Center for Models of Life
Niels Bohr Institute
University of Copenhagen
Blegdamsvej 17
2100 Copenhagen Ø
Ph:   +45 353 25260
Fax:  +45 353 25425
Mail:  cmolnbi.dk
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Models

 
Ecosystems with mutually exclusive interactions
This applet visualises a model model for the evolution of mutually excluding organisms that compete for space.

Publications

Joachim Mathiesen, Namiko Mitarai, Kim Sneppen, and Ala Trusina
Phys. Rev. Lett. 107 107:188101 (2011)
1108.2011

 
Fractal shapes in multiple disease model
Diseases emerge, persist and vanish in an ongoing battle for available hosts. Hosts, on the other hand, defend themselves through development of immunity. This applet illustrates a multi disease system, where hosts that carry many diseases have smaller chances of transmitting each of them. This system develops towards a steady state, where spreading of individual diseases self-organizes to a state close to that of critical percolation. That is, disease clusters will have fractal shapes as shown in the picture. To be published

Publications

 
Coverage of mRNA by Ribosomes and mRNA Half Life
Bacterial mRNAs are translated by closely spaced ribosomes and degraded from the 5′-end, with half-lives of around 2 min at 37 °C in most cases. Ribosome-free or “naked” mRNA is known to be readily degraded, but the initial event that inactivates the mRNA functionally has not been fully described. Here, we characterize a determinant of the functional stability of an mRNA, which is located in the early coding region. Using literature values for the mRNA half-lives of variant lacZ mRNAs in Escherichia coli, we modeled how the ribosome spacing is affected by the translation rate of the individual codons. When comparing the ribosome spacing at various segments of the mRNA to its functional half-life, we found a clear correlation between the functional mRNA half-life and the ribosome spacing in the mRNA region approximately between codon 20 and codon 45. From this finding, we predicted that inserts of slowly translated codons before codon 20 or after codon 45 should shorten or prolong, respectively, the functional mRNA half-life by altering the ribosome density in the important region.

Publications

Margit Pedersen, Søren Nissen, Namiko Mitarai, Sine Lo Svenningsen, Kim Sneppen, and Steen Pedersen
J. Mol. Biol. 407:35 (2011)


Namiko Mitarai, Kim Sneppen, Steen Pedersen
J. Mol. Biol. 382:236 (2008)


 

Publications

 
Modelling the Spatial Dynamics of Culture Spreading in the Presence of Cultural Strongholds
Cultural competition has throughout our history shaped and reshaped the geography of boundaries between humans. Language and culture are intimately connected and linguists have used key words as makers to quantify the dynamics of information spreading in societies with strong culture centre. One prominent example, which also is addressed here, is Kyoto&s historical impact on japanese culture. Based on shared properties of linguistic maps, we construct a first minimal model to describe the interplay between information flow and geography. In particular, we show that spreading of information over Japan in the pre-modern time can be described as a Eden growth process, with noise levels corresponding to coherent spatial patches of sizes given by a single days walk, and with patch-to-patch communication time comparable to the time between human generations.

L. Lizana, N. Mitarai, N. Hiizu and K. Sneppen

Publications

L. Lizana, N. Mitarai, H. Nakanishi, and K. Sneppen
Phys. Rev. E 83:066116 (2011)
1101.3998

 
Sustainability of Virulence in a Phage-Bacterial Ecosystem
Virulent phages and their bacterial hosts represent an unusual sort of predator-prey system where each time a prey is eaten, hundreds of new predators are born. It is puzzling how, despite the apparent effectiveness of the phage predators, they manage to avoid driving their bacterial prey to extinction. Here we consider a phage-bacterial ecosystem on a two-dimensional (2-d) surface and show that homogeneous space in itself enhances coexistence. Different behavioral mechanisms can facilitate coexistence in a spatial environment. For example, we find that when the latent times of the phage are allowed to evolve, selection favors “mediocre killers,” since voracious phage rapidly deplete local resources and go extinct. Our model system thus emphasizes the differences between short-term proliferation and long-term ecosystem sustainability.

Publications

Silja Heilmann, Kim Sneppen and Sandeep Krishna
Journal of Virology 84: (2010)


 
Urdar
Many microbial ecologies exhibit cross-feeding where the waste-products of one species are metabolised by other members of the ecosystem. This system investigates this phenomenon from an abstract point of view by considering digital agents which transform binary strings from a common pool of resources. This systems exhibits a large degree of species co-existence, especially when the inflow of energy to the system is low.

