frey, E., Evolutionary game theory: Theoretical concepts
and applications to microbial communities, Phys. A Stat.
Mech. Its Appl., 2010 , vol. 389, pp. 4265– 4298. do i 10.1016/
j.physa.2010.02.047
Fuhrman, J.A., Microbial community structure and its
functional implications, Nature, 2009, vol. 459, pp. 193–
199. doi 10.1038/nature08058
Gimel’farb, A.A., Ginzburg, L.R., Poluektov, R.A.,
Pykh, Yu.A., and Ratner, V.A., Dinamicheskaya teoriya bio-
logicheskikh populyatsii (Dynamic Theory of Biological
Populations), Nauka, 1974.
Ginovart, M., Löpez, D., and Valls, J., INDISIM, an indi-
vidual-based discrete simulation model to study bacterial
cultures, J. Theor. Biol., 2002, vol. 214, pp. 305–319. doi
10.1006/jtbi.2001.2466
Grimm, V., Berger, U., Bastiansen, F., Eliassen, S., Ginot, V.,
Giske, J., Goss-Custard, J., Grand, T., Heinz, S.K., Huse, G.,
Huth, A., Jepsen, J.U., Jørgensen, C., Mooij, W.M.,
Müller, B., et al., A standard protocol for describing individ-
ual-based and agent-based models, Ecol. Modell., 2006,
vol. 198, pp. 115–126. doi 10.1016/j.ecolmodel.2006.04.023
Halfen, L.N. and Castenholz, R.W., Gliding Motility in the
Blue-Green Alga Oscillatoria Princeps, 1971.
Hecker, M., Lambeck, S., Toepfer, S., van Someren, E.,
and Guthke, R., Gene regulatory network inference: Data
integration in dynamic models – A review, Biosystems, 2009,
vol. 96, pp. 86–103. doi 10.1016/j.biosystems.2008.12.004
Henrichsen, J., Bacterial surface translocation: A survey and a
classification, Bacteriol. Rev., 1972, vol. 36, pp. 478–503.
Henson, M.A. and Hanly, T.J., Dynamic flux balance anal-
ysis for synthetic microbial communities, IET Syst. Biol.,
2014, vol. 8, pp. 214–229. doi 10.1049/iet-syb.2013.0021
Ishii, N., Robert, M., Nakayama, Y., Kanai, A., and
Tomita, M., Toward large-scale modeling of the microbial
cell for computer simulation, J. Biotechnol., 2004, vol. 113,
pp. 281–294. doi 10.1016/j.jbiotec.2004.04.038
Karr, J.R., Sanghvi, J.C., MacKlin, D.N., Gutschow, M.V.,
Jacobs, J.M., Bolival, B., Assad-Garcia, N., Glass, J.I., and
Covert, M.W., A whole-cell computational model predicts
phenotype from genotype, Cell, 2012, vol. 150, pp. 389–
401. doi 10.1016/j.cell.2012.05.0 44
Karunakaran, E., Mukherjee, J., Ramalingam, B., and
Biggs, C.A., “Biofilmology:” A multidisciplinary review of
the study of microbial biofilms, Appl. Microbiol. Biotechnol.,
2011, vol. 90, pp. 1869–1881. doi 10.1007/s00253-011-3293-4
Klimenko, A.I., Matushkin, Y.G., Kolchanov, N.A., and
Lashin, S.A., Modeling evolution of spatially distributed
bacterial communities: A simulation with the haploid evo-
lutionary constructor, BMC Evol. Biol., 2015, vol. 15, p. S3.
doi 10.1186/1471-2148-15-S1-S3
Klitgord, N. and Segre, D., Environments that induce syn-
thetic microbial ecosystems, PLoS Comput. Biol., 2010,
vol. 101, pp. 1435–1439. doi 10.1371/Citation
Knibbe, C., Fayard, J.-M., and Beslon, G., The topology of
the protein network influences the dynamics of gene order:
From systems biology to a systemic understanding of evolu-
tion, Artif. Life, 2008, vol. 14, pp. 149–156. doi 10.1162/
artl.2008.14.1.149
Kolmakova, O.V., Modern methods for determining species-
specific biogeochemical functions of bacterioplankton, Zh.
