These are the topics of interest in the group. Please follow the links in the titles or each topic for details.
I. Mathematical modeling
1. Stochastic reaction engineering: For systems that have a small number of molecules of each reactant (e.g. two DNA binding sites, 10 molecules of a transcription factor), the reaction dynamics are described by an approach that takes into account this restriction to discrete states, and the fact that reactions are probabilistic not deterministic. The research goal is to identify conditions for which this approach is preferable, and analyze the effect of reaction network structure on the dynamics of the probability distribution of the reactant concentrations (and not just the mean concentration, as described by deterministic kinetics). This work involves knowledge of advanced mathematics and chemical reaction engineering.
2. Modeling Protein Expression: The DNA-to-functional-protein process is studied in order to tease out the effects and implications of their nonlinear nature of this process and the presence of positive and negative feedback loops. Specific processes we are studying are miRNA biogenesis, regulation and action; and self-regulated sumoylation and ubiquitination.
3. Skin biology: The signaling and metabolism in keratinocytes, melanocytes and other skin cells leads to pigmentation changes (vitiligo, tanning) and skin disorders (atopic dermatitis, psoriasis). The objective is to have a mathematical model that describes normal and diseased skin conditions.
4. Intracellular pathways: We analyze several intracellular pathways to gain insight into possible dynamical responses. In particular we are interested in pathways with incoherent or paradoxical regulators, and pathways with competing signals or substrates.
5. Systems Pharmacology: Pharmacokinetics is the study of the dynamics of drug distribution in the body, and pharmacodynamics the study of th effects of the drug on the body. The research goal is to construct mechanistic models of these processes so that there is an ability to predict the effect of a drug based on a few physical properties. This is sometimes referred to as PBPK or physiology-based-pharmacokinetics. Both the dynamics of the drug delivery system (e.g. sustained release formulations) and the drug concentrations and effects on the body can me investigated using mathematical modeling approaches. When coupled to a mathematical model for the disease, it results in a quantitative systems pharmacology model. Ongoing work attempts to construct such models for tuberculosis treatment effects.
II. Data Analysis
In our lab we also analyse the experimental data from our collaborators, though we try not to get drawn into development of new methods for data analysis relevant for biological data (large variability, low number of replicates, few treatments/time-points). A variety of data from transcriptomic to cell culture media composition have been analysed.
Other topics:
1. Developmental biology: The process of formation of an adult from a fertilized egg is characterized at almost all stages by an intricate system of biological signaling that defines the final pattern of the adult. A lot of details about the biological components are known, principally through molecular biology studies (gene deletions/overexpresion/ectopic expression) that lead to a change in the normal pattern. The research goal is to construct mathematical models corresponding to the biological processes occurring during development of specific systems. The model will then be used to analyze reported experimental results, and suggest new experiments. Another area of interest is the robustness of the normal pattern in the presence of environmental fluctuations and genetic defects. Mathematical models can be used to predict the sensitivity of the pattern to changing protein concentrations.