Publications

 
Time walkers and spatial dynamics of ageing information
The value of information decays with time and its distribution is essential for living system's ability to coordinate and adapt. Random walkers are often used to model this distribution process and, in doing so, one effectively assumes that information maintains its relevance over time. However, the value of information in social and biological systems often changes over time and must continuously be updated. To capture the spatial dynamics of ageing information, we introduce the time walkers. A time walker moves just like a random walker, but interacts with traces left by other walkers, some representing older information, some newer.

Publications

L. Lizana, M. Rosvall and K. Sneppen
Phys. Rev. Lett. 104:040603 (2010)
0910.4045

 
Modeling the origin of interest groups
Social networks represent communication channels and therefore also limits on information access in a society. The applet considers agents who try to bypass these information constraints, driving an ever-changing social network. The model emphasizes communication barriers in the system as the driving force behind group formation.

Publications

M. Rosvall and K. Sneppen
Phys. Rev. E 79:026111 (2009)
0809.4803

 
Nucleosome Mediated Transcription Regulation
Expression of genes are regulated by transcription factors (TF) that typically binds to certain operator sites upstream of the promoter for the gene. Procaryotic transcription initiation are mostly regulated through a direct contact between the transcription factor a RNA polymeraze (RNAP) at the promoter. For eucaryotes, the multiplicity of regulatory sites on typical genes and the ubiguetous cooperativity of eucaryotic gene regulation suggest indirect actions of transcription factors. In particular, the fact that upstream regulatory regions of genes often includes tenth of kilo bases of DNA, many operator sites and modulation by multiple transcription factors raises the question on how so many proteins bound on such a wide region of DNA can influence the 20-40nm RNAP-mediator complex on the promoter region.

Publications

Kim Sneppen, Mille A Micheelsen & Ian B Dodd
Molecular Systems Biology 4:182 (2008)


 
Dynamics of Transcription Initiation and promoter-mediated noize
The applet simulate 3 basic step that initiates reading the information of DNA. The applet also has options to show burst-like transcription initiations separated by long silence periods due to the recriutment of open complexes or the formation of dead-end complex.

Publications

Namiko Mitarai, Ian B. Dodd, Michael T. Crooks, Kim Sneppen
PLoS Comput. Biol. 4:e1000109 (2008)


 
Combinatorics of feedback
This applet simulates the regulation of uptake and metabolism of small molecules in cells. The applet allows you to explore the different ways of combining negative and positive feedback to regulate the level and flux of the molecule.

Publications

Kim Sneppen, Sandeep Krishna, Szabolcs Semsey
Annual Review of Biophysics 39:43 (2010)


Maria Werner, Szabolcs Semsey, Kim Sneppen, Sandeep Krishna
PLoS ONE 4:e4923 (2009)


Sandeep Krishna, Szabolcs Semsey, Kim Sneppen
Proc. Natl. Acad. Sci. USA 104:20815 (2007)


 
Dynamics of Opinions and Social Structures
Social groups with widely different music tastes, political convictions, and religious beliefs emerge and disappear on scales from extreme subcultures to mainstream mass-cultures. Several positive feedback mechanisms drive the diversity of beliefs in social systems. Some of these mechanisms can be analyzed in terms of a hugely simplified model of a dynamic network that incorporates basic feedback between information assembly through communication and formation of social connections.

Publications

M. Rosvall, K. Sneppen
0: (2007)
0708.0368

 
Interactive Model of Dynamical Epigenetics
The stability and heritability of the modified states of nucleosomes are modeled as a positive feedback, where modified nucleosomes recruit enzymes that modify other nucleosomes. The applet presents an interactive version of this ongoing dynamical process. In particular one may examine the effect of recruitment strength versus external noise, the effect of system size, consequences of various degrees of locality in the recruitment processes, and one can also explore how the stability of heritable states depends on nucleosome replacement at cell division. We encourage the reader to play with the applet and thereby gain intuition on the interplay between assumed processes and final distribution of epigenetic states of the modeled segment of the chromosome.

Publications

Ian B. Dodd, Mille A. Micheelsen, Kim Sneppen and Geneviève Thon
Cell 129:813-822 (2007)


 
Protein Synthesis: Ribosome Traffic on a mRNA
This applet presents a model for protein synthesis, where ribosomes move along a mRNA. Initiation rate, termination rate, and the rate of translation for each codon affect the behavior.

