Mathematical and computational analysis of intracelluar dynamics 9

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Chapter 9
Future Work


The level of details considered in a model usually depends on the biological question
at hand. While a detailed model is comparatively more realistic, inclusion of
substantial biochemical steps with unknown mechanisms and kinetics which requires
arbitrary assumptions might render the model to be less realistic than expected.
Moreover, solving for the model dynamics becomes computationally intensive as the
number of model components increases. A more pragmatic approach however is to
update a model as and when new biological mechanisms relevant to the study are
elucidated. Nonetheless, as a model cannot possibly include all known and unknown
details, it is at best an approximation of the actual biological process being studied.
Without exceptions, the models developed in this thesis have limitations. These
limitations and suggestions to overcome them in future work are discussed below.


9.1 Models of the p53-AKT network


Admittedly, the p53-AKT network analyzed is merely a part of a more elaborate
control system deciding between cell survival and death. Furthermore, the results
would apply only to cells that rely chiefly on the p53-AKT network for regulation of
cell survival and death. Other pathways regulating cell survival and death do exist in
other cell types; for example, ERK could promote AKT-independent cell survival

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pathways (Nair et al., 2004; Ganguli and Wasylyk, 2003). Nevertheless, they can be
incorporated into the p53-AKT models to extend the results to other cell types. On

the other hand, while the impingement of general growth factor and DNA damage
signaling on the p53-AKT network are taken into account, the models do not consider
specific and other known or unknown details of the regulation of p53 and AKT. In
particular, different forms of p53 are ignored to reduce the number of variables and
unknown mechanistic and kinetic parameters in the models. However, specific forms
of p53 that are relevant to its apoptotic activity should be considered in future studies
when the biochemical activities are characterized.

Predictions of various apoptotic thresholds have recently been reported from
models that considered the caspase activation cascade only (Fussenegger et al., 2000;
Bentele et al., 2004; Eissing et al., 2004, 2005; Hua et al., 2005; Stucki and Simon,
2005; Bagci et al., 2006; Legewie et al., 2006; Aldridge et al., 2006). In these
models, the activation of caspases is predicted to be an all-or-none system that is
similar to the bistability phenomenon predicted by the p53-AKT models. A
challenging future study will also include these published models and all known
downstream apoptotic pathways from p53 and AKT (Section 2.5 of Chapter 2) to
understand how the predicted apoptotic threshold at the upstream p53-AKT network
impinges on the predicted apoptotic thresholds at the downstream caspase network.

Finally, it would be interesting to see if a stochastic model of the p53-AKT
network could also predict bistability and limit cycles, and if so, whether stochastic
effects could cause random switching between the two steady states. Stochastic
effects are usually significant under low numbers of molecules per cell such as the

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number of mRNA molecules. A p53-AKT stochastic model can be converted from
the deterministic p53-AKT models developed in this thesis (Turner et al., 2004).


9.2 Model for approximating co-transcriptional

binding accessibilities


In the event that dystrophin-specific splicing factors significantly affect the
mechanism of exon recognition, the results of the analyses might differ and they
might have to be considered in the model. Nevertheless, elucidation of such factors,
if any, is experimentally difficult. Alternatively, model validation is easier by using
insights obtained from the analyses to predict AON target sites and test for their
efficiency in exon skipping. Testing of about 30 such sites is ongoing in our
collaborator’s lab.

As the pre-mRNA co-transcriptional secondary structures are derived from a
prediction algorithm, the accuracy of the model is limited by the accuracy of such
algorithms. However, the use of vast numbers of predicted secondary structures that
averaged 44,582 of them per exon (Appendix A-17) in the analyses is expected to
spread out the prediction error of mfold. Nevertheless, an interesting future work is to
use other prediction algorithms to predict the pre-mRNA co-transcriptional secondary
structures and compare their results of analyses.

Lastly, another future work that has therapeutic applications is to apply the
model to other genes whose mutations caused genetic diseases. Examples of such

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genes are beta-globin gene in thalassemia (Suwanmanee et al., 2002; Gorman et al.,
2000; Sazani and Kole, 2003; Dominski and Kole, 1993) and OA1 gene in ocular
albinism (Vetrini et al., 2006). Analogous to the case of Duchene muscular
dystrophy, point mutations causing nonsense codons or shift in reading frame are the
main causes of these genetic diseases. Therefore, selective exon skipping mediated
by AONs to remove the mutations could be a possible therapeutic strategy. The
insights that co-transcriptional binding accessibility is a key factor influencing AON

efficiency in inducing exon skipping can be applied to these genes to predict AON
target sites for efficient exon skipping.