arXiv subjects

Kim Sneppen

Publications and source records attributed to Kim Sneppen.

At least 55 records · Page 3Linked to original sources

arXiv2007

On Gene Duplication Models for Evolving Regulatory Networks

Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted that growth via duplication would act as an implicit way of preferential attachment, and thereby provide the observed broad degree distributions of molecular networks. Results: We extend current models of gene duplication and rewiring by including directions and the fact that molecular networks are not a result of unidirectional growth. We introduce upstream sites and downstream shapes to quantify potential links during duplication and rewiring. We find that this in itself generates the observed scaling of transcription factors for genome sites in procaryotes. The dynamical model can generate a scale-free degree distribution, p(k)&prop; 1/k^γ, with exponent γ=1 in the non-growing case, and with γ>1 when the network is growing. Conclusions: We find that duplication of genes followed by substantial recombination of upstream regions could generate main features of genetic regulatory networks. Our steady state degree distribution is however to broad to be consistent with data, thereby suggesting that selective pruning acts as a main additional constraint on duplicated genes. Our analysis shows that gene duplication can only be a main cause for the observed broad degree distributions, if there is also substantial recombinations between upstream regions of genes.

q-bio.PE↗

arXiv2007

UV-induced mutagenesis in Escherichia coli SOS response: A quantitative model

Escherichia coli bacteria respond to DNA damage by a highly orchestrated series of events known as the SOS response, regulated by transcription factors, protein-protein binding and active protein degradation. We present a dynamical model of the UV-induced SOS response, incorporating mutagenesis by the error-prone polymerase, Pol V. In our model, mutagenesis depends on a combination of two key processes: damage counting by the replication forks and a long term memory associated with the accumulation of UmuD'. Together, these provide a tight regulation of mutagenesis resulting, we show, in a "digital" turn-on and turn-off of Pol V. Our model provides a compact view of the topology and design of the SOS network, pinpointing the specific functional role of each of the regulatory processes. In particular, we suggest that the recently observed second peak in the activity of promoters in the SOS regulon (Friedman et al., 2005, PLoS Biol. 3, e238) is the result of a positive feedback from Pol V to RecA filaments.

q-bio.MN↗

arXiv2006

Propagation of fluctuations in interaction networks governed by the law of mass action

Using an example of physical interactions between proteins, we study how perturbations propagate in interconnected networks whose equilibrium state is governed by the law of mass action. We introduce a comprehensive matrix formalism which predicts the response of this equilibrium to small changes in total concentrations of individual molecules, and explain it using a heuristic analogy to a current flow in a network of resistors. Our main conclusion is that on average changes in free concentrations exponentially decay with the distance from the source of perturbation. We then study how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. An exact analytic expression for the decay constant is obtained for the case of uniform interactions on the Bethe lattice. Our general findings are illustrated using a real biological network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations.

q-bio.MN↗

arXiv2006

Fear and its implications for stock markets

The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend. These empirical asymmetries predict that stock index drops are more common on a relatively short time scale than the corresponding raises. We present several empirical examples of such asymmetries. Furthermore, a simple model featuring occasional short periods of synchronized dropping prices for all stocks constituting the index is introduced with the aim of explaining these facts. The collective negative price movements are imagined triggered by external factors in our society, as well as internal to the economy, that create fear of the future among investors. This is parameterized by a ``fear factor'' defining the frequency of synchronized events. It is demonstrated that such a simple fear factor model can reproduce several empirical facts concerning index asymmetries. It is also pointed out that in its simplest form, the model has certain shortcomings.

physics.data-an↗

arXiv2006

Genetic Regulation of Fluxes: Iron Homeostasis of Escherichia coli

Iron is an essential trace-element for most organisms. However, because high concentration of free intracellular iron is cytotoxic, cells have developed complex regulatory networks that keep free intracellular iron concentration at optimal range, allowing the incorporation of the metal into iron-using enzymes and minimizing damage to the cell. We built a mathematical model of the network that controls iron uptake and usage in the bacterium Escherichia coli to explore the dynamics of iron flow. We simulate the effect of sudden decrease or increase in the extracellular iron level on intracellular iron distribution. Based on the results of simulations we discuss the possible roles of the small RNA RyhB and the Fe-S cluster assembly systems in the optimal redistribution of iron flows. We suggest that Fe-S cluster assembly is crucial to prevent the accumulation of toxic levels of free intracellular iron when the environment suddenly becomes iron rich.

