Comparison of methods for reconstruction of models for gene expression regulation

1
Comparison of methods for reconstruction of
models for gene expression regulation

• 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 inter.cm_at_mail.ru

• 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
• compare linear and nonlinear 1 differential
  models of gene expression regulation
• study various data processing methods influence
  on the models behavior
• test and compare the considered models on the
  base of some available data 2

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.
Linear model with time delay
z(t) target gene expression
y(t) regulator gene expression a, b and ?
model parameters This model differs from more
commonly used linear model dz/dt  a  b  y(t),
by presence of parameter ?, which is introduced
to reflect delay in effect exerted on target by
regulator gene.
Nonlinear model
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
• smoothing cubic spline with given maximum
  deviation in the node ("corridor spline")
• smoothing cubic spline with fixed weight
  parameter
• nuclear smoothing with Epanechnikov core
• 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 its
  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
• 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.
• Spellman,P.T., Sherlock,G., Zhang,M.,
  Iyer,V.,Anders,K., Eisen,M., Brown,P.,
  Botstein,D. and Futcher,B. (1998) Comprehensive
  identi?cation of cell cycle-regulated genes of
  the yeast Saccharomyces cerevisiae by microarray
  hybridization. Mol. Biol. Cell, 9, 32733297.
• Thomas P. Runarsson, Xin Yao. Stochastic Ranking
  for Constrained Evolutionary Optimization. IEEE
  Transactions on evolutionary computation, vol. 4,
  No. 3, september 2000.

These methods are demonstrated on
Above smoothing of YIL131C probe profile from
microarray, used in 2. Below derivative of
smoothing.