Page 43 - Biosystems Engineering

24 Cha pte r O n e

genes, represented by these clusters centers, are likely to fit the fuzzy
model described in Fig. 1.9. For example, from the top row in Fig. 1.10,
we can see that an increasing activator and decreasing repressor would
cause the target gene to increase quickly. These cluster triplets make
sense intuitively and should be included in analysis. Figure 1.10
(bottom row) shows counterexamples to the combinations shown on
the top. These cluster triplets do not make sense intuitively and
should not be included in analysis.
There are many potential causes for noise, mostly originating from
the stochastic nature of gene interactions and microarray technology.
Investigating and using appropriate methods of conjunction and rule
aggregation will increase resilience of the fuzzy logic–based gene regu-
latory model to noise. Ressom et al. (2003a) investigated the noise sen-
sitivity of four models: Woolf and Wang’s method, Mamdani’s model,
Kosko’s standard additive model (SAM), and a hybrid model that
attempts to take the best attributes of the Mamdani’s model and SAM.
It was observed that Mamdani’s model has the best performance.
Sokhansanj et al. (2004) introduced an approach to gene network
modeling based on a scalable linear variant of fuzzy logic, which was
applied to real quantitative data where there were many inputs. The
linear fuzzy logic model assigns distinct fuzzy rules for each indi-
vidual input to a given output. After each individual rule is built, the
intermediate evaluations of the fuzzy state of the output variables are
aggregated by a fuzzy union operation (logic OR). This is different
from traditional fuzzy logic, which defines all the rules related to the
combinations of inputs. The advantage of the linear fuzzy model is
that it can deal with complex multicomponent regulation because
only rules for individual input and output are required.
Genetic algorithms have also been used to decipher genetic net-
works from microarray data (Kikuchi et al. 2003; Shin and Iba 2003).
Ando and Iba (2001) developed an inference algorithm based on GAs
and applied it to the optimization of the influence matrix of gene regu-
latory network. The GA inference method itself is not enough for the
application of real data. It is suggested that the combination of GAs
and clustering and perturbation analysis will make it easier and more
accurate to infer gene networks from microarray expression data.
Herrero et al. (2003) applied time-lagged correlation to study the
effect of genes at time t over them at t + 1. Noting that correlation is only
an indication, but not a proof, of a causal relationship, they introduced
a permutation test that takes into account the multiple testing nature of
the results to check the reliability of their method. Also, to obtain a non-
redundant dataset of gene expression profiles, they applied clustering
as a preprocessing step to reduce the dataset’s dimensionality. Through
this approach Herrero et al. (2003) built a genetic network from time
series expression profiles of yeast genes corresponding to 18 time points
of alpha factor-arrested cells. Schmitt et al. (2004) adopted the time-series