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We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.

Heat shock proteins (Hsps) are overexpressed in many tumors, but are downregulated in some tumors. To check for a direct effect of Ha-Ras val12 on HSP70 transcription, we transiently expressed the oncoprotein in Rat1 fibroblasts and monitored its effect on HSP70b promoterdriven reporter gene. We show that expression of Ha-Ras val12 induced this promoter. Promoter analysis via systematic deletions and point mutations revealed that Ha-Ras val12 induces HSP70b transcription via heat shock elements (HSEs). Also, Ha-Ras val12 induction of HSEmediated transcription was dramatically reduced in HSF1À/À cells. Yet, residual effect of Ha-Ras val12 that was still measured in HSF1À/À cells suggests that some of the Ha-Ras val12 effect is Hsf1-independent. When HSF1À/À cells, stably expressing Ha-Ras val12 , were grown on soft agar only small colonies were formed suggesting a role for heat shock factor 1 (Hsf1) in Ha-Ras val12 -mediated transformation. Although Ha-ras Val12 seems to be an inducer of HSP70's expression, we found that in Ha-ras Val12-transformed fibroblasts expression of this gene is suppressed. This suppression is correlated with higher sensitivity of Ha-ras val12 -transformed cells to heat shock. We suggest that Ha-ras Val12 is involved in Hsf1 activation, thereby inducing the cellular protective response. Cells that repress this response are perhaps those that acquire the capability to further proliferate and become transformed clones.

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