q-bio.MN↗

arXiv2006

Network Models of Phage-Bacteria Coevolution

Bacteria and their bacteriophages are the most abundant, widespread and diverse groups of biological entities on the planet. In an attempt to understand how the interactions between bacteria, virulent phages and temperate phages might affect the diversity of these groups, we developed a novel stochastic network model for examining the co-evolution of these ecologies. In our approach, nodes represent whole species or strains of bacteria or phages, rather than individuals, with "speciation" and extinction modelled by duplication and removal of nodes. Phage-bacteria links represent host-parasite relationships and temperate-virulent phage links denote prophage-encoded resistance. The effect of horizontal transfer of genetic information between strains was also included in the dynamical rules. The observed networks evolved in a highly dynamic fashion but the ecosystems were prone to collapse (one or more entire groups going extinct). Diversity could be stably maintained in the model only if the probability of speciation was independent of the diversity. Such an effect could be achieved in real ecosystems if the speciation rate is primarily set by the availability of ecological niches.

q-bio.PE↗

arXiv2006

Synchronization Model for Stock Market Asymmetry

The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this, we introduce a market model consisting of randomly fluctuating stocks that occasionally synchronize their short term draw-downs. These synchronous events are parameterized by a ``fear factor'', that reflects the occurrence of dramatic external events which affect the financial market.

physics.soc-ph↗

arXiv2006

Longevity of orders is related to the longevity of their constituent genera rather than genus richness

Longevity of a taxonomic group is an important issue in understanding the dynamics of evolution. In this respect a key observation is that genera, families or orders can each be assigned a characteristic average lifetime [Van Valen, L., (1973) Evolutionary Theory 1, 1-30]. Using the fossil marine animal genera database [Sepkoski, J.J.Jr. (2002) A Compendium of Fossil Marine Animal Genera, Bull. Am. Paleontol. 363, 563 pp.] we here examine key determinants for robustness of a higher taxonomic group in terms of the characteristics of its constituents. We find insignificant correlation between the size of an order and its stability against extinction, whereas we observe amazingly large correlation between the lifetime of an order and the lifetime of its constituent genera.

q-bio.PE↗

arXiv2006

Structure and function of negative feedback loops at the interface of genetic and metabolic networks

The molecular network in an organism consists of transcription/translation regulation, protein-protein interactions/modifications and a metabolic network, together forming a system that allows the cell to respond sensibly to the multiple signal molecules that exist in its environment. A key part of this overall system of molecular regulation is therefore the interface between the genetic and the metabolic network. A motif that occurs very often at this interface is a negative feedback loop used to regulate the level of the signal molecules. In this work we use mathematical models to investigate the steady state and dynamical behaviour of different negative feedback loops. We show, in particular, that feedback loops where the signal molecule does not cause the dissociation of the transcription factor from the DNA respond faster than loops where the molecule acts by sequestering transcription factors off the DNA. We use three examples, the bet, mer and lac systems in E. coli, to illustrate the behaviour of such feedback loops.

q-bio.MN↗

arXiv2005

Degree Landscapes in Scale-Free Networks

We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent nodes corresponds to smooth landscapes (social networks), hierarchical networks to one-mountain landscapes (the Internet), and degree-disassortative networks without hierarchical features to rough landscapes with several mountains. We also generate ridge landscapes to model networks organized under constraints imposed by the space the networks are embedded in, associated to spatial or, in molecular networks, to functional localization. To quantify the topology, we here measure the widths of the mountains and the separation between different mountains.

