Intrinsic noise and Hill dynamics in the p53 system

A common pathway to cancer: Oncogenic mutations abolish p53 oscillations

The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly, they exhibit a mixed pattern of interactions in tumors, such as co-occurrence, mutual exclusivity, and paradoxically, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics, we employ Hopf bifurcation analysis to show that these alterations have a common mode of action, to abolish the oscillatory competence of p53, thereby, we suggest, impairing its tumor suppressive function. In this analysis, diverse genetic alterations, widely associated with human cancers clinically, have a unified mechanistic explanation of their role in oncogenesis.

Synchronization in stress p53 network

We study transition of the temporal behaviours of p53 and MDM2 in a stress p53-MDM2-NO regulatory network induced by a bioactive molecule NO (Nitric Oxide). We further study synchronization among a group of identical stress systems arranged in a 3D array with nearest neighbour diffusive coupling. The role of NO and the effect of noise are investigated. In the single system study, we found three distinct types of temporal behaviour of p53, namely oscillation death, damped oscillation and sustained oscillation, depending on the amount of stress induced by NO, indicating how p53 responds to incoming stress. The correlation among coupled systems increases as the value of the coupling constant (ϵ) is increased (γ increases) and becomes constant after a certain value of ϵ. The permutation entropy spectra H(ϵ) for p53 and MDM2 as a function of ϵ are found to be different due to direct and indirect interaction of NO with respective proteins. We find γ versus ϵ for p53 and MDM2 to be similar in a deterministic approach but different in a stochastic approach, and the separation between γ of the respective proteins as a function of ϵ decreases as system size increases. The role of NO is found to be two-fold: stress induced by NO is prominent at small and large values of ϵ but synchrony induced by it dominates in the moderate range of ϵ. Excess stress induces apoptosis.

Dynamics of posttranslational modifications of p53

The latest experimental evidence indicates that acetylation of p53 at K164 (lysine 164) and K120 may induce directly cell apoptosis under severe DNA damage. However, previous cell apoptosis models only studied the effects of active and/or inactive p53, that is, phosphorylation/dephosphorylation of p53. In the present paper, based partly on Geva-Zatorsky et al. (2006) and Batchelor et al. (2008), we propose a new cell apoptosis network, in which p53 has three statuses, that is, unphosphorylated p53, phosphorylated p53, and acetylated p53. The time delay differential equations (DDEs) are formulated based on our network to investigate the dynamical insights of p53-induced cell apoptosis. In agreement with experiments (Loewer et al. (2010)), our simulations indicate that acetylated p53 accumulates gradually and then induces the proapoptotic protein Bax under enough DNA damage. Moreover, phosphorylated p53 oscillates and initiates cell repair during DNA damage.

Numerical simulation of airway dimension effects on airflow patterns and odorant deposition patterns in the rat nasal cavity

The sense of smell is largely dependent on the airflow and odorant transport in the nasal cavity, which in turn depends on the anatomical structure of the nose. In order to evaluate the effect of airway dimension on rat nasal airflow patterns and odorant deposition patterns, we constructed two 3-dimensional, anatomically accurate models of the left nasal cavity of a Sprague-Dawley rat: one was based on high-resolution MRI images with relatively narrow airways and the other was based on artificially-widening airways of the MRI images by referencing the section images with relatively wide airways. Airflow and odorant transport, in the two models, were determined using the method of computational fluid dynamics with finite volume method. The results demonstrated that an increase of 34 µm in nasal airway dimension significantly decreased the average velocity in the whole nasal cavity by about 10% and in the olfactory region by about 12% and increased the volumetric flow into the olfactory region by about 3%. Odorant deposition was affected to a larger extent, especially in the olfactory region, where the maximum odorant deposition difference reached one order of magnitude. The results suggest that a more accurate nasal cavity model is necessary in order to more precisely study the olfactory function of the nose when using the rat.