Download BIOINFORMATICS APPLICATIONS NOTE Vol. 18

BIOINFORMATICS APPLICATIONS NOTE
Vol. 18 no. 0 2002
Pages 1–2
Genexp—a genetic network simulation
environment
Tra Thi Vu and Jiri Vohradsky ∗
Institute of Microbiology, CAS, Videnska 1083, 142 20 Prague, Czech Republic
Received on February 5, 2002; revised on March 27, 2002; accepted on April 26, 2002
ABSTRACT
Summary: An environment for simulation of dynamics
of genetic regulatory networks is presented. The model
is based on the recurrent neural network principle and
allows to interactively simulate various genetic regulatory
interactions under different features of the system. The
results are displayed graphically.
Availability: http://proteom.biomed.cas.cz/genexp
Contact: [email protected]
INTRODUCTION
The vast quantity of data generated by genomic expression
arrays affords researchers a significant opportunity to
transform biology, medicine, and pharmacology using
systematic computational methods. The availability of
transcriptomic (and eventually proteomic) expression data
promises to have a profound impact on the understanding
of basic cellular processes, the diagnosis and treatment
of disease, and the efficacy of designing and delivering
targeted therapeutics. Particularly relevant to these objectives is the development of a deeper understanding of the
various mechanisms by which cells control and regulate
the transcription of their genes by their mathematical
representation.
Several approaches to the modeling of cell regulatory
pathways have been published recently. Those based on
recurrent neural networks (Vohradsky, 2001a,b; Marnellos
and Mjolsness, 1998; Marnellos et al., 2000) have been
shown to be potentially very useful. The regulatory
process is considered as the combinatorial action of gene
products on the rate of expression of a particular gene.
The action is modulated by a particular transfer function
to generate response curves, which correspond to those
observed in natural processes. The accumulation of gene
product, controlled by the regulators, is modified by the
degradation, which is usually presented as a first order
chemical reaction. Such models proved to be capable
of describing known, already quite complex, systems;
moreover it was capable of predicting the behavior
of the system in experimentally inaccessible situations
∗ To whom the correspondence should be addressed.
c Oxford University Press 2002
(Vohradsky, 2001a,b). This implies that having a tool
which would allow the simulation of the dynamic behavior
of a genetic network under different conditions would be
useful for the analysis of such systems.
In this paper, we present a program based on this concept, which allows to simulate the process of gene expression of a complex regulatory network. The model allows
users to compute and display time series of the amounts
of the gene products involved in a specified regulatory
process under various combinations of parameters.
THE MODEL
The principle has been published previously (Vohradsky,
2001a,b). Here we will only briefly mention the fundamentals of the algorithm.
Let assume that the modeled regulatory system S is
formed by n genes (nodes of the network), which can
control each other including itself. The level of regulatory
influence of a particular gene product i on a gene j is given
by a weight wi j . All the weights form the weight matrix:
W = (wi j )nxn ,
i = 1, . . . , n
j = 1, . . . , n
(1)
Nonzero values define connections between nodes of the
network.
Applying the regulatory effect on each gene for all nodes
of the system S, the regulatory effect can be defined as:
gi =
1
,
1 + exp − j wi j y j − bi
i = 1, . . . , n (2)
where bias bi represents an external input, in this case
translated as a reaction delay parameter, and yi j are concentrations of gene products of the system. Equation (2)
describes the regulatory effect on gene i transformed by a
sigmoidal function to the interval 0, 1.
The rate of expression of a target gene i (dyi /dt) is then
given by the formula:
dyi
= k1i gi − k2i yi
dt
(3)
1
T.T.Vu and J.Vohradsky
where k1i and k2i are gene product i accumulation and
degradation rate constants respectively.
The decay rate constant k2 can be expressed using
protein half-life t1/2 by the formula:
k2 = ln 2/t1/2
(4)
The whole model is formed by a set of differential
equations:
1
dyi
= k1i
dt
1 + exp − j wi j yi − bi
−(ln 2/t1/2i )yi ,
i = 1, . . . , n.
(5)
The changes in the accumulation of a gene product
is computed using modified Runge–Kutta method as
implemented in MATLAB ‘ode45’ function.
IMPLEMENTATION OF THE MODEL
The free parameters of the model, which are user defined,
are:
connection weight matrix:
maximal rate of expression
(accumulation rate constant) vector:
vector of protein half lifes:
delay parameters vector:
initial level of expression vector:
W = (wi j )nxn
k1 = (k1i ); i = 1, . . . , n
t1/2 = (t1/2i ); i = 1, . . . , n
b = (bi ); i = 1, . . . , n
y0 = (y0i ); i = 1, . . . , n
The number n of nodes (genes) involved in the regulatory process defines the dimension of the matrix and the
length of the vectors.
The program communicates with the user by means of
five windows, which are classified into two parts: The
input includes the Gene-Expression window (GE), the
Edit-Data window (ED) and Notepad window (NP); and
the output includes the Select-Node window (SN) and the
Plot-of-Model window (PM). To start a simulation loop,
the user can choose either to edit an existing data file or
to create a new one. If number of genes of the system is
lower than 15 a special editor is invoked, if higher the data
are edited in NOTEPAD. The Edit-Data window (ED) is
used to edit parameters of the model (mentioned above).
After editing the current data are checked for consistency,
and the SN and PM windows are opened. There user can
select which kinetic profiles to plot in the PM window, and
for what time interval. The PLOT button in SN invokes the
simulation procedure, which uses the currently edited data
and displays resulting curves in the PM window.
CONCLUSIONS
Here we present a user friendly program, based on a
neural network model of gene expression, which allows
the behavior of arbitrarily designed genetic regulatory
network for different parameters and time intervals to be
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simulated, especially how the system would be affected
if some of its parts were influenced by an outside action,
such as the change in protein stability or activity, or e.g.
by gene disruption. It can be useful for the analysis of a
studied network or for planning experiments, which would
confirm or reject suggested or expected network topology
i.e. the regulatory interaction among genes of the system.
The program was designed and tested for various x86
processors and different MS Windows versions. It can
run either as a stand-alone compiled application under
MS Windows environment or in MATLAB using a set
of scripts. All scripts and compiled version for Matlab
6.1 and MS Windows environment, together with installer
and help files, are freely available at the above-mentioned
address.
ACKNOWLEDGEMENTS
The authors wish to thank Jeremy Ramsden for discussion
and comments on the manuscript. The work was supported
by grants of GACR No. 204/00/1253 and GACAS No.
GA204/02/1452.
REFERENCES
Marnellos,G. and Mjolsness,E. (1998) A gene network approach
to modeling early neurogenesis in Drosophila. Pac. Symp.
Biocomput., 30–41.
Marnellos,G., Deblandre,G.A., Mjolsness,E. and Kintner,C. (2000)
Delta-Notch lateral inhibitory patterning in the emergence of
ciliated cells in Xenopus: experimental observations and a gene
network model. Pac. Symp. Biocomput., 329–340.
Vohradsky,J. (2001a) Neural model of the genetic network. J. Biol.
Chem., 276, 36168–36173.
Vohradsky,J. (2001b) Neural network model of gene expression.
Faseb J., 15, 846–854.
To be balanced at final stage