Catálogo de publicaciones - libros

Networks is tool to describe systems composed of many different units which each typically interact with a few of the other units. Networks thus used to quantify complex systems from the intricate interactions of proteins inside a living cell, to ecosystems, social systems and computer networks. In most cases the network quantify communication channels in the system. Thus directly connected nodes communicates easy, while more distant nodes only obtain exchange information through a number of intermediate steps. In fact already in 1982 a detailed study of social networks within university departments revealed that mutual information of one member about another one was decaying exponentially with their distance, and increased linearly with number of common friends (degenerate paths). We will take this viewpoint and consider a Network as a description of who get direct information from who, and which parts that has to resort to second hand or even more inaccurate information: networks quantify the extent to which complex systems operate under the constraints of a limited information horizon.

The community structure in complex networks has been a popular topic in recent literature. It is present in all types of complex networks ranging from bio-molecular networks, where it reflects functional associations between proteins to information networks such as the The World Wide Web (WWW). The World Wide Web – a quintessential large complex network – presents formidable challenge for the efficient information retrieval and ranking. Google has reached its current position as the world’s most popular search engine by efficient and ingenious utilization of topological properties of this WWW network for ranking of individual webpages. The topological structure of the WWW network is characterized by a strong community structure in which groups of webpages (e.g. those devoted to a common topic) are densely interconnected by hyperlinks. We study how such network architecture affects the average Google ranking of individual webpages in the community. We demonstrate that the Google rank of community webpages could either increase or decrease with the density of inter-community links depending on the exact balance between average in- and out-degrees in the community.

A variety of sources such as radiation, chemical mutagens and products of metabolism induce damage to the genomes of organisms very often, from bacteria to man. Damage can be fatal for the organism since it can prevent DNA replication, and thus cell division. Evolution has given rise to elaborate mechanisms to either repair or bypass this damage. Upon encountering damage to their genomes, bacteria such as respond by activating the SOS network, consisting of about forty genes whose task is to repair/bypass the DNA damage, in order to enable DNA replication. The SOS genetic network deploys a variety of specific functions such as detecting damage, repairing it correctly by nucleotide excision (the NER mechanism) or by recombination, and if these functions do not succeed, bypassing damage by mutagenesis. The activation of all these functions requires a high degree of coordination and regulation, whose understanding is poor in spite of decades of study. I will survey recent findings in which the execution of the response was followed at the level of individual cells. These findings illuminate certain aspects of the concerted response, which are inacccessible to techniques in which large cell ensembles are interrogated. In particular, the findings show that the response exhibits highly precise modulations in the activation of a number of gene promoters, modulations which posess a digital character. Importantly, the precise timing mechanism responsible for the modulations is independent of the cell cycle, the main built-in clock of the cell. Genes responsible for the precision are identified. I will also highlight the importance of this network as one of the main forces driving the evolution of bacterial genomes.

We have performed an experimental study of slow crack front propagation through a weak plane of a transparent Plexiglas block. Spatial random toughness fluctuations along the weak interface generate a rough crack line in pinning locally the crack front, and leads to an intermittent dynamics of the crack front line. Using a high speed and high resolution camera we are able to capture the features of this complex dynamics.

We investigate systems of nature driven by combinations of diffusive growth, size fragmentation and fragment coagulation. In particular we derive and solve analytically rate equations for the size distribution of fragments and demonstrate the applicability of our models in very different systems of nature, ranging from the distribution of ice crystal sizes from the Greenland ice sheet to the length distribution of α-helices in proteins. Initially, we consider processes where coagulation is absent. In this case the diffusion-fragmentation equation can be solved exactly in terms of Bessel functions. Introducing the coagulation term, the full non-linear model can be mapped exactly onto a Riccati equation that has various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, exp(–), for large , and observe a crossover from the Bessel function for intermediate values of .

The main general idea, main topic of my lecture today is photobiological paradox of vision. The core of the paradox is: light in vision is not only a carrier of information, but also a risk factor of damage to the eye structures, first of all to the retina and to the layer of cell behind the retina – so called retinal pigment epithelium. In fact, the same paradox is real to other photobiological process – to photosynthesis. In this case light is used not only to convert and accumulate energy but also light can damage the photosynthetic molecular machinery. In both cases complex photoprotective systems, along with physiological system of visual reception or photosynthesis, have been developed in the course of evolution. In both cases the sophisticated photoprotective systems are able to solve the paradox of both photobiological processes. The impairment of these systems can lead in case of vision to human retina diseases or play role in progression of eye diseases like age-related macula degeneration, and in case of photosynthesis to destruction of plant cells or photosynthetic microorganisms.

Recent studies of complex systems indicate that real networks are far from random, instead having a highly robust, large-scale architecture that is governed by strict organizational principles. Here, we will focus on cellular networks, discussing their scale-free and hierarchical features. We will first discuss a few central network models, before illustrating the major network characteristics using examples primarily from bacterial metabolic networks. Additionally, as the interactions in real networks have unequal strengths, we discuss the interplay between network topology and reaction fluxes in cellular metabolic networks, as provided by the flux balance method. We find that the utilization of the metabolic networks is both globally and locally highly inhomogeneous, dominated by “hot-spots” that represent connected set of high-flux pathways.

The fantastic properties of the brain are due to an intricate interplay between billions of neurons (nerve cells) connected in a complex network. A central challenge is to understand this network behavior and establish connections between properties at the microscopic level (single neurons) and observed brain activity at the macroscopic systems level. After a brief introduction to the brain, cortex and neurons, various mathematical models describing single neurons are outlined: biophysically realistic compartmental models, simplified spiking neuron models and firing-rate models. Then examples of network modeling of the early visual system are described with particular emphasis on mechanistic (“physics-type”) modeling of the response of relay cells in the dorsal lateral geniculate nucleus to visual spot stimuli. Finally an example of cortical population modeling related to the question of the neural mechanism behind short-term memory, is given.

We study the complex dynamics of microspheres dispersed in ferrofluids subjected to external oscillating magnetic fields, see Fig. 1.

Optical tweezers are often used in connection with other techniques to study physical properties of biological systems. In particular, this combination has often been used to study elastic properties of individual strands of nucleic acids. The DNA used in this study is the shortest so far reported, only 1.1 μm, 20 times its persistence length. We use two different experimental geometries, one in which the axis of the micropipette is orthogonal to that of the stretched polymer and one where the axis of the micropipette is parallel to the stretched polymer. By comparing the force-extension data to the predictions of the celebrated worm-like-chain model (Marko and Siggia, 1995), we find that the results obtained using the orthogonal geometry have severe problems, the force increases slower than expected with extension of the polymer. Also, the expected plateau at the transition away from the B-form of dsDNA is not horizontal. However, if instead one uses the parallel geometry the data obtained are fit well by the worm-likechain model. This difference can be explained by the elasticity of the micropipette, which can be crucial to take into account when using micropipettes in connection with optical tweezers.