Publications

Namiko Mitarai, Kim Sneppen, Steen Pedersen
J. Mol. Biol. 382:236 (2008)


 
Degree landscapes in scale-free networks
A model which achieves hub-hub separation in scale-free networks while being a small-world. This is done by rewiring according to randomly assigned rankings for each node. The concept of degree-landscapes is illustrated.

Publications

Jacob Bock Axelsen, Sebastian Bernhardsson, Martin Rosvall, Kim Sneppen, Ala Trusina
Phys. Rev. E 74:036119 (2006)
physics/0512075

Ala Trusina, Sergei Maslov, Petter Minnhagen, Kim Sneppen
Phys. Rev. Lett. 92:178702 (2004)
cond-mat/0308339

 
History of Life on Earth
This applet presents the known part of the fossil record, as collected by Sepkoski. The applet opens for a illustrative way to examine birth, expansion and collapse of taxonomic orders. The presentation supplements the data analysis of the work referenced below.

Publications

Stefan Bornholdt, Kim Sneppen, and Hildegard Westphal
Theory in Biosciences: doi: 10.1007/s12064-008-0053-9 0: (2009)
q-bio.PE/0608033

 
Phage-bacteria coevelution
Co-evolution of bacteria, virulent and temperate phages are examined in a network model where where nodes are whole strains of bacteria and phages. Events are speciations and extinctions on the strain lavel, thus coarse graining over population numbers. Basic features of the ecological interactions are incorporated into the model in the form of extinction propabilities that depends on links.

Publications

Martin Rosvall, Ian B. Dodd, Sandeep Krishna, Kim Sneppen
Phys. Rev. E 74:66105 (2006)
q-bio.PE/0609031

 
Boids in Chamonix
In our center we make simple models of our surrounding world using the assumption that the complicatedness of the world is an illusion. This applet exemplify this approach by showing that simple rules can give rise to complex behaviour. Also it illustrates that the information horizon of the modelled birds are connected to development of cooperative behaviour, which here takes the form of flok behaviour. The information horizon aspect of the applet is complementary to the applet on interplay between communication and social structure, see M. Rosvall and K. Sneppen, Phys. Rev. E 74, 016108 (2006)

Publications

Martin Rosvall og Kim Sneppen
Phys. Rev. E 74:16108 (2006)
physics/0512105

A. Trusina, M. Rosvall, K. Sneppen
Phys. Rev. Lett. 94:238701 (2004)
cond-mat/0412064

 
Modeling self-organization of communication and topology in social networks
We take that model in "Self-Assembling of Information in Networks" one step further and give the agents a social mobility. The agents can thereby get new acquaintances to meet different interests. The model opens for study of interplay between communication activity/habbits and emergence of social structure.

Publications

Martin Rosvall og Kim Sneppen
Phys. Rev. E 74:16108 (2006)
physics/0512105

Martin Rosvall and Kim Sneppen
Phys. Rev. Lett. 91:178791 (2003)
cond-mat/0308399

 
Self-Assembly of Information in Networks
We show that it is possible to build a reliable perception of the whole through repeated small talks. We simply let agents memorize the acquaintances that provided the newest information about other agents together with the age of this information.

Publications

Martin Rosvall og Kim Sneppen
Europhys. Lett. 74:1109 (2006)
abs/physics/0603218

 
Network alignment
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. This applet illustrates quantitative methods of network comparison based on network architecture and signaling logic.

Publications

Ala Trusina, Kim Sneppen, I.B. Dodd, K.E. Shearwin and J.B. Egan.
Plos Computational Biology 1:7 (2005)
q-bio.MN/0511047

 
Traffic on DNA
A mathematical model for transcriptional interference by RNA polymerase traffic in Escherichia coli. The model deals with the interference between the two promoters pA and pS. The RNAPs are injected onto the DNA through binding and formation of sitting duck complexes at the respective promoters, followed by subsequent formation of elongating complexes.

Publications

I.B. Dodd, K.E. Shearwin and K. Sneppen
J. Mol. Biol. 369:1200 (2007)


Sneppen K, Dodd IB, Shearwin KE, Palmer AC, Schubert RA, Callen BP, Egan JB
J. Mol. Biol. 346:399 (2005)


 
Limited information
Navigation is a challenging problem for everyday life. The problem arises because the amount of available information typically is limited and often insufficient. We here abstract this problem to be navigation between a source and a target on different networks.

