A mathematical model of a P53 oscillation network triggered by DNA damage

Taking the interaction between a DNA damage repair module, an ATM module, and a P53--MDM2 oscillation module into account, this paper presents a mathematical model of a P53 oscillation network triggered by a DNA damage signal in individual cells. The effects of the DNA damage signal and the delay time of P53-induced MDM2 expression on the behaviours of the P53 oscillation network are studied. In the oscillatory state of the P53--MDM2 oscillator, it is found that the pulse number of P53--P oscillation increases with the increase of the initial DNA damage signal, whereas the amplitude and the period of P53--P oscillation are fixed for different initial DNA damage signals, and the period numbers of P53--P oscillations decrease with the increase of time delay of MDM2 expression induced by P53. These theoretical predictions are consistent with previous experimental results. The combined negative feedback of P53--MDM2 with the time delay of P53-induced MDM2 expression causes oscillation behaviour in the P53 network.

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

This paper studies the asymptotic behavior of solutions for nonlinear RLCnetwoiks which have the following form The function p i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditiolts. Under the assumption that every element value involving voltage source is asymptotically constallt, we establish four creteria for all solutiolls of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited uonliltear circuits.This results generalize those of Brayton and Moser[1,2].

Circadian rhythms driving a fast-paced root clock implicate species-specific regulation in Medicago truncatula

Plants have a hierarchical circadian structure comprising multiple tissue-specific oscillators that operate at different speeds and regulate the expression of distinct sets of genes in different organs.However,the identity of the genes differentially regulated by the circadian clock in different organs,such as roots,and how their oscillations create functional specialization remain unclear.Here,we profiled the diurnal and circadian landscapes of the shoots and roots of Medicago truncatula and identified the conserved regulatory sequences contributing to transcriptome oscillations in each organ.We found that the light-dark cycles strongly affect the global transcriptome oscillation in roots,and many clock genes oscillate only in shoots.Moreover,many key genes involved in nitrogen fixation are regulated by circadian rhythms.Surprisingly,the root clock runs faster than the shoot clock,which is contrary to the hierarchical circadian structure showing a slow-paced root clock in both detached and intact Arabidopsis thaliana(L.)Heynh.roots.Our result provides important clues about the species-specific circadian regulatory mechanism,which is often overlooked,and possibly coordinates the timing between shoots and roots independent of the current prevailing model.