physics.soc-ph↗

arXiv2005

Functional alignment of regulatory networks: A study of temperate phages

The relationship between the design and functionality of molecular networks is now a key issue in biology. Comparison of regulatory networks performing similar tasks can give insights into how network architecture is constrained by the functions it directs. We here discuss methods of network comparison based on network architecture and signaling logic. Introducing local and global signaling scores for the difference between two networks we quantify similarities between evolutionary closely and distantly related bacteriophages. Despite the large evolutionary separation between phage $λ$ and 186 their networks are found to be similar when difference is measured in terms of global signaling. We finally discuss how network alignment can be used to to pinpoint protein similarities viewed from the network perspective.

q-bio.MN↗

arXiv2005

Spiky oscillations in NF-kB signalling

The NF-kB signalling system is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Recent experiments have found oscillations in the nuclear-cytoplasmic translocation of the NF-kB transcription factor. How the cell uses the oscillations to differentiate input conditions and send specific signals to downstream genes is an open problem. We shed light on this issue by examining the small core network driving the oscillations, which, we show, is designed to produce periodic spikes in nuclear NF-kB concentration. The oscillations can be used to regulate downstream genes in a variety of ways. In particular, we show that genes to whose operator sites NF-kB binds and dissociates fast can respond very sensitively to changes in the input signal, with effective Hill coefficients in excess of 20.

q-bio.MN↗

arXiv2004

Correlations in Networks associated to Preferential Growth

Combinations of random and preferential growth for both on-growing and stationary networks are studied and a hierarchical topology is observed. Thus for real world scale-free networks which do not exhibit hierarchical features preferential growth is probably not the main ingredient in the growth process. An example of such real world networks includes the protein-protein interaction network in yeast, which exhibits pronounced anti-hierarchical features.

cond-mat.dis-nn↗

arXiv2004

Self Organized Scale-Free Networks from Merging and Regeneration

We consider the self organizing process of merging and regeneration of vertices in complex networks and demonstrate that a scale-free degree distribution emerges in a steady state of such a dynamics. The merging of neighbor vertices in a network may be viewed as an optimization of efficiency by minimizing redundancy. It is also a mechanism to shorten the distance and thus decrease signaling times between vertices in a complex network. Thus the merging process will in particular be relevant for networks where these issues related to global signaling are of concern.

nlin.AO↗

arXiv2004

A simple model for self organization of bipartite networks

We suggest a minimalistic model for directed networks and suggest an application to injection and merging of magnetic field lines. We obtain a network of connected donor and acceptor vertices with degree distribution $1/s^2$, and with dynamical reconnection events of size $Δs$ occurring with frequency that scale as $1/Δs^3$. This suggest that the model is in the same universality class as the model for self organization in the solar atmosphere suggested by Hughes et al.(PRL {\bf 90} 131101).

nlin.AO↗

arXiv2004

Hierarchy Measures in Complex Networks

Using each node's 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 $γ$ -- the exponent of a degree distribution -- reaching its highest possible value for $γ\leq 2$ and quickly approaching zero for $γ>3$.

cond-mat.soft↗

arXiv2003

Competition between Diffusion and Fragmentation: An Important Evolutionary Process of Nature

We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we solve exactly in terms of Bessel functions. The stationary state is a universal Bessel distribution described by one parameter, which fits perfectly experimental data from two very different system of nature, namely, the distribution of ice crystal sizes from the Greenland ice sheet and the length distribution of alpha-helices in proteins.

cond-mat.stat-mech↗

arXiv2003

Diffusion on Complex Networks : A way to probe their large scale topological structures

A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to real-world networks like a friendship network of known modular structure, and an Internet routing network. For the friendship network, its known structure is well reproduced. In case of the Internet, where the structure is far less well-known, one indeed finds a modular structure, and modules can roughly be associated with individual countries. Quantitatively the modular structure of the Internet manifests itself in an approximately 10 times larger participation ratio of its slowest decaying modes as compared to the null model -- a random scale-free network. The extreme edges of the Internet are found to correspond to Russian and US military sites.

cond-mat.stat-mech↗