Person: Milo, Ron
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Milo, Ron
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Publication A proof for loop-law constraints in stoichiometric metabolic networks(BioMed Central, 2012) Noor, Elad; Lewis, Nathan E; Milo, RonBackground: Constraint-based modeling is increasingly employed for metabolic network analysis. Its underlying assumption is that natural metabolic phenotypes can be predicted by adding physicochemical constraints to remove unrealistic metabolic flux solutions. The loopless-COBRA approach provides an additional constraint that eliminates thermodynamically infeasible internal cycles (or loops) from the space of solutions. This allows the prediction of flux solutions that are more consistent with experimental data. However, it is not clear if this approach over-constrains the models by removing non-loop solutions as well. Results: Here we apply Gordan’s theorem from linear algebra to prove for the first time that the constraints added in loopless-COBRA do not over-constrain the problem beyond the elimination of the loops themselves. Conclusions: The loopless-COBRA constraints can be reliably applied. Furthermore, this proof may be adapted to evaluate the theoretical soundness for other methods in constraint-based modeling.Publication Oscillations and Variability in the P53 System(Nature Publishing Group, 2006) Geva-Zatorsky, Naama; Rosenfeld, Nitzan; Itzkovitz, Shalev; Sigal, Alex; Dekel, Erez; Yarnitzky, Talia; Liron, Yuvalal; Polak, Paz; Alon, Uri; Milo, Ron; Lahav, GalitUnderstanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time.Publication Protein Dynamics in Individual Human Cells: Experiment and Theory(Public Library of Science, 2009) Cohen, Ariel Aharon; Kalisky, Tomer; Mayo, Avi; Geva-Zatorsky, Naama; Danon, Tamar; Issaeva, Irina; Perzov, Natalie; Sigal, Alex; Alon, Uri; Isalan, Mark; Kopito, Ronen; Milo, RonA current challenge in biology is to understand the dynamics of protein circuits in living human cells. Can one define and test equations for the dynamics and variability of a protein over time? Here, we address this experimentally and theoretically, by means of accurate time-resolved measurements of endogenously tagged proteins in individual human cells. As a model system, we choose three stable proteins displaying cell-cycle–dependant dynamics. We find that protein accumulation with time per cell is quadratic for proteins with long mRNA life times and approximately linear for a protein with short mRNA lifetime. Both behaviors correspond to a classical model of transcription and translation. A stochastic model, in which genes slowly switch between ON and OFF states, captures measured cell–cell variability. The data suggests, in accordance with the model, that switching to the gene ON state is exponentially distributed and that the cell–cell distribution of protein levels can be approximated by a Gamma distribution throughout the cell cycle. These results suggest that relatively simple models may describe protein dynamics in individual human cells.Publication BioNumbers—The Database of Key Numbers in Molecular and Cell Biology(Oxford University Press, 2009) Milo, Ron; Jorgensen, Paul Conrad; Moran, Uri; Weber, Griffin; Springer, MichaelBioNumbers (http://www.bionumbers.hms.harvard.edu) is a database of key numbers in molecular and cell biology—the quantitative properties of biological systems of interest to computational, systems and molecular cell biologists. Contents of the database range from cell sizes to metabolite concentrations, from reaction rates to generation times, from genome sizes to the number of mitochondria in a cell. While always of importance to biologists, having numbers in hand is becoming increasingly critical for experimenting, modeling, and analyzing biological systems. BioNumbers was motivated by an appreciation of how long it can take to find even the simplest number in the vast biological literature. All numbers are taken directly from a literature source and that reference is provided with the number. BioNumbers is designed to be highly searchable and queries can be performed by keywords or browsed by menus. BioNumbers is a collaborative community platform where registered users can add content and make comments on existing data. All new entries and commentary are curated to maintain high quality. Here we describe the database characteristics and implementation, demonstrate its use, and discuss future directions for its development.