Network topology determines dynamics of the mammalian MAPK1,2 signaling network: bifan motif regulation of C-Raf and B-Raf isoforms by FGFR and MC1R.

Activation of the fibroblast growth factor (FGFR) and melanocyte stimulating hormone (MC1R) receptors stimulates B-Raf and C-Raf isoforms that regulate the dynamics of MAPK1,2 signaling. Network topology motifs in mammalian cells include feed-forward and feedback loops and bifans where signals from two upstream molecules integrate to modulate the activity of two downstream molecules. We computationally modeled and experimentally tested signal processing in the FGFR/MC1R/B-Raf/C-Raf/MAPK1,2 network in human melanoma cells; identifying 7 regulatory loops and a bifan motif. Signaling from FGFR leads to sustained activation of MAPK1,2, whereas signaling from MC1R results in transient activation of MAPK1,2. The dynamics of MAPK activation depends critically on the expression level and connectivity to C-Raf, which is critical for a sustained MAPK1,2 response. A partially incoherent bifan motif with a feedback loop acts as a logic gate to integrate signals and regulate duration of activation of the MAPK signaling cascade. Further reducing a 106-node ordinary differential equations network encompassing the complete network to a 6-node network encompassing rate-limiting processes sustains the feedback loops and the bifan, providing sufficient information to predict biological responses.

A deterministic model of growth factor-induced angiogenesis.

Understanding the formation and structure of a capillary network is critical for any reparative strategy since the capillary network dictates tissue survival, hemodynamics, and mass transport. Vascular assembly and patterning has largely been studied using a reductionist approach where a particular endothelial cell molecular pathway or cellular mechanism is investigated as a relatively closed system. This trend of research has yielded a staggering wealth of genes, proteins, and cells that play critical roles in angiogenesis and some have resulted in successful targeted angiogenic therapies. However, these genes, proteins, and cells do not exist in discrete closed systems, rather they are intimately coupled across spatial and temporal dimensions. Designing experiments to study a single or group of perturbations is fraught with confounding complications. An integrative tool is required that incorporates gene, protein, and cell information and appropriately describes the complex systems behavior of vascular assembly and patterning. In this paper, we propose a new deterministic mathematical formulation to model growth factor-induced angiogenesis. Conductivity of the extracellular matrix for the movement/extension of capillary sprouts is a new concept introduced to account for the heterogeneity and anisotropy of the extracellular matrix. The replacement of traditional endothelial cell density by the capillary indicator function enhances the capabilities of capturing the capillary network sharply in a fine scale (i.e., tracking the dynamics of the tip in uni-cellular scale). Major mechanisms including cell proliferation, sprout branching, and anastomosis are incorporated directly into this continuous mathematical model and model parameters are perturbed to determine the strength of their effect on angiogenesis. The model is fully deterministic and generates the overall dendritic structure of the capillary network morphologically similar to those observed in vivo. The simulations "capture" significant vascular patterning, such as vascular loops and backward growth. Moreover, the simulations provide a deeper understanding of the influence of extracellular matrix on angiogenesis and vascular patterning. An advantage of this model is that the complex physical, chemical and biological processes in angiogenesis can be described and consequently analyzed by a mathematical system with self-contained information.

Model predictions of MDM2 mediated cell regulation.

In this work we present a mathematical approach to elucidate possible mechanisms involving mdm2 in the regulation of the cell cycle. It has been experimentally shown that the over-expression of MDM2 leads to decoupling of DNA synthesis with mitosis resulting in polyploidy cells with multiple copies of their genomes. The function of MDM2 that uncouples the DNA synthesis phase (S) and the Mitosis phase (M) is unclear. To answer this question, we first formulate a mathematical model of the dynamics of the cell cycle regulatory proteins during the DNA synthesis phase and mitosis. This model is then tested for bifurcation that produces period doubling cascades that we relate to the biological event of polyploidy. The model formulation, the underlying biology, and the bifurcation results to delineate the unknown function of MDM2 are presented. Based on reproducing known experimental result of polyploidy in MDM2 overexpressed cells, we propose several possible functions of mdm2, i.e., possible interactions with the other cell cycle regulating proteins that will result in uncoupling the S and M phases. We conclude that the most likely unknown function of MDM2 leading to the decoupling of the S and M phases is an obstruction of the activation of Cdc25C by MDM2.

Theoretical and experimental evidence for hysteresis in cell proliferation.

We propose a mathematical model for the regulation of the G1-phase of the mammalian cell cycle taking into account interactions of cyclin D/cdk4, cyclin E/cdk2, Rb and E2F. Mathematical analysis of this model predicts that a change in the proliferative status in response to a change in concentrations of serum growth factors will exhibit the property of hysteresis: the concentration of growth factors required to induce proliferation is higher than the concentration required to maintain proliferation. We experimentally confirmed this prediction in mouse embryonic fibroblasts in vitro. In agreement with the mathematical model, this indicates that changes in proliferative mode caused by small changes in concentrations of growth factors are not easily reversible. Based on this study, we discuss the importance of proliferation hysteresis for cell cycle regulation.