Kim Sneppen

Specificity and stability in topology of protein networks

Molecular networks guide the biochemistry of a living cell on multiple levels: Its metabolic and signaling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory network. To address topological properties of these two networks, we quantified correlations between connectivities of interacting nodes and compared them to a null model of a network, in which all links were randomly rewired. We found that for both interaction and regulatory networks, links between highly connected proteins are systematically suppressed, whereas those between a highly connected and low-connected pairs of proteins are favored. This effect decreases the likelihood of cross talk between different functional modules of the cell and increases the overall robustness of a network by localizing effects of deleterious perturbations.

Statistical Multifragmentation of Nuclei

After an introduction to the main subject: break-up of nuclear matter, some elementary concepts from heavy ion dynamics are introduced. We discuss the collision process within a three step scenario, including fragmentation into many pieces of the interacting nuclei. The partition of the multiparticle system into clusters is discussed. The various components of the energy of a fragment assembly at the break up stage are introduced. They are generalizations of the Weissacker-energies. We consider the thermodynamics of a gaseous mixture of fragments in equilibrium. The thermodynamic probability determining the weight of a given partition is calculated. Some results of calculations are discussed.

Theoretical Analysis of Epigenetic Cell Memory by Nucleosome Modification

Chromosomal regions can adopt stable and heritable alternative states resulting in bistable gene expression without changes to the DNA sequence. Such epigenetic control is often associated with alternative covalent modifications of histones. The stability and heritability of the states are thought to involve positive feedback where modified nucleosomes recruit enzymes that similarly modify nearby nucleosomes. We developed a simplified stochastic model for dynamic nucleosome modification based on the silent mating-type region of the yeast Schizosaccharomyces pombe. We show that the mechanism can give strong bistability that is resistant both to high noise due to random gain or loss of nucleosome modifications and to random partitioning upon DNA replication. However, robust bistability required: (1) cooperativity, the activity of more than one modified nucleosome, in the modification reactions and (2) that nucleosomes occasionally stimulate modification beyond their neighbor nucleosomes, arguing against a simple continuous spreading of nucleosome modification.

Statistical multifragmentation of nuclei

Abstract A statistical formulation of the multifragmentation of finite nuclei is given. The approach considers the generalization of the liquid-drop model for hot nuclei and allows one to calculate thermodynamic quantities characterizing the nuclear ensemble at the disassembly stage. It is shown how to determine probabilities of definite partitions of finite nuclei and how to apply a Monte Carlo method. The importance of including finite-size effects is shown by comparison with infinite-like systems.

Detection of topological patterns in complex networks: correlation profile of the internet

A general scheme for detecting and analyzing topological patterns in large complex networks is presented. In this scheme the network in question is compared with its properly randomized version that preserves some of its low-level topological properties. Statistically significant deviation of any topological property of a network from this null model likely reflects its design principles and/or evolutionary history. We illustrate this basic scheme using the example of the correlation profile of the Internet quantifying correlations between degrees of its neighboring nodes. This profile distinguishes the Internet from previously studied molecular networks with a similar scale-free degree distribution. We finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the Internet to the appropriate null model.

Networks and cities: an information perspective.

Traffic is constrained by the information involved in locating the receiver and the physical distance between sender and receiver. We here focus on the former, and investigate traffic in the perspective of information handling. We replot the road map of cities in terms of the information needed to locate specific addresses and create information city networks with roads mapped to nodes and intersections to links between nodes. These networks have the broad degree distribution found in many other complex networks. The mapping to an information city network makes it possible to quantify the information associated with locating specific addresses.

Sustained oscillations and time delays in gene expression of protein Hes1

A number of genes change their expression pattern dynamically by displaying oscillations. In a few important cases these oscillations are sustained and can work as molecular clocks, as in the well-known cases of the circadian clock [1] and the cell cycle [2]. In other cases the oscillations in protein expression are connected with the response to external stimuli, as reported for protein p53 after induction by DNA damage [3] or as reported in association to speci¢city in gene expression [4]. Recently oscillations have been observed for the Hes1 system studied in the very interesting paper [5]. The Hes1 system is particularly interesting because it is connected with cell di¡erentiation, and the temporal oscillations of the Hes1 system may thus be associated with the formation of spatial patterns in development. Oscillations may be obtained by a closed loop of inhibitory couplings, provided that there are at least three di¡erent elements [5,6]. Alternatively, it was noted in the study of the p53 network [7] that a time delay in one of the components can give rise to oscillations also in a system composed of only two species (in this case, p53 and mdm2). We suggest that time delay can be a general mechanism which produces oscillatory responses in a more economical way than three-species inhibitory networks do. A delay in a biological system can typically be related to transcription and translation times, and to transport between cellular compartments. An example is the Hes1 system recently examined in [5]. In this system the protein Hes1 represses the transcription of its own mRNA, and the system displays oscillations in both the concentration of the protein and of its mRNA. To explain this behavior, the authors of [5] suggest a third, hidden factor which would complete a three-species inhibitory network of the kind discussed in [6]. There is however no direct evidence for such a factor. Furthermore, since there is a non-negligible time for transport between the cell nucleus, where the protein controls mRNA transcription, and the cytoplasm, where mRNA is translated into the protein, we feel compelled to suggest a simpler scenario. We want to test the hypothesis that Hes1 and its mRNA are su⁄cient ingredients to produce oscillations in the system. The equations for the concentrations [mRNA] and [Hes1] read

Epigenetics as a first exit problem.

We develop a framework to discuss the stability of epigenetic states as first exit problems in dynamical systems with noise. We consider in particular the stability of the lysogenic state of the lambda prophage. The formalism defines a quantitative measure of robustness of inherited states.

Modularity and extreme edges of the internet.

We study the spectral properties of a diffusion process taking place on the Internet network focusing on the slowest decaying modes. These modes identify an underlying modular structure roughly corresponding to individual countries. For instance, in the slowest decaying mode the diffusion current flows from Russia to U.S. military sites. Quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale-free network. We propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network. For the 100 slowest decaying modes of the Internet this fraction is approximately 30%. Finally, we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes.

Hierarchy measures in complex networks.

Using each nodes degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with gamma, the exponent of a degree distribution, reaching its highest possible value for gamma</=2 and quickly approaching zero for gamma>3.