Sib. Fed. Univ., Ser. Biol., 2013, vol. 6, no. 1, pp. 73–95.
852
RUSSIAN JOURNAL OF GENETICS: APPLIED RESEARCH Vol. 6 No. 8 2016
KLIMENKO et al.
Kutalik, Z., Razaz, M., and Baranyi, J., Connection
between stochastic and deterministic modelling of micro-
bial growth, J. Theor. Biol., 2005, vol. 232, pp. 285–299. doi
10.1016/j.jtbi.200 4.08.013
Larsen, P., Hamada, Y., and Gilbert, J., Modeling micro-
bial communities: Current, developing, and future technol-
ogies for predicting microbial community interaction, J.
Biotechnol., 2012, vol. 160, pp. 17–24. doi 10.1016/j.jbio-
tec.2012.03.009
Laspidou, C.S. and Rittmann, B.E., Evaluating trends in
biofilm density using the UMCCA model, Wate r Re s., 2004,
vol. 38, pp. 3362–33672. doi 10.1016/j.watres.2004.04.051
Lencstre Fernandes, R., Nierychlo, M., Lundin, L., Peder-
sen, A.E., Puentes Tellez, P.E., Dutta, A., Carlquist, M.,
Bolic, A., Schäpper, D., Brunetti, A.C., Helmark, S.,
Heins, A.L., Jensen, A.D., Nopens, I., Rottwitt, K., et al.,
Experimental methods and modeling techniques for descrip-
tion of cell population heterogeneity, Biotechnol. Adv., 2011,
vol. 29, pp. 575–599. doi 10.1016/j.biotechadv.2011.03.007
Leslie, P.H., On the use of matrices in certain population
mathematics, Biometrika, 1945. doi 10.2307/2332297
Likhoshvai, V.A. and Ratushny, A.V., Generalized Hill
function method for modeling molecular processes, J. Bio-
inf. Comput. Biol., 2007, vol. 05, pp. 521–531. doi 10.1142/
S0219720007002837
Likhoshvai, V.A., Khlebodarova, T.M., Ratushnyi, A.V.,
Lashin, S.A., Turnaev, I.I., Podkolodnaya, O.A., Anan’ko, E.A.,
Smirnova, O.G., Ibragimova, S.S., and Kolchanov, N.A.,
Computer genetic designer: Mathematical modeling of
genetic and metabolic subsystems of E. coli, in The Role of
Microorganisms in Functioning of Living Systems: Fundamen-
tal Problems and Bioengineering Applications, Vlasov, V.V. ,
Degermendzhi, A.G., Kolchanov, N.A., Parmon, V.N.,
and Repin, E.A., Eds., Novosibirsk: Izd. SO RAN, 2010.
Logofet, D.O. and Belova, I.N., Nonnegative matrices as a
tool to model population dynamics: Classical models and
contemporary expansions, Fundam. Prikl. Mat., 2007,
vol. 13, pp. 145–164.
Mahadevan, R. and Henson, M.A., Genome-based model-
ing and design of metabolic interactions in microbial com-
munities, Comput. Struct. Biotechnol. J., 2012, vol. 3, pp. 1–7.
doi 10.5936/csbj.201210008
Mburu, N., Rousseau, D.P.L., Stein, O.R., and Lens, P.N.L.,
Simulation of batch-operated experimental wetland meso-
cosms in AQUASIM biofilm reactor compartment, J. Envi-
ron. Manage., 2014, vol. 134, pp. 100–108. doi 10.1016/
j.jenvman.2014.01.005
Monod, J., La technique de culture continue. Theorie et
applications, Ann. Inst. Pasteur, 1950, vol. 79, pp. 391–410.
Netrusov, A.I. and Kotova, I.B., Mikrobiologiya (Microbi-
ology), Moscow: Akademiya, 2007.
