Julius Adebayo and Dr. Sean Warnick, Department of Computer Science
Networks of controlled dynamical systems exhibit a variety of interconnection patterns that can be interpreted as the structure of a system. One such interpretation of system structure is a system’s signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function (DSF). Previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs, i.e., for systems to be reconstructed, each observed state must be independently controlled by an input for the structure of the system to be reconstructible. The work done extended these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. Given the previous set of results, reconstruction of the DSF of a system was limited to systems where independent state perturbation is possible. This extension is important because it broadens the applicability of the identifiability conditions, enabling the design of network
reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the scientist.
The extension resulted in the derivation of a theorem that is proven in my honors thesis (August 2012), the proof of the theorem is presented in the thesis. I am not presenting here because it involves quite a bit of technical detail and adequate explication of previous work.
This work shows the necessary and sufficient identifiability conditions for the reconstruction of the dynamical structure function given a system’s transfer function matrix G. These results are applicable to the network reconstruction problem even in the cases when the control matrix P is not diagonal. This extension is significant because it identifies when systems that do not necessarily have independent perturbation of measured states are reconstructible. Future work involves the implementation of the new theorem developed here in matlab and other software packages. In addition to this, the work presented here also needs to be refined before it can be applied to actual biological systems because it does not take into account the significant amount of noise usually present in biological data. These directions are interesting areas where the work developed in this thesis can be further extended. Effective network reconstruction algorithms should be able to give structural representations that enable further understanding of different biological processes. A descriptive network would enable a systems-level understanding of such pathways. Network reconstruction is significant because it can elucidate pathways implicated in diseases such as cancer, malaria, and other complicated diseases that target and rewire molecular signaling pathways.
In order to solve the problem presented in the proposal I followed the steps described in the proposal and worked closely with my mentor in order to arrive at a reasonable extension for the previous results. Having constant contact with the mentor and being able to learn about the field of computational biology. This is a really exciting field, and I am so excited about learning about this field, so that when I go back home to Nigeria, I can make a meaningful impact there through my experiences. Having a wonderful mentoring experience has shown me what the model mentoring experience should be like. This mentoring experience has taught me how one can balance having an intense workload, a family, and additional expectations with mentoring undergraduates the way Dr. Warnick has done. He has been a role model in a lot of different ways.
The following results were achieved as a result of the extension presented: Presentation at the College of Physical and Mathematical Sciences Spring Research Conference 2011, Harvard Systems Biology Conference on Disease, Paper Submitted to the IEEE Transactions Journal, Chapter 1 and Overview of Honors Thesis, Harvard systems biology summer internship, iGEM competition (Gold medal ). Additional paper also submitted to molecular systems biology. Currently applying for additional awards as well as graduate school.
Like I indicated in my thank you letter, I am really thankful for the donation and the ability to be able to pursue research because of the donor. I will continually be thankful to BYU and the donor in particular. The orca experience was extremely valuable in making develop as a researcher.