Publications

M. Rosvall, P. Minnhagen, K. Sneppen
Phys. Rev. E. 71:66111 (2005)
cond-mat/0412051

K. Sneppen, A. Trusina, M. Rosvall
Europhys. Lett. 69:853 (2005)
cond-mat/0407055

M. Rosvall, A. Gronlund, P. Minnhagen, K. Sneppen
Phys. Rev. E 72:46117 (2005)
cond-mat/0505400

A. Trusina, M. Rosvall, K. Sneppen
Phys. Rev. Lett. 94:238701 (2004)
cond-mat/0412064

 
Merging in bipartite networks
One way to interpret this merging model of a bipartite network is to consider the nodes as sunspots and the links as the associated magnetic field-lines in the solar atmosphere. Two sunspots of the same polarity merge to a larger sunspot and when two sunspots of different polarity merge the magnetic field-lines annihilate and energy is released.

Publications

K. Sneppen, M. Rosvall, A. Trusina and P. Minnhagen
Europhys. Lett. 67:394 (2004)


P. Minnhagen, M. Rosvall, K. Sneppen and A. Trusina.
Physica A 340:724 (2004)
cond-mat/0406752

 
Merging
Merging or aggregation is a dynamical process in many systems and it gives rise to fractal size-distributions. For example, companies, the autonomous system of the Internet and the sun activity of magnetic field lines reconnections are networks that undergo processes that resembles the merging process.

Publications

Beom Jun Kim, Ala Trusina, Petter Minnhagen, Kim Sneppen
: (2004)
nlin.AO/0403006

P. Minnhagen, M. Rosvall, K. Sneppen and A. Trusina.
Physica A 340:724 (2004)
cond-mat/0406752

 
Translation regulation
In the unfolded protein response in S. cerevisiae a reservoir of passive mRNA is converted to an active short-lived mRNA that is open for translation. Optimal response is obtained when active mRNA has high decay rate compared to both the conversion rate and the decay rate of passive mRNA. In that case the translation regulation can provide the observed pulse of chaperones that fast restore protein folding conditions in the endoplasmic reticulum.

Publications

Jacob Bock Axelsen and Kim Sneppen
Phys. Biol. 1:159 (2004)


 
Information Networks
In a society the information horizon is set by each individual's social contacts, which in turn is a part of the global network of human communication. One simple goal for individuals is to be central. Thus we model a society where players try to be as close as possible to everybody else by moving their social connections. Local communication gives rise to global organization.

Publications

Martin Rosvall and Kim Sneppen
Phys. Rev. Lett. 91:178791 (2003)
cond-mat/0308399

 
Physics of Fashion Fluctuations
Fashions and perception of value is a social phenomenon which is associated to positive feedback and communication in a society. Here we model the how the attention of different products changes as people trade and talks about these products.

Publications

R. Donangelo and K. Sneppen
Physica A 316:581 (2002)
cond-mat/0309549

 
Modeling the Evolution
Speciation and extinction in the evolution, modeled in a coarse grained 1-dimensional ecosystem. Species in the ecosystem do not suffer extinction independently of each other. The overall macroevolutionary pattern supports cooperativity, even on the scale of the global ecosystem.

Publications

Per Bak and Kim Sneppen
Phys. Rev. Lett. 71:4083 (1993)


 
Dynamics of Fronts, discrete models
This applet deals with a propagating front, which may be water or coffee pushed/dragged through a porous media like paper or one may think about the outer boundary of a bacterial colony. The model is schematic, and in particular assume that movements is always upwards.

Publications

K. Sneppen
Phys. Rev. Lett. 69:3539 (1992)


 
Dynamics of Transcription Initiation
Dyamics of Transcription Initiation. The applet simulate 3 basic step that initiates reading the information of DNA. Also the applet describe different ways this piece of DNA (a gene) can be regulated by another molecule.

Publications

 
Chaotic Fronts: The Kuramoto-Sivashinsky equation
Instabilities and positive feedback are central themes in dynamical systems and sometimes in biology. This applet deals with simplest spatio-temporal instability, where a part of the front gets more ahead when its already ahead.

Publications

T. Sams, K. Sneppen, M. H. Jensen, C. Ellegaard, B. E. Christensen and U. Trane
Phys. Rev. Lett. 79:313 (1997)


K. Sneppen, J. Krug, M. H. Jensen, C. Jayaprakash, and T. Bohr.
Phys. Rev. A 46:0 (1992)


 

Publications