Niu, B., Wang, H., Duan, Q., and Li, L., Biomimicry of
quorum sensing using bacterial lifecycle model, BMC Bioinf.,
2013, vol. 14, no. 8, p. S8. doi 10.1186/1471-2105-14-S8-S8
O’Donnell, A.G., Young, I.M., Rushton, S.P., Shirley, M.D.,
and Crawford, J.W., Visualization, modelling and predic-
tion in soil microbiology, Nat. Rev. Microbiol., 2007, vol. 5,
pp. 689–699. doi 10.1038/nrmicro1714
Oberhardt, M.A. and Palsson, B.Ø, Papin, J.A., Applica-
tions of genome-scale metabolic reconstructions, Mol. Syst.
Biol., 2009, vol. 5. doi 10.1038/msb.2009.77
Pfeiffer, T. and Schuster, S., Game-theoretical approaches
to studying the evolution of biochemical systems, Trends
Biochem. Sci., 2005, vol. 30, pp. 20–25. doi 10.1016/
j.tibs.2004.11.006
Price, N.D., Reed, J.L., and Palsson, B.Ö, Genome-scale
models of microbial cells: Evaluating the consequences of
constraints, Nat. Rev. Microbiol., 2004, vol. 2, pp. 886–897.
doi 10.1038/nrmicro1023
Ramkrishna, D., Population Balances: Theory and Applica-
tions to Particulate Systems in Engineering, Chemical Engi-
neering, 2000.
Riznichenko, G.Yu., Matematicheskie modeli v biofizike i
ekologii (Mathematical Models in Biophysics and Ecology),
Moscow, Izhevsk: Inst. Komp’yut. Issled., 2003.
Riznichenko, G.Yu. and Rubin, A.B., Matematicheskie
modeli biologicheskikh produktsionnykh protsessov (Mathe-
matical Models of Biological Production Processes), Mos-
cow: Izd. MGU, 1993.
Rudge, T.J., Steiner, P.J., Phillips, A., and Haseloff, J.,
Computational modeling of synthetic microbial biofilms,
ACS Synth. Biol., 2012, vol. 1, no. 8, pp. 345–352. doi
10.1021/sb300031n
Salli, K.M. and Ouwehand, A.C., The use of in vitro model
systems to study dental biofilms associated with caries: A
short review, J. Oral Microbiol., 2015, vol. 7. doi 10.3402/
jom.v7.26149
Sauer, U., Heinemann, M., and Zamboni, N., GENETICS:
Getting closer to the whole picture, Science, 2007, vol. 316,
pp. 550–551. doi 10.1126/science.1142502
Scheffer, M., Baveco, J.M., DeAngelis, D.L., Rose, K.A.,
and van Nes, E.H., Super-individuals a simple solution for
modelling large populations on an individual basis, Ecol.
Modell., 1995, vol. 80, pp. 161–170. doi 10.1016/030 4-
3800(94)00055-M
Scheibe, T.D., Mahadevan, R., Fang, Y., Garg, S., Long, P.E.,
and Lovley, D.R., Coupling a genome-scale metabolic
model with a reactive transport model to describe in situ
uranium bioremediation, Microb. Biotechnol., 2009, vol. 2,
pp. 274 – 2 86. d o i 10.1111 / j .1751-7915.200 9.0008 7.x
Schuster, S., Fell, D.A., and Dandekar, T., A general defi-
nition of metab olic p athways u seful for systematic organiza-
tion and analysis of complex metabolic networks, Nat. Bio-
technol., 2000, vol. 18, pp. 326–332. doi 10.1038/73786
Segrè, D., Vitkup, D., and Church, G.M., Analysis of opti-
mality in natural and perturbed metabolic networks, Proc.
