The protein expression process is an intricate and regulated process, as described in this review. There are several aspects where mathematical models are not available. Our group is trying to develop detailed models for sub-processes in order to eventually build a model that spans the entire process.
Regulation of transcription: We have developed a model for autocatalytic production of the transcription factor TBP. A paper describing those results is available here for personal/academic use. We are also interested in 'designer' regulatory modules. As part of a study on the robustness of patterning, we predicted that stochastic switching on of normally inactive genes is more harmful than stochastic switching off of normally active genes.
miRNA: We have developed a model for one miRNA acting on one mRNA and shown that known mechanisms can lead to unexpected outcomes, for instance the upregulation of target protein levels due to miRNA action. A paper describing those results has recently been published, a copy is available here for personal use. We have also developed a method to incorporate intronic miRNA effects in existing mathematical models for cellular processes, for example the cell cycle, described in this paper. We have shown that competition of multiple miRNA for the same mRNA can possibly lead to such unexpected outcomes even when each miRNA individually has a negative effect on target expression. A paper describing that hypothesis can be found here, or a preliminary version including supplementary information is uploaded below. We are also interested in developing models for miRNA biogenesis, including the mechanism for intronic miRNAs. This work is part of Dimpal's PhD research.
Sumoylation and ubiquitination: We are interested in exploring through mathematical models self-regulation of the sumoylation and ubiquitination cycles, in particular their effect on substrate discrimination and time required for the system to respond to perturbations.