Transcript Comparison of methods for reconstruction of models for

Comparison of methods for reconstruction of
models for gene expression regulation
Motivation
Gene regulatory networks control structure and functions of cells, it is the basis of cell
differentiation, morphogenesis and adaptation. DNA microarray technology provides
us with huge amount of data gene expression. There are a number of methods that
use data from microarray time series for construction mathematical models of gene
expression regulation.
Main assumption for such methods is: if one gene (regulator gene) somehow affects
the level of expression of another (target gene) then we can establish some form of
relationship between their expression profiles.
Main question: what kind of relationship most closely reflects the real biological
process. This question has not definite answer yet. In this work we have compared
linear model with time delay and nonlinear model to simulate gene expressions.
Objectives:
1) compare linear and nonlinear [1] differential models of gene expression regulation
2) study various data processing methods influence on the models behavior
3) test and compare the considered models on the base of some available data [2]
Linear model with time delay
dz(t)
 a  b  y(t  Δ)
dt
A.A. Shadrin1,*, I.N. Kiselev,1F.A. Kolpakov2,1
1Technological
Institute of Digital Techniques SB RAS, Novosibirsk, Russia
2Institute of Systems Biology, Novosibirsk, Russia
*Corresponding author: [email protected]
Optimization methods:
Different types of optimization algorithms were tested: simulated annealing,
evolutionary algorithm and advanced method of gradient descent. Good speed and
accuracy evolutionary algorithm described in [3] has shown.
Comparison of models:
Models were tested on the Saccharomyces cerevisiae gene expression [2], measured
as amounts of mRNA using microarrays at 18 time points over two cell cycle periods
(one measurement every 7 minutes for 119 minutes). We selected small subset
composed of 5 target (with probes: YER1059W, YFR057W, YAL040C, YPR119W,
YPL163C) and 4 regulator genes (YMR016C, YPL075W, YIL131C, YER111C). Real
relationship between genes, represented by these probes were obtained from
YEASTRACT open database. For four of five target genes the best regulator, found by
nonlinear model, is real regulator of corresponding target, according to YEASTRACT,
but only two best regulators found by linear model confirmed as real.
z(t) — target gene expression
y(t) — regulator gene expression
a, b and Δ — model parameters
This model differs from more commonly used linear model: dz/dt = a + b × y(t), by
presence of parameter Δ, which is introduced to reflect delay in effect exerted on
target by regulator gene.
Nonlinear model
dz(t )
k
1

 k 2  z(t )
(  w y( t )  b )
dt
1 e
z(t) — target gene expression
y(t) — regulator gene expression
k1 — parameter reflecting the maximum level of expression
k2 — parameter expressing the intensity of degradation
w — weight of the regulator
b — parameter responsible for transcription initiation delay,
caused by independent from the regulator gene effects
Data smoothing methods
Implementation of both models requires representation of gene profiles in continuous
function form. The nature of microarray data (processing and measurement errors)
makes interpolation inefficient. Thus to obtain gene profile continuous representation
and to suppress data noise, smoothing methods are preferable. Tested smoothing
methods:
1) smoothing cubic spline with given maximum deviation in the node ("corridor spline")
2) smoothing cubic spline with fixed weight parameter
3) nuclear smoothing with Epanechnikov core
4) least squares smoothing method with a basis of Chebyshev polynomials
shows YPR119W target profile, reconstructed
by linear (above) and nonlinear (below) models. Each figure
contains initial YPR119W profile from microarray, and its
best and worst reconstruction.
Results:
• The study performed on the example of two models demonstrated best results
when spline with a fixed weighting parameter and the evolutionary algorithm [3]
were used.
• The major virtue of linear model is it’s computational simplicity and opportunity to
process large amount of data.
• Nonlinear model is much more harder computationally, but it allows to obtain
results of higher quality by taking into account biological specificity of the process.
• The models were implemented within BioUML workbench, freely available on
website: http://www.biouml.org.
Conclusion:
• Choice of methods for data smoothing and parameters optimization could strongly
influence the behavior of the model under other conditions, hence, each study
requires individual approach to select the most (or more) optimal methods.
• Information, obtained with any model along, has very limited value, to get reliable
information about gene interactions many versatile sources should be involved.
Acknowledgments:
This work was supported by EU grants FP6 №037590 “Net2Drug”
and FP7 №202272 “LipidomicNet”.
References:
These methods are demonstrated on
Above: smoothing of YIL131C probe profile from
microarray, used in [2]. Below: derivative of smoothing.
1. Tra Thi Vu, Jiri Vohradsky (2007) Nonlinear differential equation model for quantification of
transcriptional regulation applied to microarray data of Saccharomyces cerevisiae. Nucleic
Acids Research, Vol. 35, No. 1.
2. Spellman,P.T., Sherlock,G., Zhang,M., Iyer,V.,Anders,K., Eisen,M., Brown,P., Botstein,D. and
Futcher,B. (1998) Comprehensive identification of cell cycle-regulated genes of the yeast
Saccharomyces cerevisiae by microarray hybridization. Mol. Biol. Cell, 9, 3273–3297.
3. Thomas P. Runarsson, Xin Yao. Stochastic Ranking for Constrained Evolutionary Optimization.
IEEE Transactions on evolutionary computation, vol. 4, No. 3, september 2000.