Natl. Acad. Sci. U.S.A., 2002, vol. 99, pp. 15112–15117. doi
10.1073/pnas.232349399
Shrout, J.D., A fantastic voyage for sliding bacteria, Trends
Microbiol., 2015, vol. 23, pp. 244–246. doi 10.1016/
j.tim.2015.03.001
Song, H.-S., Cannon, W., Beliaev, A., and Konopka, A.,
Mathematical modeling of microbial community dynamics: a
methodological review, Processes, 2014, vol. 2, pp. 711–752.
doi 10.3390/pr2040711
Stauffer, D., Kunwar, A., and Chowdhury, D., Evolution-
ary ecology in silico: Evolving food webs, migrating popu-
lation and speciation, Phys. A (Amsterdam, Neth.), 2005,
vol. 352, pp. 202–215. doi 10.1016/j.physa.2004.12.036
Tang, Y. and Valocchi, A.J., An improved cellular automaton
method to model multispecies biofilms, Water Res. , 2013,
vol. 47, pp. 5729–5742. doi 10.1016/j.watres.2013.06.055
RUSSIAN JOURNAL OF GENETICS: APPLIED RESEARCH Vol. 6 No. 8 2016
A REVIEW OF SIMULATION AND MODELING APPROACHES 853
Tindall, M.J., Maini, P.K., Porter, S.L., and Armitage, J.P.,
Overview of mathematical approaches used to model bacte-
rial chemotaxis II: Bacterial populations, Bull. Math. Biol.,
2008a. doi 10.1007/s11538-008-9322-5
Tindall, M.J., Porter, S.L., Maini, P.K., Gaglia, G., and
Armitage, J.P., Overview of mathematical approaches used
to model bacterial chemotaxis I: The single cell, Bull. Math.
Biol., 2008b. doi 10.1007/s11538-008-9321-6
Tomita, M., Hashimoto, K., Takahashi, K., Shimizu, T.,
Matsuzaki, Y., Miyoshi, F., Saito, K., Tanida, S., Yugi, K.,
Venter, J., and Hutchison, C., E-CELL: Software environ-
ment for whole-cell simulation, Bioinf., 1999, vol. 15,
pp. 72–84. doi 10.1093/bioinformatics/15.1.72
Tomita, M., Whole-cell simulation: A grand challenge of
the 21st century, Trends Biotechnol., 2001, vol. 19, pp. 205–
210. doi 10.1016/S0167-7799(01)01636-5
Turing, A.M., The chemical theory of morphogenesis, Phi-
los. Trans. R. Soc., 1952, vol. 13, p. 1.
Wanner, O. and Morgenroth, E., Biofilm modeling with
AQUASIM, Wat er S ci. Tec hno l., 2004, vol. 49, pp. 137–
144.
Wimpenny, J.W.T. and Colasanti, R., A unifying hypothe-
sis for the structure of microbial biofilms based on cellular
automaton models, FEMS Microbiol. Ecol., 1997. doi
10.1016/S0168-6 496(96)00078-5
Wimpenny, J., Manz, W., and Szewzyk, U., Heterogeneity
in biofilms, FEMS Microbiol. Rev., 2000. doi 10.1016/
S0168-6445(00)00052-8
Wolfe, B.E. and Dutton, R.J., Review fermented foods as
experimentally tractable microbial ecosystems, Cell, 2015,
vol. 161, pp. 49–55. doi 10.1016/j.cell.2015.02.034
Wooley, J.C., Godzik, A., and Friedberg, I., A primer on
metagenomics, PLoS Comput. Biol., 2010. doi 10.1371/
journal.pcbi.1000667
Zomorrodi, A.R. and Maranas, C.D., OptCom: A multi-
level optimization framework for the metabolic modeling
and analysis of microbial communities, PLoS Comput. Biol.,
2012, vol. 8. doi 10.1371/journal.pcbi.1002363
Zomorrodi, A.R., Islam, M.M., and Maranas, C.D.,
D-OptCom: Dynamic multi-level and multi-objective met-
abolic modeling of microbial communities, ACS Synth.
Biol., 2014, vol. 3, pp. 247–257. doi 10.1021/sb4001307
Translated by E. Makeeva
