  Co-localization of networks of genes in the nucleus is thought to play an
important role in determining gene expression patterns. Based upon experimental
data, we built a dynamical model to test whether pure diffusion could account
for the observed co-localization of genes within a defined subnuclear region. A
simple standard Brownian motion model in two and three dimensions shows that
preferential co-localization is possible for co-regulated genes without any
direct interaction, and suggests the occurrence may be due to a limitation in
the number of available transcription factors. Experimental data of chromatin
movements demonstrates that fractional rather than standard Brownian motion is
more appropriate to model gene mobilizations, and we tested our dynamical model
against recent static experimental data, using a sub-diffusion process by which
the genes tend to colocalize more easily. Moreover, in order to compare our
model with recently obtained experimental data, we studied the association
level between genes and factors, and presented data supporting the validation
of this dynamic model. As further applications of our model, we applied it to
test against more biological observations. We found that increasing
transcription factor number, rather than factory number and nucleus size, might
be the reason for decreasing gene co-localization. In the scenario of
frequency- or amplitude-modulation of transcription factors, our model
predicted that frequency-modulation may increase the co-localization between
its targeted genes.
